An overlap expansion method for improving ab initio model potentials: anisotropic intermolecular potentials of N2, CO, and C2H2 with He*(2(3)S)

An overlap expansion method is proposed for improving ab initio model potentials. Correction terms are expanded in terms of overlap integrals between orbitals of the interacting system. The method is used to improve ab initio model potentials for N2+He*(2(3)S), CO+He*(2(3)S), and C2H2+He*(2(3)S). Physical meanings of the optimization are elucidated in terms of target orbitals. Correction terms are found to be dominated by the components of HOMO, LUMO, next-HOMO, and next-LUMO on the target molecule. The present overlap expansion method using a limited number of correction terms related to frontier orbitals provides an efficient and intuitive approach for construction of highly anisotropic intermolecular interaction potentials.     

On-the-fly localization of electronic orbitals in Car-Parrinello molecular dynamics

The ab initio molecular-dynamics formalism of Car and Parrinello is extended to preserve the locality of the orbitals. The supplementary term in the Lagrangian does not affect the nuclear dynamics, but ensures "on the fly" localization of the electronic orbitals within a periodic supercell in the Gamma-point approximation. The relationship between the resulting equations of motion and the formation of a gauge-invariant Lagrangian combined with a gauge-fixing procedure is briefly discussed. The equations of motion can be used to generate a very stable and easy to implement numerical integration algorithm. It is demonstrated that this algorithm can be used to compute the trajectory of the maximally localized orbitals, known as Wannier orbitals, in ab initio molecular dynamics with only a modest increase in the overall computer time. In the present paper, the new method is implemented within the generalized gradient approximation to Kohn-Sham density-functional theory employing plane wave basis sets and atomic pseudopotentials. In the course of the presentation, we briefly discuss how the present approach can be combined with localized basis sets to design fast linear scaling ab initio molecular-dynamics methods.     

The investigation of ion—formamide interactions by ab initio model calculations

The effect of the cation—molecule and anion—molecule interactions on the frequency shift of the stretching vibrations are discussed in terms of ab initio 4–31 G calculations performed for the model formamide complexes with Li⁺ and F⁻ ions. The bonding of these systems is discussed qualitatively in the light of the localized orbitals.     

Ab initio fragment orbital‐based theory

A new formulation of ab initio theory is presented that treats a large molecule in terms of wave functions of its constituent molecular subunits (to be called fragments). The method aims to achieve near conventional ab initio accuracy but using a truncated set of fragment orbitals with a consequent drastic reduction of computing time and storage requirement. Illustrative calculations are presented for the molecule amino‐nitro‐stilbene. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Molecular electrostatic fields from bond fragments

We apply completely transferable, strictly localized molecular orbitals for the calculation of molecular electrostatic fields. This approach, derived from our previous bond fragment method for the calculation of molecular electrostatic potentials, reduces computational efforts drastically. The fields around small molecules containing first- and second-row atoms are systematically overestimated as compared with ab initio calculations with a minimal STO -3G basis set. However, deviations can be corrected by a simple multiplicative factor, which means that the overall shape of the potential and field around the molecule is correctly reproduced. Our approximate field can be used to determine possible hydration sites around molecules as proposed earlier by Peinel and coworkers. Application of the method is illustrated on the formamide molecule.     

Prediction and rationalization of protein pKa values using QM and QM/MM methods

We describe the development and application of a computational method for the prediction and rationalization of pKa values of ionizable residues in proteins, based on ab initio quantum mechanics (QM) and the effective fragment potential (EFPs) method (a hybrid QM/MM method). The theoretical developments include (1) a covalent boundary method based on frozen localized orbitals, (2) divide-and-conquer methods for the ab initio computation of protein EFPs consisting of multipoles up to octupoles and dipole polarizability tensors, (3) a method for computing vibrational free energies for a localized molecular region, and (4) solutions of the polarized continuum model of bulk solvation equations for protein-sized systems. The QM-based pKa prediction method is one of the most accurate methods currently available and can be used in cases where other pKa prediction methods fail. Preliminary analysis of the computed results indicate that many pKa values (1) are primarily determined by hydrogen bonds rather than long-range charge-charge interactions and (2) are relatively insensitive to large-scale dynamical fluctuations of the protein structure.     

Gradients of the polarization energy in the effective fragment potential method

The effective fragment potential (EFP) method is an ab initio based polarizable classical method in which the intermolecular interaction parameters are obtained from preparative ab initio calculations on isolated molecules. The polarization energy in the EFP method is modeled with asymmetric anisotropic dipole polarizability tensors located at the centroids of localized bond and lone pair orbitals of the molecules. Analytic expressions for the translational and rotational gradients (forces and torques) of the EFP polarization energy have been derived and implemented. Periodic boundary conditions (the minimum image convention) and switching functions have also been implemented for the polarization energy, as well as for other EFP interaction terms. With these improvements, molecular dynamics simulations can be performed with the EFP method for various chemical systems.     

The generalized valence bond π orbitals of ethylene and allyl cation

Using a fixed sigma core obtained from full electron ab initio Hartree-Fock calculations, the spatially projected GVB orbitals for the pi electron systems of ethylene and allyl cation are reported. The GVB(SP) method generates wavefunctions possessing the correct spatial and spin symmetry without restricting the nature of the individual orbitals. The GVB(SP) wavefunction provides a simple interpretation of the molecule in terms of orbitals each containing a single electron. The resulting total energies and excitation energies agree very well with full configuration interaction calculations.     

EHMO方法的分子轨道定域化

用Foster-Boys的定域化准则讨论了EHMO方法的分子轨道定域化问题,提出用双中心重叠积分近似计算双中心轨道偶极矩积分方法,得到的EHMO定域分子轨道与严格定域化结果接近,与从头计算方法的定域化结果定性一致。     

An ab initio method for approximation of the frozen molecular fragment

An ab initio method for calculation on many-electron molecular systems with the approximation of the inactive part of a molecule by frozen molecular fragment is presented. In the following method the SCF calculations are performed in two series. First the molecular orbitals resulting from the first SCF calculation (modest basis set) are localized. In the second SCF run, the basis set is extended for the active part of the molecule, while molecular orbitals of the inactive part, selected from the localized set, are kept frozen. The results are in good agreement with the extended basis set calculation.     

Molecule intrinsic minimal basis sets. II. Bonding analyses for Si4H6 and Si2 to Si10

The method, introduced in the preceding paper, for recasting molecular self-consistent field (SCF) or density functional theory (DFT) orbitals in terms of intrinsic minimal bases of quasiatomic orbitals, which differ only little from the optimal free-atom minimal-basis orbitals, is used to elucidate the bonding in several silicon clusters. The applications show that the quasiatomic orbitals deviate from the minimal-basis SCF orbitals of the free atoms by only very small deformations and that the latter arise mainly from bonded neighbor atoms. The Mulliken population analysis in terms of the quasiatomic minimal-basis orbitals leads to a quantum mechanical interpretation of small-ring strain in terms of antibonding encroachments of localized molecular-orbitals and identifies the origin of the bond-stretch isomerization in Si4H6. In the virtual SCF/DFT orbital space, the method places the qualitative notion of virtual valence orbitals on a firm basis and provides an unambiguous ab initio identification of the frontier orbitals.     

虚轨道定域化

通过引入虚轨道定域化函数，扩展了集居数的定域化方法，在从头算STO－3G水平上用护展后的方法计算无机小分子、烷烃、卤代烷、醇、胺及共轭烃等，结果表明，定域占据轨道与定域虚轨道的系数和能级分布相似的规律。     

On the transferability of Fock matrix elements

The transferability of Fock matrix elements in the linear combination of atomic orbitals molecular orbital scheme is analysed using localized orbitals. It is shown that this transferability is dependent on the transferability of these localized orbitals and the neglect of long-range contributions from partially cancelling Coulomb nuclear attraction and electron repulsion terms. A theoretical basis is thus provided for the simulated ab initio molecular orbital and related methods. Various corrections previously introduced in an ad hoc manner are shown to be justified. Transferability in both the closed shell and open shell schemes is analysed.     

线形碳元素簇合物的成键性质

在ab initio 3-21G水平上, 用能量梯度法优化了线性碳元素簇合物C_n~e(n为成簇原子个数, e为电荷)的平衡几何结构. 所得的电离势随成簇原子个数的改变, 呈现出不同程度的奇偶交替变化趋势. 在ab initio计算基础上, 用Boys方法, 对其占据正则分子轨道进行定域化变换, 得到了它们的定域分子轨道. 对定域分子轨道性质的分析表明, 线性碳元素簇合物中, 主要键型有双中心σ和π健, 双中心弯键和三中心香蕉健, 以及多中心σ和π健. 这种键型的多样化可视为小元素簇的成健特征. 此外, 通过对其成键性质的分析, 讨论了线性碳元素簇的稳定性. 对于小碳元素簇, 化学键的共轭性对其稳定性具有十分显著的作用.     

Molecule intrinsic minimal basis sets. I. Exact resolution of ab initio optimized molecular orbitals in terms of deformed atomic minimal-basis orbitals

A method is presented for expressing the occupied self-consistent-field (SCF) orbitals of a molecule exactly in terms of chemically deformed atomic minimal-basis-set orbitals that deviate as little as possible from free-atom SCF minimal-basis orbitals. The molecular orbitals referred to are the exact SCF orbitals, the free-atom orbitals referred to are the exact atomic SCF orbitals, and the formulation of the deformed "quasiatomic minimal-basis-sets" is independent of the calculational atomic orbital basis used. The resulting resolution of molecular orbitals in terms of quasiatomic minimal basis set orbitals is therefore intrinsic to the exact molecular wave functions. The deformations are analyzed in terms of interatomic contributions. The Mulliken population analysis is formulated in terms of the quasiatomic minimal-basis orbitals. In the virtual SCF orbital space the method leads to a quantitative ab initio formulation of the qualitative model of virtual valence orbitals, which are useful for calculating electron correlation and the interpretation of reactions. The method is applicable to Kohn-Sham density functional theory orbitals and is easily generalized to valence MCSCF orbitals.     

Localization measure and maximum delocalization in molecular systems

A mathematically well-defined measure of localization is presented based on Mulliken's orbital populations. It is shown that this quantity equals 1 for core- and lone-pair orbitals, 2 for two-atomic bonds, 6 for benzene rings, etc., and it is applicable for delocalized canonical HF orbitals as well. The definition of this quantity is general in the sense that ab initio MOS with overlapping AO expansion, and semiempirical wave functions using the ZDO approximation as well, can be treated. The localization quantity is essentially “intrinsic,” i.e., no subdivision of the molecule is required. For N-electron wave functions, mean delocalization can be defined. This measure is not invariant to unitary transformations of the one-electron orbitals, characterizing in this way the localized or extended representation of the N-electron wave function. It can be proven, however, that for unitary transformed wave functions a maximum delocalization exists which depends only on the physical (N-electron) properties of the molecule. It is shown that inhomogeneous charge distribution can cause strong electron localization in molecular systems. The delocalization of the canonical Hartree–Fock orbitals, the Parr–Chen circulant orbitals, and the optimum delocalized orbitals is studied by numerical calculations in extended systems.     

Decomposing total IR spectra of aqueous systems into solute and solvent contributions: a computational approach using maximally localized Wannier orbitals

The theoretical principles underpinning the calculation of infrared spectra for condensed-phase systems in the context of ab initio molecular dynamics have been recently developed in literature. At present, most ab initio molecular dynamics calculations are restricted to relatively small systems and short simulation times. In this paper we devise a method that allows well-converged results for infrared spectra from ab initio molecular dynamics simulations using small systems and short trajectories characteristic of simulations typically performed in practice. We demonstrate the utility of our approach by computing the imaginary part of the dielectric constant epsilon"(omega) for H2O and D2O in solid and liquid phases and show that it compares well with experimental data. We further demonstrate that maximally localized Wannier orbitals can be used to separate the individual contributions of different molecular species to the linear spectrum of complex systems. The new spectral decomposition method is shown to be useful in present-day ab initio molecular dynamics calculations to compute the magnitude of the "continuous absorption" generated by excess protons in aqueous solutions with good accuracy even when other species present in the solutions absorb strongly in the same frequency window.     

链烃,环状烃和多面体烃的定域分子轨道研究

采用GAUSSAN 80程序对一系列直链烷烃、环状烃和多面体烷烃进行STO-3G基组下的曲initio计算,在所得非定域分子轨道自洽场结果的基础上,利用Boys方法进行定域化,进而研究了这些分子的定域分子轨道的键弯曲性质、轨道能量和集居数与几何结构之间的关系,用上述结果对一些典型分子的稳定性进行了讨论。     

A new fragment-based approach for calculating electronic excitation energies of large systems

We present a new fragment-based scheme to calculate the excited states of large systems without necessity of a Hartree-Fock (HF) solution of the whole system. This method is based on the implementation of the renormalized excitonic method [M. A. Hajj et al., Phys. Rev. B 72, 224412 (2005)] at ab initio level, which assumes that the excitation of the whole system can be expressed by a linear combination of various local excitations. We decomposed the whole system into several blocks and then constructed the effective Hamiltonians for the intra- and inter-block interactions with block canonical molecular orbitals instead of widely used localized molecular orbitals. Accordingly, we avoided the prerequisite HF solution and the localization procedure of the molecular orbitals in the popular local correlation methods. Test calculations were implemented for hydrogen molecule chains at the full configuration interaction, symmetry adapted cluster/symmetry adapted cluster configuration interaction, HF/configuration interaction singles (CIS) levels and more realistic polyene systems at the HF/CIS level. The calculated vertical excitation energies for lowest excited states are in reasonable accordance with those determined by the calculations of the whole systems with traditional methods, showing that our new fragment-based method can give good estimates for low-lying energy spectra of both weak and moderate interaction systems with economic computational costs.     

Large systems at ab initio multireference level: a cheap treatment thanks to a division into fragments

Thanks to the use of localized orbitals and the subsequent possibility of neglecting long-range interactions, the linear-scaling methods have allowed to treat large systems at ab initio level. However, the limitation of the number of active orbitals in a complete active space self consistent-field (CASSCF) calculation remains unchanged. The method presented in this paper suggests to divide the system into fragments containing only a small number of active orbitals. Starting from a guess wave function, each orbital is optimized in its corresponding fragment, in the presence of the other fragments. Once all the fragments have been treated, a new set of orbitals is obtained. The process is iterated until convergence. At the end of the calculation, a set of active orbitals is obtained, which is close to the exact CASSCF solution, and an accurate CASSCF energy can be estimated.