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Going beyond “no-pair relativistic quantum chemistry”
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10.1063/1.4811795
/content/aip/journal/jcp/139/1/10.1063/1.4811795
http://aip.metastore.ingenta.com/content/aip/journal/jcp/139/1/10.1063/1.4811795

Figures

Image of FIG. 1.
FIG. 1.

Diagrammatical representation of the second order energy (65) . (a) two-body direct; (b) two-body exchange; (c) one-body. The horizontal dashed line represents the instantaneous Coulomb/Breit interaction. For the state, the particles (upgoing lines) and holes (downgoing lines) are {, } and , respectively. The one-body potential represented by the square is (57) . For the state, the particles and holes are {, , , } and , respectively. The one-body potential is (59) . A global negative sign should be inserted to the terms of .

Image of FIG. 2.
FIG. 2.

Diagrammatical representation of the potential (77) . Free orbital lines directed upwards and downwards represent PES and NES, respectively. The internal orbital lines for the electron vacuum polarization (6) and (7) and self-energy (8) and (9) can be both PES and NES, whether occupied or not. Both the dashed and wavy lines represent the instantaneous Coulomb/Breit interaction. The cross indicates the counter potential −.

Image of FIG. 3.
FIG. 3.

Diagrammatical representation of the first order wave operator Ω (72) . Free orbital lines directed upwards and downwards represent PES and NES, respectively. The internal orbital lines for the electron vacuum polarization (6) and (7) and self-energy (8) and (9) can be both PES and NES, whether occupied or not. Both the dashed and wavy lines represent the instantaneous Coulomb/Breit interaction. The cross indicates the counter potential −.

Image of FIG. 4.
FIG. 4.

Time-ordered Feynman diagrams for the -operators (79)–(106) with instantaneous interactions.

Image of FIG. 5.
FIG. 5.

Non-retarded Feynman diagrams for the second order energy. The numbers in brackets refer to the diagrams in Fig. 4 . The retarded diagrams are obtained by replacing one or two Coulomb photons with transverse photons.

Image of FIG. 6.
FIG. 6.

Non-retarded Feynman diagrams for the first order energy. The retarded diagrams are obtained by replacing the Coulomb photon with a transverse photon.

Image of FIG. 7.
FIG. 7.

Disconnected but linked Feynman diagrams: (a), (b), and (c) go with Figs. 5 (1), 5 (2, 3), and 5 (4, 5), respectively.

Tables

Generic image for table
Table I.

The spectrum of relativistic Hamiltonians. SC: Schrödinger-Coulomb; A1C: spin-free part of A2C; A2C: approximate two-component; X1C: spin-free part of X2C; X2C: exact two-component; Q4C: quasi-four-component; DCB: no-pair Dirac-Coulomb-Breit; PI-DCB: potential-independent DCB; eQED: effective (non-retarded) QED.

Generic image for table
Table II.

Degeneracy ( ) of low-order Feynman diagrams. : number of electron-field contractions between two different vertices enumerated in an ascending order; : number of electron-field contractions within the same vertex; : number of possible assignments of the photon interactions; = (1, + 2 ) × (1, ).

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/content/aip/journal/jcp/139/1/10.1063/1.4811795
2013-07-02
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Going beyond “no-pair relativistic quantum chemistry”
http://aip.metastore.ingenta.com/content/aip/journal/jcp/139/1/10.1063/1.4811795
10.1063/1.4811795
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