SCF-CI studies on the electronic ground state of water: Potential energy hypersurface and spectroscopic constants

Large-scale Hartree-Fock self-consistent field calculations, employing extended Gaussian basis sets, and configuration interaction studies are performed to calculate the energy hypersurface of the electronic ground state of the water molecule and to investigate the accuracy requirements in view of the determination of molecular spectroscopic constants. From the calculated points on the hypersurface the theoretical equilibrium geometry, the force field through fourth order, the spectroscopic constants _i, x_ij, _i as well as the Darling-Dennison and Fermi resonance constants are evaluated. The CI surface yields an equilibrium structure for H₂O withr _e = 0.9501 Å and _e=105.33 ° (r _exp = 0.9572 Å and _exp = 104.52 °). The vibrational levels are obtained with a systematic error of about 2 percent and the rotational constants to about 1 percent compared to spectroscopic data. The relative energy maximum corresponding to the linear structure with = is calculated to be 11890cm^–1, within the error limits of the values deduced from experimental measurements.     

MRCI potential energy curves and spectroscopic constants of the ground and low-lying excited states of HgCd

The multireference configuration interaction (MRCI) electronic energy calculations with different basis sets have been performed on the ground state (X¹Σ) and three low-lying excited states (³Σ, ¹Π and ³Π) of HgCd dimer. The obtained potential energy curves (PECs) are fit to analytical potential energy functions (APEFs) using the Murrell–Sorbie potential function. Spectroscopic constants are calculated using the APEFs. Based on the PECs, the vibrational levels of each state are predicted. Our equilibrium positions of the X¹Σ state and ³Π state are in excellent agreement with the experimental reports.     

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.     

The vibrational ground state rotational spectroscopic constants and structure of the HCN dimer

Rotational spectra have been assigned for four isotopic species of the linear HCN dimer in the vibrational ground state. The spectroscopic constants are

     

5.

Generalized relativistic effective core potential calculations of the adiabatic potential curve and spectroscopic constants for the ground electronic state of the Ca2 molecule     

Nikolai S. Mosyagin  Aleksander N. Petrov  Anatoly V. Titov  Andrei V. Zaitsevskii 《International journal of quantum chemistry》2013,113(20):2277-2281

The potential curve, dissociation energy, equilibrium internuclear distance, and spectroscopic constants for the ground state of the Ca₂ molecule are calculated with the help of the generalized relativistic effective core potential method, which allows one to exclude the inner core electrons from the calculations and to take the relativistic effects into account effectively. Extensive generalized correlation basis sets were constructed and used. The scalar relativistic coupled cluster method with corrections for high‐order cluster amplitudes is used for the correlation treatment. The results are analyzed and compared with the experimental data and corresponding all‐electron results. © 2013 Wiley Periodicals, Inc.     

6.

Fourth-order MB-RSPT calculations of the spectroscopic constants and potential energy curve of F2     

Miroslav Urban  Jozef Noga  Vladimír Kellö 《Theoretical chemistry accounts》1983,62(6):549-562

The spectroscopic constants and the potential energy curve of F₂ were calculated, using the fourth-order MB-RSPT with a single-determinant RHF starting wave function. With an extended [5s4p2d1f] basis set we obtained the equilibrium bond distance and the harmonic vibrational frequency with a relative error of about 0.5%, these are in very good agreement with experiment. In calculations of the potential energy curve for distances larger than about 1.4 R_e the method breaks down. We analysed the effect of the individual fourth-order contributions: single, double, triple and quadruple excitations. The role of the renormalization term was stressed in the discussion of various approximations to the full fourth-order energy and in comparison with other related approaches. The basis set effect has been also examined.     

7.

Diagrammatic perturbation theory: Potential curves for the ground state of the carbon monoxide molecule     

Stephen Wilson 《International journal of quantum chemistry》1977,12(4):609-622

Diagrammatic many-body perturbation theory is used to calculate the potential energy function for the X¹ σ+ state of the CO molecule near the equilibrium nuclear configuration. Spectroscopic constants are derived from a number of curves which are obtained from calculations taken through third order in the energy. By forming [2/1] Padé approximants to the constants we obtain: r_e = 1.125 Å (1.128 Å), B_e = 1.943 cm^?1 (1.9312 cm^?1), a^B_e = 0.0156 cm^?1 (0.0175 cm^?1), W_e = 2247 cm^?1 (2170 cm^?1), W_eX_e = 12.16 cm^?1 (13.29 cm^?1), where the experimental values are given in parenthesis.     

8.

The potential energy function for the ground state of CCl calculated from spectroscopic data     

A. A. urkus 《Chemical physics letters》1988,150(6):416-418

The dissociation energy (D_e= 57754±872 cm⁻¹ has been estimated for the ground state of CCl⁺ by fitting a Hulburt-Hirschfelder potential to the RKR turning points. This value of D_e has been used together with molecular constants B_e, ω_e, a_i (i= 1–6) and R_e obtained by Gruebele and co-workers to construct a potential energy function for CCl⁺ in the form of a perturbed Morse oscillator.     

9.

SCF-CI calculations of the potential energy curve and one-electron property curves of theX 1∑ g + ground state of N2     

William I. Ferguson 《Theoretical chemistry accounts》1981,59(5):527-532

The energy and important one-electron properties of the nitrogen molecule are evaluated in the¹ _g ⁺ ground state for various internuclear separations near the equilibrium geometry, at the SCF-CI level. Both our Roos CI and Graphical Unitary Group (GUG) programs were used in performing single and multiple root CI computations. The one-electron properties included are the quadrupole and hexadecapole moments (both with respect to the centre of mass) and the electric field gradient at the N nucleus. Dependence of the properties upon the vibrational quantum number are evaluated using the Dunham analysis scheme.     

10.

Potential energy functions for an intramolecular proton transfer reaction in the ground and excited state     

Alessandro Cembran  Jiali Gao 《Theoretical chemistry accounts》2007,118(1):211-218

We describe the development of empirical potential functions for the study of the excited state intramolecular proton transfer reaction in 1-(trifuloroacetylamino)-naphtaquinone (TFNQ). The potential is a combination of the standard CHARMM27 force field for the backbone structure of TFNQ and an empirical valence bond formalism for the proton transfer reaction. The latter is parameterized to reproduce the potential energies both in the ground and the excited state, determined at the CASPT2 level of theory. Parameters describing intermolecular interactions are fitted to reproduce molecular dipole moments computed at the CASSCF level of theory and to reproduce ab initio hydrogen bonding energies and geometries for TFNQ-water bimolecular complexes. The utility of this potential energy function was examined by computing the potentials of mean force for the proton transfer reactions in the gas phase and in water, in both electronic states. The ground state PMF exhibits little solvent effects, whereas computed potential of mean force shows a solvent stabilization of 2.5 kcal mol⁻¹ in the product state region, suggesting proton transfer is more pronounced in polar solvents, consistent with experimental findings. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Contribution to the Fernando Bernardi Memorial Issue.     

11.

Potential energy curves for NiH and NiH2     

M. P. Guse  R. J. Blint  A. B. Kunz 《International journal of quantum chemistry》1977,11(5):725-732

The potential energy curves for the NiH and linear HNiH molecules resulting from the 3d⁸4s² and 3d⁹4s configuration of nickel are calculated using the unrestricted Hartree–Fock and perfect pairing generalized valence bond methods. NiH bonding in the 3d⁸4s² configuration is by means of an sp hybrid orbital which comes from the 4s² shell leaving a singly occupied nonbonding orbital free to bond to another hydrogen atom. The bond to the 3d⁹4s configuration contains primarily the 4s orbital leaving an empty orbital in the nickel 3d shell which in turn bonds very weakly with another hydrogen. These results are compared to similar studies of the hydrogen atom on Sc, Mn and Cu and some implications for hydrocarbon catalysis are considered.     

12.

A new "spectroscopic" potential energy surface for formaldehyde in its ground electronic state     

Yachmenev A  Yurchenko SN  Jensen P  Thiel W 《The Journal of chemical physics》2011,134(24):244307

We report a new "spectroscopic" potential energy surface (PES) of formaldehyde (H(2)(12)C(16)O) in its ground electronic state, obtained by refining an ab initio PES in a least-squares fitting to the experimental spectroscopic data for formaldehyde currently available in the literature. The ab initio PES was computed using the CCSD(T)/aug-cc-pVQZ method at 30 840 geometries that cover the energy range up to 44 000 cm(-1) above equilibrium. Ro-vibrational energies of formaldehyde were determined variationally for this ab initio PES by means of the program TROVE [Theoretical ROtation-Vibration Energies; S. N. Yurchenko, W. Thiel, and P. Jensen, J. Mol. Spectrosc. 245, 126 (2007)]. The parameter values in the analytical representation of the PES were optimized in fittings to 319 ro-vibrational energies with J = 0, 1, 2, and 5. The initial parameter values in the fittings were those of the ab initio PES, the ro-vibrational eigenfunctions obtained from this PES served as a basis set during the fitting process, and constraints were imposed to ensure that the refined PES does not deviate unphysically from the ab initio one in regions of configuration space not sampled by the experimental data. The resulting refined PES, referred to as H(2)CO-2011, reproduces the available experimental J ≤ 5 data with a root-mean-square error of 0.04 cm(-1).     

13.

Structural and energy properties study using the AM1 calculations of aza-azulenes in their ground state     

K. Elblidi  A. Boucetta  B. Benali  A. Kadiri  C. Cazeau-Dubroca  G. Nouchi  M. Pesquer 《Journal of Molecular Structure》1995,343(1-3):57-62

AM1 calculations with complete optimization have been carried out on the azulene molecule and its derivatives such as 1-aza-azulene and 1,3-diaza-azulene. We show that AM1 is an appropriate method for predicting the structure and energy properties of azulene. Experimental values are found with good accuracy and computer results are analogous to those obtained by sophisticated methods such as the ab initio method (6-31G^*). We describe a complete theoretical study of the structural and energy properties of 1-aza-azulene and 1,3-diaza-azulene in their ground states using the same method with full geometry optimization. From the theoretical finding, the most stable conformations are proposed. Otherwise, these geometrical conformations are preserved in order to determine some spectroscopic values of these compounds using the CNDO/M method. Our results are in qualitative agreement with the experimental data.     

14.

Complete Cl calculations on the ground state of HeH     

D.B. Knowles  J.N. Murrell  J.P. Braga 《Chemical physics letters》1984,110(1):40-42

Complete Cl calculations on the van der Waals molecule HeH with a large Gaussian basis set give the depth of the potential well as c = 0.50 meV and a minimum at R_m = 3.64 Å. An analytical function has been fitted to the ab initio points and to the best estimates of the dispersion energy coefficients. One further parameter in the potential has been chosen to reproduce the HeH scattering cross section.     

15.

Extended Hartree–Fock calculations for the helium ground state     

Roland Lefebvre  Yves G. Smeyers 《International journal of quantum chemistry》1967,1(4):403-419

The extended Hartree–Fock (EHF) wave function of an n-electron system is defined (Löwdin, Phys. Rev. 97 , 1509 (1955)) as the best Slater determinant built on one-electron spin orbitals having a complete flexibility and projected onto an appropriate symmetry subspace. The configuration interaction equivalent to such a wavefunction for the ¹S state of a two-electron atom is discussed. It is shown that there is in this case an infinite number of solutions to the variational problem with energies lower than that of the usual Hartree–Fock function, and with spin orbitals satisfying all the extremum conditions. Two procedures for obtaining EHF spin orbitals are presented. An application to the ground state of Helium within a basic set made up of 4(s), 3(p₀), 2(d₀) and 1 (f₀) Slater orbitals has produced 90% of the correlation energy.     

16.

Theoretical investigation of the low-lying electronic states of the alkaline hydride BeH2+ ion: Potential energy curves, spectroscopic constants, vibrational levels, and transition dipole functions     

M. Farjallah  C. Ghanmi  H. Berriche 《Russian Journal of Physical Chemistry A, Focus on Chemistry》2012,86(8):1226-1235

The structure and spectroscopic properties of the alkaline hydride BeH²⁺ ion have been investigated using an ab initio approach based on nonempirical pseudopotentials and parameterized l-dependent polarization potentials. The adiabatic potential energy curves and their spectroscopic constants for the ground and seventeen excited electronic states, dissociating into Be⁺(2s, 2p, 3s, 3p, 3d, 4s, 4p, and 4d) + H⁺ and Be²⁺ + H(1s and n = 2), of ²??⁺, ²??, and ²?? symmetries have been determined. As no experimental data are available, our results are discussed and compared with the few existing theoretical calculations. A very good agreement has been found with the previous theoretical data for the ground state; however many potential energy curves for the higher excited states are presented here, for the first time. Numerous avoided crossings between electronic states for ²??⁺ and ²?? symmetries have been localized and analyzed. Their existence is related to the interaction between the electronic states and to the charge transfer process between the two ionic systems Be²⁺H and Be⁺H⁺. In addition, we have calculated the vibrational energy level spacings of the bound electronic states. Furthermore, the adiabatic transition dipole functions from the X ²??⁺ and 2²??⁺ states to the higher excited states of ²??⁺ and ²?? symmetries have been evaluated and compared with the available theoretical work. This study represents the necessary initial step towards the investigation of the charge transfer processes in collision between Be⁺-H⁺ and Be²⁺-H.     

17.

Multiresolution potential energy surfaces for vibrational state calculations     

Kiyoshi Yagi  So Hirata  Kimihiko Hirao 《Theoretical chemistry accounts》2007,118(3):681-691

A compact and robust many-mode expansion of potential energy surfaces (PES) is presented for anharmonic vibrations of polyatomic molecules, where the individual many-mode terms are approximated with various different resolutions, i.e., electronic structure methods, basis sets, and functional forms. As functional forms, the following three representations have been explored: numerical values on a grid, cubic spline interpolation, and a Taylor expansion. A useful index is proposed which rapidly identifies important many-mode terms that warrant a high resolution. Applications to water and formaldehyde demonstrate that the present scheme can increase the efficiency of the PES computation by a factor of up to 11 with the errors in anharmonic vibrational frequencies being no worse than ~ 10cm⁻¹.     

18.

Potential energy curves for Li₂     

D.K. Watson  C.J. Cerjan  S. Guberman  A. Dalgarno 《Chemical physics letters》1977,50(2):181-186

A model potential method is used to calculate the potential curves of a large number of states of the lithium molecule and comparisons are made with other theoretical and experimental data. Agreement is generally satisfactory. Several bound states are predicted that have not been identified experimental including a ³Σ^?_g state that dissociates into two excited atoms.     

19.

Molecular constants for the 1Σ+ ground state of the ArH+ ion     

Pavel Rosmus 《Theoretical chemistry accounts》1979,51(4):359-362

From the near equilibrium PNO-CEPA potential and dipole moment curves the following molecular constants for the ¹⁺ ground state of the ArH⁺ ion have been calculated: r _e = 1.286Å, _e = 2723 cm^–1, _{e e} = 56 cm^–1, D ₀ = 3.89 eV and ₀ = 2.384 D. The rotationless radiative lifetimes of the five lowest vibrational states are predicted to be 2.28, 1.2, 0.85, 0.64, 0.46 for ArH⁺ and 9.09, 4.71, 3.27, 2.55 and 2.11 for ArD⁺, respectively (all values are in milliseconds and in ascending order of the vibrational levels).Dedicated to Prof. Hermann Hartmann on the occasion of his 65th birthday.     

20.

Calculation of spectroscopic constants for the ground electronic states of CsK, CsLi, and RbLi molecules     

A. D. Smirnov 《Journal of Structural Chemistry》2007,48(1):21-27

Vibrational, rotational, and centrifugal constants are calculated for the ground electronic states of CsK, CsLi, and RbLi molecules. This calculation is performed on the basis of potential curves constructed in this work in a wide range of internuclear distances.     

isotope	-B0 (MHz)	DJ (kHz)	xN1 (MHz)	xN2 (MHz)
HC14N-HC14N	1745.80973(50)	2.133(30)	?4.0973(200)	?4.4400(190)
HC14N-HC15N	1700.30190(30)	1.939(40)	?4.1059(10)	-
HC15N-HC14N	1729.92082(20)	2.023(30)	-	?4.4339(6)
HC15N-HC15N	1684.28825(25)	1.900(30)	-	-

Generalized relativistic effective core potential calculations of the adiabatic potential curve and spectroscopic constants for the ground electronic state of the Ca2 molecule

The potential curve, dissociation energy, equilibrium internuclear distance, and spectroscopic constants for the ground state of the Ca₂ molecule are calculated with the help of the generalized relativistic effective core potential method, which allows one to exclude the inner core electrons from the calculations and to take the relativistic effects into account effectively. Extensive generalized correlation basis sets were constructed and used. The scalar relativistic coupled cluster method with corrections for high‐order cluster amplitudes is used for the correlation treatment. The results are analyzed and compared with the experimental data and corresponding all‐electron results. © 2013 Wiley Periodicals, Inc.     

Fourth-order MB-RSPT calculations of the spectroscopic constants and potential energy curve of F2

The spectroscopic constants and the potential energy curve of F₂ were calculated, using the fourth-order MB-RSPT with a single-determinant RHF starting wave function. With an extended [5s4p2d1f] basis set we obtained the equilibrium bond distance and the harmonic vibrational frequency with a relative error of about 0.5%, these are in very good agreement with experiment. In calculations of the potential energy curve for distances larger than about 1.4 R_e the method breaks down. We analysed the effect of the individual fourth-order contributions: single, double, triple and quadruple excitations. The role of the renormalization term was stressed in the discussion of various approximations to the full fourth-order energy and in comparison with other related approaches. The basis set effect has been also examined.     

Diagrammatic perturbation theory: Potential curves for the ground state of the carbon monoxide molecule

Diagrammatic many-body perturbation theory is used to calculate the potential energy function for the X¹ σ+ state of the CO molecule near the equilibrium nuclear configuration. Spectroscopic constants are derived from a number of curves which are obtained from calculations taken through third order in the energy. By forming [2/1] Padé approximants to the constants we obtain: r_e = 1.125 Å (1.128 Å), B_e = 1.943 cm^?1 (1.9312 cm^?1), a^B_e = 0.0156 cm^?1 (0.0175 cm^?1), W_e = 2247 cm^?1 (2170 cm^?1), W_eX_e = 12.16 cm^?1 (13.29 cm^?1), where the experimental values are given in parenthesis.     

The potential energy function for the ground state of CCl calculated from spectroscopic data

The dissociation energy (D_e= 57754±872 cm⁻¹ has been estimated for the ground state of CCl⁺ by fitting a Hulburt-Hirschfelder potential to the RKR turning points. This value of D_e has been used together with molecular constants B_e, ω_e, a_i (i= 1–6) and R_e obtained by Gruebele and co-workers to construct a potential energy function for CCl⁺ in the form of a perturbed Morse oscillator.     

SCF-CI calculations of the potential energy curve and one-electron property curves of theX 1∑ g + ground state of N2

The energy and important one-electron properties of the nitrogen molecule are evaluated in the¹ _g ⁺ ground state for various internuclear separations near the equilibrium geometry, at the SCF-CI level. Both our Roos CI and Graphical Unitary Group (GUG) programs were used in performing single and multiple root CI computations. The one-electron properties included are the quadrupole and hexadecapole moments (both with respect to the centre of mass) and the electric field gradient at the N nucleus. Dependence of the properties upon the vibrational quantum number are evaluated using the Dunham analysis scheme.     

Potential energy functions for an intramolecular proton transfer reaction in the ground and excited state

We describe the development of empirical potential functions for the study of the excited state intramolecular proton transfer reaction in 1-(trifuloroacetylamino)-naphtaquinone (TFNQ). The potential is a combination of the standard CHARMM27 force field for the backbone structure of TFNQ and an empirical valence bond formalism for the proton transfer reaction. The latter is parameterized to reproduce the potential energies both in the ground and the excited state, determined at the CASPT2 level of theory. Parameters describing intermolecular interactions are fitted to reproduce molecular dipole moments computed at the CASSCF level of theory and to reproduce ab initio hydrogen bonding energies and geometries for TFNQ-water bimolecular complexes. The utility of this potential energy function was examined by computing the potentials of mean force for the proton transfer reactions in the gas phase and in water, in both electronic states. The ground state PMF exhibits little solvent effects, whereas computed potential of mean force shows a solvent stabilization of 2.5 kcal mol⁻¹ in the product state region, suggesting proton transfer is more pronounced in polar solvents, consistent with experimental findings. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Contribution to the Fernando Bernardi Memorial Issue.     

Potential energy curves for NiH and NiH2

The potential energy curves for the NiH and linear HNiH molecules resulting from the 3d⁸4s² and 3d⁹4s configuration of nickel are calculated using the unrestricted Hartree–Fock and perfect pairing generalized valence bond methods. NiH bonding in the 3d⁸4s² configuration is by means of an sp hybrid orbital which comes from the 4s² shell leaving a singly occupied nonbonding orbital free to bond to another hydrogen atom. The bond to the 3d⁹4s configuration contains primarily the 4s orbital leaving an empty orbital in the nickel 3d shell which in turn bonds very weakly with another hydrogen. These results are compared to similar studies of the hydrogen atom on Sc, Mn and Cu and some implications for hydrocarbon catalysis are considered.     

A new "spectroscopic" potential energy surface for formaldehyde in its ground electronic state

We report a new "spectroscopic" potential energy surface (PES) of formaldehyde (H(2)(12)C(16)O) in its ground electronic state, obtained by refining an ab initio PES in a least-squares fitting to the experimental spectroscopic data for formaldehyde currently available in the literature. The ab initio PES was computed using the CCSD(T)/aug-cc-pVQZ method at 30 840 geometries that cover the energy range up to 44 000 cm(-1) above equilibrium. Ro-vibrational energies of formaldehyde were determined variationally for this ab initio PES by means of the program TROVE [Theoretical ROtation-Vibration Energies; S. N. Yurchenko, W. Thiel, and P. Jensen, J. Mol. Spectrosc. 245, 126 (2007)]. The parameter values in the analytical representation of the PES were optimized in fittings to 319 ro-vibrational energies with J = 0, 1, 2, and 5. The initial parameter values in the fittings were those of the ab initio PES, the ro-vibrational eigenfunctions obtained from this PES served as a basis set during the fitting process, and constraints were imposed to ensure that the refined PES does not deviate unphysically from the ab initio one in regions of configuration space not sampled by the experimental data. The resulting refined PES, referred to as H(2)CO-2011, reproduces the available experimental J ≤ 5 data with a root-mean-square error of 0.04 cm(-1).     

Structural and energy properties study using the AM1 calculations of aza-azulenes in their ground state

AM1 calculations with complete optimization have been carried out on the azulene molecule and its derivatives such as 1-aza-azulene and 1,3-diaza-azulene. We show that AM1 is an appropriate method for predicting the structure and energy properties of azulene. Experimental values are found with good accuracy and computer results are analogous to those obtained by sophisticated methods such as the ab initio method (6-31G^*). We describe a complete theoretical study of the structural and energy properties of 1-aza-azulene and 1,3-diaza-azulene in their ground states using the same method with full geometry optimization. From the theoretical finding, the most stable conformations are proposed. Otherwise, these geometrical conformations are preserved in order to determine some spectroscopic values of these compounds using the CNDO/M method. Our results are in qualitative agreement with the experimental data.     

Complete Cl calculations on the ground state of HeH

Complete Cl calculations on the van der Waals molecule HeH with a large Gaussian basis set give the depth of the potential well as c = 0.50 meV and a minimum at R_m = 3.64 Å. An analytical function has been fitted to the ab initio points and to the best estimates of the dispersion energy coefficients. One further parameter in the potential has been chosen to reproduce the HeH scattering cross section.     

Extended Hartree–Fock calculations for the helium ground state

The extended Hartree–Fock (EHF) wave function of an n-electron system is defined (Löwdin, Phys. Rev. 97 , 1509 (1955)) as the best Slater determinant built on one-electron spin orbitals having a complete flexibility and projected onto an appropriate symmetry subspace. The configuration interaction equivalent to such a wavefunction for the ¹S state of a two-electron atom is discussed. It is shown that there is in this case an infinite number of solutions to the variational problem with energies lower than that of the usual Hartree–Fock function, and with spin orbitals satisfying all the extremum conditions. Two procedures for obtaining EHF spin orbitals are presented. An application to the ground state of Helium within a basic set made up of 4(s), 3(p₀), 2(d₀) and 1 (f₀) Slater orbitals has produced 90% of the correlation energy.     

Theoretical investigation of the low-lying electronic states of the alkaline hydride BeH2+ ion: Potential energy curves, spectroscopic constants, vibrational levels, and transition dipole functions

The structure and spectroscopic properties of the alkaline hydride BeH²⁺ ion have been investigated using an ab initio approach based on nonempirical pseudopotentials and parameterized l-dependent polarization potentials. The adiabatic potential energy curves and their spectroscopic constants for the ground and seventeen excited electronic states, dissociating into Be⁺(2s, 2p, 3s, 3p, 3d, 4s, 4p, and 4d) + H⁺ and Be²⁺ + H(1s and n = 2), of ²??⁺, ²??, and ²?? symmetries have been determined. As no experimental data are available, our results are discussed and compared with the few existing theoretical calculations. A very good agreement has been found with the previous theoretical data for the ground state; however many potential energy curves for the higher excited states are presented here, for the first time. Numerous avoided crossings between electronic states for ²??⁺ and ²?? symmetries have been localized and analyzed. Their existence is related to the interaction between the electronic states and to the charge transfer process between the two ionic systems Be²⁺H and Be⁺H⁺. In addition, we have calculated the vibrational energy level spacings of the bound electronic states. Furthermore, the adiabatic transition dipole functions from the X ²??⁺ and 2²??⁺ states to the higher excited states of ²??⁺ and ²?? symmetries have been evaluated and compared with the available theoretical work. This study represents the necessary initial step towards the investigation of the charge transfer processes in collision between Be⁺-H⁺ and Be²⁺-H.     

Multiresolution potential energy surfaces for vibrational state calculations

A compact and robust many-mode expansion of potential energy surfaces (PES) is presented for anharmonic vibrations of polyatomic molecules, where the individual many-mode terms are approximated with various different resolutions, i.e., electronic structure methods, basis sets, and functional forms. As functional forms, the following three representations have been explored: numerical values on a grid, cubic spline interpolation, and a Taylor expansion. A useful index is proposed which rapidly identifies important many-mode terms that warrant a high resolution. Applications to water and formaldehyde demonstrate that the present scheme can increase the efficiency of the PES computation by a factor of up to 11 with the errors in anharmonic vibrational frequencies being no worse than ~ 10cm⁻¹.     

Potential energy curves for Li2

A model potential method is used to calculate the potential curves of a large number of states of the lithium molecule and comparisons are made with other theoretical and experimental data. Agreement is generally satisfactory. Several bound states are predicted that have not been identified experimental including a ³Σ^?_g state that dissociates into two excited atoms.     

Molecular constants for the 1Σ+ ground state of the ArH+ ion

From the near equilibrium PNO-CEPA potential and dipole moment curves the following molecular constants for the ¹⁺ ground state of the ArH⁺ ion have been calculated: r _e = 1.286Å, _e = 2723 cm^–1, _{e e} = 56 cm^–1, D ₀ = 3.89 eV and ₀ = 2.384 D. The rotationless radiative lifetimes of the five lowest vibrational states are predicted to be 2.28, 1.2, 0.85, 0.64, 0.46 for ArH⁺ and 9.09, 4.71, 3.27, 2.55 and 2.11 for ArD⁺, respectively (all values are in milliseconds and in ascending order of the vibrational levels).Dedicated to Prof. Hermann Hartmann on the occasion of his 65th birthday.     

Calculation of spectroscopic constants for the ground electronic states of CsK, CsLi, and RbLi molecules

Vibrational, rotational, and centrifugal constants are calculated for the ground electronic states of CsK, CsLi, and RbLi molecules. This calculation is performed on the basis of potential curves constructed in this work in a wide range of internuclear distances.