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# The all configuration mean energy multiconfiguration self-consistent-field method. I. Equal configuration weights

## Abstract

The All Configuration Mean Energy (ACME) conditions are a special case of state averaging for Multiconfigurational Self-Consistent-Field (MCSCF) orbital optimisation. The method is formulated using the Graphical Unitary Group Approach (GUGA) in which the Configuration State Function (CSF) basis is represented as walks within a Shavitt graph. This graphical formulation leads to efficient recursive algorithms for the energy and reduced density matrices (RDM) that are independent of the CSF dimension and that scale only as O(n2) where n is the number of occupied orbitals. The Hamiltonian matrix diagonalization step is obviated and the CSF expansion coefficients are neither referenced nor required. This allows MCSCF orbital optimisation to be performed for essentially unlimited numbers of active orbitals and arbitrarily large CSF expansions. The discussion includes various types of CSF expansion spaces, the partitioning of the essential and redundant orbital optimisation parameters, the computation of the spin-density, and the formulation of state-specific analytic gradients and nonadiabatic coupling for high-level electronic structure methods that use the ACME MCSCF orbitals.

- Authors:

- Argonne National Lab. (ANL), Lemont, IL (United States)

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Chemical Sciences, Geosciences & Biosciences Division

- OSTI Identifier:
- 1543139

- Grant/Contract Number:
- AC02-06CH11357

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Molecular Physics

- Additional Journal Information:
- Journal Volume: 117; Journal Issue: 17; Journal ID: ISSN 0026-8976

- Publisher:
- Taylor & Francis

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; MCSCF; analytic gradient; electronic structure; nonadiabatic coupling; state averaging

### Citation Formats

```
Shepard, Ron, and Brozell, Scott R. The all configuration mean energy multiconfiguration self-consistent-field method. I. Equal configuration weights. United States: N. p., 2019.
Web. doi:10.1080/00268976.2019.1635275.
```

```
Shepard, Ron, & Brozell, Scott R. The all configuration mean energy multiconfiguration self-consistent-field method. I. Equal configuration weights. United States. doi:10.1080/00268976.2019.1635275.
```

```
Shepard, Ron, and Brozell, Scott R. Fri .
"The all configuration mean energy multiconfiguration self-consistent-field method. I. Equal configuration weights". United States. doi:10.1080/00268976.2019.1635275.
```

```
@article{osti_1543139,
```

title = {The all configuration mean energy multiconfiguration self-consistent-field method. I. Equal configuration weights},

author = {Shepard, Ron and Brozell, Scott R.},

abstractNote = {The All Configuration Mean Energy (ACME) conditions are a special case of state averaging for Multiconfigurational Self-Consistent-Field (MCSCF) orbital optimisation. The method is formulated using the Graphical Unitary Group Approach (GUGA) in which the Configuration State Function (CSF) basis is represented as walks within a Shavitt graph. This graphical formulation leads to efficient recursive algorithms for the energy and reduced density matrices (RDM) that are independent of the CSF dimension and that scale only as O(n2) where n is the number of occupied orbitals. The Hamiltonian matrix diagonalization step is obviated and the CSF expansion coefficients are neither referenced nor required. This allows MCSCF orbital optimisation to be performed for essentially unlimited numbers of active orbitals and arbitrarily large CSF expansions. The discussion includes various types of CSF expansion spaces, the partitioning of the essential and redundant orbital optimisation parameters, the computation of the spin-density, and the formulation of state-specific analytic gradients and nonadiabatic coupling for high-level electronic structure methods that use the ACME MCSCF orbitals.},

doi = {10.1080/00268976.2019.1635275},

journal = {Molecular Physics},

number = 17,

volume = 117,

place = {United States},

year = {2019},

month = {6}

}

*Citation information provided by*

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Web of Science

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