Lingchun Song

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.

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.

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.

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 m4, 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.

A practical valence bond method: a configuration interaction method approach with perturbation theoretic facility.

The previously developed valence bond configuration interaction (VBCI) method (Wu, W.; Song, L.; Cao, Z.; Zhang, Q.; Shaik, S., J. Phys. Chem. A, 2002, 105, 2721) that borrows the general CI philosophy of the MO theory, is further extended in this article, and its methodological features are improved, resulting in three accurate and cost‐effective procedures: (a) the effect of quadruplet excitation is incorporated using the Davidson correction, such that the new procedure reduces size consistency problems, with due improvement in the quality of the computational results. (b) A cost‐effective procedure, named VBCI(D, S), is introduced. It includes doubly excited structures for active electrons and singly excited structures for inactive pairs. The computational results of VBCI(D, S) match those of VBCISD with much less computational effort than VBCISD. (c) Finally, a second‐order perturbation theory is utilized as a means of configuration selection, and lead to considerable reduction of the computational cost, with little or no loss in accuracy. Applications of the new procedures to bond energies and barriers of chemical reactions are presented and discussed.

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.

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.

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.

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 Znβ, 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 Znβ. 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 Znα or the μ‐hydroxo bridge between the α‐ and β‐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.

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).