# A geometric initial guess for localized electronic orbitals in modular biological systems

## Abstract

Recent first-principles molecular dynamics algorithms using localized electronic orbitals have achieved O(N) complexity and controlled accuracy in simulating systems with finite band gaps. However, accurately deter- mining the centers of these localized orbitals during simulation setup may require O(N ^{3}) operations, which is computationally infeasible for many biological systems. We present an O(N) approach for approximating orbital centers in proteins, DNA, and RNA which uses non-localized solutions for a set of fixed-size subproblems to create a set of geometric maps applicable to larger systems. This scalable approach, used as an initial guess in the O(N) first-principles molecular dynamics code MGmol, facilitates first-principles simulations in biological systems of sizes which were previously impossible.

- Authors:

- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Univ. of Chicago, IL (United States)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1393357

- Report Number(s):
- LLNL-TR-738503

- DOE Contract Number:
- AC52-07NA27344

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 59 BASIC BIOLOGICAL SCIENCES; 74 ATOMIC AND MOLECULAR PHYSICS; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE

### Citation Formats

```
Beckman, P. G., Fattebert, J. L., Lau, E. Y., and Osei-Kuffuor, D..
```*A geometric initial guess for localized electronic orbitals in modular biological systems*. United States: N. p., 2017.
Web. doi:10.2172/1393357.

```
Beckman, P. G., Fattebert, J. L., Lau, E. Y., & Osei-Kuffuor, D..
```*A geometric initial guess for localized electronic orbitals in modular biological systems*. United States. doi:10.2172/1393357.

```
Beckman, P. G., Fattebert, J. L., Lau, E. Y., and Osei-Kuffuor, D.. Mon .
"A geometric initial guess for localized electronic orbitals in modular biological systems". United States.
doi:10.2172/1393357. https://www.osti.gov/servlets/purl/1393357.
```

```
@article{osti_1393357,
```

title = {A geometric initial guess for localized electronic orbitals in modular biological systems},

author = {Beckman, P. G. and Fattebert, J. L. and Lau, E. Y. and Osei-Kuffuor, D.},

abstractNote = {Recent first-principles molecular dynamics algorithms using localized electronic orbitals have achieved O(N) complexity and controlled accuracy in simulating systems with finite band gaps. However, accurately deter- mining the centers of these localized orbitals during simulation setup may require O(N3) operations, which is computationally infeasible for many biological systems. We present an O(N) approach for approximating orbital centers in proteins, DNA, and RNA which uses non-localized solutions for a set of fixed-size subproblems to create a set of geometric maps applicable to larger systems. This scalable approach, used as an initial guess in the O(N) first-principles molecular dynamics code MGmol, facilitates first-principles simulations in biological systems of sizes which were previously impossible.},

doi = {10.2172/1393357},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Mon Sep 11 00:00:00 EDT 2017},

month = {Mon Sep 11 00:00:00 EDT 2017}

}