 


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.,
In addition, EPT is used to determine Dyson orbitals. A Dyson
orbital is a generalization of a frozen, HartreeFock 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 densityfunctional theory (DFT) and resembles that of
wavefunction 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 EOMCCSD, 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
secondorder MøllerPlesset perturbation theory (MP2).
Several final states are usually accessible; finalstate 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 [13]
Third order [4]
Partial third order (P3) [5, 6]
Renormalized partial third order (P3+) [7, 8]
Outer Valence Green Function (OVGF) [912]
Twoparticlehole TammDancoff approximation (2phTDA) [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, 1825]
Algorithms [19, 2628]
General references [29, 30]
[1] D.J. Thouless, The Quantum Mechanics of ManyBody Systems, Academic Press, New York, 1961.
[2] W.P. Reinhardt, J.D. Doll, Direct Calculation of Natural Orbitals by Many‐Body Perturbation Theory: Application to Helium, J. Chem. Phys. 50 (1969) 27672768.
[3] J.D. Doll, W.P. Reinhardt, Manybody Green's functions for finite, nonuniform systems. Applications to closedshell atoms, J. Chem. Phys. 57 (1972) 11691184.
[4] L.S. Cederbaum, Direct calculation of ionization potentials of closedshell atoms and molecules, Theor. Chim. Acta 31 (1973) 239260.
[5] J.V. Ortiz, Partial thirdorder quasiparticle theory: comparisons for closedshell ionization energies and an application to the Borazine photoelectron spectrum, J. Chem. Phys. 104 (1996) 75997605.
[6] A.M. Ferreira, G. Seabra, O. Dolgounitcheva, V.G. Zakrzewski, J.V. Ortiz, Application and testing of diagonal, partial thirdorder electron propagator approximations, Understanding Chem. React. 22 (2001) 131160.
[7] J.V. Ortiz, An efficient, renormalized selfenergy for calculating the electron binding energies of closedshell molecules and anions, Int. J. Quantum Chem. 105 (2005) 803808.
[8] J.V. Ortiz, Electron propagator theory: an approach to prediction and interpretation in quantum chemistry, Wiley Interdisciplinary Reviews: Computational Molecular Science 3 (2013) 123142.
[9] L.S. Cederbaum, Onebody Green's function for atoms and molecules. Theory and application, J. Phys. B 8 (1975) 290303.
[10] W. von Niessen, J. Schirmer, L.S. Cederbaum, Computational methods for the oneparticle Green's function, Comput. Phys. Rep. 1 (1984) 57125.
[11] V.G. Zakrzewski, J.V. Ortiz, J.A. Nichols, D. Heryadi, D.L. Yeager, J.T. Golab, Comparison of perturbative and multiconfigurational electron propagator methods, Int. J. Quantum Chem. 60 (1996) 2936.
[12] J.V. Ortiz, The electron propagator picture of molecular electronic structure, Comput. Chem.
Rev. Current Trends 2 (1997) 161.
[13] L.S. Cederbaum, W. Domcke, Theoretical aspects of ionization potentials and photoelectron spectroscopy: a Green's function approach, Adv. Chem. Phys. 36 (1977) 205344.
[14] J. Schirmer, L.S. Cederbaum, The twoparticlehole TammDancoff approximation (2phTDA) equations for closedshell atoms and molecules, J. Phys. B 11 (1978) 18891900.
[15] J. Schirmer, L.S. Cederbaum, O. Walter, New approach to the oneparticle Green's function for finite Fermi systems, Physical Review A 28 (1983) 12371259.
[16] J. Schirmer, G. Angonoa, On Greenfunction calculations of the static selfenergy part, the ground state energy, and expectation values, J. Chem. Phys. 91 (1989) 17541761.
[17] J.V. Ortiz, A nondiagonal, renormalized extension of partial thirdorder quasiparticle theory: comparisons for closedshell ionization energies, J. Chem. Phys. 108 (1998) 10081014.
[18] H.H. Corzo, J.V. Ortiz, Electron Propagator Theory: Foundations and Predictions,
Adv. Quantum Chem. 74 (2017) 267298.
[19] J.V. Ortiz, V.G. Zakrzewski, O. Dolgounitcheva, Oneelectron pictures of electronic structure: propagator calculations on photoelectron spectra of aromatic molecules, in: J.L. Calais, E. Kryachko (Eds.), Conceptual Perspectives in Quantum Chemistry, Kluwer, Dordrecht, 1997, pp. 465517.
[20] J.V. Ortiz, Toward an exact oneelectron picture of chemical bonding,
Adv. Quantum Chem. 35 (1999) 3352.
[21] R. FloresMoreno, J. Melin, O. Dolgounitcheva, V.G. Zakrzewski, J.V. Ortiz, Three approximations to the nonlocal and energydependent correlation potential in electron propagator theory, Int. J. Quantum Chem. 110 (2010) 706715.
[22] V.G. Zakrzewski, O. Dolgounitcheva, A.V. Zakjevskii, J.V. Ortiz,
Ab initio electron propagator methods: applications to fullerenes and nucleic acid fragments,
Annu. Rep. Comput. Chem. 6 (2010) 7994.
[23] R. FloresMoreno, J.V. Ortiz, Efficient and Accurate Electron Propagator Methods and Algorithms, in: J. Leszczynski, M.K. Shukla (Eds.), Practical Aspects of Computational Chemistry: Methods, Concepts and Applications, Springer Netherlands, Dordrecht, 2010, pp. 117.
[24] V.G. Zakrzewski, O. Dolgounitcheva, A.V. Zakjevskii, J.V. Ortiz,
Ab initio electron propagator calculations on electron detachment energies of fullerenes,
macrocyclic molecules, and nucleotide fragments, Adv. Quantum Chem. 62 (2011) 105136.
[25] J.V. Ortiz, Interpreting Bonding and Spectra With Correlated, OneElectron Concepts From
Electron Propagator Theory,
Annu. Rep. Comput. Chem. 13 (2017) 139182.
[26] V.G. Zakrzewski, J.V. Ortiz, Semidirect algorithms in electron propagator calculations, Int. J. Quantum Chem., Quantum Chem. Symp. 28 (1994) 2327.
[27] V.G. Zakrzewski, J.V. Ortiz, Semidirect algorithms for thirdorder electron propagator calculations, Int. J. Quantum Chem. 53 (1995) 583590.
[28] V.G. Zakrzewski, O. Dolgounitcheva, J.V. Ortiz, Improved algorithms for renormalized electron propagator calculations, Int. J. Quantum Chem. 75 (1999) 607614.
[29] J. Linderberg, Y. Öhrn, Propagators in Quantum Chemistry, Second Edition, WileyInterscience, Hoboken NJ, 2004.
[30] P. Jørgensen, J. Simons, Second QuantizationBased Methods in Quantum Chemistry, Academic Press, New York, 1981.
 