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 electronic structure of the molecule ScBr

The potential energy curves have been investigated for the 23 lowest electronic states in the ^2s+1Λ^± representation of the molecule ScBr via CASSCF and MRCI (single and double excitations with Davidson correction) calculations. Seventeen electronic states have been studied theoretically for the first time. The harmonic frequency ω_e, the internuclear distance r_e, and the electronic energy with respect to the ground state T_e 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, R_max) have been calculated for electronic states up to the vibrational level v = 32. The comparison of these values to the theoretical and experimental results available in the literature shows a good agreement. © 2007 Wiley Periodicalsm Inc. Int J Quantum Chem, 2008     

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 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 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     

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     

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     

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.     

CEPA calculations on open-shell molecules. III. Potential curves for the six lowest excited states of He2 in the vicinity of their equilibrium distances

CEPA-PNO and PNO-CI calculations have been performed for the potential energy curves of the He ₂ ⁺ ground state and the six lowest excited states of He₂ in the range of 1.4 a₀ ≤R ≤ 3.5 a₀. The calculated equilibrium distances as well as the spectroscopic constants are in very good agreement with molecular constants as derived experimentally from the rotation-vibration spectrum of He₂ by Ginter, except for thec ³∑ _g ⁺ state. This latter discrepancy is probably due to an “obligatory” hump in thec ³∑ _g ⁺ state occurring at 3.5 a₀ which cannot be properly treated in our calculation. The relative energetic positions of the six lowest states and their ionization energies are reproduced by our calculations with an accuracy of 0–400 cm⁻¹. Extrapolation of our results to infinite basis sets leads to estimates of the dissociation energies of He₂ excited states which cannot be measured spectroscopically because of the humps in all these states.     

基态PuOH分子的多体展式分析势能函数

Using the density functional method B3LYP with relativistic effective core potential(RECP)for Pu atom,thelow-lying excited states(~4Σ~ ,~6Σ~ ,~8Σ~ )for three structures of PuOH molecule were optimized.The results showthat the ground state is X~6Σ~ of the linear Pu-O-H(C_(∞v)),its corresponding equilibrium geometry and dissociationenergy are R_(Pu-O)=0.20595 nm,R_(O-H)=0.09581 nm and —8.68 eV,respectively.At the same time,two other me-tastable structures [PuOH(C_s)and H-Pu-O(C_(∞v)] were found.The analytical potential energy function has alsobeen derived for whole range using the many-body expansion method.This potential energy function represents theconsiderable topographical features of PuOH molecule in detail,which is adequately accurate in the whole potentialsurface and can be used for the molecular reaction dynamics research.     

Theoretical structure of the low‐laying electronic states of the molecule YBr

An ab initio CASSCF and MRCI (single and double excitation plus Davidson correction) calculation have been performed for the molecule YBr. The potential energy curves of 20 electronic states in the representation ^2s+1Λ^(+/?) (neglecting the spin‐orbit effects) and 41 states in the representation Ω^(+/?) [including the spin‐orbit (SO) effects] have been calculated along with the corresponding spectroscopic constants. The SO effects are taken into account via a semi‐empirical SO pseudo‐potential for the yttrium atom, while they have been neglected for bromine. Very good agreement is displayed by comparing the present results with those obtained experimentally, up to now, of the three states X¹Σ⁺, (1)²Π, and (2)¹Σ⁺. New results have been obtained for 17 states ^2s+1Λ^(+/?), and their SO components yet not observed or calculated. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Theoretical calculation of the electronic states with spin‐orbit effects of the molecule NaRb

The potential energy curves of the molecule NaRb have been calculated for the 60 low‐lying electronic states in the Ω‐representation. Using an ab‐initio method the calculation is based on nonempirical pseudo‐potential in the interval 3.0a_o ≤ R ≤ 44.0a_o of the internuclear distance. The spin‐orbit effects have been taken into account through a semiempirical spin‐orbit pseudo‐potential added to the electrostatic Hamiltonian with Gaussian basis sets for both atoms. The spectroscopic constants have been calculated for 42 states and the components of the spin‐orbit splitting have been identified for the states (1, 2, 5)³Π and (1, 2)³Δ. The comparison of the present results with those available in literature shows a good agreement, whereas the other results, to the best of our knowledge, are given here for the first time. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Theoretical study of low‐lying electronic states of the LiRb+ molecular ion: Structure,spectroscopy and transition dipole moments

The electronic structure and the spectroscopic properties for low‐lying electronic states of the LiRb⁺ molecular ion, dissociating into Li (2s, 2p, 3s, 3p, 3d, 4s, and 4p) + Rb⁺ and Li⁺ + Rb (5s, 5p, 4d, 6s, 6p, 5d, and 7s), have been investigated using an ab initio approach based on non‐empirical pseudo potentials for the Li and Rb cores and parametrized l‐dependent polarization potential. We have determined the adiabatic potential energy curves and their spectroscopic constants for many electronic states of ²Σ⁺, ²Π, and ²Δ symmetries. A satisfying agreement, for the spectroscopic constants, has been obtained for the ground and the first excited states with the available theoretical works. Potential energy curves were presented, for the first time, for the higher excited states. In addition, we have localised and analysed the avoided crossings between electronic states of ²Σ⁺ and ²Π symmetries. Their existences can be related to the interaction between the potential energy curves and to the charge transfer process between the two ionic systems Li⁺Rb and LiRb⁺. Moreover, we have determined the transition dipole moments from X²Σ⁺ and 2²Σ⁺ states to higher excited states of ²Σ⁺ and ²Π symmetries. For our best knowledge, no experimental data on the LiRb⁺ molecular ion is available. These theoretical data can help experimentalists to optimize photoassociative formation of ultracold LiRb⁺ molecular ion and their longevity in a trap or in an optical lattice. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Theoretical treatment of predissociation of the CO (3sσ) B and (3pσ) C1Σ+ Rydberg states based on a rigorous adiabatic representation

Ab initio multireference configuration interaction calculations for adiabatic potential curves, nonadiabatic couplings 〈φ _i (R,r)|d/dR|φ _j (R,r)〉 and 〈φ _i (R,r)|d²/dR ²|φ _j (R,r)〉, and nuclear kinetic energy corrections 〈dφ _i (R,r)/dR|dφ _i (R,r)/dR〉 for the (3sσ) B and (3pσ) C¹Σ⁺ Rydberg states of the CO molecule have been carried out. The energy positions and predissociation linewidths for the observed vibrational levels of these two states have been determined in a rigorous adiabatic representation by the complex scaling method employing a basis of complex scaled harmonic vibrational functions in conjunction with the Gauss-Hermite quadrature method to evaluate the complex Hamiltonian matrix elements. The present treatment correctly reproduces the observed trends in energies and line broadening for vibrational levels of the B¹Σ⁺ state and represents an improvement over the previous treatment in literature. The errors in the determined spacings of the v = 0–4 vibrational levels of the C¹Σ⁺ state are less than 2% compared with measured data. The predissociation linewidths for the v=3,4 levels of the C¹Σ⁺ state are found to be 4.9 and 8.9 cm⁻¹, respectively, in good agreement with the observed values. Received: 23 March 1998 / Accepted: 27 July 1998 / Published online: 9 October 1998     

Electronic,spectra, and spin orbit interaction for FrAr van der Waals system

The potential energy curves and spectroscopic constants of the ground and many excited states of the FrAr van der Waals system have been determined using a one‐electron pseudopotential approach. The Fr⁺ core and the electron–Ar interactions are replaced by effective potentials. The Fr⁺Ar core–core interaction is incorporated using the accurate CCSD(T) potential of Hickling et al. (Phys. Chem. Chem. Phys. 2004, 6, 4233). This approach reduces the number of active electrons of the FrAr van der Waals system to only one valence electron, which permits the use of very large basis sets for the Fr and Ar atoms. Using this technique, the potential energy curves of the ground and many excited states are calculated at the self consistent field (SCF) level. In addition, the spin–orbit interaction is also considered using the semiempirical scheme for the states dissociating into Fr (7p) and Fr (8p). The FrAr system is not studied previously and its potential interactions, spectroscopic constants and dipole functions are presented here for the first time. Furthermore, we have predicted the X²Σ⁺–A²Π_1/2, X²Σ⁺–AΠ_3/2, X²Σ⁺–B²Σ_1/2⁺, X²Σ⁺–3²Π_1/2, X²Σ⁺–3²Π_3/2, and X²Σ⁺–5²Σ_1/2⁺ absorption spectra. © 2012 Wiley Periodicals, Inc.     

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.     

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     

An ab initio potential energy surface and spectroscopic constants for the XΣg state of NO2

A three-dimensional potential energy function has been calculated for the X¹Σ⁺_g state of NO⁺₂ from ab initio MRD-CI data. With this PE function, converged vibrational calculations have also been performed for ten vibrational states, with the aid of a computer program developed in the present work for this purpose. The calculated harmonic frequencies, vibrational term values and rotational constants are in good agreement with experimental data.     

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.