An Introduction to
Computational Chemistry
Theory
Experiment
Solution
Computation
Computational Chemistry
CHM 425/525 Fall 2010 Dr. Martin
What is Computational Chemistry?

Use of computers to aid chemical inquiry,
including, but not limited to:
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–
–
–
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Molecular Mechanics (Classical Newtonian Physics)
Semi-Empirical Molecular Orbital Theory
Ab Initio Molecular Orbital Theory
Density Functional Theory
Molecular Dynamics
Quantitative Structure-Activity Relationships
Graphical Representation of Structures/Properties
Levels of Calculation
Molecular mechanics...quick, simple;
accuracy depends on parameterization.
 Semi-empirical molecular orbital
methods...computationally more
demanding, but possible for moderate sized
molecules, and generally more accurate.
 Ab initio molecular orbital methods...much
more demanding computationally, generally
more accurate.

Levels of Calculation...
Density functional theory…more efficient
and often more accurate than ab initio calc.
 Molecular dynamics…solves Newton’s laws
of motion for atoms on a potential energy
surface; temperature dependent; can locate
minimum energy conformations.
 QSAR…used to predict properties of new
structures or predict structures that should
have certain properties (e.g., drugs)

Relative Computational “Cost”
Molecular mechanics...cpu time scales as
square of the number of atoms...
 Calculations can be performed on a
compound of ~MW 300 in a minute on a pc,
or in a few seconds on a parallel computer.
 This means that larger molecules (even large
peptides) and be modeled by MM methods.

Relative Computation “Cost”
Semi-empirical and ab initio molecular
orbital methods...cpu time scales as the third
or fourth power of the number of atomic
orbitals (basis functions) in the basis set.
 Semi-empirical calculations on ~MW 300
compound take a few minutes on a pc,
seconds on a parallel computer (cluster).

Molecular Mechanics

Employs classical
(Newtonian) physics
Assumes Hooke’s Law
forces between atoms
(like a spring between
two masses)
Estretch = ks (l -
lo)2
Bond Stretching Energy
350
300
Energy, kcal/mol

250
200
150
100
50
0
0
graph: C-C; C=O
1
2
Internuclear Distance
3
Molecular Mechanics...
Similar calculations for other deviations
from “normal” geometry (bond angles,
dihedral angles)
 Based on simple, empirically derived
relationships between energy and bond
angles, dihedral angles, and distances
 Ignores electrons and effect of p systems!
 Very simple, yet gives quite reasonable,
though limited results, all things considered.

Properties calculated by MM:
“Steric” or Total energy = sum of various
artificial energy components, depending on
the program...not a “real” measurable energy.
 Enthalpy of Formation (sometimes)
 Dipole Moment
 Geometry (bond lengths, bond angles,
dihedral angles) of lowest energy
conformation.

Molecular Mechanics Forcefields
MM2, MM3 (Allinger)
 MMX (Gilbert, in PCModel)
 MM+ (HyperChem’s version of MM2)
 MMFF (Merck Pharm.)
 Amber (Kollman)
 OPLS (Jorgensen)
 BIO+ (Karplus, part of CHARMm)
 (others)

Semi-Empirical
Molecular Orbital Theory
Uses simplifications of the Schrödinger
equation to estimate the energy of a system
(molecule) as a function of the geometry
and electronic distribution.
 The simplifications require empirically
derived (not theoretical) parameters (or
fudge factors) to allow calculated values
to agree with observed values.

Properties calculated by
molecular orbital methods:
Energy (enthalpy of formation)
 Dipole moment
 Orbital energy levels (HOMO, LUMO,
others)
 Electron distribution (electron density)
 Electrostatic potential
 Vibrational frequencies (IR spectra)

Properties calculated by
molecular orbital methods...
HOMO energy (Ionization energy)
 LUMO energy (electron affinity)
 UV-Vis spectra (HOMO-LUMO gap)
 Acidity & Basicity (proton affinity)
 NMR chemical shifts and coupling
constants
 others
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Semi-Empirical MO Theory Types
Hückel (treats p electrons only)
 CNDO, INDO, ZINDO
 MINDO/3
 MNDO
 AM1, PM3 (currently most widely used)
Collections of these are found in AMPAC,
MOPAC, HyperChem, Spartan, Titan, etc.

Ab Initio Molecular Orbital Theory
Uses essentially the same (Schrödinger)
equation as semi-empirical MO calculation
 Introduces fewer approximations, therefore
needs fewer parameters (“fudge factors”)
 Is more “pure” in relation to theory; if theory
is correct, should give more accurate result.
 Takes more cpu time because there are fewer
approximations.
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Variations of Ab Initio Theory
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HF (Hartree-Fock)
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Moller-Plesset perturbation theory
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includes some electron correlation; MP2, MP3
Configuration Interaction
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electron experiences a ‘sea’ of other electrons
QCISD, QCSID(T)
All of the above involve choices of basis sets:
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STO-3G, 3-21G, 6-31+G, 6-311G**, etc. (many)
Basis Sets

STO-3G (Slater-type orbitals
approximated by 3 Gaussian functions)
Split Basis Sets...
Use two sizes of Gaussian functions to
approximate orbitals:
 3-21, 6-31, 6-311 (large and small orbitals)
 additional features which can be added to any
basis set:
–
–
–
polarization functions (mixes d,p with p,s orbitals)
e.g., 6-31G** [= 6-31G(d,p)]
diffuse functions + (allows for distant interactions)
Molecular Geometry

Molecular geometry
can be described by
three measurements:
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bond length (l)
bond angle (a)
dihedral angle (q)
l
H
H
H
C
H C
H
a H
H
q
H
H
H
H
H
Bond length
Distance between nuclei of adjacent atoms
that are covalently bonded (can also
describe distance between non-covalently
bonded, or non-bonded atoms)
 But atoms are in constant motion, even at
absolute zero! How do we define the
“distance” between them?
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Measurements of bond length
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X-ray crystallography
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Gas Phase electron diffraction
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distances in crystalline solid; only ‘heavy’ atoms
geometry may differ from solution phase
weighted average distances in gas phase
not a single conformation; solvent effects
ignored
Neutron diffraction
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only heavy atoms included
Equilibrium bond length
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Molecules exist in an
ensemble of energy states
which depends on T.
Several vibrational and
rotational states are
Energy
populated for each
electronic state.
Geometry optimization
computations determine
the equilibrium bond
length.
r0, r1, r2...
v3
v2
v1
v0
zero point
energy
eq. bond length
Distance between atoms
Units of Measurement
Bond lengths are usually reported in
Angstroms (1Å = 10-10 m = 100 pm); this is
not an SI unit, but it is convenient because
most bond lengths are of 1 to 2 Å.
 Angles are measured in degrees.
 Potential energy is usually measured in
kcal/mol (1 kcal/mol = 4.184 kJ/mol).

Some Applications...
Calculation of reaction pathways & energies
 Determination of reaction intermediates and
transition structures
 Visualization of orbital interactions (forming
and breaking bonds as a reaction proceeds)
 Shapes of molecules, including large
biomolecules
 Prediction of molecular properties

…more Applications
QSAR (Quantitative Structure-Activity
Relationships)
 Remote interactions (those beyond normal
covalent bonding distance)
 Docking (interaction of molecules, such as
pharmaceuticals with biomolecules)
 NMR chemical shift prediction

Modeling Charge-Transfer Complexation
of Amines with Singlet Oxygen

N-O “bond” distance = 1.55 Å
DqN = +0.35esu DqOdistal = -0.33 esu

Modeling Aggregation Effects
on NMR Spectra
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N-Phenylpyrrole has
a concentrationdependent NMR
spectrum, in which the
protons are shifted
upfield (shielded) at
higher concentrations.
We hypothesized that
aggregation was
responsible.
Modeling Aggregation Effects
on NMR Spectra...
Two monomers were modeled in different positions
m a p o
parallel to one another, and the energy
was plotted vs. X and Y. The NMR of
the minimum complex was calculated.
7.8
7.6
7.4
m
o

mean dimer
(calc'd.)
7.2
6.8 
7.0

pa
mean monomer
(calc'd.)
8.2
8.0
7.8
7.6
7.4
7.2
7.0
6.8 
Orbital Perturbations
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Proximity of orbitals
results in perturbation.
This shows methane
with one H 2.0Å above
the middle of the p bond
of ethene
This leads to alterations
in the magnetic field,
which affects the NMR
chemical shift
Magnetic Shielding Surfaces