Index
A
Abrikosov notation (of diagrams), 83–88
Abrikosov diagrams, see Diagrams
Adiabatic limit, 50–52, 55, 72, 199, 293, 294
Algebraic propagator methods, 241–254
see also Equations-of-motion
see also Superoperator formalism
Algebraic-diagrammatic construction
(ADC)
for self-energy, 135–140
for electron propagator, 147–155
for polarization propagator, 205–214
formulation of RPA, 233–236
Anticommutation relations, 21–22, 29
Antisymmetrization
of wave functions, 3–7
operator, 6, 9, 16
B
Bethe–Salpeter equation, 198
Binary product, see Superoperator formalism
Brillouin theorem, 271
C
Closed loop, see Fermion line
Compactness property, 143, 144
Configuration Interaction (CI), 187–191
full CI (FCI), 187
Contractions (of operator pairs), 63–64, 200
contraction schemes, 65, 67, 70–72, 76,
200, 201, 203, 301
Convergence factor, 33–34, 38, 40, 103, 197,
290–294, 314
Correlated excited states (CES), 161, 206,
241, 245, 258
Coupled-cluster (CC) methods
biorthogonal CC (BCC), 255, 257–266,
304–308
CC linear response (CCLR), 255, 312
equation-of-motion CC (EOM-CC), 223,
255
ground-state CC, 255–258
multi-reference CC, 257
symmetry-adapted cluster CI (SAC-CI),
255
Creation operator, see Operators
Cross sections
photoionization cross section, 35
D
Density, see electron density
Destruction operator, see Operators
Diagrams
Abrikosov diagrams, 75, 88–93, 116,
118, 139, 202, 213
Feynman diagrams, 62, 65–70, 75–83,
84, 87, 100, 106, 108, 111, 115, 200–
204, 213, 235, 287, 289, 293, 294, 301
Goldstone (time-ordered) diagrams, 95,
100–108, 117, 118, 138–140, 150, 152,
155, 203, 209, 210, 213, 234, 235, 287–
294, 302
Hubbard diagrams, 303, 304
linked/unlinked diagrams, 68–70, 75,
304
self-energy diagrams, see Self-energy
strictly connected diagrams, 302, 304
Dipole sum rule, see Sum rules
Dyson equation, 111–134
© Springer Nature Switzerland AG 2018
J. Schirmer, Many-Body Methods for Atoms, Molecules and Clusters, Lecture
Notes in Chemistry 94, https://doi.org/10.1007/978-3-319-93602-4
329
A
Abrikosov notation (of diagrams), 83–88
Abrikosov diagrams, see Diagrams
Adiabatic limit, 50–52, 55, 72, 199, 293, 294
Algebraic propagator methods, 241–254
see also Equations-of-motion
see also Superoperator formalism
Algebraic-diagrammatic construction
(ADC)
for self-energy, 135–140
for electron propagator, 147–155
for polarization propagator, 205–214
formulation of RPA, 233–236
Anticommutation relations, 21–22, 29
Antisymmetrization
of wave functions, 3–7
operator, 6, 9, 16
B
Bethe–Salpeter equation, 198
Binary product, see Superoperator formalism
Brillouin theorem, 271
C
Closed loop, see Fermion line
Compactness property, 143, 144
Configuration Interaction (CI), 187–191
full CI (FCI), 187
Contractions (of operator pairs), 63–64, 200
contraction schemes, 65, 67, 70–72, 76,
200, 201, 203, 301
Convergence factor, 33–34, 38, 40, 103, 197,
290–294, 314
Correlated excited states (CES), 161, 206,
241, 245, 258
Coupled-cluster (CC) methods
biorthogonal CC (BCC), 255, 257–266,
304–308
CC linear response (CCLR), 255, 312
equation-of-motion CC (EOM-CC), 223,
255
ground-state CC, 255–258
multi-reference CC, 257
symmetry-adapted cluster CI (SAC-CI),
255
Creation operator, see Operators
Cross sections
photoionization cross section, 35
D
Density, see electron density
Destruction operator, see Operators
Diagrams
Abrikosov diagrams, 75, 88–93, 116,
118, 139, 202, 213
Feynman diagrams, 62, 65–70, 75–83,
84, 87, 100, 106, 108, 111, 115, 200–
204, 213, 235, 287, 289, 293, 294, 301
Goldstone (time-ordered) diagrams, 95,
100–108, 117, 118, 138–140, 150, 152,
155, 203, 209, 210, 213, 234, 235, 287–
294, 302
Hubbard diagrams, 303, 304
linked/unlinked diagrams, 68–70, 75,
304
self-energy diagrams, see Self-energy
strictly connected diagrams, 302, 304
Dipole sum rule, see Sum rules
Dyson equation, 111–134
© Springer Nature Switzerland AG 2018
J. Schirmer, Many-Body Methods for Atoms, Molecules and Clusters, Lecture
Notes in Chemistry 94, https://doi.org/10.1007/978-3-319-93602-4
329