Part of LOM

This blog is part of web activities of the Laboratory of Organic Materials (LOM) of the Institute of Solid State Physics of the University of Latvia.

Thursday, November 10, 2016

Differentiation step in Polar=Gamma

This is quite important note for those who wish to alter the defaults. 

Gaussian 09 Reference explains that the electric field step size is set by the option Step=N, by which the actual step size is set to 0.0001N atomic units (a. u.). This is, however, true only if you use double-numerical differentiation (done by Link 111). If You use numerical differentiation only once (like You do in Polar=Gamma calculations to obtain second hyperpolarizability γ), Link 106 is invoked instead, and it has different defaults. Namely, electric step field size is then 3 times smaller than it would be for Link 111, either by using the defaults or by reading user-specified values. So, when I had in the Route section
which, I thought, would do the calculation with the default field strengths of ±0.0003 a. u., I got instead
The following finite field(s) will be applied:  
An electric field of             -1.0000D-04  0.0000D+00  0.0000D+00
so -0.0001 a. u. Because Link 106 is invoked in Gamma calculations, and not the Link 111, for which finite-field parameters are specified by default!
In fact, this seems to me quite logical. In the "old times", finite-field (FF) and coupled-perturbed HF/KS (CPHF/CPKS) were used in standalone fashion as alternative methods for computing the hyperpolarizability β; then, of course, double-numerical differentiation was used, and maybe that is why the default "language" of parameter input is for the corresponding Link 111. Now, however, the second hyperpolarizability calculations are introduced into Gaussian, but only in a "hybrid" fashion of numerically differentiating β tensor. So, the Link 106 is now in use, but with different optimal parameters.

Sadly, these differences are listed only in the Gaussian IOp Reference. So, be aware of it and carry on Your research.

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