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.     

GeO分子激发态的电子结构和跃迁性质的组态相互作用方法研究

应用多参考组态相互作用方法计算了GeO分子的第一解离极限(Ge(³P_g)+O(³P_g))对应的18个Λ-S电子态的电子结构. 计算中纳入了Ge原子的3d轨道电子的内壳层-价壳层电子关联效应、标量相对论效应和Davidson修正. 基于计算的电子态的电子结构, 通过求解径向Schrödinger方程获得了束缚电子态的光谱常数R_e, T_e, ω_e, ω_eχ_e, B_e, 理论计算给出的这些电子态的光谱常数与之前的实验结果符合得很好. 计算了电子态的电偶极矩随核间距的变化, 分析了电子态的组态成分的变化对电偶极矩的影响. 计算的势能曲线表明, 激发态A¹Π, 1¹Σ^-, D¹Δ, a³Π, a’³Σ⁺, d³Δ 和 e³Σ^-的绝热激发能密集地分布于26000-37000 cm^-1范围内, 这些密集分布的电子态之间的相互作用对振动波函数有明显扰动作用. 借助于激发态之间的自旋-轨道耦合矩阵元, 阐明了邻近的激发态对A¹Π和a³Π的扰动作用. 基于计算的A¹Π-X¹Σ⁺和A’¹Σ⁺-X¹Σ⁺跃迁的电偶极跃迁矩和Franck-Condon 因子, 给出了A¹Π 和A’¹Σ⁺态的最低的六个振动能级的辐射寿命.     

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.     

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.     

icMRCI+Q理论研究BF~+离子电子态的光谱性质和预解离机理

采用考虑Davidson修正的内收缩多参考组态相互作用(icMRCI+Q)方法,结合相关一致基组aug-ccpV5Z和aug-cc-pV6Z,计算了BF+离子前两个离解极限B~+(~1S_g)+(~2P_u)和B+(~3P_u)+F(~2P_u)对应的14个Λ-S态(X~2Σ~+,1~2Π,2~2Π,2~2Σ~+,1~4Σ~+,1~4△,1~4Σ~-,1~2△,1~2Σ~-,3~2Σ~+,1~4Π,2~4Π,2~4Σ~+和3~2Π)和30个Ω态的势能曲线.在势能曲线的计算中,考虑了旋轨耦合效应、核价相关和标量相对论修正以及将参考能和相关能分别外推至完全基组极限.基于得到的势能曲线,获得了束缚和准束缚的12个A-S态和28个Ω态的光谱常数,并且X~2Σ~+态的光谱常数与已有的实验结果符合.此外,计算了BF分子X~1Σ~+态到BF+离子X~2Σ~+,1~2Π和2~2Σ~+态的垂直电离势和绝热电离势,并且BF~+(X~2Σ~+)←BF(X~1Σ~+)的垂直电离势和绝热电离势与相应的实验结果非常符合.由X~2Σ~+,2~2Π,1~4Σ~+,3~2Σ~+和3~2Π态和其他的激发A-S态势能曲线的交叉现象,借助于计算的旋轨耦合矩阵元,首次分析了X~2Σ~+和3~2Π态的预解离机理以及2~2Π(v′≥9),1~4Σ~+(v′≥4)和3~2Σ~+(v′≥4)的振动能级受到其他电子态的微扰.计算了30个Ω态离解极限处的相对能量,并且与实验结果十分符合.最后计算了2~2Π(v′=0—9)—X~2Σ~+,2~2Σ~+(v′=0—2)—X~2Σ~+,(3)1/2—(1)1/2~(势阱一)和(2)3/2(v′=0—9)—(1)1/2~(势阱一)跃迁的Franck-Condon因子、爱因斯坦自发辐射系数和辐射寿命.     

一氟化碳电子态的光谱性质和预解离机理的理论研究

采用考虑Davidson修正的内收缩多参考组态相互作用(icMRCI+Q)方法结合相关一致基组aug-cc-pV5Z和aug-cc-pV6Z首次计算了一氟化碳(CF)11个Λ-S 态(X²Π , a⁴Σ^-, A²Σ⁺, B²Δ, 1⁴Π, 1²Σ^-, 2⁴Π, 1^{4}Δ , 1⁴Σ⁺, 2²Σ^-和2⁴Σ^-) 所产生的25个Ω 态的势能曲线. 计算中考虑了旋轨耦合效应、核价相关和标量相对论修正以及将参考能和相关能分别外推至完全基组极限. 基于得到的势能曲线, 获得了束缚和准束缚的Λ-S态和Ω 态的光谱常数, 与已有的实验结果非常符合. 分析了束缚和准束缚的Λ-S态在各自平衡核间距R_e处的主要电子组态. 由于1⁴Π 和2⁴Π态的避免交叉, 发现准束缚态2⁴Π. 由Λ-S态势能曲线的交叉现象, 借助于计算的旋轨耦合矩阵元, 分析了a⁴Σ^-和B²Δ 态的预解离机理. 计算了25个Ω 态的离解关系, 给出了它们的离解极限. 最后研究了A²Σ⁺-X²Π 跃迁特性, 本文计算得到的A²Σ⁺-X²Π跃迁的Frank-Condon 因子和辐射寿命与已有实验值也符合得非常好.     

SiCl自由基X2Π和A2Σ+态的光谱性质

采用内收缩多参考组态相互作用(ic MRCI)方法结合Dunning等相关一致基,计算Si Cl自由基X²Π和A²Σ⁺态的势能曲线.讨论参考能和相关能外推对X²Π和A²Σ⁺态光谱的影响.对势能进行相对论修正及核价修正计算.拟合势能曲线得到X²Π和A²Σ⁺态的光谱常数.它们与实验结果一致.利用Breit-Pauli算符,计算旋轨耦合效应,得到X²Π_1/2和X²Π_3/2的势能曲线、并计算它们的光谱常数.求解双原子分子核运动的径向SchrÖdinger方程,获得无转动SiCl自由基2个Λ-S态及X²Π态的耦合分裂态的全部振动态.得到J=0时X²Π态的自旋-轨道耦合常数、较高振动态的惯性转动常数以及X²Π_1/2和X²Π_3/2的振动能级等分子常数.     

激光冷却OH分子的理论研究

采用高精度的多参考组态相互作用方法计算OH分子基态和第一激发态的势能曲线.为获得更精确的计算结果,在计算过程中考虑Davidson修正、标量相对论效应、核价相关效应和自旋轨道耦合效应.基于计算的Λ-S和?态的势能曲线,对一维径向薛定谔方程进行数值求解,得到各个电子态的光谱数据,与已报道的实验值和理论值相符合.获得OH分子的永久偶极矩、跃迁偶极矩、振动能级、Franck-Condon因子及辐射寿命,结果表明,A~2Σ~+→X~2Π跃迁具有高度对角化的Franck-Condon因子(0.9053)和短的辐射寿命(5.8363×10~(-7)s),符合激光冷却分子的条件.制定了激光冷却OH分子的具体方案,计算得到激光冷却跃迁A~2Σ~+→X~2Π所需的三束激光波长,主光束波长为307.1532 nm,两束重抽运激光波长为344.9163和349.7659 nm.计算结果为超冷OH分子的实验制备提供重要的理论依据.     

LiCl~–阴离子的光谱性质和跃迁性质

采用多参考组态相互作用方法结合全电子基组计算了LiCl~-阴离子5个电子态(X~2Σ~+,A~2Π,B~2Σ~+,3~2Σ~+,2~2Π)的电子结构.为了得到精确的光谱常数,计算中考虑了Davidson修正、芯-价电子关联效应和自旋-轨道稱合效应.拟合得到各电子态的光谱常数、分子常数、自发辐射速率和自发辐射寿命.基态的光谱常数与实验值和其他理论值符合较好,同时报道了LiCl~-阴离子激发态的光谱常数以及其到基态的跃迁性质.计算结果表明A~2Π?X~2Σ~+跃迁具有高对角分布的弗兰克-康登因子f₀₀,第一激发态A~2Π有较短的自发辐射寿命.构造A~2Π(v’)? X~2Σ~+(v")准循环跃迁进行激光冷却LiCl~-阴离子需要一束主激光和两束抽运激光.以上结果预测了激光冷却LiCl~-阴离子是可行的.     

Na_2~+离子较低电子态势能曲线和光谱常数的理论研究

通过多组态相互作用方法,结合原子有效芯势与极化势,利用非收缩的高斯基函数,计算了Na_2~+分子对应最低9个解离限的36个电子态的势能曲线.基于计算获得的束缚态势能曲线,拟合给出了相应的光谱常数,并与已有的实验和理论结果进行了比较.同时,给出了部分电子态的振动-转动能级和一些同类态避免交叉点的信息.计算获得的光谱信息对冷原子分子光谱与动力学的研究具有参考价值.     

~6Li~(32)S双原子分子的光谱和辐射跃迁理论研究

在aug-cc-pV5Z/CASSCF/MRCI水平上讨论了~6Li~(32)S双原子分子的9个较低能量电子态(X~2∏,a~4△,B~2△,b~4△,A~2∑~+,C~2∏,F~2∑~-,E~2∑~+和D~2∏)的势能函数和光谱常数;其中基态平衡核间距、谐振频率、转动常数等均与实验值相符;b~4∏,C~2∏,D~2∏态的平衡核间距均超过了0.4 nm,并且离解能较小,不稳定.D~2∏态是离子对态,离解极限为Li~+(~1S_g)+S~-(~1S_g).预测了最低激发态A~2∑~+跃迁到基态X~2∏的电子跃迁偶极矩、爱因斯坦自发发射系数、弗兰克-康登因子和辐射寿命.     

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)     

An Accurate Calculation of Potential Energy Curves and Transition Dipole Moment for Low-Lying Electronic States of CO

In this paper, potential energy curves for the X 1 Σ+ , a3 Π, a′3 Σ+ , d3 , A1 Π and I 1 Σ states of CO have been calculated using complete active space self-consistent field and multi-reference configuration interaction methods. The calculations have been performed at 108 nuclear separations from 0.7 to 4.0 A by the aug-cc-PV5Z basis set. Spectroscopic constants for the six low-lying electronic states are found in good agreement with experimental data. The vibrational states of the X1Σ+ and A1Π states are also calculated, which are reliable and accurate by comparison with the experimental data and the other theoretical values. The transition dipole moment (TDM) shows that the TDM of the two states (X1Σ + A1Π) are reduced strongly with increase of bond length.     

基于ab initio的BD~+离子激光冷却理论研究

基于相关一致基组aug-cc-pV5Z,采用内收缩多参考组态相互作用方法计算了BD~+离子两个最低解离极限B~+(~1Sg)+D(~2Sg)和B+(~3Pu)+D(~2Sg)对应的5个Λ—S态(X~2Σ~+,A~2Π,B~2Σ+,a~4Π和b~4Σ~+)的势能曲线和跃迁偶极矩.根据计算结果,求解核运动的径向薛定谔方程得到相应电子态的振-转光谱常数、Franck-Condon(F-C)因子和振动能级辐射寿命.其中A~2Π—X~2Σ~+的F-C因子(f_(00)=0.923)、辐射寿命(τ=235 ns)满足激光直接冷却的条件.因此,我们基于分子转动跃迁提出了一个可实现Doppler激光冷却的光循环方案:A~2Π_(1/2)(υ′=0)—X~2Σ+(υ′′=0,1),其中υ′=0中包含2个转动能级,υ′′=0和υ′′=1中分别包含6个和4个转动能级.根据方案,模拟了激光冷却过程中的分子布居数动力学变化过程,并计算了初速度为100 m/s的BD~+,历经5.4 ms散射1150个光子可减速到4.6 m/s、温度为13 mK.     

Differential cross sections for electron impact excitation of molecular hydrogen using the momentum-space multichannel optical method

In the present work, the momentum-space multichannel optical method is employed in four-state close-coupling calculations to study the electronic excitation of H_2 molecules by electron-impact. Particularly, differential cross sections for the X~1Σ_g~+→ b~3Σ_u~+, X~1Σ_g~+→ aΣ_g~+, and X~1Σ_g~+→ c~3Π_u transitions are reported. Comparison is made with the available experimental and theoretical results.     

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.     

BeC分子基态和低激发态光谱性质和解析势能函数

BeC是一个具有丰富低激发电子态的分子,本文基于动态权重完全活性空间自冾场方法获得的参考波函数,采用多参考组态相互作用方法对BeC分子进行高精度的从头计算,获得了BeC分子X~3Σ~-,A~3Π,b~1Δ,c~1Π和d~1Σ~+共5个电子态的势能曲线.为了获得精确的光谱结果,在计算中考虑了标量相对论效应修正,并把相互作用能外推至完全基组极限.在此基础上获得了这些态的光谱常数和偶极距,以及一些允许跃迁的跃迁偶极距、弗兰克-康登因子和辐射寿命.最后,通过扩展的Rydberg函数拟合获得了基态势能曲线精确的解析表达式.     

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.     

75As32S+和75As34S+离子的光谱常数与分子常数

采用内收缩多参考组态相互作用(MRCI)方法, 结合Dunning系列相关一致基, 分别对⁷⁵As³²S⁺和⁷⁵As³⁴S⁺离子的X³Σ^-和A¹Π电子态的势能曲线进行了计算, 进一步拟合势能曲线, 得到各电子态的光谱常数与分子常数. 首先, 采用MRCI方法结合相关一致基, aug-cc-pV5Z, 对AsS⁺离子的X³Σ^-和A¹Π 电子态进行了计算, 获得相应的势能曲线; 然后, 为进一步提高势能曲线的精度, 对其进行了三种修正计算. 采用Davidson(+Q)方法修正MRCI 方法计算过程中存在的基组大小不一致缺陷; 利用二阶Douglas-Kroll哈密顿近似, 在cc-pVQZ基组水平, 修正了相对论效应对势能曲线的影响; 利用两点能量外推法, 在aug-cc-pVQZ和aug-cc-pV5Z基组水平对各能量点的势能值进行了外推, 得到完全基组极限处的势能曲线. 最后, 利用修正(包括Davidson修正、相对论修正和基组外推)后的势能曲线, 通过Vibrot程序, 求解双原子分子核运动的径向Schrödinger方程, 并进行同位素质量识别, 得到⁷⁵As³²S⁺和⁷⁵As³⁴S⁺离子两个电子态的光谱常数(T_e, R_e, ω_e, ω_ex_e, α_e 和B_e)和分子常数(G(ϒ), B_v, D_v).     

用差分收敛法研究NaLi分子部分电子态的完全振动能谱

基于双核分子振动能级的普遍表达式和差分收敛法(difference converging method, DCM), 利用微分思想将DCM应用于双核分子体系完全振动能谱的研究中. 应用DCM方法, 分别选用实验上获得的一组(10条)精确的振动能级, 对NaLi分子3¹Π, 4¹Π 和A¹Σ⁺电子态进行了研究, DCM的研究结果正确重复了已知数据并预测出了在实验上未能获得的包含高激发态在内的完全振动能谱数据, 同时计算得到了这3个电子态的振动光谱常数.