Block-Localized Wavefunction (BLW) Based Two-State Approach for Charge Transfers between Phenyl Rings.

The block-localized wave function (BLW) method is the simplest and most efficient variant of ab initio valence bond (VB) theory which defines electron-localized resonance states following the conventional VB concepts. Here, a BLW-based two-state approach is proposed to probe the charge/hole transfer reactions within the Marcus-Hush model. With this approach, both the electronic coupling and reorganization energies can be derived at the ab initio level. Pilot applications to the electron/hole transfers between two phenyl rings are presented. Good exponential correlation between the electronic coupling energy and the donor-acceptor distance is shown, whereas the inner-sphere reorganization shows little geometric dependency. Computations also support the assumption in Marcus theory that the thermal electron transfer barrier (ΔG*), which is a sum of the reaction barrier (ΔEa) for electron/hole transfer and the coupling energy (VAB), is a quarter of the reorganization energy (λ).

On the Interfragment Exchange in the X-Pol Method.

The inclusion of exchange repulsion terms in the explicit polarization (X-Pol) model is examined by antisymmetrizing the X-Pol Hartree-product wave function; this yields XPol with full eXchange, called X-Pol-X. When the monomers are treated by Hartree-Fock theory, this calculation can be accomplished by using the formalism of block-localized wave functions (BLW) that has been used in a variety of applications. In this case the block-localized structure in the X-Pol-X wave function allows for decomposition of the full Fock matrix of a dimension of M blocks into M smaller Fock matrices. The method is illustrated by considering two trimer structures of water clusters, and it is found that the total exchange repulsion energies in these hydrogen-bonding test cases are adequately treated and-to a good approximation- are pairwise additive. We also present a formalism to yield a simplified Fock matrix by making use of the neglect of interfragment differential overlap (NIDO) approximation, which is less severe than the neglect of diatomic differential overlap (NDDO) approximation.

A Non-Orthogonal Block-Localized Effective Hamiltonian Approach for Chemical and Enzymatic Reactions.

The effective Hamiltonian-molecular orbital and valence bond (EH-MOVB) method based on non-orthogonal block-localized fragment orbitals has been implemented into the program CHARMM for molecular dynamics simulations of chemical and enzymatic reactions, making use of semiempirical quantum mechanical models. Building upon ab initio MOVB theory, we make use of two parameters in the EH-MOVB method to fit the barrier height and the relative energy between the reactant and product state for a given chemical reaction to be in agreement with experiment or high-level ab initio or density functional results. Consequently, the EH-MOVB method provides a highly accurate and computationally efficient QM/MM model for dynamics simulation of chemical reactions in solution. The EH-MOVB method is illustrated by examination of the potential energy surface of the hydride transfer reaction from trimethylamine to a flavin cofactor model in the gas phase. In the present study, we employed the semiempirical AM1 model, which yields a reaction barrier that is more than 5 kcal/mol too high. We use a parameter calibration procedure for the EH-MOVB method similar to that employed to adjust the results of semiempirical and empirical models. Thus, the relative energy of these two diabatic states can be shifted to reproduce the experimental energy of reaction, and the barrier height is optimized to reproduce the desired (accurate) value by adding a constant to the off-diagonal matrix element. The present EH-MOVB method offers a viable approach to characterizing solvent and protein-reorganization effects in the realm of combined QM/MM simulations.

Explicit polarization (X-Pol) potential using ab initio molecular orbital theory and density functional theory.

The explicit polarization (X-Pol) method has been examined using ab initio molecular orbital theory and density functional theory. The X-Pol potential was designed to provide a novel theoretical framework for developing next-generation force fields for biomolecular simulations. Importantly, the X-Pol potential is a general method, which can be employed with any level of electronic structure theory. The present study illustrates the implementation of the X-Pol method using ab initio Hartree-Fock theory and hybrid density functional theory. The computational results are illustrated by considering a set of bimolecular complexes of small organic molecules and ions with water. The computed interaction energies and hydrogen bond geometries are in good accord with CCSD(T) calculations and B3LYP/aug-cc-pVDZ optimizations.

Molecular dynamics simulations of the detoxification of paraoxon catalyzed by phosphotriesterase.

Combined QM(PM3)/MM molecular dynamics simulations together with QM(DFT)/MM optimizations for key configurations have been performed to elucidate the enzymatic catalysis mechanism on the detoxification of paraoxon by phosphotriesterase (PTE). In the simulations, the PM3 parameters for the phosphorous atom were reoptimized. The equilibrated configuration of the enzyme/substrate complex showed that paraoxon can strongly bind to the more solvent-exposed metal ion Zn(beta), but the free energy profile along the binding path demonstrated that the binding is thermodynamically unfavorable. This explains why the crystal structures of PTE with substrate analogues often exhibit long distances between the phosphoral oxygen and Zn(beta). The subsequent SN2 reaction plays the key role in the whole process, but controversies exist over the identity of the nucleophilic species, which could be either a hydroxide ion terminally coordinated to Zn(alpha) or the micro-hydroxo bridge between the alpha- and beta-metals. Our simulations supported the latter and showed that the rate-limiting step is the distortion of the bound paraoxon to approach the bridging hydroxide. After this preparation step, the bridging hydroxide ion attacks the phosphorous center and replaces the diethyl phosphate with a low barrier. Thus, a plausible way to engineer PTE with enhanced catalytic activity is to stabilize the deformed paraoxon. Conformational analyses indicate that Trp131 is the closest residue to the phosphoryl oxygen, and mutations to Arg or Gln or even Lys, which can shorten the hydrogen bond distance with the phosphoryl oxygen, could potentially lead to a mutant with enhanced activity for the detoxification of organophosphates.

An Effective Hamiltonian Molecular Orbital-Valence Bond (MOVB) Approach for Chemical Reactions Applied to the Nucleophilic Substitution Reaction of Hydrosulfide Ion and Chloromethane.

An effective Hamiltonian mixed molecular orbital and valence bond (EH-MOVB) method is described to obtain an accurate potential energy surface for chemical reactions. Building upon previous results on the construction of diabatic and adiabatic potential surfaces using ab initio MOVB theory, we introduce a diabatic-coupling scaling factor to uniformly scale the ab initio off-diagonal matrix element H(12) such that the computed energy of reaction from the EH-MOVB method is in agreement with the target value. The scaling factor is very close to unity, resulting in minimal alteration of the potential energy surface of the original MOVB model. Furthermore, the relative energy between the reactant and product diabatic states in the EH-MOVB method can be improved to match the experimental energy of reaction. A key ingredient in the EH-MOVB theory is that the off-diagonal matrix elements are functions of all degrees of freedom of the system and the overlap matrix is explicitly evaluated. The EH-MOVB method has been applied to the nucleophilic substitution reaction between hydrosulfide and chloromethane to illustrate the methodology and the results were matched to reproduce the results from ab initio valence bond self-consistent valence bond (VBSCF) calculations. The diabatic coupling (the off-diagonal matrix element in the generalized secular equation) has small variations along the minimum energy reaction path in the EH-MOVB model, whereas it shows a maximum value at the transition state and has nearly zero values in the regions of the ion-dipole complexes from VBSCF calculations. The difference in the diabatic coupling stabilization is attributed to the large overlap integral in the computationally efficient MOVB method.

Perspective on Diabatic Models of Chemical Reactivity as Illustrated by the Gas-Phase S(N)2 Reaction of Acetate Ion with 1,2-Dichloroethane.

Diabatic models are widely employed for studying chemical reactivity in condensed phases and enzymes, but there has been little discussion of the pros and cons of various diabatic representations for this purpose. Here we discuss and contrast six different schemes for computing diabatic potentials for a charge rearrangement reaction. They include (i) the variational diabatic configurations (VDC) constructed by variationally optimizing individual valence bond structures and (ii) the consistent diabatic configurations (CDC) obtained by variationally optimizing the ground-state adiabatic energy, both in the nonorthogonal molecular orbital valence bond (MOVB) method, along with the orthogonalized (iii) VDC-MOVB and (iv) CDC-MOVB models. In addition, we consider (v) the fourfold way (based on diabatic molecular orbitals and configuration uniformity), and (vi) empirical valence bond (EVB) theory. To make the considerations concrete, we calculate diabatic electronic states and diabatic potential energies along the reaction path that connects the reactant and the product ion-molecule complexes of the gas-phase bimolecular nucleophilic substitution (S(N)2) reaction of 1,2-dichloethane (DCE) with acetate ion, which is a model reaction corresponding to the reaction catalyzed by haloalkane dehalogenase. We utilize ab initio block-localized molecular orbital theory to construct the MOVB diabatic states and ab initio multi-configuration quasidegenerate perturbation theory to construct the fourfold-way diabatic states; the latter are calculated at reaction path geometries obtained with the M06-2X density functional. The EVB diabatic states are computed with parameters taken from the literature. The MOVB and fourfold-way adiabatic and diabatic potential energy profiles along the reaction path are in qualitative but not quantitative agreement with each other. In order to validate that these wave-function-based diabatic states are qualitatively correct, we show that the reaction energy and barrier for the adiabatic ground state, obtained with these methods, agree reasonably well with the results of high-level calculations using the composite G3SX and G3SX(MP3) methods and the BMC-CCSD multi-coefficient correlation method. However, a comparison of the EVB gas-phase adiabatic ground-state reaction path with those obtained from MOVB and with the fourfold way reveals that the EVB reaction path geometries show a systematic shift towards the products region, and that the EVB lowest-energy path has a much lower barrier. The free energies of solvation and activation energy in water reported from dynamical calculations based on EVB also imply a low activation barrier in the gas phase. In addition, calculations of the free energy of solvation using the recently proposed SM8 continuum solvation model with CM4M partial atomic charges lead to an activation barrier in reasonable agreement with experiment only when the geometries and the gas-phase barrier are those obtained from electronic structure calculations, i.e., methods i-v. These comparisons show the danger of basing the diabatic states on molecular mechanics without the explicit calculation of electronic wave functions. Furthermore, comparison of schemes i-v with one another shows that significantly different quantitative results can be obtained by using different methods for extracting diabatic states from wave function calculations, and it is important for each user to justify the choice of diabatization method in the context of its intended use.

Block-Localized Density Functional Theory (BLDFT), Diabatic Coupling, and Their Use in Valence Bond Theory for Representing Reactive Potential Energy Surfaces.

A multistate density functional theory in the framework of the valence bond model is described. The method is based on a block-localized density functional theory (BLDFT) for the construction of valence-bond-like diabatic electronic states and is suitable for the study of electron transfer reactions and for the representation of reactive potential energy surfaces. The method is equivalent to a valence bond theory with the treatment of the localized configurations by using density functional theory (VBDFT). In VBDFT, the electron densities and energies of the valence bond states are determined by BLDFT. A functional estimate of the off-diagonal matrix elements of the VB Hamiltonian is proposed, making use of the overlap integral between Kohn-Sham determinants and the exchange-correlation functional for the ground state substituted with the transition (exchange) density. In addition, we describe an approximate approach, in which the off-diagonal matrix element is computed by wave function theory using block-localized Kohn-Sham orbitals. The key feature is that the electron density of the adiabatic ground state is not directly computed nor used to obtain the ground-state energy; the energy is determined by diagonalization of the multistate valence bond Hamiltonian. This represents a departure from the standard single-determinant Kohn-Sham density functional theory. The multistate VBDFT method is illustrated by the bond dissociation of H2+ and a set of three nucleophilic substitution reactions in the DBH24 database. In the dissociation of H2+, the VBDFT method yields the correct asymptotic behavior as the two protons stretch to infinity, whereas approximate functionals fail badly. For the S(N)2 nucleophilic substitution reactions, the hybrid functional B3LYP severely underestimates the barrier heights, while the approximate two-state VBDFT method overcomes the self-interaction error, and overestimates the barrier heights. Inclusion of the ionic state in a three-state model, VBDFT(3), significantly improves the computed barrier heights, which are found to be in accord with accurate results. The BLDFT method is a versatile theory that can be used to analyze conventional DFT results to gain insight into chemical bonding properties, and it is illustrated by examining the intricate energy contributions to the ion-dipole complex stabilization.

An efficient algorithm for energy gradients and orbital optimization in valence bond theory.

An efficient algorithm for energy gradients in valence bond theory with nonorthogonal orbitals is presented. A general Hartree-Fock-like expression for the Hamiltonian matrix element between valence bond (VB) determinants is derived by introducing a transition density matrix. Analytical expressions for the energy gradients with respect to the orbital coefficients are obtained explicitly, whose scaling for computational cost is m(4), where m is the number of basis functions, and is thus approximately the same as in HF method. Compared with other existing approaches, the present algorithm has lower scaling, and thus is much more efficient. Furthermore, the expression for the energy gradient with respect to the nuclear coordinates is also presented, and it provides an effective algorithm for the geometry optimization and the evaluation of various molecular properties in VB theory. Test applications show that our new algorithm runs faster than other methods.

On the construction of diabatic and adiabatic potential energy surfaces based on ab initio valence bond theory.

A theoretical model is presented for deriving effective diabatic states based on ab initio valence bond self-consistent field (VBSCF) theory by reducing the multiconfigurational VB Hamiltonian into an effective two-state model. We describe two computational approaches for the optimization of the effective diabatic configurations, resulting in two ways of interpreting such effective diabatic states. In the variational diabatic configuration (VDC) method, the energies of the diabatic states are variationally minimized. In the consistent diabatic configuration (CDC) method, both the configuration coefficients and orbital coefficients are simultaneously optimized to minimize the adiabatic ground-state energy in VBSCF calculations. In addition, we describe a mixed molecular orbital and valence bond (MOVB) approach to construct the CDC diabatic and adiabatic states for a chemical reaction. Note that the VDC-MOVB method has been described previously. Employing the symmetric S(N)2 reaction between NH(3) and CH(3)NH(3)(+) as a test system, we found that the results from ab initio VBSCF and from ab initio MOVB calculations using the same basis set are in good agreement, suggesting that the computationally efficient MOVB method is a reasonable model for VB simulations of condensed phase reactions. The results indicate that CDC and VDC diabatic states converge, respectively, to covalent and ionic states as the molecular geometries are distorted from the minimum of the respective diabatic state along the reaction coordinate. Furthermore, the resonance energy that stabilizes the energy of crossing between the two diabatic states, resulting in the transition state of the adiabatic ground-state reaction, has a strong dependence on the overlap integral between the two diabatic states and is a function of both the exchange integral and the total diabatic ground-state energy.

Incorporation of a QM/MM buffer zone in the variational double self-consistent field method.

The explicit polarization (X-Pol) potential is an electronic-structure-based polarization force field, designed for molecular dynamics simulations and modeling of biopolymers. In this approach, molecular polarization and charge transfer effects are explicitly treated by a combined quantum mechanical and molecular mechanical (QM/MM) scheme, and the wave function of the entire system is variationally optimized by a double self-consistent field (DSCF) method. In the present article, we introduce a QM buffer zone for a smooth transition from a QM region to an MM region. Instead of using the Mulliken charge approximation for all QM/MM interactions, the Coulombic interactions between the adjacent fragments are determined directly by electronic structure theory. The present method is designed to accelerate the speed of convergence of the total energy and charge density of the system.

The variational explicit polarization potential and analytical first derivative of energy: Towards a next generation force field.

A previous article proposed an electronic structure-based polarizable potential, called the explicit polarization (X-POL) potential, to treat many-body polarization and charge delocalization effects in polypeptides. Here, we present a variational version of the X-POL potential, in which the wave function of the entire molecular system is variationally optimized to yield the minimum total electronic energy. This allows the calculation of analytic gradients, a necessity for efficient molecular dynamics simulations. In this paper, the detailed derivations of the Fock matrix and analytic force are presented and discussed. The calculations involve a double self-consistent-field procedure in which the wave function of each fragment is self-consistently optimized in the presence of other fragments, and in addition the polarization of the entire system is self-consistently optimized. The variational X-POL potential has been implemented in the Chemistry at Harvard Molecular Mechanics (CHARMM) package and tested successfully for small model compounds.

Heterolytic bond dissociation in water: why is it so easy for C4H9Cl but not for C3H9SiCl?

The recently developed (Song, L.; Wu, W.; Zhang, Q.; Shaik, S. J. Phys. Chem. A 2004, 108, 6017-6024) valence bond method coupled to a polarized continuum model (VBPCM) is used to address the long standing conundrum of the heterolytic dissociation of the C-Cl and Si-Cl bonds, respectively, in tertiary-butyl chloride and trimethylsilyl chloride in condensed phases. The method is used here to compare the bond dissociation in the gas phase and in aqueous solution. In addition to the ground state reaction profile, VB theory also provides the energies of the purely covalent and purely ionic VB structures as a function of the reaction coordinate. Accordingly, the C-Cl and Si-Cl bonds are shown to be of different natures. In the gas phase, the resonance energy arising from covalent-ionic mixing at equilibrium geometry amounts to 42 kcal/mol for tertiary-butyl chloride, whereas the same quantity for trimethylsilyl chloride is significantly higher at 62 kcal/mol. With such a high value, the root cause of the Si-Cl bonding is the covalent-ionic resonance energy, and this bond belongs to the category of charge-shift bonds (Shaik, S.; Danovich, D.; Silvi, B.; Lauvergnat, D.; Hiberty, P. C. Chem.- Eur. J. 2005, 11, 6358). This difference between the C-Cl and Si-Cl bonds carries over to the solvated phase and impacts the heterolytic cleavages of the two bonds. For both molecules, solvation lowers the ionic curve below the covalent one, and hence the bond dissociation in the solvent generates the two ions, Me3E+ Cl- (E = C, Si). In both cases, the root cause of the barrier is the loss of the covalent-ionic resonance energy. In the heterolysis reaction of Si-Cl, the covalent-ionic resonance energy remains large and fully contributes to the dissociation energy, thereby leading to a high barrier for heterolytic cleavage, and thus prohibiting the generation of ions. By contrast, the covalent-ionic resonance energy is smaller for the C-Cl bond and only partially contributes to the barrier for heterolysis, which is consequently small, leading readily to ions that are commonly observed in the classical SN1 mechanism. Thus, the reluctance of R3Si-X molecules to undergo heterolysis in condensed phases and more generally the rarity of free silicenium ions under these conditions are experimental manifestations of the charge-shift character of the Si-Cl bond.

Block-localized wavefunction (BLW) method at the density functional theory (DFT) level.

The block-localized wavefunction (BLW) approach is an ab initio valence bond (VB) method incorporating the efficiency of molecular orbital (MO) theory. It can generate the wavefunction for a resonance structure or diabatic state self-consistently by partitioning the overall electrons and primitive orbitals into several subgroups and expanding each block-localized molecular orbital in only one subspace. Although block-localized molecular orbitals in the same subspace are constrained to be orthogonal (a feature of MO theory), orbitals between different subspaces are generally nonorthogonal (a feature of VB theory). The BLW method is particularly useful in the quantification of the electron delocalization (resonance) effect within a molecule and the charge-transfer effect between molecules. In this paper, we extend the BLW method to the density functional theory (DFT) level and implement the BLW-DFT method to the quantum mechanical software GAMESS. Test applications to the pi conjugation in the planar allyl radical and ions with the basis sets of 6-31G(d), 6-31+G(d), 6-311+G(d,p), and cc-pVTZ show that the basis set dependency is insignificant. In addition, the BLW-DFT method can also be used to elucidate the nature of intermolecular interactions. Examples of pi-cation interactions and solute-solvent interactions will be presented and discussed. By expressing each diabatic state with one BLW, the BLW method can be further used to study chemical reactions and electron-transfer processes whose potential energy surfaces are typically described by two or more diabatic states.

The physical origin of large covalent-ionic resonance energies in some two-electron bonds.

This study uses valence bond (VB) theory to analyze in detail the previously established finding that alongside the two classical bond families of covalent and ionic bonds, which describe the electron-pair bond, there exists a distinct class of charge-shift bonds (CS-bonds) in which the fluctuation of the electron pair density plays a dominant role. Such bonds are characterized by weak binding, or even a repulsive, covalent component, and by a large covalent-ionic resonance energy RE(cs) that is responsible for the major part, or even for the totality, of the bonding energy. In the present work, the nature of CS-bonding and its fundamental mechanisms are analyzed in detail by means of a VB study of some typical homonuclear bonds (H-H, H3C-CH3, H2N-NH2, HO-OH, F-F, and Cl-Cl), ranging from classical-covalent to fully charge-shift bonds. It is shown that CS-bonding is characterized by a covalent dissociation curve with a shallow minimum situated at long interatomic distances, or even a fully repulsive covalent curve. As the atoms that are involved in the bond are taken from left to right or from bottom to top of the periodic table, the weakening effect of the adjacent bonds or lone pairs increases, while at the same time the reduced resonance integral, that couples the covalent and ionic forms, increases. As a consequence, the weakening of the covalent interaction is gradually compensated by a strengthening of CS-bonding. The large RE(cs) quantity of CS-bonds is shown to be an outcome of the mechanism necessary to establish equilibrium and optimum bonding during bond formation. It is shown that the shrinkage of the orbitals in the covalent structure lowers the potential energy, V, but excessively raises the kinetic energy, T, thereby tipping the virial ratio off-balance. Subsequent addition of the ionic structures lowers T while having a lesser effect on V, thus restoring the requisite virial ratio (T/-V = 1/2). Generalizing to typically classical covalent bonds, like H-H or C-C bonds, the mechanism by which the virial ratio is obeyed during bond formation is primarily orbital shrinkage, and therefore the charge-shift resonance energy has only a small corrective effect. On the other hand, for bonds bearing adjacent lone pairs and/or involving electronegative atoms, like F-F or Cl-Cl, the formation of the bond corresponds to a large increase of kinetic energy, which must be compensated for by a large participation or covalent-ionic mixing.

A valence bond study of the dioxygen molecule.

The dioxygen molecule has been the subject of valence bond (VB) studies since 1930s, as it was considered as the first "failure" of VB theory. The object of this article is to provide an unambiguous VB interpretation for the nature of chemical bonding of the molecule by means of modern VB computational methods, VBSCF, BOVB, and VBCI. It is shown that though the VBSCF method can not provide quantitative accuracy for the strongly electronegative and electron-delocalized molecule because of the lack of dynamic correlation, it still gives a correct qualitative analysis for wave function of the molecule and provides intuitive insights into chemical bonding. An accurate quantitative description for the molecule requires higher levels of VB methods that incorporate dynamic correlation. The potential energy curves of the molecule are computed at the various VB levels. It is shown that there exists a small hump in the PECs of VBSCF for the ground state, as found in previous studies. However, higher levels of VB methods dissolve the hump. The BOVB and VBCI methods reproduce the dissociation energies and other physical properties of the ground state and the two lowest excited states in very good agreement with experiment and with sophisticated MO based methods, such as the MRCI method.

Identity SN2 reactions X- + CH3X --> XCH3 + X- (X=F, Cl, Br, and I) in vacuum and in aqueous solution: a valence bond study.

The recently developed (L. Song, W. Wu, Q. Zhang, S. Shaik, J. Phys. Chem. A 2004, 108, 6017) valence bond method coupled with a polarized continuum model (VBPCM) has been applied to the identity SN2 reaction of halides in the gas phase and in aqueous solution. The barriers computed at the level of the breathing orbital VB method (P. C. Hiberty, J. P. Flament, E. Noizet, Chem. Phys. Lett. 1992, 189, 259), BOVB and VBPCM//BOVB, are comparable to CCSD(T) and CCSD(T)//PCM results and to experimentally derived barriers in solution (W. J. Albery, M. M. Kreevoy, Adv. Phys. Org. Chem. 1978, 16, 85). The reactivity parameters needed to apply the valence bond state correlation diagram (VBSCD) method (S. Shaik, J. Am. Chem. Soc. 1984, 106, 1227), were also determined by VB calculations. It has been shown that the reactivity parameters along with their semiempirical derivations provide a satisfactory qualitative and quantitative account of the barriers.

Barriers of hydrogen abstraction vs halogen exchange: an experimental manifestation of charge-shift bonding.

This paper shows that the differences between the barriers of the halogen exchange reactions, in the H + XH systems, and the hydrogen abstraction reactions, in the X + HX systems (X = F, Cl, Br), measure the covalent-ionic resonance energies of the corresponding X-H bonds. These processes are investigated using CCSD(T) calculations as well as the breathing-orbital valence bond (BOVB) method. Thus, the VB analysis shows that (i) at the level of covalent structures the barriers are the same for the two series and (ii) the higher barriers for halogen exchange processes originate solely from the less efficient mixing of the ionic structures into the respective covalent structures. The barrier differences, in the HXH vs XHX series, which decrease as X is varied from F to I, can be estimated as one-quarter of the covalent-ionic resonance energy of the H-X bond. The largest difference (22 kcal/mol) is calculated for X = F in accord with the finding that the H-F bond possesses the largest covalent-ionic resonance energy, 87 kcal/mol, which constitutes the major part of the bonding energy. The H-F bond belongs to the class of "charge-shift" bonds (Shaik, S.; Danovich, D.; Silvi, B.; Lauvergnat, D. L.; Hiberty, P. C. Chem. Eur. J. 2005, 21, 6358), which are all typified by dominant covalent-ionic resonance energies. Since the barrier difference between the two series is an experimental measure of the resonance energy quantity, in the particular case of X = F, the unusually high barrier for the fluorine exchange reaction emerges as an experimental manifestation of charge-shift bonding.

XMVB: a program for ab initio nonorthogonal valence bond computations.

An ab initio nonorthogonal valence bond program, called XMVB, is described in this article. The XMVB package uses Heitler-London-Slater-Pauling (HLSP) functions as state functions, and calculations can be performed with either all independent state functions for a molecule or preferably a few selected important state functions. Both our proposed paired-permanent-determinant approach and conventional Slater determinant expansion algorithm are implemented for the evaluation of the Hamiltonian and overlap matrix elements among VB functions. XMVB contains the capabilities of valence bond self-consistent field (VBSCF), breathing orbital valence bond (BOVB), and valence bond configuration interaction (VBCI) computations. The VB orbitals, used to construct VB functions, can be defined flexibly in the calculations depending on particular applications and focused problems, and they may be strictly localized, delocalized, or bonded-distorted (semidelocalized). The parallel version of XMVB based on MPI (Message Passing Interface) is also available.