Hosung Sun

Abinitio effective valence shell Hamiltonian for the neutral and ionic valence states of N, O, F, Si, P, and S

The effective valence shell Hamiltonian, Hv, which acts within a finite valence space and exactly describes all the valence state energies, is applied to several atomic systems. The n=2 (L shell) Hv of the first row atoms, N, O, and F and n=3 (M shell) s and p orbital Hv of the second row atoms, Si, P, and S, are evaluated through second order using STO 5s4p2d and 6s5p3d basis sets, respectively. The calculations are equivalent to a (perturbative) Bk approximation which incorporates all excited configurations and which chooses the primary (valence) space as all the valence K2(2s)m(2p)n and K2L6(3s)m(3p)n configurations, respectively. Using the calculated matrix elements of Hv, the energies of all the valence states of the neutrals and ions are simultaneously determined from a single ab initio calculation on only one charge state of each of these atomic systems. To understand the dependence of Hv on the choice of core and valence orbitals, several sets of orbitals, obtained within the same primitive orbita...

Conjecture on the Rate of Vibrational Relaxation of a Diatomic Molecule in a Monatomic Lattice

In this paper we use a simple model—a substitutional diatomic molecule in a linear monatomic chain—to examine the problem of intermolecular vibrational relaxation in the solid phase. A binary collision theory of vibrational deactivation is proposed for the relaxation process, with the motion of the collision partners governed by the normal modes of the lattice. The collision frequency is calculated by using an analysis similar to that of the Slater theory of unimolecular reactions. The model calculations predict the relaxation time to be very long compared with the vibrational period of the diatomic molecule. We thus conclude that, in a molecular crystal composed of polyatomic molecules, the excitation energy will be removed by the surrounding medium, not by the transformation of internal energy into lattice modes, but rather by other processes such as the formation of vibration excitons etc.

Abinitio third order effective valence shell Hamiltonian calculations for first row diatomic hydrides

Ab initio effective valence shell Hamiltonian Hv calculations are presented through third order for the correlation energies of CH, NH, and OH at their equilibrium internuclear distance. The valence shell consists of the 2σ, 3σ, 1π, and 4σ orbitals. This represents the first quasidegenerate third order many‐body perturbation calculation of Hv for molecules with more than two valence electrons. As in the atomic case, a single Hv calculation provides correlation energies for all neutral valence states as well as for the positive and negative ion valence states of the hydrides. Calculated vertical excitation energies are in good agreement with those obtained from large configuration interaction calculations. Four‐electron effective interactions, present in the third order expansion of Hv, are evaluated. These four‐electron terms make significant contributions to the energies of many states. Technical difficulties are discussed which are related to Hv calculations with large valence spaces that violate the qu...

Ab initio effective valence shell hamiltonian calculation of the valence state potential curves of CH and CH

Abstract The third-order ab initio effective valence shell hamiltonian of quasi-degenerate many-body perturbation theory is calculated for the valence state potential curves of CH and CH + simultaneously. The results are in accord with experiment and configuration interaction calculations, and they have applications to experiments on the D 2 Π state of CH and B 1 Δ of CH + .

Abinitio effective valence Hamiltonian description of electron correlation for the neutral and ion valence states of transition metal atoms

Results of second order ab initio effective valence shell. Hamiltonian calculations are reported, where all the valence states of Ti through Ti t+4 are computed simultaneously. The correlation energies of higher lying 4S23dn, 4S3dn+1 and 3dn+2 states and the ground state of Ti are reported. (AIP)

Application of quasidegenerate many‐body perturbation theory to the calculation of molecular excited valence state negative ion Feshbach resonances

Quasidegenerate many‐body perturbation theory (QDMBPT) is shown to generate a good method for representing the abstract Feshbach projectors, required in the evaluation of the energies of negative ion resonances, provided the valence space is sufficiently large to produce a good zeroth order description of these valence state resonances. Our recent advances in extending third order QDMBPT to large valence spaces are utilized to calculate potential curves and spectroscopic constants for the lowest four excited states of CH− and the vertical electron affinities to excited states of NH− and OH−. The experimentally assigned a 1Δ excited state of CH− is confirmed by the calculations, and a few more bound resonant molecular states are predicted. A simple one electron molecular orbital model is extracted from the large scale calculations to describe the zeroth order electronic structure of the excited states of CH−, NH−, and OH−.

Molecular properties by ab initio quasidegenerate many‐body perturbation theory effective Hamiltonian method: Dipole and transition moments of CH and CH+

The ab initio effective valence shell Hamiltonian method, based on quasidegenerate many‐body perturbation theory, is generalized to calculate molecular properties as well as the valence state energies which have previously been determined for atoms and small molecules. Our approach is applicable to both expectation values and transition moments of any molecular property within and between the valence states, respectively. The procedure requires the evaluation of effective operators for each molecular property. Effective operators are perturbatively expanded in powers of correlation and contain contributions from excitations outside of the large multireference valence space. Expectation values and transition moments are the diagonal and off‐diagonal matrix elements, respectively, of the effective property operators between the eigenfunctions of the correlated effective Hamiltonian. Calculations for dipole moments of and transition moments between several low lying states of CH and CH+ to first order in the...

Ab initio calculation of the effective valence shell hamiltonian of carbon: Simultaneous treatment of neutral and ion states

Abstract The n = 2 effective valence shell hamiltonian, H v , of carbon is evaluated through second order using 3 P Hartree—Fock orbitals (5s4p) with added d functions to provide results within a few percent of the spd convergence limits. The calculated H v is employed to evaluate the n = 2 valence states of C, C − , C + , C 2+ and C 3+ with an average deviation of the 21 excitation energies, ionization potentials and electron affinity from experimental values of 0.32 eV. Three-electron parts of H v contribute substantially to a number of these excitation energies.

The correlated pi‐Hamiltonian of trans‐butadiene as calculated by the ab initio effective valence shell Hamiltonian method: Comparison with semiempirical models

The pi‐electron Hamiltonian Hπ of trans‐butadiene is calculated using the effective Hamiltonian quasidegenerate many‐body perturbation theory formalism to include ‘‘correlation’’ contributions. When four tight, valencelike orbitals are employed, the calculated Hπ reproduces experimental and calculated (by configuration interaction) valence state excitation energies, but fails to obtain the diffuse Rydberg‐like pi‐electron states which interleave the valence spectrum. The addition of a pair of Rydberg molecular orbitals to the valence shell leads to an effective Hamiltonian Hv which accurately describes both valence and Rydberg states simultaneously. These results provide an explanation as to why semiempirical pi‐electron theories have required the use of different parameters, particularly resonance integrals, to calculate different properties. Our calculated Hπ contains hybrid, exchange, and multicenter two‐electron integrals which are customarily ignored to varying degrees in zero differential overlap (Z...

Application of the effective valence shell Hamiltonian method to accurate estimation of valence and Rydberg states oscillator strengths and excitation energies for π electron systems

The ab initio effective valence shell Hamiltonian (Hv) is used to compute the low lying vertical excitation energies and oscillator strengths for ethylene, trans-butadiene, benzene and cyclobutadiene. Calculated excitation energies and oscillator strengths of ethylene, trans-butadiene and benzene to various valence and Rydberg states are in good agreement with experiment and with values from other highly correlated computations. The present work further investigates the dependence of Hv computations on the nature and choice of the molecular orbitals and provides a comprehensive study of the convergence with respect to the enlargement of the valence space. Minimal valence space Hv computations yield very accurate estimates of the excitation energies for the low lying excited triplet states and are slightly poorer (a deviation of ⩽0.5 eV from experiment) for low lying excited singlet states. More accurate low lying singlet state excitation energies are achieved by slightly enlarging the valence space to inc...