MRCI+Q study of the low-lying electronic states of CdF including spin-orbit coupling

Cd F molecule, which plays an important role in a great variety of research fields, has long been subject to numerous researchers. Due to the unstable nature and heavy atom Cd containing in the Cd F molecule, electronic states of the molecule have not been well studied. In this paper, high accurate ab initio calculations on the Cd F molecule have been performed at the multi-reference configuration interaction level including Davidson correction(MRCI + Q). Adiabatic potential energy curves(PECs) of the 14 low-lying Λ–S states correlating with the two lowest dissociation limits Cd(~1S_g) + F(~2P_u) and Cd(~3P_u) + F(~2P_u) have been constructed. For the bound Λ–S and ? states, the dominant electronic configurations and spectroscopic constants are obtained,and the calculated spectroscopic constants of bound states are consistent with previous experimental results. The dipole moments(DMs) of 2 Σ+ and 2Π are determined, and the spin–orbit(SO) matrix elements between each pair of X2Σ+, 22Σ+, 12Π, and 22Π are obtained. The results indicate that the sudden changes of DMs and SO matrix elements arise from the variation of the electronic configurations around the avoided crossing region. Moreover,the Franck–Condon factors(FCFs), the transition dipole moments(TDMs), and radiative lifetimes of low-lying states-the ground state X2Σ+are determined. Finally, the transitional properties of 22Π–X2Σ+and 22Σ+–X2Σ+are studied. Based on our computed spectroscopic information of Cd F, the feasibility and challenge for laser cooling of Cd F molecule are discussed.     

Accurate ab initio study of low-lying electronic states of phosphorus nitride radical

This paper employs the highly accurate valence internally contracted multireference configuration interaction method to investigate the potential energy curves (PECs) for the ground state (X 1 Σ +) and two low-lying excited states (A 1 Π and D 1 of phosphorus nitride (PN) radical with the correlation-consistent basis set,aug-cc-pV6Z,in the valence range.Relativistic effects are considered in these calculations.The spectroscopic constants of the X 1 Σ + and A 1 Π states are calculated based on the PECs,and the results are in good accord with the available experimental data.The first 30 vibrational states for the X 1 Σ + state and the first 40 vibrational states for theA 1 Π state are determined when J=0.For each vibrational state,molecular constants G(υ),B(υ) and D(υ) are also attained.     

Ab initio MRCI＋Q study on potential energy curves and spectroscopic parameters of low-lying electronic states of CS＋

Carbon monosulfide molecular ion （CS＋）, which plays an important role in various research fields, has long been attracting much interest. Because of the unstable and transient nature of CS＋, its electronic states have not been well investigated. In this paper, the electronic states of CS＋ are studied by employing the internally contracted multireference configuration interaction method, and taking into account relativistic effects （scalar plus spin–orbit coupling）. The spin–orbit coupling effects are considered via the state-interacting method with the full Breit–Pauli Hamiltonian. The potential energy curves of 18 Λ–S states correlated with the two lowest dissociation limits of CS＋ molecular ion are calculated, and those of 10 lowest Ω states generated from the 6 lowest Λ–S states are also worked out. The spectroscopic constants of the bound states are evaluated, and they are in good agreement with available experimental results and theoretical values. With the aid of analysis of Λ–S composition of Ω states at different bond lengths, the avoided crossing phenomena in the electronic states of CS＋ are illuminated. Finally, the single ionization spectra of CS （X1Σ＋） populating the CS＋（X2Σ1/2＋, A2Π3/2, A2Π1/2, and B2Σ1/2＋） states are simulated. The vertical ionization potentials for X2Σ1/2＋, A2Π3/2, A2Π1/2, and B2Σ1/2＋ states are calculated to be 11.257, 12.787, 12.827, and 15.860 eV, respectively, which are accurate compared with previous experimental results, within an error margin of 0.08 eV~0.2 eV.     

SbS电子基态及激发态势能曲线和振动能级的理论研究

运用多参考组态相互作用(MRCI+Q)方法,对硫化锑(SbS)能量最低的3个?-S离解极限的所有电子态以及考虑自旋-轨道耦合效应后分裂所得的Ω态进行了计算.得到27个?-S电子态及能量最低的12个Ω态的电子结构、光谱常数和振动能级等信息. Sb原子和S原子能级的计算值与实验值相符很好.分析表明自旋-轨道耦合效应对光谱常数与振动能级的影响总体上并不显著.对X(3/2)→X(1/2), 2(1/2)→X(1/2), 4(1/2)→X(1/2), 5(1/2)→X(1/2)及6(1/2)→X(1/2)跃迁的振动光谱进行了模拟与分析,其中X(3/2)→X(1/2)谱带位于中红外波段,其他谱带均位于可见光波段.此外,对氮族元素硫化物的电子态进行了验证计算,计算结果与已有实验结果吻合较好,体现了同族元素代换后相关物性的渐变规律性.     

BeCl分子电子激发态的多参考组态相互作用计算

运用含Davidson修正的多参考组态相互作用方法,在aug-cc-pVTZ基组水平上,对BeCl分子基态和相同多重度的几个低电子激发态进行了势能扫描计算.通过群论原理确定各电子态对称性及离解极限.将其中基态(X²Σ⁺)和第一激发态(A²Π})对应的势能曲线拟合到Murrell-Sorbie解析势能函数形式,得到基态(X²Σ⁺)的离解能及主要光谱常数(括号中为文献[6]提供的实验值)为D_e=3.74eV,R_e=0.18173nm(0.17970),w_e=857.4cm¹(847.2),w_ex_e=5.03cm^-1(5.14),B_e=0.7103cm^-1(0.7285),α_e=0.0059cm^-1(0.0069),第一激发态(A²Π)的D_e=3.02eV,R_e=0.18369nm(0.18211),w_e=832.7cm^-1(822.1),w_ex_e=5.93cm^-1(5.24),B_e=0.6953cm^-1(0.7094),α_e=0.0065cm^-1(0.0068),计算结果与实验值符合得较好.另外,通过Level程序求解双原子径向核运动的Schrödinger方程得到J=0时BeCl分子这两个电子态的全部振动能级.     

BP+基态和激发态的势能曲线和光谱性质的研究

本文利用量子化学中的多参考组态相互作用方法(MRCI), 在aug-cc-pVQZ级别计算了在环境科学中具有重要作用的离子BP⁺. 得到了对应三个离解极限B⁺(¹S_g)+P(⁴S_u), B⁺(¹S_g)+P(²D_u)以及B⁺(¹S_g)+P(²P_u)的6个Λ-S态势能曲线. 在计算中还考虑了Davidson修正(+Q)和标量相对论效应, 用以提高计算精度. 通过分析Λ-S态的电子结构, 确认了电子态的多组态特性. 计算中首次纳入了旋轨耦合效应, 获得了由BP⁺离子的6个Λ-S态分裂出的10个Ω 态的势能曲线. 计算得到的势能曲线表明相同对称性的Ω 态的势能曲线存在着明显的避免交叉. 在得到的Λ-S态和Ω 态的势能曲线的基础上, 运用LEVEL8.0程序通过求解核径向的Schrödinger 方程, 得到了相应的Λ-S态和Ω 态的光谱常数T_e, R_e, ω_e, ω_eχ_e, B_e和D_e, 其中基态X⁴∑^-的光谱常数与已有的理论值符合的非常好, 文中其他电子态的光谱常数均为首次报道. 关键词： 多参考组态相互作用方法(MRCI) 势能曲线 光谱常数 旋轨耦合效应     

多参考组态相互作用方法研究BS+离子的势能曲线和光谱性质

利用量子化学从头计算方法MRCI+Q在AVQZ级别上对BS⁺离子进行了研究. 通过计算得到了与BS⁺离解极限B⁺（¹S_g）+S（³P_g）和B⁺（¹S_g）+S（¹D）对应的5个Λ-S态,确认了BS⁺离子的基态为X³∏电子态,而第一激发态¹∑⁺的激发能T_e仅仅为564.53 cm^-1. 首次纳入的旋轨耦合效应（SOC）使得BS⁺的5个Λ-S态分裂成为9个Ω态,原有的两个离解极限分裂为B⁺（¹S₀）+S（³P₂）,B⁺（¹S₀）+S（³P₁）,B⁺（¹S₀）+（³P₁）以及B⁺（¹S₀）+S（¹D₂）. 在考虑自旋轨道耦合效应之后,Ω态的基态为X2态. 通过势能曲线（PECs）可以发现所得到的Λ-S态和Ω态均为束缚态,利用LEVEL8.0程序拟合得到了对应电子态的光谱常数,这些结果可以为实验和理论方面进一步研究BS⁺的光谱性质提供准确的电子结构信息. 关键词： 势能曲线 光谱参数 多参考组态相互作用方法 Q)')" href="#">Davidson修正(+Q)     

Highly accurate theoretical study on spectroscopic properties of SH including spin–orbit coupling

The multi-reference configuration interaction method plus Davidson correction(MRCI+Q) are adopted to study the low-lying states of SH with consideration of scalar relativistic effect, core-valence(CV) electron correlation, and spin–orbit coupling(SOC) effect. The SOC effect on the low-lying states is considered by utilizing the full Breit–Pauli operator. The potential energy curves(PECs) of 10 Λ–S states and 18 ? states are calculated. The dipole moments of 10 Λ–S states are calculated, and the variation along the internuclear distance is explained by the electronic configurations. With the help of calculated SO matrix elements, the possible predissociation channels of A~2Σ+, c4Σ-and F~2Σ-are discussed. The Franck–Condon factors of A~2Σ~+–X~2Π, F~2Σ~-–X~2Π and E~2Σ~+–X~2Π transitions are determined, and the radiative lifetimes of A~2Σ+and F~2Σ-states are evaluated, which are in good agreement with previous experimental results.     

Configuration interaction study on low-lying states of AlCl molecule

High-level ab initio calculations of the Λ–S states for aluminum monoiodide(Al Cl) molecule are performed by utilizing the explicitly correlated multireference configuration interaction(MRCI-F12) method. The Davidson correction and scalar relativistic correction are investigated in the calculations. Based on the calculation by the MRCI-F12 method, the spin–orbit coupling(SOC) effect is investigated with the state-interacting technique. The adiabatic potential energy curves(PECs) of the 13 Λ–S states and 24 Ω states are calculated. The spectroscopic constants of bound states are determined,which are in accordance with the results of the available experimental and theoretical studies. Finally, the transition properties of 0~+(2)–X0~+, 1(1)–X0~+, and 1(2)–X0~+ transitions are predicted, including the transition dipole moments(TDMs),Franck–Condon factors(FCFs), and the spontaneous radiative lifetimes.     

SiH自由基分子激发态的多参考组态相互作用计算简

运用含Davidson修正的多参考组态相互作用(MRCI+Q)方法,在def2-qzvpp基组水平上对SiH自由基分子对应最低三个离解限Si(3 P,1 D,1 S)+H(2 S)的共6个双重态X2Π,A2Δ,B2∑-,C2∑+,D2∑+,F2Π和2个四重态a4∑-,b4 P在0.1nm~0.6nm范围内进行了势能扫描计算.得出X2Π,A2Δ和a4∑-态为典型的束缚态,其离解能分别为3.17eV,0.96eV和1.49eV,平衡核间距分别为0.1523nm,0.1533nm和0.1499nm.其中B2∑-态在接近基态平衡核间距处与A2Δ态极为靠近,且在R=0.1764nm与A2Δ态发生交叉,导致SiH最主要的电子激发跃迁A2Δ-X2Π中仅主要观测到(0-0)带,这与实验结果完全一致.C2∑+和D2∑+态在R=0.1799nm处发生由于对称性相同而出现回避交叉.对于束缚态X2Π,A2Δ,D2∑+和a4∑-,数值求解核运动的径向Schrdinger方程预测出各电子态所有可能的振动能级和转动常数,进而拟合得到的光谱常数与已有的实验数据符合较好.     

An ab initio investigation of the low-lying electronic states of Bell

Potential energy curves （PECs） for the ground state （X2∑＋） and the four excited electronic states （A2∏, B2∏, C2∑＋, 4∏） of a Bell molecule are calculated using the multi-configuration reference single and double excited configuration interaction （MRCI） approach in combination with the aug-cc-pVTZ basis sets. The calculation covers the internuclear distance ranging from 0.07 nm to 0.70 nm, and the equilibrium bond length Re and the vertical excited energy Te are determined directly. It is evident that the X2∑＋, A2∏, B2∏, C2∑＋ states are bound and 4∏ is a repulsive excited state. With the potentials, all of the vibrational levels and inertial rotation constants are predicted when the rotational quantum number J is set to be equal to zero （J = 0） by numerically solving the radial SchrSdinger equation of nuclear motion. Then the spectroscopic data are obtained including the rotation coupling constant w e, the anharmonic constant WeXe, the equilibrium rotation constant Be, and the vibration-rotation coupling constant ae. These values are compared with the theoretical and experimental results currently available, showing that they are in agreement with each other.     

Low-lying electronic states of CuN calculated by MRCI method

The high accuracy ab initio calculation method of multi-reference configuration interaction(MRCI) is used to compute the low-lying eight electronic states of CuN.The potential energy curves(PECs) of the X~3∑~-,1~3Π,2~3∑~-,1~3△,1~1△,1~1∑~-,1~1Π,and ~5∑~- in a range of R=0.1 nm-0.5 nm are obtained and they are goodly asymptotes to the Cu(~2S_g) + N(~4S_u) and Cu(~2S_g)+N(~2D_u) dissociation limits.All the possible vibrational levels,rotational constants,and spectral constants for the six bound states of X~3∑~-,1~3Π,2~3∑~-,1~1△,1~1∑~-,and 1~1 Π are obtained by solving the radial Schrdinger equation of nuclear motion with the Le Roy provided Level 8.0 program.Also the transition dipole moments from the ground state X~3∑~- to the excited states 1~3Π and 2~3∑~- are calculated and the result indicates that the 2~3∑-X~3∑ transition has a much higher transition dipole moment than the 1~3Π-X~3∑~- transition even though the l~3Π state is much lower in energy than the 2~3∑~- state.     

从头计算研究BCl+基态和激发态的势能曲线和光谱性质

基于相关一致极化4zeta(aug-cc-pVQZ)基组, 应用量子化学从头计算中高水平的多参考组态相互作用方法计算了BCl⁺ 两个离解极限B⁺(¹S_g)+Cl(²P_u)和B (²P_u)+Cl⁺ (³P_g)的14个Λ-S态势能曲线. 在计算中考虑了Davidson修正(+Q)和标量相对论效应, 并首次在计算中考虑了BCl⁺ 的旋轨耦合效应, 获得了由能量最低的4个Λ-S态分裂出的7个Ω 态. 计算结果表明相同对称性的Ω 态的势能曲线存在着非常明显的避免交叉. 通过分析Λ-S态的电子结构, 得到了各态的电子跃迁特性, 并确认了电子态的多组态性质. 使用LEVEL程序通过求解径向的Schrödinger方程得到了束缚Λ-S 和Ω态的光谱参数D_e, R_e, T_e, ω_e, ω_eχ_e和B_e. 通过和已有的Λ-S态X²∑⁺ 的实验数据进行对比发现, 本文所得的计算结果与实验结果非常一致. 而文中其他电子态的光谱参数均为首次报道. 关键词： 势能曲线 光谱参数 多参考组态相互作用方法 旋轨耦合     

BeF~+离子电子态的光谱常数研究

采用从头计算方法(Ab)研究BeF~+离子的光谱性质.在icMRCI+Q/Q5+CV+DK的理论水平下计算得到了BeF~+离子的16个态的势能曲线,为了提高精确度,对势能曲线进行核价相关修正及相对论修正两种修正计算,画出了16个态的势能曲线图.拟合势能曲线得到其光谱常数(D_e,T_e,R_e,ω_e,ω_ex_e,ω_ey_e,B_e,α_e和β_e).分别计算了各个振动态对应的的振动能级.     

Theoretical study of potential energy curves,spectroscopic constants,and radiative lifetimes of low-lying states in an SeO molecule

<正>The low-lying potential energy curves of the SeO molecule are computed by means of an ab initio multireference configuration interaction technique,taking into account relativistic(scalar plus spin-orbit coupling) effects.The spectroscopic constants ofΩstates for X~3∑~-,a~1△,b~1∑~+,A~3Π,A′~3△,and A″~3∑~+ states are obtained,and they are in good accordance with available experimental values.The Franck-Condon factors and transition dipole moments to the ground state are computed,and the natural radiative lifetimes of low-lyingΩstates are theoretically obtained. Comparisons of the natural lifetimes ofΩstates with previous experimental results and those of isovalent TeO molecule are made.     

An ab initio investigation of the low-lying electronic states of BeH

Potential energy curves(PECs) for the ground state(X 2 Σ +) and the four excited electronic states(A 2 Π,B 2 Π,C 2 Σ +,4 Π) of a BeH molecule are calculated using the multi-configuration reference single and double excited configuration interaction(MRCI) approach in combination with the aug-cc-pVTZ basis sets.The calculation covers the internuclear distance ranging from 0.07 nm to 0.70 nm,and the equilibrium bond length R e and the vertical excited energy T e are determined directly.It is evident that the X2Σ+,A2Π,B2Π,C2Σ+ states are bound and 4Π is a repulsive excited state.With the potentials,all of the vibrational levels and inertial rotation constants are predicted when the rotational quantum number J is set to be equal to zero(J = 0) by numerically solving the radial Schr¨odinger equation of nuclear motion.Then the spectroscopic data are obtained including the rotation coupling constant ω e,the anharmonic constant ωexe,the equilibrium rotation constant Be,and the vibration-rotation coupling constant αe.These values are compared with the theoretical and experimental results currently available,showing that they are in agreement with each other.     

Theoretical study of potential energy curves,spectroscopic constants,and radiative lifetimes of low-lying states in SeO molecule

The low-lying potential energy curves of SeO molecule are computed by means of ab initio multireference configuration interaction technique, taking into account relativistic (scalar plus spin-orbit coupling) effects. The spectroscopic constants of Ω states for X³Σ^-, a¹Δ, b¹Σ⁺, A³Π, A'³Δ, and A"³Σ⁺ states are obtained, and they are in good accordance with available experimental values. The Franck-Condon factors and transition dipole moments to the ground state are computed, and the natural radiative lifetimes of low-lying Ω states are theoretically obtained. Comparisons of the natural lifetimes of Ω states with previous experimental results and those of isovalent TeO molecule are made.     

从头计算研究BP分子的势能曲线和光谱性质

利用高精度的量子化学从头计算MRCI+Q方法结合相关一致aug-cc-pVQZ基组计算了磷化硼分子X3Π,3Σ-,5Π和5Σ-态的势能曲线,计算所得的电子态在大键长位置处收敛于同一个离解极限B(2Pu)+P(4Su).为了得到更精确的结果,计算中首次纳入了旋轨耦合(SOC)效应,使得BP分子的4个Λ-S态分裂成为15个Ω态,其中3Π0+态被确定为基态.此外,SOC效应还使两个三重态X3Π和3Σ-分裂出的0+和1态的势能曲线产生了避免交叉,表明在当前的计算中考虑SOC效应是非常必要的.利用LEVEL8.0程序对计算所得的Λ-S态和Ω态的势能曲线进行拟合,得到了相应的光谱常数,通过与其他理论和实验工作进行比较,可知我们的结果更加精确、完整,可以为实验和理论方面进一步研究BP分子的光谱性质提供可靠的参考.     

GeS分子基态和低激发态的势能曲线与光谱性质

本文以aug-cc-pv5Z为基组, 采用考虑Davidson修正的多参考组态相互作用方法(MRCI+Q)得到了GeS分子基态(X¹Σ⁺)和5个低激发态(1¹Σ, 1¹Δ, A¹Π, 1⁵Σ⁺, 2⁵Σ⁺)的势能曲线. 计算结果表明: 2⁵Σ⁺态为排斥态, 其余5个态为束缚态; 6个态有着共同的离解通道, 离解极限均为Ge(³P)+S(³P). 利用计算得到的势能曲线得了X¹Σ⁺, 1¹Σ^-, 1¹Δ, A¹Π和1⁵Σ⁺态的垂直跃迁能T_e, 平衡键长R_e, 离解能D_e, 谐振频率ω_e, 非谐性常数ω_ex_e及平衡位置的电偶极矩. X¹Σ⁺态的R_e 为2.034 Å, D_e 为5.728 eV, ω_e为571.73 cm^-1, ω_ex_e为1.6816 cm^-1, 平衡位置的电偶极矩为1.9593 Debye. 激发态1¹Σ, 1¹Δ, A¹Π, 1⁵Σ⁺的T_e 依次为25904.81, 26209.22, 32601.19, 43770.26 cm^-1; R_e依次为2.313, 2.322, 2.188, 2.8790 Å; D_e依次为2.524, 2.487, 1.694, 0.3036 eV, ω_e依次为358.90, 353.08, 376.32, 134.96 cm^-1; ω_ex_e依次为1.2421, 1.2151, 1.6608, 1.9095 cm^-1; 平衡位置的电偶极矩依次为1.3178, 1.4719, 1.5917, -1.9785 Debye. 通过求解核运动的薛定谔方程得到了J=0时X¹Σ⁺, 1¹Σ^-, 1¹Δ, A¹Π和1⁵Σ⁺态前30个振动态的振动能级G_v和分子常数B_v, 得到的结果和已有的实验值及其他理论值符合较好.     

LiC分子基态及其低电子激发态的多参考组态相互作用方法研究

采用包含Davidson修正的多参考组态相互作用(MRCI+Q)方法结合6-311++G(3df,3pd)基组计算了LiC分子基态(X4Σ-)以及五个低电子激发态(a2Π,b2Δ,c2Σ-,d2Σ+,A4Π)的势能曲线.将得到的势能曲线拟合到Murrell-Sorbie解析势能函数形式,确定了对应态的平衡结构Re、谐振频率ωe和离解能De等光谱数据,计算值与仅有的几个其他结果进行了比较.通过求解核运动的薛定谔方程首次报道了LiC分子几个低电子态在J=0下的振动能级、转动惯量和六个离心畸变常数(Dν,Hν,Lν,Mν,Nν和Oν).