Subject: True Parameter of VWN Functional of Gaussian98W

From: "TELKUNI" <[email-masked]>
Date: Wed, 15 Aug 2001 17:08:35 +0900

Hello! CCLers

  I'm leaning the correlation functional "VWN " and try to use it on Gaussian98W.
I would like to know true G98W's VWN parameter.

  According to the original paper of VWN (S. H. Vosko, L. Wilk, and M. Nusair: Can. J. 
Phys. vol.58, 1200 (1980)), the functional employs the parameters as follows:
x0(x-zero) = -0.409286, b = 13.0720, c = 42.7298 (in Section4).

 But the other books and articles, there are different combination of parameters, 
for example(paramagnetic state): x0 = -0.10498, b = 3.72744, c = 12.9352 (by Density
Functional Theory And Its Application - Japanese).

  I think G98W might employ the original paper's parameters, but I don't know the 
articles nor method to check it. If you know the method(for example: using IOp option) 
or articles, please teach me.

  All responses, I will appreciate. 
  I will summarize them and send to CCL.

  Best regards,
  Telkuni

----------------------------------------------
               Telkuni Tsuru     

  Kyushyu Electronic Technology and Research

          [email-masked]
----------------------------------------------

---

From: Christoph van Wüllen <[email-masked]>
Date: Wed, 15 Aug 2001 14:32:37 +0200

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.

---

From: Matt Challacombe <[email-masked]>
Date: Wed, 15 Aug 2001 05:52:01 -0600

Right, you will want to have a look at the very helpfull paper:

@article{Hertwig97,
        author = {R. H. Hertwig  and W. Koch},
        title = {On the parameterization of the local correlation functional.
                 What is Becke-3-LYP?},
        journal = {Chem. Phys. Lett.},
        year = {1997 },
        volume = 268,
        number = {5-6},
        pages = {345-351},
        month = {APR 18}
}

Good luck!  

-Matt

PS. This is your brain.  This is your brain on VWN, any questions?
-- a quote from the MESA dft module

On Wednesday 15 August 2001 02:08 am, TELKUNI wrote:
> Hello! CCLers
>
>   I'm leaning the correlation functional "VWN " and try to use it on
> Gaussian98W. I would like to know true G98W's VWN parameter.
>
>   According to the original paper of VWN (S. H. Vosko, L. Wilk, and M.
> Nusair: Can. J. Phys. vol.58, 1200 (1980)), the functional employs the
> parameters as follows: x0(x-zero) = -0.409286, b = 13.0720, c = 42.7298 (in
> Section4).
>
>  But the other books and articles, there are different combination of
> parameters, for example(paramagnetic state): x0 = -0.10498, b = 3.72744, c
> = 12.9352 (by Density Functional Theory And Its Application - Japanese).
>
>   I think G98W might employ the original paper's parameters, but I don't
> know the articles nor method to check it. If you know the method(for
> example: using IOp option) or articles, please teach me.
>
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-- 
Matt Challacombe, Ph.D.           http://www.t12.lanl.gov/~mchalla/ 
Los Alamos National Laboratory    email: [email-masked]           
Group T-12, Mail Stop B268        phone: (505) 665-5905           
Los Alamos, New Mexico  87545     fax:   (505) 665-3909