Abstract
The paper addresses the problem of the self-interaction correction (SIC) in static calculations of atoms and molecules. Key observable is the electron removal energy, the energy required to remove one electron from the given system and to leave it in a definite hole state whereby we discuss hole states not only in the Highest Occupied Molecular Orbital (HOMO), but also deeper lying holes. To that end, we employ a newly developed technique to compute a stationary state for a configuration with a definite hole in a chosen single-particle state. We also compare two different definitions of removal energies, first, the genuine one taking the difference of the total energy of the original system and the energy of final system sustaining the hole, and second, simply the single-particle energy in the original system. According to Koopman’s theorem, both should be close to each other. Four different systems are considered, one atom and three molecules with different bond types, covalent, metallic, and dipolar. The general result is that any SIC brings considerable improvement as compared to the initial Local-Density Approximation (LDA), the better the closer the hole stays to the HOMO. There are variations between different SIC approximations whereby systems with strong binding (atom and covalent molecule) show least variations. Here, the quality of Koopman’s theorem is very satisfying for the HOMO and degrades slightly toward deeper binding. Systems with metallic or dipolar binding are more reactive and show stronger changes with approximation and hole level.
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References
Weissbluth M (1978) Atoms and molecules. Academic Press, San Diego
Ghosh P (1983) Introduction to photoelectron spectroscopy. Wiley, New York
Pabst S, Greenman L, Ho P, Mazziotti D, Santra R (2011) Phys Rev Lett 106:053003
Arnold C, Larivière-Loiselle C, Khalili K, Inhester L, Welsch R, Santra R (2020) J Phys B 53:164006
Baruah T, Pederson MR (2006) J Chem Phys 125:164706
Martin RM, Reining L, Ceperley DM (2016) Interacting electrons: theory and computational approaches. Cambridge University Press, Cambridge
Parr RG, Yang W (1989) Density-functional theory of atoms and molecules. Oxford University Press, Oxford
Dreizler RM, Gross EKU (1990) Density functional theory: an approach to the quantum many-body problem. Springer-Verlag, Berlin
Kohn W (1999) Rev Mod Phys 71:1253
Gross EKU, Kohn W (1990) Adv Quant Chem 21:255
Gross EKU, Dobson JF, Petersilka M (1996) Top Curr Chem 181:81
Kohanoff J (2006) Electronic structure calculations for solids and molecules: theory and computational methods. Cambridge University Press, Cambridge
Reinhard PG, Suraud E (2004) Introduction to cluster dynamics. Wiley, New York
Marques MAL, Ullrich CA, Nogueira F (eds) (2006) Time-dependent density functional theory, lecture notes in physics, vol 706. Springer, Berlin
Fennel T, Meiwes-Broer KH, Tiggesbäumker J, Dinh PM, Reinhard PG, Suraud E (2010) Rev Mod Phys 82:1793
Ullrich C (2012) Time-dependent density-functional theory: concepts and applications. Oxford University Press, Oxford
Perdew JP, Zunger A (1981) Phys Rev B 23:5048
Kohn W, Sham LJ (1965) Phys Rev 140:1133
Schwarz K (1978) Chem Phys Lett 57(4):605
Kümmel S, Kronik L, Perdew JP (2004) Phys Rev Lett 93:213002
Nieminen RM (1999) Curr Opin Solid State Mater Sci 4:493
Giovannini UD, Varsano D, Marques MAL, Appel H, Gross EKU, Rubio A (2012) Phys Rev A 85:062515
Casida ME, Salahub DR (2000) J Chem Phys 113:8918
Becke AD (1988) Phys Rev A 38:3098
Perdew JP, Burke K, Ernzerhof M (1996) Phys Rev Lett 77:3865
Perdew JP (1979) Chem Phys Lett 64:127
Pederson MR, Heaton RA, Lin CC (1984) J Chem Phys 80(5):1972
Goedecker CUS (1997) Phys Rev A 55:1765
Vydrov OA, Scuseria GE (2004) J Chem Phys 121:8187
Hofmann D, Klüpfel S, Klüpfel P, Kümmel S (2012) Phys Rev A 85:062514
Klüpfel S, Klüpfel P, Jónsson H (2012) J Chem Phys 137:124102
Svane A (1996) Phys Rev B 53:4275
Klüpfel S, Klüpfel P, Jónsson H (2011) Phys Rev A 84:050501
Messud J, Dinh PM, Reinhard PG, Suraud E (2008) Phys Rev Lett 101:096404
Sharp RT, Horton GK (1953) Phys Rev 30:317
Kümmel S, Kronik L (2008) Rev Mod Phys 80:3
Chen J, Krieger JB, Li Y, Iafrate GJ (1996) Phys Rev A 54:3939
Krieger JB, Li Y, Iafrate GJ (1992) Phys Rev A 45:101
Fermi E, Amaldi E (1934) Accad Ital Rome 6:117
Legrand C, Suraud E, Reinhard PG (2002) J Phys B 35:1115
Ciofini I, Adamo C, Chermette H (2005) Chem Phys 309:67
Klüpfel P, Dinh PM, Reinhard PG, Suraud E (2013) Phys Rev A 88:052501
Koopmans T (1933) Physica 1:104
Perdew JP, Levy M (1997) Phys Rev B 56:16021
Pohl A, Reinhard PG, Suraud E (2000) Phys Rev Lett 84:5090
Pohl A, Reinhard PG, Suraud E (2003) Phys Rev A 68:053202
Marc Vincendon, Dinh Phuong Mai, Romaniello Pina, Reinhard Paul-Gerhard, Suraud Éric (2013) Eur Phys J D 67(5):97
Dinh PM, Gao CZ, Klüpfel P, Reinhard PG, Suraud E, Vincendon M, Wang J, Zhang FS (2014) Eur Phys J D 68:239
Wopperer P, Dinh PM, Reinhard PG, Suraud E (2015) Phys Rep 562:1
Mundt M, Kümmel S, Huber B, Moseler M (2006) Phys Rev B 73(20):205407
Goedecker S, Teter M, Hutter J (1996) Phys Rev B 54:1703
Hartwigsen C, Goedecker S, Hutter J (1998) Phys Rev B 58:3641
Messud J, Dinh PM, Reinhard PG, Suraud E (2008) Ann. Phys. (N.Y) 324:955
Dinh P, Romaniello P, Reinhard PG, Suraud E (2013) Phys Rev A 87:032514
Dinh PM, Reinhard PG, Suraud E, Vincendon M (2015) Adv At Mol Opt Phys 64:87
Mundt M, Kümmel S (2006) Phys Rev A 74(2):022511
Mundt M, Kümmel S, van Leeuwen R, Reinhard PG (2007) Phys Rev A 75(5):050501
Messud J, Dinh PM, Reinhard PG, Suraud E (2008) Chem Phys Lett 461:316
Ciofini I, Chermette H, Adamo C (2003) Chem Phys Lett 380:12
Calvayrac F, Reinhard PG, Suraud E, Ullrich CA (2000) Phys Rep 337:493
Reinhard PG, Cusson RY (1982) Nucl Phys A 378:418
Blum V, Lauritsch G, Maruhn JA, Reinhard PG (1992) J Comp Phys 100:364
Perdew JP, Wang Y (1992) Phys Rev B 45:13244
Kümmel S, Brack M, Reinhard PG (1999) Eur Phys J D 9:149
Pederson MR, Heaton RA, Lin CC (1985) J Chem Phys 82:2688
Maruhn J, Reinhard PG, Suraud E (2010) Simple models of many-fermions systems. Springer, Berlin
Wrigge G, Hoffmann MA, von Issendorff B (2002) Phys Rev A 65:063201
Wopperer P, Dinh PM, Suraud E, Reinhard PG (2012) Phys Rev A 85:015402
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One of the authors (P.-G. Reinhard) thanks the regional computing center of the Friedrich-Alexander university (RRZE) for supplying resources for the extensive calculations.
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Reinhard, P.G., Suraud, E. Self-interaction-correction and electron removal energies. Theor Chem Acc 140, 63 (2021). https://doi.org/10.1007/s00214-021-02753-w
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DOI: https://doi.org/10.1007/s00214-021-02753-w