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Ionic Solvation in formic acid, MO SCF calculations on solvated univalent ions
15 June 1973
CHEMICAL PHYSICS LETTERS
Volume 20, number 3
IONIC
SOLVATION
MO SCF CALCULATIONS
IN FORMIC
ON SQLVATED
ACID. UNIVALENT
IONS
Bernd M. RODE lnstitut fi;r A norganische md A nalytische khemie der Universitiit Innsbruck, Austria Received 9 Apri! 1973
CND0/2 calculations have been performed for the mono-, di- and tetra-solvates of Li+, Na+ and Cl- with formic acid. The most stable position for the cations is found to bc between the CH hydrogen and carbonyl osygen, confirming similar concblsions from esperimentsl results. The calculated changes in electron densities agree well with observations in ’ H-NMR spectra. Calculated solvation energies are found to S~XWthe right relative order for the cations,although absolute values are too high. For the anion, also the absolute value is in reasonable agreement with esperiment. CNDO minimum geometries, charge distributions and bond indices are given for all solvates and discussed in respect to possible mcthodical errcrs.
1. Introduction
some cation-ligand distances come out too high, and an artifici$ly increased charge transfer is observed, a
1.1. Experimental background
qualitative agreement with ab initio reslults can be found in most details. Recent studies on the interaction of formaldehyde and the Li+ ion by both, ab initio and semi-empirical methods [7] prove the artificial charge transfer in CNDO/2 calculations to result from the neglect of inner-shell electrons. It could be shown, however, the polarization of the ligand, as obtained by CNDOI2, as being essentially the same as that resulting from ab initio calculations, Thus, the qualitative features of change in eleclron density of the ligand caused by the ion are described correctly. This was of special interest for a comparison with chemical shifts observed in nuclear magnetic resonance spectra. These studies were further intended to yield satisfactory quantum chemical information supporting a qualitative discussion of the structure and energy situation of the solvates under investigation. The calculations were carried out with the CDC computer of the University of Innsbruck, using QCPE” program 141 in a modified version, computing autc-
IH-NMR investigations of solutions of alkali chlorides in anhydrous formic acid showed a remarkable downfield shift of the CH-proton signal when compared to the pure solvent, obviously due to solvation
effects
[I].
This observation
can be ex-
plairled assuming the cation to take up a position quite close to the CH-hydrbgen, leading thus to the observed decrease of electron density at this atom. The calcuIations reported here, were intended to confirm this assumption by means of quantum chemical treatment. I.2. Methodical aspects MO SCF methods have been applied successfully to several solvation problems [Z-7]. Ab initio calculations, however, are only suitable for smaller systems, i.e.,‘solvates with very few and small solvent molecules since they require very high computing times. As to semi-empirical calculations, the CND0/2
method [&lo] has proved to give qualitatively similar results [2,3, 5, 71. Although energies and 3’66
* Quantum Chemistry Program Exchange, Bloomington, diana, USA.
In-
Volume 20, number 4
CHEMICAL PHYSICS LETTERS
H
0
Li’
.,._..... H- c
/
Li* \
15June1973
a-c
/ ‘0
O-H
H’
Ia)
(b)
H ‘c -0
L? o/
Lie
‘H
(cl
(d)
Fig. 1. Basic possibilities for formic acid during salvation. matically geometrical energy. Parametrization
values [8-lo]
&O \ H
the
approach
parameters
of a cation to
for lowest
total
has been kept at the original
.
2. Results and discussion 2.1. Cations 2.1. I. Position of the cation
For the determination of the most probable position of the cation in relation to the solvent molecule, calculations were performed simulating the approach of Li+ and Na’ to one HCOOH molecule. The CNDO minimum geometry of formic acid (‘H-C = 1.115 a, rczo = 1.260 A, rc_o = 1.342 A, rO_H = 1.029 A, all bond angles kept at 120”) was not varied during this procedure. For a rough estimation of the energetically most favoured situation, four basic possibilities were investigated, as is illustrated in fig. 1, a-d. The lowest energy minimum was obtained for the approach Ic, followed by the values for an approach in H-C-, O=C-, and O-C-directions, respectively. This indicates the cation to favour the neighbourhood of the CH hydrogen as to be expected from the results of the IH-NMR measurements. On the other hand, the carbonyl oxygen proves to enable a more effective bonding to the cation than the carboxyl oxygen. In terms of popular figurative considerations, this could be explained by a greater polarizability of in electrons compared with lone-pair electrons. Good shapes for the energy curves were obtained
Fig. 2. Energy curves for the approach of the Lit ation formic acid according to the directions given in fig. I.
to
for all types of approach, as can be seen in fig. 2 (for Lif) and fig. 3 (for Na+). For both ions nearIy identicaI pictures result. It should be remembered, however, that CNDO geometries for solvated cations can turn out incorrect in respect to the angular dependence of the energy minimum, predicting pyramidal arrangements to be more stable than planar ones [3,4, 1 i]. TZs could be shown to be a general methodical artefact of CND0/2 by comparison to ab initio results [3,4, 111. For this reason, planar arrangement was maintained throughout our calculations. 2.1.2. Minimum geornem’es ofthe solvates For the monosolvates of Lif and Na+, CNDO minimum geometries were calculated varying ali bond lengths except the O-H distance. The distance of the cation to the carbon atom has been denoted x, its vertical distance to the C-O axis asy, positive in the 367
Volume 20, number 4
CHEMICkL PHYSICS LETTERS
15 June 1973
energies per solvent molecule for the different solvates. 2.1.4. Charge densities Within the solvate, a considerable charge transfer seems to take place from formic acid towards the cation (see table 3). As mentioned above, this is partly a result oi the approximations of the CNDO method, however, the polarization of the solvent molecule due to this interaction with the cation, can be expected to be qualitatively correct. Compared to the free HCOOH molecule, charge densities on all atoms are found to decrease more or less. Only the densities of carbonyl oxygen, CH hydrogen and carbon are listed in table 3, as these atoms are closest to the cation and will be affected directly. Most interesting is the decrease of the electron density on the hydrogen atom, which corresponds very well with the observed downfield shifts in the NhlR.
Fig. 3. Energy curves for the approach of the NaC cation to formic acid according to the directions given in fig. 1.
direction towards the CH hydrogen. For di- and tetrasolvates (linear and tetrahedral configuration), the same geometry as for the corresponding monosolvates was retained, except for tire value of x (Me+... C dis-
tance). The geometrical parameters are listed in table 1. Bond angles were again kept at 120” in agreement with former quantum chemical investigations of formic acid [ 12-141. 2.1.3. Stabilizationenergies The absolute values for the stabilization energies are definitely too high, as is to be expected for positively charged molecules. Their relative order with increasing solvation number, however, agrees with similar calculations on hydrated ions [3,5]. The ratio of rhe calculated solvation energies for Li+ and Na+ is found to be I .25 for the tetra-solvates, in fairly good agreement with the corresponding experimental value of 1.17 [ 15 J . Table 2 lists the values for stabilization 361
2.1.5. Boifd indices The peculiar situation of the cation in the solvates is of special interest in regard to the bonding between the ion and the solvent molecules. The Wiberg bond index [ 16 J has proved to be successfully applicable to such problems [l I, 171, Our results lead to the fairly surprising picture, showing bonding of the cation to the CH hydrogen, as well as to the carbonyl oxygen and carbon (see table 4). The bond order for the interaction cation-solvent molecule, given by the sum of these three indices decreases with increasing solvation number, yet amounts to a considerable value of 1.6 for both tetra-solvates. A critical study of these results by means of ab
initio methods is in preparation. In any case, however, the existence of some bonding between cation and CH hydrogen seems to fit well the facts obtained by other investigations.
Calculations have been performed only for the Clanion, since the corresponding experimental work was carried ou’t with alkali chlorides [ 11. The position of the anion was assumed to be in the O-H-direction forming a hydrogen bond. Hydrogen bonded systems can be treated well by CND0/2 cai-
culations, as could be proved by numerous studies
Volume 20, number 4
1.5June 1973
CHEhIICAL PHYSICS LETTJZRS
Table 1 Minimum bond lengths (in A) for cationic solvates (n = salvation number) end total energy (in au) -~ Ion
n
‘C=O
‘H-C
‘C-O
‘0-H
a)
X
Y
TotaL energy
b-0
Li+
1 2 4
1.150 1.150 1.150
1.281 1.281 1.281
1.330 1.330 1.330
1.029 1.029 1.029
2.412 2.413 2.577
0.492 0.492 0.492
-45.48609 -90.96713 -181.83482
Naf
1 2 4
1.136 1.136 1.136
1.275 1.275 1.275
1.333 1.333 1.333
:.029 i.029 1.029
3.047 3.030 3.050
0.4&5 0.485 0.485
-45.43359 -90.86662 -1SL.72463
a) Parameter not varied.
Table 2 Calculated solvation energies per solvent molecule @E/n) and experimental ionic solvation energies (kcal mole-‘) (n =
Table 5 Calculated solvation energies and Wiberg bond indices for solvates of CI- (!I = solvation number)
solvation number) Li+
Na’
1 2 4
103.1 101.1
70.5 70.3
86.4
69.0
esp. [ 151
116.0
99.5
Table 3 Charge densities on CH hydrogen, carbonyl oxygen, carbon and cation qH
40
4C
qhfe
HCOOH Li(HCOOH)+
1.006 0.946
6.297 6.225
3.631 3.561
0.330
Li(HCOOH)i Li(HCOOH)i
0.935 0.950
6.226 6.254
3.559 3.575
0.650 0.933
Na(HCOOH)+
0.969
6.254
3.578
0.229
Na(HCOOH);
0.962
6.250
3.578
0.464
Na(HCOOH$
0.956
6.245
3.579
0.906
Table 4 Wiberg bond indices Bi for cationic solvntes (n = salvation numbor)
Ion
tI
BJMe-H
BIMe-O
B’hle-C
c BI/rz
Li+
1 2 4
0.144 0.142 0.114
0.242 0.228 0.131
0.213 0.211 0.162
0.599 0.581 0.407
Na+
1 2 4
0.087 0.088 0.088
0.19s 0.199 0.186
0.145 0.147 0.146
0.430 0.433 0.420
n
filn (kcal mole-*)
B1CI-H
BJO-H
Z Bl/R
1
38.3 33.0 25 .o
0.237 0.181 0.123
0.660 0.713 0.783
0.897 0.894 0.906
2 4
[ 12- 14, 17- 191. Since, on the other hand, CNDO energies for negatively charged systems are often in reasonable agreement with experimental v&es [ 181,
application of this method for the investigation of the solvated Cl- promised to represent a good example for quantum chemical treatment of such probIe.ms. Again the geometry of the monosolvate (with linear 0-H...CI bond) was varied to CNDO minimum values for all bond lengths (angles were kept at 120” as before). For the di- and tetra-solvated anion, only the Cl...H distance was varied with respect to lowest total energy. The minimum bond lengths which were obtained from the mono-solvate are (in A): ‘H-C = 1.123, rczo = 1.268, rc_o = 1,328 xtd T~_~ = 1.085. The O-H distance is considerably enlarged quite similar to systems with strong hydrogen bonds [ 17, 181. The H...Cl distance was found to be 1.635 ,& for the monoand di-solvate and 1.70 1 a for the (tetrahedral) tetrasolvate. Stabilization energies and bond indices are listed in table 5. As mentioned before these enerw values should not be compared directly with the results obttied
369
Volume 20, number’4
CHEMICALPHYSICS LElTERS
for cations because of methodical artefacts. The comparison with the experimentally determined value of solvation energy for Cl- of 78.3 kcal mole-’ [ 151, however, is quite satisfactory. Remembering that energy values calculated for such species usually do not exceed experimental valises for more than 10-X%, we can estimate the average number of solvent molecules in the first sphere of the so!vate. It turns out to be between two and three. This fits quite well with general ideas about the solvation of anions in so!vents like formic acid. With increasing number cf solvent molecules the bonding between hydrogen and chlorine weakens. At the same time, however, this decrease is co-npensated for by reinforcement of the bonding to the oxygen, thereby keeping the bond order of the whole hydrogen bond system rather constant (see bond indices, table 5). The calculated charge distributions show the anionic electron density to remain more or less concentrated at the chlorine atom (7.690 in the tetra-solvate) and a slight decrease of negative charge on all the other atoms except the bridge-hydrogen. Although this charge transfer may be overrated again, this methodical artefzct is expected to be smaller than for cations
because of the assignment of sufficient basis functions to chlorine and their occupation with electrons, which can bo polarized. From
the methodical
point
of view,
the results
re-
ported here seem to prove the CND0/2 method to be
successfully applicable for quantum chemical treatment of solvation phenomena in formic acid and, to yield supplementary information confirming experimental results.
Acknowledgement
I consider it a pieasant duty to acknowledge the great stimulation and help for this work which I owe
1.5 June 1973
to the personal contact with Doz. Dr. P. Schuster, Institut fiir Theoretische Chemie, University of Vienna, and freely supplied information about his own results
prior to publication. I am also very indebted to the “Rechenzentrum” of the University of Innsbruck for the generous supply with computer time.
References [ l] B.M. Rode, Z. Anorg. Aug. Chem., to be published.
[ 21 P. Schuster and H.W. Preuss, Chem. Phys. Letters 11 (1971) 35. [3] P. Rusregger, H. Lischka and P. Schuster, Theoret. Chtn. Acta 24 (1972) 191. [4] H. Lischka, Th. Plesser and P. Schuster, Chem. Phys. Letters 6 (1970) 263. [5] K.G. Breitschwerdt and H. Kistenmacher, Chem. Phys. Letters 14 (1972) 285. [6] G.H.F. Diercksen and W.P. Kraemer, Chem. Phys. Letters 5 (1970) 570. I71 P. Russegger and P. Schuster, Chem. Phys. Letters 19 (1973) 2.54. [81 J.A. Pople, D.P. Santry and G.A. Segal, J. Chem. Phys. 43 (1965) 129. 191 J.A. Pople and G.A. Segal, J. Chem. Phys. 43 (1965) 136. ilol J.A. Pople and G.A. Segal, J. Chem. Phys. 44 (1966) 3289. P. Russcgger.
Thesis,
Univ.
Vicnm
(1972).
P. Schuster, Intern. J. Quantum Chem. 3 (1969) 851. P. Schuster and Th. Funck, Chem. Phys. Letters 2
(1968) 587. [I41 B.hl. Rode and A. Engelbrecht, Monatsh. Chem., to be published. 1151 G.P. Kotlyarova and E.F. Ivanova, Zh. Fiz. Khim. 40 (1966) 997. 1161K.W. Wiberg,Tetrahcdron 24 (1968) 1083. and W. Jakubetz, Chem. 1171 B.M. Rode, A. Engeibrecht Phys. Letters 18 (1973) 285. 1181 P. Schuster, Theoret. Chim. Acta 19 (1970) 212. [I91 P.A. Kollmann and L.C. Allen, J. Am. Chem. Sot. 92 (1970) 753.
CHEMICAL PHYSICS LETTERS
Volume 20, number 3
IONIC
SOLVATION
MO SCF CALCULATIONS
IN FORMIC
ON SQLVATED
ACID. UNIVALENT
IONS
Bernd M. RODE lnstitut fi;r A norganische md A nalytische khemie der Universitiit Innsbruck, Austria Received 9 Apri! 1973
CND0/2 calculations have been performed for the mono-, di- and tetra-solvates of Li+, Na+ and Cl- with formic acid. The most stable position for the cations is found to bc between the CH hydrogen and carbonyl osygen, confirming similar concblsions from esperimentsl results. The calculated changes in electron densities agree well with observations in ’ H-NMR spectra. Calculated solvation energies are found to S~XWthe right relative order for the cations,although absolute values are too high. For the anion, also the absolute value is in reasonable agreement with esperiment. CNDO minimum geometries, charge distributions and bond indices are given for all solvates and discussed in respect to possible mcthodical errcrs.
1. Introduction
some cation-ligand distances come out too high, and an artifici$ly increased charge transfer is observed, a
1.1. Experimental background
qualitative agreement with ab initio reslults can be found in most details. Recent studies on the interaction of formaldehyde and the Li+ ion by both, ab initio and semi-empirical methods [7] prove the artificial charge transfer in CNDO/2 calculations to result from the neglect of inner-shell electrons. It could be shown, however, the polarization of the ligand, as obtained by CNDOI2, as being essentially the same as that resulting from ab initio calculations, Thus, the qualitative features of change in eleclron density of the ligand caused by the ion are described correctly. This was of special interest for a comparison with chemical shifts observed in nuclear magnetic resonance spectra. These studies were further intended to yield satisfactory quantum chemical information supporting a qualitative discussion of the structure and energy situation of the solvates under investigation. The calculations were carried out with the CDC computer of the University of Innsbruck, using QCPE” program 141 in a modified version, computing autc-
IH-NMR investigations of solutions of alkali chlorides in anhydrous formic acid showed a remarkable downfield shift of the CH-proton signal when compared to the pure solvent, obviously due to solvation
effects
[I].
This observation
can be ex-
plairled assuming the cation to take up a position quite close to the CH-hydrbgen, leading thus to the observed decrease of electron density at this atom. The calcuIations reported here, were intended to confirm this assumption by means of quantum chemical treatment. I.2. Methodical aspects MO SCF methods have been applied successfully to several solvation problems [Z-7]. Ab initio calculations, however, are only suitable for smaller systems, i.e.,‘solvates with very few and small solvent molecules since they require very high computing times. As to semi-empirical calculations, the CND0/2
method [&lo] has proved to give qualitatively similar results [2,3, 5, 71. Although energies and 3’66
* Quantum Chemistry Program Exchange, Bloomington, diana, USA.
In-
Volume 20, number 4
CHEMICAL PHYSICS LETTERS
H
0
Li’
.,._..... H- c
/
Li* \
15June1973
a-c
/ ‘0
O-H
H’
Ia)
(b)
H ‘c -0
L? o/
Lie
‘H
(cl
(d)
Fig. 1. Basic possibilities for formic acid during salvation. matically geometrical energy. Parametrization
values [8-lo]
&O \ H
the
approach
parameters
of a cation to
for lowest
total
has been kept at the original
.
2. Results and discussion 2.1. Cations 2.1. I. Position of the cation
For the determination of the most probable position of the cation in relation to the solvent molecule, calculations were performed simulating the approach of Li+ and Na’ to one HCOOH molecule. The CNDO minimum geometry of formic acid (‘H-C = 1.115 a, rczo = 1.260 A, rc_o = 1.342 A, rO_H = 1.029 A, all bond angles kept at 120”) was not varied during this procedure. For a rough estimation of the energetically most favoured situation, four basic possibilities were investigated, as is illustrated in fig. 1, a-d. The lowest energy minimum was obtained for the approach Ic, followed by the values for an approach in H-C-, O=C-, and O-C-directions, respectively. This indicates the cation to favour the neighbourhood of the CH hydrogen as to be expected from the results of the IH-NMR measurements. On the other hand, the carbonyl oxygen proves to enable a more effective bonding to the cation than the carboxyl oxygen. In terms of popular figurative considerations, this could be explained by a greater polarizability of in electrons compared with lone-pair electrons. Good shapes for the energy curves were obtained
Fig. 2. Energy curves for the approach of the Lit ation formic acid according to the directions given in fig. I.
to
for all types of approach, as can be seen in fig. 2 (for Lif) and fig. 3 (for Na+). For both ions nearIy identicaI pictures result. It should be remembered, however, that CNDO geometries for solvated cations can turn out incorrect in respect to the angular dependence of the energy minimum, predicting pyramidal arrangements to be more stable than planar ones [3,4, 1 i]. TZs could be shown to be a general methodical artefact of CND0/2 by comparison to ab initio results [3,4, 111. For this reason, planar arrangement was maintained throughout our calculations. 2.1.2. Minimum geornem’es ofthe solvates For the monosolvates of Lif and Na+, CNDO minimum geometries were calculated varying ali bond lengths except the O-H distance. The distance of the cation to the carbon atom has been denoted x, its vertical distance to the C-O axis asy, positive in the 367
Volume 20, number 4
CHEMICkL PHYSICS LETTERS
15 June 1973
energies per solvent molecule for the different solvates. 2.1.4. Charge densities Within the solvate, a considerable charge transfer seems to take place from formic acid towards the cation (see table 3). As mentioned above, this is partly a result oi the approximations of the CNDO method, however, the polarization of the solvent molecule due to this interaction with the cation, can be expected to be qualitatively correct. Compared to the free HCOOH molecule, charge densities on all atoms are found to decrease more or less. Only the densities of carbonyl oxygen, CH hydrogen and carbon are listed in table 3, as these atoms are closest to the cation and will be affected directly. Most interesting is the decrease of the electron density on the hydrogen atom, which corresponds very well with the observed downfield shifts in the NhlR.
Fig. 3. Energy curves for the approach of the NaC cation to formic acid according to the directions given in fig. 1.
direction towards the CH hydrogen. For di- and tetrasolvates (linear and tetrahedral configuration), the same geometry as for the corresponding monosolvates was retained, except for tire value of x (Me+... C dis-
tance). The geometrical parameters are listed in table 1. Bond angles were again kept at 120” in agreement with former quantum chemical investigations of formic acid [ 12-141. 2.1.3. Stabilizationenergies The absolute values for the stabilization energies are definitely too high, as is to be expected for positively charged molecules. Their relative order with increasing solvation number, however, agrees with similar calculations on hydrated ions [3,5]. The ratio of rhe calculated solvation energies for Li+ and Na+ is found to be I .25 for the tetra-solvates, in fairly good agreement with the corresponding experimental value of 1.17 [ 15 J . Table 2 lists the values for stabilization 361
2.1.5. Boifd indices The peculiar situation of the cation in the solvates is of special interest in regard to the bonding between the ion and the solvent molecules. The Wiberg bond index [ 16 J has proved to be successfully applicable to such problems [l I, 171, Our results lead to the fairly surprising picture, showing bonding of the cation to the CH hydrogen, as well as to the carbonyl oxygen and carbon (see table 4). The bond order for the interaction cation-solvent molecule, given by the sum of these three indices decreases with increasing solvation number, yet amounts to a considerable value of 1.6 for both tetra-solvates. A critical study of these results by means of ab
initio methods is in preparation. In any case, however, the existence of some bonding between cation and CH hydrogen seems to fit well the facts obtained by other investigations.
Calculations have been performed only for the Clanion, since the corresponding experimental work was carried ou’t with alkali chlorides [ 11. The position of the anion was assumed to be in the O-H-direction forming a hydrogen bond. Hydrogen bonded systems can be treated well by CND0/2 cai-
culations, as could be proved by numerous studies
Volume 20, number 4
1.5June 1973
CHEhIICAL PHYSICS LETTJZRS
Table 1 Minimum bond lengths (in A) for cationic solvates (n = salvation number) end total energy (in au) -~ Ion
n
‘C=O
‘H-C
‘C-O
‘0-H
a)
X
Y
TotaL energy
b-0
Li+
1 2 4
1.150 1.150 1.150
1.281 1.281 1.281
1.330 1.330 1.330
1.029 1.029 1.029
2.412 2.413 2.577
0.492 0.492 0.492
-45.48609 -90.96713 -181.83482
Naf
1 2 4
1.136 1.136 1.136
1.275 1.275 1.275
1.333 1.333 1.333
:.029 i.029 1.029
3.047 3.030 3.050
0.4&5 0.485 0.485
-45.43359 -90.86662 -1SL.72463
a) Parameter not varied.
Table 2 Calculated solvation energies per solvent molecule @E/n) and experimental ionic solvation energies (kcal mole-‘) (n =
Table 5 Calculated solvation energies and Wiberg bond indices for solvates of CI- (!I = solvation number)
solvation number) Li+
Na’
1 2 4
103.1 101.1
70.5 70.3
86.4
69.0
esp. [ 151
116.0
99.5
Table 3 Charge densities on CH hydrogen, carbonyl oxygen, carbon and cation qH
40
4C
qhfe
HCOOH Li(HCOOH)+
1.006 0.946
6.297 6.225
3.631 3.561
0.330
Li(HCOOH)i Li(HCOOH)i
0.935 0.950
6.226 6.254
3.559 3.575
0.650 0.933
Na(HCOOH)+
0.969
6.254
3.578
0.229
Na(HCOOH);
0.962
6.250
3.578
0.464
Na(HCOOH$
0.956
6.245
3.579
0.906
Table 4 Wiberg bond indices Bi for cationic solvntes (n = salvation numbor)
Ion
tI
BJMe-H
BIMe-O
B’hle-C
c BI/rz
Li+
1 2 4
0.144 0.142 0.114
0.242 0.228 0.131
0.213 0.211 0.162
0.599 0.581 0.407
Na+
1 2 4
0.087 0.088 0.088
0.19s 0.199 0.186
0.145 0.147 0.146
0.430 0.433 0.420
n
filn (kcal mole-*)
B1CI-H
BJO-H
Z Bl/R
1
38.3 33.0 25 .o
0.237 0.181 0.123
0.660 0.713 0.783
0.897 0.894 0.906
2 4
[ 12- 14, 17- 191. Since, on the other hand, CNDO energies for negatively charged systems are often in reasonable agreement with experimental v&es [ 181,
application of this method for the investigation of the solvated Cl- promised to represent a good example for quantum chemical treatment of such probIe.ms. Again the geometry of the monosolvate (with linear 0-H...CI bond) was varied to CNDO minimum values for all bond lengths (angles were kept at 120” as before). For the di- and tetra-solvated anion, only the Cl...H distance was varied with respect to lowest total energy. The minimum bond lengths which were obtained from the mono-solvate are (in A): ‘H-C = 1.123, rczo = 1.268, rc_o = 1,328 xtd T~_~ = 1.085. The O-H distance is considerably enlarged quite similar to systems with strong hydrogen bonds [ 17, 181. The H...Cl distance was found to be 1.635 ,& for the monoand di-solvate and 1.70 1 a for the (tetrahedral) tetrasolvate. Stabilization energies and bond indices are listed in table 5. As mentioned before these enerw values should not be compared directly with the results obttied
369
Volume 20, number’4
CHEMICALPHYSICS LElTERS
for cations because of methodical artefacts. The comparison with the experimentally determined value of solvation energy for Cl- of 78.3 kcal mole-’ [ 151, however, is quite satisfactory. Remembering that energy values calculated for such species usually do not exceed experimental valises for more than 10-X%, we can estimate the average number of solvent molecules in the first sphere of the so!vate. It turns out to be between two and three. This fits quite well with general ideas about the solvation of anions in so!vents like formic acid. With increasing number cf solvent molecules the bonding between hydrogen and chlorine weakens. At the same time, however, this decrease is co-npensated for by reinforcement of the bonding to the oxygen, thereby keeping the bond order of the whole hydrogen bond system rather constant (see bond indices, table 5). The calculated charge distributions show the anionic electron density to remain more or less concentrated at the chlorine atom (7.690 in the tetra-solvate) and a slight decrease of negative charge on all the other atoms except the bridge-hydrogen. Although this charge transfer may be overrated again, this methodical artefzct is expected to be smaller than for cations
because of the assignment of sufficient basis functions to chlorine and their occupation with electrons, which can bo polarized. From
the methodical
point
of view,
the results
re-
ported here seem to prove the CND0/2 method to be
successfully applicable for quantum chemical treatment of solvation phenomena in formic acid and, to yield supplementary information confirming experimental results.
Acknowledgement
I consider it a pieasant duty to acknowledge the great stimulation and help for this work which I owe
1.5 June 1973
to the personal contact with Doz. Dr. P. Schuster, Institut fiir Theoretische Chemie, University of Vienna, and freely supplied information about his own results
prior to publication. I am also very indebted to the “Rechenzentrum” of the University of Innsbruck for the generous supply with computer time.
References [ l] B.M. Rode, Z. Anorg. Aug. Chem., to be published.
[ 21 P. Schuster and H.W. Preuss, Chem. Phys. Letters 11 (1971) 35. [3] P. Rusregger, H. Lischka and P. Schuster, Theoret. Chtn. Acta 24 (1972) 191. [4] H. Lischka, Th. Plesser and P. Schuster, Chem. Phys. Letters 6 (1970) 263. [5] K.G. Breitschwerdt and H. Kistenmacher, Chem. Phys. Letters 14 (1972) 285. [6] G.H.F. Diercksen and W.P. Kraemer, Chem. Phys. Letters 5 (1970) 570. I71 P. Russegger and P. Schuster, Chem. Phys. Letters 19 (1973) 2.54. [81 J.A. Pople, D.P. Santry and G.A. Segal, J. Chem. Phys. 43 (1965) 129. 191 J.A. Pople and G.A. Segal, J. Chem. Phys. 43 (1965) 136. ilol J.A. Pople and G.A. Segal, J. Chem. Phys. 44 (1966) 3289. P. Russcgger.
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(1968) 587. [I41 B.hl. Rode and A. Engelbrecht, Monatsh. Chem., to be published. 1151 G.P. Kotlyarova and E.F. Ivanova, Zh. Fiz. Khim. 40 (1966) 997. 1161K.W. Wiberg,Tetrahcdron 24 (1968) 1083. and W. Jakubetz, Chem. 1171 B.M. Rode, A. Engeibrecht Phys. Letters 18 (1973) 285. 1181 P. Schuster, Theoret. Chim. Acta 19 (1970) 212. [I91 P.A. Kollmann and L.C. Allen, J. Am. Chem. Sot. 92 (1970) 753.