[en] The aim of this work is to dissociate, in the wave function describing the vibration-rotation motion of a diatomic molecule, the effect of the rotation from the pure vibration wave function and to give the analytic expression of this rotational effect. 14 refs, 5 figs, 14 tabs

[en] Ab initio CASSCF/MRCI calculations have been performed for the molecule LaCl, for 11 molecular states in the representation ^2S+1Λ^(+/-) (neglecting spin-orbit effects). The corresponding 25 molecular states in the representation Ω^(+/-) (including spin-orbit effects) have been subsequently determined using a semi-empirical spin-orbit pseudopotential built up for lanthanum. Calculated potential energy curves and spectroscopic constants are reported, to the best of our knowledge they are the first ones for excited states of this molecule. Comparison of present data with experimental results available in literature show a good agreement

[en] A theoretical study of the electronic structure of Rb₂⁺ has been performed, including or not spin-orbit (SO) coupling. Potential energy curves for all the molecular states dissociating up to the limit Rb⁺+Rb(7s ²S_1/2) (i.e., 26 states in the representation ²Λ⁽⁺⁾_g,u and 38 states in the representation Ω_g,u) are displayed. Equilibrium distances, transition energies and depths for the wells predicted at short and large range of R are reported. The existence of some of the long-range wells are confirmed by a specific model. Extensive tables of energy values versus internuclear distances are available at the following address: http://lasim.univ-lyon1.fr/allouche/rb2plus.htm

[en] Full text.By taking into consideration the spin-orbit effect, the potential energy has been calculated over a wide range of internuclear distance for numerous electronic states of symmetry ²□⁺, ²□, ²□ and Ω of the molecular ion RbCs+ and by using the package CIPSI (Configuration Interaction by Perturbation of multiconfiguration wave function Selected Iterative) of Laboratoire de Physique Quantique (Toulouse-France). This calculation is done by using an ab initio method based on non-empirical pseudopotentials, parameterized l-dependent polarization potentials. Molecular orbitals for the molecular ion RbCs+ were derived from Self Consistent Field calculations (SCF), and full valence Configuration Interaction (CI) calculations were performed. A rovibrational study is done by calculating the eigenvalues E_v, the rotational constant B_v, teh centrifugal distortion constant D_v (up to 120 vibrational levels) and the spectroscopic constants for four bound states ²Λ⁺ and Ω. To the best of our knowledge, neither theoretical noe experimental data are available in the literature for the molecular ion RbCs+. Extensive tables of energy values versus internuclear distance are displayed at the following address http:lasim.univ-lyon1.fr/allouche/mcs.htm

[en] For a transition vJ↔v'J' (J'=J±1) the eigenvalues and the eigenfunctions of the two considered states can be expressed respectively in terms of one variable m (transition number), relating these two states, as E _vm = Σ_i=0 e_v⁽ⁱ⁾mⁱ, Ψvm=_i=0 φ_v⁽ⁱ⁾m and E_v'm=Σ_i=oe_v'⁽ⁱ⁾mⁱ , Ψ_v'm=Σ_i=o ..., where m=[J'(J'+1)-J(J+1)]/2, and the coefficients e_v⁽ⁱ⁾, ..._v⁽ⁱ⁾, e_v⁽ⁱ⁾ and ..._v⁽ⁱ⁾ are given by analytical expressions. This new expansion in the perturbation theory permits a direct calculation of many factors in spectroscopy that are expanded in terms of m as the line intensities, the wave number of a transition, the Herman-Wallis coefficients, ... etc. The numerical application shows that the present unconventional approach in the perturbation theory provides a simple and accurate method for the calculation of the eigenvalues and the eigenfunctions for the two considered states of the molecule CO and for the calculation of the Herman-Wallis coefficients for the ground state of the molecule HCl. (Author)

[en] Full text.The molecular activities in ultra-cold alkali atom trapping stimulate theoretical developments to compute relevant adiabatic potential curves, especially in the framework of the pseudopotential methods. For these methods the molecular ion KRb+ is treated as system with one active electron moving in a field of two ionic cores, where core valence electron interactions are presented by an effective potential. Potential energies have been calculated over a wide range of internuclear distance (5.0-60a_o) for the lowest states of symmetry ²Σ, ²Π, ²Δ and Ω for the molecular ion KRb+. To avoid an over estimation of the dissociation energy the perturbative treatment is replaced by an l-dependent core-polarization potential of the Foucrault et al. For the one valence electron of the two considered atoms, we recalculated the polarization potential cut-off parameters r_k^l, and r_Rb^l by taking l=0,1,2 and r_i²=r_i³. Molecular orbital for the molecular ion KRb+ were derived from Self Consistent Field calculations (SCF), and full valence Configuration Interaction (IC) calculations were performed. Extensive tables of energy values versus internuclear distance are displayed and molecular spectroscopic constants have been derived, for the first time, for the bound states with regular shape

[en] Full text.By using an ab initio calculation with the spin-orbit effect the potential energy has been calculated over a wide range of internuclear distance (5.0-60a_o) for numerous electronic states of symmetry ²Σ⁺, ²Π, ²Δ and Ω for the molecular ion KCs+. To avoid an over estimation of the dissociation energy the perturbative treatment is replaced by an l-dependent core-polarization potential of the Foucrault et al. For the atoms K and Cs we used respectively the following Gaussian basis sets: (8s 7p 4d/ 7s 5p 2d) and (7s 6p 5d/ 8s 7p 6d). Core-valence effect, including core polarization and core-valence correlation are taken into consideration. Molecular orbital for the molecular ion KCs+ were derived from Self Consistent Field calculations (SCF), and full valence Configuration Interaction (IC) calculations were performed. By using a canonical functions approach a rovibrational study is done for calculating the eigenvalues E_v, the rotational constant B_v, the centrifugal distortion constant D_v (up to 120 vibrational levels) and the spectroscopic constants for eight bound states ²Λ⁺ and Ω. Extensive tables of energy values versus internuclear distance are displayed at the following address http:lasim.univ-lyon1.fr/allouche/mcs.htm

[en] Since there is lack in the excited electronic states of alkaline earth compound, candidate for ultracold investigation, and by using an ab initio calculation the potential energy curves have been obtained for the lowest electronic states in the 2s+1Λ(±) representation below 53000 cm-1 along with the harmonic frequency w_e, the internuclear distance r_e, the rotational constant B_e, and the electronic energy with respect to the ground state T_e. The comparison of these values to the theoretical and experimental results available in the literature shows a good agreement. (author)

[en] The problem of the rotational effect in the rovibrational matrix elements M_υJ^υ'J' =<Ψ_υJ|f(r)Ψ_υ'J'> is considered. Rayleigh-Schroedinger perturbation theory is used to show that, for any diatomic electronic potential U(r) (even of the RKR type) and for any operator f(r), the rotational factor G_υυ'(J,J')M_υJ^υ'J'/M_υO^υ'O' is given by G_υυ'(J,J')G_υυ'^(O) + G_υυ'⁽¹⁾m + G_υυ'⁽²⁾m² + ... with m=[J'(J'+1)-J(J+1)]/2. The coefficients G_υυ'⁽⁰⁾, G_υυ'⁽¹⁾ and G_υυ'⁽²⁾ are simply deduced from the integrals < Y_υ|f|Y_υ'>, in which Y denotes the pure vibrational wavefunction Ψ_υ⁽⁰⁾, or a successive perturbative correction Ψ_υ⁽¹⁾, Ψ_υ⁽²⁾,... Numerical applications to the RKR potential of the X 0_g⁺ state of I₂ (for the transitions υ=0 and δυ ≤8 with m = -5, -10, -15) and to the Dunham potentials of the ground states of HCl (for the transitions υ=0 and δυ≤7 with m = -2, -4, -6, -8) and HF molecules (for the transitions υ=0 and δυ≤5 with m-2, -4, -6, -8) shows the satisfactory accuracy of the present formulation. (Author)

[en] Full text: The renewed interest on the spectroscopic study of the alkali dimers, and the need for a theoretical prediction of this molecule, encourage us to present in this work a theoretical study of the electronic structure of the molecule LiRb. An investigation of the lowest states of the symmetry ^1,3Σ⁺, ^1,3Π, and ^1,3Δ for this molecule is done. The potential energy is calculated over a wide range internuclear distance (5-60a_o) for the corresponding 36 lowest states. This calculation is done by ab-initio methods founded on quantum considerations, a non-empirical pseudopotentials and parameterized core polarization potentials. Molecular orbitals are derived from Hartree-Fock approximation, followed by Self Consistent Field (SCF) and full valence Configuration Interaction (CI) calculations. The calculated dissociation energies are compared to experimental results for the 7 lowest dissociation limits. Molecular spectroscopic constants are calculated for the bound states with regular shape. To the best of our knowledge, the potential energies of the considered electronic states and the spectroscopic constants are given here for the first time