# Magnetizability and rotational g tensors for density fitted local second-order Møller-Plesset perturbation theory using gauge-including atomic orbitals

## Abstract

In this paper, we present theory and implementation of an efficient program for calculating magnetizabilities and rotational g tensors of closed-shell molecules at the level of local second-order Møller-Plesset perturbation theory (MP2) using London orbitals. Density fitting is employed to factorize the electron repulsion integrals with ordinary Gaussians as fitting functions. The presented program for the calculation of magnetizabilities and rotational g tensors is based on a previous implementation of NMR shielding tensors reported by S. Loibl and M. Schütz [J. Chem. Phys. 137, 084107 (2012)]. Extensive test calculations show (i) that the errors introduced by density fitting are negligible, and (ii) that the errors of the local approximation are still rather small, although larger than for nuclear magnetic resonance (NMR) shielding tensors. Electron correlation effects for magnetizabilities are tiny for most of the molecules considered here. MP2 appears to overestimate the correlation contribution of magnetizabilities such that it does not constitute an improvement over Hartree-Fock (when comparing to higher-order methods like CCSD(T)). For rotational g tensors the situation is different and MP2 provides a significant improvement in accuracy over Hartree-Fock. The computational performance of the new program was tested for two extended systems, the larger comprising about 2200 basismore »

- Authors:

- Institute of Physical and Theoretical Chemistry, University of Regensburg, Universitätsstraße 31, D-93040 Regensburg (Germany)

- Publication Date:

- OSTI Identifier:
- 22308987

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ACCURACY; DENSITY; ELECTRON CORRELATION; ELECTRONS; HARTREE-FOCK METHOD; MOLECULES; NUCLEAR MAGNETIC RESONANCE; PERTURBATION THEORY; TENSORS

### Citation Formats

```
Loibl, Stefan, and Schütz, Martin, E-mail: martin.schuetz@chemie.uni-regensburg.de.
```*Magnetizability and rotational g tensors for density fitted local second-order Møller-Plesset perturbation theory using gauge-including atomic orbitals*. United States: N. p., 2014.
Web. doi:10.1063/1.4884959.

```
Loibl, Stefan, & Schütz, Martin, E-mail: martin.schuetz@chemie.uni-regensburg.de.
```*Magnetizability and rotational g tensors for density fitted local second-order Møller-Plesset perturbation theory using gauge-including atomic orbitals*. United States. doi:10.1063/1.4884959.

```
Loibl, Stefan, and Schütz, Martin, E-mail: martin.schuetz@chemie.uni-regensburg.de. Mon .
"Magnetizability and rotational g tensors for density fitted local second-order Møller-Plesset perturbation theory using gauge-including atomic orbitals". United States. doi:10.1063/1.4884959.
```

```
@article{osti_22308987,
```

title = {Magnetizability and rotational g tensors for density fitted local second-order Møller-Plesset perturbation theory using gauge-including atomic orbitals},

author = {Loibl, Stefan and Schütz, Martin, E-mail: martin.schuetz@chemie.uni-regensburg.de},

abstractNote = {In this paper, we present theory and implementation of an efficient program for calculating magnetizabilities and rotational g tensors of closed-shell molecules at the level of local second-order Møller-Plesset perturbation theory (MP2) using London orbitals. Density fitting is employed to factorize the electron repulsion integrals with ordinary Gaussians as fitting functions. The presented program for the calculation of magnetizabilities and rotational g tensors is based on a previous implementation of NMR shielding tensors reported by S. Loibl and M. Schütz [J. Chem. Phys. 137, 084107 (2012)]. Extensive test calculations show (i) that the errors introduced by density fitting are negligible, and (ii) that the errors of the local approximation are still rather small, although larger than for nuclear magnetic resonance (NMR) shielding tensors. Electron correlation effects for magnetizabilities are tiny for most of the molecules considered here. MP2 appears to overestimate the correlation contribution of magnetizabilities such that it does not constitute an improvement over Hartree-Fock (when comparing to higher-order methods like CCSD(T)). For rotational g tensors the situation is different and MP2 provides a significant improvement in accuracy over Hartree-Fock. The computational performance of the new program was tested for two extended systems, the larger comprising about 2200 basis functions. It turns out that a magnetizability (or rotational g tensor) calculation takes about 1.5 times longer than a corresponding NMR shielding tensor calculation.},

doi = {10.1063/1.4884959},

journal = {Journal of Chemical Physics},

number = 2,

volume = 141,

place = {United States},

year = {Mon Jul 14 00:00:00 EDT 2014},

month = {Mon Jul 14 00:00:00 EDT 2014}

}