An energy decomposition analysis for intramolecular non-covalent interaction in solvated environment

In this work, the intra-EDA method, which is a recently developed energy decomposition analysis scheme for intramolecular non-covalent interaction is extended from gas phase to solvated environment. It is the first analysis scheme that performs analysis for intramolecular interaction in solution. By fragmentation scheme, a molecule is divided into intramolecular interacting fragments and environmental fragments via single bond homolysis breaking. The solvent effect is taken into account by implicit solvation model. Intramolecular interaction free energy is estimated as the separated treatment of inter-fragment interactions in dielectric environment. The analysis results highlight the importance of solvent effects to intramolecular non-covalent interaction.     

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.     

分子间相互作用的研究——-价轨道模型势从头算能量分解法

研究分子间相互作用是了解液体,固体性质和结构以及气体性质的关键,也是研究化学和生物化学催化机制及化学反应途径的重要方面.因此,近几年来这个领域的理论和实验研究引起了人们广泛的兴趣并取得了长足的进步.特别值得指出的是Morokuma等提出的基于单行列式从头算的能量分解法,较好地解决了很多体系中分子间相互作用的本质问题,受到了理论化学界的普遍重视.但是这种方法很费计算机时间,对于较大的体系,特别是含有重原子的体系,应用受到了限制.因此简化这种方法,使它能够比较容     

Pair interaction energy decomposition analysis

The energy decomposition analysis (EDA) by Kitaura and Morokuma was redeveloped in the framework of the fragment molecular orbital method (FMO). The proposed pair interaction energy decomposition analysis (PIEDA) can treat large molecular clusters and the systems in which fragments are connected by covalent bonds, such as proteins. The interaction energy in PIEDA is divided into the same contributions as in EDA: the electrostatic, exchange-repulsion, and charge transfer energies, to which the correlation (dispersion) term was added. The careful comparison to the ab initio EDA interaction energies for water clusters with 2-16 molecules revealed that PIEDA has the error of at most 1.2 kcal/mol (or about 1%). The analysis was applied to (H2O)1024, the alpha helix, beta turn, and beta strand of polyalanine (ALA)10, as well as to the synthetic protein (PDB code 1L2Y) with 20 residues. The comparative aspects of the polypeptide isomer stability are discussed in detail.     

Energy decomposition analysis for intramolecular non-covalent interaction in solvated environment

In this work, the intra-EDA method, which is a recently developed energy decomposition analysis scheme for intramolecular non-covalent interaction is extended from gas phase to solvated environment. It is the first analysis scheme that performs analysis for intramolecular interaction in solution. By fragmentation scheme, a molecule is divided into intramolecular interacting fragments and environmental fragments via single bond homolysis breaking. The solvent effect is taken into account by implicit solvation model. Intramolecular interaction free energy is estimated as the separated treatment of inter-fragment interactions in dielectric environment. The analysis results highlight the importance of solvent effects to intramolecular non-covalent interaction.     

Energy decomposition analysis based on a block-localized wavefunction and multistate density functional theory

An interaction energy decomposition analysis method based on the block-localized wavefunction (BLW-ED) approach is described. The first main feature of the BLW-ED method is that it combines concepts of valence bond and molecular orbital theories such that the intermediate and physically intuitive electron-localized states are variationally optimized by self-consistent field calculations. Furthermore, the block-localization scheme can be used both in wave function theory and in density functional theory, providing a useful tool to gain insights on intermolecular interactions that would otherwise be difficult to obtain using the delocalized Kohn-Sham DFT. These features allow broad applications of the BLW method to energy decomposition (BLW-ED) analysis for intermolecular interactions. In this perspective, we outline theoretical aspects of the BLW-ED method, and illustrate its applications in hydrogen-bonding and π-cation intermolecular interactions as well as metal-carbonyl complexes. Future prospects on the development of a multistate density functional theory (MSDFT) are presented, making use of block-localized electronic states as the basis configurations.     

Bond energy analysis revisited and designed toward a rigorous methodology

The present study theoretically revisits and numerically assesses two-body energy decomposition schemes including a newly proposed one. The new decomposition scheme is designed to make the equilibrium bond distance equivalent with the minimum point of bond energies. Although the other decomposition schemes generally predict the wrong order of the C-C bond strengths of C(2)H(2), C(2)H(4), and C(2)H(6), the new decomposition scheme is capable of reproducing the C-C bond strengths. Numerical assessment on a training set of molecules demonstrates that the present scheme exhibits a stronger correlation with bond dissociation energies than the other decomposition schemes do, which suggests that the new decomposition scheme is a reliable and powerful analysis methodology.     

On the use of a MO polarized basis for the analysis of the interaction energy in molecular interactions: Application to amine complexes

A variant of the interaction energy decomposition scheme proposed by Morokuma which gives more emphasis to polarized MOS is presented and tested on complexes of amines with Li⁺, BH₃, and SO₂. A more systematic utilization of polarized MOS (i.e., of orbitals of the interacting molecules computed with the SCF formalism in the Coulombic field of the other molecular components of the system) is adopted, and the connection of this decomposition of the supermolecule interaction energy with perturbation approaches utilizing such polarized MOS is discussed.     

Improved SCF interaction energy decomposition scheme corrected for basis set superposition effect

A modified scheme for SCF interaction energy decomposition has been proposed where the nonphysical basis set superposition error (BSSE ) has been corrected by means of the counterpoise method. A new procedure to separate the exchange and induction energy terms free of nonphysical BSSE has been tested in the case of the H₂O dimer. The first order BSSE appears to be non-negligible for strong hydrogen bonded complexes. In addition the scheme allows separation of the long-controversial charge-transfer contribution within the induction term, which has been considerably overestimated in previous studies.     

Fragment interaction analysis based on local MP2

We have developed a fragment interaction analysis based on local MP2 (FILM) in the context of the fragment molecular orbital (FMO) scheme. The primary purpose of this work is to provide a tool for analyzing inter-fragment interaction associated with dispersion interactions in a large molecule such as protein and DNA. Our implementation of local MP2 (LMP2) is based on the algorithm developed by Pulay and Werner. A potential of FILM was demonstrated using the human immunodeficiency virus type 1 protease (HIV-1 PR) complexed with lopinavir (LPV). The total energy, binding affinity, and inter-fragment interaction energy (IFIE) by the FMO method using LMP2 were compared with those obtained by canonical MP2 and the site-specific information in dispersion interaction was obtained. It turned out that the FILM is a useful tool for analyzing the dispersion interaction between an amino acid residue and a specific site of a ligand.     

Analysis on solvated molecules with a new energy partitioning scheme for intra- and intermolecular interactions

A new partitioning scheme for the total energy of molecules is presented. In the scheme, the Hartree-Fock total energy of a molecular system is represented as the sum of one- and two-center terms exactly. The present method provides physically reasonable behavior for a wide range of interactions, and intermolecular interaction is treated equivalently with intramolecular interaction. The method is applied to analysis on the inter- and intramolecular interactions of molecular complexes both in gas phase and in aqueous solution. The results strongly indicate that the present method is a powerful tool to understand not only the bonding nature of molecules but also interaction between molecules.     

Kinetic energy decomposition scheme based on information theory

We proposed a novel kinetic energy decomposition analysis based on information theory. Since the Hirshfeld partitioning for electron densities can be formulated in terms of Kullback–Leibler information deficiency in information theory, a similar partitioning for kinetic energy densities was newly proposed. The numerical assessments confirm that the current kinetic energy decomposition scheme provides reasonable chemical pictures for ionic and covalent molecules, and can also estimate atomic energies using a correction with viral ratios.     

Dispersion-corrected energy decomposition analysis for intermolecular interactions based on the BLW and dDXDM methods

As the simplest variant of the valence bond (VB) theory, the block-localized wave function (BLW) method defines the intermediate electron-localized state self-consistently at the DFT level and can be used to explore the nature of intermolecular interactions in terms of several physically intuitive energy components. Yet, it is unclear how the dispersion interaction affects such a kind of energy decomposition analysis (EDA) as standard density functional approximations neglect the long-range dispersion attractive interactions. Three electron densities corresponding to the initial electron-localized state, optimal electron-localized state, and final electron-delocalized state are involved in the BLW-ED approach; a density-dependent dispersion correction, such as the recently proposed dDXDM approach, can thus uniquely probe the impact of the long-range dispersion effect on EDA results computed at the DFT level. In this paper, we incorporate the dDXDM dispersion corrections into the BLW-ED approach and investigate a range of representative systems such as hydrogen-bonding systems, acid-base pairs, and van der Waals complexes. Results show that both the polarization and charge-transfer energies are little affected by the inclusion of the long-range dispersion effect, which thus can be regarded as an independent energy component in EDA.     

A new energy decomposition scheme for molecular interactions within the Hartree-Fock approximation

A new method is proposed for the analysis of components of molecular interaction energy within the Hartree-Fock approximation. The Hartree-Fock molecular orbitals of the isolated molecules are used as the basis for the construction of Fock matrix of the supermolecule. Then certain blocks of this matrix are set to zero subject to specify boundary conditions of the supermolecule molecular orbitals, and the resultant matrix is diagonalized iteratively to obtain the desired energy components. This method can be considered as an extension of our previous method, but has an advantage in the explicit definition of the charge transfer energy, placing it on an equal footing with the exchange and polarization terms. The new method is compared with existing perturbation methods, and is also applied to the energy and electron density decomposition of (H₂O)₂.     

Local and nonlocal contributions to molecular first-order hyperpolarizability: a Hirshfeld partitioning analysis

Based on first-principles calculations, a decomposition scheme is proposed to investigate the molecular site-specific first-order hyperpolarizability (β) responses by means of Hirshfeld population analysis and finite field method. For a molecule, its β is decomposed into local and nonlocal contributions of individual atoms or groups. The former describes the response within the atomic sphere, while the latter describes the contributions from interatomic charge transfer. This scheme is then applied to six prototypical donor-acceptor (D-A) or D-π-A molecules for which the local and nonlocal hyperpolarizabilities are evaluated based on their MP2 density. Both the local and nonlocal parts exhibit site-specific characteristics, but vary differently with molecular structures. The local part depends mainly on the atomic attributes such as electronegativity and charge state, as well as its location in the molecule, while the nonlocal part relates to the ability and distance of charge delocalization within the molecule, increasing rapidly with molecular size. The proposed decomposition scheme provides a way to distinguish atomic or group contributions to molecular hyperpolarizabilities, which is useful in the molecular design for organic nonlinear optical materials.     

Attractive electron–electron interactions within robust local fitting approximations

An analysis of Dunlap's robust fitting approach reveals that the resulting two‐electron integral matrix is not manifestly positive semidefinite when local fitting domains or non‐Coulomb fitting metrics are used. We present a highly local approximate method for evaluating four‐center two‐electron integrals based on the resolution‐of‐the‐identity (RI) approximation and apply it to the construction of the Coulomb and exchange contributions to the Fock matrix. In this pair‐atomic resolution‐of‐the‐identity (PARI) approach, atomic‐orbital (AO) products are expanded in auxiliary functions centered on the two atoms associated with each product. Numerical tests indicate that in 1% or less of all Hartree–Fock and Kohn–Sham calculations, the indefinite integral matrix causes nonconvergence in the self‐consistent‐field iterations. In these cases, the two‐electron contribution to the total energy becomes negative, meaning that the electronic interaction is effectively attractive, and the total energy is dramatically lower than that obtained with exact integrals. In the vast majority of our test cases, however, the indefiniteness does not interfere with convergence. The total energy accuracy is comparable to that of the standard Coulomb‐metric RI method. The speed‐up compared with conventional algorithms is similar to the RI method for Coulomb contributions; exchange contributions are accelerated by a factor of up to eight with a triple‐zeta quality basis set. A positive semidefinite integral matrix is recovered within PARI by introducing local auxiliary basis functions spanning the full AO product space, as may be achieved by using Cholesky‐decomposition techniques. Local completion, however, slows down the algorithm to a level comparable with or below conventional calculations. © 2013 Wiley Periodicals, Inc.     

An analysis of the interaction energy in some SN2 reactions

The interaction energy between an incoming group X^– and the substrate CRH₂Y at the geometry of the transition state (TS) for bimolecular nucleophilic substitution reactions (with X, Y, and R equal to H and F) has been subjected to decomposition according to the Morokuma scheme. The influence of the basis set and of the geometry chosen for the TS is examined. The results bring out regular trends in the different terms of the decomposition along the whole set of reactions, but they are not sufficient to give a rationale of the energetic factors involved in these reactions.     

Unravelling the origin of intermolecular interactions using absolutely localized molecular orbitals

An energy decomposition analysis (EDA) method is proposed to isolate physically relevant components of the total intermolecular interaction energies such as the contribution from interacting frozen monomer densities, the energy lowering due to polarization of the densities, and the further energy lowering due to charge-transfer effects. This method is conceptually similar to existing EDA methods such as Morokuma analysis but includes several important new features. The first is a fully self-consistent treatment of the energy lowering due to polarization, which is evaluated by a self-consistent field calculation in which the molecular orbital coefficients are constrained to be block-diagonal (absolutely localized) in the interacting molecules to prohibit charge transfer. The second new feature is the ability to separate forward and back-donation in the charge-transfer energy term using a perturbative approximation starting from the optimized block-diagonal reference. The newly proposed EDA method is used to understand the fundamental aspects of intermolecular interactions such as the degree of covalency in the hydrogen bonding in water and the contributions of forward and back-donation in synergic bonding in metal complexes. Additionally, it is demonstrated that this method can be used to identify the factors controlling the interaction of the molecular hydrogen with open metal centers in potential hydrogen storage materials and the interaction of methane with rhenium complexes.