# Sum-rule corrections: A route to error cancellations in correlation matrix renormalisation theory

## Abstract

Here, we recently proposed the correlation matrix renormalisation (CMR) theory to efficiently and accurately calculate ground state total energy of molecular systems, based on the Gutzwiller variational wavefunction (GWF) to treat the electronic correlation effects. To help reduce numerical complications and better adapt the CMR to infinite lattice systems, we need to further refine the way to minimise the error originated from the approximations in the theory. This conference proceeding reports our recent progress on this key issue, namely, we obtained a simple analytical functional form for the one-electron renormalisation factors, and introduced a novel sum-rule correction for a more accurate description of the intersite electron correlations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method.

- Authors:

- Ames Lab. and Iowa State Univ., Ames, IA (United States)

- Publication Date:

- Research Org.:
- Ames Laboratory (AMES), Ames, IA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1357795

- Report Number(s):
- IS-J-9317

Journal ID: ISSN 0026-8976; TRN: US1702447

- Grant/Contract Number:
- AC02-07CH11358

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Molecular Physics

- Additional Journal Information:
- Journal Volume: 115; Journal Issue: 5; Journal ID: ISSN 0026-8976

- Publisher:
- Taylor & Francis

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 74 ATOMIC AND MOLECULAR PHYSICS; correlation matrix renormalisation; sum rule; Gutzwiller approximation

### Citation Formats

```
Liu, C., Liu, J., Yao, Y. X., Wang, C. Z., and Ho, K. M..
```*Sum-rule corrections: A route to error cancellations in correlation matrix renormalisation theory*. United States: N. p., 2017.
Web. doi:10.1080/00268976.2017.1278800.

```
Liu, C., Liu, J., Yao, Y. X., Wang, C. Z., & Ho, K. M..
```*Sum-rule corrections: A route to error cancellations in correlation matrix renormalisation theory*. United States. doi:10.1080/00268976.2017.1278800.

```
Liu, C., Liu, J., Yao, Y. X., Wang, C. Z., and Ho, K. M.. Mon .
"Sum-rule corrections: A route to error cancellations in correlation matrix renormalisation theory". United States.
doi:10.1080/00268976.2017.1278800. https://www.osti.gov/servlets/purl/1357795.
```

```
@article{osti_1357795,
```

title = {Sum-rule corrections: A route to error cancellations in correlation matrix renormalisation theory},

author = {Liu, C. and Liu, J. and Yao, Y. X. and Wang, C. Z. and Ho, K. M.},

abstractNote = {Here, we recently proposed the correlation matrix renormalisation (CMR) theory to efficiently and accurately calculate ground state total energy of molecular systems, based on the Gutzwiller variational wavefunction (GWF) to treat the electronic correlation effects. To help reduce numerical complications and better adapt the CMR to infinite lattice systems, we need to further refine the way to minimise the error originated from the approximations in the theory. This conference proceeding reports our recent progress on this key issue, namely, we obtained a simple analytical functional form for the one-electron renormalisation factors, and introduced a novel sum-rule correction for a more accurate description of the intersite electron correlations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method.},

doi = {10.1080/00268976.2017.1278800},

journal = {Molecular Physics},

number = 5,

volume = 115,

place = {United States},

year = {Mon Jan 16 00:00:00 EST 2017},

month = {Mon Jan 16 00:00:00 EST 2017}

}

Works referenced in this record:

##
Self-Consistent Equations Including Exchange and Correlation Effects

journal, November 1965

- Kohn, W.; Sham, L. J.
- Physical Review, Vol. 140, Issue 4A, p. A1133-A1138