Danny L. Yeager

Comparison of perturbative and multiconfigurational electron propagator methods

Ionization energies below 20 eV of 10 molecules calculated with electron propagator techniques employing Hartree-Fock orbitals and multiconfigurational self-consistent field orbitals are compared. Diagonal and nondiagonal self-energy approximations are used in the perturbative formalism. Three diagonal methods based on second- and third-order self-energy terms, all known as the outer valence Greens function, are discussed. A procedure for selecting the most reliable of these three versions for a given calculation is tested. Results with a polarized, triple ζ basis produce root mean square errors with respect to experiment of approximately 0.3 eV. Use of the selection procedure has a slight influence on the quality of the results. A related, nondiagonal method, known as ADC(3), performs infinite-order summations on several types of self-energy contributions, is complete through third-order, and produces similar accuracy. These results are compared to ionization energies calculated with the multiconfigurational spin-tensor electron propagator method. Complete active space wave functions or close approximations constitute the reference states. Simple field operators and transfer operators pertaining to the active space define the operator manifold. With the same basis sets, these methods produce ionization energies with accuracy that is comparable to that of the perturbative techniques.

A multiconfigurational time-dependent hartree-fock approach

Abstract An extension of the time-dependent Hartree-Fock approximation to employ a multiconfiguration Hartree-Fock state as reference state has been developed. Preliminary multiconfiguration time-dependent Hartree-Fock calculations with the ground state of the Be atom using the configurations 2s 2 and 2p 2 show a maximum deviation from the experimental excitation energies of 0.31 eV for the lowest 16 excitations, with an average deviation of 0.18 eV.

Convergency studies of second and approximate second order multiconfigurational Hartree−Fock procedures

The convergency of second order and approximate second order multiconfigurational Hartree−Fock procedures has been examined. Preliminary calculations on Be and O2 show that second order procedures straightforwardly can be applied and converged in a few iterations both for ground and excited states. Approximate second order schemes such as the ’’super CI’’ approach converged much slower. The present calculations preserve orbital orthogonality explicitly in each iteration without using a Schmidt, Lowdin, or other orthogonalization procedure.

Excitation energies in Be: A comparison of multiconfigurational linear response and full configuration interaction calculations

Using a 〈9s9p5d〉 contracted GTO basis we have calculated low‐lying excitation energies of singlet and triplet symmetry for the Be atom using Δfull CI, ΔCI(1s) with double occupancy in the 1s orbital, multiconfiguration linear response (MCLR), and ΔMCSCF approaches. The Δfull CI results agree very closely with the experimental excitation energies except for higher excitations where obvious basis set defects occur. The MCLR calculations shows that with an adequately chosen MCSCF reference state the MCLR calculation is capable of mimicking the Δfull CI results. The MCLR results are closer to the Δfull CI results than the ΔCI(1s). The ΔMCSCF excitation energies show that this approach can only be used with extreme care to determine excitation energies.

Multiconfigurational electron propagator (MCEP) ionization potentials for general open shell systems

We have developed a multiconfigurational electron propagator (MCEP) technique for the theoretical determination of ionization potentials for general open shell and highly correlated atomic and molecular systems. In order to do this, we have used and extended the generalized spin‐symmetry adapted operators of Pickup and Mukhopadhyay. To properly account for correlation effects we have additionally included ionization and electron affinity operators analogous to the ‖Γ〉〈0‖ state transfer operators necessary in multiconfigurational linear response. MCEP ionization potentials and ionization process probabilities have been evaluated for both O2 and N2 and used to carry out detailed examination and interpretation of the respective PES and ESCA spectra. The MCEP results are extremely encouraging for both principal and shake‐up I.P.′s. For example, using 〈5s4p1d〉 contracted Gaussian basis sets the principal valence ionization potentials to bound ionic states are calculated within ±0.3 eV of experiment for both N2...

Guaranteed convergence in ground state multiconfigurational self‐consistent field calculations

We show how an optimization constraint algorithm of Fletcher that guarantees convergence to the lowest state of a given symmetry may be practically implemented in a multiconfigurational self‐consistent field (MCSCF) calculation. Other MCSCF procedures in current use have not been proven mathematically to guarantee convergence. Calculations on the ground states of N2 and CO show that rapid and efficient convergence is obtained with the Fletcher restricted step size algorithm.

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...

The multiconfigurational spin‐tensor electron propagator method for determining vertical principal and shake‐up ionization potentials for open shell and highly correlated atoms and molecules

We propose and develop the multiconfigurational spin‐tensor electron propagator (MCSTEP) technique for the theoretical determination of vertical ionization potentials (IPs) and electron affinities (EAs) for general open‐shell and highly correlated atoms and molecules. We obtain these equations from a Green’s function or electron propagator approach where we properly couple electron removal and addition tensor operators to a multiconfigurational tensor state. To account for important shake‐up effects and to achieve a ‘‘balance’’ in initial and final state correlation corrections, we include in MCSTEP ionization and electron affinity operators analogous to the ‖c〉〈0‖ state transfer operators necessary in multiconfigurational linear response. In repartitioned MCSTEP (RMCSTEP) we augment the MCSTEP operator manifold with operators of the form a+iajak by first employing partitioning theory to estimate their contributions and then repartitioning only the important operators into the primary space. In this way, ...

Assignments in the electronic spectrum of water

To explain the inelastic feature at 4.5 eV in the spectrum of water and to study its spectrum in some detail, we have carried out several calculations on the excited states of water using the equations‐of‐motion method. We conclude that the calculated vertical excitation energy of 6.9 eV for the ^3B_1 state corresponds to the strong feature at 7.2 eV observed in low‐energy electron scattering spectrum. The 4.5 eV inelastic process almost certainly does not correspond to a vertical excitation of water at the ground state geometry. The other excitation energies and oscillator strengths agree well with experiment.

Equations of motion method: Excitation energies and intensities in formaldehyde

We have used the equations of motion method to study the excitation energies and intensities of electronic transitions in formaldehyde. The calculated excitation energies and oscillator strengths agree well with experiment and suggest explanations for some unusual features recently observed in the optical absorption and electron scattering spectrum of formaldehyde in the vacuum ultraviolet.