THE GMFCI METHOD IN THE CONVIV CODE: GETTING
THE BEST OF TWO WORLDS
Patrick Cassam-Chenaı̈,a
a
Laboratoire J. A. Dieudonné, UMR 7351 du CNRS, Faculté des Sciences,Univ. Nice Sophia Antipolis, Nice, France.
[email protected]
The generalized mean field configuration interaction (GMFCI) method is a very general
method to solve a molecular Schrödinger equation [1]. It encompasses in a unified formalism both variational and perturbative techniques, and, more importantly, empowers the
users to optimally combine them in order to reduce the computational effort for a given
accuracy goal [2]. It has been applied successfully to the nuclear motion Hamiltonian of
molecules of astrobiological interest such as ethylene oxyde, or of atmospherical interest
such as methane [3, 4, 5, 6]. It has been implemented in the CONVIV code which can
deal with both rectilinear and curvilinear coordinates. So, large amplitude degrees of
freedom can also be treated efficiently as has been demonstrated recently on the HOOH
case example.
In the first part of this talk, the GMFCI theory will be recalled. Demonstrations of
its effectiveness will be provided on several examples. The second part of the talk will
present the extension of the perturbative treatment to deal with quasi-degenerate zeroorder states. We will illustrate on the 2ν3 -band of methane, how to tune up the order of
perturbation and the size of the quasi-degenerate space to minimize computational cost.
The last part of the talk will illustrate on hydrogen peroxyde, the advantage of using a
generalized mean field to deal with the large amplitude torsional mode of this molecule.
−0.2
−0.4
o1
o2
−0.6
Absolute error (cm−1)
0.0
quasi−degenerate space: P0P6
6000
6050
6100
6150
6200
6250
6300
Wave number (cm−1)
Figure 1: Absolute error on the rotational levels (J ≤ 7) of the 2ν3 -band of methane with mean field
(o1: red) and generalized mean field (o2: blue). The order 2 GMF superHamiltonian calculation required
only 2.1 h of CPU time see Tab.1.
Table 1: CPU times for superHamiltonian construction on a node of an HP cluster (each node has 2
processors Intel(R) E5-2670 - 2.60 GHz - 8 cores with 64 GigaBytes memory). The notation “on-X”
refers to order n generalized mean field with sum on spectator basis functions truncated at the X th
function. If no “X” is specified all the 16792 vibrational functions were used. Order 2 is not parallelized.
See [2] for details.
quasi-deg.
space
dimension
o2
o3-4237
o3
o4-530
o4-1232
o4-2143
2ν3
6
0.2 s
-
1.0 h
3.4 h
2.1 d
11 d
(ν1 + 2ν2 )//2ν3
9
0.5 s
-
2.1 h
7.3 h
4.6 d
23 .7 d
(ν1 + ν3 )// · · · //4ν2
38
7.4 s
-
35.5h
5.0d
75 .6 d
-
P4
140
2 min
30.8 h
19 .7 d
66 .6 d
-
-
P0-P5
530
24 min
18 .3 d
281 .0 d
-
-
-
P0-P6
1232
2.1 h
98 .9 d
-
-
-
-
P0-P7
2143
6.4 h
-
-
-
-
-
References
[1] P. Cassam-Chenaı̈,B. Suo, W. Liu, Phys. Rev. A (012502) 92.2015
[2] P. Cassam-Chenaı̈, G. Rousseau, A. Ilmane, Y. Bouret, M. Rey, J. Chem. Phys 143
(2015) 034107.
[3] P. Cassam-Chenaı̈ and J. Liévin, Int. J. Quantum Chem. 93 (2003) 245-264.
[4] P. Cassam-Chenaı̈, J. Liévin, Journal of Computational Chemistry 27 (2006) 627-640.
[5] P. Cassam-Chenaı̈, A. Ilmane, J. Math. Chem. 50 (2012) 652-667.
[6] P. Cassam-Chenaı̈ and J. Liévin, J. Mol. Spectrosc. 291 (2013) 77-84.