CCL:G: Gaussian03 reproduces published O3LYP results.
- From: Giovanni Scalmani <giovanni---gaussian.com>
- Subject: CCL:G: Gaussian03 reproduces published O3LYP results.
- Date: Thu, 09 Oct 2008 16:08:14 -0400
Sent to CCL by: Giovanni Scalmani [giovanni%gaussian.com]
Our reference to reproduce OLYP and O3LYP results has been the following
paper: W.-M. Hoe, A.J. Cohen, N.H. Handy, Chem. Phys. Letters 341 (2001) 319-328
("O3LYP paper").
There are some ambiguities in the description of O3LYP in this paper. If we
interpret these ambiguities one way, we get the same results as other programs
but cannot reproduce the results in the paper. If we interpret them the other
way,
we can reproduce the results in the paper. Gaussian 03 revision D and later
have been fixed to agree with the paper. The full details are given below.
According to the paper, the OPTX exchange functional is defined as
Rho^(4/3)*(A1*Cx + A2*Y^2) where Y = (g*x^2)/(1+g*x^2)
and Rho is the density (alpha or beta), Cx is (3/4)*(6/PI)^(1/3), g=0.006 and
x is the reduced density gradient x = |Grad_Rho|/(Rho^(4/3)). The two
parameters
are defined as follows A1=1.05151 and A2=1.43169. These values of the
parameters
allowed us to reproduce the OLYP results.
Later in the paper, the authors give the values of the parameters for the
O3LYP functional: A=0.1161 (% of exact exchange), B=0.9262 and C=0.8133.
However,
assuming that B is A1 and C is A2, produces results different from those in the
paper. Using the values A1=0.9262 and A2=0.8133*1.43169 produces results in
agreement with the paper.
In Gaussian03 Rev. C.01 both the keywords OLYP and O3LYP were made available,
but only OLYP gave results in agreement with the O3LYP paper, while O3LYP
give wrong results. Setting IOp(3/77=0813309262) did not fixed the problem,
but rather led to A1=0.9262 and A2=0.8133. Starting from Rev. D.01 the value of
A2=0.8133*1.43169 was used by default and we were finally able to reproduce the
published O3LYP results.
Following are the details of some calculations that can be easily carried out
with Gaussian03 to reproduce the results from Table 2 of the O3LYP paper. The
agreement is very good for the H and He atoms, while is less than perfect for
heavier atoms. However, given the larger absolute values of the energy and the
uncertainty in the details of the calculations that were carried out to produce
the published results (basis set, integration grid, SCF convergence, etc.), we
are still confident that our implementation is correct.
Nota that, G03 Rev. C.01 using IOp(3/77=0813309262) - which apparently agrees
with other implementations of O3LYP - is clearly not able to reproduce the
published data with the same accuracy.
Basis set:
- O3LYP paper : "PVQZ" (possibly from the CADPAC library,
no literature
reference is given)
- following calculations: cc-pVQZ (5d,7f)
Integration grid:
- O3LYP paper : "high accuracy grid"
- following calculations: int(grid=499974) (499 radial and 974 angular points)
SCF convergence:
- O3LYP paper : unspecified
- following calculations: scf(tight) (RMS DP<1.0d-08, Max DP< 1.0d-06,
DE<1.0d-6)
Table 2: "Errors is total atomic energies (in hartrees)
(theory-experiment)"
Exact energies: H = -0.5000, He = -2.9037, Li = -7.4781, Be = -14.6674,
F = -99.7339, Ne = -128.9376.
H atom
======
G03 Rev. G03 Table 2
E.01 BLYP +0.0022 +0.0022
E.01 OLYP +0.0016 +0.0015
E.01 B3LYP (with VWN5) +0.0010 +0.0010
E.01 O3LYP +0.0002 +0.0001
C.01 O3LYP+IOp(3/77=0813309262) +0.0072
E.01 B97-1 -0.0028 -0.0028
He atom
=======
G03 Rev. G03 Table 2
E.01 BLYP -0.0031 -0.0031
E.01 OLYP -0.0035 -0.0036
E.01 B3LYP (with VWN5) -0.0042 -0.0042
E.01 O3LYP -0.0064 -0.0065
C.01 O3LYP+IOp(3/77=0813309262) +0.0173
E.01 B97-1 -0.0031 -0.0031
Li atom
=======
G03 Rev. G03 Table 2
E.01 BLYP -0.0033 -0.0045
E.01 OLYP -0.0073 -0.0083
E.01 B3LYP (with VWN5) -0.0038 -0.0045
E.01 O3LYP -0.0095 -0.0102
C.01 O3LYP+IOp(3/77=0813309262) +0.0302
E.01 B97-1 -0.0070 -0.0078
Be atom
=======
G03 Rev. G03 Table 2
E.01 BLYP +0.0070 +0.0059
E.01 OLYP +0.0008 -0.0004
E.01 B3LYP (with VWN5) +0.0087 +0.0080
E.01 O3LYP -0.0001 -0.0010
C.01 O3LYP+IOp(3/77=0813309262) +0.0569
E.01 B97-1 +0.0027 +0.0021
F atom
=======
G03 Rev. G03 Table 2
E.01 BLYP -0.0296 -0.0307
E.01 OLYP -0.0108 -0.0123
E.01 B3LYP (with VWN5) -0.0048 -0.0055
E.01 O3LYP -0.0058 -0.0070
C.01 O3LYP+IOp(3/77=0813309262) +0.1138
E.01 B97-1 -0.0091 -0.0097
Ne atom
=======
G03 Rev. G03 Table 2
E.01 BLYP -0.0290 -0.0303
E.01 OLYP -0.0120 -0.0138
E.01 B3LYP (with VWN5) +0.0002 -0.0006
E.01 O3LYP -0.0053 -0.0068
C.01 O3LYP+IOp(3/77=0813309262) +0.1221
E.01 B97-1 -0.0050 -0.0057