过渡金属体系非线性光学性质计算的ECP基组研究

有效核势(ECP)方法是计算含有过渡金属体系的电子结构及物理性质的有效方法. 本文比较了一系列典型的ECP基组对计算含过渡金属体系非线性光学性质精度的影响. 分别在HF, MP2和DFT理论水平上对过渡金属元素使用不同的ECP基组, 计算了几个过渡金属有机化合物的静态一阶超极化率β₀. 研究结果表明: 使用有效核势计算含过渡金属体系时, 核电子的选取是提高计算精度的前提, ns和np电子应该和nd电子一同作为价电子处理; 对于重原子, 必须考虑自旋-轨道耦合相对论效应. 经过综合评估, 认为使用Stuttgart/Dresden赝势的ECP基组, MHF, 在计算含有过渡金属体系非线性光学性质方面是比较好的基组; Stuttgart RSC 1997和SBKJC VDZ相对而言是较好的基组; 基组Lanl2dz, Hay-Wadt MB (n＋1)和Hay-Wadt VDZ (n＋1)由于没有考虑自旋-轨道耦合, 计算精确度次之; 而基组CRENBL和CRENBS计算的偏差要大一些, 尤其是CRENBS基组由于价电子选择得太少而导致与实验值的偏差最大.     

Compatibility of correlation‐consistent basis sets with a hybrid Hartree–Fock/density functional method

The present study examines the feasibility of combining the correlation‐consistent basis sets developed by Dunning and coworkers with the hybrid Hartree–Fock/density functional method B3LYP. Furthermore, extrapolation to the complete basis set (CBS) limit minimizes errors due to the presence of an incomplete basis set and can act as a rigorous test of the limitations of the B3LYP method. Equilibrium geometries, energies, and harmonic vibrational frequencies were determined for a series of well‐studied, yet computationally challenging, small inorganics and their respective ions. The results were then extrapolated to the CBS limit, where applicable, and compared to experiment. It was found that a union between the hybrid Hartree–Fock/density functional B3LYP method and Dunning's augmented correlation‐consistent basis sets gave results that were comparable to molecular orbital methods that explicitly account for electron correlation. Furthermore, the minimum basis set necessary to attain reasonable results for the systems studied was aug‐cc‐pVTZ. Upgrading to the aug‐cc‐pVQZ level and subsequent extrapolation to the CBS limit further improved the overall agreement with the experiment. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 207–216, 1999     

Adaptation of one‐electron basis sets to spatial confinements

A method that generates out of a given orbital basis set its analog appropriate for describing the effects of a spatial confinement is presented. The method is based on the requirement that the one‐particle model spaces for the confined and for the unconfined systems are equivalent in the sense of a criterion derived from the basis‐set‐generating eigenvalue equations. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 341–347, 1999     

All‐electron relativistic computations on the low‐lying electronic states,bond length,and vibrational frequency of CeF diatomic molecule with spin–orbit coupling effects

Ab initio all‐electron computations have been carried out for Ce⁺ and CeF, including the electron correlation, scalar relativistic, and spin–orbit coupling effects in a quantitative manner. First, the n‐electron valence state second‐order multireference perturbation theory (NEVPT2) and spin–orbit configuration interaction (SOCI) based on the state‐averaged restricted active space multiconfigurational self‐consistent field (SA‐RASSCF) and state‐averaged complete active space multiconfigurational self‐consistent field (SA‐CASSCF) wavefunctions have been applied to evaluations of the low‐lying energy levels of Ce⁺ with [Xe]4f¹5d¹6s¹ and [Xe]4f¹5d² configurations, to test the accuracy of several all‐electron relativistic basis sets. It is shown that the mixing of quartet and doublet states is essential to reproduce the excitation energies. Then, SA‐RASSCF(CASSCF)/NEVPT2 + SOCI computations with the Sapporo(‐DKH3)‐2012‐QZP basis set were carried out to determine the energy levels of the low‐lying electronic states of CeF. The calculated excitation energies, bond length, and vibrational frequency are shown to be in good agreement with the available experimental data. © 2018 Wiley Periodicals, Inc.     

Substitution effects in the 15N NMR chemical shifts of heterocyclic azines evaluated at the GIAO‐DFT level

A systematic study of the accuracy factors for the computation of ¹⁵N NMR chemical shifts in comparison with available experiment in the series of 72 diverse heterocyclic azines substituted with a classical series of substituents (CH₃, F, Cl, Br, NH₂, OCH₃, SCH₃, COCH₃, CONH₂, COOH, and CN) providing marked electronic σ‐ and π‐electronic effects and strongly affecting ¹⁵N NMR chemical shifts is performed. The best computational scheme for heterocyclic azines at the DFT level was found to be KT3/pcS‐3//pc‐2 (IEF‐PCM). A vast amount of unknown ¹⁵N NMR chemical shifts was predicted using the best computational protocol for substituted heterocyclic azines, especially for trizine, tetrazine, and pentazine where experimental ¹⁵N NMR chemical shifts are almost totally unknown throughout the series. It was found that substitution effects in the classical series of substituents providing typical σ‐ and π‐electronic effects followed the expected trends, as derived from the correlations of experimental and calculated ¹⁵N NMR chemical shifts with Swain–Lupton's F and R constants.     

Gaussian basis sets for first‐, third‐, and fourth‐row positive and negative ions

An improved generator coordinate Hartree–Fock (HF) method is used to generate accurate triple‐optimized Gaussian basis sets for the cations from He⁺ (Z=2) through Ne⁺ (Z=10) and from K⁺ (Z=19) through Xe⁺ (Z=54), and for the anions from H⁻ (Z=1) through F⁻ (Z=9) and from K⁻ (Z=19) through I⁻ (Z=53). For all ions here studied, our ground‐state HF total energies are better than those calculated with the generator coordinate HF method, using optimized Gaussian basis sets of the same size. For all ions studied, the largest difference between our total energy values and the corresponding results obtained with a numerical HF method is equal to 3.434 mhartrees for Te⁺. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 126–130, 2001     

Error and stability analysis of numerical solution for the time fractional nonlinear Schrödinger equation on scattered data of general‐shaped domains

In present work, a kind of spectral meshless radial point interpolation (SMRPI) technique is applied to the time fractional nonlinear Schrödinger equation in regular and irregular domains. The applied approach is based on erudite combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which play as basis functions in the frame of SMRPI. It is proved the scheme is unconditionally stable with respect to the time variable in and also convergent by the order of convergence , . In the current work, the thin plate spline are used as the basis functions and to eliminate the nonlinearity, a simple predictor‐corrector (P‐C) scheme is performed. It is shown that the SMRPI solution, as a complex function, is suitable one for the time fractional nonlinear Schrödinger equation. The results of numerical experiments are compared to analytical solutions to confirm the reliable treatment of these stable solutions. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1043–1069, 2017