Peifeng Su

Energy decomposition analysis of covalent bonds and intermolecular interactions

An energy decomposition analysis method is implemented for the analysis of both covalent bonds and intermolecular interactions on the basis of single-determinant Hartree-Fock (HF) (restricted closed shell HF, restricted open shell HF, and unrestricted open shell HF) wavefunctions and their density functional theory analogs. For HF methods, the total interaction energy from a supermolecule calculation is decomposed into electrostatic, exchange, repulsion, and polarization terms. Dispersion energy is obtained from second-order Møller-Plesset perturbation theory and coupled-cluster methods such as CCSD and CCSD(T). Similar to the HF methods, Kohn-Sham density functional interaction energy is decomposed into electrostatic, exchange, repulsion, polarization, and dispersion terms. Tests on various systems show that this algorithm is simple and robust. Insights are provided by the energy decomposition analysis into H(2), methane C-H, and ethane C-C covalent bond formation, CH(3)CH(3) internal rotation barrier, water, ammonia, ammonium, and hydrogen fluoride hydrogen bonding, van der Waals interaction, DNA base pair formation, BH(3)NH(3) and BH(3)CO coordinate bond formation, Cu-ligand interactions, as well as LiF, LiCl, NaF, and NaCl ionic interactions.

Classical Valence Bond Approach by Modern Methods

National Natural Science Foundation of China[20873106]; Ministry of Science and Technology[2011CB808504]; Israel Science Foundation[ISF 53/09]

Continuous and smooth potential energy surface for conductorlike screening solvation model using fixed points with variable areas

Rigorously continuous and smooth potential energy surfaces, as well as exact analytic gradients, are obtained for a conductorlike screening solvation model (CPCM, a variant of the general COSMO) with Hartree-Fock (RHF, ROHF, UHF, and MCSCF) and density functional theory (R-DFT, RO-DFT, and U-DFT) methods using a new tessellation scheme, fixed points with variable areas (FIXPVA). In FIXPVA, spheres centered at atoms are used to define the molecular cavity and surface. The surface of each sphere is divided into 60, 240, or 960 tesserae, which have positions fixed relative to the sphere center and areas scaled by switching functions of their distances to neighboring spheres. Analytic derivatives of the positions and areas of the surface tesserae with respect to atomic coordinates can be obtained and used to evaluate the solvation energy gradients. Due to the accurate analytic gradients and smooth potential energy surface, geometry optimization processes using these methods are stable and convergent.

Energy Decomposition Scheme Based on the Generalized Kohn–Sham Scheme

In this paper, a new energy decomposition analysis scheme based on the generalized Kohn-Sham (GKS) and the localized molecular orbital energy decomposition analysis (LMO-EDA) scheme, named GKS-EDA, is proposed. The GKS-EDA scheme has a wide range of DFT functional adaptability compared to LMO-EDA. In the GKS-EDA scheme, the exchange, repulsion, and polarization terms are determined by DFT orbitals; the correlation term is defined as the difference of the GKS correlation energy from monomers to supermolecule. Using the new definition, the GKS-EDA scheme avoids the error of LMO-EDA which comes from the separated treatment of EX and EC functionals. The scheme can perform analysis both in the gas and in the condensed phases with most of the popular DFT functionals, including LDA, GGA, meta-GGA, hybrid GGA/meta-GGA, double hybrid, range-separated (long-range correction), and dispersion correction. By the GKS-EDA scheme, the DFT functionals assessment for hydrogen bonding, vdW interaction, symmetric radical cation, charge-transfer, and metal-ligand interaction is performed.

VBSM: A Solvation Model Based on Valence Bond Theory

A new solvation model, called VBSM, is presented. The model combines valence bond (VB) theory with parameters determined for the SM6 solvation model (Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Chem. Theo. Comp. 2005, 1, 1133-1152). VBSM, like SM6, is based on the generalized Born (GB) approximation for bulk electrostatics and atomic surface tensions to account for cavitation, dispersion, and solvent structure (CDS). The solvation free energy of VBSM includes (i) a self-consistent polarization term obtained by using VB atomic charges in a GB reaction field with a VB self-consistent field procedure that minimizes the total energy of the system with respect to the valence bond orbitals and (ii) a geometry-dependent CDS term to account for deviations from bulk-electrostatic solvation. Test calculations for a few systems show that the liquid-phase partial atomic charges obtained by VBSM are in good agreement with liquid-phase charges obtained by charge model CM4 (Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Chem. Theo. Comp. 2005, 1, 1133-1152). Free energies of solvation are calculated for two prototype test cases, namely, for the degenerate S(N)2 reaction of Cl(-) with CH(3)Cl in water and for a Menshutkin reaction in water. These calculations show that the VBSM method provides a practical alternative to single-configuration self-consistent field theory for solvent effects in molecules and chemical reactions.

Free energy decomposition analysis of bonding and nonbonding interactions in solution

A free energy decomposition analysis algorithm for bonding and nonbonding interactions in various solvated environments, named energy decomposition analysis-polarizable continuum model (EDA-PCM), is implemented based on the localized molecular orbital-energy decomposition analysis (LMO-EDA) method, which is recently developed for interaction analysis in gas phase [P. F. Su and H. Li, J. Chem. Phys. 130, 074109 (2009)]. For single determinant wave functions, the EDA-PCM method divides the interaction energy into electrostatic, exchange, repulsion, polarization, desolvation, and dispersion terms. In the EDA-PCM scheme, the homogeneous solvated environment can be treated by the integral equation formulation of PCM (IEFPCM) or conductor-like polarizable continuum model (CPCM) method, while the heterogeneous solvated environment is handled by the Het-CPCM method. The EDA-PCM is able to obtain physically meaningful interaction analysis in different dielectric environments along the whole potential energy surfaces. Test calculations by MP2 and DFT functionals with homogeneous and heterogeneous solvation, involving hydrogen bonding, vdW interaction, metal-ligand binding, cation-π, and ionic interaction, show the robustness and adaptability of the EDA-PCM method. The computational results stress the importance of solvation effects to the intermolecular interactions in solvated environments.

DFVB: A Density-Functional-Based Valence Bond Method

A new ab initio valence bond method with density-functional-based correlation correction, so-called DFVB, is presented. In the DFVB method, the dynamic correlation energy is taken into account by use of density correlation functional(s), while the static correlation energy is covered by the VBSCF wave function. Owing to incorporation of DFT methods, DFVB provides an economic route to improving the accuracy of ab initio VB theory. Various tests of the method are presented, including the spectroscopic parameters of a series of diatomic molecules, the dipole moments of the NF molecule for different electronic states, and the singlet-triplet gaps of the diradical species, chemical reactions barriers, and total charge-shift resonance energies. These tests show that DFVB is capable of providing high accuracy with relatively low computational cost by comparison to the currently existing post-VBSCF methods.

Red-Shifting versus Blue-Shifting Hydrogen Bonds: Perspective from Ab Initio Valence Bond Theory.

Both proper, red-shifting and improper, blue-shifting hydrogen bonds have been well-recognized with enormous experimental and computational studies. The current consensus is that there is no difference in nature between these two kinds of hydrogen bonds, where the electrostatic interaction dominates. Since most if not all the computational studies are based on molecular orbital theory, it would be interesting to gain insight into the hydrogen bonds with modern valence bond (VB) theory. In this work, we performed ab initio VBSCF computations on a series of hydrogen-bonding systems, where the sole hydrogen bond donor CF3H interacts with ten hydrogen bond acceptors Y (═NH2CH3, NH3, NH2Cl, OH(-), H2O, CH3OH, (CH3)2O, F(-), HF, or CH3F). This series includes four red-shifting and six blue-shifting hydrogen bonds. Consistent with existing findings in literature, VB-based energy decomposition analyses show that electrostatic interaction plays the dominating role and polarization plays the secondary role in all these hydrogen-bonding systems, and the charge transfer interaction, which denotes the hyperconjugation effect, contributes only slightly to the total interaction energy. As VB theory describes any real chemical bond in terms of pure covalent and ionic structures, our fragment interaction analysis reveals that with the approaching of a hydrogen bond acceptor Y, the covalent state of the F3C-H bond tends to blue-shift, due to the strong repulsion between the hydrogen atom and Y. In contrast, the ionic state F3C(-) H(+) leads to the red-shifting of the C-H vibrational frequency, owing to the attraction between the proton and Y. Thus, the relative weights of the covalent and ionic structures essentially determine the direction of frequency change. Indeed, we find the correlation between the structural weights and vibrational frequency changes.

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.

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.