Valence bond theory for chemical dynamics

This essay provides a perspective on several issues in valence bond theory: the physical significance of semilocal bonding orbitals, the capability of valence bond concepts to explain systems with multireferences character, the use of valence bond theory to provide analytical representations of potential energy surfaces for chemical dynamics by the method of semiempirical valence bond potential energy surfaces (an early example of specific reaction parameters), by multiconfiguration molecular mechanics, by the combined valence bond-molecular mechanics method, and by the use of valence bond states as coupled diabatic states for describing electronically nonadiabatic processes (photochemistry). The essay includes both ab initio and semiempirical approaches.     

Computation of curve-crossing diagrams by approximate valence bond method

Avoided crossing diagram parameters for the radical exchange reaction and the concerted exchange of two and three bonds are computed by using the approximated valence bond method, which is a nonorthogonal configuration interaction (CI) semiempirical method among the valence bond configuration functions. Here, each valence bond configuration function is a spin-adapted combination of Slater determinants constructed from the Heitler-London or Coulson-Fischer hybrid orbitals. Atomic orbitals integrals are evaluated using semiempirical philosophy, and these provide considerable saving of computer time compared with the most standard ab initio multistructure valence bond methods. The results indicate that the approximate valence bond method is capable of yielding reasonable results for the avoided crossing diagram parameters. These results also indicate that the diagram gap (G) is the decisive factor for the stability of symmetric clusters, X_n, although no clear correlation between the gap G and the geometric distortion is found for different values of n. © 1996 John Wiley & Sons, Inc.     

Bond orders and valences from ab initio wave functions

The definition and properties of the bond order and valence indices calculated from ab initio wave functions are summarized. Their physical interpretation relationships to the exchange effects in bonding and generalization to correlated wave functions are also discussed. Some examples with typical bond order and valence values are shown.     

On bond orders and valences in the Ab initio quantum chemical theory

The concept of bond order and valence indices calculated at the ab initio level is discussed in connection with their close relationship to the nonclassical exchange effects in bonding. An improved definition of bond order and free valence indices is given for the open-shell SCF (UHF ) case, and the generalization of the bond order and valence indices to correlated wave functions is also introduced.     

Interatomic and intraatomic analysis of the density matrix: applications to chlorobenzenes

Bond orders and valence indices have been evaluated employing Mayer’s definitions with orthogonalized atomic orbitals (OAO) obtained from L?wdin orthogonalization over an STO-3G basis set in anab initio formalism. It has been observed that the eigenvalues of the submatrices associated with bond order orbitals. natural hybrid orbitals and natural bond orbitals also reproduce the same values of the bond orders and the valence indices which in turn are quite close to the classical values. Bond orders obtained by a similarity transformation of theab initio density matrix differ appreciably in numerical magnitude.     

Near ab initio quality molecular electrostatic potential maps using hybridization displacement charges at PM3 level and effects of geometrical changes in amino groups

Charge distributions, dipole moments, and molecular electrostatic potentials (MEP) around several molecules consisting of carbon, nitrogen, oxygen, fluorine, sulfur, and chlorine atoms were studied using the PM3 semiempirical method and the results compared with those obtained using ab initio calculations at the RHF/6‐31G** level. Thus it is shown that relative MEP values near different atoms can be obtained using hybridization displacement charges (HDC) obtained by employing PM3 density matrices that usually agree quite satisfactorily with the ab initio ones. Further, positions of ab initio MEP minima are correctly located and the corresponding relative MEP values usually correctly predicted using the PM3(HDC) charges distributed continuously in three dimensions according to the forms of squares of valence s atomic orbitals. The necessary parameters for HDC calculations using the PM3 method were optimized. It is shown how within the frameworks of both PM3 and AM1 methods the π electrons or lone pairs associated with amino group nitrogen atoms and ring atoms can be satisfactorily treated in different situations. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 299–312, 2001     

Integration of Graph Theory and Quantum Chemistry for Structure-Activity Relationships

Abstract

The objective of this article is to outline both graph-theoretically based and quantum chemically based structural indices of potential use in quantitative structure activity correlations. We consider graph-theoretical indices such as the connectivity index, topological index, Wiener index and molecular ID indices. Several structural and geometry-dependent indices can be derived from semiempirical and ab initio quantum calculations based on the charge densities, overlap matrices, frontier orbitals, molecular hardness, free valence, density matrices, quantum spectral difference indices, quantum spectral indices and bond matrices. Finally, the use of electrostatic potentials and charge densities for the prediction of reactive sites will be discussed.     

Atom and Bond Fukui Functions and Matrices: A Hirshfeld‐I Atoms‐in‐Molecule Approach

The Fukui function is often used in its atom‐condensed form by isolating it from the molecular Fukui function using a chosen weight function for the atom in the molecule. Recently, Fukui functions and matrices for both atoms and bonds separately were introduced for semiempirical and ab initio levels of theory using Hückel and Mulliken atoms‐in‐molecule models. In this work, a double partitioning method of the Fukui matrix is proposed within the Hirshfeld‐I atoms‐in‐molecule framework. Diagonalizing the resulting atomic and bond matrices gives eigenvalues and eigenvectors (Fukui orbitals) describing the reactivity of atoms and bonds. The Fukui function is the diagonal element of the Fukui matrix and may be resolved in atom and bond contributions. The extra information contained in the atom and bond resolution of the Fukui matrices and functions is highlighted. The effect of the choice of weight function arising from the Hirshfeld‐I approach to obtain atom‐ and bond‐condensed Fukui functions is studied. A comparison of the results with those generated by using the Mulliken atoms‐in‐molecule approach shows low correlation between the two partitioning schemes.     

On heteroaromaticity of nucleobases. Bond lengths as multidimensional phenomena

Three hundred and nine carbon-carbon, carbon-nitrogen, and carbon-oxygen pi-bond lengths in high precision crystal structures of 31 purine and pyrimidine nucleobases were related to the Pauling pi-bond order, its analogues corrected to crystal packing effects, the numbers of non-hydrogen atoms around the bond, and the sum of atomic numbers of the bond atoms. Principal Component Analysis (PCA) and Hierarchical Cluster Analysis (HCA) demonstrated that the bond lengths in the nucleobases are three-dimensional phenomenon, characterized by nine distinct classes of bonds. Bond lengths predicted by Linear Regression models, Pauling Harmonic Potential Curves, Multiple Linear Regression, Principal Component, and Partial Least Squares Regression were compared to those calculated by molecular mechanics, semiempirical, and ab initio methods using PCA-HCA procedure on the calculated bond lengths, statistical parameters, and structural aromaticity indices. Incorporation of crystal packing effects into bond orders makes multivariate models to be competitive to semiempirical results, while further improvement of quantum chemical calculations can be achieved by geometry optimization of molecular clusters.     

Two-electron valence indices from the Kohn-Sham orbitals

The recent Hartree-Fock (HF) difference approach to the chemical valence indices (ionic and covalent), formulated in the framework of the pair-density matrix, is implemented within the Kohn-Sham (KS) density functional theory (DFT). The valence numbers are quadratic in terms of displacements of the molecular spin-resolved charge-and-bond-order (CBO) matrix elements, relative to values in the separated atoms limit (SAL). It is shown that the global valence represents a generalized “distance” quantity measuring a degree of similarity between the two CBO matrices: the molecular and SAL. Numerical values for typical molecules exhibiting single and multiple bonds demonstrate that the KS orbitals give rise to these new bond valences in good agreement with both chemical and HF predictions. This KS bond multiplicity analysis is applied to the chemisorption system including the allyl radical and a model surface cluster of molybdenum oxide. It is concluded that the quadratic valence analysis represents a valuable procedure for extracting useful chemical information from standard DFT calculations. © 1997 John Wiley & Sons, Inc.     

Valence bond calculations of hydrogen transfer reactions: a general predictive pattern derived from theory

Hydrogen abstraction reactions of the type X(*) + H-H' --> X-H + H'(*) (X = F, Cl, Br, I) are studied by ab initio valence bond methods and the VB state correlation diagram (VBSCD) model. The reaction barriers and VB parameters of the VBSCD are computed by using the breathing orbital valence bond and valence bond configuration interaction methods. The combination of the VBSCD model and semiempirical VB theory leads to analytical expressions for the barriers and other VB quantities that match the ab initio VB calculations fairly well. The barriers are influenced by the endo- or exothermicity of the reaction, but the fundamental factor of the barrier is the average singlet-triplet gap of the bonds that are broken or formed in the reactions. Some further approximations lead to a simple formula that expresses the barrier for nonidentity and identity hydrogen abstraction reactions as a function of the bond strengths of reactants and products. The semiempirical expressions are shown to be useful not only for the model reactions that are studied in this work, but also for other nonidentity and identity hydrogen abstraction reactions that have been studied in previous articles.     

Theoretical study of C24N4 molecule

Both ab initio 6-31G, 3-21G and STO-3G basis sets and semiempirical PM3 and AM1 molecular orbital calculations are carried out on the C₂₄N₄ molecule of the T_d symmetry group. Results on the fully optimized structure which constrained T_d symmetry, molecular orbitals and vibrational frequency were obtained by both ab initio and semiempirical methods. The binding energy and various thermodynamic properties were also calculated via the PM3 and AM1 semiempirical methods. All the evidence of this work proves that the C₂₄N₄ molecule is stable and that its four six-membered rings with a remarkable delocalized C…C bond are similar to the related rings in the C₆₀ buckminsterfullerene structure.     

Modified valence indices from the two-particle density matrix

The modified ionic and covalent valence indices are introduced, defined in the framework of the two-particle density matrix, with respect to the reference state of separated atoms or ions (SAL ). They include only quadratic contributions in changes of the molecular charge-and-bond order matrix elements, relative to the SAL . General properties of the modified valence indices are examined and illustrative qualitative results for model systems are presented. Numerical UHF SCF MO valence data for selected diatomic and triatomic molecules are reported and interpreted in terms of the valence saturation effect and the ionic vs. covalent valence competition. A three-orbital valence model of a symmetric transition state of the bond-forming–bond-breaking reaction supports the BEBO model postulate of preservation of the total “bond order.” The model predictions are compared with the UHF numerical values. © 1994 John Wiley & Sons, Inc.     

An extensible and systematic force field,ESFF, for molecular modeling of organic,inorganic, and organometallic systems

ESFF is a rule-based force field designed for modeling organic, inorganic, and organometallic systems. To cover this broad range of molecular systems, ESFF was developed in an extensible and systematic manner. Several unique features were introduced including pseudoangle and a dot product function representing torsion energy terms. The partial atomic charges that are topology-dependent are determined from ab initio (DFT) calculated electronegativity and hardness for valence orbitals. The van der Waals parameters are charge-dependent, and correlated with the ionization potential for atoms in various valence states. To obtain a set of well-defined and physically meaningful parameters, ESFF employs semiempirical rules to translate atomic-based parameters to parameters typically associated with a covalent valence force field. The atomic parameters depend not only on atom type, but also on internal type, thus resulting in a more accurate force field. This article presents the theory and the method used to develop the force field. The force field has been applied to molecular simulations of a wide variety of systems including nucleic acids, peptides, hydrocarbons, porphyrins, transition metal complexes, zeolites, and organometallic compounds. Agreement with the experimental results indicates that ESFF is a valuable tool in molecular simulations for understanding and predicting both crystal and gas phase molecular structures.     

价键理论新进展

概要介绍了现代价键理论的几个主要方法,并讨论了它们各自的特点及其发展现状,并重点介绍了键表方法的基本理论、计算程序及一些应用。     

A new scaling procedure to correct semiempirical MEP and MEP-derived properties

Summary The MNDO, AM1, PM3, and ab initio 6–31G^* and 6–31+G^* MEPs for 21 neutral and 12 charged molecules were computed in layers ranging from 1.2 to 2.0 times the van der Waals radii of atoms. Semiempirical and ab initio MEPs for each layer and two groups of layers were compared to gain insight into the relationships between semiempirical and ab initio MEPs. A detailed statistical study allowed us to obtain a new set of scaling coefficients able to correct the semiempirical MEPs to provide better representations of the ab initio values. The corrected semiempirical MEPs were used to obtain electrostatic charges, whose quality was tested by the comparison between semiempirical Coulombic MEPs and ab initio quantum mechanical MEPs.     

VBEFP: a valence bond approach that incorporates effective fragment potential method

An ab initio explicit solvation valence bond (VB) method, called VBEFP, is presented. The VBEFP method is one type of QM/MM approach in which the QM part of system is treated within the ab initio valence bond scheme and the solvent water molecules are accounted by the effective fragment potential (EFP) method, which is a polarized force field approach developed by Gordon et al. (J. Chem. Phys. 1996, 105, 1968). This hybrid method enables one to take the first-solvation shell and heterogeneous solvation effects into account explicitly with VB wave function. Therefore, the nature of chemical bonding and the mechanism of chemical reactions with explicit solvent environments can be explored at the ab inito VB level. In this paper, the hydrated metal-ligand complexes [M(2+)L](H(2)O)(n) (M(2+): Mg(2+), Zn(2+); L: NH(3), CH(2)O) are studied by the VBEFP method. Resonance energy and bond order are computed, and the influence of the solvent coordination and hydrogen bonding to the metal-ligand bonding are explored in the paper.