New algorithm for nonorthogonal ab initio valence bond calculations II: Subgraph-driven method

The permanent method for nonorthogonal VB calculations is extensively developed, and the so-called subgraph-driven procedure is proposed. To achieve high efficiency, the summation of a huge number of permanents is treated as a whole system, and the intermediate quantities, the contracted-cofactors of various orders, are introduced for the systematic summation. These intermediate quantities can be characterized by pairing graphs of 2n elements (n = 1, 2, ... 1/2N – 2). Some test calculations for systems of up to 20 electrons are performed. The practice shows that this method is highly efficient, and the CPU time increases in a quite moderate way with the increasing number of electrons.On leave from Chemistry Department, Xiamen University, 361005 Xiamen, PR China.     

Tautomerism of protonated imidazoles: A perspective from ab initio valence bond theory

The tautomerism of protonated imidazoles concerns one aromatic (1H-Imi+) and one nonaromatic (4H-Imi+) tautomers. Both experiments and computations have shown that substituents to the imidazole ring can change the relative stability of tautomers. A detailed theoretical study of the inherent mechanism would benefit the rational design of experimental syntheses related to imidazoles. In this work, we used the block-localized wavefunction (BLW) method to explore the factors governing the tautomerism between 1H-Imi+ and 4H-Imi+. While π resonance always favors the aromatic tautomer 1H-Imi+, the aromaticity noticeably reduces with electron donating groups (EDGs) as substituents due to the increased π-π repulsion, leading to the stability of 4H-Imi+ over 1H-Imi+ with EDGs such as NH₂ and OH. For electron withdrawing groups (EWGs), the reduced π-π repulsion promotes the aromatic stability and favors 1H-Imi+. DFT computations were also performed to study the tautomerism mechanisms. Results show that tautomerism can hardly occur in gaseous phase, but in aqueous solution, water molecules can build hydrogen bonding network with 1H-Imi+ and facilitate the hydrogen transfers.     

Paired-permanent approach for VB theory (Ⅱ)——An ab initio spin-free VB program

Paired-permanent approach for VB theory is extensively developed. Canonical expansion of a paired-permanent is deduced. Furthermore, it is shown that a paired-permanent may be expressed in terms of the products of sub-paired-permanents of any given order and their corresponding minors. An ab initio spin-free valence bond program, called Xiamen, is implemented by using paired-permanent approach. Test calculation shows that Xiamen package is more efficient than some other programs based on the traditional VB algorithm, and it provides a new practical tool for quantum chemistry.     

Wheland intermediates: an ab initio valence bond study

The traditional resonance model for electrophilic attacks on substituted aromatic rings is revisited using high level valence bond (VB) calculations. A large π-donation is found in the X = NH(2) case and a weaker one for the X = Cl case, not only for ortho and para isomers but also for the meta case, which can be explained by considering five (not three) fundamental VB structures. No substantial π-effect is found in the X = NO(2) case, generally viewed as π-attractive.     

Resonance and aromaticity: an ab initio valence bond approach

Resonance energy is one of the criteria to measure aromaticity. The effect of the use of different orbital models is investigated in the calculated resonance energies of cyclic conjugated hydrocarbons within the framework of the ab initio Valence Bond Self-Consistent Field (VBSCF) method. The VB wave function for each system was constructed using a linear combination of the VB structures (spin functions), which closely resemble the Kekulé valence structures, and two types of orbitals, that is, strictly atomic (local) and delocalized atomic (delocal) p-orbitals, were used to describe the π-system. It is found that the Pauling-Wheland's resonance energy with nonorthogonal structures decreases, while the same with orthogonalized structures and the total mean resonance energy (the sum of the weighted off-diagonal contributions in the Hamiltonian matrix of orthogonalized structures) increase when delocal orbitals are used as compared to local p-orbitals. Analysis of the interactions between the different structures of a system shows that the resonance in the 6π electrons conjugated circuits have the largest contributions to the resonance energy. The VBSCF calculations also show that the extra stability of phenanthrene, a kinked benzenoid, as compared to its linear counterpart, anthracene, is a consequence of the resonance in the π-system rather than the H-H interaction in the bay region as suggested previously. Finally, the empirical parameters for the resonance interactions between different 4n+2 or 4n π electrons conjugated circuits, used in Randi?'s conjugated circuits theory or Herdon's semi-emprical VB approach, are quantified. These parameters have to be scaled by the structure coefficients (weights) of the contributing structures.     

Consistent valence force-field parameterization of bond lengths and angles with quantum chemical ab initio methods applied to some heterocyclic dopamine D3-receptor agonists

To secure a broad utilization of molecular mechanics in medicinal chemistry appropriate parameters (e.g., reference values and force constants) are required to describe correctly all possible atomic interactions. For this purpose parameters for bond lengths and bond angles were derived for some heterocyclic dopamine D₃-receptor agonists. Some new atom types were introduced and consistent valence force-field (CVFF) was supplied with several bond-stretching and angle-bending force constants as well as reference values. Representative fragments containing these missing parameters were minimized at the HF/6-31G* level of theory using Gaussian-92. After frequency calculation, corresponding force constants were extracted from the Hessian matrix. The values were then appropriately converted and scaled. Also, reference values were taken from quantum mechanically minimized structures, applying the same basis set. The transferability of the calculated force constants to CVFF was investigated using fragments with already known parameters. The quality of the extended force field was checked in comparison with “automatic parameters” and ab initio-minimized structures. Finally, the evaluated procedure was applied successfully to related structures. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 935–946, 1998     

The application of cholesky decomposition in valence bond calculation

The Cholesky decomposition (CD) technique, used to approximate the two‐electron repulsion integrals (ERIs), is applied to the valence bond self‐consistent field (VBSCF) method. Test calculations on ethylene, C_2nH_2n+2, and C_2nH_4n?2 molecules (n = 1–7) show that the performance of the VBSCF method is much improved using the CD technique, and thus, the integral transformation from basis functions to VB orbitals is no longer the bottleneck in VBSCF calculations. The errors of the CD‐based ERIs and of the total energy are controlled by the CD threshold, for which a value of 10^?6 ensures to control the total energy error within 10^?6 Hartree. © 2016 Wiley Periodicals, Inc.     

Implementation of molecular symmetry in valence bond calculation

A novel strategy for the construction of many-electron symmetry-adapted wave function is proposed for ab initio valence bond (VB) calculations and is implemented for valence bond self-consistent filed (VBSCF) and breathing orbital valence bond (BOVB) methods with various orbital optimization algorithms. Symmetry-adapted VB functions are constructed by the projection operator of symmetry group. The many-electron symmetry-adapted wave function is expressed in terms of symmetry-adapted VB functions, and thus the VB calculations can be performed with the molecular symmetry restriction. Test results show that molecular symmetry reduces the computational cost of both the iteration numbers and CPU time. Furthermore, excited states with specific symmetry can be conveniently obtained in VB calculations by using symmetry-adapted VB functions.     

VB2000: Pushing valence bond theory to new limits

Full valence bond (VB) calculations for a system of N electrons have always been hindered by the rapidly growing value of N!, which effectively imposes a limit N < 20. Often, however, not all electrons in a molecule are of interest; if we focus on a “group” G of N_G electrons (e.g., in an “active” region), then it is N_G! that sets the limit. In this work, group function (GF) theory is used to represent a molecule as a collection of interacting electron groups, each with a many‐electron wave function of any chosen form (e.g., VB, MO‐SCF, MCSCF), and each GF is optimized individually in a step‐by‐step process. An efficient VB algorithm allows for up to 14 electrons in any VB group and this combination of GF and VB methods greatly extends the range of feasibility of molecular calculations with VB‐type wave functions: Thus, (1) a large system can be divided into any number of smaller subsystems (groups); (2) each group may contain any chosen number of electrons; (3) the form of any group function (including its level of accuracy) may be chosen at will by the program user. A number of sample calculations are briefly presented. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

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.     

价键方法中的非活性轨道优化新算法

本文通过引进一组正交的辅助非活性轨道和与它正交的辅助活性轨道,将价键理论方法中的冻核近似推广到轨道非正交的情形,得到了体系能量及其对非活性轨道的梯度解析表达式,简化了价键自洽场方法中非正交轨道能量梯度的计算．该方法的标度为（Na＋1）m^4,其中Na和m分别是活性轨道和基函数的个数．分析表明,与现有的其他算法相比较,该方法具有更低的计算标度,因而计算效率更高．     

Paired-permanent approach to valence bond theory

A new function called paired-permanent is defined and widely discussed, and a practicable procedure for evaluations of paired-permanents is proposed, which is similar to the Laplace method for determinants. Using the concept of paired-permanents, an efficient algorithm is presented for evaluating the Hamiltonian and overlap matrix elements in the spin-free form of valence bond (VB) theory. With the new algorithm, a spin-free wavefunction is simply written as a paired-permanent, and an overlap matrix element may be obtained by evaluating a corresponding paired-permanent. Meanwhile, the Hamiltonian matrix element is expressed in terms of the summation of the products of electronic integrals and the corresponding sub-paired-permanents     

An ab initio valence bond study on cyclopenta-fused naphthalenes and fluoranthenes

To probe the effect of external cyclopenta-fusion on a naphthalene core, ab initio valence bond (VB) calculations have been performed, using strictly atomic benzene p-orbitals and p-orbitals that are allowed to delocalize, on naphthalene (1), acenaphthylene (2), pyracylene (3), cyclopenta[b,c]acenaphthylene (4), fluoranthene (5), and cyclopenta[c,d]fluoranthene (6). For the related compounds 1-4 and 5,6 the total resonance energies (according to Pauling's definition) are similar. Partitioning of the total resonance energy in contributions from the possible 4n + 2 and 4n pi-electron conjugated circuits shows that only the 6pi-electron conjugated circuits (benzene-like) contribute to the resonance energy. The results show that cyclopenta-fusion does not extend the pi system in the ground state; the five-membered rings act as peri-substituents. As a consequence, the differences in (total) resonance energy do not coincide with the differences in thermodynamic stability. Notwithstanding, the relative energies of the Kekule structures can be estimated using Randic's conjugated circuits model.     

Factors determining bond angles from a classical valence bond perspective. Covalent structure of H2O

We identify the energy contributions that govern the interorbital and internuclear angles in the classical covalent structure of H₂O. The central atom valence state term plays a primary role in H₂O and other AH₂ molecules as well. Lone pair interactions of three different types are also of major significance.On leave 1977–78 at the University of California, Santa Barbara