# Workshop report on large-scale matrix diagonalization methods in chemistry theory institute

## Abstract

The Large-Scale Matrix Diagonalization Methods in Chemistry theory institute brought together 41 computational chemists and numerical analysts. The goal was to understand the needs of the computational chemistry community in problems that utilize matrix diagonalization techniques. This was accomplished by reviewing the current state of the art and looking toward future directions in matrix diagonalization techniques. This institute occurred about 20 years after a related meeting of similar size. During those 20 years the Davidson method continued to dominate the problem of finding a few extremal eigenvalues for many computational chemistry problems. Work on non-diagonally dominant and non-Hermitian problems as well as parallel computing has also brought new methods to bear. The changes and similarities in problems and methods over the past two decades offered an interesting viewpoint for the success in this area. One important area covered by the talks was overviews of the source and nature of the chemistry problems. The numerical analysts were uniformly grateful for the efforts to convey a better understanding of the problems and issues faced in computational chemistry. An important outcome was an understanding of the wide range of eigenproblems encountered in computational chemistry. The workshop covered problems involving self- consistent-field (SCF), configurationmore »

- Authors:

- eds.

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Energy Research, Washington, DC (United States)

- OSTI Identifier:
- 465681

- Report Number(s):
- ANL/MCS-TM-219; CONF-9605268-Absts.

ON: DE97004423

- DOE Contract Number:
- W-31109-ENG-38

- Resource Type:
- Conference

- Resource Relation:
- Conference: Large-scale matrix diagonalization methods in chemistry theory institute, Argonne, IL (United States), 20-22 May 1996; Other Information: PBD: Oct 1996

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 40 CHEMISTRY; 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; 66 PHYSICS; CHEMISTRY; NUMERICAL SOLUTION; MATRIX ELEMENTS; MATRICES; MEETINGS; ITERATIVE METHODS; EIGENVALUES; MOLECULES; EIGENSTATES; PARALLEL PROCESSING; QUANTUM MECHANICS; VIBRATIONAL STATES

### Citation Formats

```
Bischof, C.H., Shepard, R.L., and Huss-Lederman, S.
```*Workshop report on large-scale matrix diagonalization methods in chemistry theory institute*. United States: N. p., 1996.
Web.

```
Bischof, C.H., Shepard, R.L., & Huss-Lederman, S.
```*Workshop report on large-scale matrix diagonalization methods in chemistry theory institute*. United States.

```
Bischof, C.H., Shepard, R.L., and Huss-Lederman, S. Tue .
"Workshop report on large-scale matrix diagonalization methods in chemistry theory institute". United States.
doi:. https://www.osti.gov/servlets/purl/465681.
```

```
@article{osti_465681,
```

title = {Workshop report on large-scale matrix diagonalization methods in chemistry theory institute},

author = {Bischof, C.H. and Shepard, R.L. and Huss-Lederman, S.},

abstractNote = {The Large-Scale Matrix Diagonalization Methods in Chemistry theory institute brought together 41 computational chemists and numerical analysts. The goal was to understand the needs of the computational chemistry community in problems that utilize matrix diagonalization techniques. This was accomplished by reviewing the current state of the art and looking toward future directions in matrix diagonalization techniques. This institute occurred about 20 years after a related meeting of similar size. During those 20 years the Davidson method continued to dominate the problem of finding a few extremal eigenvalues for many computational chemistry problems. Work on non-diagonally dominant and non-Hermitian problems as well as parallel computing has also brought new methods to bear. The changes and similarities in problems and methods over the past two decades offered an interesting viewpoint for the success in this area. One important area covered by the talks was overviews of the source and nature of the chemistry problems. The numerical analysts were uniformly grateful for the efforts to convey a better understanding of the problems and issues faced in computational chemistry. An important outcome was an understanding of the wide range of eigenproblems encountered in computational chemistry. The workshop covered problems involving self- consistent-field (SCF), configuration interaction (CI), intramolecular vibrational relaxation (IVR), and scattering problems. In atomic structure calculations using the Hartree-Fock method (SCF), the symmetric matrices can range from order hundreds to thousands. These matrices often include large clusters of eigenvalues which can be as much as 25% of the spectrum. However, if Cl methods are also used, the matrix size can be between 10{sup 4} and 10{sup 9} where only one or a few extremal eigenvalues and eigenvectors are needed. Working with very large matrices has lead to the development of},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Tue Oct 01 00:00:00 EDT 1996},

month = {Tue Oct 01 00:00:00 EDT 1996}

}