Chérif F. Matta

How dependent are molecular and atomic properties on the electronic structure method? Comparison of Hartree-Fock, DFT, and MP2 on a biologically relevant set of molecules

This article compares molecular properties and atomic properties defined by the quantum theory of atoms in molecules (QTAIM) obtained from three underlying levels of theory: MP2(full), density functional theory (DFT) (B3LYP), and Hartree‐Fock (H‐F). The same basis set (6‐311++G(d,p)) has been used throughout the study. The calculations and comparisons were applied to a set of 30 small molecules representing common fragments of biological molecules. The molecular properties investigated are the energies and the electrostatic moments (up to and including the quadrupoles), and the atomic properties include electron populations (and atomic charge), atomic dipolar and quadrupolar polarizations, atomic volumes, and corrected and raw atomic energies. The Cartesian distance between dipole vectors and the Frobenius distance between the quadrupole tensors calculated at the three levels of theory provide a measure of their correlation (or lack thereof). With the exception of energies (atomic and molecular), it is found that both DFT and H‐F are in excellent agreement with MP2, especially with regards to the electrostatic mutipoles up to the quadrupoles, but DFT and MP2 agree better in almost all studied properties (with the exception of molecular geometries). QTAIM properties whether obtained from H‐F, DFT(B3LYP), or MP2 calculations when used in the construction of empirical correlations with experiment such as quantitative structure‐activity‐(or property)‐relationships (QSAR/QSPR) are equivalent (because the properties calculated at the three levels are very highly correlated among themselves with r2 typically >0.95, and therefore preserving trends). These results suggest that the massive volume of results that were published in the older literature at the H‐F level is valid especially when used to study trends or in QSAR or QSPR studies, and, as long as our test set of molecules is representative, there is no pressing need to re‐evaluate them at other levels of theory except when inadequate basis sets were used by todays standards. Extensive tabulation of molecular and atomic properties at the three theoretical levels is available in the Supporting Information, including optimized geometries, molecular energies, virial ratios, molecular electrostatic moments up to and including hexadecapoles, atomic populations, atomic volumes, atomic electrostatic moments up to and including the quadrupoles, and atomic energies.

On atom-atom 'short contact' bonding interactions in crystals.

The electron density distribution ρ(r) contains the information needed to quantitatively analyze bonding interactions between atoms, exhibiting short, medium or long inter-nuclear distances. Atom–atom bonding interactions, the orientation of molecules in the space and crystal structure are all inter-determined.

Comparison of localization and delocalization indices obtained with Hartree–Fock and conventional correlated methods: Effect of Coulomb correlation

Atomic populations and localization [λ(A)] and delocalization [δ(A,B)] indices (LIs and DIs) are calculated for a large set of molecules at the Hartree–Fock (HF), MP2, MP4(SDQ), CISD, and QCISD levels with the 6‐311++G(2d,2p) basis set. The HF method and the conventional correlation methods [MP2, MP4(SDQ), CISD, and QCISD] yield distinct sets of LIs and DIs. Yet, within the four conventional correlation methods the differences in atomic populations and LIs and DIs are small. Relative to HF, the conventional correlation methods [MP2, MP4(SDQ), CISD, QCISD] yield virtually the same LIs and DIs for molecules with large charge separations while LIs and DIs that differ significantly from the HF values—the LIs are increased and DIs decreased—are obtained for bonds with no or small charge separations. Such is the case in the archetypal homopolar molecules HCCH, H2CCH2, CH3CH3, and “protonated cyclopropane” C3H  7+ , in which case the bonding may be atypical. Relative to HF, the typical effect of the conventional correlation methods is to decrease the DI between atoms.

Effect of absolute laser phase on reaction paths in laser-induced chemical reactions

Potential surfaces, dipole moments, and polarizabilities are calculated by ab initio methods [unrestricted MP2(full)/6-311++G(2d,2p)] along the reaction paths of the F+CH4 and Cl+CH4 reaction systems. It is found that in general dipole moments and polarizabilities exhibit peaks near the transition state. In the case of X=F these peaks are on the products side and in the case of X=Cl they are on the reactants side indicating an early transition state in the case of fluorine and a late transition state in the case of chlorine. An analysis of the geometric changes along the reaction paths reveals a one-to-one correspondence between the peaks in the electric properties and peaks in the rate of change of certain internal geometric coordinates along the reaction path. Interaction with short infrared intense laser fields pulses leads to the possibility of interferences between the dipole and polarizability laser-molecule interactions as a function of laser phase. The larger dipole moment in the Cl+CH4 reaction can lead to the creation of deep wells (instead of energy barriers) and new strongly bound states in the transition state region. This suggests possible coherent control of the reaction path as a function of the absolute phase of the incident field, by significant modification of the potential surfaces along the reaction path and, in particular, in the transition state region.

Atoms‐in‐molecules study of the genetically encoded amino acids. III. Bond and atomic properties and their correlations with experiment including mutation‐induced changes in protein stability and genetic coding

This article presents a study of the molecular charge distributions of the genetically encoded amino acids (AA), one that builds on the previous determination of their equilibrium geometries and the demonstrated transferability of their common geometrical parameters. The properties of the charge distributions are characterized and given quantitative expression in terms of the bond and atomic properties determined within the quantum theory of atoms‐in‐molecules (QTAIM) that defines atoms and bonds in terms of the observable charge density. The properties so defined are demonstrated to be remarkably transferable, a reflection of the underlying transferability of the charge distributions of the main chain and other groups common to the AA. The use of the atomic properties in obtaining an understanding of the biological functions of the AA, whether free or bound in a polypeptide, is demonstrated by the excellent statistical correlations they yield with experimental physicochemical properties. A property of the AA side chains of particular importance is the charge separation index (CSI), a quantity previously defined as the sum of the magnitudes of the atomic charges and which measures the degree of separation of positive and negative charges in the side chain of interest. The CSI values provide a correlation with the measured free energies of transfer of capped side chain analogues, from the vapor phase to aqueous solution, yielding a linear regression equation with r2 = 0.94. The atomic volume is defined by the van der Waals isodensity surface and it, together with the CSI, which accounts for the electrostriction of the solvent, yield a linear regression (r2 = 0.98) with the measured partial molar volumes of the AAs. The changes in free energies of transfer from octanol to water upon interchanging 153 pairs of AAs and from cyclohexane to water upon interchanging 190 pairs of AAs, were modeled using only three calculated parameters (representing electrostatic and volume contributions) yielding linear regressions with r2 values of 0.78 and 0.89, respectively. These results are a prelude to the single‐site mutation‐induced changes in the stabilities of two typical proteins: ubiquitin and staphylococcal nuclease. Strong quadratic correlations (r2 ∼ 0.9) were obtained between ΔCSI upon mutation and each of the two terms ΔΔH and TΔΔS taken from recent and accurate differential scanning calorimetry experiments on ubiquitin. When the two terms are summed to yield ΔΔG, the quadratic terms nearly cancel, and the result is a simple linear fit between ΔΔG and ΔCSI with r2 = 0.88. As another example, the change in the stability of staphylococcal nuclease upon mutation has been fitted linearly (r2 = 0.83) to the sum of a ΔCSI term and a term representing the change in the van der Waals volume of the side chains upon mutation. The suggested correlation of the polarity of the side chain with the second letter of the AA triplet genetic codon is given concrete expression in a classification of the side chains in terms of their CSI values and their group dipole moments. For example, all amino acids with a pyrimidine base as their second letter in mRNA possess side‐chain CSI ≤ 2.8 (with the exception of Cys), whereas all those with CSI > 2.8 possess an purine base. The article concludes with two proposals for measuring and predicting molecular complementarity: van der Waals complementarity expressed in terms of the van der Waals isodensity surface and Lewis complementarity expressed in terms of the local charge concentrations and depletions defined by the topology of the Laplacian of the electron density. A display of the experimentally accessible Laplacian distribution for a folded protein would offer a clear picture of the operation of the “stereochemical code” proposed as the determinant in the folding process. Proteins 2003;52:360–399.

An Atoms‐In‐Molecules study of the genetically‐encoded amino acids: I. Effects of conformation and of tautomerization on geometric, atomic, and bond properties

The theory of Atoms‐In‐Molecules (AIM) is a partitioning of the real space of a molecule into disjoint atomic constituents as determined by the topology of the electron density, ρ(r). This theory identifies an atom in a molecule with a quantum mechanical open system and, consequently, all of the atoms properties are unambiguously defined. AIM recovers the basic empirical cornerstone of chemistry: that atoms and functional groups possess characteristic and additive properties that in many cases exhibit a remarkable transferability between different molecules. As a result, the theory enables the theoretical synthesis of a large molecule and the prediction of its properties by joining fragments that are predetermined as open systems. The present article is the first of a series (in preparation) that explore this possibility for polypeptides by determining the transferability of the building blocks: the amino acid residues. Transferability of group properties requires transferability of the electron density ρ(r), which in turn requires the transferability of the geometric parameters. This article demonstrates that these parameters are conformation‐insensitive for a representative amino acid, leucine, and that the atomic and bond properties exhibit a corresponding transferability. The effects of hydrogen bonding are determined and a set of geometrical conditions for the occurrence of such bonding is identified. The effects of transforming neutral leucine into its zwitter‐ionic form on its atomic and bond properties are shown to be localized primarily to the sites of ionization. Proteins 2000;40:310–329.

Atomic contributions to bond dissociation energies in aliphatic hydrocarbons

This paper explores the atomic contributions to the electronic vibrationless bond dissociation enthalpy (BDE) at 0 K of the central C-C bond in straight-chain alkanes (C(n)H(2n+2)) and trans-alkenes (C(n)H(2n)) with an even number of carbon atoms, where n=2, 4, 6, 8. This is achieved using the partitioning of the total molecular energy according to the quantum theory of atoms in molecules by comparing the atomic energies in the intact molecule and its dissociation products. The study is conducted at the MP2(full)6-311++G(d,p) level of theory. It is found that the bulk of the electronic energy necessary to sever a single C-C bond is not supplied by these two carbon atoms (the alpha-carbons) but instead by the atoms directly bonded to them. Thus, the burden of the electronic part of the BDE is primarily carried by the two hydrogens attached to each of the alpha-carbons and by the beta-carbons. The effect drops off rapidly with distance along the hydrocarbon chain. The situation is more complex in the case of the double bond in alkenes, since here the burden is shared between the alpha-carbons as well as the atoms directly bonded to them, namely, again the alpha-hydrogens and the beta-carbons. These observations may lead to a better understanding of the bond dissociation process and should be taken into account when locally dense basis sets are introduced to improve the accuracy of BDE calculations.

Fluorine-fluorine spin-spin coupling constants in aromatic compounds: correlations with the delocalization index and with the internuclear separation.

This paper describes a new empirical approach for the evaluation of fluorine-fluorine spin-spin coupling constants (J(FF)) in aromatic compounds. The correlations between J(FF) and the delocalization index calculated within the framework of the theory of atoms in molecules (AIM) and with the fluorine-fluorine internuclear separation are investigated. Both the internuclear separation and the delocalization index are found to be highly correlated with J(FF). A regression model in which the experimental J(FF) coupling constant is fitted exponentially to the internuclear separation and linearly to the delocalization index yields a squared correlation coefficient as high as 0.96 for a data set consisting of 33 coupling constants spread over a range of 85 Hz.

Atoms-in-molecules study of the genetically encoded amino acids. II. Computational study of molecular geometries

The geometries of the 20 genetically encoded amino acids were optimized at the restricted Hartree–Fock level of theory using the 6‐31+G* basis set. A detailed comparison showed the calculated geometries to be in excellent agreement with those determined by X‐ray crystallography. The study demonstrated that the geometric parameters for the main‐chain group and for the bonds and common functional groups of the side‐chains exhibit a high degree of transferability among the members of this set of molecules. This geometric transferability is a necessary prerequisite for the corresponding transferability of their electron density distributions and hence of their bond and atomic properties. The transferability of the electron distributions will be demonstrated and exploited in the following paper of this series, which uses the topology of the electron density to define an atom within the quantum theory of atoms in molecules. Particular features of the geometries of the amino acids are discussed. It has been shown, for example, how the apparent anomaly of the CαN bond length in a peptide being shorter than in the charged species CαNH  +3 is resolved when the charge separation is gauged by the differences in the charges of the Cα and N atoms as opposed to the use of formal charges. A compilation of literature sources on experimental geometries covering each member of the 20 amino acids is presented. A set of rules for labeling the atoms and bonds, complementing the generally accepted IUPAC‐IUB rules, is proposed to uniquely identify every atom and bond in the amino acids. Proteins 2002;48:519–538.

Electron-density descriptors as predictors in quantitative structure–activity/property relationships and drug design

The use of electron density-based molecular descriptors in drug research, particularly in quantitative structure--activity relationships/quantitative structure--property relationships studies, is reviewed. The exposition starts by a discussion of molecular similarity and transferability in terms of the underlying electron density, which leads to a qualitative introduction to the quantum theory of atoms in molecules (QTAIM). The starting point of QTAIM is the topological analysis of the molecular electron-density distributions to extract atomic and bond properties that characterize every atom and bond in the molecule. These atomic and bond properties have considerable potential as bases for the construction of robust quantitative structure--activity/property relationships models as shown by selected examples in this review. QTAIM is applicable to the electron density calculated from quantum-chemical calculations and/or that obtained from ultra-high resolution x-ray diffraction experiments followed by nonspherical refinement. Atomic and bond properties are introduced followed by examples of application of each of these two families of descriptors. The review ends with a study whereby the molecular electrostatic potential, uniquely determined by the density, is used in conjunction with atomic properties to elucidate the reasons for the biological similarity of bioisosteres.