Finding optimal finite field strengths allowing for a maximum of precision in the calculation of polarizabilities and hyperpolarizabilities

The finite field method, widely used for the calculation of static dipole polarizabilities or the first and second hyperpolarizabilities of molecules and polymers, is thoroughly explored. The application of different field strengths and the impact on the precision of the calculations were investigat...

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Bibliographic Details
Published in:Journal of computational chemistry 2013-06, Vol.34 (17), p.1497-1507
Main Authors: Mohammed, Ahmed A. K., Limacher, Peter A., Champagne, Benoît
Format: Article
Language:English
Subjects:
error reduction
Finite element analysis
finite field method
hyperpolarizability
Molecules
Numerical analysis
Polymers
polynomial fitting
Richardson extrapolation
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Summary:The finite field method, widely used for the calculation of static dipole polarizabilities or the first and second hyperpolarizabilities of molecules and polymers, is thoroughly explored. The application of different field strengths and the impact on the precision of the calculations were investigated. Borders could be defined and characterized, establishing a range of feasible field strengths that guarantee reliable numerical results. The quality of different types of meshes to screen the feasible region is assessed. Extrapolation schemes are presented that reduce the truncation error and allow to increase the precision of finite field calculations by one to three orders of magnitude. © 2013 Wiley Periodicals, Inc. The precision of second hyperpolarizability calculations using the finite field approach can be refined combining the results of several different field strengths. Each entry of a column m is a linear combination of the two adjacent values from the m−1 column. Colored values indicate good precision. The reference value in atomic units is the second hyperpolarizability of neon at the HF/t‐aug‐cc‐pVQZ level of theory.
ISSN:0192-8651
1096-987X
DOI:10.1002/jcc.23285