True Parameter of VWN Functional of Gaussian98W

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.
 --
 ========================================================================
 Huub van Dam                               E-mail: h.j.j.vandam #*at*# dl.ac.uk
 CCLRC Daresbury Laboratory                  phone: +44-1925-603362
 Daresbury, Warrington                         fax: +44-1925-603634
 Cheshire, UK
 WA4 4AD
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