Degenerate symmetry-adapted perturbation theory of weak interactions between closed- and open-shell monomers: application to Rydberg states of helium hydride

Symmetry-adapted perturbation theory is extended to the (quasi) degenerate, open-shell case. The new formalism is tested in calculations of the interaction energies for a helium atom in the ground state interacting with an excited hydrogen atom. It is shown that the method gives satisfactory results if the coupling with higher Rydberg states of the dimer is small, as is the case for the A²Σ⁺,B²Π,E²Π,3²Π, and 1²Δ states of HeH. For the C²Σ⁺ state convergence of the method is very slow, but it can be improved by including the n=3 states in the model space. Received: 3 June 1998 / Accepted: 9 September 1998 / Published online: 7 December 1998     

Dissociative recombination of HeH+. I. Rovibrational spectrum of HeH Rydberg states

The repulsive ground electronic state X²Σ⁺ of HeH is strongly coupled to the Rydberg states at small interatomic distances. Such large couplings also occur between some of the Rydberg states. HeH⁺ ions that capture an electron in a Rydberg state end up in separated He and H atoms by indirect predissociation. This paper presents a study of potential functions and pertinent matrix elements involving the lowest electronic states: the ²Σ⁺ states, X, A, C, and D, and the ²Π states B and E. Individual transition rates as well as total radiative and non-radiative lifetimes have been computed for the lowest vibrational and rotational levels. Received: 22 June 1998 / Accepted: 21 August 1998 / Published online: 12 October 1998     

Possible long-lived quartet resonance states of CO−

Two states of CO⁻ which are expected to live longer than the well-known ²Π shape resonance are examined and the results obtained are compared with the analogous states of the isoelectronic N₂ ⁻ system. The ⁴Σ⁻ and ⁴Π states are found to be stable with respect to dissociation. The latter state is also stable with respect to single-electron loss to its parent neutral state. The lifetime of this state is supposed to be long, but not necessarily long enough to allow detection in a mass spectrometer. Received: 28 May 1998 / Accepted: 23 July 1998 / Published online: 9 October 1998     

Ab-initio study on low-lying states of the TiSi molecule

 The electronic structure of the TiSi molecule was examined using two types of multireference single and double excitation configuration interactions with highly extended basis sets, one including valence correlation and the other including valence and core–valence correlation. A multireference coupled-pair approximation (MRCPA) was further applied to the latter. The calculations suggest a ⁵Δ ground state, and the lowest excited state is ³Π and is only slightly (0.12 eV as estimated by MRCPA) above the ground state. The spectroscopic constants of the low-lying ¹Δ, ³Δ, ¹Π, ⁵Π, and ⁷Σ⁺ states as well as the ⁵Δ ground state and the ³Π excited states were evaluated, and we found that the molecule has only a weak σ bond and that six of the eight valence electrons essentially do not contribute to the bonding. The bonding nature of TiSi in these states is discussed in comparison with the TiC molecule. Received: 7 October 2000 / Accepted: 8 January 2001 / Published online: 3 May 2001     

A theoretical study on the ionization of OCS with an analysis of vibrational structures of the photoelectron spectrum

 Ab initio calculations have been performed to study the molecular structures and vibrational levels of the four low-lying ionic states (1, 2²Π, and 1, 2²Σ⁺) of carbonyl sulfide. The global regions of the potential-energy surfaces have been obtained by multireference single and double excitation configuration interaction calculations. Vibrational calculations using explicit vibrational Hamiltonians have been used for vibrational analysis. The equilibrium molecular structures and a vibrational analysis of the four ionic states are presented. The theoretical ionization intensity curves including the vibrational structures of the ionic states are also presented and are compared with the photoelectron spectrum. Received: 20 January 2001 / Accepted: 22 August 2001 / Published online: 30 October 2001     

Spin-orbit and spin-spin couplings in He2 and He2−

The spin-orbit and the spin-spin coupling constants of the ⁴Π_g state of the He₂ ⁻ ion, of the parent a³Σ_u ⁺, and of the b³Π_g states of He₂ have been evaluated by a multireference configuration interaction method. The theoretical spin-spin splittings of the a³Σ_u ⁺ state and the R-dependent spin-spin function are found to be in excellent agreement with experiment, with deviations in the range of a few MHz. The theoretical spin-orbit constants and splittings of the b³Π_g state are larger than the experimental values by about 370 MHz. The spin-orbit coupling constant of the ⁴Π_g state of He₂ ⁻ is␣estimated to be three times smaller than in the b³Π_g state, but one of the intramultiplet off-diagonal spin-spin interactions is predicted to give a large contribution to the fine structure of the metastable ion. The theoretical fine structure constants for the He₂ ⁻ ion are expected to␣aid future spectroscopic investigations of the fine structure splittings of the negative ion. Received: 14 April 1998 / Accepted: 27 July 1998 / Published online: 19 October 1998     

Recombination of silicon ions by electron capture from atomic hydrogen and helium

 Ab initio potential-energy curves and coupling matrix elements of the Σ and Π molecular states involved in the collision of the Si²⁺, Si³⁺ and Si⁴⁺ multicharged ions on atomic hydrogen and helium have been determined by means of configuration interaction methods. The total and partial electron capture cross sections have been determined using a semiclassical or a quantal approach in the 0.002–0.1 au velocity range. A detailed comparison with very recent theoretical and experimental rate coefficient results is made. Received: 14 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

Expansion coefficients and moments of electron momentum densities for singly charged ions

Numerical Hartree–Fock calculations of the first three coefficients of the MacLaurin expansion and the leading coefficient of the large-p asymptotic expansion of the electron momentum densities Π(p) are reported for 54 singly charged atomic cations from He⁺ (atomic number Z = 2) to Cs⁺ (Z = 55) and 43 anions from H⁻ (Z = 1) to I⁻ (Z = 53) in their experimental ground states. We also report all the finite moments <p ^k > (−2≤k≤+4) of the momentum densities Π(p) for the above-mentioned 97 ionic species. The results are compared with the previous ones for neutral atoms [Koga and Thakkar (1996) J Phys B 29: 2973], and the dependence of the expansion coefficients and moments on nuclear charge is discussed among isoelectronic species. Received: 20 November 1998 / Accepted: 15 January 1999 / Published online: 7 June 1999     

Diatomic potential well depths from analyses of high-resolution electron energy spectra for autoionizing collision complexes

High-resolution energy spectra of electrons released in Penning ionization collisions of metastable rare gas atoms Rg*(ns) (Rg = He, Ne, Ar, Kr, Xe) with several open-shell and closed-shell atoms are analyzed to determine the well depth of the potential energy curve which describes the respective autoionizing collision complex. We thereby elucidate trends in the chemical interaction of Rg* with closed-shell target atoms A(ns ²) and establish a basis for detailed comparison with the respective interactions involving open-shell, ground state alkali atoms A(ns). From electron energy spectra due to␣associative ionization (RgH⁺ formation) in Rg* + H(1s) collisions, we determine binding energies for the RgH⁺(¹Σ) ground state potential (Rg = Ne, Ar, Kr, Xe) with uncertainties around 0.03 eV. Received: 30 June 1998 / Accepted: 5 August 1998 / Published online: 28 October 1998     

Calculation of ground- and excited-state potential energy curves for barium-rare gas complexes in a pseudopotential approach

Adiabatic potential curves for the ground state and several low-lying excited states of the barium atom interacting with Ne, Ar, Kr and Xe have been obtained from valence ab initio configuration-interaction calculations. Atomic cores are replaced by scalar-relativistic l-dependent pseudopotentials, while core-polarization potentials are used for describing correlation contributions of the rare-gas atoms and the Ba²⁺ cores. Implications of the resulting potential curves for the interpretation of experimental data are discussed, together with first applications of the curves for calculating absorption profiles of the (6s ²)¹S→(6p)¹P Ba transition. Received: 7 April 1998 / Accepted: 27 July 1998 / Published online: 12 October 1998     

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     

Multiconfigurational study on the synchronous mechanisms of the ClO self-reaction leading to Cl or Cl<Subscript>2</Subscript>

For studying the adiabatic and nonadiabatic mechanisms of the ClO (X ²Π) + ClO (X ²Π) → ClOOCl → 2Cl (² P _u) + O₂ (X ³Σ _g ⁻) reaction (1) and the ClO (X ²Π) + ClO (X ²Π) → ClOOCl → Cl₂ (X ¹Σ _g ⁺) + O₂ (X ³Σ _g ⁻) reaction (2), we calculated, by partial geometry optimizations under the C₂ constraint, the O–O and O–Cl dissociation potential energy curves (PECs) from the five low-lying states of ClOOCl at the CASPT2 level. The CASSCF minimum-energy crossing point (MECP) between the potential energy surfaces of the 1 ¹A ground state [correlating with the product of reaction (1)] and the 1 ³B state [correlating with the product of reaction (2)] states was also determined. Based on the CAS calculation results (PECs, energies, and spin–orbit coupling at the MECP), we predict that reaction (1) occurs along pathway 1: ClO (X ²Π) + ClO (X ²Π) → ClOOCl (1 ¹A) → 2Cl (² P _u) + O₂ (X ³Σ _g ⁻) and that reaction (2) occurs along pathway 2: ClO (X ²Π) + ClO (X ²Π) → ClOOCl (1 ¹A) → 1 ¹A/1 ³B MECP (142.4 cm⁻¹) → ClOOCl (1 ³B) → Cl₂ (X ¹Σ _g ⁺) + O₂ (X ³Σ _g ⁻). The needed energies (relative to the reactant) for pathways 1 and 2 are predicted to be 5.3 and 11.1 kcal/mol, respectively, which indicates that reaction (1) is more favorable than reaction (2). The present work supports the traditional photochemical model for ozone degradation: ClOOCl (1 ¹A), formed by two ClO (X ²Π), can directly produce O₂ plus two Cl atoms.     

Direct relativistic MP2: properties of ground state CuF, AgF and AuF

A computer program for the calculation of the MP2 energy correction for a Kramers-restricted Dirac-Hartree-Fock four component wave-function is presented. In the spirit of the integral-driven direct SCF scheme the algorithm has been developed as direct MP2, calculating integrals as they are needed and avoiding the integral storage bottle-neck of conventional MP2. Relativistic MP2 is applied to ground state (¹Σ⁺) CuF, AgF and AuF. Received: 15 December 1996 / Accepted: 2 April 1997     

Experimental and Theoretical Studies on the Characteristics of Atmospheric Pressure Glow Discharge with Liquid Cathode

This study investigated the characteristics of an atmospheric pressure air-glow discharge with a liquid cathode. Distilled water was utilized as the cathode. The electric field strength, gas temperature as well as the emission intensity of some N₂(C³Π_u → B³Π_g) and OH (A²Σ⁺ → X²Π) bands were measured at a discharge current ranging from 15 to 50 mA. Based upon the data obtained, the reduced electric field strength, E/N, and effective vibrational temperatures for N₂(C³Π_u, X¹Σ _g ⁺ ) and OH (A²Σ⁺) were examined. The electron energy distribution function (EEDF) and some electron parameters (average energy, electron density and rate coefficients) were obtained based on a numerical solution of the Boltzmann kinetic equation. The result showed that the EEDF was not in equilibrium and the effective vibrational temperatures for N₂(C³Π_u, X¹Σ _g ⁺ ) were essentially higher than the gas temperatures.     

Electronic spectra and molecular constants of zirconium mononitride

The electronic spectra and structure of zirconium mononitride were considered. The electronic vibrational-rotational spectrum of ZrN was obtained by intracavity laser spectroscopy within the 550–750 nm region. The spectrum was analyzed and the molecular constants of the ground X²Σ and excited A²Π electronic states were calculated. On the basis of the obtained experimental data and critical analysis of all the information on ZrN spectrum studies, the most reliable set of molecular constant values was recommended.     

Spin-projected coupled-cluster theory with single and double excitations

Coupled-cluster (CC) theory including single (S) and double (D) excitations and carried out with a spin-unrestricted Hartree–Fock (UHF) reference wave function is free from S + 1 spin contamination as can be confirmed by an analysis of the expectation value of the spin operator, Ŝ ². Contamination by the S + 2 contaminant can be projected out by an approximate procedure (APCCSD) with a projection operator, P^, represented by the product of the spin annihilation operators ? _{s+ 1} and ?_s+2. The computational cost of such a projection scales with O(M ⁶) (M is the number of basis functions). The APCCSD energy obtained after annihilation of the S + 2 contaminant can be improved by adding triple (T) excitations in a perturbative way, thus leading to APCCSD(T) energies. For the 17 examples studied, the deviation of the UHF-CCSD(T) energies from the corresponding full configuaration interaction values is reduced from 4.0 to 2.3 mhartree on the average as a result of annihilating the S + 2 contaminant in an approximate way. In the case of single-bond cleavage, APCSSD leads to a significant improvement of the energy in the region where the bonding electrons recouple from a closed shell to an open shell singlet electron pair. Received: 13 April 2000 / Accepted: 12 July 2000 / Published online: 24 October 2000     

Calculating the molecular constants for the B1Πu, C1Πu, (1)1Πg, and (2) Σ g+ electronic states of the rubidium dimer

The vibrational, rotational, and centrifugal constants are calculated for the B ¹Π _u , C ¹Π _u , (1) ¹Π _g , and (2) electronic states of a ⁸⁵Rb₂ molecule. The calculations are based on the semi-empirical potential curves obtained in this work. The results from calculating the molecular constants are compared with experimental data. The Franck-Condon factors and R _v′v″ centroids are calculated for the electronic transitions B ¹Π _u -X ¹Σ _g ⁺, C ¹Π _u -X ¹Σ _g ⁺, C ¹Π _u -(1) ¹Π _g , and C ₁Π _u -(2) ¹Σ _g ⁺.