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     

SAC-CI general-R study of the ionization spectrum of HCl

The valence ionization spectrum of HCl is studied by symmetry-adapted-cluster configuration-interaction general-R and SD-R methods. The general-R method describes well the peak positions and intensities of seven satellite lines observed below the double ionization threshold. The twinning shake-up states due to the (4σ)⁻¹ state and the Rydberg states of HCl⁺ are correctly reproduced. Received: 26 June 1998 / Accepted: 9 September 1998 / Published online: 8 February 1999     

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     

Analytic UHF-CCSD(T) second derivatives: implementation and application to the calculation of the vibration-rotation interaction constants of NCO and NCS

An implementation of analytic open-shell UHF-CCSD(T) second derivatives is presented. To demonstrate applicability and test the accuracy of the UHF-CCSD(T) approach for the determination of spectroscopical parameters, vibration-rotation interaction constants were calculated for the ground (1²Π) and first electronically excited (1²Σ) states of the NCO and NCS radicals. In addition, harmonic vibrational frequencies for both states, the Renner-Teller parameter for the ground state, as well as the 1²Π→1²Σ excitation energy are reported. While the computed values are in good agreement with reliable experimental information for NCO, most of the data presented for NCS are predictions of quantities not well known from experiment. Received: 4 May 1998 / Accepted: 27 July 1998 / Published online: 12 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     

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     

The spin-forbidden reaction CH(2∏) + N2→ HCN + N(4S) revisited I. Ab initio study of the potential energy surfaces

High-level ab initio electronic structure theories have been applied to investigate the detailed reaction mechanism of the spin-forbidden reaction CH(²∏) + N₂ → HCN + N(⁴S). The G2M(RCC) calculations provide accurate energies for the intermediates and transition states involved in the reaction, whereas the B3LYP/6-311G(d,p) method overestimates the stability of some intermediates by as much as about 10 kcal/mol. A few new structures have been found for both the doublet and quartet electronic states, which are mainly involved in the dative pathways. However, due to the higher energies of these structures, the dominant mechanism remains the one involving the C ₂ intersystem-crossing step. The C ₂ minima on the seam of crossing (MSX) structures and the spin-orbit coupling between the doublet and quartet electronic states are rather close to those found in previous studies. Vibrational frequencies orthogonal to the normal of the seam which have been applied in a separate publication to calculate the rate of the CH(²∏) + N₂ → HCN + N(⁴S) reaction with a newly proposed nonadiabatic transition-state theory for spin-forbidden reactions have been calculated at the MSX from first principles. Received: 23 June 1998 / Accepted: 21 September 1998 / Published online: 8 February 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     

Excited states of acetylene: a CASPT2 study

Valence and low-lying Rydberg states of acetylene (C₂H₂) are reexamined in the singlet as well as in the triplet manifold. The major goal of this work is a better understanding of the valence states that contribute to the low-energy electron-energy-loss spectrum recorded under conditions where transitions to triplet states are enhanced. An appropriate theoretical treatment of these states has to include the low-lying Rydberg states because of their energetic proximity to some of the valence states. The CASSCF/CASPT2 method provides a suitable framework for such a task. For some important states the geometry was optimized at the CASPT2 level to allow a comparison with the results of other highly accurate methods that have been applied to acetylene in the past. Received: 11 June 1998 /Accepted: 30 July 1998 / Published online: 19 October 1998     

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     

RISM-SCF study of the free-energy profile of the Menshutkin-type reaction NH3+CH3Cl→NH3CH3++Cl− in aqueous solution

The free-energy profile for the Menshutkin-type reaction NH₃ + CH₃Cl → NH₃CH₃ ⁺ + Cl⁻ in aqueous solution is studied using the RISM-SCF method. The effect of electron correlation on the free-energy profile is estimated by the RISM-MP2 method at the HF optimized geometries along the reaction coordinate. Solvation was found to have a large influence on the vibrational frequencies at the reactant, transition state and product; these vibrational frequencies are utilized to calculate the zero-point energy correction of the free-energy profile. The computed barrier height and reaction exothermicity are in reasonable agreement with those of experiment and previous calculations. The change of solvation structure along the reaction path is represented by radial distribution functions between solute-solvent atomic sites. The mechanisms of the reaction are discussed from the view points of solute electronic and solvation structures. Received: 26 June 1998/Accepted: 28 August 1998 / Published online: 2 November 1998     

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     

Semidiffuse states of diatomic molecules: Configuration interaction studies of the lowest 2Σ+ and 2Δ states of NS,SiF, and CCl

It has been shown by ab initio configuration-interaction methods that the lowest ²Σ⁺ states of NS and SiF are ‘semidiffuse’ states, like the B ²Σ⁺ state of PO. The lowest ²Σ⁺ state of CCl also appears to be semidiffuse, although here the situation is not so clear. Semidiffuse states require diffuse orbitals in the wavefunction, but they are not Rydberg states. The second ²Σ⁺ state of each molecule is shown to be the lowest ns Rydberg state, whereas the third ²Σ⁺ state is a valence state for NS and CCl, and a 4po Rydberg state for SiF. The lowest ²δ state of each molecule derives from the 7σ → 3π valence configuration. Comparison with available experimental information shows, in general, good agreement.     

Theoretical study of the valence π → π* excited states of polyacenes: anthracene and naphthacene

The valence π → π ^* excited states of anthracene and naphthacene are studied with multireference perturbation theory with complete active space self-consistent field reference functions. The predicted spectra provide a consistent assignment of all one- and two-photon spectra and T-T spectra of low-lying valence π → π ^* excited states of anthracene and naphthacene. The present theory predicts the valence π → π ^* excitation energies with an accuracy of 0.15 eV for anthracene and of 0.25 eV or better for naphthacene. The excited states of anthracene and naphthacene are compared with those of benzene and naphthalene studied previously. The present calculations predict that, going from anthracene to naphthacene, there is a symmetry reversal of the two lowest singlet state transitions, but not for the triplet, just as indicated by the experimental data. Some general trends of polyacene excited states are discussed based on the calculated results for benzene to naphthacene. Conclusive results obtained for anthracene and naphthacene can be used as a model for understanding the excited states of larger polyacenes. Received: 22 April 1998 / Accepted: 6 July 1998 / Published online: 28 September 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     

Potential energy curves and spectral properties for electronic states of F2 and F+2

Potential energy (PE) curves for the Rydberg states of F₂, and for the ground and lowest two electronic states each of symmetry ²Π_g,u, ²Δ_g,u and ²Σ^±_g,u of F⁺₂, have been obtained using modest-sized configuration-interaction calculations. These PE curves have been used to calculate spectroscopic constants for the electronic states and the results agree reasonably well with the limited experimental and theoretical results previously reported. The theoretical PE curves for the Rydberg states of F₂ are found to be strongly perturbed by valence-Rydberg-ionic interactions and these perturbations appear to be responsible for certain features in recently reported electron energy-loss spectra in F₂. The corresponding electronic wavefunctions have been used to calculate the electronic transition moment, as a function of the internuclear distance, for dipole-allowed transitions between the lowest excited electron state of each symmetry and the appropriate ground electronic state. The radiative emission probabilities, natural lifetimes, and absorption oscillator strengths, for each band system, are also reported here. The predicted lifetimes for vibrational levels of the A ²Π_u of electronic state in F⁺₂ vary from 1.3–1.5 μs and agree reasonably well with the single available set of measurements. The predicted radiative lifetimes for the higher electronic states of F⁺₂ are substantially longer and fall into the range 5–100 ms.     

Ab initio calculations find 2,2-disilylcyclopentane-1,3-diyl is a singlet diradical with a high barrier to ring closure

Ab initio calculations on the lowest singlet and triplet states of 2,2-disilylcyclopentane-1,3-diyl find that the singlet lies well below the triplet. The C ₂ singlet diradical is calculated to be a minimum on the potential energy surface with an enthalpic barrier to ring closure of ΔH ^‡ ₂₉₈ = 13.5 kcal/mol at the CASPT2/6-31G* level of theory. The energy of the 1,3-divinyl-substituted singlet diradical is calculated to be only 0.8 kcal/mol higher than that of 5,5-disilyl-1,3-divinylbicyclo[2.1.0]pentane at this level of theory, but the transition state for their equilibration is computed to be 12.8 kcal/mol above the diradical in energy. Received: 2 July 1998 / Accepted: 4 August 1998 / Published online: 16 November 1998