Quantum Monte Carlo with Jastrow-valence-bond wave functions

We consider the use in quantum Monte Carlo calculations of two types of valence bond wave functions based on strictly localized active orbitals, namely valence bond self-consistent-field and breathing-orbital valence bond wave functions. Complemented by a Jastrow factor, these Jastrow-valence-bond wave functions are tested by computing the equilibrium well depths of the four diatomic molecules C(2), N(2), O(2), and F(2) in both variational Monte Carlo and diffusion Monte Carlo. We show that it is possible to design compact wave functions based on chemical grounds that are capable of describing both static and dynamic electron correlations. These wave functions can be systematically improved by inclusion of valence bond structures corresponding to additional bonding patterns.     

Variational biorthogonal valence bond descriptions of 1,3-dipoles

The variational biorthogonal valence bond method is applied to the π-electrons of six 1,3-dipoles (CH₂N₂, HCNO, CH₂NHO, N₂O, O₃, NO₂). The results are compared with those from other valence bond techniques, including a detailed comparison with the spin-coupled valence bond approach. For CH₂N₂, HCNO, CH₂NHO, and N₂O, zwitterionic structures are predicted and it is shown that the variational biorthogonal valence bond method leads to orbitals and configuration weights which are essentially indistinguishable from those of the spin-coupled valence bond method. However, for O₃ and NO₂ the techniques give contradictory results. The biorthogonal valence method predicts O₃ and NO₂ to be spin-paired diradicals. Evidence from other calculations on O₃ is discussed. © 1994 by John Wiley & Sons, Inc.     

Ab initio calculation of maximum bond order hybrid orbitals

Summary The maximum bond order hybrid orbital (MBOHO) procedure is tested onab initio level by use of the density matrix in Löwdin orthogonalized atomic orbital basis. The direct MBOHO calculation based on the whole density matrix includes also the hybridization of the inner atomic orbitals, and the MBOHO calculation based on the valence orbital part of the density matrix considers only the hybridization of the valence atomic orbitals. The concrete MBOHO calculations based on theab initio calculation with STO-3G basis show that the components of the s atomic orbitals in MBOHOs and the maximum bond orders obtained from the two kinds of MBOHO calculations are very close to each other, and that the two kinds of MBOHOs all have the excellent correlativity with the nuclear spin-spin coupling constants.The project supported by National Natural Science Foundation of China and the Excellent Young University Teacher's Foundation of State Education Commission of China.     

价键理论新进展

概要介绍了现代价键理论的几个主要方法,并讨论了它们各自的特点及其发展现状,并重点介绍了键表方法的基本理论、计算程序及一些应用。     

Valence : A Massively Parallel Implementation of the Variational Subspace Valence Bond Method

This work describes the software package, Valence , for the calculation of molecular energies using the variational subspace valence bond (VSVB) method. VSVB is an ab initio electronic structure method based on nonorthogonal orbitals. Important features of practical value include high parallel scalability, wave functions that can be constructed automatically by combining orbitals from previous calculations, and ground and excited states that can be modeled with a single configuration or determinant. The open-source software package includes tools to generate wave functions, a database of generic orbitals, example input files, and a library build intended for integration with other packages. We also describe the interface to an external software package, enabling the computation of optimized molecular geometries and vibrational frequencies. © 2019 Wiley Periodicals, Inc.     

价键理论中的组态相互作用

近 2 0年来 ,从头计算水平的价键 (VB)方法得到了人们的重视 ,并广泛应用于化学反应等问题的研究[1～ 5] ,然而目前价键理论的计算方法仍然很不完善 .用 VBSCF方法进行计算虽然比较简单 ,能正确地描述化学反应的形成机理 ,但数值结果不理想 ;而用 BOVB方法[4 ] 进行计算虽然可以得到较好的计算结果 ,但存在收敛困难等问题 .分子轨道理论中的组态相互作用是一种简单直接的电子相关能计算方法 ,显然这一方法可以应用于价键方法中 .然而与分子轨道理论方法不同 ,在价键方法中 ,无法直接得到空轨道 ,此外如何选取激发价键函数使得计算结果…     

A valence bond study of the oxygen molecule

Ab initio valence bond calculations are performed for the three lowest states of the oxygen molecule (³Σ⁻_g, ¹Δ_g, and ¹Σ⁺_g). One objective of the present study was to make a contribution to previous valence bond discussions about the oxygen “double” bond. Further, we study the origin of a small barrier in the potential energy surface of the ground state. Two compact models are employed to maintain the clear picture that can be offered by the valence bond method. The first model has only the Rumer structures that are essential for bonding and a proper dissociation. The second model, in addition, has structures which represent excited atoms. These prove to be important for the dissociation energies. For both models, the orbitals are fully optimized. The spectroscopic data obtained are significantly better than are the (few) valence bond results on O₂ that have been published and have the quality of multiconfiguration self-consistent field calculations in which the same valence space is used. The “hump” in the potential energy surface of the ground state is shown to arise from a spin recoupling. The free atoms correspond to a spin coupling that is incapable of describing the formation of bonds. Only at short distances, an alternative spin coupling provides bonding and the repulsive curve is converted into an attractive one. Our results on this subject support a valence bond explanation previously given by McWeeny [R. McWeeny, Int. J. Quantum Chem. Symp. 24 , 733 (1990)]. © 1996 John Wiley & Sons, Inc.     

Computational developments in generalized valence bond calculations

In this article a procedure for generating starting orbitals for generalized valence bond (GVB) calculations is presented. This is achieved by selecting orbitals which correspond to specific bonds or electron pairs. These orbitals can be identified from the localized molecular orbitals, for both occupied and virtual orbitals, which are obtained through a unitary transformation of the Hartree-Fock canonical molecular orbitals using the Boys's localization method. A scheme has also been implemented which achieves optimum convergence of the pairwise orbital optimization. An object-oriented GVB program is developed which automatically generates reliable initial GVB orbitals, leading to proper and fast convergence. © 1996 by John Wiley & Sons, Inc.     

Rotational isomerism and barriers to internal rotation in 3-halopropenes byscf-mo methods

Electronic structures of 3 halopropenes have been investigated through semiempiricalscf-mo calculations using valence basis sets of atomic orbitals (ao) constructed from Slater type orbitals (sto). The electronic structures of stable conformers have been predicted and the corresponding calculated dipole moments show good agreement with experimental data. The considerable differences between the dipole moments of various conformers confirm the hindrance to internal rotation about the C−C bond, i.e., the existence of a definite potential barrier to rotation. The barrier heights hindering the internal rotation in each system are also estimated.     

Interatomic and intraatomic analysis of the density matrix: applications to chlorobenzenes

Bond orders and valence indices have been evaluated employing Mayer’s definitions with orthogonalized atomic orbitals (OAO) obtained from L?wdin orthogonalization over an STO-3G basis set in anab initio formalism. It has been observed that the eigenvalues of the submatrices associated with bond order orbitals. natural hybrid orbitals and natural bond orbitals also reproduce the same values of the bond orders and the valence indices which in turn are quite close to the classical values. Bond orders obtained by a similarity transformation of theab initio density matrix differ appreciably in numerical magnitude.     

The orthogonality problem in valence bond calculations

The energy of the π-electron system in benzene has been obtained by means of valence bond calculations using orthogonal and nonorthogonal basis orbitals at different levels of configuration interaction, which shows the influence of the orthogonalization procedures.     

The error due to neglecting the core spin–orbit splitting in valence ZORA calculations with frozen core approximation and its elimination

In valence zeroth-order regular approximation (ZORA) calculations with frozen core approximation, when the basis set optimized to the related scalar relativistic ZORA calculations is used, neglecting the core spin–orbit splitting may result in additional basis set truncation errors. It is found that the error is negligible for most elements except the 6p-block elements. When the basis set is extended by a p-type STO function put on the 6p element atoms with the ζ value proper to 5p_1/2 orbitals, the error can be reduced to be negligible. The calculated atomic properties related to valence orbitals can be improved greatly by use of this extended basis set. The frozen core approximation calculations of some molecules containing Tl, Pb and Bi with closed shells show that neglecting the core spin–orbit splitting only slightly affects the calculated bond lengths and bond energies, and the calculated molecular property can also be improved slightly by use of the extended basis sets.     

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.     

Fully relativistic calculations of ThF4

Based on the results of first‐principles density functional theory calculations of the electronic structure of ThF₄ in solid state and molecular form, the study of the Th6p, 5f, 6d, 7s and F2s, 2p states was done. We used the fully relativistic cluster discrete variational method with the local exchange‐correlation potential. The hybridization of F2p and Th5f, 6d, 7s, 7p states in the valence molecular orbitals (VMOs) in the region 0–10 eV and of F2s and Th6p states in the inner valence molecular orbitals (IVMOs) in the region 10–50 eV was studied. The results of relativistic cluster calculations are compared with those obtained for ThF₄ molecule. The energies of ionization of VMOs and of IVMOs were evaluated on the basis of the ground‐state and Slater's transition‐state calculations. The MO energy levels provide a satisfactory interpretation of experimental photoelectron spectra. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Bonding of the chain structure for novel boranes B_(3k+)H_(5k+p+3)~-

The molecular orbitals obtained from conventional quantum chemistry calculations, are expressed in terms of symmetrized valence bond functions of fragment, and a direct picture of chemical bonding can be drawn easily. This method is utilized, together with extended Huckel calculations, to interpret the bonding properties of a centipede-like chain structure for novel laser-producing boranes B3k+pH5k+p+3- which is constructed from the repeated unit B3H5 linked to each other by three B-H-B bonds.     

Optimized spin-coupled virtual orbitals

The goal of obtaining accurate potential energy surfaces for the study of intermolecular forces is of fundamental importance. In this article, we propose a new method to generate a set of virtual orbitals optimized in such a way to give very compact valence bond (VB) wave functions with the same accuracy of very large VB calculations. These optimized virtual orbitals, completely free from BSSE, are developed in the framework of spin coupled theory. Test calculations on the He ··· LiH system are presented together with a comparison with previous studies. © 1996 John Wiley & Sons, Inc.     

The V state of ethylene: valence bond theory takes up the challenge

The ground state and first singlet excited state of ethylene, so-called N and V states, respectively, are studied by means of modern valence bond methods. It is found that extremely compact wave functions, made of three VB structures for the N state and four structures for the V state, provide an N → V transition energy of 8.01 eV, in good agreement with experiment (7.88 eV for the N → V transition energy estimated from experiments). Further improvement to 7.96/7.93 eV is achieved at the variational and diffusion Monte Carlo (MC) levels, respectively, VMC/DMC, using a Jastrow factor coupled with the same compact VB wave function. Furthermore, the measure of the spatial extension of the V state wave function, 19.14 a ₀ ² , is in the range of accepted values obtained by large-scale state-of-the-art molecular orbital-based methods. The σ response to the fluctuations of the π electrons in the V state, known to be a crucial feature of the V state, is taken into account using the breathing orbital valence bond method, which allows the VB structures to have different sets of orbitals. Further valence bond calculations in a larger space of configurations, involving explicit participation of the σ response, with 9 VB structures for the N state and 14 for the V state, confirm the results of the minimal structure set, yielding an N → V transition energy of 7.97 eV and a spatial extension of 19.16 a ₀ ² for the V state. Both types of valence bond calculations show that the V state of ethylene is not fully ionic as usually assumed, but involving also a symmetry-adapted combination of VB structures each with asymmetric covalent π bonds. The latter VB structures have cumulated weights of 18–26 % and stabilize the V state by about 0.9 eV. It is further shown that these latter VB structures, rather than the commonly considered zwitterionic ones, are the ones responsible for the spatial extension of the V state, known to be ca. 50 % larger than the V state.     

A two-step method of calculation of the electronic structure of molecules with heavy atoms: Theoretical aspect

An approach for a space-separated calculation of the wave function in the valence and core regions of a molecule is proposed. As the first step, the calculation of the orbitals (or two-component spinors in the relativistic case) in the valence region by the effective core potential (ECP ) method is performed. Then, it is followed by a restoration of orbitals (four-component spinors) expanded on spherical harmonics in the core regions of heavy atoms. Theoretical questions of the variational calculation of the molecular orbitals are considered in some core region limited by a sphere. Inclusion from the electronic cloud outside this region is reduced by the necessity of taking into account the orthonormality and boundary conditions together with an effective external field in respect to the selected core region. This method may be used for calculation of matrix elements of operators that are singular near nuclei (P, T-odd interactions, hyperfine structure, etc.). A substantial computational saving can be reached because the method enables, by the most optimal way, to combine the advantages of two well-developed approaches: molecular ECP calculations in the Gaussian basis set and one-center numerical atomic calculations with an external field. It is especially important when the relativistic effects are taken into account. © 1996 John Wiley & Sons, Inc.