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Monte Carlo simulation of 1,2-dichloroethane in dilute benzene solution
345
Journal of Molecular Structure (Theochem), 181 (1988) 345-352 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
MONTE CARLO SIMULATION OF 1,2-DICHLOROETHANE DILUTE BENZENE SOLUTION
IN
PERE ALEMANY and EUDALD VILASECA* Departament de Quimica Fkica, Facultat de Quimica, Universitat de Barcelona, C/Marti i Franqub, 1,08028-Barcelona (Spain) (Received 17 August 1987)
ABSTRACT A Monte Carlo simulation of 1,2-dichloroethane in dilute benzene solution was carried out in order to investigate the “benzene effect” on the mean dipole moment of this solute. An appreciable conformational change was observed in the 1,2-dichloroethane molecule when it was introduced into liquid benzene.
INTRODUCTION
The values obtained in the measurement of the dipole moment of 1,2-dichloroethane in dilute solution in non-polar solvents are rather different from those observed in the vapor phase (Table 1). The difference is more substantial in the case of benzene solutions. The so-called “benzene effect” has been the object of several studies [ 1,4-61, the main conclusion of which is that no stable solute-solvent complexes are formed in the dissolution [5]. There is TABLE 1 Measured dipole moments of 1,2-dichloroethane in different solvents [l] and in vapor phase [ 2,3]. The dissolution values are measured at 20” C. The vapor phase values correspond to 32 and 35°C respectively Solvent
Dipole moment (in debye)
Cyclohexane Carbon tetrachloride p-Xylene Benzene
1.43,1.46 1.47,1.38,1.56 1.68,1.63,1.58 1.82,1.78, 1.85
Vapor
1.12,1.18
*To whom correspondence should be addressed.
0166-1280/88/$03.50
0 1988 EIsevier Science Publishers B.V.
346
also experimental evidence that the C-Cl bond dipole moment is not appreciably increased in liquid benzene. It seems, then, that the 1,2dichloroethane molecule is forced by the solvent to change its conformational equilibrium by increasing the population of the gauche conformations (with greater dipole moment) and decreasing the population of the non-polar tram conformation. A Monte Carlo simulation of this dilute solution may give more information on that solvent effect and a preliminary calculation is presented here. POTENTIAL
FUNCTIONS
Benzene-benzene
interactions
The potential model used consisted of six Lennard-Jones (12,6) interaction sites on each molecule situated on the CH groups at a distance B from the center of the ring. The interaction energy between two solvent molecules was given by the expression
(1) with t/k= 77 K, a=3.5 A and B= 1.756 A. These parameter values were obtained by Evans and Watts in a previous MC simulation of liquid benzene [ 71. 1,2-Dichloroethane-benzene
interactions
In the solute molecule four Lennard-Jones+electrostatic (12,6,1) interaction sites were defined, two of them in the chlorine atoms and the others in the CH, groups. In the benzene molecules six Lennard-Jones (12,6) interaction sites, situated on the CH groups, and 18 electrostatic interaction sites were defined. A positive charge, q, was situated on each CH group and two -0.5 q net charges were situated in the middle of each C-C bond at 0.6328 A up and down the molecular plane [8]. Thus, the potential function for the solute-
TABLE 2 Potential parameters corresponding to the solute-solvent -‘kmCHI &H-C, CCH-CHz &H-C,
9n9se2
419058.9 kcal Al2 mol-’ 380101.9 kcal 2’ mol-’ 71.257 kcal A6 mol-’ 85.065 kcal A6 mol-’ 10.38 kcal A mol-’
potential function
347
solvent interaction was VSD =
A, -iiT-
rij
c,
rt
1
(2)
The potential parameters (Table 2) were obtained by fitting the potential function to the energy values found for a great number of dimer configurations by using the semiempirical MNDO method of Dewar et al. [ 91. Internal rotation potential The following expression was used ~(8)=~~,(~+COS8)+~~2(~-cOs~~)+~~~(~+cos~6)
(3)
with the parameter values V, = 1.933, V2= - 0.333 and V,= 2.567 kcal mol-l, as used by Jorgensen in the simulation of pure liquid 1,2dichloroethane [lo]. SIMULATION CONDITIONS
The Monte Carlo simulation was carried out at 298 K with a sample of benzene and 1,2-dichloroethane (124: 1). The system was kept in a cube with an edge of 27.217 A according to the benzene density (0.0062 Am3) at this temperature. Periodic boundary conditions were employed by embedding the cube in an infinite net of cubes with identical composition and configuration. A preliminary set of 700 000 configurations was generated to bring the system from the unrealistic initial configuration to equilibrium. After this, 280 000 equilibrium configurations were generated. With them, the structural properties were computed. At each step, one molecule was selected at random and all its coordinates were randomly changed. The maximum displacement of its center of mass was 20.12 A on each axis direction, and its three Eulerian angles were modified within a +_22.0” range. The solute molecule was kept fixed at the center of the cube and only its rotational angle was modified. The maximum angular variation was 2 33.0’. These maximum values for the coordinate variations produced an acceptance rate of nearly 50% for both the new configurations of dissolution and the new conformations of solute. In order to accelerate the calculations, the molecule to be moved at each step was not selected completely randomly but higher preference was assigned to the solute and to its nearest solvent molecules. At each configuration a weighting value of l/ri2 was assigned to each molecule i, where ri is the distance from this molecule to the solute. The normalization of the weighting values yielded the probability of moving each molecule. The probability of modifying the internal coordinates of the solute was equated to the probability of moving its nearest solvent molecule. A potential cut-off radius of 12.0 A was used for the benzene-benzene inter-
348
actions. The solute potential was cut at a distance equal to half the edge of the simulation cube.
RESULTS AND DISCUSSION
Several solvent-solvent and solute-solvent radial distribution functions were computed during the simulations (Figs. 1 and 2).
(b)
Fig. 1. Benzene-benzene center of mass-center of mass (a), center of mass-site (c) radial distribution functions.
(b ) , and site-site
349
The benzene-benzene g(r) functions are similar to those obtained by Evans and Watts for the pure liquid [ 71. However, the shoulder they found at 4.2 A in the center of mass-center of mass g (r ) function has become a marked peak in the dissolution. This result means that the corresponding configuration (‘stacked’, with the molecular planes parallel and the interaction sites nearly coincident) is more favored in dissolution. The greater peak at 6.4 A corresponds to the center of mass distance of the dimer which has the two molecules with,perpendicular molecular planes. The benzene-benzene center of mass-site g(r) function shows a peak at about 5 A corresponding to the distances found in the more stable dimer oriGlRi
3.n
(a)
2.”
l.u
0.G
d 0.0
0.0 2.0
5.0
4.0 R/R
8.0
10.0
L.
0.0
2.0
4.0
6.0
E.0
10.0
R/R
Fig. 2.1,2-dichloroethane-benzene center of mass-center of mass (a), Cl-center of mass (b), and Cl-site (c) radial distribution functions.
350
entation (with the molecular planes placed perpendicularly). The shoulder around 4 A corresponds to the distances in the ‘stacked’ dimer. The benzene-benzene site-site g(r) function does not give any information since the great number (36) of site-site distances for each pair of molecules smooths out its profile. The center of mass solute-solvent radial distribution function (Fig. 2) shows a peak around 5.5 A which corresponds to the first solvation shell. The analysis N. MBL.
N. M0L.
3.0
1.0
(a)
(b)
I
2.0
0.5
1.0
0.0
-J -4.0
-2.0
0.0
0.0
2.0
f
/
4
-0.2
0.0
ENERGY IKCRL/MBLI
ENERGY
Fig. 3. Distribution of the benzene-benzene energies. rRiI”“ENLr 11.067 (a)
0.2
0.4 IKCRL/MBL
0.6 I
(a) and 1,2-dichloroethane-benzene
(b) interaction
FEirOUENCY
-1
il.“0
r
--
(bl
Fig. 4. Distribution of the internal rotation angle of 1,2-dichloroethane dilute benzene solution.
in (a) vapor phase, (b)
351
of the solute-solvent potential function indicates that the more favorable interactions occur when the benzene molecule approaches the solute with the CH groups between the two centers of mass. The minimum appears around 5.5 A and small differences are observed for different approach directions. The special packing mode of the benzene molecule, due to its planar form, can be seen as the reason for the short distance (8.5 A) at which the second peak is found in the center of mass solute-solvent g(r) function. A benzene molecule with its molecular plane perpendicular to a first shell molecule has its center of mass at about 8.4 A from the center of the solute. The solute-solvent chlorine-center of mass g(r) function shows two broad maxima that correspond to the distances from the chlorines to the two types of solvating molecules described above. On the other hand, no information can be obtained from the chlorine-site radial distribution function. The benzene-benzene energy distribution function (Fig. 3) shows a peak at -1.0 kcal mol-l which confirms the idea of Evans and Watts [7] that the liquid benzene adopts a structure that resembles that of the crystalline solid. A smooth variation of the distribution function would indicate a less structured disposition of the solvent molecules. The solute-solvent energy distribution function (Fig. 3) has no marked peak (apart from the 0.0 kcal mol-’ one), which indicates that there is no specially preferred solute-solvent interaction in the dissolution, and thus, there is no formation of a stable solute-solvent complex. The analysis of the solute rotational angle distribution (Fig. 4) indicates that the 1,2-dichloroethane in benzene dissolution shows a conformational equilibrium very different from that in the vapor phase. The gauche populations are increased while a diminution of the tram population is observed. This implies an increase of the mean dipole moment. The dipole moment of a given conformation of 1,2-dichloroethane can be expressed as the resultant of the sum of the two CH, group dipoles. The decomposition of each group dipole into two components, axial and normal to the molecular axis, indicates that the global dipole depends only on the relative orientation of the normal components. Thus, if & is the normal component of each CH, group dipole and 0, the angle the two normal components form in the conformation i, the square dipole moment, p: of the molecule for this conformation is
,U~=2V?12(1+COS8i) Performing
the conformational
(p2)=2m2(1+(cose))
(4) average (5)
352
The potential function for the internal rotation of 1,2-dichloroethane (eqn. (3) ) yields a value of (cos 19) = - 0.06607 for this molecule at 25 “C. This result and the global dipole, 1.1 D [l], found for 1,2-dichloroethane in vapor phase at this temperature yield a normal component of CH, group dipole moment of 1.34 D. The new angular distribution obtained for 1,2-dichloroethane in benzene solution (Fig. 4) yields (cos 0) = -0.1225. The inclusion in eqn. (5) of this value and the value of m found for the free molecule yield a root mean square dipole moment of 1.77 D. This result is quite reasonable when compared with those measured in dissolution (Table 1) . Although, at the current state of these calculations, we do not have enough results to present conclusive affirmations, we think that this conformational change is due, to a great extent, to a steric solvent influence rather than to particular electrostatic interactions. The gauche conformations may be favored by an entropic effect and because its higher dipole moment is more stabilized by the surrounding dielectric medium. More studies on this problem are still in progress. ACKNOWLEDGEMENTS
We are very grateful to the Centre d’Informatica celona for the use of their computational sources.
de la Universitat
de Bar-
REFERENCES 1 2 3 4 5 6 7 8 9 10
N. Shiratori, H. Takahashi and K. Higasi, Bull. Chem. Sot. Jpn., 48 (1975) 1423. R.A. Oriani and C.P. Smyth, J. Chem. Phys., 17 (1949) 1174. K. Kveseth, Acta Chem. Stand. Ser. A, 32 (1978) 51. N. Oi and J.F. Coetzee, J. Am. Chem. Sot., 91 (1969) 2478. 0. Kiyohara and K. Arakawa, Bull. Chem. Sot. Jpn., 43 (1970) 3037. A. Morita, H. Takahashi and K. Higasi, Bull. Chem. Sot. Jpn., 45 (1972) 1045. D.J. Evans and R.O. Watts, Mol. Phys., 31 (1976) 83; 32 (1976) 93. R.A. Nemenoff, J. Snir and H. Scheraga, J. Phys. Chem., 82 (1978) 2513. M.J.S. Dewar and W. Thiel, J. Am. Chem. Sot., 99 (1977) 4899,4907; M.J.S. Dewar and H.S. Rzepa, J. Comput. Chem., 4 (1983) 158. W.L. Jorgensen, J. Am. Chem. Sot., 103 (1981) 677.
Journal of Molecular Structure (Theochem), 181 (1988) 345-352 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
MONTE CARLO SIMULATION OF 1,2-DICHLOROETHANE DILUTE BENZENE SOLUTION
IN
PERE ALEMANY and EUDALD VILASECA* Departament de Quimica Fkica, Facultat de Quimica, Universitat de Barcelona, C/Marti i Franqub, 1,08028-Barcelona (Spain) (Received 17 August 1987)
ABSTRACT A Monte Carlo simulation of 1,2-dichloroethane in dilute benzene solution was carried out in order to investigate the “benzene effect” on the mean dipole moment of this solute. An appreciable conformational change was observed in the 1,2-dichloroethane molecule when it was introduced into liquid benzene.
INTRODUCTION
The values obtained in the measurement of the dipole moment of 1,2-dichloroethane in dilute solution in non-polar solvents are rather different from those observed in the vapor phase (Table 1). The difference is more substantial in the case of benzene solutions. The so-called “benzene effect” has been the object of several studies [ 1,4-61, the main conclusion of which is that no stable solute-solvent complexes are formed in the dissolution [5]. There is TABLE 1 Measured dipole moments of 1,2-dichloroethane in different solvents [l] and in vapor phase [ 2,3]. The dissolution values are measured at 20” C. The vapor phase values correspond to 32 and 35°C respectively Solvent
Dipole moment (in debye)
Cyclohexane Carbon tetrachloride p-Xylene Benzene
1.43,1.46 1.47,1.38,1.56 1.68,1.63,1.58 1.82,1.78, 1.85
Vapor
1.12,1.18
*To whom correspondence should be addressed.
0166-1280/88/$03.50
0 1988 EIsevier Science Publishers B.V.
346
also experimental evidence that the C-Cl bond dipole moment is not appreciably increased in liquid benzene. It seems, then, that the 1,2dichloroethane molecule is forced by the solvent to change its conformational equilibrium by increasing the population of the gauche conformations (with greater dipole moment) and decreasing the population of the non-polar tram conformation. A Monte Carlo simulation of this dilute solution may give more information on that solvent effect and a preliminary calculation is presented here. POTENTIAL
FUNCTIONS
Benzene-benzene
interactions
The potential model used consisted of six Lennard-Jones (12,6) interaction sites on each molecule situated on the CH groups at a distance B from the center of the ring. The interaction energy between two solvent molecules was given by the expression
(1) with t/k= 77 K, a=3.5 A and B= 1.756 A. These parameter values were obtained by Evans and Watts in a previous MC simulation of liquid benzene [ 71. 1,2-Dichloroethane-benzene
interactions
In the solute molecule four Lennard-Jones+electrostatic (12,6,1) interaction sites were defined, two of them in the chlorine atoms and the others in the CH, groups. In the benzene molecules six Lennard-Jones (12,6) interaction sites, situated on the CH groups, and 18 electrostatic interaction sites were defined. A positive charge, q, was situated on each CH group and two -0.5 q net charges were situated in the middle of each C-C bond at 0.6328 A up and down the molecular plane [8]. Thus, the potential function for the solute-
TABLE 2 Potential parameters corresponding to the solute-solvent -‘kmCHI &H-C, CCH-CHz &H-C,
9n9se2
419058.9 kcal Al2 mol-’ 380101.9 kcal 2’ mol-’ 71.257 kcal A6 mol-’ 85.065 kcal A6 mol-’ 10.38 kcal A mol-’
potential function
347
solvent interaction was VSD =
A, -iiT-
rij
c,
rt
1
(2)
The potential parameters (Table 2) were obtained by fitting the potential function to the energy values found for a great number of dimer configurations by using the semiempirical MNDO method of Dewar et al. [ 91. Internal rotation potential The following expression was used ~(8)=~~,(~+COS8)+~~2(~-cOs~~)+~~~(~+cos~6)
(3)
with the parameter values V, = 1.933, V2= - 0.333 and V,= 2.567 kcal mol-l, as used by Jorgensen in the simulation of pure liquid 1,2dichloroethane [lo]. SIMULATION CONDITIONS
The Monte Carlo simulation was carried out at 298 K with a sample of benzene and 1,2-dichloroethane (124: 1). The system was kept in a cube with an edge of 27.217 A according to the benzene density (0.0062 Am3) at this temperature. Periodic boundary conditions were employed by embedding the cube in an infinite net of cubes with identical composition and configuration. A preliminary set of 700 000 configurations was generated to bring the system from the unrealistic initial configuration to equilibrium. After this, 280 000 equilibrium configurations were generated. With them, the structural properties were computed. At each step, one molecule was selected at random and all its coordinates were randomly changed. The maximum displacement of its center of mass was 20.12 A on each axis direction, and its three Eulerian angles were modified within a +_22.0” range. The solute molecule was kept fixed at the center of the cube and only its rotational angle was modified. The maximum angular variation was 2 33.0’. These maximum values for the coordinate variations produced an acceptance rate of nearly 50% for both the new configurations of dissolution and the new conformations of solute. In order to accelerate the calculations, the molecule to be moved at each step was not selected completely randomly but higher preference was assigned to the solute and to its nearest solvent molecules. At each configuration a weighting value of l/ri2 was assigned to each molecule i, where ri is the distance from this molecule to the solute. The normalization of the weighting values yielded the probability of moving each molecule. The probability of modifying the internal coordinates of the solute was equated to the probability of moving its nearest solvent molecule. A potential cut-off radius of 12.0 A was used for the benzene-benzene inter-
348
actions. The solute potential was cut at a distance equal to half the edge of the simulation cube.
RESULTS AND DISCUSSION
Several solvent-solvent and solute-solvent radial distribution functions were computed during the simulations (Figs. 1 and 2).
(b)
Fig. 1. Benzene-benzene center of mass-center of mass (a), center of mass-site (c) radial distribution functions.
(b ) , and site-site
349
The benzene-benzene g(r) functions are similar to those obtained by Evans and Watts for the pure liquid [ 71. However, the shoulder they found at 4.2 A in the center of mass-center of mass g (r ) function has become a marked peak in the dissolution. This result means that the corresponding configuration (‘stacked’, with the molecular planes parallel and the interaction sites nearly coincident) is more favored in dissolution. The greater peak at 6.4 A corresponds to the center of mass distance of the dimer which has the two molecules with,perpendicular molecular planes. The benzene-benzene center of mass-site g(r) function shows a peak at about 5 A corresponding to the distances found in the more stable dimer oriGlRi
3.n
(a)
2.”
l.u
0.G
d 0.0
0.0 2.0
5.0
4.0 R/R
8.0
10.0
L.
0.0
2.0
4.0
6.0
E.0
10.0
R/R
Fig. 2.1,2-dichloroethane-benzene center of mass-center of mass (a), Cl-center of mass (b), and Cl-site (c) radial distribution functions.
350
entation (with the molecular planes placed perpendicularly). The shoulder around 4 A corresponds to the distances in the ‘stacked’ dimer. The benzene-benzene site-site g(r) function does not give any information since the great number (36) of site-site distances for each pair of molecules smooths out its profile. The center of mass solute-solvent radial distribution function (Fig. 2) shows a peak around 5.5 A which corresponds to the first solvation shell. The analysis N. MBL.
N. M0L.
3.0
1.0
(a)
(b)
I
2.0
0.5
1.0
0.0
-J -4.0
-2.0
0.0
0.0
2.0
f
/
4
-0.2
0.0
ENERGY IKCRL/MBLI
ENERGY
Fig. 3. Distribution of the benzene-benzene energies. rRiI”“ENLr 11.067 (a)
0.2
0.4 IKCRL/MBL
0.6 I
(a) and 1,2-dichloroethane-benzene
(b) interaction
FEirOUENCY
-1
il.“0
r
--
(bl
Fig. 4. Distribution of the internal rotation angle of 1,2-dichloroethane dilute benzene solution.
in (a) vapor phase, (b)
351
of the solute-solvent potential function indicates that the more favorable interactions occur when the benzene molecule approaches the solute with the CH groups between the two centers of mass. The minimum appears around 5.5 A and small differences are observed for different approach directions. The special packing mode of the benzene molecule, due to its planar form, can be seen as the reason for the short distance (8.5 A) at which the second peak is found in the center of mass solute-solvent g(r) function. A benzene molecule with its molecular plane perpendicular to a first shell molecule has its center of mass at about 8.4 A from the center of the solute. The solute-solvent chlorine-center of mass g(r) function shows two broad maxima that correspond to the distances from the chlorines to the two types of solvating molecules described above. On the other hand, no information can be obtained from the chlorine-site radial distribution function. The benzene-benzene energy distribution function (Fig. 3) shows a peak at -1.0 kcal mol-l which confirms the idea of Evans and Watts [7] that the liquid benzene adopts a structure that resembles that of the crystalline solid. A smooth variation of the distribution function would indicate a less structured disposition of the solvent molecules. The solute-solvent energy distribution function (Fig. 3) has no marked peak (apart from the 0.0 kcal mol-’ one), which indicates that there is no specially preferred solute-solvent interaction in the dissolution, and thus, there is no formation of a stable solute-solvent complex. The analysis of the solute rotational angle distribution (Fig. 4) indicates that the 1,2-dichloroethane in benzene dissolution shows a conformational equilibrium very different from that in the vapor phase. The gauche populations are increased while a diminution of the tram population is observed. This implies an increase of the mean dipole moment. The dipole moment of a given conformation of 1,2-dichloroethane can be expressed as the resultant of the sum of the two CH, group dipoles. The decomposition of each group dipole into two components, axial and normal to the molecular axis, indicates that the global dipole depends only on the relative orientation of the normal components. Thus, if & is the normal component of each CH, group dipole and 0, the angle the two normal components form in the conformation i, the square dipole moment, p: of the molecule for this conformation is
,U~=2V?12(1+COS8i) Performing
the conformational
(p2)=2m2(1+(cose))
(4) average (5)
352
The potential function for the internal rotation of 1,2-dichloroethane (eqn. (3) ) yields a value of (cos 19) = - 0.06607 for this molecule at 25 “C. This result and the global dipole, 1.1 D [l], found for 1,2-dichloroethane in vapor phase at this temperature yield a normal component of CH, group dipole moment of 1.34 D. The new angular distribution obtained for 1,2-dichloroethane in benzene solution (Fig. 4) yields (cos 0) = -0.1225. The inclusion in eqn. (5) of this value and the value of m found for the free molecule yield a root mean square dipole moment of 1.77 D. This result is quite reasonable when compared with those measured in dissolution (Table 1) . Although, at the current state of these calculations, we do not have enough results to present conclusive affirmations, we think that this conformational change is due, to a great extent, to a steric solvent influence rather than to particular electrostatic interactions. The gauche conformations may be favored by an entropic effect and because its higher dipole moment is more stabilized by the surrounding dielectric medium. More studies on this problem are still in progress. ACKNOWLEDGEMENTS
We are very grateful to the Centre d’Informatica celona for the use of their computational sources.
de la Universitat
de Bar-
REFERENCES 1 2 3 4 5 6 7 8 9 10
N. Shiratori, H. Takahashi and K. Higasi, Bull. Chem. Sot. Jpn., 48 (1975) 1423. R.A. Oriani and C.P. Smyth, J. Chem. Phys., 17 (1949) 1174. K. Kveseth, Acta Chem. Stand. Ser. A, 32 (1978) 51. N. Oi and J.F. Coetzee, J. Am. Chem. Sot., 91 (1969) 2478. 0. Kiyohara and K. Arakawa, Bull. Chem. Sot. Jpn., 43 (1970) 3037. A. Morita, H. Takahashi and K. Higasi, Bull. Chem. Sot. Jpn., 45 (1972) 1045. D.J. Evans and R.O. Watts, Mol. Phys., 31 (1976) 83; 32 (1976) 93. R.A. Nemenoff, J. Snir and H. Scheraga, J. Phys. Chem., 82 (1978) 2513. M.J.S. Dewar and W. Thiel, J. Am. Chem. Sot., 99 (1977) 4899,4907; M.J.S. Dewar and H.S. Rzepa, J. Comput. Chem., 4 (1983) 158. W.L. Jorgensen, J. Am. Chem. Sot., 103 (1981) 677.