Title: A finite difference Davidson procedure to sidestep full ab initio hessian calculation: Application to characterization of stationary points and transition state searches

Abstract

The cost of calculating nuclear hessians, either analytically or by finite difference methods, during the course of quantum chemical analyses can be prohibitive for systems containing hundreds of atoms. In many applications, though, only a few eigenvalues and eigenvectors, and not the full hessian, are required. For instance, the lowest one or two eigenvalues of the full hessian are sufficient to characterize a stationary point as a minimum or a transition state (TS), respectively. We describe here a method that can eliminate the need for hessian calculations for both the characterization of stationary points as well as searches for saddle points. A finite differences implementation of the Davidson method that uses only first derivatives of the energy to calculate the lowest eigenvalues and eigenvectors of the hessian is discussed. This method can be implemented in conjunction with geometry optimization methods such as partitioned-rational function optimization (P-RFO) to characterize stationary points on the potential energy surface. With equal ease, it can be combined with interpolation methods that determine TS guess structures, such as the freezing string method, to generate approximate hessian matrices in lieu of full hessians as input to P-RFO for TS optimization. This approach is shown to achieve significantmore » cost savings relative to exact hessian calculation when applied to both stationary point characterization as well as TS optimization. The basic reason is that the present approach scales one power of system size lower since the rate of convergence is approximately independent of the size of the system. Therefore, the finite-difference Davidson method is a viable alternative to full hessian calculation for stationary point characterization and TS search particularly when analytical hessians are not available or require substantial computational effort.« less

Authors:

Sharada, Shaama Mallikarjun ^[1]; Bell, Alexis T. ^[1]; Head-Gordon, Martin ^[2]

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+ Show Author Affiliations

1. Univ. of California, Berkeley, CA (United States). Dept. of Chemical and Biomolecular Engineering
2. Univ. of California, Berkeley, CA (United States). Dept. of Chemistry

Publication Date:

Mon Apr 28 00:00:00 EDT 2014

Research Org.:

Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Org.:

USDOE Office of Science (SC)

OSTI Identifier:

1571013

Grant/Contract Number:  

AC02-05CH11231

Resource Type:

Accepted Manuscript

Journal Name:

Journal of Chemical Physics

Additional Journal Information:

Journal Volume: 140; Journal Issue: 16; Journal ID: ISSN 0021-9606

Publisher:

American Institute of Physics (AIP)

Country of Publication:

United States

Language:

English

Subject:

74 ATOMIC AND MOLECULAR PHYSICS