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AB initio SCF LCAO MO study of the HOH…Cl− hydrogen bond
Vc!tie
19, number 1
CtiEMICAL
AB l-NIT10 SCF LCA?
MO STUDY
PHYSICS LETTERS
OF THE HOH..
1 March 1973
.C1- HYDROGEN
BOND
Lucjan PIELA* Centre Europe’e;l dt Calcul Atomfque et Molhclllarie, 91-Campus d’Orsay, France Received 13 November
1972
Ab initio SCF LCAO hi0 calculations for the [ HzO.. Cl] - complex have been performed. The energy of the linear hydrogen bond has been found to be.lower than the energy of the bifurcated one. The difference of the energies is about 3 kcai/mole. The calculated equilibrium distance between the oxygen and chlorine atoms equals 5.75 au. The’interaction energy of the chlorine anion and the rigid water molecule amounts to -19 kcal/mole. The optim.&tion of the OH bond length in the complex (linear hydrogen bond) leads to an interaction energy of -19.5 kcal/mole (the experimental value equals -13.1 kcal/mole). As a resuit of the hydrogen bond formation the OH bond length increases by 0.08 au.
The interaction ion-water molecule is of special interest in many problems of electrochemistry, solution structure, crystal structure and spectroscopy. In aqueous solutions and in crystals of hydrates the ion interacts with a great number of the water molecules. However, only a few of these molecules form the first shell having contact with the ion and interacting directly with it. The number of such molecules, the so-called coordination number, can be determined experimentally. However, the resu!t obtained depends very strongly on the experimental method used. It would be important to have certain information at least about the interaction of an ion with only one wa?cr molecule. In 1970 the interaction energies between the water molecule and various halogenic anions and aikali cations were determined experimentally by using the mass spectroscopy technique-[ 11. During the last two years many
theoreiicai ab initio calculations have been performed for the water molecule-halogenic
anion and the water mo!ecule-alkali cation systems. The complexes of the water molecuie with the lithh&cation [2-61, the sodium cation [.5] and the fluorine anion 12-41 have been investigated by using l
Correspondence to permanent address: Quantum Chemistry Labqratory; University of Warsaw, Warsaw 22, Pasteura 7, Pol&d:
the SCF LCAO MO method. In all cases gaussian-type functions have been chosen for the atomic orbitals. In the present paper the energy of the complex of the water molecule and the chlorine anion has been calculated by using the ab initio SCF LCAC MO method with Slater-type orbit&. In the calculations an almost double zeta basis set has been used to describe the orbitals for 28 electrons of the system. The interaction energy has been evaluated as the difference between the energy of the complex and the sum of the SCF energies of the water molecule and the Cl- ion. The calculations have been realized on an IBM 370/l 65 usins the Stevens program. The computation time for one point was equal to about 21 minutes. The atomic.orbitals used in the calculation for the water molecule are given in the first two columns of table 1. This is the double zeta basis set with the exception the inner shell single orbital Is0 of the oxygen atom. The exponents in the Slater-type orbit& have been chosen identical’to
those used in wavefunctipn
III of Aung et al. [?‘I. Our wavefunction for the water molecule is poorer than that of Aung et al., because the latter includes additionally 3d orbit& of the oxy gen atom. For the fixed basis set the geometry of the water molecule has been optimized. The lowest total cnerb is equal to-?5.9591-au and corresponds to an HOH, angle (Y: 108.6O and an OH bond,length e& = 1.842 :
.
.,
Volume 19, number 1
CHEMICAL PHYSICS LETTERS
Table 1 The basis of the Sfater-type
Table 2 The SCF energy )in au) c&the fH20..
atomic orbit&
Cl-
H2O
“-
orbital
exponent
orbital
exponent
1%
kl 2sci
ZPb IsH(i $1
7.65 1.74 2.9Q 1% 3.60 1.33
2si;‘I 3scl 3h 2Wl
*s’w(l
2.47
*ptr
xi.70a) 4.9261 6.9833 2.0091 3.3416 5.3574 9.5 670 1.6092 2.8587
2so 2sb 2po
,2)
3Wl 3Pi31 a; The exponent
cticulnted
I March 1973
derrote: the
distanct (in au)
the oxygen
alom
.C1]-cornpi&. Rx1
between the chIorine atom and
System kc1
H”O-H
/H. 0 ,w. : Ci-
. . .cl-
4.5
-535.168
5.0 5.25 5.5 5.75 6.0 6.5
-535.218 -535.227 Gj35.232 -535.233 -535.232 -
-
-535.226 -533.228 a) -535.226
a) The calcuhted energy minimum for the bifurcated hydrogen bond equals -5 35.228 GIUand corresponds to RQQ 6.01S.a~ (1 au = 0.529172 A).
frcm the Slater rules.
has been calculated from the familiar Slater rules. The calculated SCF energy of the chlorine anion equals -459.244 au. The basis set in the SCF calculations for the [HOH. . .Cl]- complex consists of the atomic orbit& previously used in the calculations for the separated systems. To obtaiti information about the geometry of the complex two series of calculations have been made. In the first series the anion was shifted along the line of one of the OH bonds (see fig. la). In the second series the position of the anion was changed along the bisector of the HOH angle (fig. lb). In both cases the optimal geometry of the isolated water mofecule has been assumed. The results are given in table 2. In the next type of calculation the geometry of the interacting water molecule was changed. For vardistance the Iength r1. of the ious values of the&t OH bond (fig. la) was varied to optimize the rl and &-i values. The results of the cdcufation are listed in tabIe 3. As one can see from table 2~thi: most stable structure of the water-chlorine anion complex corresponds to the linear hydrogen bond (fig. la) and not to the bifurcated one (fig.- 1b). This agrees with the results of. the CNDO/2 calculations [4] and with the ab initio investigation of the [I&O. :.F]-,compIex [2A] .,‘I% difference between the energies of the two ‘possible structures equals 3 kcallmole. The binding energy car: responding to the more stable s&u&e is equal to -’
orbital
au. The experiment gives Q = 104.5’ and Rnrl = 1.81 au [Sj. In the SCF calculations for the chlorine anion also an almost double zeta basis has been used. The basis for this ion is represented in the last two coIumns of table 1. The orbital exponents have been chosen according to Ciementi’s results 191 of the double zeta basis investigalion. The exponent of the single I scl “11
H
-‘“\b!L_ s---
\ ‘07 3
a
0
H
3
2-
‘1
.- __-_
--..-“..*
4
_
Cl
(3)
2
\
H,
(b)
Fig. 1. The geometry used in the calc~at~ons for the [H;O.. .\“l]- system. The angle a: = 108.6’. Distances in au. ..,
‘. ..
,I
.’
‘,
.., ..‘,
.
.
.’
:
.-
13s
Volume
19, number
CHEMICAL Pi-iYSICS LETTERS
1
Table 3 The SCF energy
(in au) for the [HzO..
Xl]- complex as a
function of the OH bond length rI (fig. la) and theROCl distance. Distances in au (1 &I = 0.5 29 172 A) ROCl
5.0 5.25 5.5 5.75 6.0
r1 1.842”)
1.942
2.042
-535.218 -535.227 -535.232
-535.218 -535.228 -535.233
-535.214 -535.225 -535.230
-535.233 -535.2?.2
-535.234b) -535.233
-535.231 -535.230
a) The value corresponding to the isolated water molecule. b, The interpolated minimum energy position (parabolic interpoiation) corresponds to r, = 1.92 au and Rml = 5.75 au.
about -19 kcal/mole and the equilibrium distance is R WI = 5.75 au. The variation of both Rocl and the bond length r1 of one of the OH bonds (table 3) does not change the optimum value of the &, distance. The r1 value corresponding to the energy minimum is equal to 1.92 au. This means that as a consequence of the hydrogen bond forrna?ion the OH bond length becomes greater-by OKI au. The binding energy corresponding to the optimized I&1 and r1 values equals -19.5 kcal,/mole. The comparison with the interaction energies calculated for the complexes of Li’, Na+and F- with the water’molecule [2-61 shows that the [H20.. Cl]- complex has the smallest binding energy. -Also the experiment [l] leads to the same conclusion. The experimental interaction energy for the complex _
1 March
1973
equals -13.1 k&/mole. The CND0/2 calculations [4] give --23.5 kcal/mole. All these results show that the interaction energy between the chlorine anion and the water molecule is much greater than the interaction energy of two warer molecules which is equal to -4.84 kcal/mole, as calculated by Diercksen [IO]. As a consequence, in aqueous solutions many of the water-water hydrogen bonds should be broken and new hydrogen bonds with Cl- anions should be created. The author is very much indebted to Professor C. Moser for the possibility of staying at CECAM and for many helpful discussions.
Rezerences
[II
VI [31 I41 I51 161 [7] [8]
I. DiidiEand
P. Kebarle, J. Phys. Chem. 74 (1970) 1466,1477. G.H.F. Diercksen and W.P. Kraemer, Chem. Phys. Letters 5 (19’10) 570. P. Schuster and H.-W. Preuss, Chem. Phys. Letters 11 (197 1) 35. K.G. Breitschwerdt and H. Kistenmacher, Chem. Phys. Letters 14 (1972) 288. G.H.F. Diercksen and W.P. Kraemer, Theoret. Chim. Acta 23 (1972) 387. E. Clementi and H. Popkie, J. Chem. Phys. 57 (1972) 1077. S. Aung, R.M. Pitzer and S.1. Chan, J. Chem. Phys. 49 (1968) 2071. L.E. Sutton,ed.,.Spec. Pub). No. 18 (Chcm. Sot., London, 1965). E. Clementi, J. Chem. Phys. 40 (1964) 1944.
191 [IO] G.H.F.
Diercksen,
Chem.
Phys.
Let:ers
4 (1969)
373.
19, number 1
CtiEMICAL
AB l-NIT10 SCF LCA?
MO STUDY
PHYSICS LETTERS
OF THE HOH..
1 March 1973
.C1- HYDROGEN
BOND
Lucjan PIELA* Centre Europe’e;l dt Calcul Atomfque et Molhclllarie, 91-Campus d’Orsay, France Received 13 November
1972
Ab initio SCF LCAO hi0 calculations for the [ HzO.. Cl] - complex have been performed. The energy of the linear hydrogen bond has been found to be.lower than the energy of the bifurcated one. The difference of the energies is about 3 kcai/mole. The calculated equilibrium distance between the oxygen and chlorine atoms equals 5.75 au. The’interaction energy of the chlorine anion and the rigid water molecule amounts to -19 kcal/mole. The optim.&tion of the OH bond length in the complex (linear hydrogen bond) leads to an interaction energy of -19.5 kcal/mole (the experimental value equals -13.1 kcal/mole). As a resuit of the hydrogen bond formation the OH bond length increases by 0.08 au.
The interaction ion-water molecule is of special interest in many problems of electrochemistry, solution structure, crystal structure and spectroscopy. In aqueous solutions and in crystals of hydrates the ion interacts with a great number of the water molecules. However, only a few of these molecules form the first shell having contact with the ion and interacting directly with it. The number of such molecules, the so-called coordination number, can be determined experimentally. However, the resu!t obtained depends very strongly on the experimental method used. It would be important to have certain information at least about the interaction of an ion with only one wa?cr molecule. In 1970 the interaction energies between the water molecule and various halogenic anions and aikali cations were determined experimentally by using the mass spectroscopy technique-[ 11. During the last two years many
theoreiicai ab initio calculations have been performed for the water molecule-halogenic
anion and the water mo!ecule-alkali cation systems. The complexes of the water molecuie with the lithh&cation [2-61, the sodium cation [.5] and the fluorine anion 12-41 have been investigated by using l
Correspondence to permanent address: Quantum Chemistry Labqratory; University of Warsaw, Warsaw 22, Pasteura 7, Pol&d:
the SCF LCAO MO method. In all cases gaussian-type functions have been chosen for the atomic orbitals. In the present paper the energy of the complex of the water molecule and the chlorine anion has been calculated by using the ab initio SCF LCAC MO method with Slater-type orbit&. In the calculations an almost double zeta basis set has been used to describe the orbitals for 28 electrons of the system. The interaction energy has been evaluated as the difference between the energy of the complex and the sum of the SCF energies of the water molecule and the Cl- ion. The calculations have been realized on an IBM 370/l 65 usins the Stevens program. The computation time for one point was equal to about 21 minutes. The atomic.orbitals used in the calculation for the water molecule are given in the first two columns of table 1. This is the double zeta basis set with the exception the inner shell single orbital Is0 of the oxygen atom. The exponents in the Slater-type orbit& have been chosen identical’to
those used in wavefunctipn
III of Aung et al. [?‘I. Our wavefunction for the water molecule is poorer than that of Aung et al., because the latter includes additionally 3d orbit& of the oxy gen atom. For the fixed basis set the geometry of the water molecule has been optimized. The lowest total cnerb is equal to-?5.9591-au and corresponds to an HOH, angle (Y: 108.6O and an OH bond,length e& = 1.842 :
.
.,
Volume 19, number 1
CHEMICAL PHYSICS LETTERS
Table 1 The basis of the Sfater-type
Table 2 The SCF energy )in au) c&the fH20..
atomic orbit&
Cl-
H2O
“-
orbital
exponent
orbital
exponent
1%
kl 2sci
ZPb IsH(i $1
7.65 1.74 2.9Q 1% 3.60 1.33
2si;‘I 3scl 3h 2Wl
*s’w(l
2.47
*ptr
xi.70a) 4.9261 6.9833 2.0091 3.3416 5.3574 9.5 670 1.6092 2.8587
2so 2sb 2po
,2)
3Wl 3Pi31 a; The exponent
cticulnted
I March 1973
derrote: the
distanct (in au)
the oxygen
alom
.C1]-cornpi&. Rx1
between the chIorine atom and
System kc1
H”O-H
/H. 0 ,w. : Ci-
. . .cl-
4.5
-535.168
5.0 5.25 5.5 5.75 6.0 6.5
-535.218 -535.227 Gj35.232 -535.233 -535.232 -
-
-535.226 -533.228 a) -535.226
a) The calcuhted energy minimum for the bifurcated hydrogen bond equals -5 35.228 GIUand corresponds to RQQ 6.01S.a~ (1 au = 0.529172 A).
frcm the Slater rules.
has been calculated from the familiar Slater rules. The calculated SCF energy of the chlorine anion equals -459.244 au. The basis set in the SCF calculations for the [HOH. . .Cl]- complex consists of the atomic orbit& previously used in the calculations for the separated systems. To obtaiti information about the geometry of the complex two series of calculations have been made. In the first series the anion was shifted along the line of one of the OH bonds (see fig. la). In the second series the position of the anion was changed along the bisector of the HOH angle (fig. lb). In both cases the optimal geometry of the isolated water mofecule has been assumed. The results are given in table 2. In the next type of calculation the geometry of the interacting water molecule was changed. For vardistance the Iength r1. of the ious values of the&t OH bond (fig. la) was varied to optimize the rl and &-i values. The results of the cdcufation are listed in tabIe 3. As one can see from table 2~thi: most stable structure of the water-chlorine anion complex corresponds to the linear hydrogen bond (fig. la) and not to the bifurcated one (fig.- 1b). This agrees with the results of. the CNDO/2 calculations [4] and with the ab initio investigation of the [I&O. :.F]-,compIex [2A] .,‘I% difference between the energies of the two ‘possible structures equals 3 kcallmole. The binding energy car: responding to the more stable s&u&e is equal to -’
orbital
au. The experiment gives Q = 104.5’ and Rnrl = 1.81 au [Sj. In the SCF calculations for the chlorine anion also an almost double zeta basis has been used. The basis for this ion is represented in the last two coIumns of table 1. The orbital exponents have been chosen according to Ciementi’s results 191 of the double zeta basis investigalion. The exponent of the single I scl “11
H
-‘“\b!L_ s---
\ ‘07 3
a
0
H
3
2-
‘1
.- __-_
--..-“..*
4
_
Cl
(3)
2
\
H,
(b)
Fig. 1. The geometry used in the calc~at~ons for the [H;O.. .\“l]- system. The angle a: = 108.6’. Distances in au. ..,
‘. ..
,I
.’
‘,
.., ..‘,
.
.
.’
:
.-
13s
Volume
19, number
CHEMICAL Pi-iYSICS LETTERS
1
Table 3 The SCF energy
(in au) for the [HzO..
Xl]- complex as a
function of the OH bond length rI (fig. la) and theROCl distance. Distances in au (1 &I = 0.5 29 172 A) ROCl
5.0 5.25 5.5 5.75 6.0
r1 1.842”)
1.942
2.042
-535.218 -535.227 -535.232
-535.218 -535.228 -535.233
-535.214 -535.225 -535.230
-535.233 -535.2?.2
-535.234b) -535.233
-535.231 -535.230
a) The value corresponding to the isolated water molecule. b, The interpolated minimum energy position (parabolic interpoiation) corresponds to r, = 1.92 au and Rml = 5.75 au.
about -19 kcal/mole and the equilibrium distance is R WI = 5.75 au. The variation of both Rocl and the bond length r1 of one of the OH bonds (table 3) does not change the optimum value of the &, distance. The r1 value corresponding to the energy minimum is equal to 1.92 au. This means that as a consequence of the hydrogen bond forrna?ion the OH bond length becomes greater-by OKI au. The binding energy corresponding to the optimized I&1 and r1 values equals -19.5 kcal,/mole. The comparison with the interaction energies calculated for the complexes of Li’, Na+and F- with the water’molecule [2-61 shows that the [H20.. Cl]- complex has the smallest binding energy. -Also the experiment [l] leads to the same conclusion. The experimental interaction energy for the complex _
1 March
1973
equals -13.1 k&/mole. The CND0/2 calculations [4] give --23.5 kcal/mole. All these results show that the interaction energy between the chlorine anion and the water molecule is much greater than the interaction energy of two warer molecules which is equal to -4.84 kcal/mole, as calculated by Diercksen [IO]. As a consequence, in aqueous solutions many of the water-water hydrogen bonds should be broken and new hydrogen bonds with Cl- anions should be created. The author is very much indebted to Professor C. Moser for the possibility of staying at CECAM and for many helpful discussions.
Rezerences
[II
VI [31 I41 I51 161 [7] [8]
I. DiidiEand
P. Kebarle, J. Phys. Chem. 74 (1970) 1466,1477. G.H.F. Diercksen and W.P. Kraemer, Chem. Phys. Letters 5 (19’10) 570. P. Schuster and H.-W. Preuss, Chem. Phys. Letters 11 (197 1) 35. K.G. Breitschwerdt and H. Kistenmacher, Chem. Phys. Letters 14 (1972) 288. G.H.F. Diercksen and W.P. Kraemer, Theoret. Chim. Acta 23 (1972) 387. E. Clementi and H. Popkie, J. Chem. Phys. 57 (1972) 1077. S. Aung, R.M. Pitzer and S.1. Chan, J. Chem. Phys. 49 (1968) 2071. L.E. Sutton,ed.,.Spec. Pub). No. 18 (Chcm. Sot., London, 1965). E. Clementi, J. Chem. Phys. 40 (1964) 1944.
191 [IO] G.H.F.
Diercksen,
Chem.
Phys.
Let:ers
4 (1969)
373.