Electron Propagator Calculations of Vertical Electron Binding Energies and Dyson Orbitals in Gaussian 16

Filip Pawłowski and J. V. Ortiz

Electron propagator theory (EPT) is used for ab initio calculations of vertical electron binding energies (VEBEs) of atoms, molecules and ions, e.g.,

vertical ionization potentials (VIPs) of molecules (example input and output),
vertical electron affinities (VEAs) of molecules (example input and output),
vertical electron detachment energies (VEDEs) of anions (example input and output),
ground-state and excited-state energies of radicals inferred from vertical electron attachment energies (VEAEs) of cations (example input and output).

In addition, EPT is used to determine Dyson orbitals. A Dyson orbital is a generalization of a frozen, Hartree-Fock canonical molecular orbital (CMO) that is modified by the effects of orbital relaxation and electron correlation.

EPT methods start with the simple Koopmans's theorem (KT) result and systematically improve upon it to approach exact VEBEs. This strategy differs from density-functional theory (DFT) and resembles that of wave-function theory (WFT) methods. An advantage of EPT over evaluation of total energies for initial and final states with WFT (e.g. ΔMP2, ΔCCSD(T)) is calculating VEBEs directly. Unlike many direct WFT methods, such as EOM-CCSD, EPT calculations yield a single Dyson orbital for each VEBE.

In general, the P3+ and NR2 EPT methods have a computational cost comparable to and accuracy surpassing second-order Møller-Plesset perturbation theory (MP2). Several final states are usually accessible; final-state excitation energies may be inferred from differences of VEBEs.

(Arithmetic scaling below refers to IPs; click on the figure or table to enlarge.)

Previous version of this tutorial (for Gaussian 09 users)

References

Second order [1-3]
Third order [4]
Partial third order (P3) [5, 6]
Renormalized partial third order (P3+) [7, 8]
Outer Valence Green Function (OVGF) [9-12]
Two-particle-hole Tamm-Dancoff approximation (2ph-TDA) [13, 14]
Renormalized third order (3+) [12]
Third order algebraic diagrammatic contruction (ADC3) [15, 16]
Nondiagonal renormalized second order (NR2) [17, 18]
EPT reviews [8, 12, 18-25]
Algorithms [19, 26-28]
General references [29, 30]

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