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RHF potential energy surface for the collinear reaction of Na with HF
525
JournalofMolecularStructure,142(1986)525-528 Elsevier Science Publishers B.V., Amsterdam -PrintedinThe Netherlands
RHF POTENTIAL HF.
ENERGY
SURFACE
M. PANIAGUAl,
J.M. GARCIA
FOR THE COLLINEAR
DE LA "EGAl,
J.R. ALVAREZ
J.C. SANZl, J.M. AL"ARIN02 and A. LAGANA3 1 Departamento de Quimica Fisica y Quimica Universidad
Ciencias.
Autonoma
Madrid. Spain. 2 Departamento de Quimica
Facultad
OF Na WITH
COLLADOl,
Cuantica.
de Madrid.
Fisica.
REACTION
Facultad
Cantoblanco,
de Quimica.
de Salamanca. 37008 Salamanca. Spain. 3 Dipartimento di Chimica dell'Universita.
06100
de
28049
Universidad
Perugia.
Italy.
ABSTRACT The potential energy surface for the reaction of Na and HF has been obtained from a RHF direct minimization method using an ex tended GTO basis set. Features of the surface were examined by fitting calculated values using cubic splines. The transition state occurs in the exit channel 40.9 Kcal/mole above the reactants asymptote. Possible dynamical properties of the system are also discussed.
INTRODUCTION The collision
of an alkali
gen halide
molecule
be studied
in detail
More
recently
constants
using
molecular
experimental
have been
with
HF (refs.
been
obtained
or alkaline
earth
atom with
(M + HX) was the first elementary
carried
8-13).
beam
measurements
techniques
a hydro-
reaction (refs.
of state-to-state
to
l-7).
rate
out for Na, K, Ba, Sr and Ca reacting
Detailed
crossed
molecular
for the Li + HF, Li + HCl
(ref.
beams
data
have
14) and Ca + HF (ref.
15) reactions. In spite reactions, dimensional (refs.
of the theoretical only
potential
17-19).
Be + HF (ref. inadequacy
is given
These
energy studies
"ab initio"
surface were
"ab initio"
of a closed
in ref.
20 where
with
19) systems.
RHF approach
shell
importance studies
of M + HX
of the three-
(PES) have been
concerned
18) and Mg + HF (ref.
of an
the breaking
and practical
a few complete
carried
out
Li + HF (ref. An example
for the description
system
into two open
"ab initio"
PES calculated
shell
17)
of the of
fragments
for the colli-
526 near Mg + HF reaction
with
the rearrangement
sed shell by Chen
As in the previous
shell
the basis
ion. Therefore,
to obtain
The Pople
the final
For the fluorine Gaussian
polarization
et al. 621121;52
orbitals.
minimization
ve control cubic
perform
a virtual
In order interaction near
fairly
RESULTS
broad
range
of the internal
set was
(ref. 22)
0.07.
As a con-
performed
is of
using
In this minimization of the displace-
Newton-Raphson
length
method
and,
A retrospecti-
is made
using
a
(or interpolation) direction
from the point extended
we generated
et al. 6221~52
so determined.
distances
21) for
of exponent
set
length
the extrapolation
a sufficiently
reaction,
23.24).
as a trial
the
of expo-
for the calculation
the displacement
step starting
to obtain
allow
of lowest description
of interest
the potential
us to
energy. of the
for a colli-
energy
for a
coordinates.
AND DISCUSSION
Asymptotic
properties
re we compare on energies results
along
(ref.
atom basis
Gaussian
of the trial
at the internuclear
chemical
P functions
from a modified
Finally
approximation.
set
of exponent
(refs.
to the
of the F- ne-
the Clementi
set used
in
for calculating
Gaussian
The sodium
to the new point
of the correctness
of the Fock operators
P functions
RHF calculati.ons were
as well
are obtained is made
set,
procedure
the direction
a jump
thus,
basis
set. Here,
set of P functions
contracted
the size of the basis
ment vector
a
the collinear
description
set used
set of P functions
33 atomic
the above
basis
atom we used
sequence,
a direct
the work
we present
basis
by adding
accurate
effects.
with
Gaussian
(ref. 22) adding
set
a supplementary
procedure
dealing
to one clo-
characteristics.
a supplementary
contracte
With
leading
In this paper
et al. 31G contracted
atom with
the Clementi
system
(see for example
optimized
a more
nent one.
with
are compared.
used when
(ref. 20) concerned
set was
gative
0.21 to allow
fragments
the latter
work
in order
the hydrogen
shell
we use a contracted
F atom
PES was:
be profitably
CALCULATION
Mg + HF reaction, addition,
RHF and MC methods
III for Li + HF).
that presents
"AB INITIO"
both
can still of an open
and one open
and Schaefer
RHF study
THE
using
the RHF method
However,
of the PES are illustrated
the calculated
equilibrium
and the equilibrium
distances,
frecuencies
with
in Table
1 whe-
the dissociati-
the experimental
(ref. 25) for the HF, NaF and NaH molecules.
527 TABLE EXPERIMENTAL
1
AND CALCULATED
RESULTS
FOR THE DIATOMS
W
Diatom
NaF HF NaH genergies
talc.
exp.
talc.
exp.
talc.
exp.
89.4
124.4
3.71
3.64
612.9
536
108.5
141.2
1.74
1.73
4097.1
4138.3
33.7
46.7
3.65
3.57
1177.9
1172.2
in Kcal/mole.
12distances in atomic
A graphical
representation
1. Isoenergetic
contours
spline
of the minimum
energy
occurs
tes that
at RNaF
Kcal/mole
stabilizes
occurs
to reaction
the reactant
rresponding
value
that of collinear
state
lies
This
complex.
channel
and that
figure
approach, close
Li + HF. The position channel
at R
NaF
features
is concerned,
is quite
indica-
of 2.5
behavior
for the Be + HF and Mg + HF systems
in the exit
also
All these
in the collinear
asymptote,
the aid of distortion
the dynamic state
in Fig.
little
and RHF = 1.84 a.". a well
in characterizing
double tion
saddle.
with
that
in the entrance
an intermediate
role
PES is given
obtained
1 shows
As far as the transition
above
than
PES were
Figure
a sideways
= 5.52 a.".
ight of the barrier Kcal/mole
of this
path
through
an important
the reaction.
of the collinear
interpolation.
reaction
play
units.
in cm -1 .
Cfrequencies
a cubic
C
e
of
the he40.9
to the cobut almost
of the transi-
= 3.74 a.". and RHF =
2.68 a-u..
REFERENCES 1 E.H. Taylor and S. Datz, J. Chem. Phys. 23 (1955) 1711. 2 E.E. Greene, A.L. Moursund and J. Ross, Adv. Chem. Phys. -10 (1966) 135. 3 K.T. Gillen, C. Riley and R.B. Bernstein, J. Chem. Phys. -50 (1969) 4019. 4 H.W. Cruse, P.J. Dagdigian and R.N. Zare, Faraday Discuss. Chem. sot. 55 (1973) 277. 5 J.C. Pruett, F.R. Grabiner and P.R. Brooks, J. Chem. Phys. -63 (1975) 1173. 6 D.R. Herschbach, Faraday Discuss. Chem. Sot. 62 (1977) 162. 7 B.A. Blackwell, J.C. Polanyi and J.J. Sloan, Chem. Phys. -30 (1978) 299.
528
Pi-g.
1.
RHF collinear
PES for Na + HF
(energies
in Kcal/mole).
8 J.G. Pruett and R.N. Zare, J. Chem. Phys. 64 (1976) 1774. 9 Z. Karny and R.N. Zare, J. Chem. Phys. 68 -978) 3360. J.C. PoGnyi and J.J. Sloan, J. 10 F.E. Bartoszek, B.A. Blackwell, Chem. Phys. 74 (1981) 3400. and J.G. Pruett, J. Chem. Phys. 77 (1982) 740. 11 A. Torres-Fixo 43. 12 F. Heismann and H.J. Loesch, Chem. Phys. 64 (198n L. Potthast and H.J. Loesch, Chem. Phys. -78 13 M. Hoffmeister, (1983) 369. P.Casavecchia, P.W.Tiedemann, J.J.Valentini and 14 C.H.Becker, Y.T.Lee, J. Chem. Phys. 73 (1980) 2833. 15 F.Engelke and K.H.MeiwesEoer, Chem. Phys. Lett. 108 (1984) 132. 16 Theory of Chemical Reaction Dynamics, CECAM/NATO Advanced Research Workshop. (1985). 17 M.M.L. Chen and H.F. Schaefer III, J. Chem. Phys. 72 (1980) 4376. 93. 18 S. Chapman, M. Dupuis and S. Green, Chem. Phys. 7871983) 19 M.Paniagua, J.M.Garcia de la Vega, J.R.Alvarez Calado, J.C.Sanz, J.M.Alvariiio and A.Lagana, Chem. Phys. (in press). 20 M. Paniagua, J.M. Garcia de la Vega, J.M. Alvarino and A. LaganB, J. Mol. Struct. (Theochem), 120 (1985) 475. 21 R.Ditchfield, W.J.Hehre and J.A.Pople, J. Chem. Phys. 54 (1971) 22 L.Gianolio R.Pavani and E.Clementi, Gaz. Chim. It. 10871978) 181 and 23 J.Fern&ndez Rico, J.M.Garcia de la Vega, J.I.Fernhndez-Alonso P.Fantucci, J. Comp. Chem. 4 (1983) 33. 24 J. Fernandez Rico, M. Paniagua, J-1. Fernandez-Alonso and P. Fantucci, J. Comp. Chem. 4 (1983) 41. 25 K.P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure, Vol. 4, Constants of Diatomic Molecules (van Nostrand, Princeton, 1979).
JournalofMolecularStructure,142(1986)525-528 Elsevier Science Publishers B.V., Amsterdam -PrintedinThe Netherlands
RHF POTENTIAL HF.
ENERGY
SURFACE
M. PANIAGUAl,
J.M. GARCIA
FOR THE COLLINEAR
DE LA "EGAl,
J.R. ALVAREZ
J.C. SANZl, J.M. AL"ARIN02 and A. LAGANA3 1 Departamento de Quimica Fisica y Quimica Universidad
Ciencias.
Autonoma
Madrid. Spain. 2 Departamento de Quimica
Facultad
OF Na WITH
COLLADOl,
Cuantica.
de Madrid.
Fisica.
REACTION
Facultad
Cantoblanco,
de Quimica.
de Salamanca. 37008 Salamanca. Spain. 3 Dipartimento di Chimica dell'Universita.
06100
de
28049
Universidad
Perugia.
Italy.
ABSTRACT The potential energy surface for the reaction of Na and HF has been obtained from a RHF direct minimization method using an ex tended GTO basis set. Features of the surface were examined by fitting calculated values using cubic splines. The transition state occurs in the exit channel 40.9 Kcal/mole above the reactants asymptote. Possible dynamical properties of the system are also discussed.
INTRODUCTION The collision
of an alkali
gen halide
molecule
be studied
in detail
More
recently
constants
using
molecular
experimental
have been
with
HF (refs.
been
obtained
or alkaline
earth
atom with
(M + HX) was the first elementary
carried
8-13).
beam
measurements
techniques
a hydro-
reaction (refs.
of state-to-state
to
l-7).
rate
out for Na, K, Ba, Sr and Ca reacting
Detailed
crossed
molecular
for the Li + HF, Li + HCl
(ref.
beams
data
have
14) and Ca + HF (ref.
15) reactions. In spite reactions, dimensional (refs.
of the theoretical only
potential
17-19).
Be + HF (ref. inadequacy
is given
These
energy studies
"ab initio"
surface were
"ab initio"
of a closed
in ref.
20 where
with
19) systems.
RHF approach
shell
importance studies
of M + HX
of the three-
(PES) have been
concerned
18) and Mg + HF (ref.
of an
the breaking
and practical
a few complete
carried
out
Li + HF (ref. An example
for the description
system
into two open
"ab initio"
PES calculated
shell
17)
of the of
fragments
for the colli-
526 near Mg + HF reaction
with
the rearrangement
sed shell by Chen
As in the previous
shell
the basis
ion. Therefore,
to obtain
The Pople
the final
For the fluorine Gaussian
polarization
et al. 621121;52
orbitals.
minimization
ve control cubic
perform
a virtual
In order interaction near
fairly
RESULTS
broad
range
of the internal
set was
(ref. 22)
0.07.
As a con-
performed
is of
using
In this minimization of the displace-
Newton-Raphson
length
method
and,
A retrospecti-
is made
using
a
(or interpolation) direction
from the point extended
we generated
et al. 6221~52
so determined.
distances
21) for
of exponent
set
length
the extrapolation
a sufficiently
reaction,
23.24).
as a trial
the
of expo-
for the calculation
the displacement
step starting
to obtain
allow
of lowest description
of interest
the potential
us to
energy. of the
for a colli-
energy
for a
coordinates.
AND DISCUSSION
Asymptotic
properties
re we compare on energies results
along
(ref.
atom basis
Gaussian
of the trial
at the internuclear
chemical
P functions
from a modified
Finally
approximation.
set
of exponent
(refs.
to the
of the F- ne-
the Clementi
set used
in
for calculating
Gaussian
The sodium
to the new point
of the correctness
of the Fock operators
P functions
RHF calculati.ons were
as well
are obtained is made
set,
procedure
the direction
a jump
thus,
basis
set. Here,
set of P functions
contracted
the size of the basis
ment vector
a
the collinear
description
set used
set of P functions
33 atomic
the above
basis
atom we used
sequence,
a direct
the work
we present
basis
by adding
accurate
effects.
with
Gaussian
(ref. 22) adding
set
a supplementary
procedure
dealing
to one clo-
characteristics.
a supplementary
contracte
With
leading
In this paper
et al. 31G contracted
atom with
the Clementi
system
(see for example
optimized
a more
nent one.
with
are compared.
used when
(ref. 20) concerned
set was
gative
0.21 to allow
fragments
the latter
work
in order
the hydrogen
shell
we use a contracted
F atom
PES was:
be profitably
CALCULATION
Mg + HF reaction, addition,
RHF and MC methods
III for Li + HF).
that presents
"AB INITIO"
both
can still of an open
and one open
and Schaefer
RHF study
THE
using
the RHF method
However,
of the PES are illustrated
the calculated
equilibrium
and the equilibrium
distances,
frecuencies
with
in Table
1 whe-
the dissociati-
the experimental
(ref. 25) for the HF, NaF and NaH molecules.
527 TABLE EXPERIMENTAL
1
AND CALCULATED
RESULTS
FOR THE DIATOMS
W
Diatom
NaF HF NaH genergies
talc.
exp.
talc.
exp.
talc.
exp.
89.4
124.4
3.71
3.64
612.9
536
108.5
141.2
1.74
1.73
4097.1
4138.3
33.7
46.7
3.65
3.57
1177.9
1172.2
in Kcal/mole.
12distances in atomic
A graphical
representation
1. Isoenergetic
contours
spline
of the minimum
energy
occurs
tes that
at RNaF
Kcal/mole
stabilizes
occurs
to reaction
the reactant
rresponding
value
that of collinear
state
lies
This
complex.
channel
and that
figure
approach, close
Li + HF. The position channel
at R
NaF
features
is concerned,
is quite
indica-
of 2.5
behavior
for the Be + HF and Mg + HF systems
in the exit
also
All these
in the collinear
asymptote,
the aid of distortion
the dynamic state
in Fig.
little
and RHF = 1.84 a.". a well
in characterizing
double tion
saddle.
with
that
in the entrance
an intermediate
role
PES is given
obtained
1 shows
As far as the transition
above
than
PES were
Figure
a sideways
= 5.52 a.".
ight of the barrier Kcal/mole
of this
path
through
an important
the reaction.
of the collinear
interpolation.
reaction
play
units.
in cm -1 .
Cfrequencies
a cubic
C
e
of
the he40.9
to the cobut almost
of the transi-
= 3.74 a.". and RHF =
2.68 a-u..
REFERENCES 1 E.H. Taylor and S. Datz, J. Chem. Phys. 23 (1955) 1711. 2 E.E. Greene, A.L. Moursund and J. Ross, Adv. Chem. Phys. -10 (1966) 135. 3 K.T. Gillen, C. Riley and R.B. Bernstein, J. Chem. Phys. -50 (1969) 4019. 4 H.W. Cruse, P.J. Dagdigian and R.N. Zare, Faraday Discuss. Chem. sot. 55 (1973) 277. 5 J.C. Pruett, F.R. Grabiner and P.R. Brooks, J. Chem. Phys. -63 (1975) 1173. 6 D.R. Herschbach, Faraday Discuss. Chem. Sot. 62 (1977) 162. 7 B.A. Blackwell, J.C. Polanyi and J.J. Sloan, Chem. Phys. -30 (1978) 299.
528
Pi-g.
1.
RHF collinear
PES for Na + HF
(energies
in Kcal/mole).
8 J.G. Pruett and R.N. Zare, J. Chem. Phys. 64 (1976) 1774. 9 Z. Karny and R.N. Zare, J. Chem. Phys. 68 -978) 3360. J.C. PoGnyi and J.J. Sloan, J. 10 F.E. Bartoszek, B.A. Blackwell, Chem. Phys. 74 (1981) 3400. and J.G. Pruett, J. Chem. Phys. 77 (1982) 740. 11 A. Torres-Fixo 43. 12 F. Heismann and H.J. Loesch, Chem. Phys. 64 (198n L. Potthast and H.J. Loesch, Chem. Phys. -78 13 M. Hoffmeister, (1983) 369. P.Casavecchia, P.W.Tiedemann, J.J.Valentini and 14 C.H.Becker, Y.T.Lee, J. Chem. Phys. 73 (1980) 2833. 15 F.Engelke and K.H.MeiwesEoer, Chem. Phys. Lett. 108 (1984) 132. 16 Theory of Chemical Reaction Dynamics, CECAM/NATO Advanced Research Workshop. (1985). 17 M.M.L. Chen and H.F. Schaefer III, J. Chem. Phys. 72 (1980) 4376. 93. 18 S. Chapman, M. Dupuis and S. Green, Chem. Phys. 7871983) 19 M.Paniagua, J.M.Garcia de la Vega, J.R.Alvarez Calado, J.C.Sanz, J.M.Alvariiio and A.Lagana, Chem. Phys. (in press). 20 M. Paniagua, J.M. Garcia de la Vega, J.M. Alvarino and A. LaganB, J. Mol. Struct. (Theochem), 120 (1985) 475. 21 R.Ditchfield, W.J.Hehre and J.A.Pople, J. Chem. Phys. 54 (1971) 22 L.Gianolio R.Pavani and E.Clementi, Gaz. Chim. It. 10871978) 181 and 23 J.Fern&ndez Rico, J.M.Garcia de la Vega, J.I.Fernhndez-Alonso P.Fantucci, J. Comp. Chem. 4 (1983) 33. 24 J. Fernandez Rico, M. Paniagua, J-1. Fernandez-Alonso and P. Fantucci, J. Comp. Chem. 4 (1983) 41. 25 K.P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure, Vol. 4, Constants of Diatomic Molecules (van Nostrand, Princeton, 1979).