Subject: True Parameter of VWN Functional of Gaussian98W

From: "Van Dam, HJJ (Huub)" <[email-masked]>
Date: Thu, 16 Aug 2001 09:10:39 +0100

The problem discussed here is typical for some issues related to DFT
calculations: How do you know what a program actually calculates when
you ask for a certain functional (e.g. B3LYP). This problem can be
tackled by collecting highly accurate reference data, complete
mathematical definitions of the functionals, and finally actual
implementations of functionals. We have now a collection of  functionals
and associated data available online at

    http://www.dl.ac.uk/DFTlib

With respect to the B3LYP question we agree with Christoph van Wuellen
that the Gaussian implementation is the right one because they
'invented' it. An implementation and associated reference data of the
functional equivalent to the one in Gaussian is given on our website.
The reference to Stephens et al. (1994) is the original reference to
B3LYP, the confusion around the VWN part was later clearified by Hertwig
and Koch (1997). The findings of Hertwig and Koch are reflected in the
Gaussian online technical documentation (Frisch et al., 1998).

Huub van Dam.

> 1.) Gaussian VWN functional uses the parameters given in *table* 3 of
> the VWN paper. These parameters approximate the RPA results, not the
> Monte-Carlo results! These parameters are used for the closed-shell
and
> completely spin-polarized (only alpha spin electrons) cases.
>
> 2.) Gaussian VWN does not use the RPA spin stiffness parameters to
inter-
> polate between these two cases, but uses the interpolation valid for
the
> exchange energy of a uniform electron gas. (I do not know what
happened that
> they chose this option).
>
> With the TZ basis sets of Ahlrichs and Schafer you should get the
following
> energies
>
> Atom:   He(ground state)   He(1s2s Triplet)      N Atom(Quartet)
>
> HF       -2.85989543        -1.79100228           -54.40232895
> LDA3     -2.86994363        -1.77391426           -54.26495985
> LDA5     -2.83256107        -1.73613023           -54.13356852
> BLYP     -2.90460692        -1.79477978           -54.58993091
> B3LYP    -2.91302754        -1.80220154           -54.60420134
>
> Things to note:
> (1) open shell calculations done spin-unrestricted. Hartree-Fock
results
>      given for comparison (if they do not agree, something is wrong
with
>      the basis set).
> (2) The three examples cover the three cases (spin-unpolarized,
completely
>      spin-polarized, partially spin-polarized) mentioned above (the
inter-
>      polation problem only shows up for the N atom).
> (3) LDA3 = the LDA functional implemented in Gaussian
>      LDA5 = the LDA functional used by the rest of us (i.e. SVWN5 in
G98)
> (4) B3LYP contains LDA3 (I guess this is the right choice, since B3LYP
was
>      'invented' by the Gaussian developers).
> (5) I implemented these functionals in my own program and got the same

>      results, the only way to *really* know what is implemented in
G98.
> (6) I suggest that my numbers are checked by others, so that our
community
>      knowns which functional is which. Please use highly accurate
numerical
>      grids. If the reference numbers should be obtained with another
basis
>      set, please make a suggestion.

--

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Huub van Dam                               E-mail: [email-masked]
CCLRC Daresbury Laboratory                  phone: +44-1925-603362
Daresbury, Warrington                         fax: +44-1925-603634
Cheshire, UK
WA4 4AD

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