J. V. Ortiz

Partial third‐order quasiparticle theory: Comparisons for closed‐shell ionization energies and an application to the Borazine photoelectron spectrum

Valence ionization energies of a set closed‐shell molecules calculated in a partial third‐order (P3) quasiparticle approximation of the electron propagator have an average absolute error of 0.19 eV. Diagonal elements of the self‐energy matrix include all second‐order and some third‐order self‐energy diagrams. Because of its fifth power dependence on basis set size and its independence from electron repulsion integrals with four virtual indices, this method has considerable potential for large molecules. Formal and computational comparisons with other electron propagator techniques illustrate the advantages of the P3 procedure. Additional applications to benzene and borazine display the efficacy of the P3 propagator in assigning photoelectron spectra. In the borazine spectrum, 2E′ and 2A2′ final states are responsible for an observed feature at 14.76 eV. Another peak at 17.47 eV is assigned to a 2E′ final state.

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.

Electron binding energies of TCNQ and TCNE

Ab initio electron propagator calculations on tetracyanoquinodimethane (TCNQ) and tetracyanoethylene (TCNE) produce accurate predictions of vertical ionization energies and electron affinities. Plots of Feynman–Dyson amplitudes associated with each ionization process represent how the electron distribution changes from initial to final states. Calculated electron detachment energies of the TCNQ dianion imply that two states of the TCNQ anion are bound with respect to the neutral molecule. Configuration interaction calculations on the TCNQ anion confirm this result.

Ionization energies of anthracene, phenanthrene, and naphthacene

Ab initio electron propagator calculations on the lowest vertical ionization energies of anthracene, phenanthrene, and naphthacene have been performed with the partial third order and outer valence Green’s function approximations. Agreement with photoelectron spectra is very close, enabling the clarification of previous assignments, some of which were contradictory. With the present approximations, Feynman–Dyson amplitudes are equivalent to canonical molecular orbitals. Plots of these one‐electron functions aid in the interpretation of the spectra by revealing patterns of delocalization and locations of nodes.

A test of partial third order electron propagator theory: Vertical ionization energies of azabenzenes

Vertical ionization energies of pyradine, pyridazine, pyrimidine, pyrazine, s‐triazine, and s‐tetrazine are calculated with partial third order electron propagator theory. Extensive reorderings of final states are produced by correlation corrections to Koopmans’s theorem results. The partial third order (P3) quasiparticle method succeeds in producing the correct order of final states and close agreement with photoelectron spectra. Because P3 is more efficient than the outer valence Green’s function and other methods based on the third order self‐energy, it shows considerable promise for predicting photoelectron spectra of large molecules.

Electron propagator calculations on linear and branched carbon cluster dianions

Electron propagator calculations have been performed on linear carbon cluster dianions from C2−7 to C2−10 and on branched C2−7, C2−9, and C2−11 structures which have a central, tricoordinate carbon bound to three branches with alternating long and short bonds. The more stable, branched isomer of C2−7 has a positive vertical ionization energy, but the linear form does not. While linear C2−10 is stable with respect to electron loss, it is not possible to decide from these calculations whether linear C2−8 and C2−9 have the same property. There is evidence that better calculations would obtain bound C2−8 and C2−9 species. Vertical ionization energies of all branched dianions are positive. Feynman–Dyson amplitudes for dianion ionization energies display delocalized π bonding, with the two terminal carbons of the longest branches making the largest contributions.

Calculation and interpretation of total energies in electron propagator theory

Ground state total energies and one‐electron density matrices can be calculated from contour integrals over the electron propagator. Ionization energies and corresponding Feynman–Dyson amplitudes are related simply to ground state properties. Total energy formulas derived from electron propagator theory are transparent generalizations of Hartree–Fock expressions. Computationally useful methods for evaluating integrals over the Coulson contour are derived. An approximate integration scheme is introduced and compared to exact results. Several decouplings of the electron propagator that have been employed frequently for electron binding energies are used to calculate size‐extensive total energies. These methods do not yield satisfactory correlation energies, but they provide a reasonable account of bending potentials for water, ammonia, and methane. Total energy contributions derived from propagator poles and residues are calculated as a function of bond angle distortions. These results are compared with sim...

Semidirect electron propagator calculations on chlorobenzene ionization energies

Abstract Electron propagator calculations on the lowest twelve vertical ionization energies of chlorobenzene are performed with a semidirect algorithm. The OVGF and P3 approximations, where Feynman-Dyson amplitudes are equal to canonical molecular orbitals, were employed. The Cl pπ orbital destabilizes the b1 component of e1g set of benzene to produce the molecular orbital associated with the lowest ionization energy. Whereas the second highest occupied molecular orbital is nearly identical to a component of the benzene e1g set, the corresponding vertical ionization energy is larger than the lowest ionization energy of benzene. Holes corresponding to two higher final states have mostly Cl 3p character. The remaining molecular orbitals strongly resemble their benzene counterparts, but significant Cl admixtures are present in most cases. Basis set comparisons indicate that the predicted order of final states is reliable. Up to 284 contracted functions are used.