Electron Propagator Calculations Research Articles

Second‐order shakeup terms in electron propagator calculations on F2 and H2O2

Second‐order shakeup terms in electron propagator calculations on F2 and H2O2

Ionization Energies of Acridine, Phenazine, and Diazaphenanthrenes

Ab initio electron propagator calculations on the lowest vertical ionization energies of acridine, phenazine, and five diazaphenanthrene isomers have been performed with the partial third order and outer valence Green's function approximations of electron propagator theory. Agreement with photoelectron spectra is very close, enabling the clarification of previous assignments. Numerous misorderings of final states from Koopmans's theorem are revealed. 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 localization. Many final-state holes exhibit considerable mixing between nitrogen, lone-pair hybrids, and σ-bonding lobes.

Semidirect electron propagator calculations on chlorobenzene ionization energies

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 p π orbital destabilizes the b 1 component of e 1 g 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 e 1 g 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.

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.

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.

Dichlorobenzene Ionization Energies

Electron propagator calculations on the lowest 14 vertical ionization energies of the para, meta, and ortho isomers of dichlorobenzene are performed using the OVGF and P3 approximations, where Feynman−Dyson amplitudes are equivalent to canonical molecular orbitals. Cl p orbitals destabilize the e1g set of benzene to produce the molecular orbitals associated with the two lowest ionization energies. Holes corresponding to four 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. Previous assignments for m-dichlorobenzene are confirmed, and remaining uncertainties in the ortho and para spectra are resolved. Basis sets with up to 304 contracted functions are used. Agreement with experimental ionization energies is close.

Semidirect algorithms for third‐order electron propagator calculations

AbstractAn efficient procedure for third‐order electron propagator calculations of ionization energies and electron affinities is reported. Diagonal self‐energy expressions that are suitable for large molecules are empolyed. The outer‐valence Green's function method also is implemented. An integral transformation program for direct and semidirect algorithms is modified to store only nonzero integrals according to Abelian point group symmetry. Contributions to self‐energy matrix elements that depend on electron repulsion integrals with four virtual orbital indices are computed in a direct way. Intermediate batches of integrals are created by sort procedures while avoiding storage of transformed integrals in the main memory. This method permits calculation of electron binding energies for C with a 231 atomic orbital basis and for Zn(C5H5)2 with a 220 atomic orbital basis on an IBM RISC/6000 Model 550. During these calculations, the CPU is engaged approximately 90% of the time. © 1995 John Wiley & Sons, Inc.

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.

Electronic spectra of finite polyenes and polyacetylene obtained by electron and polarization propagator calculations

Polyacetylene and the short polyenes are used as common test cases for demonstrating the capability of electron and polarization propagator theory to simulate various types of molecular electronic spectra.

Vertical ionization energies of cubane

Electron propagator calculations in the outer valence Green function approximation are applied to cubane, an Oh isomer of C8H8, with various basis sets. The order of the vertical, cationic states is consistent in all basis sets and levels of electron correlation: 2T2g, 2T2u, 2E2g,2T1u, 2A2u, 2A1g The third and fourth states, 2Eg and 2T1u, have nearly identical energies at the equilibrium geometry of cubane. Qualitative interpretations at the molecular orbital level and correlation effects on splittings of final states are discussed.

Electron binding energies of linear C3, C5, C7, and C9 clusters

Electron propagator calculations are performed on the vertical ionization energies and electron affinities of linear C3, C5, C7, and C9 clusters with a variety of correlation approximations and basis sets. Estimates of adiabatic electron affinities are made as well, and are in excellent agreement with experiment. A bound, excited state of C−9 has been found. Correlation effects are large for the electron affinity calculations and for many vertical ionization energies. The Koopmans description of final states is valid for the Feynman–Dyson amplitudes, but for many cationic states there is considerable shakeup character.

Electron propagator theory of ZnCH3, Zn(CH3)2, and related ions

Electron propagator calculations on electron affinities of ZnCH+3 and ionization energies of ZnCH−3 provide ZnCH3 excitation energies. Excited states involving promotion of an electron from one Zn-centered hybrid to another, as well as Zn–C bond to Zn-centered hybrid charge-transfer states, are obtained. The lowest excited state, which is of the former type with an unpaired electron in a Zn-centered, p-like hybrid orbital, lies 2.98 eV above the ground state, in close agreement with spectroscopic results. A charge-transfer state, where two electrons reside in a Zn-centered, s-like hybrid orbital and an unpaired electron is described by a Zn–C bond orbital, is 4.48 eV above the ground state. Additional excited states also have been calculated. Vertical ionization energies of ZnCH−3, as well as the vertical ionization energy and several vertical electron affinities of ZnCH+3, have been determined. ZnCH3’s adiabatic ionization energy, 7.06 eV, and adiabatic electron affinity, 0.95 eV, have been inferred from additional calculations. Vertical ionization energies of Zn(CH3)2 are calculated with similar techniques and are in excellent agreement with photoelectron spectrum results. Bond energies for the dissociation of one or both methyl groups have been determined as well.

Semidirect algorithms in electron propagator calculations

Electron propagator calculations have been executed with a semi-direct algorithm that generates only a subset of transformed electron repulsion integrals and that takes advantage of Abelian point group symmetry. Diagonal self-energy expressions that are advantageous for large molecules are employed. Illustrative calculations with basis sets in excess of 200 functions include evaluations of the ionization energies of C{sup 2{minus}}{sub 7} and Zn(C{sub 5}H{sub 5}){sub 2}. In the former application, a bound dianion is obtained for a D{sub 3h} structure. In the latter, many final states of the same symmetry are calculated without difficulty.

Conformationally induced localization in the electronic structure of polysilanes

Ab initio electron propagator calculations with a double {lambda} effective core potential basis on the vertical electron binding energies of oligomeric models of polysilane chains reveal the effects of gauche conformational defects on electronic structure. When a gauche defect lies between two all-trans segments of unequal lengths, most of the probability density for the Feynman-Dyson amplitudes corresponding to the lowest ionization energy or the largest electron affinity resides on the longer segment. The energy gap between cationic and anionic states increases when a gauche defect is introduced, but the effect is larger when the defect is in the middle of the chain. These trends are explained in terms of simple bond function models suggested by examination of the Feynman-Dyson amplitudes.

Electron propagator theory of BS 2 and BS −2 electronic structure

Electron propagator calculations on the vertical and adiabatic ionization energies of BS − 2 yield structural information on ground and excited states of BS 2. Analytical gradient techniques for BS 2 geometry optimizations and renormalized self-energies for the evaluation of vertical ionization energies are employed. The calculated adiabatic electron affinity of BS 2 is 3.63 eV. Geometry optimizations and force constant calculations arrive at D ∞h structures for all states. Harmonic vibrational frequencies are in reasonable agreement with experimental spectra. Adiabatic excitation energies of BS 2 are inferred from the anion's adiabatic ionization energies. Potential and electric field expectation values of the Feynman-Dyson amplitudes provide a one-electron picture of how removal of an electron leads to bond length changes.

Electron propagator theory of BO2 and BO−2 electronic structure

Electron propagator calculations on the vertical and adiabatic ionization energies of BO2− yield structural information on ground and excited states of BO2. Analytical gradient techniques for BO2 geometry optimizations and renormalized self-energies for the evaluation of vertical ionization energies are employed. The calculated adiabatic electron affinity of BO2 is 4.65 eV. Geometry optimizations and force constant calculations arrive at D∞h structures for all states. Harmonic vibrational frequencies are in reasonable agreement with experimental spectra. Adiabatic excitation energies of BO2 are inferred from the anion’s adiabatic ionization energies. Potential and electric field expectation values of the Feynman–Dyson amplitudes provide a one-electron picture of how removal of an electron leads to bond length changes.

Coupled-cluster reference electron propagator calculations on the ionization energies of O 2

Electron propagator calculations of various levels are compared with coupled-cluster and Fock-space coupled-cluster methods on O 2 ionization energies where final states are dominated by a single configuration. Among the electron propagator method is an approximation that employs correlations to reference state density matrices from a coupled-cluster singles and doubles calculation. The closest agreement between the two classes of methods occurs between renormalized electron propagator approximations and the Δ coupled-cluster singles and doubles method,e ven though the latter is not, like the Fock-space methods, a direct method for ionization energies. Basis set effects are also examined. Vertical ionization energies within 0.2 eV of experiment obtain with the coupled-cluster reference electron propagator calculations

A simplified model of oligosilane ionization energies

A b initio electron propagator calculations with effective core potentials on Si and a double ζ basis produce accurate vertical ionization energies and Feynman–Dyson amplitudes (FDA’s) for oligosilanes. The calculations determine variations in ionization energies and ground state total energies with respect to bond angle and dihedral angle distortions and obtain excellent agreement with photoelectron spectra and with previous all-electron calculations with larger basis sets. Second order, diagonal self energies contain the bulk of the relaxation and correlation effects. FDA’s accompanying the ionization energies are built from Si–Si bond functions. Phase relationships between neighboring bond functions determine how bond angles affect the ionization energies of Si3H8. The variation of ionization energies with respect to dihedral angles in the Si backbones of Si4H10 and Si5H12 depends on phase relationships between first non-neighbor bond functions.

Electron propagator theory of bonding in saturated silicon chains

Ab initio electron propagator calculations produce accurate electron binding energies and Feynman-Dyson amplitudes for oligosilanes as a function of bond angle and dihedral angle distortions. Ground state energies are also calculated for equilibrium and distorted structures. While the ground state energies are fairly insensitive to the distortions, changes in electron binding energies can be much larger. Examination of the Feynman-Dyson amplitudes leads to an electronic structure model that is based on phase relationships between bond orbital and antibond orbitals that are localized in SiSi bond regions. This model is successful in explaining the calculated shifts in electron binding energies and changes in polymer absorption spectra.

Electron propagator calculations on the ionization energies of CrH −, MnH − and FeH −

Electron propagator calculations with unrestricted Hartree-Fock reference states yield the ionization energies of the title anions. Spin contamination in the anionic reference state is small, enabling the use of second-and third-order self-energies in the Dyson equation. Feynman-Dyson amplitudes for these ionizations are essentially identical to canonical spin-orbitals. For most of the final states, these consist of an antibonding combination of an sp metal hybrid, polarized away from the hydrogen, and hydroegen s functions. In one case, the Feynman-Dyson amplitude consists of nonbonding d functions. Calculated ionization energies are within 0.5 eV of experiment.