Introduction There has been a very significarnt resurgence of interest in ab initio valence bond calculations recently. This is because the VB calculation based on nonorthogonal basis can provide intuitive understandi...Introduction There has been a very significarnt resurgence of interest in ab initio valence bond calculations recently. This is because the VB calculation based on nonorthogonal basis can provide intuitive understanding about many very important phenomena in chemistry. However, practical calculation based on nonorthogonal basis is still a great challenge even to deal with a quite small system due to the well-known N! (or展开更多
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 ...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展开更多
This paper presents an efficient algorithm for energy gradients in valence bond self-consistent field(VBSCF) method with non-orthogonal orbitals.The frozen core approximation method is extended to the case of non-orth...This paper presents an efficient algorithm for energy gradients in valence bond self-consistent field(VBSCF) method with non-orthogonal orbitals.The frozen core approximation method is extended to the case of non-orthogonal orbitals.The expressions for the total energy and its gradients are presented by introducing auxiliary orbitals,where inactive orbitals are orthogonal,while active orbitals are non-orthogonal themselves but orthogonal to inactive orbitals.It is shown that our new algorithm has a low scaling of(Na+1)m4,where Na and m are the numbers of the active orbitals and basis functions,respectively,and is more efficient than the existing VBSCF algorithms.展开更多
Recently we proposed a systematic treatment involving the use of weight of resonance structures （RS）<sup>[1a]</sup>, and showed that the fundamental ideas of the resonance theory （RT） are correct wholl...Recently we proposed a systematic treatment involving the use of weight of resonance structures （RS）<sup>[1a]</sup>, and showed that the fundamental ideas of the resonance theory （RT） are correct wholly, and the Dewar resonance energy （RE）, bond order P<sub>st</sub> and charge density qx can be calculated simultaneously from RS<sub>s</sub> of a molecule. For heteroconjugated molecules these formulas展开更多
OX_(2)(X=halogen)molecules was studied theoretically.Calculation results show that delocalizedπ_(3)^(6) bonds exist in their electronic structures and O atoms adopt the sp^(2) type of hybridization,which violates the...OX_(2)(X=halogen)molecules was studied theoretically.Calculation results show that delocalizedπ_(3)^(6) bonds exist in their electronic structures and O atoms adopt the sp^(2) type of hybridization,which violates the prediction of the valence shell electron pair repulsion theory of sp^(3) type.Delocalization stabilization energy is proposed to measure the contribution of delocalizedπ_(3)^(6) bond to energy decrease and proves to bring extra-stability to the molecule.These phenomena can be summarized as a kind of coordinating effect.展开更多
文摘Introduction There has been a very significarnt resurgence of interest in ab initio valence bond calculations recently. This is because the VB calculation based on nonorthogonal basis can provide intuitive understanding about many very important phenomena in chemistry. However, practical calculation based on nonorthogonal basis is still a great challenge even to deal with a quite small system due to the well-known N! (or
基金Project supported by the National Natural Science Foundation of Chinathe State Key Project Foundation for Basic Researches
文摘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
基金Supported by the National Natural Science Foundation of China (Grant Nos. 20533020, 20873106)the National Basic Research Program of China (Grant No. 204CB719902)
文摘This paper presents an efficient algorithm for energy gradients in valence bond self-consistent field(VBSCF) method with non-orthogonal orbitals.The frozen core approximation method is extended to the case of non-orthogonal orbitals.The expressions for the total energy and its gradients are presented by introducing auxiliary orbitals,where inactive orbitals are orthogonal,while active orbitals are non-orthogonal themselves but orthogonal to inactive orbitals.It is shown that our new algorithm has a low scaling of(Na+1)m4,where Na and m are the numbers of the active orbitals and basis functions,respectively,and is more efficient than the existing VBSCF algorithms.
文摘Recently we proposed a systematic treatment involving the use of weight of resonance structures （RS）<sup>[1a]</sup>, and showed that the fundamental ideas of the resonance theory （RT） are correct wholly, and the Dewar resonance energy （RE）, bond order P<sub>st</sub> and charge density qx can be calculated simultaneously from RS<sub>s</sub> of a molecule. For heteroconjugated molecules these formulas
基金supported by the Provincial Innovation and Entrepreneurship Training Program of Jiangsu Province(No.201910319079Y)。
文摘OX_(2)(X=halogen)molecules was studied theoretically.Calculation results show that delocalizedπ_(3)^(6) bonds exist in their electronic structures and O atoms adopt the sp^(2) type of hybridization,which violates the prediction of the valence shell electron pair repulsion theory of sp^(3) type.Delocalization stabilization energy is proposed to measure the contribution of delocalizedπ_(3)^(6) bond to energy decrease and proves to bring extra-stability to the molecule.These phenomena can be summarized as a kind of coordinating effect.
