MRCI study on spectroscopic and molecular properties of four low-lying electronic states of the BO radical

The potential energy curves (PECs) of four low-lying electronic states of the BO radical, including two ²Σ⁺ and two ²Π states, have been studied 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 combination with the cc-pV5Z basis set for internuclear separations from 0.05 to 2.0 nm. The effect on the PECs by the relativistic correction has been taken into account. With these PECs, the spectroscopic parameters (T_e, D₀, D_e, R_e, ω_e, ω_ex_e, α_e and B_e) of two main isotopologues (¹¹B¹⁶O and ¹⁰B¹⁶O) have been determined. These parameters have been compared in detail with those of previous investigations reported in the literature, and excellent agreement has been found between the available data and the present results. By solving the radial Schrödinger equation of nuclear motion, 60 vibrational states for the ¹¹B¹⁶O(X²Σ⁺), 60 for the ¹⁰B¹⁶O(X²Σ⁺), 66 for the ¹¹B¹⁶O(A²Π) and 64 for the ¹⁰B¹⁶O(A²Π) are predicted for the non-rotating molecule. For each vibrational state of the ¹¹B¹⁶O(X²Σ⁺), ¹⁰B¹⁶O(X²Σ⁺), ¹¹B¹⁶O(A²Π) and ¹⁰B¹⁶O(A²Π), the vibrational level G(υ), inertial rotation constant B_υ and centrifugal distortion constant D_υ have been determined. Comparison with the available data shows that the present molecular constants are reliable and accurate. The ro-vibrational levels have been calculated for the X²Σ⁺ and A²Π states of two main species for future laboratory research.     

用MRCI方法研究CS+同位素离子X2Σ+和A2Π态的光谱常数与分子常数

利用内收缩多参考组态相互作用方法和价态范围内的最大相关一致基aug-cc-pV6Z, 在0.05—0.60 nm的核间距范围内计算了CS⁺离子X²Σ+和A²Π态的势能曲线. 利用CS⁺离子的势能曲线并在同位素质量修正的基础上, 拟合出了X²Σ+和A²Π态的同位素离子^{1 关键词： 同位素识别 势能曲线 光谱常数 分子常数}     

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.     

MRCI+Q理论研究SiSe分子X1Σ+和A1Π电子态的光谱常数和分子常数

采用Davidson修正的内收缩多参考组态相互作用方法(MRCI+Q)及相关一致基aug-cc-pV5Z和aug-cc-pVQZ分别计算了SiSe分子X¹Σ⁺和A¹Π电子态的势能曲线. 为提高势能曲线的计算精度, 利用两点总能量外推公式, 将两个电子态的势能曲线外推至完全基组极限, 并对其进行了标量相对论修正, 相对论效应是在cc-pV5Z基组水平下使用三级Douglas-Kroll-Hess哈密顿算符计算的. 利用MRCI+Q/Q5+DK理论水平的势能曲线获得了这两个态的光谱常数(T_e, D_e, R_e, ω_e, ω_ex_e, ω_ey_e, B_e和α_e)和J=0时前30个振动态的B_υ和D_υ等分子常数. 其值与已有的实验结果非常一致. 本文得到的光谱常数和分子常数达到了很高精度, 能为进一步的光谱实验和理论研究提供可靠参考. 关键词： 势能曲线 基组外推和标量相对论修正 光谱常数 分子常数     

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.     

Theoretical study of spectral parameters for the γ and β band systems of NO for atmosphere and high temperature

Highly correlated ab initio calculations were performed for accurate determination of γ (A²Σ⁺-X²П) and β (B²П-X²П) band systems of NO molecule. Highly accurate multi-reference configuration interaction approach was used to investigate the potential energy curves (PECs) and transition dipole moment curves. We correctly and fully described their diffuse wave functions by the obvious balance between the valence and Rydberg character of the X²П, A²Σ⁺, B²П, C²П and D²Σ⁺ states. The PECs of the three states (X²П, A²Σ⁺ and B²П) by using the aug-cc-pV5Z (aV5Z) basis set for N and O atoms agreed well with the Rydberg–Klein–Rees potential. Moreover, the Einstein A coefficients were calculated to predict the lifetimes, where the vibrational bands included v′ = 0–8, v″ = 0–29 for γ system and v′ = 0–11, v″ = 0–31 for β system. The spectral line intensities of the γ and β systems for atmosphere and high temperature were provided.     

Ab initio calculations on the ground and excited states of InI

Potential energy curves (PECs) of the ground and the low-lying excited states of the InI molecule are computed using the internally contracted multireference singles and doubles configuration interaction with the Davidson correction (ic-MR-CISD + Q) method based on the relativistic effective core potentials (RECPs). The spectroscopic constants are obtained, including the excitation energy (T _e), the equilibrium bond distance (R _e), the dipole moment (μ_e) and the vibrational constants (ω_e and ω_e). Finally, we predict the transition dipole moments, the radiative lifetimes, and the Franc-Condon factors for the transitions of A³Π₀+ ? X¹Σ₀ ⁺ and B³Π^l ? X¹Σ₀ ⁺,. The results reveal that A³Π₀+ and B³Π_l are long-lived states with the lifetimes being of the order of microseconds.     

MRCI study of spectroscopic and molecular properties of X1Σg+ and A1Πu electronic states of the C2 radical

The potential energy curves (PECs) of X1Σ+g and A1Πu electronic states of the C2 radical have been studied 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 aug-cc-pV6Z basis set for internuclear separations from 0.08 nm to 1.66 nm. With these PECs of the C2 radical,the spectroscopic parameters of three isotopologues ( 12C2 ,12C13C and 13C2 ) have been determined. Compared in detail with previous studies reported in the literature,excellent agreement has been found. The complete vibrational levels G(υ),inertial rotation constants B υ and centrifugal distortion constants D υ for the 12C2 ,12C13C and 13C2 isotopologues have been calculated for the first time for the X1Σ+g and A1Πu electronic states when the rotational quantum number J equals zero. The results are in excellent agreement with previous experimental data in the literature,which shows that the presented molecular constants in this paper are reliable and accurate.     

Low-lying electronic states of BeH+ with the effect of inner electrons

The potential energy curves of the low-lying electronic states of BeH⁺ molecular ion are performed by using highly accurate multi-reference configuration interaction with AV5Z basis sets for H atom and ACV5Z basis set for Be atom, 1s inner shell of Be is considered as the core orbit and the active orbit, respectively, which are used to characterise the spectroscopic properties of a manifold of singlet and triplet states. Fourteen electronic states correlated with eight dissociation channels are investigated, we have found that the a³Σ⁺ and c³Σ⁺ both are bound states, the 3³Σ⁺ possesses double wells, and the C¹Σ⁺, 3³Σ⁺, 2³Π, 2¹Π, 1¹Δ, 1³Δ, 2³Δ and 2¹Δ states are studied for the first time. Transition dipole moment, Franck–Condon factors q_υ′υ^″ and Einstein coefficients A_υ′υ^″ for A¹Σ⁺–X¹Σ⁺, 2¹Π–B¹Π, c³Σ⁺–a³Σ⁺ and b³Π–a³Σ⁺ systems have been calculated. Radiative lifetime of A¹Σ⁺–X¹Σ⁺ band system has also been determined.     

Studies on the Vibrational and Rovibrational Energies and Vibrational Force Constants of Diatomic Molecular States Using Algebraic and Variational Methods

Alternative expressions for vibrational and rotational spectrum constants and energies of diatomic molecular electronic states based on perturbation theory are suggested. An algebraic method (AM) is proposed to generate a converged full vibrational spectrum from limited energy data, and a potential variational method (PVM) is suggested to produce the vibrational force constants f_n and rotational spectrum constants using the perturbation formulae and the AM vibrational constants. The AM and PVM have been applied to study 10 diatomic electronic states: the X¹Σ_g⁺ and C¹Π_u⁻ states of H₂; the X¹Σ_g⁺, A³Σ_u⁺, B′³Σ_u⁻, and B³Π_g states of N₂; the X³Σ_g⁻, A³Σ_u⁺, and c¹Σ_u⁻ states of O₂; and the X¹Σ_g⁺ state of Br₂. Calculations show that (1) the AM E_υmax converges to the correct molecular dissociation energy; (2) the AM not only reproduce the input energies, but also generate the E_υ's of high vibrational excited states which may be difficult to obtain experimentally or theoretically; (3) the PVM vibrational force constants f_n may be used to measure the relative chemical bondstrengths of different diatomic electronic states for a molecule quantitatively.     

Effects on spectroscopic properties for several low-lying electronic states of CS molecule by core-valence correlation and relativistic corrections

The potential energy curves (PECs) of six low-lying electronic states (X¹Σ⁺, a³Π, a′³Σ⁺, d³Δ, e³Σ⁻ and A¹Π) of CS molecule have been 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 with large correlation-consistent basis sets. Effects on the PECs by the core-valence correlation and relativistic corrections have been taken into account. And the two corrections are performed at the level of cc-pV5Z basis set. The way to consider the relativistic corrections is to use the second-order Douglas-Kroll Hamiltonian approximation. Using the CCSD(T), MRCI and MRCI with the Davidson modification (MRCI + Q), the PECs of electronic states involved are extrapolated to the complete basis set (CBS) limit. With the PECs, the spectroscopic parameters (T_e, R_e, ω_e, ω_ex_e, ω_ey_e, α_e, β_e, γ_e and B_e) of the six low-lying electronic states are determined. These parameters are in excellent agreement with the experimental data. The complete vibrational states are computed for the six low-lying electronic states when the rotational quantum number J equals zero, and the inertial rotation constants of the first 23 vibrational states are reported, which agree favorably with the RKR data. Comparison with the measurements shows that the two-point total-energy extrapolation scheme can obviously improve the quality of spectroscopic parameters and molecular constants.     

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.     

Electronic and vibrational spectroscopy of the low-lying states of potassium mono-sulphide KS,and comparison in the series of MS (M = Li,Na, K,Rb, Cs)

ABSTRACT

Potential energy curves (PECs) of the lowest electronic states of the potassium mono-sulphide KS have been determined with highly correlated ab initio calculations, using internally contracted multi reference interaction configuration methods including Davidson correction (MRCI?+?Q) with and without considering spin-orbit effects. For the three low-lying bound states, we report a set of spectroscopic parameters including equilibrium distances, dissociation energies, vibrational and rotational constants. The effects of spin-orbit-induced changes on these parameters are also discussed. An analysis of the properties of the three bound states, X²Π, 1²Σ⁺ and 2²Π, illustrates the common characteristics of the whole series of compounds in the MS family (M?=?Li, Na, K, Rb, Cs). Indeed, the shapes of the PECs of these bound states are strongly affected by the interactions between the two ionic states, ²Σ⁺ and ²Π, correlating at large internuclear separations (R_MS) to the first ionic dissociation limit [M⁺?+?S^?] and the electronic states correlating to the three/four lowest dissociation limits. The spectroscopy of these low-lying electronic states and the lifetime of their vibrational levels are thus affected by the spin-orbit interactions which are mainly related to the S atom and consequently common to all alkali-metal mono-sulphides.     

BF自由基X1∑+和a3∏态光谱常数和分子常数研究

采用内收缩多参考组态相互作用方法和相关一致基aug-cc-pV6Z, 对BF自由基X¹∑⁺和a³∏ 态的势能曲线进行了研究. 计算是在0.095---1.33 nm的核间距内进行的. 为获得更准确的结果, 计算中还考虑了Davidson修正、相对论修正及核价相关修正对势能曲线的影响. 相对论修正采用的方法是二阶DouglasKroll哈密顿近似, 修正计算是在cc-pV5Z基组水平上进行的. 核价相关修正使用的是cc-pCV5Z基组. 利用得到的势能曲线, 拟合出了各种修正下BF自由基X¹∑⁺和a³∏ 态的光谱常数D_e, R_e, ω_e, ω_ex_e, ω_ey_e, B_e和α_e、并与实验结果进行了比较. 结果表明: 考虑Davidson修正、相对论修正和核价相关修正后得到的光谱常数最接近实验结果. 利用修正后的势能曲线, 通过求解径向振转Schrödinger方程, 找到了转动量子数J = 0时这两个电子态的全部振动态, 并计算了每一电子态前20个振动态的振动能级、惯性转动常数和离心畸变常数, 其值与已有的实验结果较为一致. 本文得到的光谱常数和分子常数达到了很高的精度, 能为进一步的光谱实验提供可靠的参考.     

The theoretical character of the X^1∑^＋ and A^1∑^＋ states of ScN

This paper calculates the potential energy curves (PECs) of the ground state (X 1 Σ + ) and excited state (A 1 Σ + ) of ScN molecule by multireference configuration interaction method. The correct character of the PECs has been gripped while they had been improperly reported in the literature. Based on the PECs, the spectroscopic parameters and vibrational energy levels are determined, and compared with experimental data and other theoretical works available at the present.     

The electronic spectrum of silicon monotelluride radical

In the electronic spectrum of silicon monotelluride which has been produced in microwave discharges through sealed tubes, a large number of new bands belonging to theA ¹Π-X ¹Σ⁺ system (3100–3900 Å) and theE ¹Σ⁺-X ¹Σ⁺ system (2800–3100 Å) of Si¹³⁰Te has been observed. The vibrational structure analyses of these band systems have resulted in the determination of improved vibrational constants in all the three electronic states involved in these transitions. An error in the previous determination of the vibrational constants of theE ¹Σ⁺ state has been corrected. An upper limit for the dissociation energy of the silicon monotelluride has been determined to be 40,000 cm^?1.     

分子部分电子态的高阶振动能级和离解能的精确研究

鉴于K₂分子电子态的振动能谱和分子离解能D_e在实际研究和应用中的重要性,应用Sun,Ren等人提出的基于微扰理论的代数方法(AM)和基于AM的代数能量方法(AEM)研究了K₂分子的X¹Σ⁺_g,a³Σ⁺_u,0^-_g,B¹Π_{u< 关键词： 2}分子')" href="#">K₂分子 代数方法 高阶振动能级 离解能     

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.     

The RKR potential energy curves for the X1Σ+ and A1Σ+ states of RbH

The A¹Σ⁺-X¹Σ⁺ laser-excited fluorescence spectrum of RbH was observed in the 4760-to 8470-Å region, using the Ar⁺ 4765-Å exciting line, and v″ = 6–12 were observed for the first time. New spectroscopic constants were obtained for the X¹Σ⁺ and A¹Σ⁺ states of RbH. New Rydberg-Klein-Rees (RKR) potential energy curves were calculated up to v″ = 12 of the X¹Σ⁺ state and up to v′ = 14 of the A¹Σ⁺ state.     

The RKR potential energy curves for the X1Σ+ and A1Σ+ states of KH

New isotopically combined spectroscopic constants were obtained for the X¹Σ⁺ and A¹Σ⁺ states of $\text{KH}\text{KD}$. These constants were used to construct new isotopically combined Rydberg-Klein-Rees (RKR) potential energy curves up to v″ = 4 of the X¹Σ⁺ state and up to v′ = 26 of the A¹Σ⁺ state.