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Intermolecular interaction energies between trimethylamine and benzene calculated using an ab initio SCF CI approximation
Volume 145. number 6
CHEMICAL PHYSICS LETTERS
22 April 1988
INTERMOLECULAR INTERACTION ENERGIES BETWEEN TRIMETHYLAMINE AND BENZENE CALCULATED USING AN AB INITIO SCF CI APPROXIMATION
Arnold MALJNIAK a and Gunnar KARLSTR~M b aArrheniusLaboratory,Universityof Stockholm,S-106 91 Stockholm.Sweden ’ TheoreticalChemistry,ChemicalCenter,P.O.B. 1.24,S-221 00 Lund, Sweden Received 8 February 1988
Approximate SCFCI interaction energies have been calculated for a system consisting of trimethylamine and benzene. The total interaction energy is decomposed into contributions which have a physical interpretation.
1. Introduction
Considerable progress has been made in the nonempirical quantum-mechanical calculation of intermolecular energies. This progress was partly due to advances in the field of high-speed computers, but also to developments in the theory of intermolecular forces. Strong interest in computer simulations, using both Monte Carlo (MC) and molecular dynamics (MD) methods, has increased the demand for good intermolecular potentials and therefore for more detailed descriptions of intermolecular interactions. An accurate computation of the energy between two weakly interacting systems constitutes a difficult task, since such calculations must necessarily be done with large basis sets and include the computation of the dispersion energy. High-quality ab initio calculations including dispersion energy are still restricted to small and medium-size molecules [ 1-3 1. There are a number of methods for estimating the dispersion energy without explicit configuration interaction (CI) calculations, such as second-order perturbation methods [ 4-6 ] and semi-empirical treatments [ 7,8 1, Intermolecular potentials for benzene-water and benzene-benzene have previously been calculated by Karlstriim et al. [ 9 J using a SCF CI approximation. In this communication we use the same method for calculating the interaction energy between trimethylamine and benzene. One of us has studied intermolecular interactions
between quinuclidine or I-azabicyclo [ 2.2.21 octane and several solvents [ 10,111 using the nuclear spin relaxation technique, utilizing the anisotropy in the dynamics of the quinuclidine molecule as a measure of intermolecular interactions with the solvent. The anisotropy in benzene was somewhat higher than in cyclohexane, indicating a stronger association or probably preferential solvation of quinuclidine by benzene. Here we use trimethylamine as a model for quinuclidine, assuming that only the polar part of quinuclidine is of importance in determining the solvent structure in a benzene solution of quinuclidine.
2. Computational details The computational strategy followed here to calculate the interaction energy between trimethylamine and benzene is exactly that previously used for the benzene-benzene and benzene-water systems [ 9 ] and the reader is referred to this work for a full description. Only the underlying ideas will be discussed here. In order to be able to obtain reliable estimates of the total interaction energy, two problems must be solved: the first is to obtain a high-quality estimate of the interaction at the Hartree-Fock (HF) level of approximation, and the second is to obtain a dispersion correction to this interaction. The total interaction energy at the HF level can be partitioned
0 009-2614/88/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division J
537
Volume 145, number 6
CHEMICAL
PHYSICS LETTERS
into five different contributions [ 12,131, ~SCF =&.+E,ND
+-Em +&T
-+&xx,
(1)
where Ens is the electrostatic interaction, EIND the electrostatic induction term, EEX the exchange repulsion, EcT the charge transfer term and EMlx the contribution from the coupling of the different terms. If the interaction energy AEscF is corrected for basis set superposition error (BSSE) [ 141 then one may formally write (2) We define EBssEusing the Boys-Bernardi counterpoise correction [ 14 1. E ~~~E=EA(A)+E~(B)-EA(A~B)-E~(A+B).
(3) Here, the index defines the system (molecule) and the variable in parentheses defines the basis set used in the calculation. With the above definition of the BSSE it has been shown that the quantity within parentheses in eq. ( 2 ) is fairly independent of basis set [ 15 1. Consequently, for a given basis set, one wishes to estimate the first two terms in eq. (1) or (2) independently. These terms, obtained with a small basis set used in the SCF calculations, could be replaced with the corresponding terms obtained using a larger basis set. Such a method, based on a multicentre multiple expansion of the charge distributors, has previously been described by one of us [ 15 ] and is used here. The method used to obtain reliable estimates of the dispersion energy has also previously been described and is based on a second-order Meller-Plesset approach where the integrals have been approximated using a multicentre multipole expansion of the two-electron integrals [ 161. The total interaction energy may thus be written AEToT=&c~+&ssEf
t&S
+&ND
(EES )largebasisset
+EmD
+EDISP*
)amalltmisset
(4)
The main advantage of this method is that the estimates of electrostatic and induction energies are based on multicentre multipole expansions of the charge distribution [ 15] and the polarizability tensor [ 17 ] and require minimum computer time. 538
22 April 1988
The large basis set was the same as that previously used for benzene in the benzene-benzene potential, i.e. a 9s5p basis contracted to 4s2p [ 181 and augmented with one diffuse s function (exp= 0.05 for C and 0.07 for N), one diffuse p function (exp= 0.04 for C and 0.05 for N) and one d function for C and N (exp=0.8). For hydrogen, a 5s basis was contracted to 2s and augmented with one diffuse s function (exp=0.4). The minimal basis set used in the calculations consisted of 7s and 3p primitive functions on nitrogen and carbon contracted to 2s and lp, respectively
t 191. The corresponding set for hydrogen consisted of 3s functions contracted to one single function [ 20 1. This is the same basis set as previously used for the benzene dimer. The geometries of the monomers were held fixed and for benzene: rcc= 1.395 A and rcH = 1.0836 A. The geometry of trimethylamine was the same as for the corresponding moiety in quinuclidine obtained from electron diffraction [ 2 11.
3. Results and discussion Two molecular orientations were considered, see fig. 1. Orientation I refers to the case where the C, axis of trimethylamine coincides with the C, axis of benzene and one of the N-C bonds is in the same plane as a C, axis of benzene going through two hy drogens, the methyl groups point toward benzene. In orientation II, the C’, axis of trimethylamine coincides with the C2 axis of benzene, with the nitrogen lone pair pointing toward a benzene hydrogen. One of the N-C bonds is in the same plane as the C, axis of benzene. We have also calculated a few energies using an orientation similar to I, but with the nitrogen lone pair pointing toward the benzene ring; this orientation was entirely repulsive at the SCF level. In table 1, the contribution from the different basis sets, the corrections and the total interaction energy are given as a function of the intermolecular separation for the two molecules. Firstly, it should be noted that the dispersion contribution is not compensated by EBssEfor any intermolecular distance and orientation; such an accidental compensation has previously been reported [22,23] in some systems. The dispersion energy is an almost equal and clearly
Volume 145, number 6
22 April 1988
CHEMICAL PHYSICS LETTERS
tally zero, whereas the correction in II is significant, which can be understood as an effect of the large difference in the molecular polarizability, along the different axes in benzene [ 93. The electrostatic energy in both basis sets is significant, especially in orientation II, which is more comparable to a hydrogen bond structure, where electrostatic interactions are of major importance. However, the electrostatic correction for orientation II is small, implying that a minimal basis gives a relatively good description of electrostatic interactions for this geometry. The total interaction energy is about 40% larger for the orientation in which trimethylamine participates in hydrogen bond with the benzene proton. The energy of this interaction may be compared with some typical hydrogen-bonded systems such as ammonia/water (-26.2 kJ/mol) [24] or water/water (-25.2 kJ/mol) [ 251, keeping in mind that benzene is a very poor proton donor (pK,=37). The water-benzene interactions [9] show an opposite trend, the most stable orientation being the one where the symmetry axis of water and the C, axis of benzene coincide, and the hydrogens point toward the benzene ring. This difference is caused by the high positive charge density on the water protons, whereas the CH3 protons are almost uncharged.
Fig. 1.The orientations of the interacting molecules.
dominating contribution for both orientations, which is expected in a weakly interacting system. The induction energy correction in orientation I is practiTable 1 Interaction energies (in kJ/mol) between trimethylamine and benzene. The two orientations are described in the text
orientation 4.23 4.50 4.76 5.03 5.29 5.82
1 9.4 2.5 -0.3 -1.3 -1.5 -1.2
4.1 2.7 1.5 0.8 0.4 0.1
7.6 6.0 4.8 3.9 3.1 2.1
9.2 1.3 5.9 4.8 3.9 2.6
-1.6 -1.3 -1.1 -0.9 -0.7 -0.5
0.2 0.1 0.1 0.1 0.1 0.0
0.0 0.1 0.1 0.1 0.1 0.0
0.0 0.0 0.0 0.0 0.0 -0.0
-16.5 - 12.0 -9.0 -6.6 -4.9 -2.6
-4.1 -8.2 -8.8 -8.0 -6.1 -4.3
orientation 4.25 4.76 5.03 5.29 5.82 6.35
II 13.2 -5.6 -5.1 -4.0 -2.3 -1.3
7.7 3.5 2.1 1.1 0.2 0.0
16.6 6.6 4.6 3.2 1.8 1.1
18.8 7.2 4.8 3.3 1.8 1.0
-2.2 -0.5 -0.2 -0.1 0.0 0.1
2.1 0.6 0.3 0.2 0.1 0.0
5.3 1.4 0.7 0.5 0.2 0.0
-3.2 -0.8 -0.4 -0.3 -0.1 -0.0
-16.7 -9.0 -6.5 -4.8 -2.7 -1.6
- 1.2 - 12.4 - 10.2 -8.1 -4.8 -2.9
a) Quantity calculated with a small basis set.
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CHEMICAL PHYSICS LETTERS
References [ 1] G. Bolis, E. Clementi, D.H. Wertz, H.A. Scheraga and C. Tosi, J. Am. Chem. Sot. 105 (1983) 355. [2] 0. Matsuoka, E. Clementi and M. Yoshimine, J. Chem. Phys. 64 (1976) 1351. [3] PK. Swaminathan, A. Laaksonen, G. Corongiu and E. Clementi, J. Chem. Phys! 84 (1986) 867. [ 41 A. Meunier, B. Levy and G. Berthier, Theoret. Chim. Acta 29 (1973) 49. [ 5 ] W.A. Lathan, G.R. Pack and K. Morokuma, J. Am. Chem. See. 97 (1975) 6624. [6] E. Kochanski, J. Chem. Phys. 58 (1973) 5823. [7] W. Kofos, Theoret. Chim. 51 (1979) 219. [ 81 I. Hepburn, G. Stoles an%R. Pence, Chem. Phys. Letters 36 (1975) 451. [ 9 ] G. Karlstrom, P. Linse, A. Wallqvist and B. Jiinsson, J. Am. Chem. Sot. 105 (1983) 3777. [lo] A. Maliniak, J. Kowalewski and I. Panas, J. Phys. Chem. 88 (1984) 5628. [ II] A. Maliniak and J. Kowalewski, .I. Phys. Chem. 90 (1986) 6330.
540
22 April 1988
[ 121 K. Morokuma, J. Chem. Phys. 55 (1971) 1236. [ 131 P.A. Kollman and L.C. Allen, J. Chem. Phys. 52 (1970) 5085. [ 141 SF. Boys and B. Bernardi, Mol. Phys. 19 (1970) 558. [ 151 G. Karlstrom, Proceedings from the 5th Seminar on Computational Methods in Quantum Chemistry, Groningen (1981). [ 161 G. Karlstriim, Theoret. Chim. Acta 55 (1980) 233. [ 171 G. Karlstrijm, Theoret. Chim. Acta 60 (1982) 535. [ 181 T.H. Dunning Jr., J. Chem. Phys. 53 ( 1970) 2823. [ 191 B. Roos and P. Siegbahn, Theoret. Chim. Acta 17 (1970) 209. [20] S. Huzinaga, J. Chem. Phys. 42 (1965) 1293. [ 211 H. Schei, Q. Shen and R.L. Hilderbrandt, J. Mol. Struct. 65 (1980) 297. [22] A. Johansson, P. Kollman and S. Rothenberg, Theoret. Chim. Acta 29 (1973) 167. [23] A. Meukier, B. Levy and G. Berthier, Theoret. Chim. Acta 29 (1973) 49. [24] G.H.F. Diercksen, W.P. Kraemer and W. von Niessen, Theoret. Chim. Acta 28 (1972) 67, [ 251 G.H.F. Diercksen, W.P. Kraemer and B.O. Roos, Theoret. Chim. Acta 36 (1975) 249.
CHEMICAL PHYSICS LETTERS
22 April 1988
INTERMOLECULAR INTERACTION ENERGIES BETWEEN TRIMETHYLAMINE AND BENZENE CALCULATED USING AN AB INITIO SCF CI APPROXIMATION
Arnold MALJNIAK a and Gunnar KARLSTR~M b aArrheniusLaboratory,Universityof Stockholm,S-106 91 Stockholm.Sweden ’ TheoreticalChemistry,ChemicalCenter,P.O.B. 1.24,S-221 00 Lund, Sweden Received 8 February 1988
Approximate SCFCI interaction energies have been calculated for a system consisting of trimethylamine and benzene. The total interaction energy is decomposed into contributions which have a physical interpretation.
1. Introduction
Considerable progress has been made in the nonempirical quantum-mechanical calculation of intermolecular energies. This progress was partly due to advances in the field of high-speed computers, but also to developments in the theory of intermolecular forces. Strong interest in computer simulations, using both Monte Carlo (MC) and molecular dynamics (MD) methods, has increased the demand for good intermolecular potentials and therefore for more detailed descriptions of intermolecular interactions. An accurate computation of the energy between two weakly interacting systems constitutes a difficult task, since such calculations must necessarily be done with large basis sets and include the computation of the dispersion energy. High-quality ab initio calculations including dispersion energy are still restricted to small and medium-size molecules [ 1-3 1. There are a number of methods for estimating the dispersion energy without explicit configuration interaction (CI) calculations, such as second-order perturbation methods [ 4-6 ] and semi-empirical treatments [ 7,8 1, Intermolecular potentials for benzene-water and benzene-benzene have previously been calculated by Karlstriim et al. [ 9 J using a SCF CI approximation. In this communication we use the same method for calculating the interaction energy between trimethylamine and benzene. One of us has studied intermolecular interactions
between quinuclidine or I-azabicyclo [ 2.2.21 octane and several solvents [ 10,111 using the nuclear spin relaxation technique, utilizing the anisotropy in the dynamics of the quinuclidine molecule as a measure of intermolecular interactions with the solvent. The anisotropy in benzene was somewhat higher than in cyclohexane, indicating a stronger association or probably preferential solvation of quinuclidine by benzene. Here we use trimethylamine as a model for quinuclidine, assuming that only the polar part of quinuclidine is of importance in determining the solvent structure in a benzene solution of quinuclidine.
2. Computational details The computational strategy followed here to calculate the interaction energy between trimethylamine and benzene is exactly that previously used for the benzene-benzene and benzene-water systems [ 9 ] and the reader is referred to this work for a full description. Only the underlying ideas will be discussed here. In order to be able to obtain reliable estimates of the total interaction energy, two problems must be solved: the first is to obtain a high-quality estimate of the interaction at the Hartree-Fock (HF) level of approximation, and the second is to obtain a dispersion correction to this interaction. The total interaction energy at the HF level can be partitioned
0 009-2614/88/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division J
537
Volume 145, number 6
CHEMICAL
PHYSICS LETTERS
into five different contributions [ 12,131, ~SCF =&.+E,ND
+-Em +&T
-+&xx,
(1)
where Ens is the electrostatic interaction, EIND the electrostatic induction term, EEX the exchange repulsion, EcT the charge transfer term and EMlx the contribution from the coupling of the different terms. If the interaction energy AEscF is corrected for basis set superposition error (BSSE) [ 141 then one may formally write (2) We define EBssEusing the Boys-Bernardi counterpoise correction [ 14 1. E ~~~E=EA(A)+E~(B)-EA(A~B)-E~(A+B).
(3) Here, the index defines the system (molecule) and the variable in parentheses defines the basis set used in the calculation. With the above definition of the BSSE it has been shown that the quantity within parentheses in eq. ( 2 ) is fairly independent of basis set [ 15 1. Consequently, for a given basis set, one wishes to estimate the first two terms in eq. (1) or (2) independently. These terms, obtained with a small basis set used in the SCF calculations, could be replaced with the corresponding terms obtained using a larger basis set. Such a method, based on a multicentre multiple expansion of the charge distributors, has previously been described by one of us [ 15 ] and is used here. The method used to obtain reliable estimates of the dispersion energy has also previously been described and is based on a second-order Meller-Plesset approach where the integrals have been approximated using a multicentre multipole expansion of the two-electron integrals [ 161. The total interaction energy may thus be written AEToT=&c~+&ssEf
t&S
+&ND
(EES )largebasisset
+EmD
+EDISP*
)amalltmisset
(4)
The main advantage of this method is that the estimates of electrostatic and induction energies are based on multicentre multipole expansions of the charge distribution [ 15] and the polarizability tensor [ 17 ] and require minimum computer time. 538
22 April 1988
The large basis set was the same as that previously used for benzene in the benzene-benzene potential, i.e. a 9s5p basis contracted to 4s2p [ 181 and augmented with one diffuse s function (exp= 0.05 for C and 0.07 for N), one diffuse p function (exp= 0.04 for C and 0.05 for N) and one d function for C and N (exp=0.8). For hydrogen, a 5s basis was contracted to 2s and augmented with one diffuse s function (exp=0.4). The minimal basis set used in the calculations consisted of 7s and 3p primitive functions on nitrogen and carbon contracted to 2s and lp, respectively
t 191. The corresponding set for hydrogen consisted of 3s functions contracted to one single function [ 20 1. This is the same basis set as previously used for the benzene dimer. The geometries of the monomers were held fixed and for benzene: rcc= 1.395 A and rcH = 1.0836 A. The geometry of trimethylamine was the same as for the corresponding moiety in quinuclidine obtained from electron diffraction [ 2 11.
3. Results and discussion Two molecular orientations were considered, see fig. 1. Orientation I refers to the case where the C, axis of trimethylamine coincides with the C, axis of benzene and one of the N-C bonds is in the same plane as a C, axis of benzene going through two hy drogens, the methyl groups point toward benzene. In orientation II, the C’, axis of trimethylamine coincides with the C2 axis of benzene, with the nitrogen lone pair pointing toward a benzene hydrogen. One of the N-C bonds is in the same plane as the C, axis of benzene. We have also calculated a few energies using an orientation similar to I, but with the nitrogen lone pair pointing toward the benzene ring; this orientation was entirely repulsive at the SCF level. In table 1, the contribution from the different basis sets, the corrections and the total interaction energy are given as a function of the intermolecular separation for the two molecules. Firstly, it should be noted that the dispersion contribution is not compensated by EBssEfor any intermolecular distance and orientation; such an accidental compensation has previously been reported [22,23] in some systems. The dispersion energy is an almost equal and clearly
Volume 145, number 6
22 April 1988
CHEMICAL PHYSICS LETTERS
tally zero, whereas the correction in II is significant, which can be understood as an effect of the large difference in the molecular polarizability, along the different axes in benzene [ 93. The electrostatic energy in both basis sets is significant, especially in orientation II, which is more comparable to a hydrogen bond structure, where electrostatic interactions are of major importance. However, the electrostatic correction for orientation II is small, implying that a minimal basis gives a relatively good description of electrostatic interactions for this geometry. The total interaction energy is about 40% larger for the orientation in which trimethylamine participates in hydrogen bond with the benzene proton. The energy of this interaction may be compared with some typical hydrogen-bonded systems such as ammonia/water (-26.2 kJ/mol) [24] or water/water (-25.2 kJ/mol) [ 251, keeping in mind that benzene is a very poor proton donor (pK,=37). The water-benzene interactions [9] show an opposite trend, the most stable orientation being the one where the symmetry axis of water and the C, axis of benzene coincide, and the hydrogens point toward the benzene ring. This difference is caused by the high positive charge density on the water protons, whereas the CH3 protons are almost uncharged.
Fig. 1.The orientations of the interacting molecules.
dominating contribution for both orientations, which is expected in a weakly interacting system. The induction energy correction in orientation I is practiTable 1 Interaction energies (in kJ/mol) between trimethylamine and benzene. The two orientations are described in the text
orientation 4.23 4.50 4.76 5.03 5.29 5.82
1 9.4 2.5 -0.3 -1.3 -1.5 -1.2
4.1 2.7 1.5 0.8 0.4 0.1
7.6 6.0 4.8 3.9 3.1 2.1
9.2 1.3 5.9 4.8 3.9 2.6
-1.6 -1.3 -1.1 -0.9 -0.7 -0.5
0.2 0.1 0.1 0.1 0.1 0.0
0.0 0.1 0.1 0.1 0.1 0.0
0.0 0.0 0.0 0.0 0.0 -0.0
-16.5 - 12.0 -9.0 -6.6 -4.9 -2.6
-4.1 -8.2 -8.8 -8.0 -6.1 -4.3
orientation 4.25 4.76 5.03 5.29 5.82 6.35
II 13.2 -5.6 -5.1 -4.0 -2.3 -1.3
7.7 3.5 2.1 1.1 0.2 0.0
16.6 6.6 4.6 3.2 1.8 1.1
18.8 7.2 4.8 3.3 1.8 1.0
-2.2 -0.5 -0.2 -0.1 0.0 0.1
2.1 0.6 0.3 0.2 0.1 0.0
5.3 1.4 0.7 0.5 0.2 0.0
-3.2 -0.8 -0.4 -0.3 -0.1 -0.0
-16.7 -9.0 -6.5 -4.8 -2.7 -1.6
- 1.2 - 12.4 - 10.2 -8.1 -4.8 -2.9
a) Quantity calculated with a small basis set.
539
Volume 145, number 6
CHEMICAL PHYSICS LETTERS
References [ 1] G. Bolis, E. Clementi, D.H. Wertz, H.A. Scheraga and C. Tosi, J. Am. Chem. Sot. 105 (1983) 355. [2] 0. Matsuoka, E. Clementi and M. Yoshimine, J. Chem. Phys. 64 (1976) 1351. [3] PK. Swaminathan, A. Laaksonen, G. Corongiu and E. Clementi, J. Chem. Phys! 84 (1986) 867. [ 41 A. Meunier, B. Levy and G. Berthier, Theoret. Chim. Acta 29 (1973) 49. [ 5 ] W.A. Lathan, G.R. Pack and K. Morokuma, J. Am. Chem. See. 97 (1975) 6624. [6] E. Kochanski, J. Chem. Phys. 58 (1973) 5823. [7] W. Kofos, Theoret. Chim. 51 (1979) 219. [ 81 I. Hepburn, G. Stoles an%R. Pence, Chem. Phys. Letters 36 (1975) 451. [ 9 ] G. Karlstrom, P. Linse, A. Wallqvist and B. Jiinsson, J. Am. Chem. Sot. 105 (1983) 3777. [lo] A. Maliniak, J. Kowalewski and I. Panas, J. Phys. Chem. 88 (1984) 5628. [ II] A. Maliniak and J. Kowalewski, .I. Phys. Chem. 90 (1986) 6330.
540
22 April 1988
[ 121 K. Morokuma, J. Chem. Phys. 55 (1971) 1236. [ 131 P.A. Kollman and L.C. Allen, J. Chem. Phys. 52 (1970) 5085. [ 141 SF. Boys and B. Bernardi, Mol. Phys. 19 (1970) 558. [ 151 G. Karlstrom, Proceedings from the 5th Seminar on Computational Methods in Quantum Chemistry, Groningen (1981). [ 161 G. Karlstriim, Theoret. Chim. Acta 55 (1980) 233. [ 171 G. Karlstrijm, Theoret. Chim. Acta 60 (1982) 535. [ 181 T.H. Dunning Jr., J. Chem. Phys. 53 ( 1970) 2823. [ 191 B. Roos and P. Siegbahn, Theoret. Chim. Acta 17 (1970) 209. [20] S. Huzinaga, J. Chem. Phys. 42 (1965) 1293. [ 211 H. Schei, Q. Shen and R.L. Hilderbrandt, J. Mol. Struct. 65 (1980) 297. [22] A. Johansson, P. Kollman and S. Rothenberg, Theoret. Chim. Acta 29 (1973) 167. [23] A. Meukier, B. Levy and G. Berthier, Theoret. Chim. Acta 29 (1973) 49. [24] G.H.F. Diercksen, W.P. Kraemer and W. von Niessen, Theoret. Chim. Acta 28 (1972) 67, [ 251 G.H.F. Diercksen, W.P. Kraemer and B.O. Roos, Theoret. Chim. Acta 36 (1975) 249.