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Chamical bond in hydrogen fluoride
Volpme 2, number 8
CHEMICAL PHYSICS LETTERS
.
CHEMICAL
BOND
IN
HYDROGEN
December 1968
FLUORIDE
Martin KLESSlNGER O~-gflnisci~-Cl~e7niscl~es instttut der Linirersitiit.
34 Gb’ttingen? Cennan~~
Received 9 September 1968
Rel;ults of minimum basis SCGF calculations tm HF are reported for several internuclear distances.
Self-consistent group fupction (SCGF) calculations have proved of great value in discussing chemical bonds [l-3]. They represent a conven-
ient way of calculating ground state energies better than the corresponding SCF energies and at the same time this kind of approach has an immediate chemical appeal because it stresses the individuality of different bonds, inner shells, lone pairs etc. and allows for the determination of optimum valence hybrids which may be identified with the hybrid orbitals commonly used in qualitative discussions of structural problems [3 1. In the present note results of SCGF calculation? *vith determination af optimum valence hy‘Grids are report& Z,i- HF at several internuclear distances. Thus various ground state properties were obtained as functions of the interatomic separation. The minimum basis set of orthogonal hybrid AO’s used was consirucied from Slater Ao’s (<(ls)H = 1.6. <(ls) F = 8.7, <(%S), = <(zp)F = 2.6) by Schmidt orthogonalization of ail valence shell orbitals with respect to the fluorine inner shell, formation of suitable hybrids and symmetrical Ltiwdin orthogonalization. The total wave function of the molecule is written as .an antisymmetrized product of pair functions [4] rk(1,. . . , N) = &ICr [+A(l,
2)+B(3,4).
. . ;,
ix)
where for the bond pair *A&2)
= &j@I~ll I- C2Giqfij2t
+ lq$Ql)
+ C3lP@2l
(2)
“2 = &k-b).
(3)
with il
= d&:+b)
and
iz is the hydrogen Is orbital and b a suitable fluorine hybrid A0 given by & = (1 + x2)-$X(Zs),
+ (2&+
J.
(4)
The inner shell and lone pair functions are written as *R(l,
2) = t*I
,
(5)
where Y is an appropriate (hybrid) AO. As in the SCGF approach the total electronic energy is not invariant against the choice of hybrid AO’s for constructing the bond pair functions. optimum valence hybrids can be determined by minimizing the ground state energy E, with respect to the hybridization parameter X of eq. (4). In table 1 results are given for the optimum value X0 t of this parameter for seven internuclear dis 9 antes and are compared with results obtained using the same basis of Slater AO’s in the conventional SCF method. It is seen from the data in table 1 that xopt and therefore the percentage s-character of the valence hybrid (%s = 100h21’(1 +h2)) decreases monotonically with increasing internuclear distance as does the effective energy @f” of the separated bond pair *. The bond order X goes through a maximum between R = 1.50 and R = 2.0 au. and the polarity parameter Y (measuring the charge transferred from the hydrogen A0 to the hybrid A0 on F) goes from positive to negative in going from R = 2.0 to R = 2.5 a-u., corresponding to an electronic structure H+F” for small and H-F+ for intermediate interatomic separations_ For large R val!_ies Y increases again and tends towards zero. The same behaviour is reflected in the calculated dipole moments, but a different one is expected and found for the SCF data: for large R the gross charge QH tends towards +1 corresponding to dissociation into F- and H*. Although not very accurate the calculated charge distributions and their variations with internuciear distances are qualitatively correct as may be seen from comparison with the results of Clef For detail&-of definition and notation see ref. [l].
Volume
2. number
CHEMICAL
8
Results
SCGF
of SCGF
PHYSICS
and SCF calculations
LETTERS
Table 1 for HF at various
R = 1.25
R = 1.50
-99.24802
-99.43002
-99.49717
-99.51889
- 3.51874
-
- 2.54864
-
R = 1.73312
December
internuclear
R = 2.00
distances
R = 2.50
1968
l
R = 3.00
R = S.50
-99.50128
-99.47089
-99.44982
-
-
-
calculations Eo
2.95069
2.20921
1.79913
1.56785
1.44075
X
0.9514
0.9725
0.9741
0.9588
0.8831
0.7385
0.5473
Y
0.2900
0.1763
0.0908
0.0184
- 0.0520
- fl.0563
- 0.034L
- 0.1763
- 0.1396
P
1.4801
1.1317
0.8076
0.4719
0.0018
Xopt
0.72069
0.51651
0.39621
0.30064
0.18143
0.10436
0.056I4
8.29
3.19
1.08
0.31
-99.49050
-99.44659
-99.37808
-99.31061
21.06
34.18
ZS
13.57
SC F calculations -99.24213
Eo n(HF)
-99.41843
0.2808 -
QH
0.4562
-
1.5220
Ir
0.2682
0.2615
0.2559
0.2339
0.1921
0.2760
- 0.1537
- 0.0529
0.0633
0.1231
1.1918
0.8778.
0.5327
0.0486
- 0.5?03
and bond energy &,pt. percentage
* Ground state energy E, hybridization parameter
gross charge QH.
-99.47856
SCF
moment p in D. bond order X. polarity of bond orbit&s %s, overlap population n(HF)
Hg# in a.u.. dipole s-character
Table 2 Calculated and experimental equilibrium internuclear distance R, (in a.~.) and dissociation energy De (in eV) for HF SCGF
-
Exp.
R,
2.04
1.s4
1.73
DP
2.37
1.62
6.08
@.I449 0.1555 -
1.0155
parameter I;. and hydrogen
menti [5]. Deficiencies could easiIy be overcome by improving the set of basis functions. Table 2 gives the results for the calculated equilibrium internuclear distance Re and dissociation energy De together with the experimental data [S]. Potential energy curves calculated by the SCGF and the SCF approach are shown in fig. la
I b.)
-4.0
R(a.u.l-
R (ad
4
10
Fig.
1. Potential
energy
curves
-
t-
2.0
3.0
10
for HF. (a) SCF and SCGF results, present of Karo and Allen 161, atomic Hartree-Fock
--e--ecalcuIations, basis.
(b) SCF and SCF-Cf
results
563
Volume
2. number
8
CHEMICAL
PHYSICS
and may be compared with results of an 8CF calculation with and without CI by Karo and Allen [6] in fig. lb (the SCF curves are not identical as Karo and Ailen used a basis of atomic HartreeFock orbitals). This graph shows that by including CI within the bond pair function +A(i, 2) (eq. (2)) about the same effect is obtained as by &ensive CI within the basis of SCF-MO’s. As the SCGF calculations involve at most 3 x 3 secular problems and convergence is very rapid they are considerably faster than conventional SCF calculations even without CL This demonstrates clearly the great value of the GF approach in calculating ground state properties. In a forthcoming paper similar calculations with contracted Gaussian basis sets will be described for a number of molecules and the influence of the choice of the ba-
:.
-554
- ;;-_.-
sis set on calculated ground state properties be discussed in more detail.
_
-.
,:
.- 1 :.
1968
will
Financial support of this investigation by the Deutsche Forschungsgemeinschafft (Bad Godesberg) is gratefully acknowledged. REFERENCES [l]
M. Klessinger (1965) 3343. [2] M.Klessinger. [3] M.Klessinger.
and R. McWeeny.
J. Chem. Phys.
42
J. Chem. Phys. 43 (19G5) 117. J.Chem. Phys. 46 (1967) 3261. [41 R. McWeeny. Rev. Mod. Phys. 32 (1960) 335. [5] E. Clementi. J. Chem. Phys. 36 (1962) 33. [6] A. M. Karo and L.C. Allen. J. Chem. Phys. 31 (1959) 968.
-_
-_
-_ -_, .-
December
LETTERS
_.-
‘.‘_..
.
..-
CHEMICAL PHYSICS LETTERS
.
CHEMICAL
BOND
IN
HYDROGEN
December 1968
FLUORIDE
Martin KLESSlNGER O~-gflnisci~-Cl~e7niscl~es instttut der Linirersitiit.
34 Gb’ttingen? Cennan~~
Received 9 September 1968
Rel;ults of minimum basis SCGF calculations tm HF are reported for several internuclear distances.
Self-consistent group fupction (SCGF) calculations have proved of great value in discussing chemical bonds [l-3]. They represent a conven-
ient way of calculating ground state energies better than the corresponding SCF energies and at the same time this kind of approach has an immediate chemical appeal because it stresses the individuality of different bonds, inner shells, lone pairs etc. and allows for the determination of optimum valence hybrids which may be identified with the hybrid orbitals commonly used in qualitative discussions of structural problems [3 1. In the present note results of SCGF calculation? *vith determination af optimum valence hy‘Grids are report& Z,i- HF at several internuclear distances. Thus various ground state properties were obtained as functions of the interatomic separation. The minimum basis set of orthogonal hybrid AO’s used was consirucied from Slater Ao’s (<(ls)H = 1.6. <(ls) F = 8.7, <(%S), = <(zp)F = 2.6) by Schmidt orthogonalization of ail valence shell orbitals with respect to the fluorine inner shell, formation of suitable hybrids and symmetrical Ltiwdin orthogonalization. The total wave function of the molecule is written as .an antisymmetrized product of pair functions [4] rk(1,. . . , N) = &ICr [+A(l,
2)+B(3,4).
. . ;,
ix)
where for the bond pair *A&2)
= &j@I~ll I- C2Giqfij2t
+ lq$Ql)
+ C3lP@2l
(2)
“2 = &k-b).
(3)
with il
= d&:+b)
and
iz is the hydrogen Is orbital and b a suitable fluorine hybrid A0 given by & = (1 + x2)-$X(Zs),
+ (2&+
J.
(4)
The inner shell and lone pair functions are written as *R(l,
2) = t*I
,
(5)
where Y is an appropriate (hybrid) AO. As in the SCGF approach the total electronic energy is not invariant against the choice of hybrid AO’s for constructing the bond pair functions. optimum valence hybrids can be determined by minimizing the ground state energy E, with respect to the hybridization parameter X of eq. (4). In table 1 results are given for the optimum value X0 t of this parameter for seven internuclear dis 9 antes and are compared with results obtained using the same basis of Slater AO’s in the conventional SCF method. It is seen from the data in table 1 that xopt and therefore the percentage s-character of the valence hybrid (%s = 100h21’(1 +h2)) decreases monotonically with increasing internuclear distance as does the effective energy @f” of the separated bond pair *. The bond order X goes through a maximum between R = 1.50 and R = 2.0 au. and the polarity parameter Y (measuring the charge transferred from the hydrogen A0 to the hybrid A0 on F) goes from positive to negative in going from R = 2.0 to R = 2.5 a-u., corresponding to an electronic structure H+F” for small and H-F+ for intermediate interatomic separations_ For large R val!_ies Y increases again and tends towards zero. The same behaviour is reflected in the calculated dipole moments, but a different one is expected and found for the SCF data: for large R the gross charge QH tends towards +1 corresponding to dissociation into F- and H*. Although not very accurate the calculated charge distributions and their variations with internuciear distances are qualitatively correct as may be seen from comparison with the results of Clef For detail&-of definition and notation see ref. [l].
Volume
2. number
CHEMICAL
8
Results
SCGF
of SCGF
PHYSICS
and SCF calculations
LETTERS
Table 1 for HF at various
R = 1.25
R = 1.50
-99.24802
-99.43002
-99.49717
-99.51889
- 3.51874
-
- 2.54864
-
R = 1.73312
December
internuclear
R = 2.00
distances
R = 2.50
1968
l
R = 3.00
R = S.50
-99.50128
-99.47089
-99.44982
-
-
-
calculations Eo
2.95069
2.20921
1.79913
1.56785
1.44075
X
0.9514
0.9725
0.9741
0.9588
0.8831
0.7385
0.5473
Y
0.2900
0.1763
0.0908
0.0184
- 0.0520
- fl.0563
- 0.034L
- 0.1763
- 0.1396
P
1.4801
1.1317
0.8076
0.4719
0.0018
Xopt
0.72069
0.51651
0.39621
0.30064
0.18143
0.10436
0.056I4
8.29
3.19
1.08
0.31
-99.49050
-99.44659
-99.37808
-99.31061
21.06
34.18
ZS
13.57
SC F calculations -99.24213
Eo n(HF)
-99.41843
0.2808 -
QH
0.4562
-
1.5220
Ir
0.2682
0.2615
0.2559
0.2339
0.1921
0.2760
- 0.1537
- 0.0529
0.0633
0.1231
1.1918
0.8778.
0.5327
0.0486
- 0.5?03
and bond energy &,pt. percentage
* Ground state energy E, hybridization parameter
gross charge QH.
-99.47856
SCF
moment p in D. bond order X. polarity of bond orbit&s %s, overlap population n(HF)
Hg# in a.u.. dipole s-character
Table 2 Calculated and experimental equilibrium internuclear distance R, (in a.~.) and dissociation energy De (in eV) for HF SCGF
-
Exp.
R,
2.04
1.s4
1.73
DP
2.37
1.62
6.08
@.I449 0.1555 -
1.0155
parameter I;. and hydrogen
menti [5]. Deficiencies could easiIy be overcome by improving the set of basis functions. Table 2 gives the results for the calculated equilibrium internuclear distance Re and dissociation energy De together with the experimental data [S]. Potential energy curves calculated by the SCGF and the SCF approach are shown in fig. la
I b.)
-4.0
R(a.u.l-
R (ad
4
10
Fig.
1. Potential
energy
curves
-
t-
2.0
3.0
10
for HF. (a) SCF and SCGF results, present of Karo and Allen 161, atomic Hartree-Fock
--e--ecalcuIations, basis.
(b) SCF and SCF-Cf
results
563
Volume
2. number
8
CHEMICAL
PHYSICS
and may be compared with results of an 8CF calculation with and without CI by Karo and Allen [6] in fig. lb (the SCF curves are not identical as Karo and Ailen used a basis of atomic HartreeFock orbitals). This graph shows that by including CI within the bond pair function +A(i, 2) (eq. (2)) about the same effect is obtained as by &ensive CI within the basis of SCF-MO’s. As the SCGF calculations involve at most 3 x 3 secular problems and convergence is very rapid they are considerably faster than conventional SCF calculations even without CL This demonstrates clearly the great value of the GF approach in calculating ground state properties. In a forthcoming paper similar calculations with contracted Gaussian basis sets will be described for a number of molecules and the influence of the choice of the ba-
:.
-554
- ;;-_.-
sis set on calculated ground state properties be discussed in more detail.
_
-.
,:
.- 1 :.
1968
will
Financial support of this investigation by the Deutsche Forschungsgemeinschafft (Bad Godesberg) is gratefully acknowledged. REFERENCES [l]
M. Klessinger (1965) 3343. [2] M.Klessinger. [3] M.Klessinger.
and R. McWeeny.
J. Chem. Phys.
42
J. Chem. Phys. 43 (19G5) 117. J.Chem. Phys. 46 (1967) 3261. [41 R. McWeeny. Rev. Mod. Phys. 32 (1960) 335. [5] E. Clementi. J. Chem. Phys. 36 (1962) 33. [6] A. M. Karo and L.C. Allen. J. Chem. Phys. 31 (1959) 968.
-_
-_
-_ -_, .-
December
LETTERS
_.-
‘.‘_..
.
..-