ANCHORING THE POTENTIAL ENERGY SURFACES OF HOMOGENOUS AND
HETEROGENOUS DIMERS OF FORMALDEHYDE AND THIOFOMALDEHYDE
by
Christina Michelle Holy
A thesis submitted to the faculty of The University of Mississippi in partial fulfillment of
the requirements of the Sally McDonnell Barksdale Honors College
Oxford
May 2014
Approved by
_____________________________________
Advisor: Professor Gregory Tschumper
_____________________________________
Reader: Associate Professor Nathan Hammer
_____________________________________
Reader: Professor Susan Pedigo
© 2014
Christina Michelle Holy
ALL RIGHTS RESERVED
ii ACKNOWLEDGEMENTS
Many people in the Department of Chemistry and Biochemistry here at the University of
Mississippi were of great assistance during the work presented in this manuscript. I
would like to thank the Mississippi Center for Supercomputing Research for the use of
their computational facilities and the research group of Dr. Gregory Tschumper for their
guidance and computational assistance. Specifically, I would like to thank Eric Van
Dornshuld for his continual support and advisement throughout this research project.
Lastly, I would like to thank my advisor, Dr. Gregory Tschumper, for allowing me to
work in his laboratory as well as providing me with a worthwhile project to fulfill this
thesis requirement.
iii ABSTRACT
This work characterizes five stationary points of the formaldehyde dimer,
(CH2O)2, two of which are minima, seven newly-identified stationary points of the
formaldehyde/thioformaldehyde (mixed) dimer, CH2O/CH2S, four of which are minima,
and five newly-identified stationary points of the thioformaldehyde dimer, (CH2S)2 , three
of which are minima. Full geometry optimizations and corresponding harmonic
vibrational frequencies were performed on CH2O and CH2S as well as each of the dimer
configurations (Figures 3-5). The computations were carried out with second order
Møller-Plesset perturbation theory (MP2), with the heavy-auc-cc-pVTZ (haTZ) basis set.
Additionally, thirteen density functional theory methods were employed: B3LYP,
B3LYP-D3, B3LYP-D3(BJ), TPSS, TPSS-D3, TPSS-D3(BJ), APF, APF-D, M06-2X,
M06-2X-D3, N12SX, MN12SX, and VSXC, in conjunction with the 6-311+G(2df,2pd)
basis set. Six of these functionals are dispersion corrected with either the original D3
damping function (DFT-D3) or the Becke-Johnson damping function [DFT-D3(BJ)].
Binding energies were computed via the supermolecular approach. Single-point energies
were also computed for all optimized structures using explicitly correlated MP2-F12 and
CCSD(T)-F12 methods with the haTZ basis set. The (CH2O)2 and CH2O/CH2S global
minimum are the same at the MP2, MP2-F12, and CCSD(T) levels of theory. However,
MP2 methods overbind (CH2S)2 by as much as 1.1 kcal mol-1, effectively altering the
energetic ordering of the (CH2S)2 minima relative to the CCSD(T)-F12 energies.
iv TABLE OF CONTENTS
1
Introduction………………………………………………………………………...…1
1.1
Ionic Bonds, Covalent Bonds, and Noncovalent Interactions……………...1
1.2
Overview of Formaldehyde………………………………………………...4
1.3
Overview of Thioformaldehyde…………………………………………….5
2
Theoretical Methods………………………………………………………………8
3
Results and Discussion…………………………………………………………..10
3.1
3.2
Structures and Energies…………………………………………………….10
3.1.1
Formaldehyde Dimer…………………………………………….10
3.1.2
Mixed Dimer……………………………………………………..13
3.1.3
Thioformaldehyde Dimer………………………………………...15
DFT Analysis………………………………………………………………17
3.2.1
Formaldehyde Dimer…………………………………………….17
3.2.2
Mixed Dimer………..……………………………………………20
3.2.3
Thioformaldehyde Dimer ………………………………………..23
4
Conclusions………………………………………………………………………25
5
References………………………………………………………………………..27
v 1
Introduction
1.1
Ionic Bonds, Covalent Bonds, and Noncovalent
Interactions
The joining of two or more atoms forms a chemical compound. A stable compound
occurs when the combined atoms have a lower total energy than the separated atoms.
This attraction between atoms is termed a chemical bond. An ionic bond is a type of
chemical bond in which one atom loses one or more electrons while another atom gains
them in order to fill their electron shell and produce noble gas electron configuration.
The atom that transfers its electron(s) obtains a positive charge whereas the atom that
gains the electron(s) obtains a negative charge. These positive and negative ions attract
each other, forming the ionic bond.
A covalent bond is another type of chemical bond that involves the sharing of
electrons between atoms. It is formed when partially occupied orbitals of interacting
atoms overlap and contain a pair of electrons shared by these atoms.1 These bonds are
found in inorganic metal complexes, and also have biological relevance. For example
amino acids are held together by a special kind of covalent bond referred to as a peptide
bond in which the carboxyl group of one amino acid reacts with the amino group of
another amino acid. Additionally, the monomeric units of nucleic acids and
polysaccharides are joined by covalent bonds. Even the structure of hair is determined by
1 covalent bonds known as disulfide bonds.2 Both ionic and covalent bonds have large
bond dissociation energy, indicating a strong bond between the involved atoms.
Unlike ionic and covalent bonds, noncovalent interactions are much weaker than their
covalent counterparts and are often referred to as weak attractive interactions.1 For
example, an input of about 350 kJ mol-1 of energy is required to break a C—C single
bond, and about 410 kJ mol-1 to break a C—H bond, but as little as 4 kJ mol-1 is sufficient
to disrupt a typical van der Waals interaction.2 Types of noncovalent interaction include,
hydrogen bonds, ionic interactions, dipole-dipole interactions, ion-dipole interactions,
and van der Waals interactions.2 In hydrogen bonding, a hydrogen atom bound to an
electronegative atom (such as oxygen or nitrogen) interacts with another electronegative
atom. This allows the hydrogen atom to form a strong interaction with the loan pair on
the neighboring oxygen or nitrogen. In ionic interactions, an electrostatic interaction
forms between positively and negatively charged species or ions. A dipole-dipole
interaction occurs when two polar molecules align themselves so that their positive and
negative poles interact with each other. When an ion interacts with a polar molecule, an
ion-dipole interaction forms. Finally, van der Waals interactions arise when two adjacent
molecules form temporary dipoles due to shifting electron density, thus creating a
temporary attractive force. Noncovalent interactions are responsible for holding together
the molecules of supramolecular complexes, and therefore play an important role in
determining the structure of liquids, molecular crystals and bio-macromolecules like
DNA and proteins.2-7
Although noncovalent interactions are individually weak compared to covalent bonds,
the cumulative effect of many noncovalent interactions can be incredibly significant. For
2 instance, the noncovalent binding of an enzyme to its substrate may involve multiple
hydrogen bonds as well as several other types of noncovalent interactions.2 Additionally,
the binding of an antigen to a specific antibody and the binding of a hormone or
neurotransmitter to its cellular receptor protein depends on the cumulative effects of
many weak interactions. Furthermore, the most stable structure (or native state) of any
supramolecular complex is typically the one in which weak, noncovalent interactions are
maximized. This principle explains the folding of a single polypeptide chain into its
secondary, tertiary, and sometimes quaternary structures.3 After the initial amino acid
chain is assembled through the process of translation, the polypeptide chain then folds
into its secondary structure. The most common types of secondary structures are α
helices and β sheets. Both conformations are held together by hydrogen bonds between
the peptide bonds, but the α helix maximizes these internal hydrogen bonds, making it
the most common conformer. The side chains of the amino acids protrude from the
secondary structure and interact via noncovalent forces to stabilize the tertiary structure.
This global folding of a single polypeptide chain often represents the functional form of a
protein. However some proteins, like hemoglobin, form quaternary structure in which
subunits are held together through noncovalent interactions in order to create the function
form.2,3
Due to their importance in both biology and chemistry, noncovalent interactions
are an extremely important area of scientific research; however, experimental difficulties
often arise when studying these weak interactions. Fortunately, computational chemistry
offers a means for scientists to investigate noncovalent interactions and how they
3 influence chemical systems.8 It simulates the behavior of molecules, and as models
improve, they reflect more accurately the behavior molecules in the real world.9
1.2
Overview of Formaldehyde
As explained above, noncovalent interactions are extremely important in protein
folding and function. Specifically, noncovalent interactions between carbonyl groups
have been shown to play an important role in protein structure, folding, function, and
stability.4-7 In a cabonyl-carbonly noncovalent interaction, the delocalized lone pair of
electrons (n) from the carbonyl oxygen atom interacts with the antibonding orbital of the
nearby carbonyl group.4,7 This sort of noncovalent interaction is termed the n→π*
interaction.
Formaldehyde (Figure 1) is the simplest compound that contains a carbonyl
group. It is a naturally occurring organic compound composed of carbon, hydrogen, and
oxygen. Structurally, it is a planar molecule with C2v symmetry and has a molecular
formula of CH2O.
Figure 2: Formaldehyde (CH2O)
It was first synthesized in 1859 by the Russian chemist, Aleksandr Mikhailovich
Butlerov. This aliphatic aldehyde has countless uses. For example, morticians use
4 formaldehyde as embalming fluid, and it is used for the production of many synthetic
polymers like Bakelite, one of the first commercial synthetic plastics.10
The formaldehyde dimer [i.e. (CH2O)2] is the simplest system that can model
carbonyl-carbonyl non-covalent interactions. Over the past few decades, this dimer and
its monomeric subunit have been characterized using both experimental and
computational techiniques.11-21 Experimentally, the formaldehyde dimer has been
observed in argon and nitrogen matrices using infrared (IR)11-13 and Raman10
spectroscopy. In 1997, Ford and Glasser first characterized the potential energy surface
(PES) of the formaldehyde dimer using second-order Møller-Plesset perturbation theory
(MP2) and the 6-31++G** basis set.14 Five stationary points were reported. Structures I,
II, and III (located in Figure 3) were reported to be minima (ni = 0). Furthermore,
Structure I was found to be the global minimum with a binding energy of − 4.40 kcal
mol-1. Structure III, however, was later found to be a transition state (ni = 1) when the
largest basis set was employed.15 In 2013, Dolgonos et. al. reported structure I to be 0.8
kcal mol-1 lower in energy than structure II at the CCSD(T) (i.e. the couple-cluster
method that includes all single and double substitutions as well as a perturbative
treatment of the connected triple excitations) complete basis set (CBS) limit.21
1.3
Overview of Thioformaldehyde
Thioformaldehyde (Figure 2) is an isovalent analog of formaldehyde made up of
carbon, hydrogen, and sulfur with a molecular structure of CH2S. It is the simplest thiocarbonyl compound.
5 Figure 2: Thioformaldehyde (CH2S)
Just like formaldehyde, it is a planar molecule with C2v symmetry. Previous
spectroscopic studies on this species have been impeded by the fact that the molecule is
unstable in the gas phase under typical laboratory conditions.22 However, in 1970,
thioformaldehyde was first identified in the laboratory through the observation of its
microwave spectrum.23 Monomeric thioformaldehyde is now thought to be present in
interstellar space24 as well as associated with the Hale-Bopp comet.25 Due to modern
methods of synthesis, purification, and structural determination used in conjunction with
fast reaction techniques, a substantial amount of spectroscopic data has been obtained for
the thioformaldehyde monomer.26, 27 Additionally, investigations into the ground state
vibrational28-37, ground state rotational23, 30, 31, 35, 37-39, and excited state rotational40-42
properties have previously been performed on monomeric thioformaldehyde. Extensive
ab initio work has also targeted the structural, vibrational, and bonding properties of
monomeric thioformaldehyde.36, 43-57
Like the carbonyl functional group, thiocarbonyls can establish attractive interand intra- molecular non-covalent interactions.46, 49, 51, 52, 55, 56, 58 For instance, sulfur has
been shown to participate in hydrogen bonds that are weaker than those formed with
oxygen.45 Additionally, the sulfur containing amino acids—cystine and methionine—
which were once thought to act simply as hydrophobic moieties in protein folding, are
6 now thought to partake in significant noncovalent interactions, which may influence
tertiary protein structure.59-60
Interestingly, neither the homogenous nor the heterogeneous sulfur analogs of the
formaldehyde dimer model system have been studied. The (CH2O)2 , (CH2S)2 , and
(CH2O)/(CH2O)2 systems provide a means of comparing the noncovalent interactions
between carbonyl and thiocarbonyl groups. Insight into these noncovalent interactions is
of biological importance because it may help explain the phenomenon of protein folding.
This document presents the first detailed characterization (i.e. full optimization and
frequency calculations) of the thioformaldehyde dimer and
formaldehyde/thioformaldehyde (mixed) dimer using both ab initio electronic structure
methods and density functional theory (DFT). The stationary points of the formaldehyde
dimer are characterized for comparison. Thirteen DFT functionals were used in an
attempt to locate a DFT method that reproduced data similar to that obtained using ab
initio methods. This is significant because DFT methods are computationally less
expensive than ab initio methods, and therefore, locating a DFT method that accurately
characterizes the formaldehyde, mixed, and thioformaldehyde dimers with respect to ab
initio methods would aid in the future study of these interactions.
7 2
Theoretical Methods
Full geometry optimizations and corresponding harmonic vibrational frequencies
were performed on monomeric formaldehyde and monomeric thioformaldehyde as well
as each of the dimer configurations found in Figure 3, Figure 4, and Figure 5. The
computations were carried out with second order Møller-Plesset perturbation theory
(MP2)61-66 using the analytic gradients and Hessians available in the Gaussian 0960
software package. The heavy-aug-cc-pVTZ correlation consistent basis set68,69 (denoted
as haTZ), where non-hydrogen (i.e. heavy) atoms are augmented with diffuse functions
(i.e. cc-pVTZ for H and aug-cc-pVTZ for all other atoms), was employed when
performing MP2 computations. Additionally, thirteen density functional theory (DFT)
methods were employed, as implemented in Gaussian 09.67 These DFT implementations
include B3LYP70, 71, B3LYP-D3, B3LYP-D3(BJ), TPSS72, TPSS-D3, TPSS-D3(BJ),
APF73 , APF-D73 , M06-2X74, M06-2X-D3, N12SX75, MN12SX75, and VSXC.76 The
DFT-D3 scheme employs Grimme’s third-generation dispersion correction with the
original D3 damping functions77, while the DFT-D3(BJ) scheme employs the BeckeJonhson damping function.78 Note that the TPSS is implemented for both the exchange
and correction part of the functional (i.e. TPSSTPSS). The 6-311+G(2df,2pd)79-83 basis
set was used when performing all DFT computations. Strict convergence criteria were
employed throughout the computations.
8 The binding energies, Ebind, were computed via the supermolecular approach by
comparing the energy of each optimized dimer structure to the corresponding monomer
energy (Equation 1).
E bind = E dimer − (E monomer 1 + E monomer 2 )
(1)
Single-point €
energy computations were performed for all optimized structures
using explicitly correlated MP2-F12 [specifically MP2-F12 3C(FIX)84] and CCSD(T)F12 [specifically CCSD(T)-F12a85 with unscaled triples contribution] methods.
MP2−F12
CC−F12
Corresponding binding energies are denoted as E bind
and E bind
, respectively. All
explicitly correlated computations were performed with the haTZ basis set and include
€
€ identity (RI) basis sets implemented
the default density fitting (DF) and resolution
of the
in Molpro 2010.1.86
Minimum root means square deviations (RMSD) between un-weighted Cartesian
coordinates of the MP2 and DFT optimized geometries were computed with the
SUPERPOSE program offered in the TINKER87 software package.
For all computations, spherical harmonic basis functions (i.e. 5d and 7f) were
used rather than their Cartesian counterparts (i.e. 6d and 10f). Residual Cartesian
gradients of the optimized structures were less than 1.77 x 10-5 Eh a0-1. For all DFT
computations, a pruned integration grid having 150 radical shells and 974 angular points
per shell was employed. The frozen core approximation was used for MP2 and CCSD(T)
computations (1s, 2s, 2p-like orbitals on sulfur and 1s-like orbitals on oxygen and
carbon).
9 3
Results and Discussion
3.1
Structures and Energies
3.1.1 Formaldehyde Dimer
Five stationary points of the formaldehyde dimer, (CH2O)2, were found using
MP2 electronic structure theory and are shown in Figure 3 along with their point group
symmetries. Structure I has Cs symmetry. Structures II and III have C2h symmetry, and
Structures IV and V have C2v symmetry. Structures I-V are characterized by an edge-toface, edge-to-edge, face-to-face, non-planar head-to-tail, and planar head-to-tail
alignment of monomers, respectively. These results are consistent with the previous
work carried out by Ford and Glasser9.
The Hessian index (number of imaginary modes of vibration denoted as ni) for the
MP2 optimized (CH2O)2 structures are shown in Table 1. (CH2O)2 Structures I and II
represent minima on the MP2 PES because they have zero imaginary modes of vibration
(ni = 0). Structure IV is a transition state (ni = 1), and structures III and V are higher
order saddle points (ni > 1). The intermolecular separations of (CH2O)2 with respect to
the center of mass (COM) of each monomer (RCOM) are also listed in Table 1 and range
from 2.89 Å (Structure I) to 4.35 Å (Structure V).
10 Figure 3: (CH2O) 2 structures and point groups
The MP2, MP2-F12, and CCSD(T)-F12 binding energies of the MP2 (CH2O)2
MP2
MP2−F12
CC−F12
optimized structures ( E bind
, E bind
, and E bind
, respectively), as well as the higherCC−F12
order correlation effects ( δ MP2−F12
), defined in Equation 2, are listed in Table 1.
€
€
€
€
CC−F12
CC−F12
MP2−F12
δ MP2−F12
= E bind
− E bind
€
11 (2)
Table 1: Number of imaginary vibrational frequencies (ni), intermolecular
MP2
separation (RCOM in Å), binding energies ( E bind
), and MP2-F12/haTZ and
MP2−F12
CC−F12
CCSD(T)-F12/haTZ binding energies ( E bind
and E bind
) of the MP2 optimized
structures with the haTZ basis set. All energies are in kcal mol-1.
€
€
€
12 MP2
Good agreement is observed between MP2 and MP2-F12 binding energies ( E bind
MP2−F12
and E bind
) with deviations less than a tenth of a kcal mol-1. Furthermore, higher-order
€
CC−F12
correlation effects ( δ MP2−F12
) do not exceed 0.20 kcal mol-1 as seen in Structure II.
€
Structure I is the global minimum lying 1.08 kcal mol-1, 1.06 kcal mol-1, and 0.81 kcal
€ in energy than Structure II according to E MP2 , E MP2−F12 , and E CC−F12 ,
mol-1 lower
bind
bind
bind
respectively. The CCSD(T)-F12 binding energy difference between Structure I and II
€ previously €
(0.81 kcal mol-1) is in excellent agreement€with the
reported CCSD(T) CBS
limit electronic energy difference between Structures I and II of 0.80 kcal mol-1.17
3.1.2 Mixed Dimer
The seven, newly-identified, stationary points of the heterogeneous or “mixed”
formaldehyde/thioformaldehyde dimer, CH2O/CH2S, were found using MP2 electronic
structure theory and are shown in Figure 4 along with their point group symmetries.
Structure Ia, Ib, and II have Cs symmetry while the remaining structures (Structures IVa,
IVb, Va, and Vb) have C2v symmetry. These structures contain similar orientations to the
corresponding (CH2O)2 stationary points; however, due to the different arrangement of
the formaldehyde and thioformaldehyde monomers, many structures have two
conformers (represented a and b). A CH2O/CH2S configuration comparable to (CH2O)2
Structure III was not found.
The number of imaginary modes of vibration (ni) for the MP2 optimized
CH2O/CH2S structures are shown in Table 1. Structures Ia, Ib, II, and Va represent
minima on the MP2 PES. Structures IVa and IVb are transition states, and structure Vb
is a higher order saddle point. The RCOM values for the CH2O/CH2S structures, listed in
Table 1, are slightly larger than those of the (CH2O)2, ranging from 3.12 Å (Structure I)
13 Figure 4: (CH2O) /(CH2S) structures and point groups
to 4.88 Å (Structure Va).
MP2
MP2−F12
CC−F12
CC−F12
, E bind
, E bind
, and δ MP2−F12
for CH2O/CH2S are listed in Table 1. Just
E bind
like (CH2O)2, good agreement is observed between MP2 and MP2-F12 binding energies
MP2−F12
€ ( E MP2
€
€
) with a€maximum deviation of 0.12 kcal mol-1 as seen in Structure
bind and E bind
CC−F12
IVa. Additionally, higher-order correlation effects ( δ MP2−F12
) grown no larger than 0.37
€
€
€
14 kcal mol-1 as seen in Structure Ia. Since Structure Ia is more than 1 kcal mol-1 lower in
MP2
MP2−F12
CC−F12
energy than Structure Ib according to E bind
, E bind
, and E bind
, it is considered the
global minimum.
€
€
3.1.3 Thioformaldehyde Dimer
€
Five newly-identified stationary points of the thioformaldehyde dimer, (CH2S)2,
were found using MP2 electronic structure theory and are shown in Figure 5 along with
their point group symmetries. Just like the formaldehyde dimer, Structure I has Cs
symmetry. Structures II and III have C2h symmetry, and Structures IV and V have C2v
symmetry. Furthermore, structures I-V are characterized by an edge-to-face, edge-toedge, face-to-face, non-planar head-to-tail, and planar head-to-tail alignment of
monomers, respectively. The (CH2O)2 and (CH2S)2 structures are qualitatively similar
except Structure III. The (CH2O)2 Structure III is characterized by two anti-parallel
CH2O monomers in a near-stacked, fact-to-face orientation containing two C⋅⋅⋅O
interactions, while the two monomers in the corresponding (CH2S)2 structure slip into an
anti-parallel direction forming a face-to-face alignment of the carbonyl centers. The
number of imaginary modes of vibration (ni) for the MP2 optimized (CH2S)2 structures
are shown in Table 1. Structures I, II, and III are minima, Structure V is a transition
state, and Structure IV is a higher order saddle point on the MP2 PES. The RCOM values
for the (CH2S)2 structures, listed in Table 1, are significantly larger than those of the
(CH2O)2, growing as large as 5.22 Å as seen in Structure V.
MP2
MP2−F12
CC−F12
CC−F12
, E bind
, E bind
, and δ MP2−F12
or (CH2S)2 are also listed in Table 1. Much
E bind
like (CH2O)2 and CH2O/CH2S, good agreement is observed between MP2 and MP2-F12
€ binding
€ energies
€ ( E MP2 and€E MP2−F12 ) with deviations exceeding no more than 0.13
bind
bind
€
€
15 Figure 5: (CH2S) 2 structures and point groups
CC−F12
kcal mol-1 for Structure IV. However, higher-order correlation effects ( δ MP2−F12
) grow as
large as 1.09 kcal mol-1 for Structure I. According to explicitly correlated MP2-F12
MP2−F12
€ 0.67 kcal mol-1 lower
computations ( E bind
), Structure I is the global minimum lying
CC−F12
in energy than Structure II. In contrast, the CCSD(T)-F12 binding energies ( E bind
)
€
show Structure II to be the global minimum lying 0.30 kcal mol-1 lower in energy than
Structure I. These contrasting global minima along with the rather€large higher-order
16 correlation effects suggests that the MP2 and CCSD(T) PES could be qualitatively
different for the thioformaldehyde dimer.
3.2
DFT Analysis
3.2.1 Formaldehyde Dimer
Five stationary points of (CH2O)2 have been characterized with thirteen DFT
methods (Table 2).
Table 2: Number of imaginary vibrational frequencies (ni) of the DFT/6311+G(2df,2pd) optimized (CH2O) 2 structures as well as the number of structures
with a different number of imaginary modes from the MP2 reference structures
(δni).
In accordance with MP2 computations, all DFT functionals characterized
Structures I and II as minima (ni = 0) on the DFT PES . Structure IV appears to be a
transition state (ni = 1); however, both APF and VSXC characterize it as a minima on the
DFT PES. All DFT functionals indicate that Structure III is a higher order saddle point
17 (ni > 1). Seven DFT functionals (B3LYP-D3, TPSS-D3, B3LYP, TPSS, APF, N12SX,
and VSXC) characterize Structure V as a higher order saddle point, while the remaining
functionals consider it a transition state. The last column in Table 2 (δni) indicates the
number of DFT optimized structures that produce different imaginary vibrational
frequencies compared to the MP2 optimized structures for each DFT method. Only six
functionals characterize each series of stationary points in accordance with the MP2 level
of theory (δni = 0). These functionals include B3LYP-D3(BJ), TPSS-D3(BJ), M06-2XD3, APF-D, M06-2X, and MN12SX.
The average absolute deviations (AADs) and maximum absolute deviations
(MADs) of the Cartesian root means square deviations (RMSD) (in Å) and the difference
in intermolecular separations (ΔRCOM in Å) of the DFT optimized (CH2O)2 structures
with respect to the MP2 reference structures are listed Table 3. Additionally, deviations
DFT
of the DFT binding energies ( ΔE bind
), relative energies (ΔErel), and CCSD(T)-F12
CC−F12
binding energies ( ΔE bind
) of the DFT optimized geometries are shown in Table 3 with
€
respect to the CCSD(T)-F12 binding energies of the MP2 optimized geometries.
€ of the RMSD AADs lie within 0.10 Å, and the MADs are relatively small, the
All
largest being 0.23 Å for the VSXC functional. The ΔRCOM AADs are within 0.20 Å for
every DFT functional, and the corresponding MADs grow no larger than 0.34 Å as seen
in TPSS. Both RMSD and ΔRCOM values show how greatly the DFT optimized
geometries differ from the MP2 optimized geometries. Since these values stay relatively
low, it is clear that the DFT functionals did a good job computing the geometry of the
formaldehyde dimers. Specifically, B3LYP-D3(BJ), B3LYP-D3, and N12SX perform
18 Table 3: The average (AADs) and maximum (MADs) absolute deviations of the root
mean squared deviation (RMSD), the difference in intermolecular separation
DFT
(ΔRCOM ), deviations in DFT/6-311+G(2df,2pd) binding energies ( ΔE bind
), deviations
in relative energies (ΔErel), and deviations in CCSD(T)-F12/haTZ binding energies
CC−F12
( ΔE bind
) of the DFT/6-311+G(2df,2pd) optimized structures with respect to the
MP2/haTZ reference structures. Energy deviations (in kcal mol-1).
€
€
19 remarkably well with RMSD and ΔRCOM AADs and MADs growing no larger than 0.05
Å.
DFT
All AADs of the ΔE bind
are roughly within 1 kcal mol-1 except for VSXC, which
DFT
has a ΔE bind
of 2.79 kcal mol-1. B3LYP-D3(BJ) performs exceptionally well with a
€
DFT
AAD of only 0.09 kcal mol-1. TPSS-D3 and MN12SX also perform well with
ΔE bind
€
DFT
AADs of 0.14 kcal mol-1 for both functionals. ΔErel indicates how consistent the
ΔE bind
€
error in the DFT binding energies was compared to Structure I. All DFT methods have a
€
ΔErel AAD of less than 1 kcal mol-1 except for VSXC (1.76 kcal mol-1). N12SX has the
CC−F12
lowest ΔErel AAD of 0.17 kcal mol-1. The AADs of ΔE bind
are all less than a tenth of
a kcal mol-1 except TPSS and VSXC with values of 0.16 kcal mol-1 and 0.27 kcal mol-1,
CC−F12
respectively. B3LYP-D3(BJ), B3LYP-D3,€APF-D, and N12SX all have ΔE bind
AADs
of 0.01 kcal mol-1. These results indicate the effect geometrical deviations have on
CC−F12
€
binding energies, because ΔE bind
represents the difference between
CCSD(T)-F12
binding energies of the DFT optimized geometries with respect to the CCSD(T)-F12
€of the MP2 optimized geometries. B3LYP-D3(BJ)’s, B3LYP-D3’s,
binding energies
CC−F12
APF-D’s, and N12SX’s small ΔE bind
AADs of 0.01 kcal mol-1 indicate that differing
geometries of (CH2O)2 had little to know effect on the binding energies when using
€
those four DFT functionals.
3.2.2 Mixed Dimer
Seven newly-identified stationary points of the mixed dimer CH2O/CH2S have
been characterized with thirteen DFT methods (Table 4).
20 Table 4: Number of imaginary vibrational frequencies (ni) of the DFT/6311+G(2df,2pd) optimized (CH2O) /(CH2S) structures as well as the number of
structures with a different number of imaginary modes from the MP2 reference
structures (δni).
Structures Ia, Ib, II, and Va are minima on the DFT PES, although MN12SX and
VSXC characterize Structure Va as a transition state. Structure IVa is a transition point
according to all the DFT functionals except M06-2X-D3, M06-2X, and VSXC, which
characterize it as a minimum. Five functionals—B3LYP-D3, APF-D, B3LYP, AFP, and
N12SX—characterize Structure IVb as a transition state, which is in accordance with the
MP2 findings. Another five functionals—B3LYP-D3(BJ), TPSS-D3(BJ), TPSS-D3,
TPSS, and MN12SX—characterize Structure IVb as a higher order saddle point. The
remaining three functionals—M06-2X-D3, M06-2X, and VSXC—characterize the
structure as a minima. All functionals characterize Structure Vb as a higher order saddle
point except M062X-D3 and M062X, which consider it a transition state. None of the
DFT methods characterize all stationary points in accordance with MP2 (δni ≠ 0).
DFT
CC-F12
The AADs and MADs of RMSD, ΔRCOM, ΔE bind
, ΔErel, and ΔE bind
for
CH2O/CH2S are located in Table 3. RMSD AADs grow no larger than 0.13 Å as seen in
€
21 €
TPSS, and the MADs grow no larger than 0.25 Å as seen in VSXC. ΔRCOM AADs all lie
within 0.2 Å except for B3LYP and TPSS, which have AADs of 0.21 Å and 0.26 Å,
respectively. Much like the formaldehyde dimer, the small RMSD and ΔRCOM AADs and
MADs values indicate that the DFT functionals (with the exception of B3LYP, TPSS,
and VSXC) did a good job computing the geometry of the mixed dimer structures.
Furthermore, B3LYP-D3(BJ), B3LYP-D3, APFD, and N12SX perform remarkably well
with RMSD and ΔRCOM AADs growing no more than 0.03 Å and MADs growing no
more than 0.05 Å.
DFT
For ΔE bind
, all AADs are roughly within 1 kcal mol-1 except for VSXC, which
grows as large as 3.17 kcal mol-1. Both M06-2X-D3 and MN12SX have the smallest
€ DFT AAD of 0.30 kcal mol-1. VSXC also has the largest ΔE DFT MAD of 5.02 kcal
ΔE
bind
bind
DFT
mol-1 with the next largest being TPSS-D3, having a ΔE bind
MAD of 1.46 kcal mol-1.
€
€
Most DFT methods have an AAD ΔErel of less than 1 kcal mol-1 except for TPSS-D3(BJ),
TPSS-D3, and VSXC with values of 1.51, €
1.11, and 2.16, respectively. These three
functionals produce inconsistent binding energies and are therefore potentially bad
methods to use when performing computations on the mixed dimer system. When
CC-F12
looking at the AADs of ΔE bind
, TPSS-D3(BJ), TPSS, and VSXC perform the worst yet
again. While all other functionals lie within 0.1 kcal mol-1, these functionals grow as
€ mol-1, 0.23 kcal mol-1, and 0.23 kcal mol-1, respectively. On the other
large as 0.21 kcal
hand, B3LYP-D3(BJ), B3LYP-D3, M06-2X-D3, APF-D, M06-2X, and N12SX, have
CC-F12
extremely small ΔE bind
AADs of either 0.01 kcal mol-1 or 0.02 kcal mol-1.
€
22 3.2.3 Thioformaldehyde Dimer
Five newly-identified stationary points of the mixed dimer (CH2S)2 have been
characterized with thirteen DFT methods (Table 5).
Table 5: Number of imaginary vibrational frequencies (ni) of the DFT/6311+G(2df,2pd) optimized (CH2S) 2 structures as well as the number of structures
with a different number of imaginary modes from the MP2 reference structures
(δni).
Structures I and II are minima on the DFT PES, although VSXC characterize
Structure II as a transition point. Only dispersion corrected functionals and M06-2X
characterize Structure III as a minima. The remaining six functionals characterize it as a
transition state. Five functionals (B3LYP-D3(BJ), B3LYP-D3, M06-2X-D3, M06-2X,
and VSXC) characterize Structure IV as a minima, two functionals (TPSS-D3(BJ) and
TPSS-D3) characterize it as a transition state, and the remaining six functionals
characterize it as higher order saddle point. B3LYP-D3 and M06-2X-D3 characterize
Structure V as a minima. APFD, B3LYP, TPSS, APF, N12SX, and VSXC characterize it
23 as a transition state, while the remaining functionals characterize it as a higher order
saddle point. None of the DFT methods characterized all five stationary points in
accordance with MP2 (δni ≠ 0).
DFT
DFT
The AADs and MADs of RMSD, ΔRCOM, ΔE bind
, ΔErel, and ΔE bind
for (CH2S)2
are located in Table 3. All RMSD AADs lie within 0.10 Å except B3LYP, TPSS, and
€ 0.15 Å, respectively.
€
APF whose AADs are 0.20 Å, 0.19 Å, and
The MADs grow as
large as 0.43 Å as seen in B3LYP. For ΔRCOM, B3LYP, TPSS, and APF are again the
major outliers. All ΔRCOM AADs lie around 0.10 Å for every DFT functional except
B3LYP, TPSS, and APF, which have values of 0.41 Å, 0.40 Å, and 0.31 Å, respectively.
Thee rather large RMSD and ΔRCOM AADs and MADs values indicate that B3LYP,
TPSS, and APF performed poorly when computing the geometry of the thioformaldehyde
dimer structures.
DFT
AADs are roughly within 1 kcal mol-1 except for VSXC, which grows as
ΔE bind
large as 3.46 kcal mol -1. B3LYP offers the lowest ΔErel AAD of 0.34 kcal mol-1, while
€ TPSS-D3(BJ) provides the highest ΔE AAD of 3.76 kcal mol-1. Seven of the DFT
rel
CC-F12
functionals all have ΔE bind
AADs of 0.05 kcal mol-1 or less. These functionals include
B3LYP-D3(BJ), B3LYP-D3, M06-2X-D3, APF-D, M06-2X, N12SX, and MN12SX.
€ that small geometrical differences of (CH2S)2 had little to know effect on
This suggests
the binding energies when using these seven DFT functionals. On the other hand, the
remaining functionals all lie above 0.20 kcal mol-1 and grow as large as 0.52 kcal mol-1 as
seen in TPSS.
24 4
Conclusions
Five stationary points of the formaldehyde dimer, seven newly-identified
stationary points of the formaldehyde/thioformaldehyde (mixed) dimer, and five newlyidentified stationary points of the thioformaldehyde dimer were characterized with MP2
electronic structure theory. (CH2O)2 Structures I and II, CH2O/CH2S Structures Ia, Ib, II,
and Va, and (CH2S)2 Structures I, II, and III are all minima (ni = 0), on the MP2 potential
energy surface (PES). Deviations between the MP2 and MP2-F12 binding energies of
the MP2 optimized structures grow to be no larger than 0.13 kcal mol-1. Higher order
correlation effects of (CH2O)2 and CH2O/CH2S are small, growing to be no more than 0.2
and 0.37 kcal mol-1, respectively. However, higher order correlation effects grow to be as
large as 1.1 kcal mol-1 for (CH2S)2. According to both MP2-F12 and CCSD(T)-F12
binding energies Structure I for (CH2O)2 and Structure Ia for CH2O/CH2S are the global
minima. However, according to the MP2-F12 binding energy for (CH2S)2 , Structure I is
the global minimum (0.67 kcal mol-1 lower in energy than Structure II), while the
CCSD(T)-F12 binding energy indicates Structure II to be the global minimum (0.3 kcal
mol-1 lower in energy than Structure I). This suggests that the MP2 and CCSD(T) PES
could be qualitatively different for (CH2S)2.
Every stationary point was fully characterized with thirteen DFT methods. All DFT
functionals characterized (CH2O)2 Structures I and II and CH2O/CH2S Structures Ia, Ib,
and II as minima on the DFT PES. All DFT functionals except VSXC characterized
25 (CH2S)2 Structures I and II as minima, and only seven functionals characterized (CH2S)2
Structure III as a minimum. For the formaldehyde dimer, only six functionals (B3LYPD3(BJ), TPSS-D3(BJ), M06-2X-D3, APF-D, M06-2X, and MN12SX) predicted the same
number of imaginary frequencies as the MP2 level of theory. However, for CH2O/CH2S
and (CH2S)2 , none of the DFT methods predicted the same number of imaginary modes
of vibrations as MP2. This indicates that DFT functionals were not successful in
characterizing the modes of imaginary vibrational frequency in accordance with MP2 for
these dimer systems. B3LYP, TPSS, and VSXC DFT functionals consistently
performed poorly when computing the geometry of (CH2O)2 , CH2O/CH2S, and (CH2S)2
structures, while, B3LYP-D3(BJ), B3LYP-D3, APFD, and N12SX typically performed
DFT
well. When computing the DFT binding energies ( E bind
) of the DFT optimized
geometries, B3LYP, TPSS, APF, and VSXC perform badly compared to CCSD(T)-F12
€
binding energies of the MP2 optimized geometries
for all three dimer systems. TPSSDFT
D3(BJ) and TPSS-D3 perform poorly when computing E bind
for the thioformaldehyde
structures. There is no clear set of functionals that consistently produces good DFT
binding energies compared to CCSD(T)-F12€binding energies of the MP2 optimized
geometries.
Studying the homogenous and heterogeneous sulfur analogs of the formaldehyde
dimer model system provided a means of comparing the noncovalent interactions
between carbonyl and thiocarbonyl groups. The research found within this document
may help shed light on the noncovalent interactions involved in protein folding, and may
specifically aid in studying the interactions between the sulfur containing amino acids:
cystine and methionine.
26 5
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