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 partitionedrational function optimization (PRFO) 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 PRFO for TS optimization. This approach is shown to achieve significantmore »
 Authors:
 Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720 (United States)
 Department of Chemistry, University of California, Berkeley, California 94720 (United States)
 Publication Date:
 OSTI Identifier:
 22252982
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 140; Journal Issue: 16; Other Information: (c) 2014 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; CHEMICAL ANALYSIS; EIGENVALUES; EIGENVECTORS; FINITE DIFFERENCE METHOD; OPTIMIZATION; POTENTIAL ENERGY
Citation Formats
Sharada, Shaama Mallikarjun, Bell, Alexis T., Email: mhg@bastille.cchem.berkeley.edu, Email: bell@cchem.berkeley.edu, and HeadGordon, Martin, Email: mhg@bastille.cchem.berkeley.edu, Email: bell@cchem.berkeley.edu. A finite difference Davidson procedure to sidestep full ab initio hessian calculation: Application to characterization of stationary points and transition state searches. United States: N. p., 2014.
Web. doi:10.1063/1.4871660.
Sharada, Shaama Mallikarjun, Bell, Alexis T., Email: mhg@bastille.cchem.berkeley.edu, Email: bell@cchem.berkeley.edu, & HeadGordon, Martin, Email: mhg@bastille.cchem.berkeley.edu, Email: bell@cchem.berkeley.edu. A finite difference Davidson procedure to sidestep full ab initio hessian calculation: Application to characterization of stationary points and transition state searches. United States. doi:10.1063/1.4871660.
Sharada, Shaama Mallikarjun, Bell, Alexis T., Email: mhg@bastille.cchem.berkeley.edu, Email: bell@cchem.berkeley.edu, and HeadGordon, Martin, Email: mhg@bastille.cchem.berkeley.edu, Email: bell@cchem.berkeley.edu. Mon .
"A finite difference Davidson procedure to sidestep full ab initio hessian calculation: Application to characterization of stationary points and transition state searches". United States.
doi:10.1063/1.4871660.
@article{osti_22252982,
title = {A finite difference Davidson procedure to sidestep full ab initio hessian calculation: Application to characterization of stationary points and transition state searches},
author = {Sharada, Shaama Mallikarjun and Bell, Alexis T., Email: mhg@bastille.cchem.berkeley.edu, Email: bell@cchem.berkeley.edu and HeadGordon, Martin, Email: mhg@bastille.cchem.berkeley.edu, Email: bell@cchem.berkeley.edu},
abstractNote = {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 partitionedrational function optimization (PRFO) 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 PRFO for TS optimization. This approach is shown to achieve significant 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 finitedifference 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.},
doi = {10.1063/1.4871660},
journal = {Journal of Chemical Physics},
number = 16,
volume = 140,
place = {United States},
year = {Mon Apr 28 00:00:00 EDT 2014},
month = {Mon Apr 28 00:00:00 EDT 2014}
}

SCF and singlereference ACPF calculations were performed in order to determine the structure, stability, and harmonic vibrational frequencies of stationary points for the HCO radical in the ground ({sup 2}A{prime}) and first excited ({sup 2}A{double_prime}) states. Very large and flexible basis sets including two f functions on the heavy atoms and two d functions on hydrogen were used. The calculated geometries and vibrational frequencies are in good agreement with available experimental data. The relative stabilities are now also much better balanced compared to previous theoretical results. 41 refs., 2 figs., 8 tabs.

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