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)     

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     

采用多参考组态相互作用方法研究AsN( X1 Σ+ )自由基的光谱常数与分子常数

采用内收缩多参考组态相互作用方法和相关一致基对AsN(X ¹ Σ⁺)自由基的势能曲线进行了研究. 计算过程中对两原子分别采用不同基组,As原子为aug-cc-pV5Z基组,N原子为aug-cc-pV6Z基组. 通过最小二乘法将势能曲线拟合成Murrell-Sorbie函数,并进一步计算得到AsN(X ¹ Σ⁺)自由基的光谱常数.光谱常数分别为D_e=4.97 eV,R_e=0.16259 nm, ω_e=1061.14 cm^-1, ω_ex_e=5.4715 cm^-1, B_e=0.53919 cm^-1和α_e=0.003409 cm^-1. 通过比较发现它们与实验值符合非常好. 利用得到的解析势能函数, 求解双原子分子核运动的径向Schrödinger方程, 找到了J=0时该自由基存在的全部67个振动态. 对于每一振动态, 分别计算了振动能级、经典转折点、惯性转动常数和离心畸变常数. 与实验结果比较后发现,计算结果达到了很高的计算精度. 关键词： AsN 势能曲线 光谱常数 分子常数     

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.     

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.     

HF分子电子基态和激发态的MRCI计算

应用舍Davidson修正的多参考组态相互作用（MRCI）方法,在aug-cc-pVTZ基组水平上对HF基态及最低的多个单重和三重电子激发态进行了势能扫描计算.结合群论原理及分子的离解极限,分析了电子态势能曲线的特征,得出激发态B¹S⁺对应的离解极限为H⁺+F^-（¹S）.基于势能曲线,数值求解核运动的径向Schrodinge方程,得到J=0时束缚电子态X¹S⁺,B¹S⁺,C¹P和D¹S⁺的振动能级和转动常数,继而进行数据拟合得到电子态的光谱常数,基态X¹S⁺:ω_e=4146.94 cm^-1,ω_ez_e=88.08 cm^-1,B_e=21.22 cm^-1,a=0.785 cm^-1;B¹S⁺态:ω_e=1131.37 cm^-1,ω_ex_e=17.28 cm^-1,B_e=3.96 cm^-1,a_e=0.0215 cm^-1,C¹P态:ω_e=2696.37 cm^-1,ω_ex_e=73.43 cm^-1,B_e=15.91 cm^-1,a_e=0.776 cm^-1,D¹S⁺态:ω_e=3104.22 cm^-1,ω_ex_e=118.92 cm^-1,B_e=17.25 cm^-1,a_e=0.992 cm^-1,拟合结果与实验值吻合的较好.     

理论研究B2分子X3Σg-和A3Πu态的光谱性质

采用Davidson修正的内收缩多参考组态相互作用方法及Dunning等的相关一致基aug-cc-pV6Z计算了B₂分子X³∑_g^-和A³Π_u电子态的势能曲线.利用总能量外推公式,将两个电子态的总能量分别外推至完全基组极限.对势能曲线进行核价相关修正及相对论修正计算,得到了同时考虑两种效应修正的外推势能曲线.通过同位素质量识别,得到了主要的同位素分子¹¹B¹¹B和¹⁰B¹¹B的X³Σ_g^-和A³Ⅱ_u电子态的光谱常数T_e,R_e,ω_e,ω_ex_e,ω_ey_e,B_e,β_e和γ_e.求解双原子分子核运动的径向Schr（o|¨）dinger方程,找到了无转动的同位素分子¹¹B₂（X³Σ_g^-,A³Π_u）和¹⁰B¹¹B（X³∑_g^-,A³Π_u）的全部振动态.针对每一同位素分子的每一振动态,分别计算了其振动能级和惯性转动常数等分子常数,它们均与已有的实验结果较为一致.其中,¹⁰B¹¹B（A^Π_u）分子的光谱常数和分子常数属首次报道.     

理论研究BeS(X~1∑~+)的光谱常数及分子常数

采用Davidson校正的内收缩多参考组态相互作用方法（MRCI+Q）结合相关一致五重基cc-pV5Z在二阶Douglas-Kroll Hamiltonian近似下,计算了BeS分子X¹∑⁺态的势能曲线.对势能曲线进行核价相关效应修正计算,得到了同时含有核价相关效应修正及相对论效应的势能曲线.拟合修正的势能曲线,获得BeS（X¹∑⁺）的光谱常数R_e,ω_e,ω_ex_e,ω_ey_e,B_e,α_e,β和D₀,分别为:0.17429 nm,997.06cm^-1,6.1056 cm^-1,0.0041 cm^-1,0.7893 cm^-1,0.006657 cm^-1,6.8002×10^-9cm^-1和4.2609 eV.与已有的实验结果及其它理论结果的比较表明,本文BeS（X¹∑⁺）的光谱常数的计算结果达到了较高的精度.通过求解双原子分子核运动的径向Schr（o|¨）nger方程,找到了非转动BeS（X¹∑⁺）的前40个振动态.针对每一振动态还分别计算了相应的振动能级、惯性转动常数和离心畸变常数等分子常数.     

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.     

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.     

Accurate spectroscopic calculations of the 19 Λ-S states and 36 Ω states of the BC+ cation

This work computed the potential energy curves of 19 Λ-S states, which arose from the first five dissociation limits of BC⁺ cation, B⁺(¹S_g) + C(³P_g), B⁺(¹S_g) + C(¹D_g), B⁺(¹S_g) + C(¹S_g), C⁺(²P_u) + B(²P_u), and B⁺(¹S_g) + C(⁵S_u). The calculations were done for internuclear separations from 0.08 to 1.07 nm. The potential energy curves of 36 Ω states yielded from these Λ-S states were also calculated. Core-valence correlation and scalar relativistic correction, basis set extrapolation as well as Davidson correction were accounted for. Of these Λ-S states, the c¹Σ⁺, D³Π, 2¹Π, 2³Σ⁺, 2¹Δ, 3¹Σ⁺, and 4¹Σ⁺ had double wells; the 3³Π and 3¹Π states had three wells; the C³Σ^? and D³Π states were inverted with the spin-orbit coupling effect included; and the second wells of c¹Σ⁺, D³Π and 3¹Σ⁺ states, the second and the third wells of 3³Π state as well as the third well of 3¹Π state were very weakly bound, which well depths were smaller than 400 cm^?1. The spectroscopic parameters were determined for all the states. The vibrational properties were predicted only for some weakly bound states. The spin-orbit coupling effect on the spectroscopic parameters was evaluated.     

Spectroscopic and molecular properties of 14 selected electronic states of Si2 molecule

The potential energy curves (PECs) of the X³Σ_g⁻, D³Π_u, a¹Δ_g, b¹Π_u, H′³Σ_u⁻, K³Σ_u⁻, 1³Σ_u⁺, 1³Π_g, 2³Σ_u⁺, 2³Π_g, 3³Π_g, 3³Σ_u⁺, 2³Π_u and 2³Σ_g⁻ electronic states of the Si₂ molecule are investigated using the complete active space self-consistent field (CASSCF) method followed by the valence internally contracted multireference configuration interaction (MRCI) approach with the correlation-consistent basis sets of Dunning and co-workers. The effects on the PECs by the core-valence correlation and relativistic corrections are included. The way to consider the relativistic correction is to use the third-order Douglas-Kroll Hamiltonian approximation. The core-valence correlation correction is made with the aug-cc-pCV5Z basis set. And the relativistic correction is performed at the level of cc-pV5Z basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are also corrected for size-extensivity errors by means of the Davidson modification (MRCI+Q). The PECs of all these electronic states are extrapolated to the complete basis set limit by the total-energy extrapolation scheme. Using the PECs, the spectroscopic parameters are determined and compared with those reported in the literature. With these PECs determined by the MRCI+Q/CV+DK+56 calculations, the vibrational levels and inertial rotation constants of the first 20 vibrational states are evaluated and compared with the RKR data for these electronic states when the rotational quantum number J equals zero. On the whole, as expected, the most accurate spectroscopic parameters and molecular constants of the Si₂ molecule are determined by the MRCI+Q/CV+DK+56 calculations. And the spectroscopic parameters of the 1³Σ_u⁺, 1³Π_g, 2³Σ_u⁺, 2³Π_g, 3³Π_g, 3³Σ_u⁺, 2³Π_u and 2³Σ_g⁻ electronic states obtained by the MRCI+Q/CV+DK+56 calculations should be good prediction for future laboratory experiment.     

MRCISD calculations of the six lowest valence states of I2 −

Potential curves for the four Hund's case (a) basis electronic states (²Σ, ²Π_g, ²Π_u, and ²Σ⁺) correlating with the I(²P_u) + I^?(¹S_g) dissociation limit have been calculated at the MRCISD level of theory using an all-electron double-zeta basis set augmented with an extensive set of polarization and diffuse functions complete through i angular momentum functions. Transition moments for the dipole allowed transitions between these states are determined as a function of internuclear separation. The four Hund's case (a) curves are used to determine the six Hund's case (c) potential curves which arise when spin-orbit coupling is considered. The rovibrational eigenvalues for each of these six states are determined numerically, and standard spectroscopic constants are determined by fitting the energy of these levels to a Duham series. The results are compared with available experimental and theoretical information.     

Investigations of spectroscopic parameters and molecular constants for X1Σg+, w3Δu, and W1Δu electronic states of P2 molecule

The potential energy curves (PECs) of three low-lying electronic states (X¹Σ_g⁺, w³Δ_u, and W¹Δ_u)of P₂ molecule are investigated using the full valence complete active space self-consistent field (CASSCF) method followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach in conjunction with the correlation-consistent basis set in the valence range. The PECs of the electronic states involved are modified by the Davidson correction and extrapolated to the complete basis set (CBS) limit. With these PECs, the spectroscopic parameters of the three electronic states are determined and compared in detail with the experimental data. The comparison shows that excellent agreement exists between the present results and the available experimental data. The complete vibrational states are computed for the w³Δ_u, and W¹Δ_u electronic states when the rotational quantum number J equals zero and the vibrational level G(v), the inertial rotation constant B_v, and the centrifugal distortion constant D_v of the first 30 vibrational states are reported, which accord well with the experimental data. The present results show that the two-point extrapolation scheme can obviously improve the quality of spectroscopic parameters and molecular constants.     

Study of the covalent and triplet ionic-pairing states of the fluorine molecule with the MRDCI method

The results of nonempirical calculations of the electronic structure, spectroscopic constants, and potential-energy curves for the covalent and triplet ionic-pairing states of the F₂ molecule are presented. It is shown that the covalent 1³Π_u state is weakly bound, with the depth of the potential well of this state being of about 0.05–0.2 eV. The effect of the spin-orbital interaction on the ionic-pairing states, which can result in the perturbation of the Ω=0⁺ and Ω=1 components of the ³Σ _u ^? and ³Π_u states, is analyzed. It is demonstrated that the lasing observed at λ ≈ 157 nm is caused by the transitions between the ionic-pairing state 2³Π_g and the weakly bound covalent state 1³Π_u.     

Calculation of spectroscopic constants and radiative parameters for A1Σ u+ -X1Σ g+ and B1Πu-X1Σ g+ electronic transitions of sodium dimer

Vibrational, rotational, and centrifugal spectroscopic constants and radiative parameters, i.e., the Einstein coefficients, oscillator strengths, and wave numbers for vibrational transitions in electronic systems of bands A ¹Σ _u ⁺-X ¹Σ _g ⁺ (0 ≤ v′ ≤ 25; 0 ≤ v″ ≤ 44), B ¹Π _u -X ¹Σ _g ⁺ (0 ≤ v′ ≤ 29; 0 ≤ v″ ≤ 47), and the radiative lifetimes for the vibrational levels of excited states of the sodium dimer, are calculated. The calculations are carried out based on semiempirical potential curves constructed in this study. The calculated spectroscopic constants and radiative lifetimes are compared to the experimental values.     

Calculation of the spectroscopic constants for the electronic states A1Σ u+ , B1Πu, C1Πu, D1Σ u+ , and E1Σ u+ of the cesium dimer

The vibrational, rotational, and centrifugal distortion constants have been calculated for the electronic states A ¹Σ _u ⁺ , B ¹Π_u, C ¹Π_u, D ¹Σ _u ⁺ , and E ¹Σ _u ⁺ of the Cs₂ molecule. The calculation was performed on the basis of the semiempirical potential energy curves constructed in this paper. The calculated spectroscopic constants are compared with the experimental data. Original Russian Text ? A.D. Smirnov, 2007, published in Optika i Spektroskopiya, 2007, Vol. 102, No. 1, pp. 23–27.     

Calculation of adiabatic potentials of Li<Subscript>2</Subscript><Superscript>+</Superscript>

We report adiabatic potential energy curves of the Li₂ ⁺ molecule. Our curves are tabulated according to internuclear distance from 2 a₀ to 100 a₀. We compare our theoretical results with the ones calculated by other authors and potential energy curves derived from experiments. For the ground state and 17 excited states we calculate spectroscopic parameters and compare them with parameters obtained by other authors. For the first time we present three new minima for 3²Σ_u ⁺, 4²Σ_u ⁺ and 2²Π_g excited states. In our approach we use the configuration interaction method where only the valence electrons of Li atoms are treated explicitly. The core electrons are represented by pseudopotential. All calculations are performed by means of MOLPRO program package.     

Accurate theoretical spectroscopic investigations of the 20 Λ-S and 58 Ω states of O2+ cation including the spin–orbit coupling effect

The potential energy curves (PECs) are calculated for the 20 Λ-S states (X²Π_g, A²Π_u, B²Σ^?_g, a⁴Π_u, b⁴Σ^?_g, b′⁴Π_g, c⁴Σ^?_u, 1²Σ⁺_g, 1²Σ⁺_u, 1²Σ^?_u, 1⁴Σ⁺_g, 1⁴Σ⁺_u, 1⁴Δ_g, 1⁴Δ_u, 1⁶Σ⁺_g, 1⁶Σ⁺_u, 1⁶Π_g, 1⁶Π_u, 2⁴Π_g and 2⁴Π_u) of O₂⁺ cation and their corresponding 58 Ω states. Of these 20 Λ-S states, the 1⁶Π_u state is found to be repulsive. The 1²Σ⁺_g, 1⁴Σ⁺_u, c⁴Σ^?_u and 1⁴Δ_u states are found to possess the double well. The b⁴Σ^?_g, 1⁶Σ⁺_g, 1⁴Σ⁺_u, a⁴Π_u, A²Π_u, 1⁶Π_g and 2⁴Π_g states are found to be inverted with the spin–orbit coupling effect included. The b′⁴Π_g, 1⁶Π_g, 1⁶Σ⁺_g, 1⁴Σ⁺_u and 1⁴Δ_u states, and the second well of the 1²Σ⁺_g state are found to be the weakly bound states. The b′⁴Π_g state is found to possess one well with one barrier. The PECs are calculated by the complete active space self-consistent field method, which is followed by the internally contracted multireference configuration interaction approach with the Davidson correction in combination with the aug-cc-pV6Z basis set. The core–valence correlation and scalar relativistic corrections are included. The convergent behaviour of present calculations is discussed with respect to the basis set and theoretical level. The spin–orbit coupling effect is accounted for. The PECs are extrapolated to the complete basis set limit. The spectroscopic parameters are evaluated, and compared with available measurements. It demonstrates that the spectroscopic parameters reported here can be expected to be reliably predicted ones.     

Calculation of molecular constants for the X 1Σ g + , A 1Σ u + , B 1Πu, and a 3Σ u + electronic states of 39K2

The molecular constants are calculated for the X ¹Σ _g ⁺ , A ¹Σ _u ⁺ , B ¹Π_u, and a ³Σ _u ⁺ and electronic states of a potassium dimer. The wave functions and vibrational energies necessary for calculating the molecular constants are determined by solving the radial wave equation with the use of potential energy curves constructed by the semiempirical method. The vibrational terms, the rotational constants, and the centrifugal distortion constants calculated from the potential curves are compared with those determined from the experimental data.