The GW-method for quantum chemistry applications: Theory and implementation

Journal of Chemical Theory and Computation

Volumn 9, Issue 1, 2013, Pages 232-246

  Van Setten, M J ^a   Weigend, F ^a,b   Evers, F ^a,b  

^a KARLSRUHE INSTITUTE OF TECHNOLOGY   (Germany)

^b KARLSRUHE INSTITUTE OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84872142935     PISSN: 15499618     EISSN: 15499626     Source Type: Journal    
DOI: 10.1021/ct300648t     Document Type: Article

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89. 0 refers to the Green's function of a strictly noninteracting reference system, i.e., also without mean-field interaction.
90. For single-particle ground states (single Slater determinant) the pole positions and residues of the Green's function do not depend on z. By contrast, for ground states with more than a single Slater determinant, pole positions and residues in general do depend on z. The z -dependency takes into account that the spectral-function A (E) of interacting electron gases is not just a superposition of N Lorentzians. We add that G has a second spectral representation in terms of a sum over all the many-body states of the electron gas. In this representation the poles do not depend on z; the price to be paid for this simplification is that the number of poles appearing is not given by the number of particles, N, but by the much larger number of all many-body excitations.
91. XC, see eq 25.
92. The poles reside in the upper and the lower complex half planes. This representation is inherited from the fact that the constituting equations refer to causal Green's functions.
93. For some of the smaller molecules values do exist at fully self-consistent GW -level.(38) Since however these form only a small subset we prefer to stick in our comparison to the experimental values as a reference.
94. 2; there however the trend is less obvious due to the limited amount of data points.)
95. The only exception is SF4. Here even between TZVPP and QZVP the KS-energy levels change by more than 0.1 eV.
96. i.
97. Both benzene and naphthalene were calculated using ″really tight Tier 2″ settings since the use of a Tier 3 basis set led in these cases to an overcomplete basis set.