# Parallel scalability of Hartree–Fock calculations

## Abstract

Quantum chemistry is increasingly performed using large cluster computers consisting of multiple interconnected nodes. For a fixed molecular problem, the efficiency of a calculation usually decreases as more nodes are used, due to the cost of communication between the nodes. This paper empirically investigates the parallel scalability of Hartree–Fock calculations. The construction of the Fock matrix and the density matrix calculation are analyzed separately. For the former, we use a parallelization of Fock matrix construction based on a static partitioning of work followed by a work stealing phase. For the latter, we use density matrix purification from the linear scaling methods literature, but without using sparsity. When using large numbers of nodes for moderately sized problems, density matrix computations are network-bandwidth bound, making purification methods potentially faster than eigendecomposition methods.

- Authors:

- School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0765 (United States)
- Parallel Computing Lab, Intel Corporation, Santa Clara, California 95054-1549 (United States)

- Publication Date:

- OSTI Identifier:
- 22415491

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 10; 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; CALCULATION METHODS; CHEMISTRY; DENSITY MATRIX; EFFICIENCY; HARTREE-FOCK METHOD; PARTITION; POTENTIALS; PURIFICATION

### Citation Formats

```
Chow, Edmond, E-mail: echow@cc.gatech.edu, Liu, Xing, Smelyanskiy, Mikhail, and Hammond, Jeff R.
```*Parallel scalability of Hartree–Fock calculations*. United States: N. p., 2015.
Web. doi:10.1063/1.4913961.

```
Chow, Edmond, E-mail: echow@cc.gatech.edu, Liu, Xing, Smelyanskiy, Mikhail, & Hammond, Jeff R.
```*Parallel scalability of Hartree–Fock calculations*. United States. doi:10.1063/1.4913961.

```
Chow, Edmond, E-mail: echow@cc.gatech.edu, Liu, Xing, Smelyanskiy, Mikhail, and Hammond, Jeff R. Sat .
"Parallel scalability of Hartree–Fock calculations". United States.
doi:10.1063/1.4913961.
```

```
@article{osti_22415491,
```

title = {Parallel scalability of Hartree–Fock calculations},

author = {Chow, Edmond, E-mail: echow@cc.gatech.edu and Liu, Xing and Smelyanskiy, Mikhail and Hammond, Jeff R.},

abstractNote = {Quantum chemistry is increasingly performed using large cluster computers consisting of multiple interconnected nodes. For a fixed molecular problem, the efficiency of a calculation usually decreases as more nodes are used, due to the cost of communication between the nodes. This paper empirically investigates the parallel scalability of Hartree–Fock calculations. The construction of the Fock matrix and the density matrix calculation are analyzed separately. For the former, we use a parallelization of Fock matrix construction based on a static partitioning of work followed by a work stealing phase. For the latter, we use density matrix purification from the linear scaling methods literature, but without using sparsity. When using large numbers of nodes for moderately sized problems, density matrix computations are network-bandwidth bound, making purification methods potentially faster than eigendecomposition methods.},

doi = {10.1063/1.4913961},

journal = {Journal of Chemical Physics},

number = 10,

volume = 142,

place = {United States},

year = {Sat Mar 14 00:00:00 EDT 2015},

month = {Sat Mar 14 00:00:00 EDT 2015}

}