Intermolecular interactions in the N≡C–C≡C–H dimer

20 March 1998

Chemical Physics Letters 285 Ž1998. 198–204

Intermolecular interactions in the N ' C–C ' C–H dimer James A. Platts, Sean T. Howard, Ian. A. Fallis Department of Chemistry, UniÕersity of Wales, Cardiff, P.O. Box 912, Cardiff CF1 3TB, UK Received 3 July 1997; in final form 15 January 1998

Abstract Ab initio calculations on N ' C–C ' C–H and its anti-parallel dimer are reported, with a view to studying the intermolecular interactions present. Following initial optimisation of the monomer at the MP2r6-311q GŽd,p. level, the PES of the dimer corresponding to variations in chain separation and overlap was explored. Two minima on this surface were found, varying in their degree of overlap, but both having C 2 h symmetry. Topological charge density analysis shows these two arrangements to have qualitatively different structures. Atoms in Molecules decomposition shows the origin of the dimer stabilisation to lie in an increase in nitrogen’s population and self-stabilisation. q 1998 Elsevier Science B.V.

1. Introduction Computational studies of intermolecular interactions are becoming increasingly widespread. Primary amongst these are studies of hydrogen bonding w1,2x, while other interactions such as van der Waals forces have also been considered w3x. Few studies have considered the influence of p-systems such as triple bonds on intermolecular forces: the acetylene dimer, for example, has a T-shaped hydrogen-bonded structure rather than a parallel conformation w4x. Similar orientations are found in crystal structures of triple bond containing molecules w5,6x. In this Letter we consider the behaviour of triple bonds in p ...p interactions through the anti-parallel C 2 h dimer of linear NCCCH. This differs from previous work in that the p-system is no longer a hydrogen bond acceptor. This orientation was chosen as a model for interactions between chains where no acidic hydrogen is present. In particular carbonitrile groups conjugated to an aromatic nucleus are widely used in calamitic liquid crystalline materials. The nitrile functional group serves to increase the molec-

ular polarisabilty anisotropy Ž D a . and to provide a permanent electric dipole moment. These effects are of great importance in a number of technologically important liquid crystalline materials. The enhancement of D a serves to stabilise liquid crystalline phases ŽMaier–Saupe theory., whilst the presence of a permanent dipole moment causes the antiparallel ordering of calamitic mesogens w7x. This latter effect has the twofold consequences of mesophase stabilisation by more efficient molecular packing, particularly in systems with a mixture of saturated and unsaturated ring systems, and an effective doubling of molecular length, resulting in an increase in aspect ratio. The geometrical and energetic details of such interactions are unclear. It is for this reason that we study the C 2 h orientation of the dimer, despite the fact that a hydrogen bonded geometry is probably more stable. In addition to investigating the likely geometry and energy of such interactions, we have applied the Atoms in Molecules ŽAIM. theory, developed by Bader and others w8x to the process of dimer formation. This theory is based around the partition of a

0009-2614r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 0 9 - 2 6 1 4 Ž 9 8 . 0 0 0 6 2 - 1

J.A. Platts et al.r Chemical Physics Letters 285 (1998) 198–204

molecule into disjoint regions of space identified as atoms, each of which obeys the the same quantum mechanical theorems Žsuch as the virial theorem. as does the total system. With such a partition established, one can rigorously define atomic charges and multipole moments, which decribe the molecular charge distribution and its changes on dimer formation. The satisfaction of the atomic virial theorem allows calculation of atomic kinetic, potential, and total energies, which give direct information on the mechanism of stabilisation due to dimerisation. Topological, or critical point ŽCP., analysis is complementary to this AIM decomposition, providing information on the nature of the bonding present, either within a molecule or between distinct molecules w9x.

2. Computational All ab initio calculations were perfomed using GAUSSIAN94 w10x, running on the University of London Computing Centre’s Convex C3800. Initial geometry optimisation of NCCCH at both HF and MP2 levels used the 6-311 q GŽd,p. basis set w11– 13x. Keeping the internal geometry of the monomers fixed, the potential energy surface ŽPES. of the C 2 h dimer of NCCCH was explored at the MP2r6-311 q GŽd,p. level. First the degree of overlap of the monomers was varied at a constant chain separation ˚ ., yielding two minima. Then the chain separaŽ3.0 A tion was optimised for these two minima. The basis set superposition error in these dimer calculations was estimated using the standard counterpoise method of Boys and Bernardi w14x. AIM and topological analysis employed the AIMPAC suite of programs w15x, in particular the programs EXT94B, PROAIMV, and GRIDV. Atomic properties reported are N, the electronic population of the atom; E, the total energy of the atom; V NET , the stabilisation of the atom’s electronic charge by all the nuclei in the system; VNEO , the stabilisation of the atom’s electronic charge by its own nucleus Žthe self-stabilisation energy.; M, the atomic dipole polarisation in a given direction; Q, the atomic quadrupole polarisation. Values of r and = 2r at CP’s are reported, along with r 1 and r 2 , the distances from the CP to the atoms involved in the

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bond. All atomic and CP data are reported in atomic units.

3. Results and discussion 3.1. Geometries and energetics Table 1 reports the HF and MP2 optimised geometry and properties of the monomer NCCCH. At the HF level, the bond lengths N1 ' C2 and C3 ' C4 are much shorter than the C2–C3 length, indicating localised p-bonding in the molecule. Inclusion of electron correlation via MP2 methods increases the outer bond lengths and shortens the C2–C3 bond, suggesting increased p-electron delocalisation at this more accurate level. The molecular dipole moment, m , is diminished at the MP2 level, but the overall NyCCCHq polarity of the molecule is unchanged. The MP2 dipole is in close agreement with the experimental value of 3.73D w16x. An initial MP2 potential energy surface ŽPES. scan was performed, keeping the monomers anti˚ apart. This scan parallel ŽC 2 h symmetry. and 3.0 A located an energy minimum at a ‘‘height’’, h, Žsee ˚ precisely the optimised value for Fig. 1. of 1.18 A, the N1 ' C2 bond length reported in Table 1. This orientation, referred to as dimer 1, is one candidate for the minimum energy geometry of the C 2 h dimer. Increasing the mutual overlap of the monomers to h ˚ decreases the stabilisation of the greater than 3 A dimer somehwat, but it was decided to explore the possibility of a second minimum occurring at such an orientation. In fact, the energy is a minimum with respect to h when the nitrile and acetylene bonds are ˚ Žhereafter dimer 2.. eclipsed, with h s 3.78 A

Table 1 Molecular properties of NCCCH

˚. r ŽN1–C2.ŽA r ŽC2–C3. r ŽC3–C4. r ŽC4–H5. EŽhartree. m Ždebye. a

a

HF

MP2

1.130 1.388 1.182 1.057 y168.59151 4.10

1.181 1.376 1.222 1.066 y169.14858 3.75

Calculated using the 6-311qGŽd,p. basis set.

J.A. Platts et al.r Chemical Physics Letters 285 (1998) 198–204

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anti-parallel constraint on the chains, resulting in C i symmetry, results in decreased stabilisation of both dimers. This lends supports our assumption that the maximum stabilisation is found for a coplanar arrangement, though it is unlikely that we have found the true global minimum of the ŽNCCCH. 2 system. Fig. 1. Numbering scheme and coordinate axes used in dimer calculations.

The results of a rigid PES scan of the monomer separation, d, for the two C 2 h dimers, 1 and 2, are presented in Table 2. At the HF level, the dimers were found to be unbound relative to the free monomers Žsuggesting that electrostatics play a minor role in stabilising the dimer.; hence we report only the MP2 results. Dimer 1, in which the two nitrile groups are in close proximity, is found to have an energy minimum at an inter-chain separation of ˚ with an overall stabilisation of 12.86 kJ 3.25 A, moly1 . A counterpoise correction of this binding energy reduces this by around 6 kJ moly1 ; this is, however, only a crude estimate of the true BSSE, and the true stabilisation is likely to lie somewhere between these figures w17x. Dimer 2 is only barely ˚ but increasing this separation bound with d s 3.0 A, results in a substantial stabilisation. In fact, the en˚ has a binding energy ergy minimum at d s 3.52 A of 14.60 kJ moly1 , greater than that of dimer 1. Again, this stabilisation is reduced by a counterpoise correction by rather more than in dimer 1, to a value of around 6 kJ moly1 . Breaking the C 2 h symmetry by removing the Table 2 MP2r6-311qqG)) rigid PES scan results Žhartree.

˚. d ŽA

Dimer 1

Dimer 2

3.0 3.1 3.2 3.25 3.3 3.4 3.5 3.54 3.6 3.7

0.30125 0.30180 0.30203 0.30206 0.30204 0.30192 – – – –

– – – – 0.30215 0.30257 0.30272 0.30272 0.30268 0.30252

a

338 hartree added to the total energies.

3.2. Topological charge density analysis Bond critical point analysis of NCCCH, Table 3, supports the general finding of Table 1 that the triple bond character is essentially localised in N1 ' C2 and C3 ' C4, with the lower value of r in C2–C3 suggesting a single bond. N1 ' C2 has the highest value of r of all the bonds, and its relatively low value of = 2r does not indicate a weak or ionic bond, merely substantial polarity of this bond, as has been demonstrated by Bader and others w8x. This is also apparent in the much shorter distance from the CP to C2 than to N1. A similar analysis of both dimers reveals that the charge distribution within each monomer is virtually unchanged as a result of dimer formation. Bond CP properties in the dimers change by rather less than 1% relative to their corresponding monomer values, and are consequently not reported in Table 3. This is much less than is observed in stronger intermolecular interactions w18,19x such as hydrogen bonding. However, recent studies of van der Waals complexes w20,21x, in which monomer charge distributions are almost unperturbed by the interaction, are consistent with this finding. In the region between monomers, some curious topological features are found: these are illustrated in Fig. 2. In dimer 1, a single bond CP is found between the chains, exactly on the centre of inver-

a

Table 3 MP2r6-311qqGŽd,p. bond critical point properties Žau.

r

y= 2r

r1

r2

monomer

N1–C2 C2–C3 C3–C4 C4–H5

0.446 0.301 0.384 0.284

y0.343 y0.875 y1.070 y1.038

1.439 1.332 1.183 1.344

0.792 1.267 1.125 0.670

dimer 1

N1...N6

0.006

q0.019

3.267

3.267

dimer 2

N1...C8 ring

0.004 0.003

q0.012 q0.010

3.499 –

3.499 –

J.A. Platts et al.r Chemical Physics Letters 285 (1998) 198–204

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Fig. 2. y= 2r distributions in Ža. dimer 1 and Žb. dimer 2 Žcontour values displayed are "2.0 = 10 n , "4.0 = 10 n , "8.0 = 10 n e bohry5 , with n increasing in steps of 1 from y3; positive values of = 2r are denoted by dashed lines..

J.A. Platts et al.r Chemical Physics Letters 285 (1998) 198–204

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sion of the system. Plotting the =r trajectories which originate at this CP reveal it to link the nitrogens of each NCCCH unit, Strictly speaking therefore, only the nitrogens of each unit are interacting. In dimer 2, the inter-chain bonding is perhaps more understandable; the centre of inversion is now found to be a Ž3,q 1. or ring CP, with bond CP’s linking N1 with C8 and N6 with C3. These patterns of bonding are consistent with Bader and Bone’s recent study of van der Waals complexes w21x, in which many similar bonding patterns were observed. As in their study, the bond and ring critical points formed between the NCCCH chains have very low values of r and small, positive values of = 2r , characteristic of closed-shell interactions. 3.3. Atomic properties The atomic properties of NCCCH are presented in Table 4. They present a picture of an electronegative nitrogen withdrawing electron density from its bonded neighbour, C2. The remainder of the atoms in the monomer are close to neutrality, with the

Table 4 MP2r6-311q G)) atomic properties Žau.

exception of a positive charge of around 0.2 e on H5. All atoms have a positive z-dipole moment, indicating a polarisation of charge in a direction opposite to the charge transfer. This is commonly seen in polar systems, such as CO, where the negative end of the molecule, N1 here, repels the density of its neighbour. This polarisation acts to reduce the molecular dipole moment induced by charge transfer, but is insufficient to change the direction of the molecular dipole moment of NCCCH. All atoms are also found to have positive values of their zz-quadrupole moments, indicating depletion of electron density in the z Žaxial. direction, and polarised into the x- and y-directions. This is a typical of p systems, and such quadrupole moments have been identified with the p-electrons of double, triple, and aromatic bonds w22x. Changes in atomic properties on dimerisation allow us to explore the origins of stabilisation, both in terms of the direct, calculated changes in atomic energies and through changes in atomic multipole moments. Table 4 reports the atomic properties for dimers 1 and 2. Considering dimer 1 first, it is

a

N1

C2

C3

C4

H5

monomer

N E VNE T VNE O MZ QZZ

7.956 y55.108 y172.060 y133.150 q0.314 q0.561

5.141 y37.532 y120.136 y86.463 q0.731 q3.393

6.047 y38.024 y128.391 y90.002 q0.169 q4.274

6.048 y37.952 y120.479 y89.741 q0.285 q3.860

0.809 y0.532 y5.618 y1.097 q0.125 q0.385

dimer 1

N E VNE T VNE O MX MZ QZZ

7.975 y55.119 y202.665 y133.234 y0.021 q0.309 q0.478

5.134 y37.529 y138.227 y86.441 y0.023 q0.738 q3.294

6.035 y38.018 y146.563 y89.996 y0.024 q0.173 q4.229

6.046 y37.952 y135.860 y89.734 y0.012 q0.281 q3.842

0.810 y0.533 y7.389 y1.098 0.0 q0.126 q0.386

N 7.972 5.143 6.049 E y55.114 y37.532 y38.025 VNE T y198.756 y138.503 y149.953 VNE O y133.209 y96.469 y90.012 MX y0.004 y0.004 y0.014 MZ q0.308 q0.740 q0.172 QZZ q0.507 q3.343 q4.248 The monomer lies along the z-axis; see Fig. 1 for the orientation of the dimers.

6.035 y37.951 y140.446 y89.711 y0.035 q0.285 q3.690

0.802 y0.529 y7.947 y1.090 y0.002 q0.125 q0.376

dimer 2

a

J.A. Platts et al.r Chemical Physics Letters 285 (1998) 198–204

apparent that the largest changes occur in the basins of N1 and C2. These changes take the form of an increase in the electronic population and stabilisation of N1, and a loss of density in and destabilisation of C2. C3 too loses density to N1, and is overall destabilised. Thus, formation of dimer 1 leads to an increase in the effective electronegativity Žthe ability of an atom to stabilise charge. of N1. This may easily be rationalised in terms of the calculated atomic charges: the positively charged C2 is now in close proximity to and able to stabilise the charge distribution of N1. Conversely, the density in the basins of C2 and C3 is now repelled by the negative N1, causing a reduction in their electronegativity. Changes in the terminal atoms C4 and H5 are small, reflecting their distance from the interaction. The dipole moment of a single NCCCH unit in dimer 1, computed by summation over atomic charges and dipoles, is 3.93D. This small Ž5%. increase on the monomer value reflects the induced intramolecular charge transfer. Polarisations of the molecular charge distributions brought about by dimer formation are evident in the atomic multipole moments. Small dipole polarisations of atomic charge distributions are found in all but H5 in dimer 1. The direction of these atomic first moments Žnegative for atoms with positive x . indicate that the charge density in each atom is polarised away from the inter-molecular region, i.e. each molecular charge distribution appears to be repelling the other. This is quite unlike the situation observed in the dimer of HNO 2 w20x wherein induced atomic dipoles were found to be aligned head-to-tail. In all atoms, quadrupole polarisation is found to be diminished; again this is largest in N1 and C2, and barely significant in C4 and H5. Again, the sense of this depolarisation indicates a flow of density away from the inter-chain region, with density flowing from the x-direction and into the NCCCH axis. Still further information on the origins of stabilisation of dimer 1 may be obtained using the interand intra-atomic potential energies, which, along with the atomic repulsive energies determine the total atomic potential energy. The changes in these properties on formation of dimer 1 show that all atoms, including C4 and H5, experience large Žup to 30 hartree. increases in inter-atomic stabilisation and repulsion. The overall energy changes are obviously

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much smaller, and the role of intra-atomic stabilisation appears crucial in determining which atoms are stabilised. In particular, the only substantial increase in self stabilisation is found in N1, precisely that atom which undergoes overall stabilisation. The approach of NCCCH molecules in dimer 2, with nitrile and acetylinic groups eclipsed, leads to more complex changes in atomic properties than does formation of dimer 1. Again, N1 increases its population and is stabilised, though by rather less than in dimer 1. C2 and C3 are now barely affected by dimerisation, at least as far as their charges and energies are concerned. It is now C4 and H5, the spectators in dimer 1, who are forced to donate charge to N1 and are destabilised in the process. Thus the NCCCH molecule is able to polarise charge along its entire length in order to gain the most stable possible distribution of charge. It is again apparent that this polarisation is driven by the ability of N1 to accept more density in the dimer than in the free molecule, the other atoms sacrificing their density for the ‘‘greater cause’’ of overall stabilisation. In this orientation, a single NCCCH unit has a dipole moment of 4.10D, or 9% more than in the isolated monomer, rather more than in dimer 1. As in dimer 1, each atom in dimer 2 is dipole polarised away from the inter-chain region, apparently in an attempt to minimise repulsion.

4. Conclusions This study represents the first exploration of the potential energy surface of two anti-parallel dimers of NCCCH using high-quality correlated electronic structure methods, identifying two candidates for the energy minimum. The first corresponds to an ‘eclipsed’ orientation of the nitrile groups, with the inversion centre between the midpoints of the C ' N bonds. The second has more overlap of chains, with C ' N adjacent to C ' C bonds Žinversion centre between C–C single bonds.. Of these, the second is the more stable by around 3 kJ moly1 . This result agrees with the proposed dimer formation present in carbonitrile based liquid crystals w7x. This PES information alone may be useful in calibration of molecular dynamics simulations of ‘real’ systems such as liquid crystals, in which little is known about the

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J.A. Platts et al.r Chemical Physics Letters 285 (1998) 198–204

details of intermolecular interactions. In future studies it is intended to extend this analysis to larger systems, e.g. benzonitrile, to confirm these results for a more representative model system. Further to this, we have explored these intermolecular interactions using the topology of the charge density and the atomic properties so defined. It is established that the charge density, as characterised by the critical points ŽCPs., of a monomer within a dimer is similar to that in the free molecule. The critical points between molecules show interesting behaviour; in dimer 1 the monomers share a surface which is characterised by a single CP, linking the two nitrogens. In dimer 2, a ring structure is found, with each N linked to an acetylinic carbon. Atoms in Molecules analysis allows us to identify the source of the stabilisation of each dimer to be an increase in population and self-stabilisation of the nitrogens, the result of increased electronegativity. The source of the extra density of the Ns varies with the type of dimer, and is, generally speaking, the carbons closest to the N of the other monomer. References w1x D.S. Dudis, J.B. Everhart, T.M. Branch, S.S. Hunnicut, J. Phys. Chem. 100 Ž1996. 2083. w2x M.J. Frisch, J.A. Pople, J.E. Del Bene, J. Phys. Chem. 89 Ž1985. 3664. w3x G. Chalasinski, M.M. Szczesniak, Chem. Rev. 94 Ž1994. 94 ´ 1723, and references cited therein. w4x P. Hobza, H.L. Selzle, H.W. Schlag, Coll. Czech. Chem. Commun. 57 Ž1992. 1186. w5x K. Subramanian, S. Lakshmi, K. Rajagopalan, G. Koellner, T. Steiner, J. Mol. Struct 384 Ž1996. 121.

w6x T. Steiner, M. Tamm, A. Grzegorzewski, N. Schulte, N. Veldman, A.M.M. Schreurs, J.A. Kanters, J. Kroon, J. Vandermaas, B. Lutz, J Chem. Soc. Perkin Trans 2, 1996 2441. w7x K.J. Toyne in Thermotropic Liquid Crystals, G.W. Gray, Ed., Wiley, Chichester, 1987. w8x R.F.W. Bader, Atoms in Molecules: A Quantum Theory Clarendon Press, Oxford, 1990. w9x R.F.W. Bader, H. Essen, J. Chem. Phys. 80 Ž1984. 1943. w10x GAUSSIAN94 Rev. C3, M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. Al-Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P. Stewart, M. Head-Gordon, C. Gonzalez, J.A. Pople, Gaussian, Inc., Pittsburgh PA, 1995. w11x R. Krishnan, J.S. Binkley, J.A. Pople, J. Chem. Phys. 72 Ž1980. 650. w12x P.C. Hariharan, J.A. Pople, Theor. Chim. Acta 28 Ž1973. 213. w13x M.J. Frisch, J.A. Pople, J.S. Binkley, J. Chem. Phys. 80 Ž1984. 3265. w14x S.F. Boys, F. Bernardi, Mol. Phys. 19 Ž1970. 55. w15x F.W. Biegler-Konig, R.F.W. Bader, T.-H. Tang, J. Comput. ¨ Chem. 3 Ž1982. 317; these programs are available on request from Prof. Bader – [email protected] w16x A.A. Westenberg, E.B. Wilson, J. Am Chem. Soc. 72 Ž1950. 199. w17x M.J. Frisch, J.E. DelBene, J.S. Binkley, H.F. Schaefer, J. Chem. Phys 84 Ž1986. 2279. w18x M.T. Carroll, R.F.W. Bader, Mol. Phys. 65 Ž1988. 695. w19x J.A. Platts, S.T. Howard, B.R.F. Bracke, J.Am. Chem. Soc. 118 Ž1996. 2726. w20x J.A. Platts, S.T. Howard, K. Wozniak, Chem. Phys. Lett. 232 ´ Ž1995. 479. w21x R.G.A. Bone, R.F.W. Bader, J. Phys. Chem. 100 Ž1996. 10892. w22x R.F.W. Bader, C. Chang, J. Phys. Chem. 93 Ž1989. 2946.