# Fully relativistic complete active space self-consistent field for large molecules: Quasi-second-order minimax optimization

## Abstract

We develop an efficient algorithm for four-component complete active space self-consistent field (CASSCF) methods on the basis of the Dirac equation that takes into account spin–orbit and other relativistic effects self-consistently. Orbitals are optimized using a trust-region quasi-Newton method with Hessian updates so that energies are minimized with respect to rotations among electronic orbitals and maximized with respect to rotations between electronic and positronic orbitals. Utilizing density fitting and parallel computation, we demonstrate that Dirac–Coulomb CASSCF calculations can be routinely performed on systems with 100 atoms and a few heavy-elements. The convergence behavior and wall times for octachloridodirhenate(III) and a tungsten methylidene complex are presented. In addition, the excitation energies of octachloridodirhenate(III) are reported using a state-averaged variant.

- Authors:

- Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208 (United States)

- Publication Date:

- OSTI Identifier:
- 22416038

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 4; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ALGORITHMS; ATOMS; CONVERGENCE; DIRAC EQUATION; EXCITATION; L-S COUPLING; MOLECULES; NEWTON METHOD; OPTIMIZATION; ORGANIC CHLORINE COMPOUNDS; RELATIVISTIC RANGE; RHENATES; ROTATION; SELF-CONSISTENT FIELD; SPACE; TUNGSTEN

### Citation Formats

```
Bates, Jefferson E., and Shiozaki, Toru.
```*Fully relativistic complete active space self-consistent field for large molecules: Quasi-second-order minimax optimization*. United States: N. p., 2015.
Web. doi:10.1063/1.4906344.

```
Bates, Jefferson E., & Shiozaki, Toru.
```*Fully relativistic complete active space self-consistent field for large molecules: Quasi-second-order minimax optimization*. United States. doi:10.1063/1.4906344.

```
Bates, Jefferson E., and Shiozaki, Toru. Wed .
"Fully relativistic complete active space self-consistent field for large molecules: Quasi-second-order minimax optimization". United States.
doi:10.1063/1.4906344.
```

```
@article{osti_22416038,
```

title = {Fully relativistic complete active space self-consistent field for large molecules: Quasi-second-order minimax optimization},

author = {Bates, Jefferson E. and Shiozaki, Toru},

abstractNote = {We develop an efficient algorithm for four-component complete active space self-consistent field (CASSCF) methods on the basis of the Dirac equation that takes into account spin–orbit and other relativistic effects self-consistently. Orbitals are optimized using a trust-region quasi-Newton method with Hessian updates so that energies are minimized with respect to rotations among electronic orbitals and maximized with respect to rotations between electronic and positronic orbitals. Utilizing density fitting and parallel computation, we demonstrate that Dirac–Coulomb CASSCF calculations can be routinely performed on systems with 100 atoms and a few heavy-elements. The convergence behavior and wall times for octachloridodirhenate(III) and a tungsten methylidene complex are presented. In addition, the excitation energies of octachloridodirhenate(III) are reported using a state-averaged variant.},

doi = {10.1063/1.4906344},

journal = {Journal of Chemical Physics},

number = 4,

volume = 142,

place = {United States},

year = {Wed Jan 28 00:00:00 EST 2015},

month = {Wed Jan 28 00:00:00 EST 2015}

}