Electron Propagator Theory Research Articles

Electron propagator theory with the ground state correlated by the coupled-cluster method

Ground state electron correlation is introduced into the one-particle propagator via coupled cluster theory. This defines a similarity transformation of the Hamiltonian, which leads to the complete separation of the ionization and electron attachment aspects of the propagator. The latter makes it possible to solve for each property independently. Furthermore, the frequency (or energy) dependence which characterizes propagator theory is eliminated by introducing a wave operator formalism. It is shown that this procedure is equivalent to the summation of certain types of terms in the electron propagator perturbation expansion to infinite order. Finally, the resulting equations are found to be equivalent to those of the Fock-space coupled-cluster (or equivalently the equation of motion coupled-cluster) method, which provides an explicit wave function for each state, demonstrating the connection between these different approaches for the calculation of ionization potentials and electron affinities. Understanding this relationship permits new and powerful approximations to be proposed. © 1993 John Wiley & Sons, Inc.

Electron propagator calculations on the adiabatic electron binding energies of C3

New techniques of electron propagator theory (EPT) are applied to C3, C3+, and C3−. Gradients of second-order EPT ionization energies and electron affinities are combined with gradients of second-order many-body perturbation theory for the neutral to produce gradients of the ion total energies. Optimized geometries of the ions, vibrational frequencies, and adiabatic electron binding energies are calculated with these methods. A renormalized self-energy is used to produce improved vertical and adiabatic ionization energies and electron affinities. For the cation, the 2B2 state with C2v symmetry and the 2Σ state with C∞v symmetry are very close in energy. The optimized 2Σu structure is a transition state with an imaginary frequency of σu symmetry that lies 2.8 kcal/mol above the 2B2 state. The adiabatic ionization energy is calculated to be 11.9 eV. The anion in the 2Πg state lies 1.8 eV below the neutral in these calculations.

One-electron density matrices and energy gradients in second-order electron propagator theory

A formalism for evaluation of the effective first-order density matrices associated with second-order electron propagator theory is described. Computer implementation of this formalism affords first-order density properties, such as dipole moments, and energy gradients. Given an initial state with N electrons, this approach enables geometry optimization of the ground and excited electronic states of species with N−1 and N+1 electrons. The performance of the present method is assessed with test calculations on the formyl radical.

Total energies and energy gradients in electron propagator theory

From the second-order self-energy of electron propagator theory, one can obtain total energies for the initial, N-electron state and the final, N ± l-electron states. Recent derivations and computational studies have demonstrated the feasibility of calculating effective first-order density matrices corresponding to the electron-binding energies. One-electron properties and energy gradients of the final states are thereby made accessible. Applications to. the ground and excited states of CaCN and to C illustrate the capabilities of this method. © 1992 John Wiley & Sons, Inc.

Molecular similarity indices in electron propagator theory

Application of the concept of relaxed, first-order density matrices to electron propagator theory provides a measure of molecular similarity between a reference N-electron Hartree—Fock wavefunction and a correlated final state with N−1 electrons. Illustrative calculations on N 2 and HNO show how the similarity index, computed for various cationic final states, measures their non-Koopmans character. The similarity index provides a description that is complementary to that obtained from Koopmans' defects, Feynman—Dyson amplitudes and pole strengths.

Electron propagator theory of the ground and excited states of CaC5H5

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTElectron propagator theory of the ground and excited states of CaC5H5J. V. OrtizCite this: J. Am. Chem. Soc. 1991, 113, 9, 3593–3595Publication Date (Print):April 1, 1991Publication History Published online1 May 2002Published inissue 1 April 1991https://doi.org/10.1021/ja00009a057RIGHTS & PERMISSIONSArticle Views45Altmetric-Citations17LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (388 KB) Get e-Alerts Get e-Alerts

Electron propagator theory of the ground and excited states of calcium borohydride

Electron propagator theory of the ground and excited states of calcium borohydride

Renormalized ground states in electron propagator theory

Renormalized ground states in electron propagator theory

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.

Ionization energies of OH−3 isomers

Structures for hydride–water, hydroxide–H2 and double-Rydberg isomers of OH−3 are optimized at the MBPT(2)/6-311++G(d,p) level. While the first two isomers have nearly equal total energies, the double-Rydberg isomer is 1.68 eV less stable. Vertical ionization energies of the isomers are calculated with electron propagator theory and a 6-311++G(2d,2p) basis augmented with extra diffuse functions. The result for the hydride–water complex, 1.50 eV, is in excellent agreement with a recent photoelectron experiment, while the value for the hydroxide–H2 structure, 2.27 eV, is substantially different. Calculations are performed on a double-Rydberg anion with a pyramidal, C3v structure, yielding a vertical ionization energy of 0.43 eV. Corresponding neutral structures are optimized and provide adiabatic ionization energies. Harmonic vibrational frequencies are calculated for the anionic structures.

Electron binding energies of anionic alkali metal atoms from partial fourth order electron propagator theory calculations

Ionization energies of Li−, Na−, K−, Rb−, and Cs− are calculated with ab initio electron propagator theory. Effective core potentials are employed for K, Rb, and Cs. Third order diagonal self-energy corrections to Koopmans’s theorem are augmented with fourth order terms that are easily determined from by-products of a third order calculation. This partial fourth order procedure is derived using superoperator theory. The superiority of this method to an outer valence diagonal approximation is demonstrated for these systems. Covergence of results with respect to the order of electron interaction in the propagator self-energy and with respect to basis set improvement is studied. Agreement to within 0.1 eV of experiment is achieved. Remaining sources of error are analyzed.

Electron binding energies of anionic alkali metal triatomics from partial fourth order electron propagator theory calculations

Vertical ionization energies of Li−3, Na−3, LiNa−2, and Li2Na− are calculated with ab initio electron propagator theory. D∞h and C∞v isomers for the heteronuclear triatomics are considered. Two doublet final states with Σ symmetry are considered for each case. Koopmans’s theorem, second order, third order, and partial fourth order results form a steadily converging series. Outer valence approximation results are not similar and are probably inferior to the partial fourth order results. Convergence of results with respect to the order of electron interaction in the propagator self-energy and with respect to basis set saturation is achieved to within 0.1 eV.

Partial fourth order electron propagator theory

Third order diagonal self-energies are augmented with fourth order terms that are easily determined from by-products of a third order calculation. Comparisons are made with the outer valence approximation, a method for estimating fourth and higher order terms. The number of operations needed for all of these procedures is less than the number required for the limited two electron integral transformation. Improved one-electron reduced density matrices are another useful by-product of these calculations. The present methods are applied to calculating the ionization energies and dipole moments of the anions F−, OH−, NH, Cl−, SH−, PH2−, and CN−. The basis sets used in these calculations have been shown to be sufficiently flexible in a variety of calculations.

Vertical and adiabatic ionization energies of NH−4 isomers via electron propagator theory and many body perturbation theory calculations with large basis sets

Electron propagator theory (EPT) is applied to calculating vertical ionization energies of NH−4 in two stable geometries. The first is a complex of a hydride coordinated to one of the hydrogens of the solvent ammonia molecule, while the other isomer has tetrahedral symmetry. Both structures have been optimized using second order many body perturbation theory with a 6-311++G(d) basis. The former structure is predicted to be 0.42 eV more stable than the latter. A series of third order EPT quasiparticle calculations is carried out to demonstrate basis set saturation. The best EPT calculations give vertical ionization energies of 1.20 eV for the solvated hydride structure and 0.42 eV for the tetrahedral isomer. Both of these calculations are within 0.1 eV of anion photoelectron spectroscopy peaks and suggest that the tetrahedral isomer is responsible for one of these features. After removing an electron from the solvate structure, the complex settles into a shallow van der Waals minimum with a hydrogen atom weakly bound to the ammonia molecule. Calculations on the tetrahedral neutral indicate that there is little relaxation energy along the neutral final state potential energy surface, explaining the sharpness of the observed photoelectron peak.

Applications of electron propagator theory to the electron affinities of AsH2, SeH, Br, SbH2, TeH, and I

Electron propagator theory is applied to calculating vertical electron affinities of the title molecules. Third order and outer valence approximation quasiparticle calculations with and without effective core potentials are compared for molecules with fourth period atoms. Discrepancies between the two sets of results are small and stimulate applications to fifth period analogs. Good agreement with experiment is obtained for all the molecules; a prediction for the still unmeasured electron affinity of SbH2 is made.

Many-body theory of the ionization energies of CH3-, SiH3-, and GeH3-

Electron propagator theory is used to calculate the vertical ionization energies of CH/sub 3//sup -/, SiH/sub 3//sup -/, and GeH/sub 3//sup -/. Basis set augmentations are made until changes in the computational results are small. Adiabatic ionization energies are obtained via many-body-perturbation-theory calculations on the neutral potential energy surface. The adiabatic values are in excellent agreement with photoelectron spectroscopy measurements on CH/sub 3//sup -/ and SiH/sub 3//sup -/. Comparable calculations are made for GeH/sub 3//sup -/. Calculated vertical ionization energies are 0.51 eV for CH/sub 3//sup -/, 1.79 eV for SiH/sub 3//sup -/, and 2.01 eV for GeH/sub 3//sup -/; adiabatic counterparts are 0.19, 1.31, and 1.39 eV, respectively. Calculations employing effective core potentials for SiH/sub 3//sup -/ and GeH/sub 3//sup -/ agree closely with all-electron results. Vertical ionization energies employing these techniques are 1.88 eV for SiH/sub 3//sup -/ and 1.97 eV for GeH/sub 3//sup -/. Adiabatic effective core potential results are 1.46 eV for SiH/sub 3//sup -/ and 1.49 eV for GeH/sub 3//sup -/.

Direct versus indirect many-body methods for calculating vertical electron affinities: applications to F −, OH − , NH 2−, CN −, Cl −, SH − and PH 2−

Electron propagator theory (EPT) is applied to calculating vertical ionization energies of the anions F −, Cl −, OH −,SH −, NH 2 −, PH 2 − and CN −. Third-order and outer valence approximation (OVA) quasiparticle calculations are compared with ΔMBPT(4) (MBPT, many-body perturbation theory) results using the same basis sets. Agreement with experiment is satisfactory for EPT calculations except for F − and OH −, while the ΔMBPT treatments fail for CN −. EPT(OVA) estimates are reliable when the discrepancy between second- and third-order results is small. Computational aspects are discussed, showing relative merits of direct and indirect methods for evaluating electron binding energies.

Applying electron propagator theory to electron affinities

Electron propagator theory is used to calculate vertical ionization energies of closed shell anions. Third order diagonal self-energies are calculated using the post-Hartree–Fock utility subroutines of GAUSSIAN 82. Higher order corrections are estimated using the outer valence approximation. The number of operations needed rises no faster than the number required for the limited two-electron integral transformation. Basis set augmentations are made until changes in the computational results are small. Adiabatic ionization energies are obtained via many body perturbation theory calculations on the neutral potential energy surface. Applications to BeH- and MgH- give results in excellent agreement with photodetachment experiments.

Calculations on the vertical and adiabatic ionization energies of (H 2S) 2

After determining reliable procedures for calculating the ionization energy of H 2S using many-body perturbation theory and electron propagator theory, the same procedures are used to calculate the vertical ionization energy of the van der Waals molecule (H 2S) 2. The adiabatic ionization energy calculated for a dimer cation with a H 3S +...SH structure is in satisfactory agreement with photoionization threshold experiments. An alternative dimer cation structure with a three-electron S-S bond is also discussed.

Correlated electron propagator theory and applications for open‐shell atoms and molecules

AbstractA unitary group reformulation of electron propagator theory is used to derive the second‐order and 2p – h Tamm–Dancoff self‐energy approximations for open‐shell applications. A highest weight representation of the reference state is chosen in order to facilitate matrix element evaluation, but two special cases precluded by this choice are also discussed. Detailed numerical calculations are described for the lithium atom, oxygen molecule, and the amidogen radical.