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Intermolecular potential of the acetonitrile dimer obtained from ab initio calculations
Volume
103.
number
PHYSICS LETTERS
CHEMICAL
1
INTERMOLECULAR POTENTIAL OF THE ACETONITRILE OBTAINED FROM AB WIT10 CALCULATIONS Gianfranco Gruppu
28
July
1983;
SCF MO LCAO c&ted
interaction
Universrrti.
VIO Arclrrnrji
-70. 90123
tn final form 22 September
ab tnttio computations cnergtcs were fitted
ic term. The configurations acetonitrtle.
were carried
by an analyttcal
correspondtng
potcnttal
to the energy mtntma
review of the literature see refs. [ 1.21. The existence molecules
has been con-
firmed by more recent X-ray and neutron diffractron studies on liquid acetonitrrle [3], and by theoretical calculations of the acetonitrile dimer based on the ab initio MO method [2]. These calculations propos ed that antiparalleland head-to-tail configurations are two possible interaction modes, where the antiparallel dipole model is slightly favored. Smce these calculations were concerned only with a few interaction geometrieqit seemed interesting to obtain an analytical intermolecular potential of the acetonitrile dimer. It would then be possible to explore the whole potenttal surface, allowing a more detailed prcture of the interaction.
2. Details of calculation The basis set used throughout
this work is van
Duijneveldt’s (7,313) minimal basis set [4] contracted to (2, l/l), where the contraction coefficients are et al. [5] _The IBMOL6
those optimized
by Clementi
0 009-2614/83/s (North-Holland
Physics Publishing
03.00 0 Elsevier Science Publishers B.V. Division)
Iro[v
out for 165 contigurattons
The temperature and/or concentration dependences of several physical properties of acetonitrile are generally interpreted as being due to polar interactions of molecules in the liquid phase and in solution; for a of acetonitrile
Palermo.
1983
1. Introduction
of association
DIMER
LA MANNA
Chrmrca Teorico,
Rccened
16 December 1983
consisting
of the acetomtrde
of a 6-12
Lcnnard-Jones
fit quote well the expertmental
dimer
and the cd-
term plus a coulomb-
diffractton
data on ltquid
program i6] \ras employed on the IBM 3033 of the Palermo University Computing Centre. The bond lengths UCacetonitrile were fully optimized, whrle the CCN and HCH bond angles were kept fixed at 180° and 109.S”, respectrvely. Optunrzed vahres of the bond lengths are C-C = 1.56 A, C-N = 1.21 A and C-H = 1.19 A, significantly larger than the ehperrmental values [7] (C-C = 1.46 X C-N = 1.15 A and C-H = 1.09 A). Overestimation of bond lengths is common when minimal basis sets are used. The energy of the isolated monomer 1s- 131.4347 hartree. The calculated dipole moment is 3.64 D. m reasonable agreement with the experimental value of 3.92-3.96 D [8]. One hundred and sixty five configuratrons of the acetomtrile dimer were considered, so as to include both attractive and slightly repulsive regions The relative positions of the two acetonitrlle molecules can be defined by four parameters R, 0, 0 and y. as shown in fig. 1. The configuratrons were chosen carefully so as to describe the interaction with a limited number of calculated points The range of R was from 3.0 to 9.0 A. The sampling was especially accurate in the vicinity of the minima in order to exclude the existence of other energy minima. Only for values of R in the regions of minimum energy were all parameters varied. The basis-set superposition error has been removed using the counter-poise method [9], and the correction 55
Volume
103. number
CHEMICAL
1
PHYSICS
LETTERS
16 December
1983
according to a M&ken population analysis [ 111. Since the interaction with each hydrogen atom of the methyl group can be described with the same set
of fitting constants, 30 fitting constants were obtained. Values are given in table 1. The root-mean-square deviation of the fit is 0.8 kJ/mol;
Fig. 1. The parameters used to describe pair of acetotutrile molecules.
the arrangement
of a
for the dispersion energy was performed as outlined by Claverie and KoTos [lo]. The calculated interaction energies ranged from -11.3 to 5.8 kJ/mol.
3. The intermolecular
potential
The interaction energies of the 165 casesconsidered have been fitted with a Lennard-Jones potential supplemented with a coulombic term
(1) A, B and Care fitting constants, i and j are indices representing an atom of the first and the second molecule of acetonitrile, respectively, and qi and qi are the net charges of the atoms of acetonitrile obtained
room temperature) G 0 < 116”).
constants
N
N N N
-N
acY=w C(methyI) H-
C(cyaniW
CXcyanide)
C(cy&ide)
Ctmethyl)
C(cyanide) Cbethyl)
H C(meUvl)
C(methyI) H
H H
larger than 5.3 A.
A
B
C
0.478000921-01 0.3679215i7+04
0.114498337+08. 0.109066878+07
0.850089420+00 0.137020343+01
0.467492977-02
0.225308615+07
0.990301876+00
0.131973674-01 0.131868838+03 0.138736542-01 0.706553865+01 0.336220743+04 0.851491335+02 0.247150?73+03
0.199292965+06 0.314861528+03 0.288435649-01 0.471503201+06 0.617284285+07 0.156397988+06 0.120749303+05 ._
0.995793068+00
a)A is expressed in A6 kJ/mol. B is expressed in Al2 kJ/mol
56
is larger (3.1 G R 4 4.4 & 6S”
dimer a)
for the acetonitrile
Atoms
the 165 czes
The minimum value of R corresponding to an attractive interaction is 2.9 & for 8 = 80”. For larger values of R, the 6 interval where the interaction is attractive increases, ranging from 40’ to 135” for R = 5.3 A. This interval slowly decreases for values of
R Table I Pairwise interaction
am&g
considered, 13 points show a deviation greater than 1.5 kJ/mol. The potential obtained can be utilized for systematically exploring the interaction energy between two acetonitrile molecules in order to find configurations corresponding to minimum-energy regions. Since previous theoretical and experimental data indicate that antiparallel and head-to-tail configurations are the most important, isoenergy contour maps in the (0, R) plane for 4 = y = 0” (antiparallel configurations, fig. 2a) and for # = 180”, -y = 0” (head-to-tad configurations, fig. 3a) are reported. Fig. 2a shows that the calculated value of the interaction energy in the case of the antiparallel configuration is -11 kJ/mol for 3.3 dR d 3.8 A and 80” d 8 d 100°; the arrangements of the molecules for two configurations corresponding to the energy minimum are shown in fig. 4a. The region where the interaction energy is close to the minimum value (within the range of RTat
and C is ex$ressed
in au.
0.104315774+01
0.945223638+00 0.102621342+01 0.102062806+01 ~.994712214+00 0.100816910+01
Volume 103. number 1
16 December 1983
CHCMICAL PHYSICS LETTERS
6
50
55
co
65R&
7o
!io
Fig. 3. lsoenugy conrour maps for head-to-tad configwat~ons of the acetorutrile dimer (energy values between the hnrs III kJ/mon. (a) (0, R) phne at 0 = 180”. 7 = 0".(b) (0, R) plane ate=O”.y=00_(c)(y.R)planeat~=00,~=180”. Fig 2. isoenergy contour maps for antiparallel configuratrons of the acetonttrile dtmer (energy values between the tines in kJjmo1). (a) (0. R) plane at Q = 0”. -y= 0".(b)to,R) plane at 0 = 9lY.r = 0”. (c) (7.R) plane at 0 =90”, Q = 0”.
if the trend of energy values is examined when the angle @ is changed (at fixed values of 8 and 7 as shown in fig. 2b where 0 = 90°, 7 = O’), the value -11 kJ/
mol is obtained for -8” G Q < 7O. Modifications of the angle 7 appear to be less important; the ener,v value remains unchanged for relatively of this angle (7 = 0 2 224/(fig. 2c).
large variations
For the head-to-td configuration, an energy minimum of -6 kJ/mol is found for 6.0 < i? < 6.8 A, -23
< 8 < 23O (figs. 3a and 4b). The shape of the iso57
CHEMICAL PHYSICS LETTERS
Volume 103. nuinber 1
&?G l-G:: -+ i_( Ia)
L
\
(b) Fig. 4. Some contiguratlons
of the acetonitrile
duner correspond-
ing to rmmmum energy values. (a) Antiparallel configurationsR=~.~A,Q=O~.~= O” and 0 = 90” (left) and 80” (right).(b) Head-to-tail configurations- R = 6 5 A, Q = 180°, -y = 0” and e = 0” (top) and 20” (bottom). contour map reported in fig. 3a shows that the molecules can have an attractive interaction for distances R less than 5-S ii provided that the angle 0 increases to 40-50”. This occurs because the attractive interaction between the nitrogen of the cyanide group and hydrogen atoms of the methyl group decreases with increasing N ... H distance; thus, when 8 increases shorter R values allow an optimal hydrogennitrogen contact distance_ If the angle B is too large, shorter R values make the repulsive effect between the nitrogen and the methyl carbon important. Fluctuations of the angle @around +SO” give the same energy (fig. 3b) and deviations of the angle y from 0 to 553” do not change the energy value of 6 kJ/mol (fig 3~). For these reasons, the maps reported in fig<.
energy
3b and 3~ have a similar shape to fig. 3a.
Previous ST03G calculations I2 ] give an association enthalpy of 7 ki/mol for the antiparallel dimer at 3.5 A between the molecular axes, and 5 kJ/mol for the head-to-tail dimer for an N . . . C distance of 3.5 A. In the first case, the interaction energy is underestimated with respect to the value obtained here because the 0 value relative to the considered configuration is different (0 = 80°-100’ here, 0 = 71° (not optimized) for the STO-3G calculations). In the case 58
16 December 1983
of the head-to-tail configuration, the calculations reported here give an N . . . C distance, at the energy minimum, in the range 3.24.0 A. which Indicates that the STO-3G result of 3.5 A is reasonable. The data obtained from the energy trend of the acetonitrile dimer cannot be directly transferred to the
structure of liquid acetonitrile. Nevertheless, It IS possible to make some comparisons with the experimental diffraction data on the liquid [3]. Below 4.4 a, these experimental data give preferred orientations of the dipole axis relative to the C,-C, line m the range 90° G 0 < 125”, whereas from -5.2 A preferred orientations of 0’ < 0 < 55’ dominate. Taking into account that in our case R is defined as the distance between the C2 atoms, we can see that the results obtained here fit qutte well the diffraction data: the antiparallel configuration is preferred below R = 5 A, whereas for values of R larger than 6 A the head-to-tail configuration is predicted to dominate. A better description of the organization of the molecules in the liquid can
be obtained by using the intermolecular potential (the one reported here or any other better or of comparable accuracy) to simulate a cluster of acetonitrile molecules, at a given temperature, through the Monte Carlo method. This work is in progress.
References [l ] L.Paoloniand
S. Hauser. Bull Sot Chim Beiges 84 (1975) 219. [2] M.R. Dagnino, G. La Manna and L. Paoloru, Chem Phys Letters 39 (1976) 552. [3] H. Bertagnolti and M.D. Zeldler, MoL Phys. 35 (1978) 177. [4] F.B. van DuiJneveldt, IBM Tech. Rept. RJ945 (1971). 151 L. Glanotio. R. Pavani and E. Clementi, Gaze Chum. Ital. 108(1978) 181. (61 L. Granolio and R. Pavani, hlontedison Tech. Rept.. Istituto Donegani, DDC-771 (1977). [7 ] J.L. Duncan, D.C. MacKean and N.D. Michie. J. Mol Struck 21 (1974) 405; K. Karakida, T. Fukuyama and K. Kuchitsu. Bull. Chem. Sot. Japan 47 (1974) 299. [8j kL. MacCleUan, Tables of experimental dipole moments (Freeman. San Francisco, 1963> p_ 57. 191 S.F. BOYSand F. Berkardi MoL Phys. 19 (1970) 563. [lo] P. Claverie. m. Intermolecular Interactions: from diatomics fo biopolymers, ed. B. Pullman (Wiley, New York, 1978); w. KoT& Theoret. Chim. Acta 51(1979) 219. [ 111 R.S. Mulbken. J. Chem. Phys. 23 (1955) 1833,1841, 2338.2343.
103.
number
PHYSICS LETTERS
CHEMICAL
1
INTERMOLECULAR POTENTIAL OF THE ACETONITRILE OBTAINED FROM AB WIT10 CALCULATIONS Gianfranco Gruppu
28
July
1983;
SCF MO LCAO c&ted
interaction
Universrrti.
VIO Arclrrnrji
-70. 90123
tn final form 22 September
ab tnttio computations cnergtcs were fitted
ic term. The configurations acetonitrtle.
were carried
by an analyttcal
correspondtng
potcnttal
to the energy mtntma
review of the literature see refs. [ 1.21. The existence molecules
has been con-
firmed by more recent X-ray and neutron diffractron studies on liquid acetonitrrle [3], and by theoretical calculations of the acetonitrile dimer based on the ab initio MO method [2]. These calculations propos ed that antiparalleland head-to-tail configurations are two possible interaction modes, where the antiparallel dipole model is slightly favored. Smce these calculations were concerned only with a few interaction geometrieqit seemed interesting to obtain an analytical intermolecular potential of the acetonitrile dimer. It would then be possible to explore the whole potenttal surface, allowing a more detailed prcture of the interaction.
2. Details of calculation The basis set used throughout
this work is van
Duijneveldt’s (7,313) minimal basis set [4] contracted to (2, l/l), where the contraction coefficients are et al. [5] _The IBMOL6
those optimized
by Clementi
0 009-2614/83/s (North-Holland
Physics Publishing
03.00 0 Elsevier Science Publishers B.V. Division)
Iro[v
out for 165 contigurattons
The temperature and/or concentration dependences of several physical properties of acetonitrile are generally interpreted as being due to polar interactions of molecules in the liquid phase and in solution; for a of acetonitrile
Palermo.
1983
1. Introduction
of association
DIMER
LA MANNA
Chrmrca Teorico,
Rccened
16 December 1983
consisting
of the acetomtrde
of a 6-12
Lcnnard-Jones
fit quote well the expertmental
dimer
and the cd-
term plus a coulomb-
diffractton
data on ltquid
program i6] \ras employed on the IBM 3033 of the Palermo University Computing Centre. The bond lengths UCacetonitrile were fully optimized, whrle the CCN and HCH bond angles were kept fixed at 180° and 109.S”, respectrvely. Optunrzed vahres of the bond lengths are C-C = 1.56 A, C-N = 1.21 A and C-H = 1.19 A, significantly larger than the ehperrmental values [7] (C-C = 1.46 X C-N = 1.15 A and C-H = 1.09 A). Overestimation of bond lengths is common when minimal basis sets are used. The energy of the isolated monomer 1s- 131.4347 hartree. The calculated dipole moment is 3.64 D. m reasonable agreement with the experimental value of 3.92-3.96 D [8]. One hundred and sixty five configuratrons of the acetomtrile dimer were considered, so as to include both attractive and slightly repulsive regions The relative positions of the two acetonitrlle molecules can be defined by four parameters R, 0, 0 and y. as shown in fig. 1. The configuratrons were chosen carefully so as to describe the interaction with a limited number of calculated points The range of R was from 3.0 to 9.0 A. The sampling was especially accurate in the vicinity of the minima in order to exclude the existence of other energy minima. Only for values of R in the regions of minimum energy were all parameters varied. The basis-set superposition error has been removed using the counter-poise method [9], and the correction 55
Volume
103. number
CHEMICAL
1
PHYSICS
LETTERS
16 December
1983
according to a M&ken population analysis [ 111. Since the interaction with each hydrogen atom of the methyl group can be described with the same set
of fitting constants, 30 fitting constants were obtained. Values are given in table 1. The root-mean-square deviation of the fit is 0.8 kJ/mol;
Fig. 1. The parameters used to describe pair of acetotutrile molecules.
the arrangement
of a
for the dispersion energy was performed as outlined by Claverie and KoTos [lo]. The calculated interaction energies ranged from -11.3 to 5.8 kJ/mol.
3. The intermolecular
potential
The interaction energies of the 165 casesconsidered have been fitted with a Lennard-Jones potential supplemented with a coulombic term
(1) A, B and Care fitting constants, i and j are indices representing an atom of the first and the second molecule of acetonitrile, respectively, and qi and qi are the net charges of the atoms of acetonitrile obtained
room temperature) G 0 < 116”).
constants
N
N N N
-N
acY=w C(methyI) H-
C(cyaniW
CXcyanide)
C(cy&ide)
Ctmethyl)
C(cyanide) Cbethyl)
H C(meUvl)
C(methyI) H
H H
larger than 5.3 A.
A
B
C
0.478000921-01 0.3679215i7+04
0.114498337+08. 0.109066878+07
0.850089420+00 0.137020343+01
0.467492977-02
0.225308615+07
0.990301876+00
0.131973674-01 0.131868838+03 0.138736542-01 0.706553865+01 0.336220743+04 0.851491335+02 0.247150?73+03
0.199292965+06 0.314861528+03 0.288435649-01 0.471503201+06 0.617284285+07 0.156397988+06 0.120749303+05 ._
0.995793068+00
a)A is expressed in A6 kJ/mol. B is expressed in Al2 kJ/mol
56
is larger (3.1 G R 4 4.4 & 6S”
dimer a)
for the acetonitrile
Atoms
the 165 czes
The minimum value of R corresponding to an attractive interaction is 2.9 & for 8 = 80”. For larger values of R, the 6 interval where the interaction is attractive increases, ranging from 40’ to 135” for R = 5.3 A. This interval slowly decreases for values of
R Table I Pairwise interaction
am&g
considered, 13 points show a deviation greater than 1.5 kJ/mol. The potential obtained can be utilized for systematically exploring the interaction energy between two acetonitrile molecules in order to find configurations corresponding to minimum-energy regions. Since previous theoretical and experimental data indicate that antiparallel and head-to-tail configurations are the most important, isoenergy contour maps in the (0, R) plane for 4 = y = 0” (antiparallel configurations, fig. 2a) and for # = 180”, -y = 0” (head-to-tad configurations, fig. 3a) are reported. Fig. 2a shows that the calculated value of the interaction energy in the case of the antiparallel configuration is -11 kJ/mol for 3.3 dR d 3.8 A and 80” d 8 d 100°; the arrangements of the molecules for two configurations corresponding to the energy minimum are shown in fig. 4a. The region where the interaction energy is close to the minimum value (within the range of RTat
and C is ex$ressed
in au.
0.104315774+01
0.945223638+00 0.102621342+01 0.102062806+01 ~.994712214+00 0.100816910+01
Volume 103. number 1
16 December 1983
CHCMICAL PHYSICS LETTERS
6
50
55
co
65R&
7o
!io
Fig. 3. lsoenugy conrour maps for head-to-tad configwat~ons of the acetorutrile dimer (energy values between the hnrs III kJ/mon. (a) (0, R) phne at 0 = 180”. 7 = 0".(b) (0, R) plane ate=O”.y=00_(c)(y.R)planeat~=00,~=180”. Fig 2. isoenergy contour maps for antiparallel configuratrons of the acetonttrile dtmer (energy values between the tines in kJjmo1). (a) (0. R) plane at Q = 0”. -y= 0".(b)to,R) plane at 0 = 9lY.r = 0”. (c) (7.R) plane at 0 =90”, Q = 0”.
if the trend of energy values is examined when the angle @ is changed (at fixed values of 8 and 7 as shown in fig. 2b where 0 = 90°, 7 = O’), the value -11 kJ/
mol is obtained for -8” G Q < 7O. Modifications of the angle 7 appear to be less important; the ener,v value remains unchanged for relatively of this angle (7 = 0 2 224/(fig. 2c).
large variations
For the head-to-td configuration, an energy minimum of -6 kJ/mol is found for 6.0 < i? < 6.8 A, -23
< 8 < 23O (figs. 3a and 4b). The shape of the iso57
CHEMICAL PHYSICS LETTERS
Volume 103. nuinber 1
&?G l-G:: -+ i_( Ia)
L
\
(b) Fig. 4. Some contiguratlons
of the acetonitrile
duner correspond-
ing to rmmmum energy values. (a) Antiparallel configurationsR=~.~A,Q=O~.~= O” and 0 = 90” (left) and 80” (right).(b) Head-to-tail configurations- R = 6 5 A, Q = 180°, -y = 0” and e = 0” (top) and 20” (bottom). contour map reported in fig. 3a shows that the molecules can have an attractive interaction for distances R less than 5-S ii provided that the angle 0 increases to 40-50”. This occurs because the attractive interaction between the nitrogen of the cyanide group and hydrogen atoms of the methyl group decreases with increasing N ... H distance; thus, when 8 increases shorter R values allow an optimal hydrogennitrogen contact distance_ If the angle B is too large, shorter R values make the repulsive effect between the nitrogen and the methyl carbon important. Fluctuations of the angle @around +SO” give the same energy (fig. 3b) and deviations of the angle y from 0 to 553” do not change the energy value of 6 kJ/mol (fig 3~). For these reasons, the maps reported in fig<.
energy
3b and 3~ have a similar shape to fig. 3a.
Previous ST03G calculations I2 ] give an association enthalpy of 7 ki/mol for the antiparallel dimer at 3.5 A between the molecular axes, and 5 kJ/mol for the head-to-tail dimer for an N . . . C distance of 3.5 A. In the first case, the interaction energy is underestimated with respect to the value obtained here because the 0 value relative to the considered configuration is different (0 = 80°-100’ here, 0 = 71° (not optimized) for the STO-3G calculations). In the case 58
16 December 1983
of the head-to-tail configuration, the calculations reported here give an N . . . C distance, at the energy minimum, in the range 3.24.0 A. which Indicates that the STO-3G result of 3.5 A is reasonable. The data obtained from the energy trend of the acetonitrile dimer cannot be directly transferred to the
structure of liquid acetonitrile. Nevertheless, It IS possible to make some comparisons with the experimental diffraction data on the liquid [3]. Below 4.4 a, these experimental data give preferred orientations of the dipole axis relative to the C,-C, line m the range 90° G 0 < 125”, whereas from -5.2 A preferred orientations of 0’ < 0 < 55’ dominate. Taking into account that in our case R is defined as the distance between the C2 atoms, we can see that the results obtained here fit qutte well the diffraction data: the antiparallel configuration is preferred below R = 5 A, whereas for values of R larger than 6 A the head-to-tail configuration is predicted to dominate. A better description of the organization of the molecules in the liquid can
be obtained by using the intermolecular potential (the one reported here or any other better or of comparable accuracy) to simulate a cluster of acetonitrile molecules, at a given temperature, through the Monte Carlo method. This work is in progress.
References [l ] L.Paoloniand
S. Hauser. Bull Sot Chim Beiges 84 (1975) 219. [2] M.R. Dagnino, G. La Manna and L. Paoloru, Chem Phys Letters 39 (1976) 552. [3] H. Bertagnolti and M.D. Zeldler, MoL Phys. 35 (1978) 177. [4] F.B. van DuiJneveldt, IBM Tech. Rept. RJ945 (1971). 151 L. Glanotio. R. Pavani and E. Clementi, Gaze Chum. Ital. 108(1978) 181. (61 L. Granolio and R. Pavani, hlontedison Tech. Rept.. Istituto Donegani, DDC-771 (1977). [7 ] J.L. Duncan, D.C. MacKean and N.D. Michie. J. Mol Struck 21 (1974) 405; K. Karakida, T. Fukuyama and K. Kuchitsu. Bull. Chem. Sot. Japan 47 (1974) 299. [8j kL. MacCleUan, Tables of experimental dipole moments (Freeman. San Francisco, 1963> p_ 57. 191 S.F. BOYSand F. Berkardi MoL Phys. 19 (1970) 563. [lo] P. Claverie. m. Intermolecular Interactions: from diatomics fo biopolymers, ed. B. Pullman (Wiley, New York, 1978); w. KoT& Theoret. Chim. Acta 51(1979) 219. [ 111 R.S. Mulbken. J. Chem. Phys. 23 (1955) 1833,1841, 2338.2343.