Theoretical study with vibration–rotation and dipole moment calculations of quartet states of the CrCl molecule

The potential energy curves have been investigated for the 10 lowest quartet electronic states in the ^2s+1Λ^± representation below 30,000 cm^?1 of the molecule CrCl via CASSCF and MRCI (singly and doubly excitation with Davidson correction) calculations. The harmonic frequency ω_e, the internuclear distance r_e, the rotational constant B_e, the electronic energy with respect to the ground state T_e, and the permanent dipole moment μ have been calculated. By using the canonical functions approach, the eigenvalues E_v, the rotational constant B_v, and the abscissas of the turning points r_min and r_max have been calculated for the considered electronic states up to the vibrational level v = 19. Seven electronic states have been studied here theoretically for the first time. The comparison of these values to the theoretical results available in the literature shows a good agreement. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Theoretical electronic structure of the molecule ScI

Theoretical investigation of the 18 lowest electronic states of the molecule ScI in the representation ^2S+1Λ^(±) has been performed via CASSCF and MRCI (single and double excitation with Davidson correction) calculations. To the best of our knowledge these calculated electronic states are the first ones from ab initio methods. Thirteen electronic states between 4,500 cm^?1 and 21,000 cm^?1 have been studied for the first time and have not yet been observed experimentally. The harmonic frequency ω_e, the internuclear distance R_e, the electronic transition energy with respect to the ground state T_e, and the rotational constant B_e have been calculated for the considered electronic states. By using the canonical functions approach the eigenvalues E_υ and the rotational constants B_υ have also been calculated for the six lowest‐lying electronic states. The comparison of these results with the theoretical and the experimental data available in the literature shows a good agreement. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Theoretical study with rovibrational and dipole moment calculation of sextet states of the CrCl molecule

The potential energy curves have been investigated for the 13 lowest sextet electronic states in the representation below 53,000 cm^?1 of the molecule CrCl via CASSCF and MRCI (single and double excitation with Davidson correction) calculations. The harmonic frequency ω_e, the internuclear distance r_e, the rotational constant B_e, the electronic energy with respect to the ground state T_e, and the permanent dipole moment μ have been calculated. By using the canonical functions approach, the eigenvalues E_v, the rotational constant B_v, and the abscissas of the turning points r_min and r_max have been calculated for the considered electronic states up to the vibrational level v = 16. Nine electronic states have been studied theoretically here for the first time. The comparison of these values with the theoretical and experimental results available in the literature shows a good agreement. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Theoretical calculation of the low laying electronic states of the molecular ion RbH+

Using an ab initio method, the potential energy has been calculated for the 29 lowest molecular states of symmetries ²Σ⁺, ²Π, ²Δ for the molecular ion RbH⁺. The calculation is based on nonempirical pseudopotentials and parameterized ?‐dependent polarization potentials. Gaussian basis sets have been used for both atoms. The spectroscopic constants for 18 electronic sates have been calculated by fitting the calculated energy values to a polynomial in terms of the internuclear distance R. Through the canonical functions approach the eigenvalue E_v, the abscissas of the corresponding turning points (R_min and R_max) and the rotational constants B_v have been calculated up to 24 vibrational levels for the considered bound states. The comparison of the present results with those available in literature shows a very good agreement. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Theoretical electronic studies of aluminum monobromide and aluminum monoiodide

By using CASSCF/MRCI methods, theoretical molecular calculations have been performed for 12 electronic states for AlBr molecule and 12 electronic states for AlI molecule in the representation ^2s+1Λ (neglecting spin‐orbit effects). Calculated potential energy curves are displayed. Spectroscopic constants including the harmonic vibrational wave number ω_e, the electronic energy T_e referred to the ground state and the equilibrium internuclear distance R_e are predicted for these singlet and triplet electronic states for both AlBr and AlI molecules. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Theoretical calculation of the low laying electronic states of the molecular ion KH

Using an ab initio method the potential energy has been calculated for the 25 lowest molecular states of symmetries ²Σ⁺, ²Π, ²Δ for the molecular ion KH⁺. The calculation is based on nonempirical pseudopotentials and parameterized ℓ-dependent polarization potentials. Gaussian basis sets have been used for both atoms. The spectroscopic constants for 18 electronic sates have been calculated by fitting the calculated energy values to a polynomial in terms of the internuclear distance R. Through the canonical functions approach the eigenvalue E_v, the abscissas of the corresponding turning points (R_min and R_max) and the rotational constants B_v have been calculated up to 24 vibrational levels for the considered bound states. The comparison of the present results with those available in literature shows a very good agreement.     

Theoretical calculation of the low-lying sextet electronic states of CrF molecule

The potential energy curves have been investigated for the 12 lowest sextet electronic states in the ^2s+1Λ^(±)${}^{2s+1}{\mathrm{\Lambda }}^{(\pm )}$ representation below 53,000 cm⁻¹ of the molecule CrF via CASSCF and MRCI (single and double excitation with Davidson correction) calculations. Seven electronic states have been studied theoretically for the first time. The harmonic frequency ω_e, the internuclear distance R_e, the rotational constant B_e, the electronic energy with respect to the ground state T_e, and the permanent dipole moment μ have been calculated. By using the canonical functions approach, the eigenvalues E_v, the rotational constant B_v and the abscissas of the turning points R_min and R_max have been calculated for the considered electronic states up to the vibrational level v = 39. The comparison of these values to the theoretical and experimental results available in the literature shows a good agreement.     

OH自由基的高精度量子化学研究

采用内收缩MRCI方法(Internally Contracted Multiconfiguration-Reference Configuration Interaction)研究了OH自由基, 计算得到其基态稳定构型的键长是0.09708 nm, 对应的实验值是0.096966 nm, 第一激发态的键长是0.10137 nm,实验值是0.10121 nm. 同时得到势能曲线PECs (Potential Energy Curve), 再分别由Murrell-Sorbie势能函数拟合计算和POLFIT程序计算得到OH自由基在基态X²Π和第一激发态A²Σ⁺时的光谱数据：平衡振动频率ω_e, 非谐性常数ω_eχ_e以及高阶修正ω_eY_e, 平衡转动常数B_e, 振转耦合系数α_e, 解离能D₀和垂直跃迁能量ν₀₀. 这些理论计算结果与最新的实验值非常吻合, 精确度比前人也有很大提高. 其中我们计算得到基态OH(X²Π)的解离能D₀＝35568.86 cm^－1, 第一激发态OH (A²Σ⁺)的解离能D₀＝18953.93 cm^－1, 从第一激发态A²Σ⁺ (ν＝0)到基态X²Π (v＝0)的垂直跃迁能ν₀₀＝32496.42 cm^－1.     

Theoretical study of spectroscopic and molecular properties of several low‐lying electronic states of CO molecule

The potential energy curves (PECs) of eight low‐lying electronic states (X¹Σ⁺, a³Π, a′³Σ⁺, d³Δ, e³Σ^?, A¹Π, I¹Σ^?, and D¹Δ) of the carbon monoxide molecule have been studied by an ab initio quantum chemical method. The calculations have been performed using the complete active space self‐consistent field method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with the correlation‐consistent aug‐cc‐pV5Z basis set. The effects on the PECs by the core‐valence correlation and relativistic corrections are included. The way to consider the relativistic corrections is to use the third‐order Douglas–Kroll Hamiltonian approximation at the level of a cc‐pV5Z basis set. Core‐valence correlation corrections are performed using the cc‐pCVQZ basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are corrected for size‐extensivity errors by means of the Davidson modification (MRCI+Q). The spectroscopic parameters (D_e, T_e, R_e, ω_e, ω_ex_e, ω_ey_e, B_e, α_e, and γ_e) of these electronic states are calculated using these PECs. The spectroscopic parameters are compared with those reported in the literature. Using the Breit–Pauli operator, the spin–orbit coupling effect on the spectroscopic parameters is discussed for the a³Π electronic state. With the PECs obtained by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations, the complete vibrational states of each electronic state have been determined. The vibrational manifolds have been calculated for each vibrational state of each electronic state. The vibrational level G(ν), inertial rotation constant B_ν, and centrifugal distortion constant D_ν of the first 20 vibrational states when the rotational quantum number J equals zero are reported and compared with the experimental data. Comparison with the measurements demonstrates that the present spectroscopic parameters and molecular constants determined by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations are both reliable and accurate. © 2012 Wiley Periodicals, Inc.     

Ab initio spectroscopic study for the NaRb molecule in ground and excited states

A wide adiabatic study is performed for NaRb molecule, involving 15¹Σ⁺ electronic states including the ionic state Na^?Rb⁺, as well as 14³Σ⁺, 1–9^1,3Π, and 1–5^1,3Δ states. This investigation is performed using an ab initio approach which involves the effective core potential, the core polarization potential with l‐dependent cut‐off functions. The NaRb system has been treated as a two‐electron system and the full valence configuration interaction is easily achieved. The spectroscopic constants R_e, D_e, T_e, ω_e, ω_ex_e, B_e, and D₀ for all these states are derived. We have also computed the vibrational levels as well their spacing for different values of J. In addition, permanent and transition dipole moments are determined and analyzed. The Dunham coefficients have been used to perform experimental spacing to compare directly with our results. The present calculations on NaRb extend previous theoretical works to numerous electronic excited states in the various symmetries. © 2014 Wiley Periodicals, Inc.     

PdYH分子的结构与势能函数

用密度泛函理论的B3LYP方法, 对钯和钇原子采用SDD收缩价基函数, 氢原子采用6-311＋＋G**全电子基函数, 对PdY和PdYH体系的结构进行优化. 计算表明: PdY分子的几何构型为C_∞v, 其基态为X²Σ^＋态, 键长R＝0.24168 nm, 离解能为D_e＝2.8261 eV, 谐振频率ω_e＝254.0656 cm^－1, 并拟合得到Murrell-Sorbie势能函数; PdYH分子最稳态为C_s构型, 电子组态为¹A', 平衡核间距R_PdY＝0.24281 nm, R_YH＝0.19824 nm, 键角∠PdYH＝116.7157°, 离解能D_e＝5.6146 eV, 基态简正振动频率: 对称伸缩振动频率ν₁ (a')＝348.2909 cm^－1, 弯曲振动频率ν₂ (a')＝243.3382 cm^－1, 反对称伸缩振动频率ν₃ (a')＝1442.2695 cm^－1. 由微观过程的可逆性原理分析了分子的可能离解极限. 并用多体项展式理论方法分别导出基态PdY和PdYH分子的势能函数, 其等值势能面图准确地再现了PdY和PdYH分子的结构特征和离解能, 由此讨论了Pd＋Y＋H分子反应的势能面静态特征.     

Theoretical study of the low‐lying electronic states of the molecular ion KRb+

The potential energy curves of the molecular ion KRb⁺ have been investigated for the 60 lowest molecular states of symmetry ²Σ⁺, ²Π, ²Δ, and Ω = 1/2, 3/2, and 5/2. Using an ab initio method, the calculation has been done in a one active electron approach based on nonempirical pseudopotentials with core valence effects taken into account through parameterized l‐dependent polarization potentials. Using the canonicals functions approach a rovibrational study is done by calculating the eigenvalues E_v, the rotational constants B_v, the centrifugal distortion constants D_v (up to 135 vibrational levels), and the spectroscopic constants ω_e and B_e for the five electronic states (1)²Σ⁺, (3)²Σ⁺, (1)²Π, (1)Ω = 1/2, and (1)Ω = 3/2. No comparison of these values with other results is yet possible because they are given here for the first time. Extensive tables of energy values of E_v, B_v, and D_v are displayed at http://hplasim2.univ‐lyon1.fr/allouche . © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

CEPA calculations on open-shell molecules

Ab initio calculations at SCF and CEPA levels using large Gaussian basis sets have been performed for the two lowest electronic states,X ² Σ⁺ andA ² Π, of HeAr⁺. Spin-orbit coupling (SOC) effects have been added using a semiempirical treatment. The resulting potential curves for the three statesX,A ₁, andA ₂ have been used to evaluate molecular constants such as vibrational intervals ΔG(v + 1/2) and rotational constantsB _v as well as — by means of a Dunham expansion — equilibrium constants such asR _e , ω _e ,B _e etc. Comparison with the experimental data from UV emission spectroscopy shows that the calculated potential curves are slightly too shallow and have too large equilibrium distances:D _e = 242 cm^?1 andR _e = 2.66 Å compared to the experimental values of 262 cm^?1 and 2.585 Å, respectively, for theX ²Σ⁺ ground state. However, the ab initio calculations yield more bound vibrational levels than observed experimentally and allow for a more complete Dunham analysis, in particular for theA ₂ state. The experimental value of 154 cm^?1 for the dissociation energyD _e of this state is certainly too low; our best estimate is 180±5 cm^?1. For theA ₁ state our calculations are predictions since this state has not yet been observed experimentally.     

Quantum-mechanical treatment of molecules. I. Calculations of the potential energy curves and molecular constants of the ground and ionized states of N2

The self-consistent-field molecular-orbital method in LCAO (linear combination of atomic orbitals) approximation is applied to the ground and three ionized states of N₂ at a number of internuclear distances for the computation of the potential energy curves. In these calculations both the linear coefficients and the screening constants of the atomic orbitals have been optimized. The molecular constants ω_e, ω_ex_e, B_e, α_e, and R_e have also been calculated for the above states from the computed potential energy curves. The computed spectral results are compared with the experimental data as well as with the results reported by others from ab initio calculations.     

MRCI study on spectroscopic parameters and molecular constants of the ground state of AsP(X1Σ+) molecule

The potential energy curve (PEC) for the ground state of AsP(X¹Σ⁺) has been investigated by the highly accurate valence internally contracted multireference configuration interaction method in the Molpro2008 program package with the correlation consistent basis set. The PEC is fitted to the analytic Murrrell–Sorbie function (M–S function) from which the spectroscopic constants are determined. The present D_e, B_e, α_e, ω_eχ_e, R_e, and ω_e values are of 4.2823 eV, 0.188622 cm^?1, 0.000749 cm^?1, 1.984427 cm^?1, 2.0194 Å, and 598.60 cm^?1, respectively. In addition, by numerically solving the radial Schrödinger equation of nuclear motion in the adiabatic approximation, the total of 96 vibration states is predicted when the rotational quantum number J = 0. The complete vibration levels, classical turning points, inertial rotation, and centrifugal distortion constants are reproduced. Comparison has been made with recent theoretical and experimental data. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Electronic transition moment with spin‐orbit coupling of the molecular ion KRb+

By using the electronic wave functions obtained from an ab initio calculation, including the spin‐orbit coupling, the electronic transition moments have been investigated for two bound states of symmetry Ω = 1/2 and Ω = 3/2 of the molecular ion KRb⁺. Based on a canonical functions approach for the determination of the vibrational wave functions, the matrix elements have been calculated for the bound states considered for v = 0, 10, 20 with v′‐ v = 0, 1, 2, …, 6; by using the same canonical approach, the eigenvalues and abscissas of the corresponding turning points (r_min and r_max) have been investigated for these states that obtained from a theoretical ab initio calculation up to v = 105. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

An ab initio theoretical study of the optical spectrum of CF2

The ab initio calculation methods have been used to calculate the spectral and electronic characteristics of difluorocarbene in the ground electronic state (¹A₁), the lowest-lying singlet (¹B₁) and triplet (³B₁) states. The optimized equilibrium geometries, rotational constants, harmonic vibrational frequencies and energy gaps, electronic charges, dipole moments of these states have been computed with different basis sets. The calculated vibrational frequency of ³B₁ state (v₂=522 cm^?1) and the energy separation (2.26 eV) between ³B₁ and ¹A₁ states are in good agreement with the experimental results (519 cm^?1, 2.46 eV respectively). According to the calculations the previous assignment of vibrational symmetries of ¹B₁ state was corrected, and some experimentally undetermined vibrational frequencies were predicted.     

Ab initio calculations for the potential curves and spin–orbit coupling of Mg2

 The ground state and several low-lying excited states of the Mg₂ dimer have been studied by means of a combination of the complete-active-space multiconfiguration self-consistent-field (CASSCF)/CAS multireference second-order perturbation theory (CASPT2) method and coupled-cluster with single and double excitations and perturbative contribution of connected triple excitations [CCSD(T)] scheme. Reasonably good agreement with experiment has been obtained for the CCSD(T) ground-state potential curve but the dissociation energy of the only experimentally known A¹Σ _u ⁺ excited state of Mg₂ is somewhat overestimated at the CASSCF/CASPT2 level. The spectroscopic constants D _e, R _e and ω_e deduced from the calculated potential curves for other states are also reported. In addition, some spin–orbit matrix elements between the excited singlet and triplet states of Mg₂ have been evaluated as a function of internuclear separation. Received: 10 May 2001 / Accepted: 15 August 2001 / Published online: 30 October 2001     

Potential energy curves for ground and excited states of NaLi from ab initio calculations with effective core polarization potentials

Sixteen low-lying electronic states of NaLi are investigated by SCF/valence Cl calculations including core polarization effects by means of an effective potential. Spectroscopic constants are obtained with estimated uncertainties of ΔR_e ? 0.01 Å, Δω_e ? 0.6 cm^?1 and ΔD_e ? 80 cm^?1. From a comparison of experimental and theoretical G(υ) values, we suggest a ground-state dissociation energy of 7093 ± 5 cm^?1. Using our rovibrational energies and recently measured excitation lines, we are able to improve the T_e values and dissociation energies of five excited states to an accuracv of ±8 cm^?1.     

Ab Initio rovibrational spectrum of the NaH2 + ion–quadrupole complex

The electronic and rovibrational structure of (¹A₁) NaH₂ ⁺ has been investigated using a relativistically-corrected, all-electron coupled-cluster with singles, doubles and perturbative triples (CCSD(T)) ansatz. For the electronic ground state this ansatz yielded equilibrium Na–H bond lengths (R _e ) of 2.4208 Å and an equilibrium H–Na–H bond angle (θ_e) of 17.8°. An analytical potential energy surface (PES) was embedded in the rovibrational Hamiltonian. The PES was constructed using 118 CCSD(T) points and exhibited a residual error of 1.2 cm^?1. The rovibrational Hamiltonian was diagonalised using variational techniques. The vibrational and rovibrational eigenvectors were assigned using a configuration weight scheme in terms of normal modes and the Mulliken assignment scheme, respectively. For the ground vibrational state of (¹A₁) NaH₂ ⁺, the vibration-averaged bond lengths 〈R〉 and angle 〈θ〉 were 2.4995 Å and 17.1°, respectively. The ab initio (¹A₁) NaH₂ ⁺ PES yielded a dissociation energy (D ₀) value of 10.3 kJ mol^?1, which is in excellent agreement with the experimental value of 10.3 ± 0.8 kJ mol^?1 (Bushnell et al. in J Phys Chem 98:2044, 1994). An analytical dipole moment surface was constructed using 90 CCSD(T) points. Rovibrational spectra of (¹A₁) NaH₂ ⁺, (¹A′) NaHD⁺ and (¹A₁) NaD₂ ⁺ for v ≤ 10, J ≤ 5 were constructed using rovibrational transition moment matrix elements calculated in a novel manner that employs the analytical dipole moment surface (DMS). The rovibrational structure of the Na⁺–H₂ v _HH = 1 ← v _HH = 0 band was calculated and compared to that of Li⁺–H₂.