COMPUTATIONAL STUDY OF INORGANIC, BIOINORGANIC, AND
BIOORGANIC SYSTEMS
A Thesis
Presented to the faculty of the Department of Chemistry
California State University, Sacramento
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
Chemistry
by
Jason Scott Fell
SPRING
2013
© 2013
Jason Scott Fell
ALL RIGHTS RESERVED
ii
COMPUTATIONAL STUDY OF INORGANIC, BIOINORGANIC, AND
BIOORGANIC SYSTEMS
A Thesis
by
Jason Scott Fell
Approved by:
__________________________________, Committee Chair
Benjamin Gherman
__________________________________, Second Reader
Susan Crawford
__________________________________, Third Reader
James Miranda
____________________________
Date
iii
Student: Jason Scott Fell
I certify that this student has met the requirements for format contained in the University
format manual, and that this thesis is suitable for shelving in the Library and credit is to
be awarded for the thesis.
__________________________, Graduate Coordinator
Susan Crawford
Department of Chemistry
iv
___________________
Date
Abstract
of
COMPUTATIONAL STUDY OF INORGANIC, BIOINORGANIC, AND
BIOORGANIC SYSTEMS
by
Jason Scott Fell
Computational chemistry is growing more versatile in assisting in understanding
chemical phenomena. As computing power becomes more expeditious, so can the complexity
and rigor of quantum mechanical (QM) calculations. The goal of this thesis is to demonstrate
through computational procedures that QM calculations can help predict and explain the
complexities of the chemical phenomena within reaction mechanisms.
The first system to be studied was the catalytic mechanism of deformylation by the
metalloenzyme peptide deformylase, which is a potential antibacterial target. A biomimetic
model was used for the active site that was modified with varying substituents. Hammett plots
were used to examine trends in reaction energies with the varying substituents, which were
tracked to changes in the bond orders between the metal center and substrate throughout the
reaction. As the substituents became more electron-donating, the reaction became more
thermodynamically favorable, and as the substituents became more electron-donating or electronwithdrawing the rate of reaction decreased.
The second project examined competing pathways of electron transfer (inner sphere
versus outer sphere) between multiple metal-salens (Ni(II), Zn(II), Cu(II), and Co(II)) and
electron-deficient alkenes (methyl acrylate and acrylamide). Overall, the order of thermodynamic
favorability for electron transfer was found to be Zn(II)>Ni(II)»Co(II)>Cu(II). Results indicate a
v
kinetic preference for OS electron transfer, which holds generally across the different metal
centers and alkenes. The reduced Ni(II)- and Zn(II)-salen have significantly lower OS electron
transfer barriers versus reduced Cu(II)- and Co(II)-salen, consistent with the higher oxidation
potentials for reduced Ni(II)- and Zn(II)-salen. Reduced Ni(II)- and Zn(II)-salen likewise show a
much lower activation energy for IS electron transfer, which is attributed to ligand- versus metalbased reduction of the neutral salen in the Ni(II) and Zn(II) cases.
The last project was to design a theoretical enzyme active site (theozyme) for a MoritaBaylis-Hillman reaction that would be lower in activation energy compared to a tertiary amine
catalyzed reaction as well as an uncatalyzed reaction. Single amino acids were placed around a
transition state complex between p-nitrobenzaldehyde and acrylamide in order to stabilize the
formation of charges as well as to coordinate the reactants to an optimal arrangement. The amino
acids that stabilized the transition state the most at each position would have their individual
stabilization energies combined, and this overall stabilization then compared to the energy
barriers of the literature mechanisms. The final theozyme arrangement lowered the energy barrier
of the uncatalyzed reaction by nearly 50 kcal*mol-1, and was lower in activation energy by over
20 kcal*mol-1 compared to the literature tertiary amine catalyzed mechanisms.
_______________________, Committee Chair
Benjamin Gherman
_______________________
Date
vi
DEDICATION
First, I wish to dedicate this thesis to my parents. For many years they have supported me
in everything, from surviving cancer to graduating college to finding part time jobs. I
have so much to owe them.
Secondly, I wish to dedicate this thesis to Sara. She has been amazingly supportive of me
through all that has happened in our time together. Without her I would be tragically lost
in life.
Lastly, I dedicate this thesis to my grandfather, Adolf Fell. He has always encouraged
me to work hard in school so that I would succeed in life.
vii
ACKNOWLEDGEMENTS
Dr. Gherman
Dr. Miranda and Dr. Crawford
CSUS Chemistry Department
My fellow graduate students
California State University, Sacramento and the College of Natural Sciences and
Mathematics
CSUPERB Faculty-Student Collaborative Research Seed Grant
viii
TABLE OF CONTENTS
Page
Dedication .................................................................................................................. vii
Acknowledgements ................................................................................................... viii
List of Tables .............................................................................................................. xi
List of Figures ........................................................................................................... xiii
List of Schemes ........................................................................................................... xv
Chapter
1. INTRODUCTION ................................................................................................ 1
1.1 Quantum Mechanical Methods ................................................................. 1
1.1.1 Density Functional Theory ........................................................ 3
1.1.2 Basis Sets ................................................................................... 4
1.1.3 Geometry Optimizations and the Self Consistent Field ............. 7
1.1.4 Thermodynamic Data................................................................. 11
1.2 Electronic Effects on the Reaction Mechanism of Peptide Deformylase 13
1.3 Mechanism of Electron Transfer in Metal-Salen Mediated
Electroreductive Cyclizations…………………………………………… 16
1.4 Theoretical Enzyme Active Site Design………………………………… 17
2. ELECTRONIC EFFECTS ON THE REACTION MECHANISM OF PEPTIDE
DEFORMYLASE ................................................................................................. 19
2.1 Methods..................................................................................................... 22
2.2 Results and Discussion ............................................................................. 23
2.3 Conclusions ............................................................................................... 31
3. MECHANISM OF ELECTRON TRANSFER IN METAL-SALEN
MEDIATED ELECTROREDUCTIVE CYCLIZATIONS .................................. 32
3.1 Methods..................................................................................................... 35
3.2 Results and Discussion ............................................................................. 38
ix
3.2.1 Preliminary Results .................................................................... 39
3.2.2 Results Comparison of Inner and Outer Sphere Pathways ....... 41
3.3 Conclusions ............................................................................................... 46
4. THEORETICAL ENZYME ACTIVE SITE DESIGN ......................................... 48
4.1 Methods..................................................................................................... 51
4.2 Results and Discussion ............................................................................. 55
4.2.1 Literature Mechanism Analysis ................................................. 55
4.2.2 Single Amino Acid Analysis ..................................................... 62
4.2.3 Double Amino Acid Analysis .................................................... 65
4.2.4 Final Theozyme Design ............................................................. 67
4.3 Conclusions ............................................................................................... 67
References ................................................................................................................... 69
x
LIST OF TABLES
Tables
Page
1.
Summary of the HF SCF process..................................................................... 10
2.
Computed ΔG‡ and ΔGrxn at 25 °C with each substituent for the
deformylation reaction ............................................................................ …… 24
3.
Changes in free energy, solvation energy, and dipole moments. .…………… 28
4.
Tabulated solvation energies from the CPCM and IEF-PCM models.……… 31
5.
Summary of the relative IS energy differences between the singlet and triplet
states of Cobalt with methyl acrylate and acrylonitrile. The carbon of interest
in the substrate is labeled as such (α or β) ...................................................... 40
6.
Summary of relative energy differences between the reduced Co(II)-salen
reactants and neutral Co(II)-salen products .................................................... 40
7.
Summary of the free energy changes of electron transfer through the IS and
OS pathways. The carbon of interest in the substrate is labeled as such (α or
β) ............................................................................................................. …… 41
8.
Relative energy differences between the activation energies of the IS(α),
IS(β), and OS pathways .......................................................................... …… 42
9.
Tabulated Fukui electrophilicity indices for the β and α carbons of methyl
acrylate and acrylonitrile................................................................................. 43
10.
Tabulated Fukui nucleophilicity indices of the imine carbon of the reduced
metal-salens............................................................................................. …… 43
11.
Contribution of metal character of the LUMO of the neutral salen and the
change in mulliken charges of the metals upon reduction of the metalsalens ....................................................................................................... …… 45
12.
Half-cell oxidative and reductive voltaic potentials for the reduced metalsalens and alkenes, respectively.............................................................. …… 46
xi
13.
List of placements around the TS‡ with possible amino acids, with single
letter abbreviations, to interact with................................................................. 53
14.
The free energy and enthalpy of the TS‡ in solvent and uncatalyzed .............. 56
15.
Tabulated free energies and enthalpies of transition states and intermediates
for the water catalyzed literature mechanism .................................................. 56
16.
Tabulated free energies and enthalpies of transition states and intermediates
for the hemi-acetal formation literature mechanism ........................................ 56
17.
RDS and electronic energy comparison between Robiette et al. and current
work for the protic solvent pathway ................................................................ 61
18.
RDS and electronic energy comparison between Robiette et al. and current
work for the hemi-acetal solvent pathway ....................................................... 61
19.
Tabulated free energy barriers with each single amino acid at each position
around the TS‡ analog and the difference in activation free energies between
the uncatalyzed reaction and reaction with the amino acid present ................. 64
20.
Tabulated free energy barriers for double amino acids at each position around
the TS‡ analog with comparison to analogous single amino acid positions and
the activation energy difference versus the uncatalyzed reaction .................... 66
xii
LIST OF FIGURES
Figures
Page
1.
PDF enzyme (left) and active site (right) ....... .………………………………. 14
2.
The PDF active site modeled by a heteroscorpionate N2Sthiolate biomimetic
ligand L system ................................................... ……………………………. 15
3.
Structure of Ni(II)-salen ............. ………….…………………………………. 17
4.
PDF enzyme (left) and active site (right). .............. …………………………. 19
5.
The structure of the PATH ligand .................. .………………………………. 21
6.
The PDF active site modeled by a heteroscorpionate N2Sthiolate biomimetic
ligand L system .............................................. .………………………………. 22
7.
Plot of ΔGrxn versus σp value ......................... .………………………………. 24
8.
Plot of ΔG‡ versus σp value............................ .………………………………. 25
9.
Plot of the Fe-OH bond order in the FeLOH complex versus σp value ........... 26
10.
Plot of Fe-OFormate bond orders in the product versus σp value ........................ 26
11.
Plot of the Fe- OFormamide bond order in the TS‡ complex versus σp value .. .… 27
12.
Structure of Ni(II)-salen ................................. .………………………………. 33
13.
The s-trans (left) and s-cis (right) configurations of methyl acrylate . .……… 39
14.
The TS‡ between p-nitrobenzaldehyde and acrylamide with the possible
regions to place amino acids to stabilize the overall structure.……………… 53
15.
Graphical representation of the free energy and enthalpy change from
reactants to products in the water catalyzed literature mechanism .................. 57
16.
Graphical representation of the free energy and enthalpy change from
reactants to products in the hemi-acetal formation literature mechanism ....... 57
17.
Graphical representation of the electronic energy for the first intermediate of
the water-catalyzed pathway versus the carbon-nitrogen bond distance ......... 58
18.
Graphical representation of the electronic energy for the first intermediate of
the hemi-acetal pathway versus the carbon-nitrogen bond distance ................ 58
xiii
19.
Graphical representation of the electronic energy for the third intermediate
of the water catalyzed pathway versus the carbon-nitrogen bond distance ..... 59
20.
Graphical representation of the electronic energy for the “Hemi2”
intermediate of the hemi-acetal pathway versus the carbon-nitrogen bond
distance ............................................................................................................. 60
xiv
LIST OF SCHEMES
Schemes
Page
1.
The proposed mechanism of deformylation by PDF .. .……………………… 14
2.
The formation of a new σ bond formation between the β carbon of an alkene
and an acceptor with Ni(II) salen as the catalyst .…………………………… 16
3.
MBH reaction between p-nitrobenzaldehyde and acrylamide with quinuclidine
as a tertiary amine catalyst ............................. .………………………………. 18
4.
The proposed mechanism of deformylation by PDF .. .……………………… 20
5.
The formation of a new σ bond between the β carbon of an alkene and an
acceptor with reduced Ni(II)-salen as the catalyst .. .………………………… 32
6.
The IS mechanism between reduced Ni(II)-salen and methyl acrylate to form
Ni(II)-salen and reduced methyl acrylate ............... .………………………… 35
7.
MBH reaction between p-nitrobenzaldehyde and acrylamide with quinuclidine
as a tertiary amine catalyst ............................. .………………………………. 49
8.
The proposed hemi-acetal mechanism for a MBH reaction .………………… 51
9.
The proposed protic solvent (e.g., water) assisted mechanism for a MBH
reaction ........................................................... .………………………………. 51
xv
1
Chapter 1
INTRODUCTION
Computational chemistry is growing more versatile in assisting in understanding
chemical phenomena. As computing power becomes more expeditious, so can the
complexity and rigor of quantum mechanical (QM) calculations. By using more
sophisticated QM theory, the chemist can better model a chemical system to be studied.
Many methods and procedures have been explored in previous literature, and the quality
and certainty of the solutions obtained verify an accurate chemical model. The goal of
this thesis is to clearly demonstrate through computational procedures that QM
calculations can help predict and explain the complexities of the chemical phenomena
within reaction mechanisms.
This chapter is divided into four sections. The first section is to define and
explain QM methodologies, and a general explanation of how the electronic structure of
atoms and molecules is modeled. The next three sections will present background into
the three systems of study: the electronic effects on the reaction mechanism of peptide
deformylase, the mechanism of electron transfer in metal-salen mediated electroreductive
cyclizations, and theoretical enzyme active site design.
1.1 Quantum Mechanical Methods
To begin, the energy of a system is described by:
Hˆ  ( x, t )  E  ( x, t )
(1.1)
2
where the Hamiltonian operator (Ĥ) is operating on the eigenfunction (Ψ), which
represents the system as a wave function, and the outcome, the eigenvalue, represents the
total energy (E) of Ψ. The Hamiltonian has the form of
Hˆ  
i
2
2me
i2  
k
2
2mk
 2k  
i
k
e2 Z k
e2 Z k Zl
e2
 
rik
rkl
i  j rij
k l
(1.2)
where i and j number electrons, k and l number nuclei, ħ is Planck’s constant divided by
2π, me is the mass of an electron, mk is the mass of nucleus k, ∇2 is the Laplacian operator,
e is the charge of an electron, Z is the atomic number, and rab is the distance between
particles a and b. The first two terms of the operator represent the kinetic energy of the
electrons and nuclei, respectively. The following three terms represent the potential
energy of electron-nuclear attraction, interelectronic repulsion, and internuclear
repulsions, respectively.
Equation (1.1) has many acceptable wave functions for a given molecule, where
each Ψ is associated with a different expectation value.
The energy of a wave function
describing a chemical system can be solved by:
  Hˆ 
 
*
i
*
i
i
E
(1.3)
i
This equation proves useful as a prescription for determining the molecular energy;
however, it is still difficult to find Ψ. Instead, we can approximate Ψ with Φ, where
commonly Φ is a linear combination of atomic orbitals (vide infra). We assume that
every molecule has a ground state with Eo and Ψo, and that for every Φ approximation,
3
there is an associated E that is equal to or greater than Eo (the variational principle). The
energy of Φ is evaluated
  Hˆ   E  E
 
*
*

(1.4)
As the value of E approaches the value of Eo, the approximation of Φ approaches the
lowest energy wave function Ψ.
1.1.1 Density Functional Theory
From the present numerous QM methods in use, density functional theory (DFT)
was exclusively employed for calculations in this thesis. Other QM methods require
calculating the probability density of the electrons of the system. The wave function is
dependent on the spatial coordinates of each electron and all possible interactions with
each electron.1 Instead, DFT postulates that the energy of a molecule can be determined
from the electron density (ρ).
Electrons interact with one another and an ‘external potential,’ which refers to
nuclei at a particular geometry. ρ corresponds to a unique ‘external potential,’ which
means there is a one-to-one mapping of ρ to E. This is known as the Hohenberg-Kohn
Existence Theorem.2 The number of electrons (N) and molecular space are arguments for
density, which is used as the argument for determining the energy. The energy functional
is given as:
E   (r )  Tni   (r )  Vne   (r )  Vee   (r )  Exc   (r )
(1.5)
4
where Tni is the kinetic energy of non-interacting electrons, Vne is the nuclear-electron
interaction, Vee is the classical electron-electron repulsion and Exc is the exchangecorrelation energy of electrons.
There are many different expressions for the exchange-correlation energy, which
gives rise to the many different flavors of DFT. Earlier versions of this term were
calculated exclusively from ρ at each position (Local Density Approximation, LDA).
Evolving from LDA are inclusions of both the density at the local position and the
gradient of ρ, which is known as the gradient correction (Generalized Gradient
Approximation, GGA). Further from this, an additional correction for including the
dependence of kinetic-energy density can be included (meta-GGA). Lastly a
hybridization of both a DFT functional and Hartree-Fock (HF) exchange can be used to
calculate the exchange portion of the exchange-correlation energy.
1.1.2 Basis Sets
The basis set is a set of mathematical functions, or basis functions, designed to
model atomic orbitals (AO). Molecular orbitals (MO) are expressed as linear
combinations of the basis functions. From the basis set the wave function that describes
the chemical system is constructed. The full wave function is expressed as a Slater
determinant formed by the individual occupied MOs.
One possibility for a basis functions are Slater-type orbitals (STOs), which have a
number of qualities that make them chemically accurate. The mathematical form of a
normalized STO is
5
 (r , ,  ;  , n, l , m) 
(2 )
n
1
2
[(2n)l ]
1
2
r n 1e  Yl m ( ,  )
(1.6)
where ζ is an exponent that depends on the atomic number, n is the principle quantum
number for the valence orbital, and Yl m is the spherical harmonic function with angular
l
momentum and magnetic quantum numbers l and ml, respectively. STOs have
hydrogenic angular components and correct exponential decay with increasing r (where r
is the distance from the nucleus), which mirrors the exact orbitals of the hydrogen atom.
In order to obtain an analytical solution for an STO, the radial decay can be
changed from e r to e  r , making the AO-like function have the form of a Gaussian
2
function. The general functional form of a normalized Gaussian-type orbital (GTO) is
 ( x, y, z; , i, j, k )  [
(8 )i  j  k i ! j !k ! 12 i j k  ( x2  y2  z 2 )
] xy ze
(2i)!(2 j )!(2k )!
(1.7)
where α is an exponent controlling the width of the GTO and i, j, and k are non-negative
integers that describe orbital symmetry in Cartesian coordinates. When the sum of the
indices i, j, and k is zero, one, or two, then the GTO is expressing an s-type, p-type, or dtype orbital, respectively. When the sum of i, j, and k is one, symmetry is displayed on
the corresponding axis, yielding three possible functions which correspond to the px, py,
and pz orbitals. When the sum of the indices is two there are 6 possible functions, which
express six d-type functions (x2, y2, z2, xy, xz, and yz). The advantage of using GTOs is
that the one- and two-electron integrals, which arise in electronic structure calculations,
6
are faster to compute and have analytical solutions available. The disadvantages of using
a GTO is that the decay of a GTO is too rapid and a cusp is not formed when r = 0.
To overcome these disadvantages, linear combinations of GTOs are used to
approximate STOs, which is referred to as a ‘contracted’ basis function. One way to
increase computational flexibility is to increase the number of basis functions utilized.
Computational efficiency can be increased without loss of accuracy by distinguishing
between valence and core AOs by using more and less basis functions, respectively, to
represent those AOs. This can be done because valence AOs have more chemical
interaction due to chemical bonding than core AOs. The core AOs are typically
represented by a single basis function while the valence AOs are represented by multiple
basis functions. This is called using a ‘split-valence’ or ‘valence-multiple-ζ’ basis set.
Predicting accurate molecular geometries becomes difficult when there is
insufficient mathematical flexibility in the basis set. To further increase this flexibility,
polarization functions are added to basis sets. Polarization adds extra valence functions
corresponding to one quantum number higher of angular momentum. This would add dtype functions to second row elements and p-type functions to hydrogen.
Electrons in anions or the excited states of molecules are generally more loosely
bound than those in cations or neutral compounds. Many errors arise when there is a lack
of flexibility to describe these electrons, thus the basis set must accommodate for this
phenomena. Adding diffuse functions augments heavy atoms with an extra s-type orbital
and one set of p-type orbitals, while hydrogen atoms are augmented with an extra s-type
7
orbital. The diffuse functions have smaller α exponents so that the basis functions decay
more slowly at longer distances from the nuclei (see equation 1.8).
Heavy elements become more computationally expensive to model, in particular
due to containing so many electrons. Many of the electrons are not involved in chemical
bonding because they lie within the atomic core.3 To make calculations more efficient the
core electrons are replaced with a pseudopotential (ECP) and only the valence (large
ECP) or the valence and second outermost electron shells (small ECP) are modeled with
basis functions. This effective core potential (ECP) represents the behavior of an atomic
core, which includes Coulomb repulsion and adherence to the Pauli principle.
1.1.3 Geometry Optimizations and the Self Consistent Field
Obtaining the energy of an arbitrary structure can be interesting, however it may
not have much chemical meaning. The lowest energy structure is generally the most
probable. In order to discover the “lowest” energy structure a series of geometry
optimizations must take place.
Initially a guess wave function 𝜙 is constructed for a molecule as a linear
combination of basis functions φ (LCAO, or linear combination of atomic orbitals,
theory):
N
    ii
i 1
where αi is a coefficient and N is the number of basis functions φ. By arranging
equations (1.4) and (1.8) the energy is determined by
(1.8)
8
 (   ) Hˆ (   )
E
 (   )(   )
i
i
j
i
j
j
i
i
j
i
j
j
  H

  S
(1.9)
i
j
ij
i
j
ij
ij
ij
where Hij is the ‘resonance integral’ and Sij is the ‘overlap integral’, and both terms are
called ‘matrix elements.’ The overlap integral has a clear physical meaning that being
the extent to which two basis functions overlap in space.
The variational principle instructs that the lower E represents a better quality (i.e.,
closer to the ‘real wave function’) wave function. In order for our function (the energy)
to be at a minimum, then the derivative with respect to each of the free variables (αi) must
be zero. This gives rise to N equations of the form in equation (1.10) that must be
satisfied.
N
 (H
i 1
i
ki
 ESki )  0
(1.10)
A set of N equations with N unknowns has a solution if the determinant formed
from the coefficients of the unknowns equals zero. Notationally, equation (1.10)
becomes
H11  ES11
H1N  ES1N
0
H N 1  ES N 1
H NN  ES NN
(1.11)
9
which is called a secular equation. From this there will be N energies Ej which satisfy
this equation. Each value of Ej will give rise to a different set of coefficients, αij, which
can be found using equation (1.10) using Ej. These coefficients will define an optimal
wave function within the basis set.
Hartree-Fock (HF) theory builds upon Hartree theory by accounting for electron
spin and the Pauli exclusion principle. Previously the Hamiltonian operator, equation
(1.2), was employed; for HF theory the one-electron Fock operator is used:
Z
1
fi   i2   k  Vi HF  j
2
k rik
(1.12)
where the final term is the HF potential, which accounts for Coulomb repulsion between
electrons and exchange interactions between electrons of the same spin. This changes the
secular equation, equation (1.11), to include the new Fock matrix element Fμν instead of
the resonance integral from Hartree theory (the overlap integral S is unchanged). Fμν
takes on the form:
nuclei
1
1
1


F     2    Z k     P   |    | 
2
rk
2


k

(1.13)
The first two terms are one-electron integrals that represent the kinetic energy of
an electron and electron-nuclear attraction, respectively. The last terms are two-electron
integrals that represent coulomb repulsion and exchange interactions between electrons.
Like in Hartree theory, HF follows a procedure where an initial wave function is
guessed. From the initial wave function the density matrix is computed, and the HF
secular equation is constructed and a new set of orbital coefficients is solved. If the new
10
density matrix is sufficiently similar to the old matrix, the SCF process is concluded with
the energy and wave function for the molecular geometry having been determined.
Then the current molecular geometry is checked to see if it satisfies the
optimization criteria. If the geometry does not satisfy the optimization criteria, then a new
geometry is produced according to an optimization algorithm. This new geometry is then
subjected to the same process again until the optimization criteria are satisfied.4,5 A
summary of these steps is tabulated in table 1. It is common for optimization criteria to
include thresholds for the root mean square and maximum deviation of atomic positions
between geometry steps and the average and maximum first derivative of energy versus
atomic positions.
Step
1
2
3
4
5
6
Action
Determine basis set; guess initial wave
function; calculate initial density
matrix.
Determine matrix elements.
Create HF secular equation and solve
for N of Ej.
Determine new density matrix; if the
old and new are not similar then start
again from step 2.
Check if molecular geometry satisifies
optimization criteria; if not then new
geometry is chosen according to
optimization algorithm and start again
from step 2.
Output optimized geometry data.
Table 1: Summary of the HF SCF process.
11
This process is analogous in DFT, with the exception that we use the Kohn-Sham
one-electron operator:
nuclei
Zk
1
 (r ')
hiKS   i2  

dr ' Vxc
2
ri  rk
ri  r '
k
(1.14)
where ρ is electron density and Vxc is a functional-derivative, equation (1.15), which
accounts for the exchange-correlation potential.
VXC 
 E XC

(1.15)
Just like with HF theory, there is a secular equation to be solved, however Fµν is replaced
with Kµν:
nuclei
Zk
1
 (r ')
K      2  

dr ' Vxc 
2
r  rk
r r'
k
(1.16)
These are used in an analogous SCF process for DFT, just as in HF calculations.
1.1.4 Thermodynamic Data
In the previous section a guide for the SCF and geometry optimization processes
was discussed. However, there are more steps that must be completed in order to obtain
the proper thermodynamic data. The absolute Gibbs energy (G) of a compound is the
sum of the electronic energy (Eelec), the sum of the thermal contributions to the enthalpy
(Hthermal), zero point energy (ZPE, EZPE) and the thermal contributions to the entropy (S).
G  ( Eelec  Hthermal  EZPE )  TS
(1.17)
12
The electronic energy is sensitive to the size of the basis set. To obtain a more
accurate electronic energy, the final geometry from an optimization is taken and a singlepoint calculation is carried out using a slightly larger basis set (e.g., a geometry is
optimized with a double-zeta basis set, and the electronic energy is recalculated with a
triple-zeta basis set).
The zero point energy is the sum of the energies from the lowest vibrational level
for each vibration (ω), which is derived from the harmonic oscillator approximation
(1.15).
EZPE 
modes
1
 2 h
i
(1.18)
i
The thermal contribution to the enthalpy is the sum of the individual enthalpies
for translation (Htrans), rotation (Hrot), vibration (Hvib) and electronics (Helec). This is
analogous for the thermal contribution to the entropy.
An additional contribution to the Gibbs energy is the free energy of solvation.
Effects from solvation include larger dipole moments, interactions with induced dipoles,
and stabilization of charges. To stabilize the dipole moments of solutes, the solvent
molecules orient to oppose those moments, which induces an electric field from the
solvent with some loss of configurational freedom. This leads to increased electrostatic
interaction between the solute and solvent, and a decrease in the free energy. The solvent
then responds and reorients around the solute due to the increased dipole moment of the
solute. The structure of the solvent is altered in response to the further polarization of the
solute. This continues until the energy gain from polarization is exactly balanced from
13
the energy loss due to the decrease in entropy of the solvent. This is termed the self
consistent reaction field (SCRF). Included in the solvation is the energy the cost for
forming the so-called cavity (or cavitization energy) to place within the solute. Also
included are favorable dispersion interactions between the solute and solvent, and the
altered structure of the solvent near the solute.
Two methods are used to mimic the solvent environment: explicit solvation and
continuum solvation models. With the explicit solvation model, included in all
calculations are explicit solvent molecules surrounding the solute. However this
increases the time of computation due to the increase in the size of the system, yet a
detailed analysis of the system can be obtained (e.g., modeling a protein folding and
unfolding due to solvation effects or specific solvent-solute hydrogen bonding
interactions). The latter method replaces explicit molecules with a dielectric medium that
has properties of the solvent (such as dipole moment, dielectric constant, molecular
radius, etc.). Continuum solvation models are most suitable for general electrostatic
analysis (e.g., overall solvation energy or measure of solute polarizability). Depending
on the detail of solvent structure needed, either model is equally viable for use.
1.2 Electronic Effects on the Reaction Mechanism of Peptide Deformylase
The metalloenzyme peptide deformylase (PDF) plays a crucial role in the
biosynthesis of proteins by eubacteria (Figure 1). In a reaction catalyzed by an Fe(II)
coordination complex in the enzyme active site, PDF cleaves a formyl group from the Nterminus of nascent eubacterial proteins.6-9 Crystal structures and NMR studies indicate
that the metal ligands are Cys90, His132, and His136.6,10,11 PDF is essential for the
14
survival of bacteria, which makes PDF a promising antibacterial target. In addition,
human PDF has been recently identified, and its inhibition prevented the growth of 16
cancer lines, suggesting that PDF can be a possible anticancer target as well.12 PDF is
also of great interest in the field of bioinorganic chemistry due to PDF being the only
example of an iron metalloamidase.13
Figure 1: PDF enzyme (left) and active site (right).
The proposed mechanism for deformylation10 (Scheme 1) begins with
nucleophilic attack of the hydroxide ligand on the carbonyl carbon of the N-terminal
formyl group of the peptide. Following this there is a transformation from a tetrahedral
to a five-coordinated metal center and formation of an enzyme-formate complex.
Scheme 1: The proposed mechanism of deformylation by PDF.
15
Biomimetic modeling provides an alternative means for examining the
deformylation reaction, rather than modeling the entire protein or cropping the active site
out of the protein structure. DFT calculations performed on the 2-methyl-1[methyl-(2pyridin-2-yl-ethyl)amino]propane-2-thiol (or PATH) biomimetic model have led to very
similar results for the reaction thermodynamics compared to previous QM/MM (mixed
quantum mechanics/molecular mechanics calculations with the PDF active site.14-19 An
alternative biomimetic model that was developed is the heteroscorpionate ligand bis(3,5dimethyl-pyrazolyl)(1-methyl-1-sulfanylethyl)methane (or L) (Figure 2).20-22 Like the
PATH ligand, it also supports tetrahedral coordination around the metal center. What
makes ligand L interesting is that it can be readily substituted along the pyrazolyl groups
and the pendant arm bearing the thiolate function.21,23
Figure 2: The PDF active site modeled by a heteroscorpionate N2Sthiolate biomimetic
ligand L system.
In this research the active site of PDF was modeled using the heteroscorpionate
ligand L with varying substituents along the pyrazolyl groups in order to study the
electronic effects on the enzymatic mechanism.
16
1.3 Mechanism of Electron Transfer in Metal-Salen Mediated Electroreductive
Cyclizations
An electroreductive cyclization (ERC) is a process in which an electron-deficient
alkene that is bound to an acceptor (e.g., an aldehyde or ketone) undergoes an
electrochemically promoted reductive cyclization that forms a new σ bond between the β
carbon of the alkene and the acceptor (Scheme 2).24,25 The ERC reaction has been
applied to the total synthesis of many complex natural products and pharmaceutical
applications.26,27 Examples of these can found in coupling imines with carbonyl
compounds to form pyrrolidines and piperidines, and assisting with the synthesis of
lennoxamine, quadrone, and phorbol.26-29
Scheme 2: The formation of a new σ bond formation between the β carbon of an alkene
and an acceptor with Ni(II) salen as the catalyst.24,25
It has been shown that Ni(II)-salen (Figure 3) can be used as a mediator for ERC
reactions at a more positive potential than the unmediated reaction, which makes the
reaction become more chemoselective.25,30 Previous experimental and computational
studies by Gherman and Miranda have predicted and measured reduction potentials of
other transition metal-salens (e.g. Pd(II), Co(II), or Zn(II)).30 Theoretical electron
affinities were correlated to experimental reduction potentials, which were then used to
predict the reduction potentials for an extended group of metal-salens.
17
Figure 3: Structure of Ni(II)-salen.
The method of electron transfer from the metal-salen to the acceptor follows an
undetermined pathway.31 There are two proposed pathways of electron transfer: a direct
transfer from the metal-salen (outer sphere, OS) or through the formation of a bond
between the salen ligand and acceptor (inner sphere, IS). The OS pathway can be
described kinetically using Marcus Theory for electron transfer.32,33 The goal of this
work is to distinguish the preferred pathway of electron transfer between multiple metalsalens (Ni(II), Zn(II), Cu(II), and Co(II)) and electron-deficient alkenes (methyl acrylate
and acylamide).
1.4 Theoretical Enzyme Active Site Design
It is considered the “holy grail” for mechanistic chemists to understand and mimic
enzymes, colloquially known as biological catalysts. The combination of various
spectroscopic methods, biochemical experiments, and computational studies can be used
to construct the potential energy surface of enzyme-catalyzed reactions. The goal is to
understand the interactions between the enzyme and substrate throughout the course of
the reaction.34
Stabilizing the transition state (TS‡) relative to the ground state lowers the
activation energy (Eact), which increases the rate of reaction. Enzymes enhance reaction
rates by stabilizing the TS‡ by introducing favorable interactions with amino acids in the
active site.35 Identifying these interactions with the TS‡ is essential for catalytic design.
18
Theory and computation make it possible to obtain accurate chemical structures and
energies, which can lead to de novo design of catalysts.36 A theoretical enzyme
(theozyme) can be modeled by arranging amino acid functional side chains around a
proposed TS‡, which would lower the Eact.34,36 Theozymes have been applied beyond
reaction catalysis. Related applications include but are not limited to understanding
nonbiological processes37, solvation and receptor binding38,39, and “mini-receptor”
construction for quantitative/structure activity relationships for drug design40.
In this study an active site for a possible theozyme is modeled for a sample
Morita-Baylis-Hillman (MBH) reaction between p-nitrobenzaldehyde and acrylamide
(Scheme 3). The MBH reaction is an efficient reaction that starts with simple reagents
which are catalytically converted into functionalized products without generating waste
or byproducts.41-43 In the reaction a tertiary amine couples to an α,β-unsaturated carbonyl
compound to catalyze the formation of a new carbon-carbon bond. The goal of this study
is to design a theoretical active site for the proposed MBH reaction that lowers the
activation energy compared to a tertiary amine catalyzed reaction.
Scheme 3: MBH reaction between p-nitrobenzaldehyde and acrylamide with quinuclidine
as a tertiary amine catalyst.
19
Chapter 2
ELECTRONIC EFFECTS ON THE REACTION MECHANISM OF PEPTIDE
DEFORMYLASE
The metalloenzyme peptide deformylase (PDF) plays a crucial role in the
biosynthesis of proteins by eubacteria (Figure 4). In a reaction catalyzed by an Fe(II)
coordination complex in the enzyme active site, PDF cleaves a formyl group from the Nterminus of nascent eubacterial proteins.6-9 Crystal structures and NMR studies indicate
that the metal ligands are Cys90, His132, and His136.6,10,11 PDF is essential for the
survival of bacteria, which makes PDF a promising antibacterial target. In addition,
human PDF has been recently identified, and its inhibition prevented the growth of 16
cancer lines, suggesting that PDF can be a possible anticancer target as well.12 PDF is
also of great interest in the field of bioinorganic chemistry due to PDF being the only
example of an iron metalloamidase.13
Figure 4: PDF enzyme (left) and active site (right).
The proposed mechanism for deformylation10 (Scheme 4) begins with
nucleophilic attack of the hydroxide ligand on the carbonyl carbon of the N-terminal
20
formyl group of the peptide. Following this there is a transformation from a tetrahedral
to a five-coordinated metal center and formation of an enzyme-formate complex.
Scheme 4: The proposed mechanism of deformylation by PDF.
Biomimetic modeling provides an alternative means for examining the
deformylation reaction. The entire protein can be modeled, which can take into account
all possible protein interactions, but this introduces a considerable amount of additional
complexity. Cropping the active site alleviates the issues with modeling the whole
protein, but parts of the active site will have to be locked, which will induce some
artificiality into the study. By using a biomimetic model, the system becomes more
tractable in terms of the size of QM computations, without the need for artificial
constraints. Also, the ligand can easily be altered so that the effects of the alteration can
be observed.
Previously the 2-methyl-1[methyl-(2-pyridin-2-yl-ethyl)amino]propane-2-thiol
(pyridine-amine-thiolate, or PATH, ligand; Figure 5) ligand has been shown to promote
hydrolysis of 4-nitrophenyl acetate and tris(4-nitrophenyl) phosphate with
(PATH)Zn(Methyl) and(PATH)Zn(OH) models, respectively.17,18 Previous QM
calculations have modeled the PATH ligand with Fe(II) and Zn(II) as the metal center
and have ascertained that there is a strong preference for Fe(II) due to its ability to
21
accommodate pentacoordination.19 QM/MM (mixed quantum mechanics/molecular
mechanics) and active site modeling calculations of PDF with Zn(II) and Fe(II) modeling
the deformylation reaction have helped with explaining the metal preference of Fe(II) .4447
Brown and Gherman have utilized density functional theory (DFT) calculations on a
heteroscorpionate N2S biomimetic model (vida infra) with Fe(II), Zn(II), and Co(II)
metal centers, and determined that Fe(II) was still the favored metal, and that the
deformylation reaction was uniquely suited to PDF with an Fe(II) center.48
An alternative biomimetic model that was developed is the heteroscorpionate
ligand bis(3,5-dimethyl-pyrazolyl)(1-methyl-1-sulfanylethyl)methane (or L) (Figure 6).2022
Like the PATH ligand, it also supports tetrahedral coordination around the metal
center. What makes ligand L interesting is that it can be readily substituted along the
pyrazolyl groups and the pendant arm bearing the thiolate function.21,23 In this research
the active site of PDF was modeled using the heteroscorpionate ligand L with varying
substituents along the pyrazolyl groups in order to study the electronic effects on the
enzymatic mechanism.
Figure 5: The structure of the PATH ligand.
22
Figure 6: The PDF active site modeled by a heteroscorpionate N2Sthiolate biomimetic
ligand L system.
2.1 Methods
All computations were carried out using density functional theory with the
O3LYP functional in Gaussian03.49-52 In geometry optimizations, the 6-31G(d,p) basis
set was used for all atoms, except the metal, for which a Stuttgart effective core potential
basis set was used.53 For subsequent single-point energy calculations, the 6-311G(d,p)
basis set was used for the non-metal atoms. Vibrational frequencies were computed for
each optimized geometry in order to verify them as stationary points and to obtain zeropoint energies and thermal enthalpy and entropy corrections, such that enthalpies and
entropies at 25 °C could be obtained. Mulliken charge populations, natural population
analysis (NPA) partial atomic charges, and Wiberg bond indices were used to track
electronic changes during the deformylation reaction. Single-point solvation energies for
optimized geometries and transition states were computed with water (ε = 78.39) as the
solvent using the IEF-PCM solvation model in Gaussian03. A translational entropy
correction was included for free-energy changes computed in solution in order to account
for the difference in concentration between the 1 atm gas-phase standard-state
concentration (equal to 1/24.5 M as determined from the ideal gas law) and the 1 M
23
standard-state solution concentration.1 O3LYP was shown to optimally reproduce
ZnL(Cl) and ZnL(Acetate) metal-ligand bond lengths and angles and yield a minimal
RMSD versus crystal structures for these complexes.21,48 In modeling the deformylation
reaction, formamide was used as the model peptide which yields ammonia as the
deformylated “peptide.”
2.2 Results and Discussion
The ΔGrxn, the activation free energy (ΔG‡), and the Hammett parameter (σp) with
each of the substituents are tabulated in Table 2. From the results listed, the
deformylation reaction becomes more thermodynamically favorable as the substituents
are more electron-donating (σp < 0), where as the activation energy lowers as the value of
σp approaches 0. These trends in the thermodynamics and ΔG‡ are represented in Figures
7 and 8, respectively.
24
-1
‡
-1
ΔG (kcal*mol ) ΔGrxn (kcal*mol )
Substituent
σp
NO2
0.78
33.72
3.06
CN
0.66
30.37
0.68
CClF2
0.46
31.36
1.97
F
0.06
29.30
-0.81
H
IPR
CH3
0.00
-0.15
-0.17
29.31
29.61
29.82
0.17
-1.94
-0.74
OCH3
-0.27
30.43
-0.38
OCH(CH3 )2 -0.45
31.64
-1.81
N=CHC6 H6 -0.55
24.41
-6.51
NHCH3
-0.70
32.08
1.21
N(CH3 )2
-0.83
31.15
-5.66
Table 2: Computed ΔG‡ and ΔGrxn at 25 °C with each substituent for the deformylation
reaction.
4.00
ΔGrxn (kcal/mol)
2.00
-1.00
-0.50
0.00
0.00
-2.00
-4.00
0.50
y = 5.0007x - 0.8791
R² = 0.767
-6.00
-8.00
σP
Figure 7: Plot of ΔGrxn versus σp value.
1.00
25
34.0
ΔG‡ (kcal/mol)
33.0
y = 3.9763x2 + 0.41x + 29.822
R² = 0.5958
32.0
31.0
30.0
-1.00
-0.50
29.0
0.00
σP
0.50
1.00
Figure 8: Plot of ΔG‡ versus σp value.
Interestingly, the trend of ΔGrxn versus σp follows in tandem with the Fe-O bond
order in the initial FeLOH complex (Figure 9). As σp decreases (and as ΔGrxn decreases),
so does the bond order between the hydroxide and the iron center. As the substituents
become more electron-donating, the Fe-OH bond order in the reactant complex become
weaker, this relatively raises the energy of the FeLOH reactant complex. When the Fe-O
bond order in the product formate complex is observed, there is a similar trend (Figure
10). As σp decreases, so does the Fe-OFormate bond order in the product, which leads to a
less stable product. These changes in the bond orders in the reactant and product have
competing effects on ΔGrxn, which should cancel each other, but the slope between the
FeLOH bond order versus σp is greater than the slope of FeLOFormate bond order versus σp.
This indicates that the Fe-OH bond order in FeLOH yields a greater effect over ΔGrxn for
the deformylation reaction.
26
0.490
Fe-OH Bond Order
0.470
0.450
0.430
0.410
y = 0.0579x + 0.4273
R² = 0.8381
0.390
0.370
-1.00
-0.50
0.350
0.00
σP
0.50
1.00
Figure 9: Plot of the Fe-OH bond order in the FeLOH complex versus σp value.
Sum of Fe-O Formate Bond
Orders
0.38
-1.00
0.36
y = 0.0383x + 0.3233
R² = 0.7877
0.34
0.32
0.30
-0.50
0.28
0.00
σP
0.50
1.00
Figure 10: Plot of Fe-OFormate bond orders in the product versus σp value.
A different trend is observed with the activation free energy for the reaction. As
the substituents become more electron-withdrawing, the bond order between the iron
center and the formamide carbonyl oxygen becomes stronger in the transition state (TS‡)
27
(Figure 11), which stabilizes the TS‡ and increases the rate of the deformylation reaction.
However, this is counterbalanced by an increase in the Fe-OH bond order as σp increases,
which stabilizes the reactant and lowers the rate of reaction. These effects counter each
other, resulting with the reaction rate being fastest around a σp value of zero.
Fe-O (Formamide, TS) Bond
Order
0.230
-1.00
0.210
0.190
0.170
-0.50
0.150
0.00
σP
y = 0.0173x + 0.1886
R² = 0.5523
0.50
1.00
Figure 11: Plot of the Fe- OFormamide bond order in the TS‡ complex versus σp value.
While analyzing the trends of ΔG‡ and ΔGrxn versus σp respectively, there are
points that deviate from the general trends. Specifically the N=CHC6H5, N(CH3)2 and
NHCH3 functional groups have activation and free energies that deviate from the trends.
To explain these deviations, the changes in solvation energies and the dipole moments
were investigated and tabulated in Table 3 with the ΔG‡ and ΔGrxn.
28
-1
ΔG (kcal*mol )
‡
-1
ΔSolv (kcal*mol )
ΔDipole (Debye)
Substituent
σp
ΔGrxn
ΔG
NO2
0.78
3.06
33.72
6.93
7.60
0.01
-3.38
CN
0.66
0.68
30.37
7.67
9.69
-1.56
-2.51
CClF2
0.46
1.97
31.36
6.88
7.29
-0.29
-4.03
F
H
IPR
0.06
0.00
-0.17
-0.81
0.17
-1.94
29.30
29.31
29.61
8.57
9.85
7.85
7.66
8.48
7.89
-0.61
-0.72
-0.39
-5.22
-4.92
-3.96
CH3
-0.15
-0.74
29.82
8.11
7.79
-0.44
-4.03
OCH3
-0.27
-0.38
30.43
8.42
7.66
-0.25
-3.72
OCH(CH3 )2 -0.45
-1.81
31.64
6.38
7.01
-0.26
-3.06
N=CHC6 H5 -0.55
-6.51
24.41
-1.44
-1.17
4.54
1.23
(Prd.-Rct.) (TS-Rct.) (Prd.-Rct.) (TS-Rct.)
NHCH3
-0.70
1.21
32.08
7.20
6.36
-1.43
-2.33
N(CH3 )2
-0.83
-5.66
31.15
1.59
6.03
0.06
-2.68
Table 3: Changes in free energy, solvation energy, and dipole moments.
From the data, the ΔG‡ for N=CHC6H5 is much lower than what the surrounding
points would predict. When using the formula generated from the ΔG‡ vs. σp plot (Figure
8), an activation energy of ~30.8 kcal*mol-1 is predicted based on the σp value, which is
6.4 kcal*mol-1 higher than calculated for this substituent. When comparing the change in
solvation energy between the transition state and reactant complex of the three N-based
electron-donating groups, the energy for N=CHC6H5 is anomalously low compared to
these surrounding points by ~7 kcal*mol-1. When comparing the change in polarity from
the reactant to the TS, the polarity increases by ~4 debye higher than the surrounding
points. This increase in polarity in the TS accounts for the lower solvation energy for the
TS and for the lower energy of activation. So, ΔG‡ for N=CHC6H5 is not counted in the
activation energy trend.
29
Based on the correlation from Figure 7, the ΔGrxn for NHCH3 is predicted to be
~(-4) kcal*mol-1 based on the σp value, which is lower by ~5 kcal*mol-1 than the
calculated value. The calculated ΔGrxn differs from N=CHC6H5 and N(CH3)2 by ~7
kcal*mol-1. When comparing the change in solvation energy from the reactant to product
complexes of the three N-based electron-donating groups, the energy for NHCH3 is
higher by ~5 kcal*mol-1 than the surrounding points. When comparing the change in
polarity from reactant to product, the polarity change is significantly lower than with the
other N-based groups. This deviation accounts for the increase in the solvation energy
from reactants to products, and due to this dramatic change, the ΔGrxn of the NHCH3
complex is excluded from the ΔGrxn trend.
The ΔG‡ for N(CH3)2 is lower than what the correlation from Figure 8 predicts by
~1 kcal*mol-1 based on the σp value, due to the somewhat small change in solvation
energy (~0.5 kcal*mol-1) between the TS and the reactant complexes compared to the Nbased electron-donating groups. From the data, the ΔGrxn for N=CHC6H5 is ~1
kcal*mol-1 lower than what the correlation from Figure 7 would predict, due to a slightly
low change in solvation energy from the reactant to product complexes and an increase in
polarity from reactant to product complexes. These deviations from the respective
energy correlations are small, and, therefore, these points are still included in the
correlations.
To decrease the influence of the less reliable N-based electron-donating groups on
the ΔG‡ vs. σp and ΔGrxn vs. σp correlations, a weighted average was taken of the data.
Each energy and σp value was weighted double for all substituents, except for
30
N=CHC6H5, N(CH3)2 and NHCH3 which were only counted once. The new R2 values for
ΔG‡ and ΔGrxn vs. σp were 0.6228 and 0.7453, respectively. These new values do not
deviate significantly from the original R2 values (~ +0.02 for ΔG‡ and ~ -0.02 for ΔGrxn).
Applying a weighted average does not noticeably improve the correlation coefficients,
therefore the analysis will remain based upon the original, with equally weighted points,
correlation.
In a separate attempt to account for these “problematic” energies, a second set of
solvation single point calculations was performed using the conductor-like polarizable
continuum model (CPCM). This was done to account for any errors with the current
solvation IEF-PCM model. IEF-PCM54-58 and CPCM59,60 differ in how they model the
apparent surface charge on the solute cavity which interacts with the implicit solvent
continuum dielectric. Table 4 lists the solvation energies from both models, where the
solvation energies for the N=CHC6H5 and NHCH3 complexes are highlighted. Between
the two solvation models there appears to be no significant difference (difference is less
than ~0.5 kcal/mol) in the computed solvation energies for these two groups and for the
other substituents as well. The results indicate that the IEF-PCM solvation energies are
as reliable as those from CPCM.
31
-1
ΔSolv (kcal*mol )
CPCM Model
IEF-PCM Model
Substituent
σp
NO2
CN
CClF2
F
H
IPR
CH3
0.78
0.66
0.46
0.06
0.00
-0.17
-0.15
7.29
8.02
7.23
8.94
10.23
8.21
8.48
7.99
10.10
7.66
8.03
8.86
8.27
8.17
6.93
7.67
6.88
8.57
9.85
7.85
8.11
7.60
9.69
7.29
7.66
8.48
7.89
7.79
OCH3
-0.27
8.80
8.01
8.42
7.66
OCH(CH3 )2 -0.45
6.73
7.01
6.38
7.01
N=CHC6 H5 -0.55
-1.68
-0.99
-1.44
-1.17
(Prd.-Rct.) (TS-Rct.) (Prd.-Rct.) (TS-Rct.)
NHCH3
-0.70
7.60
6.70
7.20
6.36
N(CH3 )2
-0.83
2.47
6.90
1.59
6.03
Table 4: Tabulated solvation energies from the CPCM and IEF-PCM models.
2.3 Conclusions
In summary, by exchanging the substituents, the overall kinetics and
thermodynamics of the deformylation reaction can be greatly affected. With increasingly
electron-donating substituents, the overall process of the deformylation reaction becomes
more energetically favorable, with the N=CHC6H5 (σp = -0.55) substitute yielding the
lowest reaction energy. With increasingly electron-withdrawing and electron-donating
substituents the rate of reaction decreases, with the H substituent (σp = 0) yielding the
fastest reaction rate. The N=CHC6H5 activation energy and NHCH3 reaction energy
deviate from the ΔG‡ and ΔGrxn trends (Figures 8 and 7, respectively), respectively, due
to anomalous solvation energies, and therefore should not be included in the ΔG‡ vs. σp
and ΔGrxn vs. σp correlations, respectively.
32
Chapter 3
MECHANISM OF ELECTRON TRANSFER IN METAL-SALEN MEDIATED
ELECTROREDUCTIVE CYCLIZATIONS
An electroreductive cyclization (ERC) is a process in which an electron-deficient
alkene that is bound to an acceptor (e.g., an aldehyde or ketone) undergoes an
electrochemically promoted reductive cyclization that forms a new σ bond between the β
carbon of the alkene and the acceptor (Scheme 5).24,25 An electrohydrocyclization (EHC)
is an intramolecular electrolytic reductive coupling between two α carbons bonded to an
electron acceptor that leads to a cyclization.61 The ERC reaction has been applied to the
total synthesis of many complex natural products and pharmaceutical applications.26,27
Examples of these can be found in coupling imines with carbonyl compounds to form
pyrrolidines and piperidines, and assisting with the synthesis of the pharmaceutical
compounds lennoxamine, quadrone, and phorbol.26-29
Scheme 5: The formation of a new σ bond between the β carbon of an alkene and an
acceptor with reduced Ni(II)-salen as the catalyst.24,25
Electrocatalysts can be used to mediate ERC reactions at a more positive potential
than the unmediated reaction, resulting in a more chemoselective reaction in mild
conditions. Ni(II)-salen (Figure 12) has been used as a mediator for ERC reactions
33
previously by Miranda et al.25,30 Previous experimental and computational studies by
Gherman and Miranda have predicted and measured reduction potentials of other
transition metal-salens (e.g., Pd(II), Co(II), or Zn(II)) bearing a variety of electronwithdrawing and electron-donating substituents.30 Theoretical electron affinities were
correlated to experimental reduction potentials for an initial training set of metal-salens;
this correlation was then used to predict the reduction potentials for a test set of metalsalens. These studies have shown that the identity of the metal affects the site of
reduction (metal- versus ligand-based), which may influence the mechanism of electron
transfer.
Figure 12: Structure of Ni(II)-salen.
Currently cyclic voltammetry experiments with various chiral Ni(II)-salen
mediators attempted to determine the effectiveness of electron transfer, as well as any
possible control of stereochemistry of the final product of the EHC reaction of an α,βunsaturated diethyl ester. These experiments have shown that all Ni(II)-salen mediators
are effective electron transfer agents, and that there was a slight preference of
stereochemistry of the final EHC products.62 With the preference of stereochemistry,
there is the possibility that the electron transfer from the metal-salen to the acceptor
proceeds through a mechanism that involves the formation of a covalent chemical bond,
rather than a through-space electron transfer.
34
The mechanism of electron transfer from the metal-salen to the acceptor is an
ambiguous phenomena.31 There are two proposed pathways of electron transfer: a direct
transfer from the metal-salen (outer sphere, OS) or through the radical formation and
cleavage of a bond between the imine carbon of the reduced salen ligand and the β carbon
of the acceptor (inner sphere, IS) (Scheme 6). The OS pathway can be described
kinetically using Marcus Theory for electron transfer, while the IS pathway can be
described by Transition State Theory. 32,33 Azevedo et al. determined by ESR and UVvis spectroscopy that the nature of the diimine bridge determines the site of reduction,
where an aromatic bridge facilitates an IS transfer and an aliphatic bridge supports an OS
transfer.63 Miranda et al. postulated that both the OS and IS mechanisms were possibly
occurring simultaneously in situ, and, therefore, in competition with each other. This was
reasoned due to the formation of a side product when only in the presence of the metalsalen mediator, whereas this side product is not present in unmediated ERC reactions.25
Peters and co-workers discovered by ESR that a reduced metal-salen can have a ligand
centered reduction.64 The goal of this work is to distinguish the preferred pathway of
electron transfer between multiple metal-salens (Ni(II), Zn(II), Cu(II), and Co(II)) and
electron-deficient alkenes (methyl acrylate and acrylamide).
35
Scheme 6: The IS mechanism between reduced Ni(II)-salen and methyl acrylate to form
Ni(II)-salen and reduced methyl acrylate.
3.1 Methods
All computations were carried out using density functional theory with the B97-1
functional65,66 in Gaussian03.49 Gherman and Miranda30 performed calculations using a
variety of density functional methods in which they compared the optimized geometries
of unsubstituted and 4-hydroxy Ni(II)-salens to crystal structures for these complexes67,
and the calculated electron affinities (EA) for Ni(II)-salen with a standard aliphatic
bridging group and olefinic bridging group to literature EA values.68 B97-1 was shown
to have optimally reproduced metal-ligand bond lengths and angles and yielded minimal
RMSD values versus the crystal structures and the smallest differences with experimental
EAs compared to other functionals. In geometry optimizations, the 6-31G(d,p) basis set
was used for all atoms, except the metal, for which a Stuttgart effective core potential
basis set was used.53 For subsequent single-point energy calculations, the 6-311++G(d,p)
basis set was used for the non-metal atoms. Vibrational frequencies were computed for
each optimized geometry in order to verify them as stationary points and to obtain zeropoint energies and thermal enthalpy and entropy corrections, such that enthalpies and
entropies at 25 °C could be obtained. Single-point solvation energies for optimized
36
geometries and transition states were computed with acetonitrile (ε = 37.50) as the
solvent using the IEF-PCM solvation model in Gaussian03. For the transition state of the
IS mechanism, a translational entropy correction was included for free-energy changes
computed in solution in order to account for the difference in concentration between the 1
atm gas-phase standard-state concentration (equal to 1/24.5 M as determined from the
ideal gas law) and the 1 M standard-state solution concentration.1
For many chemical systems, a straightforward means to calculate a rate constant
for a chemical process is given by transition state theory:
kr 
k BT
exp  -G † / RT 
h
(3.1)
where kr is the rate constant, kBT/h is the Arrhenius pre-exponential factor, and G † is
the free energy change between the transition state of the rate-determining step and the
reactants. However, for the process of electron transfer, the energy of activation must
evolve to account for the reorganization of the nuclear positions of the solvent and
reactants, and the energy required for the electron to tunnel from one reactant to the
other. These transform the transition state theory equation into:
kr  Z exp  Get† / RT 
(3.2)
where Z is the collision frequency in solution and Get† is the activation free energy for
electron transfer. The activation free energy for electron transfer is given by:
G
†
et
 G   

4
2
(3.3)
37
where ΔGº is the free energy change of the chemical reaction for transferring the electron
from molecule A to molecule B and λ is the reorganization energy. The reorganization
energy is the sum of the internal reorganization of the reactants (λi) and the reorganization
of the solvent (λo).
  i  o
(3.4)
The internal reorganization energy represents the energy necessary to change the
geometry of the reactants to that of products, so that the electron transfer has the lowest
barrier. In an elementary electron transfer reaction, there are two species: the electron
donor (D) and the electron acceptor (A). So the overall reaction that takes place is:
( D)  A  D  ( A)
(3.5)
To assist with lowering the energy barrier for electron transfer, the geometry of
the reactants changes to that of the respective products. Thus the donor is in less of a
state to want to hold onto the extra electron, and the acceptor is in a better condition to
accept the electron. Therefore the internal reorganization energy is the energy necessary
to adjust the geometries of the reactants to promote the electron transfer.
i  [(ED @Dxyz )  (E A @ A xyz )]  [(ED  @D  XYZ )  (E A @ Axyz )]
(3.6)
The solvent reorganization energy is dependent on the total charge transfer (Δe),
the fast and bulk dielectric constants of the solvent (εo and ε∞, respectively), the
molecular radii (ra and rb), and the distance separating the reacting molecules (R) which
is taken to be the sum of the reactant radii. The values of εo and ε∞ are 37.50 and 1.80,
respectively, for acetonitrile. The reactants were treated as spheres, and using the
38
equation for spherical volume the respective radius for each reactant can be determined
from equation (3.8).
 1
1 1  1 1 

   
 2ra 2rb R     o 
o   e  
2
(3.7)
1
 3V  3

 r
 4 
(3.8)
These expressions, developed by R.A. Marcus, are fundamental in describing the
energetics of electron transfer.32,33,69,70
3.2 Results and Discussion
In studying the IS versus OS electron transfer, the rate was calculated with
different metal-salens and electron deficient alkenes. We chose Ni(II), Zn(II), Cu(II), and
Co(II) because previous unpublished work by Mendiola and Gherman predicted that the
site of reduction for Zn(II)-salen is ligand-based, Cu(II) shows metal-based reduction,
and Ni(II) and Co(II) have varying degrees of mixed ligand- and metal-based reduction.71
This set would cover the whole range of metal-salen types in regards to the location of
reduction. The two electron deficient alkenes studied were acrylonitrile and acrylamide
because they have laboratory use in the Miranda research group.
The IS pathway was computed according to the mechanism in Scheme 6. The
reduced metal-salen and the alkene radically form a bond on the β carbon of the alkene,
which forms a semi-stable intermediate. Then the newly formed bond is homolytically
cleaved, leaving the neutral metal-salen and the reduced alkene. The rate is connected to
39
the activation energy via transition state theory as in equation (3.1). The IS pathway was
investigated using both the β and α carbons of the alkene.
The OS pathway was computed based on the Marcus theory of electron transfer.
This pathway treats the reactants as the reduced metal-salen and the electron deficient
alkene, while the products are the neutral metal-salen and the reduced alkene. The rate
for electron transfer is specifically described by Marcus theory using equations (3.2) thru
(3.5).
3.2.1 Preliminary Results
Before obtaining information on the possible structures of the IS pathway, there
must be done a study on the initial states of some of the reactants. In particular the
stereochemistry of methyl acrylate and the spin state of Co(II) must be analyzed.
Methyl acrylate can exist in two stereochemical forms of s-cis and s-trans. Figure
13 illustrates the s-cis and s-trans configurations of methyl acrylate. The predicted
energy difference between the conformers is -0.58 kcal*mol-1, leading to an energetic
preference for the s-cis arrangement. For the rest of this investigation the s-cis form is
exclusively used.
Figure 13: The s-trans (left) and s-cis (right) configurations of methyl acrylate.
Cobalt (II), with a d7 electron configuration, can exist in two electronic states,
either the low-spin doublet state or the high-spin quartet state. In order to determine
40
which spin state is favorable, all Co(I)-salen structures were optimized in both the
respective singlet and triplet states, and Co(II)-salen was optimized in both respective
doublet and quartet states. Table 5 summarizes the relative energy differences between
the possible spin states for the intermediates and transition state structures for the IS
pathway using both the α and β carbons of the alkene as the carbon being attacked, and
Table 6 summarizes the relative energy differences between the spin states for the neutral
products and the reduced reactants.
-1
Reactants
Methyl Acrylate Cobalt
Acrylonitrile Cobalt
IS (Triplet-Singlet) ΔΔG (kcal*mol )
TS-β
Int-β
TS-α
Int-α
+1.73
+1.61
+0.30
-0.09
+1.37
+1.09
+0.32
+0.18
Table 5: Summary of the relative IS energy differences between the singlet and triplet
states of Cobalt with methyl acrylate and acrylonitrile. The carbon of interest in the
substrate is labeled as such (α or β).
-1
ΔΔG (kcal*mol )
Reduced
Neutral Co(II)Co(II)-Salen
Salen
Triplet-Singlet Quartet-Doublet
-4.88
-3.25
Table 6: Summary of relative energy differences between the reduced Co(II)-salen
reactants and neutral Co(II)-salen products.
When comparing the relative energies throughout the IS mechanism, the spin state
preferences for the neutral Co(II)-salen, reduced Co(II)-salen, and the Co(II)-salen IS
41
species are quartet, triplet, and singlet respectively. For the remainder of this
investigation, the lowest energy spin states were used exclusively for all calculations.
3.2.2 Results Comparison of Inner and Outer Sphere Pathways
Table 7 summarizes the free energy change of each step of the IS pathway with
regards to attacking either the α and β carbon of the alkene, the activation energy for the
OS pathway, and the overall free energy for the electron transfer. The IS pathway was
described as the radical formation and cleavage of a bond between the imine carbon of
the salen and acceptor (dicta prius). This formation and cleavage are geometrically and
energetically identical; therefore the energy for the transition states is only listed once.
-1
Reactants
IS ΔG (kcal*mol )
TS-β Int-β TS-α Int-α ΔG†et
11.59 11.10 26.96 27.28
12.91 12.79 27.58 27.58
21.01 19.87 37.04 36.95
28.90 28.43 42.68 42.21
7.74 7.02 21.82 23.72
8.34 7.97 21.68 22.48
Nickel
Zinc
Methyl Acrylate
Cobalt
Copper
Nickel
Zinc
Acrylonitrile
Cobalt 17.00 16.28 31.46 32.02
Copper 24.95 23.47 37.31 38.92
OS
Products
(kcal*mol-1 ) ΔGrxn (kcal*mol-1 )
9.20
-0.76
8.53
-1.91
14.39
8.75
20.35
13.93
7.87
-3.01
7.44
-4.16
13.00
18.89
6.50
11.68
Table 7: Summary of the free energy changes of electron transfer through the IS and OS
pathways. The carbon of interest in the substrate is labeled as such (α or β).
With both methyl acrylate and acrylonitrile, Zn(II)-salen produces the lowest
ΔGrxn with Ni(II) being ~1 kcal*mol-1 higher, followed by Co(II) at ~10 kcal*mol-1
higher, and lastly by Cu(II)-salen being ~5 kcal*mol-1 higher than Co(II). In all cases the
OS pathway is energetically favorable over the IS, except for the case with Ni(II) and
acrylonitrile where both are nearly energetically equivalent. For the IS pathway the β
42
carbon of the alkene is the preferred carbon for attack over the α carbon. Table 8
organizes the relative differences in energies of the activation energies for the IS(α),
IS(β), and OS pathways.
†
-1
ΔΔG et (kcal*mol )
Reactants
OS-IS(β)
OS-IS(α) IS(β)-IS(α)
Nickel
-2.39
-17.76
-15.37
Zinc
-4.39
-19.05
-14.67
Methyl Acrylate
Cobalt
-6.62
-22.65
-16.02
Copper
-8.55
-22.33
-13.78
Nickel
0.13
-13.94
-14.08
Zinc
-0.90
-14.24
-13.34
Acrylonitrile
Cobalt
-4.00
-18.46
-14.46
Copper
-6.06
-18.43
-12.37
Table 8: Relative energy differences between the activation energies of the IS(α), IS(β),
and OS pathways.
In addition to comparing the Get† between the two IS mechanisms for carbon
preference, the Fukui chemical reactivity for nucleophiles and electrophiles can assist
with this prediction.72,73 Equations (3.9) and (3.10) describes the method to calculate a
Fukui electrophilicity and nucleophilicity indices, where f and f are the respective
nucleophilicity and electrophilicity values, qne is the Mulliken charge of the atom of
interest of the neutral molecule, and qne' is the Mulliken charge of the atom of interest of
the charged molecule (cationic for the f nucleophilicity index; anionic for the f
electrophilicity index) at the neutral molecule’s geometry.74,75 The larger the value of the
electrophilicity or nucleophilicity index, the more electrophilic or nucleophilic the
respective atom is. Tables 9 and 10 list the Fukui electrophilicity values for the β and α
43
carbons of the alkenes and the Fukui nucleophilicity index of the reduced metal-salen’s
imine carbon, respectively. Based on the calculated Fukui indices, the β carbon for both
reactants is the most reactive carbon, and the imine carbons of the reduced Ni- and Znsalens are the most nucleophilic.
f  qne  qne'
(3.9)
f  qne'  qne
(3.10)
Reactant
Carbon Electrophilicity
α
0.047
Methyl Acrylate
β
0.120
α
0.110
Acrylonitrile
β
0.140
Table 9: Tabulated Fukui electrophilicity indices for the β and α carbons of methyl
acrylate and acrylonitrile.
Metal-Salen
Ni
Zn
Co
Cu
Nucleophility
0.065
0.061
0.058
0.030
Table 10: Tabulated Fukui nucleophilicity indices of the imine carbon of the reduced
metal-salens.
To further characterize the changes in the electronic structure of the metal-salens
during reduction, the change in charge on the metal upon reduction and the percent of
metal character in the LUMO of the neutral salen are shown in Table 11. Upon
44
reduction, the metal center in Co(II) and Cu(II)-salen reduces in Mulliken charge 2-4
times more so than Ni(II) and Zn(II)-salen. The small change in Mulliken charge in
Ni(II) and Zn(II)-salen suggests that the reduction is occurring primarily on the salen
ligand, whereas the relatively large change in charge in Co(II) and Cu(II)-salen suggests
that reduction is occurring primarily on the metal center. Upon further analysis, the metal
center in Co(II) and Cu(II)-salen contributes a significant degree of character to the
LUMO, while the metal center in Ni(II) and Zn(II)-salen contributes a small degree. This
analysis of the LUMO explains the small change in metal charges for Ni(II) and Zn(II)salen and the large changes for Co(II) and Cu(II)-salen, as well as the larger IS energy
barriers for Co(II) and Cu(II)-salen. The IS pathway relies on the negative charge of the
imine carbon in the reduced metal-salen, therefore the IS pathway will be unfavorable if
there is a primarily metal-centered reduction in the metal-salen, which is the case with
Co(II)- and Cu(II)-salen. This also explains why Co(II)- and Cu(II)-salen have such large
ΔΔG‡et between the OS and IS pathways, because there is more of a metal-centered
reduction in these metal-salens which leads to a stronger preference for the OS than IS
pathway.
45
Change in
% Metal Mulliken charge
Character in on metal upon
LUMO of reduction of the
Neutral Salen metal-salen
Ni(II)-Salen
4.61%
-0.090
Zn(II)-salen
0.95%
-0.078
Co(II)-Salen 45.57%
-0.244
Cu(II)-salen
59.36%
-0.387
Table 11: Contribution of metal character of the LUMO of the neutral salen and the
change in mulliken charges of the metals upon reduction of the metal-salens.
Half-cell potentials can be calculated for each individual reduction and oxidation
using the Nernst equation, equation (3.11), and the overall cell potential is given by
equation (3.12). F is the Faraday constant and n is the moles of electrons being
transferred. For this reaction n is one. Table 12 lists the half-cell oxidative and reductive
voltaic potentials for the reduced metal-salens and alkenes, respectively.
Grxn
E
 nF
(3.11)
Ecell  Ereduction  Eoxidation
(3.12)
46
Reactant
E° (V)
Ni(II)-Salen
1.96
Zn(II)-Salen
2.01
Co(II)-Salen
1.55
Cu(II)-Salen
1.32
Methyl Acrylate -1.93
Acrylonitrile
-1.83
Table 12: Half-cell oxidative and reductive voltaic potentials for the reduced metal-salens
and alkenes, respectively.
The OS pathway relies on the ability of the reduced metal-salen to transfer an
electron. Reduced Zn(II)-salen has a slightly higher oxidation potential, which in turn
leads to a slightly lower OS energy barrier. Whereas reduced Ni(II)-salen has a lower
oxidation potential by 0.05 V, which leads to a slightly higher OS energy barrier by ~0.6
kcal*mol-1. Both reduced Co(II)- and Cu(II)-salen have even lower oxidation potentials (
by ~0.60 V), which produces a significantly higher OS energy barrier by ~5 and ~10
kcal*mol-1 respectively. The higher oxidation potentials of Ni(II)- and Zn(II)-salen make
these metal-salens better electrocatalysts over Co(II)- and Cu(II)-salen. Furthermore the
lower OS energy barrier for acrylonitrile over methyl acrylate can be attributed to 0.10 V
preference for the reduction of acrylonitrile over methyl acrylate.
3.3 Conclusions
Using the approach described by Marcus has led to useful and accurate
calculations of energies of activation, electron transfer, and reaction. Unpublished work
produced by Mendiola and Gherman has taken care of the choice of which density
functional to best study the metal-salen system. These methods combined have produced
47
reasonable results that indicate that an OS electron transfer is preferred over the IS
mechanism. Overall the order of thermodynamic favorability for electron transfer was
found to be Zn(II)>Ni(II)»Co(II)>Cu(II). Acrylonitrile is a better electron acceptor than
methyl acrylate. Lastly, the β carbon is the preferred site of reduction over than α carbon
in the IS mechanism.
Zn(II)-salen produced the lowest energy barrier for an OS electron transfer with
either substrate, followed by Ni(II)-salen. However Co(II)- and Cu(II)-salen produced
much larger energies for an OS electron transfer. Ni(II)-salen produced the lowest
energy barriers for an IS electron transfer, followed closely by Zn(II)-salen. Co(II)-salen
produced much larger IS energy barriers, followed by Cu(II)-salen with the largest
barriers. Through the IS mechanism, it is possible that a chiral metal-salen could induce
stereoselectivity in a EHC reaction, which in turn would produce a final EHC product
that has a specific stereochemistry.
Marcus theory provides a unique method to understanding and predicting the
energy barrier for electron transfers on the molecular scale. These predictions can assist
with experiment to determine the most favorable species for electron transfer.
48
Chapter 4
THEORETICAL ENZYME ACTIVE SITE DESIGN
It is considered the “holy grail” for mechanistic chemists to understand and mimic
enzymes, colloquially known as biological catalysts. The combination of various
spectroscopic methods, biochemical experiments, and computational studies can be used
to construct the potential energy surface of enzyme-catalyzed reactions. The goal is to
understand the interactions between the enzyme and substrate throughout the course of
the reaction.34
Stabilizing the transition state (TS‡) relative to the ground state lowers the
activation energy (Eact), which increases the rate of reaction. Enzymes enhance reaction
rates by stabilizing the TS‡ by introducing favorable interactions with amino acids in the
active site.35 Identifying these interactions with the TS‡ is essential for catalytic design.
Theory and computation make it possible to obtain accurate chemical structures and
energies, which can lead to de novo design of catalysts.36 A theoretical enzyme
(theozyme) can be modeled by arranging amino acid functional side chains around a
proposed TS‡, which would lower the Eact.34,36 Theozymes have been applied beyond
reaction catalysis. Related applications include but are not limited to understanding
nonbiological processes37, solvation and receptor binding38,39, and “mini-receptor”
construction for quantitative structure/activity relationships for drug design.40
Previously, the complete design of an enzyme catalyst for a stereoselective
bimolecular Diels-Alder reaction has been completed both computationally and
experimentally by Siegel et al.76 No naturally occurring enzyme has been demonstrated
49
to catalyze an intermolecular Diels-Alder reaction.77 The focus was to design an active
site around the reaction between 4-carboxybenzyl trans-1,3-butadiene-1-carbamate and
N,N-dimethylacrylamide. The design strategy was to place amino acid side chains to
stabilize charges in the transition state in order to lower the energy barrier of the reaction.
After the computational design was complete, the theoretical active site was screened
through enzyme libraries for enzymes that had similar active sties. Matches were then
tested experimentally, with the best performing enzymes taken and mutated to test for
improved catalytic activity. The authors were able to design and make an enzyme
capable of catalyzing the Diels-Alder reaction to exclusively form the 3R,4S endo
product with 97% yield and 89 times faster than the uncatalyzed reaction.
In this study, an active site for a possible theozyme to catalyze a sample MoritaBaylis-Hillman (MBH) reaction between p-nitrobenzaldehyde and acrylamide will be
designed (Scheme 7). The MBH reaction is an efficient reaction that starts with simple
reagents which are catalytically converted into functionalized products without
generating waste or byproducts.41-43 In the reaction a tertiary amine couples to an α,βunsaturated carbonyl compound to catalyze the formation of a new carbon-carbon bond.
Scheme 7: MBH reaction between p-nitrobenzaldehyde and acrylamide with quinuclidine
as a tertiary amine catalyst.
50
Aggarwal et al. deciphered that the more reactive tertiary amine catalyst would
also be one of the most basic, which was quinuclidine.78 Yu et al. studied that a binary
solution of water and 1,4-dioxane and loading 100 mol % of catalyst yielded the best
results.79 Yu then successfully coupled aromatic aldehydes to form the MBH product
with acrylamide.80 The mechanism of the MBH reaction can theoretically occur through
two pathways: the formation of a hemiacetal (Scheme 8) and assisted catalysis with an
explicit protic solvent molecule (Scheme 9).81-88 Robiette et al. performed DFT
calculations with B3LYP/6-31+G*(tetrahydrofuran) on a MBH reaction between
benzaldehyde and methyl acrylate with trimethylamine catalyst to determine the
enthalpies of reaction.41 The authors discovered that the protic solvent assisted pathway
is kinetically favored.41 The electronic energies of activation for the protic solvent
pathway and hemi-acetal pathway were 25.8 kcal*mol-1 (TS3 rate-determining step) and
28.7 kcal*mol-1 (TS3-Hemi rate-determining step), respectively. The goal of this study is
to design a theoretical active site for the proposed MBH reaction that lowers the
activation energy compared to a quinuclidine catalyzed reaction.
51
Scheme 8: The proposed hemi-acetal mechanism for a MBH reaction.
Scheme 9: The proposed protic solvent (e.g., water) assisted mechanism for a MBH
reaction.
4.1 Methods
All computations were carried out using density functional theory with the
B3LYP50,89,90 functional in Gaussian0349. In geometry optimizations, the 6-31G(d,p)
basis set was used for all atoms. For subsequent single-point energy calculations, the 6311++G(d,p) basis set was used for all atoms. Vibrational frequencies were computed
for each optimized geometry in order to verify them as stationary points and to obtain
52
zero-point energies and thermal enthalpy and entropy corrections, such that enthalpies
and entropies at 25 °C could be obtained. All geometry optimizations were performed in
water solvent using the IEF-PCM solvation model in Gaussian03 because there are
charges forming in the course of the reaction, which cannot be modeled well in the gas
phase.
A translational entropy correction was included for free-energy changes
computed in solution in order to account for the difference in concentration between the 1
atm gas-phase standard-state concentration (equal to 1/24.5 M as determined from the
ideal gas law) and the 1 M standard-state solution concentration.1 B3LYP was chosen
due to the functional’s versatility of study with varying organic systems.91
The method of developing the theozyme is complex, which requires a thorough
explanation. Initially a transition state between p-nitrobenzaldehyde and acrylamide is
needed to build a theoretical active site. Around the TS‡ at individual positions, amino
acid side chains are placed to interact with the complex (Figure 14). At each position,
the amino acid will interact with the functional group to assist with lowering the energy
of the TS‡. The proposed list of amino acids, with single letter abbreviations, to interact
with each position is listed in Table 13. There is a possibility that amino acids with larger
side chains could interact with multiple points simultaneously. These positions are
denoted with a “.5”.
53
Figure 14: The TS‡ between p-nitrobenzaldehyde and acrylamide with the possible
regions to place amino acids to stabilize the overall structure.
Amino Acids
Placement
1
2
"2.5"
3
Histidine (H)
Histidine (H)
Lysine (K)
Histidine (H)
Arginine (R)
Lysine (K)
Lysine (K)
Asparagine (N)
Asparagine (N)
Asparagine (N)
Lysine (K)
Glutamine (Q)
Glutamine (Q)
Arginine (R)
Arginine (R)
"3.5"
4
Glutamine (Q) Glutamic Acid (E) Glutamic Acid (E)
Threonine (T)
Glutamine (Q)
Asparagine (N)
Glutamine (Q)
Arginine (R)
Glutamine (Q)
Serine (S)
Serine (S)
Serine (S)
Threonine (T)
Threonine (T)
Threonine (T)
Tyrosine (Y)
Histidine (H)
Asparagine (N)
Serine (S)
Tyrosine (Y)
5
Cysteine (C)
Histidine (H)
Threonine (T)
Tryptophan (W) Tryptophan (W)
"4.5"
Asparagine (N) Aspartic Acid (D) Aspartic Acid (D)
Tryptophan (W)
Tyrosine (Y)
Table 13: List of placements around the TS‡ with possible amino acids, with single letter
abbreviations, to interact with.
The first step at each point is to lock the four-atom TS‡ center, and perform a
geometry optimization with the amino acid hydrogen-bonded to the transition state
geometry. The goal of this step is to optimize the position of the amino acid and the
interaction of the amino acid with the TS‡. Once this is completed, the four-atom center
is unlocked and a transition state search with this new complex is calculated in order to
relax the TS‡ in the presence of the amino acid. Afterwards vibrational frequencies and
54
single point energies are calculated so that the free energy of this new TS‡ complex can
be obtained.
Once the energy of the TS‡ is obtained, then the energy of the “reactants” must be
calculated. The “reactants” will be the amino acid interacting with just either pnitrobenzaldehyde or acrylamide. This “reactant” complex will account for the energy of
the initial interaction, so that the overall energy change being observed between the TS‡
and “reactants” is just the proton-transfer and carbon-carbon bond formation. A
geometry optimization, followed by single-point energy and vibrational frequencies are
calculated to determine the free energy of the reactants.
This procedure that was previously described is to account the interaction of one
amino acid at one position. This is done for all possible single amino acids at each
position. Next, we will compare having an amino acid at each position versus having a
single amino acid interacting with two positions. For example, the activation energy with
an amino acid present at each position “2” and “3” will be compared to the activation
energy of a single amino acid at position “2.5.” The optimal arrangement will be chosen
based on the lowest activation energy for the reaction.
The optimal amino acid for each position will be chosen based on which amino
acid gives the lowest ΔG‡. Once all the positions have a chosen optimal amino acid, a
final ΔG‡ will be calculated based on the sum of the stabilization energy of each
individual amino acid. This value will be compared to the ΔG‡ of the uncatalyzed
reaction, the protic solvent mechanism, and the hemi-acetal pathways to determine how
effective the theozyme is.
55
4.2 Results and Discussion
In order to determine the success of the theozyme, the energy barrier of the
theozyme must be compared to the other energy barriers of the different quinuclidine
catalyzed mechanisms as well as the uncatalyzed energy barrier. Both the hemi-acetal
and protic solvent mechanisms will be modeled as described by Robiette (dicta prius)
with acrylamide and p-nitrobenzaldehyde reactants.
4.2.1 Literature Mechanism Analysis
Initial free energy and enthalpy changes for the uncatalyzed, water catalyzed and
hemi-acetal formation literature mechanisms have been tabulated in Tables 14, 15 and 16,
respectively. The free energy and enthalpy changes are graphically represented for the
protic solvent and hemi-acetal mechanisms in Figures 15 and 16, respectively. Robiette
et al. reported the formation of a first intermediate with quinuclidine bonding with the β
carbon of acrylamide, forming a zwitterion.41 Yet in this study this reported “first
intermediate” did not form. The bond distance between the β-carbon of acrylamide and
the nitrogen of quinuclidine was adjusted between 1.40 Å and 2.00 Å and the energy
measured at 0.03 Å increments to find the optimal distance between the catalyst and
initial reactant for both pathways, which is graphically depicted in Figures 17 and 18 for
the water catalyzed and hemi-acetal pathways, respectively. As the distance increases,
the energy continually decreases, meaning that no bond forms between the β-carbon of
acrylamide and the nitrogen of quinuclidine. It can be concluded that quinuclidine has
difficulty staying bound/forming a bond with acrylamide. Instead, we report that there is
a one-step synchronous formation of the second intermediate with all three reactants.
56
∆G‡Uncat. (Kcal*mol -1) 87.16
∆H‡Uncat. (Kcal*mol -1) 76.27
Table 14: The free energy and enthalpy of the TS‡ in solvent and uncatalyzed.
Step
React. TS1 Int1 TS2 Int2 TS3 Int3 TS4 Prod.
ΔG (kcal*mol-1 ) 0.00
ΔH (kcal*mol-1 ) 0.00
-
-
57.23 55.21
-
-
58.62 8.60
-
-
32.03 30.04
-
-
31.92 -3.31
Table 15: Tabulated free energies and enthalpies of transition states and intermediates for
the water catalyzed literature mechanism.
Step
ΔG
(kcal*mol-1 )
ΔH
(kcal*mol-1 )
React. TS1 Int1 TS2 Int2
TSTSTSTSHemi1
Hemi2
Hemi3
Prod.
Hemi1
Hemi3
Elim
Cleave
0.00
-
-
62.53 60.95 66.04
64.49 64.32
-
-
23.95
56.62
8.60
0.00
-
-
37.62 35.75 27.93
28.74 27.53
-
-
2.70
35.56 -3.31
Table 16: Tabulated free energies and enthalpies of transition states and intermediates for
the hemi-acetal formation literature mechanism.
57
70.00
60.00
50.00
E (kcal*mol-1)
TS2
40.00
TS4
Int2
ΔG
30.00
ΔH
20.00
10.00
0.00
Prodcuts
Reactants
-10.00
Figure 15: Graphical representation of the free energy and enthalpy change from
reactants to products in the water catalyzed literature mechanism.
80.00
70.00
E (kcal*mol-1)
60.00
TS-Hemi1
TS2
Int2
TS-Hemi3
Hemi1
50.00
TS-Cleave
40.00
ΔG
ΔH
30.00
20.00
Hemi3
10.00
0.00
Reactants
Products
-10.00
Figure 16: Graphical representation of the free energy and enthalpy change from
reactants to products in the hemi-acetal formation literature mechanism.
58
-653.035
1.40
1.50
1.60
1.70
1.80
1.90
2.00
-653.040
E (a.u.)
-653.045
-653.050
-653.055
-653.060
-653.065
Bond Distance (Å)
Figure 17: Graphical representation of the electronic energy for the first intermediate of
the water-catalyzed pathway versus the carbon-nitrogen bond distance.
-576.585
1.40
1.50
1.60
1.70
1.80
1.90
2.00
-576.590
E (a.u.)
-576.595
-576.600
-576.605
-576.610
-576.615
-576.620
Bond Distance (Å)
Figure 18: Graphical representation of the electronic energy for the first intermediate of
the hemi-acetal pathway versus the carbon-nitrogen bond distance.
It was discovered in each pathway there was another intermediate that would not
form. In the water catalyzed pathway the third intermediate does not form, this being
59
akin to the first intermediate where quinuclidine does not stay bound to acrylamide.
Another energy scan versus carbon-nitrogen bond distance was performed, measuring the
electronic energy between 1.40 Å and 2.00 Å at 0.03 Å increments. The results (Figure
19) show that as the distance increases the energy decreases linearly, which means that,
again, no carbon-nitrogen bond forms. The means that the water catalyzed pathway
essentially proceeds through two steps: the first forming a zwitterion with the three
reactants and then facilitating a proton transfer to form the product and regenerating the
catalyst.
-1203.1346
1.40
1.50
1.60
1.70
1.80
1.90
2.00
-1203.1347
E (a.u.)
-1203.1348
-1203.1349
-1203.1350
-1203.1351
-1203.1352
-1203.1353
Bond Distance (Å)
Figure 19: Graphical representation of the electronic energy for the third intermediate of
the water catalyzed pathway versus the carbon-nitrogen bond distance.
Similarly in the hemi-acetal mechanism, the “Hemi2” intermediate does not form.
This structure, similar to the third intermediate of the water catalyzed mechanism, proves
difficult for quinuclidine to stay bound. Another energy scan versus carbon-nitrogen
bond distance was performed, measuring the electronic energy between 1.40 Å and 2.00
60
Å at 0.03 Å increments. The results (Figure 20) show that as the distance increases the
energy decreases. This means that for this pathway the loss of quinuclidine and the
proton transfer are concerted.
-1,676.770
1.40
1.50
1.60
1.70
1.80
1.90
2.00
-1,676.775
E a.u.)
-1,676.780
-1,676.785
-1,676.790
-1,676.795
-1,676.800
Bond Distance (Å)
Figure 20: Graphical representation of the electronic energy for the “Hemi2” intermediate
of the hemi-acetal pathway versus the carbon-nitrogen bond distance.
In conclusion, the water catalyzed mechanism is kinetically favored over the
hemi-acetal formation mechanism. The free energy barriers of TS4 of the water
catalyzed mechanism and TS-Hemi1 of the hemi-acetal mechanism are 58.62 and 66.04
kcal*mol-1, respectively. The difference in free energy is more than 7 kcal*mol-1, which
is ~5 orders of magnitude difference in rates. When comparing these energies to the
energy barrier of the uncatalyzed reaction (87.16 kcal*mol-1), the water catalyzed and
hemi-acetal mechanisms are ~28 and ~21 kcal*mol-1 lower which leads to ~20 orders of
magnitude difference in rate. Tables 17 and 18 compare Robiette’s and our calculated
rate-determining step (RDS) and electronic activation energies for the protic and hemi-
61
acetal pathways, respectively. In Robiette’s study, the authors did not perform
vibrational frequency calculations, so the authors are not absolutely certain that the
optimized structures are true minima or transition states, and they cannot include zeropoint energies or thermal enthalpy or entropy corrections. The consequence to this is that
Robiette et al. could only calculate changes in electronic energy (ΔE‡), which is the
electronic energy difference between the reactants and transition state.
Robiette Current Work
RDS
TS3
TS4
ΔE‡ (kcal*mol-1 )
25.80
29.51
Table 17: RDS and electronic energy comparison between Robiette et al. and current
work for the protic solvent pathway.
Robiette Current Work
RDS
TS-Hemi3
TS-Cleave
ΔE‡ (kcal*mol-1 )
28.70
34.62
Table 18: RDS and electronic energy comparison between Robiette et al. and current
work for the hemi-acetal solvent pathway.
Robiette et al. concluded that the RDS for both pathways was the internal proton
transfer, and that the protic solvent mechanism was preferred over the hemi-acetal
mechanism. Our overall results agree with Robiette’s that the protic solvent mechanism
is favored over the hemi-acetal; however, we claim that in both mechanisms that the RDS
is a concerted step with a proton transfer and cleavage of catalyst, instead of just a proton
transfer. When comparing the hemi-acetal data, our electronic energy data shows that the
RDS is the final step (TS-Cleave) with the proton transfer and cleavage of the hemiacetal. From the perspective of free energy change (which includes the entropy change
62
for the reaction), the RDS is the formation of the hemi-acetal (TS-Hemi1). The change in
entropy is nearly twice as large for TS-Hemi1 (-146.93 cal*mol-1*K-1) than TS-Cleave (83.37 cal*mol-1*K-1), which leads to this shift in the RDS. Due to the subtle difference
between our and Robiette’s systems and larger differences in the computational methods
applied, we expect there to be slight variations in our results with respect to Robiette’s.
This preliminary set of data is then used as a base for comparing the results of
activation energies calculated with amino acids present. The goal is to have a lower
activation energy with the theozyme than in either of these pathways.
4.2.2 Single Amino Acid Analysis
Table 19 lists all of the energy barriers for each single amino acid at each position
around the TS‡ analog and the activation energy difference (ΔΔG‡) between the
uncatalyzed reaction and the reaction with each single amino acid, with unsuccessful
amino acids denoted with “X” (e.g., the amino acid physically moving to a new position,
transferring only the hydrogen but not forming a new carbon-carbon bond, or forming the
product/collapsing into the reactants) and the amino acid producing the lowest energy
barrier being underlined. The data shows that nearly all interacting amino acids produce
some stabilization of the TS‡ analog, with the amount of stabilization dependent on the
position. Position 1 does not affect the TS‡ very much, but it is important with
positioning p-nitrobenzaldehyde for reaction with acrylamide. Positions 2 and 3 form
anions during the reaction; therefore stabilizing those charges helps lower the energy
barrier. Position 4 was expected to primarily assist with positioning acrylamide, and
gives a small stabilization. Position 5 is intended to play a role analogous to the tertiary
63
amine catalyst, which was expected to give a rather sizeable stabilization. It was
expected that all “X.5” positions would potentially be better than an individual position
because two positions are being stabilized instead of just one. Arginine at position 2.5
stabilizes better than positions 2 and 3 by ~4 and ~6 kcal*mol-1, respectively. Position
3.5 would stabilize the TS‡ and better position acrylamide than positions 3 and 4;
however, having an amino acid at position 3.5 is nearly equal too and higher in energy
over positions 3 and 4, respectively. Position 4.5 would act as both a catalyst and assist
with positioning acrylamide, and using aspartic acid (D) lowers the energy barrier by
nearly 31 kcal*mol-1, which is over 20 kcal*mol-1 more so than either of positions 4 and
5. It was unexpected that an anionic oxygen would perform better as the catalyst than the
tertiary amine in the histidine side chain.
64
Amino Acid
H
K
N
Q
R
S
T
W
P1 ΔG (kcal*mol ) 86.02 85.84 86.34 84.67 84.58 85.56 85.85 88.22
‡
-1
ΔΔG (kcal*mol ) -1.14 -1.32 -0.82 -2.49 -2.58 -1.60 -1.31 1.06
Amino Acid
H
K
N
Q
R
S
T
W
‡
-1
X 85.29 84.93 X 85.27 85.13 83.23
P2 ΔG (kcal*mol ) 86.76
X -1.87 -2.23 X -1.89 -2.03 -3.93
ΔΔG‡ (kcal*mol-1 ) -0.40
Amino Acid
K
R
‡
-1
P2.5 ΔG (kcal*mol ) 82.83 76.63
‡
-1
ΔΔG‡ (kcal*mol-1 ) -4.33 -10.53
Amino Acid
H
K
‡
-1
X
X
P3 ΔG (kcal*mol )
‡
-1
ΔΔG (kcal*mol )
Amino Acid
X
X
N
Q
‡
-1
P3.5 ΔG (kcal*mol ) 83.56 83.97
‡
-1
ΔΔG (kcal*mol ) -3.60 -3.19
Amino Acid
D
E
‡
-1
X
X
P4 ΔG (kcal*mol )
‡
-1
X
ΔΔG (kcal*mol ) X
Amino Acid
D
E
‡
-1
P4.5 ΔG (kcal*mol ) 55.71 56.20
ΔΔG‡ (kcal*mol-1 ) -31.45 -30.96
Amino Acid
C
H
‡
-1
X
74.77
P5 ΔG (kcal*mol )
‡
-1
ΔΔG (kcal*mol )
X
-12.39
Y
84.18
-2.98
Y
80.98
-6.18
N
X
Q
X
R
83.62
S
X
T
X
W
X
Y
X
X
T
X
X
-3.54
X
X
X
X
X
H
X
N
Q
S
82.23 82.49 83.50
T
X
X
-4.93 -4.67 -3.66
X
N
X
Q
X
X
X
Table 19: Tabulated free energy barriers with each single amino acid at each position
around the TS‡ analog and the difference in activation free energies between the
uncatalyzed reaction and reaction with the amino acid present.
The optimal amino acids for each position in numerical order are: P1 - tyrosine
(Y), P2 - tyrosine (Y), P2.5 - arginine (R), P3 - arginine (R), P3.5 - asparagine (N), P4 asparagine (N), P4.5 - aspartic acid (D), and P5 - histidine (H), respectively. For the
65
double amino acid placements, the optimal amino acid at each separate position will be
used, and the energy barrier will then be compared to the respective single amino acids
interacting simultaneously at both positions.
4.2.3 Double Amino Acid Analysis
Table 20 lists all of the energy barriers for each double amino acid at each
position around the TS‡ analog along with the activation energy difference compared to
the uncatalyzed reaction, with the favored arrangement underlined. It can be noted that
the stabilization energy of the amino acid combinations is approximately equal to the sum
of the individual stabilization energies from Table 19. At position 1 it is possible that the
relatively large nitro functional group can be stabilized by two amino acids, one at each
oxygen. Positions 2 and 3 are close enough in proximity to have a single amino acid
interact with each carbonyl. The possibility of a conjugate amide interacting with
positions 3 and 4 of acrylamide may better stabilize the TS‡ and position the reactant.
Positions 4 and 5 are close in space, leaving a possibility that a single amino acid could
potentially position the reactant and catalytically promote the formation of the carboncarbon bond between acrylamide and p-nitrobenzaldehyde.
66
Amino Acid
-1
ΔG(kcal*mol )
H(P1)H(P1) R(P1)R(P1) Y(P1)Y(P1) Y(P1)
84.26
84.68
86.65
84.18
‡
-1
-2.90
ΔΔG (kcal*mol )
Amino Acid
Y(P2)R(P3)
-1
78.41
ΔG(kcal*mol )
-2.48
R(P2.5)
76.63
‡
-1
-8.75
ΔΔG (kcal*mol )
Amino Acid
R(P3)N(P4)
-1
81.57
ΔG(kcal*mol )
-10.53
N(P3.5)
83.56
‡
-1
-5.59
ΔΔG (kcal*mol )
Amino Acid
N(P4)H(P5)
-1
72.91
ΔG(kcal*mol )
-3.60
D(P4.5)
55.71
ΔΔG‡ (kcal*mol-1 )
-14.25
-0.51
-2.98
-31.45
Table 20: Tabulated free energy barriers for double amino acids at each position around
the TS‡ analog with comparison to analogous single amino acid positions and the
activation energy difference versus the uncatalyzed reaction.
At position 1, it is equally optimal to have two amino acids present than just one.
Unlike the other double amino acid trends, the stabilization energy of two amino acids at
position one is not the summation of the single energies. Since it is energetically
equivalent to have one or two amino acids, for simplicity one amino acid (Y) will be used
at position 1. At positions 2 and 3, the optimal arrangement is having single amino acid
arginine (R) at position 2.5 rather than both tyrosine (Y) and arginine (R) at positions 2
and 3, respectively, by ~2 kcal*mol-1. The optimal arrangement by ~2 kcal*mol-1 at
positions 3 and 4 is having arginine (R) and asparagine (N), respectively, rather than
single amino acid asparagine (N) at position 3.5. Lastly, having aspartic acid (D) at
position 4.5 lowers the energy barrier by ~17 kcal*mol-1 more than both asparagine (N)
and histidine (H) at positions 4 and 5, respectively. Again, the stabilization energy of the
67
double amino acid combination is nearly equal to the sum of the individual energies from
Table 19 (-17.32 kcal*mol-1). The entropy contribution for the single aspartic acid is
much smaller than the double amino acid case of N at position 4 and H at position 5
(ΔΔS = 25.97 cal*mol-1*K-1), which partly explains the difference in energy for position
4.5 versus positions 4 and 5, along with an enthalpic preference for aspartic acid over
asparagine and histidine (ΔΔH = -9.45 kcal*mol-1).
4.2.4 Final Theozyme Design
From the previous sections, the final arrangement of amino acids will be: P1 –
tyrosine (Y), P2.5 – arginine (R), P3 – arginine (R), P4 – serine (S), and P4.5 – aspartic
acid (D). Serine was chosen over asparagine for position 4 because of the steric
hindrance of aspartic acid from position 4.5, which could lead to the possibility of
asparagine forming position 3.5. Rather than positioning asparagine at position 3.5 and
reducing the TS‡ stabilization, a different amino acid was chosen that would not form the
3.5 position, and serine was the only such possibility remaining for position 3. The sum
of the individual stabilization energies is -50.42 kcal*mol-1 (versus the uncatalyzed
reaction), which produces an energy barrier of approximately 36.74 kcal*mol-1 for the
theozyme. This barrier is 21.88 kcal*mol-1 lower than the RDS of the water catalyzed
pathway, and 29.30 kcal*mol-1 lower than the RDS of the hemi-acetal pathway.
4.3 Conclusion
Based on the pathways presented by Robiette et al, the water catalyzed pathway is
the kinetically preferred pathway over the hemi-acetal pathway. We reason that in both
of these literature pathways there is a concerted action between the two reactants and
68
quinuclidine for the catalyst to bond with acrylamide and to form the new carbon-carbon
bond between acrylamide and p-nitrobenzaldehyde. We also reason that the hydrogen
transfer to form the alcohol and cleavage of the catalyst is concerted.
Using the general approach described by the literature, we successfully designed a
theozyme that lowered the energy barrier of the uncatalyzed MBH reaction between pnitrobenzaldehyde and acrylamide. This predicted barrier is much lower than that of the
RDS of both the water catalyzed and hemi-acetal pathways with a tertiary amine catalyst.
69
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