Calculation of quantum mechanical rate constants directly from ab initio atomic forces

139 Pages·2010·1.9 MB·English

Calculation of quantum mechanical rate constants directly from ab
initio atomic forces
Andri Arnaldsson
A dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
University of Washington
2007
Program Authorized to Offer Degree: Chemistry

University of Washington
Graduate School
This is to certify that I have examined this copy of a doctoral dissertation by
Andri Arnaldsson
and have found that it is complete and satisfactory in all respects,
and that any and all revisions required by the final
examining committee have been made.
Chair of the Supervisory Committee:
Hannes J´onsson
Reading Committee:
Hannes J´onsson
William P. Reinhardt
Oleg V. Prezhdo
Date:

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University of Washington
Abstract
Calculation of quantum mechanical rate constants directly from ab initio atomic
forces
Andri Arnaldsson
Chair of the Supervisory Committee:
Professor Hannes J´onsson
Chemistry
Harmonic quantum transition state theory (HQTST), sometimes referred to as ’instanton
theory’ or ’ImF theory’, has been implemented in an efficient way and tested. HQTST is
analogous to the more familiar classical harmonic transition state theory (HTST), where
the rate is estimated from the energy difference between a reactant state minimum and
a first order saddle point on the potential energy surface ridge that separates reactants
and the products, along with a prefactor derived from harmonic expansion of the potential
around both the minimum and the saddle point. The method described here makes use of a
generalized minimum mode following method to locate saddle points on the effective quan-
tum mechanical energy surface for discretized Feynman path integrals (FPI). The overall
computational cost of estimating rate constants with this method is relatively low and it is
possible to use directly atomic forces obtained from first principle calculations. The method
is also well suited for systems containing many degrees of freedom, on the order of a few
hundred. Usually, a well converged results is achieved with 500 - 700 force calls per system
replica used to represent the FPI.
The method has been tested on several one- and two-dimensional systems where more
accurate (or even analytical) solutions for the rate constant can be obtained. Not only is
it found to robust and fast, but accurate as well, yielding results within a factor of 2-3
from the exact values, indicating that the approximations inherent in the procedure are

well justified for chemically relevant systems. In addition, the method has been used for
calculating the rate of various transitions involving hydrogen atoms or molecules where
the atomic forces are derived from empirical, semi-empirical or first principle calculations.
CalculationspresentedhereincludetherateofhydrogenabstractionfromgasphaseH BN ,
3 3
hydrogen atom diffusion in Ta and Pd, adsorption/desorption of H onto/from Cu(100) and
2
Cu(110) surfaces and hydrogenation of N on Ru(0001) surface. Comparison is made with
either higher level theoretical calculations or experimental results when available, and the
agreement is found to be good in all instances.