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 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 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 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 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 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     

Character of the electronic ground state and of charge-transfer excited states in ionic solids: An ab initio cluster model approach

The electronic structure of the ground electronic state and of some special charge-transfer excited states in ionic solids is examined from the ab initio cluster model approach. Different ab initio wave functions, including a frozen orbital approach, the Hartree–Fock self-consistent field, and multireference configuration interaction wave functions, are considered and analyzed using different theoretical techniques. We explicitly consider some alkaline–earth oxides such as CaO, a more difficult case such as A1₂O₃, a transition-metal oxide such as NiO, and a system with a more complicated structure such as KNiF₃. Analysis of ab initio wave functions in terms of valence bond components shows that all these compounds are largely ionic, thus supporting the simple picture arising from the ionic model. However, the nature of the excited states is more complex. Alkaline–earth oxides lowest excited states are essentially described as charge-transfer excitations dominated by a single resonant valence bond structure and the calculated energy difference is comparable to the experimental optical gap. In the case of A1₂O₃, the electronic spectra presents excitonic features and the local charge-transfer excitation excited states provide a reasonable representation of these phenomena. Finally, several different valence bond structures are present in the lowest electronic states of KNiF₃. © 1994 John Wiley & Sons, Inc.     

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     

Deltafunction model for the helium dimer

The helium dimer ⁴He₂ has recently been detected, confirming earlier ab initio predictions of stability for a single bound state with binding energy of 1.310 mK. The predicted potential minimum is at 2.96 Å, with a radial distribution function peaking at 6.96 Å. We model this system using a Dirac bubble potential, which also admits just one bound j = 0 state. With the bubble located at 6.96 Å, an overlap of 0.9994 with the ab initio wave function is obtained. An average internuclear distance of 52.6 Å is calculated, in good agreement with the ab initio result. The root mean square deviation from the mean, 48.0 Å, indicates an enormous spread of the radial wave function. Also consistent with our model is the absence of bound states for the isotopic variants ³He⁴He and ³He₂. Cross sections for helium-helium scattering are also computed, using both a partial-wave expansion and the Born approximation. General trends in the energy dependence of the total cross section are accounted for, in qualitative agreement with experimental results. © 1995 John Wiley & Sons, Inc.     

Generalized quantum mechanical two-centre problems

For the one-electron Schrödinger equation among the solutions of which the Slater-Zener-type functions can be found, it is shown, that it can be generalized to the two-centre case only in one way, if one demands separability in prolate spheroidal coordinates, and if in addition to the Coulomb term of the potential energy there shall be an additional function of the product r ₁ · r ₂ only. The generalized problem with a potential energy of the form V(r) = ? Z₁/r₁ ? Z₂/r₂ ? Q(R)/r₁r₂ is studied for the case of two equal centres Z ₁=Z₂=Z≧0 with regard to the existence and number of bound states. The results are extended as far as possible also to the case with unequal centres. For some examples with equal centres wave functions and correlation diagrams have been computed exactly for the lowest electronic states.     

Quantum-chemical study of the geometric and electronic structure of the CoC2 molecule

DFT (B3LYP) calculations have been performed to study the CoC₂ molecule in its different geometric conformations and electronic states. The energies have been refined using ab initio multiconfigurational CASSCF/CASPT2 calculations. Both approaches are in a good semi-quantitative agreement between themselves and predict the symmetric triangular (C_2v) structure to be more stable than the linear (C_∞v) conformation. The ground state has been found to be a quartet, which can formally be regarded as an ionic Co²⁺–C₂²⁻ complex, resulting from a transfer of the two 4s electrons of the cobalt atom to the 3σ_g orbital of the C₂ ligand and distributing the remaining seven valence electrons over the split 3d orbitals.     

Favorable performance of the DFT methods in predicting the minimum‐energy structure of the lowest triplet state of WF4

The tetrahedral structure of the lowest triplet state of the WF₄ complex was examined using different variants of the density functional theory (DFT) and conventional ab initio methods. The low‐level, conventional, ab initio methods, such as SCF, MP2, MP3, and CISD, predict the tetrahedral structure to be a minimum, whereas the DFT schemes predict an imaginary frequency for the e vibrational mode. Only after recovering electron correlation effects at the MP4 and higher levels, the conventional electronic structure methods also predict the T_d structure to be a second‐order stationary point. This is not the correlation but the exchange part of the DFT functionals which is responsible for the discrepancy between the DFT and low‐level, conventional, ab initio predictions. The lowering of symmetry to C_2v leads to a minimum on the lowest triplet potential energy surface and the electronic energy difference between the T_d and C_2v stationary points amounts to 0.85 and 0.96 kcal/mol at the B3LYP and CCSD(T) levels, respectively. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 369–375, 1999     

Computed lifetimes of metastable states of the NO2+ dication

Based on the ab initio potential energy, spin-orbit coupling, electronic transition dipole moment, and radial nonadiabatic coupling functions, the energy level positions, lifetimes, and radiative transition probabilities (Einstein A coefficients) have been determined for the lowest electronic states of NO2+ using the log-amplitude-phase, stabilization, and complex-scaling methods. The calculated characteristics are in reasonable agreement to the available experimental data, thus, evidencing the reliability of the theoretical predictions for the characteristics unobserved to date. With the exception of the v相似文献   

Molecular properties of Li2+ from model potential calculations

The constructive model potential approach of Bottcher and Dalgarno is used in the calculation of some molecular properties of two electronic states, ²Σ_g⁺ and ²Π_u, of Li₂⁺ at several internuclear distances. The results agree well with ab initio calculations.     

Ab initio computations of spin-orbit interactions in polyatomic molecules. Splitting of sulfur LII,III states and singlet–triplet transitions in SO2

Spin-orbit interactions among the ground and the first few excited electronic states of SO₂, are computed with ab initio molecular wave functions and Gaussian atomic orbitals. All spin-other orbits contributions to the matrix elements are included. The computed intensity of the first singlet–triplet transition is found to be in broad agreement with experiment and sensitive to an extension of the configuration interaction expansion of molecular wave functions. Also, the splitting of sulfur L_{II ,III} states in SO₂ is derived as an example of large spin-orbit interactions among electronic states.     

Ab initio study of the ground and lower-lying excited electronic states of NiX2 and FeX2 (X=F,Cl, Br,I) molecules

The ground and lower-lying excited electronic states of FeX₂ and NiX₂ (X=F, Cl, Br, I) molecules are systematically investigated by ab initio method at the complete active space self-consistent field (CASSCF) and multiconfigurational quasi-degenerate second-order perturbation (MCQDPT2) levels of theory. It is concluded that the dynamic electron correlation has to be taken into account in the prediction of the properties for such kind of molecules. The equilibrium bond lengths r_e(M–X), force constants and harmonic vibrational frequencies are calculated for the ground and lower-lying excited electronic states. The spin-orbit coupling (SOC) effects are analysed.     

Ab initio calculations on low-lying electronic states of PdH

Potential energy curves for the low-lying electronic states of PdH have been calculated using the MRCI method with scalar relativistic and spin-orbit corrections, and all electronic states correlating to the 4d¹⁰ (¹S), 4d⁹ 5s¹ (³D), 4d⁹ 5s¹ (¹D) and 4d⁸ 5s² (³F) states of Pd were included. Potential energy curves for the individual Ω states have been obtained, and the experimentally observed spectra of both PdH and PdD isotopologues have been assigned appropriately based on the ab initio results. Einstein A coefficients were calculated for other possible transitions from the low-lying electronic states to the X²Σ⁺ ground state. Diagonal and off-diagonal matrix elements of the spin-orbit Hamiltonian were calculated for all vibrational levels of the X²Σ⁺, 1²Δ, 1²Π, 2²Σ⁺ and 3²Σ⁺ states, and it was found from the eigenvectors that the vibrational wavefunctions of the 1²Δ_3/2 and 1²Π_3/2 states are mixed significantly in both PdH and PdD isotopologues.     

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     

Magnetic Properties and Electronic Structure of Neptunyl(VI) Complexes: Wavefunctions,Orbitals, and Crystal‐Field Models

The electronic structure and magnetic properties of neptunyl(VI), NpO₂²⁺, and two neptunyl complexes, [NpO₂(NO₃)₃]^? and [NpO₂Cl₄]^2?, were studied with a combination of theoretical methods: ab initio relativistic wavefunction methods and density functional theory (DFT), as well as crystal‐field (CF) models with parameters extracted from the ab initio calculations. Natural orbitals for electron density and spin magnetization from wavefunctions including spin–orbit coupling were employed to analyze the connection between the electronic structure and magnetic properties, and to link the results from CF models to the ab initio data. Free complex ions and systems embedded in a crystal environment were studied. Of prime interest were the electron paramagnetic resonance g‐factors and their relation to the complex geometry, ligand coordination, and nature of the nonbonding 5f orbitals. The g‐factors were calculated for the ground and excited states. For [NpO₂Cl₄]^2?, a strong influence of the environment of the complex on its magnetic behavior was demonstrated. Kohn–Sham DFT with standard functionals can produce reasonable g‐factors as long as the calculation converges to a solution resembling the electronic state of interest. However, this is not always straightforward.