# Relativistic four-component static-exchange approximation for core-excitation processes in molecules

## Abstract

A generalization of the static-exchange approximation for core-electron spectroscopies to the relativistic four-component realm is presented. The initial state is a Kramers restricted Hartree-Fock state and the final state is formed as the configuration-interaction single excited state, based on the average of configurations for (n-1) electrons in n near-degenerate core orbitals for the reference ionic state. It is demonstrated that the static-exchange Hamiltonian can be made real by considering a set of time-reversal symmetric electron excitation operators. The static-exchange Hamiltonian is constructed at a cost that parallels a single Fock matrix construction in a quaternion framework that fully exploits time-reversal and spatial symmetries for the D{sub 2h} point group and subgroups. The K- and L-edge absorption spectra of H{sub 2}S are used to illustrate the methodology. The calculations adopt the Dirac-Coulomb Hamiltonian, but the theory is open ended toward improvements in the electron-electron interaction operator. It is demonstrated that relativistic effects are substantial for the L-edge spectrum of sulfur, and substantial deviations from the statistical 2:1 spin-orbit splitting of the intensity distribution are found. The average ratio in the mixed region is 1.54 at the present level of theory.

- Authors:

- Department of Physics, Chemistry and Biology, Linkoeping University, SE-581 83 Linkoeping (Sweden)
- (Italy)

- Publication Date:

- OSTI Identifier:
- 20974564

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.73.022501; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; ABSORPTION SPECTRA; CONFIGURATION INTERACTION; CORRECTIONS; DIRAC APPROXIMATION; DISTRIBUTION; ELECTRON SPECTROSCOPY; ELECTRON-ELECTRON COUPLING; ELECTRON-ELECTRON INTERACTIONS; ELECTRONS; EXCITATION; EXCITED STATES; HAMILTONIANS; HARTREE-FOCK METHOD; KRAMERS-KRONIG CORRELATION; MATRICES; MOLECULES; RELATIVISTIC RANGE; SPIN; SYMMETRY

### Citation Formats

```
Ekstroem, Ulf, Norman, Patrick, Carravetta, Vincenzo, and Istituto per i Processi Chimico-Fisici, Area della Ricerca del C.N.R., via G. Moruzzi 1, I-56124 Pisa.
```*Relativistic four-component static-exchange approximation for core-excitation processes in molecules*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.73.022501.

```
Ekstroem, Ulf, Norman, Patrick, Carravetta, Vincenzo, & Istituto per i Processi Chimico-Fisici, Area della Ricerca del C.N.R., via G. Moruzzi 1, I-56124 Pisa.
```*Relativistic four-component static-exchange approximation for core-excitation processes in molecules*. United States. doi:10.1103/PHYSREVA.73.022501.

```
Ekstroem, Ulf, Norman, Patrick, Carravetta, Vincenzo, and Istituto per i Processi Chimico-Fisici, Area della Ricerca del C.N.R., via G. Moruzzi 1, I-56124 Pisa. Wed .
"Relativistic four-component static-exchange approximation for core-excitation processes in molecules". United States.
doi:10.1103/PHYSREVA.73.022501.
```

```
@article{osti_20974564,
```

title = {Relativistic four-component static-exchange approximation for core-excitation processes in molecules},

author = {Ekstroem, Ulf and Norman, Patrick and Carravetta, Vincenzo and Istituto per i Processi Chimico-Fisici, Area della Ricerca del C.N.R., via G. Moruzzi 1, I-56124 Pisa},

abstractNote = {A generalization of the static-exchange approximation for core-electron spectroscopies to the relativistic four-component realm is presented. The initial state is a Kramers restricted Hartree-Fock state and the final state is formed as the configuration-interaction single excited state, based on the average of configurations for (n-1) electrons in n near-degenerate core orbitals for the reference ionic state. It is demonstrated that the static-exchange Hamiltonian can be made real by considering a set of time-reversal symmetric electron excitation operators. The static-exchange Hamiltonian is constructed at a cost that parallels a single Fock matrix construction in a quaternion framework that fully exploits time-reversal and spatial symmetries for the D{sub 2h} point group and subgroups. The K- and L-edge absorption spectra of H{sub 2}S are used to illustrate the methodology. The calculations adopt the Dirac-Coulomb Hamiltonian, but the theory is open ended toward improvements in the electron-electron interaction operator. It is demonstrated that relativistic effects are substantial for the L-edge spectrum of sulfur, and substantial deviations from the statistical 2:1 spin-orbit splitting of the intensity distribution are found. The average ratio in the mixed region is 1.54 at the present level of theory.},

doi = {10.1103/PHYSREVA.73.022501},

journal = {Physical Review. A},

number = 2,

volume = 73,

place = {United States},

year = {Wed Feb 15 00:00:00 EST 2006},

month = {Wed Feb 15 00:00:00 EST 2006}

}