# Anti-Hermitian part of the contracted Schroedinger equation for the direct calculation of two-electron reduced density matrices

## Abstract

A recent advance in the theory of the contracted Schroedinger equation (CSE), in which only the anti-Hermitian part of the equation is solved, permits the direct determination of ground-state two-electron reduced density matrices (2-RDM's) that yield 95%-100% of the correlation energy of atoms and molecules [D. A. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006)]. Here we discuss in detail the anti-Hermitian contracted Schroedinger equation (ACSE) and its comparison to the CSE with regard to cumulant reconstruction of RDM's, the role of Nakatsuji's theorem, and the structure of the wave function. The ACSE is also formulated in the Heisenberg representation and related to canonical diagonalization. The solution of the ACSE is illustrated with a variety of molecules including H{sub 2}O, CH{sub 2}, NH{sub 4}{sup +}, HF, and N{sub 2}, and potential energy and dipole-moment surfaces are computed for boron hydride in a polarized double-{zeta} basis set. The computed 2-RDM's very closely satisfy known N-representability conditions.

- Authors:

- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 (United States)

- Publication Date:

- OSTI Identifier:
- 20982104

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.022505; (c) 2007 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; ATOMS; BORON HYDRIDES; CATIONS; DENSITY MATRIX; DIPOLE MOMENTS; ELECTRON CORRELATION; ELECTRONS; GROUND STATES; HEISENBERG PICTURE; HERMITIAN MATRIX; HYDROFLUORIC ACID; MATHEMATICAL SOLUTIONS; MOLECULES; NITROGEN COMPOUNDS; ORGANIC COMPOUNDS; POTENTIAL ENERGY; SCHROEDINGER EQUATION; SURFACES; WATER; WAVE FUNCTIONS

### Citation Formats

```
Mazziotti, David A.
```*Anti-Hermitian part of the contracted Schroedinger equation for the direct calculation of two-electron reduced density matrices*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.022505.

```
Mazziotti, David A.
```*Anti-Hermitian part of the contracted Schroedinger equation for the direct calculation of two-electron reduced density matrices*. United States. doi:10.1103/PHYSREVA.75.022505.

```
Mazziotti, David A. Thu .
"Anti-Hermitian part of the contracted Schroedinger equation for the direct calculation of two-electron reduced density matrices". United States.
doi:10.1103/PHYSREVA.75.022505.
```

```
@article{osti_20982104,
```

title = {Anti-Hermitian part of the contracted Schroedinger equation for the direct calculation of two-electron reduced density matrices},

author = {Mazziotti, David A.},

abstractNote = {A recent advance in the theory of the contracted Schroedinger equation (CSE), in which only the anti-Hermitian part of the equation is solved, permits the direct determination of ground-state two-electron reduced density matrices (2-RDM's) that yield 95%-100% of the correlation energy of atoms and molecules [D. A. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006)]. Here we discuss in detail the anti-Hermitian contracted Schroedinger equation (ACSE) and its comparison to the CSE with regard to cumulant reconstruction of RDM's, the role of Nakatsuji's theorem, and the structure of the wave function. The ACSE is also formulated in the Heisenberg representation and related to canonical diagonalization. The solution of the ACSE is illustrated with a variety of molecules including H{sub 2}O, CH{sub 2}, NH{sub 4}{sup +}, HF, and N{sub 2}, and potential energy and dipole-moment surfaces are computed for boron hydride in a polarized double-{zeta} basis set. The computed 2-RDM's very closely satisfy known N-representability conditions.},

doi = {10.1103/PHYSREVA.75.022505},

journal = {Physical Review. A},

number = 2,

volume = 75,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}