Neon Dimer Binding : an ab initio Calculation
Alexandre Martins Dias *
Resumo: Usando o método Hartree Fock Restrito (RHF) e a teoria de Perturbação de Segunda
Ordem de Moller-Plesset (MP2) para sistemas de camada fechada, com um conjunto de funções de
base do tipo TZV (Triple Zeta Valence), como implementado no programa ab initio GAMESS, versão
4.0, para cálculos de estrutura eletrônica, este estudo apresenta o cálculo da curva de potencial para
o estado fundamental da molécula Ne2. Os resultados proporcionam uma boa predição da energia de
ligação da molécula.
Palavras-chave: Ne2, GAMESS, ab initio, RHF, MP2.
Abstract: Using Restricted Hartree Fock (RHF) method and Second Order Moller-Plesset
Disturbance theory (MP2) for closed layer systems with a set of basis functions like Triple Zeta
Valence (TZV) as implemented in the version 4.0 ab initio GAMESS program for electronic structure
calculations, this study presents a potential curve calculation for the ground state of the Ne2 molecule.
The results provide a good prediction about the molecule linking energy.
Key words: Ne2, GAMESS, ab initio, RHF, MP2.
1. INTRODUCTION
Diatomic molecules of noble gases have been
studied from several points for empirical and ab initio
calculations (TANAKA; YOSHINO, 1972; COHEN;
SCHNEIDER, 1974). The interest in these molecules
were due to the fact that they constitute a class of
molecules for laser applications (MICHELS; HOBBS;
WRIGTH, 1978). Recently, new ab initio potentials for
neon dimmer have been obtained in the studies of
molecular global simulations, condensed phase and
tests of the several basis sets for weakly interacting
system (EGGENBERGER et al., 1994; NASRABAD,
2003).
Ab initio calculations (CLEMENTI,1965) showed
that
ground
1
∑ +g
state
2
of
2
dimer
2
Ne2
2
with
4
configuration
(1σu) (1σg) (2σg) (2σu) (1πg) (1πu)4
2
2
(3σg) (3σu) , dissociates into two ground states Ne
(1s22s22p6) atoms with the total energy -257.0940 Eh
(hartrees).
Calculations based on MS-Xα (not frozen core
approximation) (KONOWALOW et al., 1972), LCAOMOSCF (GILBERT; WAHL, 1967) and VCM-Xα
(LEITE et al., 1981; DIAS, 1981; DIAS; ROSATO,
1982) methods have not shown the van der Waals
minimum for this molecule.
___________________________________________
* Professor e Coordenador da Faculdade de Ciência da
Computação da UNIFENAS - Alfenas - MG.
E-mail: [email protected]
The ab initio calculation performed in this work is a
trial to predict the binding of the Ne2 dimer, since that
recent calculations (EGGENBERGER et al., 1994;
NASRABAD, 2003) have been performed for this
purpose.
2. CALCULATION REPORTS
These ab initio calculations were performed by
RHF with 2nd order Moller-Plesset (MP2) computation
methods, as implemented into GAMESS (SCHMIDT et
al., 1993) package, for Windows PC computers
optimized by Alex A. Granovsky in Moscow State
University, using Triple Zeta Valence(TZV) with one d
function basis set, initial orbitals generated by Huckel
guess routine with molecule in D2H point symmetry
group and MP2 applied to the last orbital.
Figure 1 shows the potential curve obtained in this
work. The separated atom limit energy reached the
value of -257.090146 Eh. The minimum for total
energy of molecule has been evaluated as -257.090273
Eh at Re = 5.6 au (bohr) or 2.968 Å, assumed as the
equilibrium internuclear distance of the ground state of
the molecule. Then, the binding, obtained as the
difference between the separated atom limit and the
minimum of the potential curve, is 0.000127 Eh or
0.00346 eV.
Experimental results related by Herzberg (HUBER;
HERZBERG, 1979) and Ira N. Levine(1991) shown
0.00013 Eh or 0.0035 eV for binding energy to the
120 ________________________________________________R. Univap,São José dos Campos,SP,v.12,n.22,dez.2005.
equilibrium internuclear distance at R =5.85 au or 3.1
Å. Recent calculations (NASRABAD, 2003), using
extensive (av45z) basis set, result in a more deep
binding energy than experimental value at Re = 3.097 Å
related to the HF-limit of separated atoms.
Table 2 shows the numerical values for the total
energies from VCM-Xα, MS-Xα and LCAO-MO-SCF
methods for the same internuclear separations. These
values are plotted in Figure 2, showing repulsive
potential curves.
Ne-Ne
Table 2 - Total energies for the ground state of Ne2
Molecule for different internuclear separation, in
hartree units.
Re
LCAOc
VCM-Xα
αa
MS-Xα
αb
En erg y(au )
0.0003
1(Sigma)g+
0.0002
0.0001
0.0000
-0.0001
-0.0002
2.120
2.968
3.816
4.664
R(Angstrom)
Fig. 1 - Potential curve for the ground state of Ne2
molecule from RHF+MP2 calculations.
Table 1 sums up the numerical values for these
ab initio calculations and several others results obtained
by different methods for comparison.
Table 1 - Total energies for ground state of Ne2
molecule. All energies in hartree units and internuclear
Re distance in atomic units.
a
b
Re
RHF+MP2
4,2
-257,088405
VCM
4,4
-257,089259
4,6
-257,089749
4,8
-257,090022
5,0
-257,090167
-257,0720
5,2
-257,090238
-257,0770
c
MS-Xα
α
-257,090273
5,8
-257,090266
-257,0850
6,0
-257,090254
-257,0870
6,2
-257,090238
-257,0880
6.4
-257,090222
-257,0580
-257,090183
∞
-257,090146
-256,9490
-256,9535
-257,0640
4,0
-257,0220
-257,0225
-257,0845
5,0
-257,0720
-257,0580
-257,0925
6,0
-257,0870
-257,0635
-257,0930
∞
-257,0920
-257,0700
-257,0930
a) VCM-Xα (Leite et al., 1981; Dias, 1981; Dias; Rosato,
1982).
b)
MS-Xα with
not
frozen
core
approximation
(KONOWALOW et al., 1972).
c) LCAO-MO-SCF (GILBERT; WAHL, 1967).
R (au)
-256.740
2.50
3.50
4.50
5.50
6.50
7.50
-256.780
VCM
d
LCAO
MS
-256.820
-256.860
-256.900
-257,0925
-257,0930
-257.060
-257.100
-257,0635
-257.140
-257,0930
-257,0930
-257,090195
3,5
-257.020
6,5
7,0
-256,9980
-256.980
5,6
6,8
-256,7610
-256.940
-257,0620
-257,090208
-256,7640
LCAO
5,5
6,6
3,0
Energy (hartrees)
0.0004
Fig. 2 - Potential curves for ground state of Ne2
molecule from VCM-Xα, MS-Xα and LCAO-MO-SCF
methods.
3. FINAL REMARKS
-257,0920
-257,0700
-257,0930
a) This work.
b) VCM-Xα (Leite et al.,1981; Dias,1981; Dias;Rosato,
1982).
c) MS-Xα (Konowalow et al.,1972).
d) LCAO-MO-SCF (Gilbert;Wahl, 1967).
R. Univap,São José dos Campos,SP,v.12,n.22,dez.2005.
It is well known from early calculations with the
Restricted Hartree-Fock methods (WAHL, 1964), that it
is not easy to exhibit the binding for these class of
molecules and only half of the binding was obtained
fromthe extensive CI calculations (DAS; WAHL,
1966).
_________________________________________121
The small value of the binding for this molecule is
the main reason for the difficulties in theoretical
calculations, because of the exactness necessary by the
calculations with approximated methods, but the results
obtained in this work have shown an attractive potential
curve compared with the repulsive curves of the others
methods. In Figure 2, we observe that VCM-Xα and
MSXα methods present similar potential curves. It is
due to the muffin-tin approximations used for charge
density into some space regions of the molecule
geometry adopted in VCM calculations and MS
methods, but we observe that VCM-Xα leads to the
separated atom limit energy close to the Hartree-Fock
limit (CLEMENTI, 1965).
The results obtained for the RHF + MP2 energies
for the ground state of the Ne2 molecule in this work,
with TZV basis set as implemented into GAMESS
package, essentially shows weakly bound Ne atoms.
The separated atom limit energy obtained is in good
agreement to the HF limit (CLEMENTI, 1965), and the
binding of molecule subject of this work is close to the
experimental value.
We know that the ground state of Ne2 molecule has
the same number of electron pairs in π ligand orbitals
and π non-ligand orbitals, producing unstable state
(HUBER; HERZBERG, 1979).
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wavefunctions and Potential curves for the Ground
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J. L.; CONNOLY, J. W. D. Self-consistent-field Xα
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