Acceleration of self‐consistent field convergence in ab initio molecular dynamics simulation with multiconfigurational wave function

The Lagrange interpolation of molecular orbital (LIMO) method, which reduces the number of self‐consistent field iterations in ab initio molecular dynamics simulations with the Hartree–Fock method and the Kohn–Sham density functional theories, is extended to the theory of multiconfigurational wave functions. We examine two types of treatments for the active orbitals that are partially occupied. The first treatment, as denoted by LIMO(C), is a simple application of the conventional LIMO method to the union of the inactive core and the active orbitals. The second, as denoted by LIMO(S), separately treats the inactive core and the active orbitals. Numerical tests to compare the two treatments clarify that LIMO(S) is superior to LIMO(C). Further applications of LIMO(S) to various systems demonstrate its effectiveness and robustness. © 2014 Wiley Periodicals, Inc.     

Avoiding the use of integral lists in the ab initio LCAO SCF MO method

The suggestion is made that the storage of long lists of two-electron repulsion integrals in the LCAO SCF MO method could be avoided if such integrals were evaluated at each SCF cycle and an initial set of eigenvectors were available to lead to rapid convergence. Results are presented showing that the simulated ab initio molecular orbital (SAMO) technique provides an excellent set of initial eigenvectors for the SCF procedure.     

Wavelet transform analysis of ab initio molecular dynamics simulation: application to core-excitation dynamics of BF3

We propose a novel analysis method of ab initio molecular dynamics (AIMD) simulation using a continuous wavelet transform (c-WT) technique. The c-WT technique, one of the time-frequency signal analysis methods, provides a clear view of the dynamical information in time developments. Combined with the auto-correlation function of velocity by AIMD simulation, c-WT analysis enables us to well understand dynamical distribution, such as the vibrational properties following a change of electronic structure in a molecular system. As a practical application, AIMD simulation of core-excited BF(3) (B1s --> 2a(2) (')) is illustrated. AIMD simulation leads to the change of vibrational motion as well as structural deformation by core-excitation. The c-WT analysis clarifies the relationship between structural deformation and the related significant vibrational modes in core-excitation within 50 fs.     

Maximum overlap symmetry molecular orbitals in conjugated systems

The application of the maximum overlap symmetry orbital (MOSO) method to conjugated systems is discussed briefly. The MOSO method can be employed to construct not only the symmetry orbitals and the molecular orbitais in alternant conjugated systems, but also the symmetry orbitais in non-alternant systems. It is shown that under the Hückel approximation the matrix MM⁺ can be written out directly from the molecular skeleton and may be treated by using chemical graph theory. Because the matrix MM⁺ of a system can be regarded as the Huckel matrix of a smaller system, the maximum overlap symmetry molecular orbital (MOSMO) calculation results can be easily obtained from those of the smaller systems. For homonuclear conjugated systems and for systems in which two kinds of atom appear altemantly, the MOSMOs and the corresponding molecular orbital (MO) energies obtained by the MOSMO calculation are the same as the MOs and the MO energies calculated by the Hückel molecular orbital method.     

计算化学在分子轨道教学中的应用

分子轨道理论是理解分子电子结构与微观性质的重要理论之一,也是本科生与研究生结构化学教学中的重点与难点。学生对原子轨道组合形成分子轨道、分子轨道能级交叉混合等知识的理解缺乏形象直观、定量的认识。本文通过基于量子化学或密度泛函理论的Gaussian 03计算软件,计算、绘制并分析了F_2、O_2、N_2、HF、CO等的分子轨道能级图,将学生较难理解的内容定量、直观地呈现出来,形象地解释了分子轨道成键原则与电子填充原则等分子轨道理论中的重难点,加深了学生对分子轨道理论的理解,特别是sp轨道混杂导致的σ_(2p_z)与π_(2p)轨道能级交叉这一难点,激发了学生学习的主动性和积极性,提高了教学质量。在此基础上,利用分子轨道理论分析了CO_2的电子结构,使学生学会应用分子轨道理论解决实际问题,巩固了相关课堂理论知识。     

Is a radical bridge a route to strong exchange interactions in lanthanide complexes? A computational examination

The origin of very strong antiferromagnetic exchange in N(2)(3-) bridged complex, [{[(Me(3)Si)(2)N](2)Gd(THF)}(2)(μ-η(2):η(2)-N(2))](-) (1) has been probed using density functional theory (DFT) combined with molecular orbital (MO) and natural bond orbital (NBO) analysis. The analysis helps us to propose a generic mechanism of coupling for a {2p-4f} class of compounds.     

Relationship between the biological potency of polychlorinated dibenzo-p-dioxins and their electronic states.

The molecular orbital (MO) method, as one approach explaining the structure-activity of polychlorinated dibenzo-p-dioxins (PCDDs), was used to understand the relationship between the biological activities and electronic state or highest occupied molecular orbital (homo) phase symmetry of PCDDs. The structure-activity relationship of PCDDs could be explained by the difference between the homo and lowest unoccupied molecular orbital (lumo) energy levels (delta epsilon: difference of epsilon homo and epsilon lumo) which indicates orbital mixing with other molecules. The magnitude of biological activity was consistent with the following order: 2,3,7,8-tetraCDD greater than 1,2,3,7,8-pentaCDD greater than 1,2,3,7,8,9-hexaCDD greater than 2,3,7-triCDD greater than 2,8-diCDD, with the order of decreasing delta epsilon by Hückel MO calculation. Our method can also estimate a magnitude of biological activity for PCDDs. The structure requirement for high toxicity suggested that the electronic states of PCDDs showed a small value difference (delta epsilon) and S1S2 phase symmetry on the homo for PCDDs. These results indicate that the electron states of PCDDs, which are based on the binding interaction of PCDDs to a cytosolic Ah receptor, play an important role in the appearance of their activity.     

Theories of the chemical bond and its true nature

Two different models for chemical bond were developed almost simultaneously after the Schrödinger formulation of quantum theory. These are known as the valence bond (VB) and molecular orbital (MO) theories. Initially chemists preferred the VB theory and ignored the MO theory. Now the VB theory is almost dropped out of currency. The context of discovery and Linus Pauling’s overpowering influence gave the VB theory its initial advantage. The current universal acceptance of the MO theory is due to its ability to provide direct interpretation of many different types of experiments now being pursued. In current research both localized bonds and delocalized charge distributions play important roles and the MO theory has been successful in giving a good account of both.     

Orbital symmetry,orbital stability,and orbital pairing rules for organic reactions in the ground state

A generalization of the Hartree–Fock molecular orbital (MO) theory for treating diradical intermediates was explained pictorially by drawing molecular orbitals of diradical species such as ring-opened trimethylene. The generalized MO theory applied to elucidate electronic mechanisms of concerted, ionic, radical, and ion-radical reactions of organic reactants in the ground state. Generalized MO computations revealed the most essential characteristics of these reactions and mutal relationships between the worlds of Woodward–Hoffmann and Hughes–Ingold. Generalized MO studies supported our orbital symmetry, stability and pairing rules for concerted, ionic and radical reactions in the ground state, respectively. An extension of MO treatments to excited states reactions was briefly pointed out in relation to the density and spin correlation functions by the multireference CI wave functions.     

Calculations of the optical spectra of hydrocarbon radical cations based on Koopmans' theorem

The first few bands in the optical spectra of radical cations can often be interpreted in terms of A-type transitions that involve electron promotions from doubly occupied to the singly occupied molecular orbital (SOMO) and/or B-type transition which involve electron promotion from the SOMO to virtual molecular orbitals. We had previously demonstrated that, by making use of Koopmans' theorem, the energies of A-type transitions can be related to orbital energy differences between lower occupied MOs and the highest occupied MO (HOMO) in the neutral molecule, calculated at the geometry of the radical cation. We now propose that the energies of B-type transitions can be related similarly to energy differences between the lowest unoccupied MO (LUMO) and higher virtual MOs in the dication, also calculated at the geometry of the radical cation, by way of an extension of Koopmans' theorem to virtual MOs similar to that used sometimes to model resonances in electron scattering experiments. The optical spectra of the radical cations of several polyenes and aromatic compounds, the matrix spectra of which are known (or presented here for the first time), and for which CASSCF/CASPT2 calculations are available, are discussed in terms of these Koopmans-based models. Then the spectra of five poly(bicycloalkyl)-protected systems and that of hexabenzocoronene, compounds not amenable to higher level calculations, are examined and it is found that the Koopmans-type calculations allow a satisfactory interpretation of most of the features in these spectra. These simple calculations therefore provide a computationally inexpensive yet effective way to assign optical transitions in radical ions. Limitations of the model are discussed.     

An optimum strategy for solution chemistry using semiempirical molecular orbital method: Importance of description of charge distribution

For the purpose to execute direct dynamics calculation in solution chemistry, we propose an optimum strategy for solution chemistry using semiempirical molecular orbital (MO) method with neglect of diatomic differential overlap (NDDO) approximation with specific solution reaction parameters (SSRP), i.e., the NDDO‐SSRP method. In this strategy, the empirical parameters of the semi‐empirical MO method were optimized individually for target molecule or ion by reference to the ab initio MO calculation data for many configurations on the potential energy surface near the reaction path. For demonstration, the NDDO‐SSRP method was applied to two molecules and two ions (OH^?, H₂O, NH₃, NH₄⁺) at their equilibrium states in aqueous solution, respectively. Accordingly, it was verified that both the potential energy surface and the charge distribution of these solutes in aqueous solution are dramatically improved to reproduce themselves accurately at ab initio MO calculation level. In conclusion, it is expected that the NDDO‐SSRP method should become quite useful for dynamic and statistical applications to chemical reaction systems in solution. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Simultaneous determination of nuclear and electronic wave functions without Born–Oppenheimer approximation: Ab initio NO+MO/HF theory

We develop a simultaneous determination method of nuclear and electronic wave functions without the Born–Oppenheimer approximation. We examine two expanding methods, namely, molecular orbital (MO)-type and valence bond (VB)-type expansions for a nuclear orbital, which is a one-particle wave function of a nucleus. The VB-type expansion is shown to be more accurate than the MO-type one because of the local nature of the nuclei. We also investigate the basis function expansion of the nuclear orbital and propose a scheme to determine the orbital exponent for the nuclear basis function. Numerical calculations confirm the accuracy and feasibility of the present method. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Ab initio calculation of the electronic structure of the [Co(CN)6]3− ion

Ab initio LCAO SCF MO calculations were carried out on the ion [Co(CN)₆]^3? with double-zeta type wavefunctions. The results showed differences with previous semi-empirical calculations in the relative energy level of the mainly metal-dπ molecular orbital and in other respects.     

Band deconvolution analysis of the absorption and magnetic circular dichroism spectral data of a planar phthalocyanine dimer

The electronic absorption and magnetic circular dichroism spectral data of a phthalocyanine dicopper complex that is deduced to be very planar and to share a common benzene ring have been studied by band deconvolution analysis. The results were compared with those of the molecular orbital (MO) calculations within the framework of the Pariser-Parr-Pople (PPP) approximation. The results of the band deconvolution analysis are in good agreement with those of the PPP calculations, allowing many bands to be reasonably assigned on the basis of the MO calculations. The validity of the PPP method for the MO calculation of large molecules is also emphasized.     

Density functional theory investigation of the polarizability and second hyperpolarizability of polydiacetylene and polybutatriene chains: treatment of exact exchange and role of correlation

The static polarizability and second hyperpolarizability of increasingly large polydiacetylene and polybutatriene (PBT) chains have been evaluated using the optimized effective potential for exact exchange (OEP-EXX) method developed by Yang and Wu [Phys. Rev. Lett. 89, 143002 (2002)], where the unknown part of the effective potential is expressed as a linear combination of Gaussian functions. Various conventional atomic orbital basis sets were employed for the exchange potential (X basis) as well as for the Kohn-Sham orbitals [molecular orbital (MO) basis]. Our results were compared to coupled-perturbed Hartree-Fock (CPHF) calculations and to ab initio correlated values obtained at various levels of approximation. It turns out that (a) small conventional basis sets are, in general, unsatisfactory for the X basis; (b) the performance of a given X basis depends on the MO basis and is generally improved when using a larger MO basis; (c) these effects are exaggerated for the second hyperpolarizability compared to the polarizability; (d) except for the second hyperpolarizability of PBT chains, using 6-311++G** for the X basis gives reasonable agreement with the CPHF results for all MO basis sets; (e) our results suggest that in the limit of a complete X basis the OEP-EXX values may approach the CPHF data; and (f) in general, the quality of a given conventional X basis degrades with the length of the oligomer, which correlates with the fact that the number of X basis functions becomes a smaller fraction of the number required to reproduce exactly the finite-basis-set Hartree-Fock energies. Linear and especially nonlinear electric field responses constitute a very stringent test for assessing the quality of functionals and potentials; appropriately tailored basis sets are needed to describe the latter. Finally, this study further highlights the importance of electron correlation effects on linear and nonlinear responses, for which correlated functionals with OEP are required.     

Ab initio molecular dynamics with discrete variable representation basis sets: techniques and application to liquid water

Finite temperature ab initio molecular dynamics (AIMD), in which forces are obtained from "on-the-fly" electronic structure calculations, is a widely used technique for studying structural and dynamical properties of chemically active systems. Recently, we introduced an AIMD scheme based on discrete variable representation (DVR) basis sets, which was shown to have improved convergence properties over the conventional plane wave (PW) basis set [Liu,Y.; et al. Phys. Rev. B 2003, 68, 125110]. In the present work, the numerical algorithms for the DVR based AIMD scheme (DVR/AIMD) are provided in detail, and the latest developments of the approach are presented. The accuracy and stability of the current implementation of the DVR/AIMD scheme are tested by performing a simulation of liquid water at ambient conditions. The structural information obtained from the present work is in good agreement with the result of recent AIMD simulations with a PW basis set (PW/AIMD). Advantages of using the DVR/AIMD scheme over the PW/AIMD method are discussed. In particular, it is shown that a DVR/AIMD simulation of liquid water in the complete basis set limit is possible with a relatively small number of grid points.     

Molecular orbital study of anthracene photo-oxidation

The light stimulated interaction of anthracene and oxygen was studied by the MO (molecular orbital) method. Using the principle of orbital symmetry conservation, the interactions anthracene-oxygen in the ground and first excited states and in various geometric arrangements were classified as symmetry allowed or forbidden. The results indicate that the photo-oxidation of anthracene is catalysed by transition metals.     

The calculation of molar polarizabilities by the CNDO/2 method: Correlation with the hydrophobic parameter,log P

Results of molecular orbital (MO) calculations by the complete neglect of differential overlap (CNDO /2) method on 50 small molecules are reported. The summation of calculated atomic polarizabilities are equated with molecular polarizabilities, and these are compared with experimentally determined values. It is found that there is very good agreement between calculated and experimental molecular polarizability. This provides a reliable method for the determination of molecular polarizabilities for compounds for which experimental values are not known. The relationship between log P and polarizability is discussed and analyzed in terms of contributions from electronic components to the partitioning energy.     

An atomic orbital-based reformulation of energy gradients in second-order Møller-Plesset perturbation theory

A fully atomic orbital (AO)-based reformulation of second-order M?ller-Plesset perturbation theory (MP2) energy gradients is introduced, which provides the basis for reducing the computational scaling with the molecular size from the fifth power to linear. Our formulation avoids any transformation between the AO and the molecular orbital (MO) basis and employs pseudodensity matrices similar to the AO-MP2 energy expressions within the Laplace scheme for energies. The explicit computation of perturbed one-particle density matrices emerging in the new AO-based gradient expression is avoided by reformulating the Z-vector method of Handy and Schaefer [J. Chem. Phys. 81, 5031 (1984)] within a density matrix-based scheme.