Electron propagator theory: an approach to prediction and interpretation in quantum chemistry

Abstract

Electron propagator theory provides a practical means of calculating electron binding energies, Dyson orbitals, and ground‐state properties from first principles. This approach to ab initio electronic structure theory also facilitates the interpretation of its quantitative predictions in terms of concepts that closely resemble those of one‐electron theories. An explanation of the physical meaning of the electron propagator's poles and residues is followed by a discussion of its couplings to more complicated propagators. These relationships are exploited in superoperator theory and lead to a compact form of the electron propagator that is derived by matrix partitioning. Expressions for reference‐state properties, relationships to the extended Koopmans's theorem technique for evaluating electron binding energies, and connections between Dyson orbitals and transition probabilities follow from this discussion. The inverse form of the Dyson equation for the electron propagator leads to a strategy for obtaining electron binding energies and Dyson orbitals that generalizes the Hartree–Fock equations through the introduction of the self‐energy operator. All relaxation and correlation effects reside in this operator, which has an energy‐dependent, nonlocal form that is systematically improvable. Perturbative arguments produce several, convenient (e.g. partial third order, outer valence Green's function, and second‐order, transition‐operator) approximations for the evaluation of valence ionization energies, electron affinities, and core ionization energies. Renormalized approaches based on Hartree–Fock or approximate Brueckner orbitals are employed when correlation effects become qualitatively important. Reference‐state total energies based on contour integrals in the complex plane and gradients of electron binding energies enable exploration of final‐state potential energy surfaces. © 2012 John Wiley & Sons, Ltd. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods

CaH Rydberg series, oscillator strengths and photoionization cross sections from Molecular Quantum Defect and Dyson Orbital theories

“…[14,15] For the i-th electron affinity of a cationic ground state with N-1 electrons, the corresponding Dyson orbital reads (1) where xk is the space-spin coordinate of electron k. This ab initio approach may be systematically improved to the exact limit by incorporating more terms in the self-energy operator. In the present study, the self-energy operator is calculated in the 3+ approximation, a method that includes all third-order and many higher-order terms in the self-energy operator through a renormalization procedure.…”

“…We have inferred vertical excitation energies of ns, np, nd and nf Rydberg series of CaH in the 1.8-5.5 eV energy range from differences of electron affinities of CaH + calculated with electron-propagator methods. [14,15] Because this approach also yields Dyson orbitals that connect the ground state of CaH + to ground and excited states of CaH, atomic contributions to the Rydberg orbitals may be identified.…”

Excitation energies, photoionization cross sections, and asymmetry parameters of the methyl and silyl radicals

“…Electron affinities and electron detachment energies may be calculated by solving the Dyson equation, [17][18][19] a convenient form of which reads…”

“…[12][13][14][15][16] In this work, we have determined excitation energies of a number of Rydberg states of CH 3 and SiH 3 by using electron propagator methods. [17][18][19] Vertical electron affinities of the corresponding, closed-shell cations have been calculated with several electron-propagator approximations and basis sets with many diffuse functions that are capable of describing the Rydberg states of the radicals. Excitation energies of the radicals may be inferred from differences between the electron affinities.…”

Communication: Explicitly correlated formalism for second-order single-particle Green’s function

“…Whereas GF formalism is dominant in condensed phase physics as a step beyond the mean-field description, it has also enjoyed a sustained, albeit a less prominent, presence in the molecular electronic structure. 2,3 The single-particle GF, or electron propagator, has primarily been employed as a computationally efficient route to post-mean-field ionization potentials (IP) and electron affinities (EA) and, more generally, spectral functions necessary to interpret various photoelectron spectroscopies; recently self-consistent GF theory has been revisited as a route to quantum embedding and to finite-temperature electronic structure. 4,5 Here we present a general, explicitly correlated formalism for computing single-particle Green's functions.…”