3519
J . Phys. Chem. 1991,95, 3519-3522
Induced Dipole Moments In Acetylene Complexes C. Ruth Le Sueur? Anthony J. Stone,* University Chemical Laboratory, Lensfeld Road, Cambridge CB2 1 E W.England
and Patrick W. Fowler Department of Chemistry, University of Exeter, Exeter EX4 4QD, England (Received: August 21, 1990; In Final Form: November 9, 1990)
The induced dipole moments of a number of van der Waals complexes containing acetylene have been calculated from the distributed multipole moments and the distributed polarizabilities of the monomers. The induced moments calculated for the equilibrium structures are generally in close agreement with the experimental values (where available), and differences can be understood in terms of zero-point motion in the loosely bound complexes.
Introduction Dimer formation in the gas phase is often accompanied by a substantial change in net dipole moment. Dipole enhancements in hydrogen-bonded or other complexes of polar and quadrupolar molecules can amount to several tenths of a debye; e.g. Ap = 0.60 D (OCO-.HF)l and Ap = 0.49 D (OC.-BF3).2 Models based on the theory of long-range intermolecular forces account successfully for the angular and strength of binding in many such complexes and can also be used to give semiquantitative predictions of the interaction-induced dipole m ~ m e n t . ~The , ~ key element in the modeling of geometries has turned out to be the concise but accurate description of the monomer charge densities given by a distributed multipole analysis (DMA);I0 in predictions of dipole moments, a distributed polarizability analysis (DPA)I1 gives similarly accurate descriptions of the response of each monomer to the highly nonuniform field of its partner. The combined DMA/DPA model for dipole moments was first8 applied to heterodimers of the type B-HX (B = OC, OCO, N,; X = F, CI) and then9 to clusters involving BF,. The physical basis of the model is a simple one: the interaction dipole is the vector sum of the moments induced in each monomer by electrostatic interaction with the charge density of its partner. The results, summarized in Table I, show excellent agreement with experiment. l4 Experimental structures are now available for a series of polar complexes of acetylene, in which this molecule takes several different roles. It acts as a proton acceptor in HCCH/HF,I5J6 HCCH/HCI,” and HCCH/HCN,’* as a proton donor in HCCH/C0,I9 HCCH/N2,20and the newly discovered linear complex with hydrogen as both donor and acceptor in (HCCH)2:2 and as a participant in the non-H-bonded complexes HCCH/C0223and HCCH/Ar.24-26 In the present paper, we calculate interaction dipoles A p for all nine complexes within the DMA/DPA model, compare with measured values (summarized in Table 11) where known,16q21-26 and discuss the significance of induced dipoles in different geometrical isomers of HCCH/CO.
Method For each monomer molecule, we performed an SCF calculation at the equilibrium geometry to determine distributed multipoles up to rank 4 (hexadecapoie) on each atom, followed by a coupled Hartree-Fock perturbation calculation of the distributed polarizabilities to rank 2 on each atom, except that hydrogen sites were not used for the distributed polarizabilities of acetylene. These values were then used in electrostatic calculations to determine the induced dipole moments in the van der Waals complexes. The basis sets used for acetylene and hydrogen cyanide were the “extended 6-31G”basis sets of the CADPAC program,27 which are obtained from the standard 6-31G basis sets of Pople et aL2*by ‘Present address: Department of Physics and Astronomy, University College London, Gower Street, London WClE 6BT, England.
TABLE I: Calculated Induced Moments (D)for a Range of C o m ~ l e x e *s ~ ~ ~ A--.B ApA Ape Apt* ApeXW Nz***HCI 0.210 0.055 0.265 0.25 ... N2*..HF 0.371 0.043 0.412 OC..-HCI 0.245 0.136 0.381 0.39 OC.. * H F 0.454 0.096 0.550 ... OCO.-*HCI 0.320 0.121 0.441 0.45 OCO.**HF 0.548 0.069 0.617 0.60 AP ..BF3 0.165 0.021 0.186 0.176 N,**.BF3 0.252 0.114 0.366 0.35 OC*.*BF, 0.297 0.169 0.467 0.482
Weak
ref 8,12 8 8,12 8 8,13 1,8
2,9 2,9 2,9
“Ap’ is the contribution induced in A by the proximity of B, and a similar definition applies to Ape.
TABLE 11: Experimental Values of tbe Total Dipoles (D)Where
Known p complex HCCH*..HF 2.368 HCCH...NCH 3.42 HCCH***HCCH 0.28
ref 16 21 22
complex p HCCH***COZ 0.161 HCCH.-.Ar 0.027
ref 23 24
adding diffuse s and p functions and two sets of rather diffuse polarization functions. The polarizabilities for carbon dioxide were (1) Baiocchi, F. A.; Dixon, T. A.; Joyner, C. H.; Klemperer, W. J . Chem. Phys. 1981, 74, 6544. (2) Janda, K. C.; Bernstein, L. S.; Steed, J. M.; Novick, S.E.; Klemperer, W. J. Am. Chem. SOC.1978, 100, 8074. (3) Buckingham, A. D.; Fowler, P. W. J . Chem. Phys. 1983, 79, 6426. (4) Buckingham, A. D.; Fowler, P. W. Can. J . Chem. 1985, 63, 2018. ( 5 ) Hurst, G. J. 8.; Fowler, P. W.; Stone, A. J.; Buckingham, A. D. Inr. J . Quantum Chem. 1986,29, 1223. (6) Buckingham, A. D.; Fowler, P. W. J. Mol. Srrucr. 1988, 189, 203. (7) Fowler, P. W.; Tole, P. J . Mol. Struct. 1988, 189, 121. (8) Buckingham, A. D.; Fowler, P. W.; Stone, A. J. Int. Reo. Phys. Chem. 1986, 5, 107. (9) Fowler, P. W.;Stone, A. J. J . Phys. Chem. 1987, 91, 509. (10) Stone, A. J. Chem. Phys. Lett. 1981, 83, 233. (11) Stone, A. J. Mol. Phys. 1985,56, 1065. (12) Altman, R. S.;Marshall, M. D.; Klemperer, W. Faraday Discuss. Chem. Soc. 1982, No. 73, 116; J. Chem. Phys. 1983,79,57. Altman, R.S.; Marshall, M. D.; Klemperer, W.; Krupnov, A. J . Chem. Phys. 1983,79,52. (13) Altman, R. S.;Marshall, M. D.; Klemperer, W. J. Chem. Phys. 1982, 77, 4344. (14) We have discovered that the data used for the calculation on OC-BF3 reported in ref 9 were incorrect. Table I shows the corrected values; the agreement with experiment remains good. (15) Read, W. G.; Flygare, W. H. J . Chem. Phys. 1982. 76, 2238. (16) Nelson, D. D.; Fraser, G. T.; Klemperer, W. J. Chem. Phys. 1985, 82, 4483. (17) Legon, A. C.; Aldrich, P. D.; Flygare, W.H. J . Chem. Phys. 1981, 75, 625. (18) Aldrich, P. D.; Kukolich, S.J.; Campbell, E.J. J . Chem. Phys. 1983, 78, 3521. (19) Marshall, M. D.; Prichard, D. G.; Muenter, J. S.J . Chem. Phys. 1989, 90, 6049.
0022-3654/91/2095-3519$02.50/00 1991 American Chemical Society
3520 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991
Le Sueur et al.
TABLE 111: Calculated Induced Moments for Certain Configurations Of CIHy*.HX (X F, c1, CN)'
3.08 3.08 3.08 3.08 3.08 3.08 3.08 3.08 3.08 3.08
90 90 90 90 90 90 90 90 90 90
3.70 3.70 3.70 3.70 3.70 3.70 3.70 3.70 3.70 3.70
90 90 90 90 90 90 90 90 90 90
4.22 4.22 4.22 4.22 4.22 4.22 4.22 4.22 4.22 4.22
90 90 90 90 90 90 90 90 90 90
0
5 IO 15 20 25 30 2 4 6 0 5
IO 15 20 25 30 2 4 6 0
5
IO 15 20 25 30 2 4 6
C2H2' * *HF 0 0 0 0.063 0 0.124 0 0.179 0 0.228 0 0.268 0 0.300 90 0 90 0 90 0
0 0 0 0 0 0 0 0.015 0.029 0.044
-0.628 -0.624 -0.612 -0.592 -0.564 -0.529 -0.487 -0.627 -0.624 -0.619
0.051 0.098 0.138 0.168 0.191 0.205 0 0 0
0 0 0 0 0 0 0 0.011 0.023 0.034
-0.515 -0.513 -0.505 -0.491 -0.469 -0.439 -0.400 -0.514 -0.512 -0.509
C2H2***HCN 0 0 0 0.048 0 0.091 0 0.127 0 0.156 0 0.175 0 0.188 90 0 0 90 90 0
0 0 0 0 0 0 0 0.011 0.021 0.031
-0.504 -0.500 -0.487 -0.466 -0.437 -0.402 -0.363 -0.503 -0.500 -0.495
C2H2**.HCI 0 0
0 0 0 0 0 0 90 90 90
a For a definition of angles, see Figure I . Apx, Apy, and Apz are the induced dipole components in the axis system shown in Figure I .
calculated by using the 5s4p2d basis from the CADPAC library, but the distributed multipoles were taken from the calculations by Amos et aLZ9in which a 5s4p3dlf basis was used. We also used the 5s4p2d basis set for carbon monoxide and nitrogen. For hydrogen fluoride the basis used was 6sSp3d/4s3p, and for hydrogen chloride it was 7s6p3d/4s3p. For argon, we used the polarizabilities calculated by McEachran et aL30 The multipole moments and polarizabilities are available as supplementary material, Tables S1 and S2, respectively. In the tables accompanying the following sections, the structures are usually described in terms of the distance R between the centers of mass, the angle d1 between the C2H2axis and the vector joining the centers of mass, the angle flz between the axis of the second molecule and the center-of-mass vector, and the dihedral angle 4 (see Figure 1). Note that where the second molecule is not centrosymmetric, its axis is defined as being directed toward (20)Nandi, R. N.; Prichard, D. G.; Muenter, J. S. To be submitted for publication. (21) Block, P. A.; Jucks, K. W.: Pedersen, L. G.; Miller, R. E. Chem. fhys. 1989, 139, 15. (22)Prichard, D. G.; Nandi, R. N.; Muenter, J. S. J . Chem. fhys. 1988, 89, I IS. Fraser, G.T.;Suenram, R. D.; Lovas, F. J.; Pine, A. S.;Hougen, J. T.; Lafferty, W. J.: Muenter, J. S. J . Chem. fhys. 1988, 89, 6028. (23)Prichard, D. 0.;Nandi, R. N.; Muenter, J. S.; Howard, B. J. J. Chem. fhys. 1988,89, 1245. Muenter, J. S.J . Chem. fhys. 1989, 90,4048. (24)DeLeon, R. L.; Muenter, J. S.J . Chem. fhys. 1980. 72, 6020. (25)Muenter, J. S. To be submitted for publication. (26)Ohshima, Y.; lida, M.; Endo, Y. Chem. Phys. Len. 1989, 161, 202. (27)Amos, R. D.; Rice., J. E. CADPAC: The Cambridge Analytical Derivatives Package, issue 4.0.Cambridge University, 1987. (28)Hehre, W. J.; Ditchfield, R.; Pople. J. A. J . Chem. fhys. 1971, 56, 2257. (29)Amos. R. D.; Handy, N. C.; Knowles, P. J.; Rice, J. E.; Stone, A. J. J. fhys. Chcm. 1985,89, 2186. (30) McEachran, R. P.; Ryman, A. G.; Stauffer, A. D. J . fhys. E 1977, 10, L681. McEachran, R. P.;Stauffer, A. D.;Greita, S. J . Phys. B 1979,12, 3119.
R
Z
Figure 1. Definition of coordinates used to describe the geometries of the complexes. The Z axis runs from the center of mass of molecule 1 through the center of mass of molecule 2. TABLE I V Calculated Induced Moments for Certain Planar Configurations of CzH2- C O and CzHz.. -Nz and Near-Linear C ~ f l g u n t i oOf~ CzHz***NCH' RIA 0,ldea &Idea AuJD A d D C2HZ...CO 5.01 0 0 0 0.213 5.01 0 20 -0.03 1 0.185 5.01 0 40 -0.03I 0.120 5.01 0 60 -0.013 0.06I 0 80 0.002 5.01 0.035 5.01 0 100 0.004 0.044 120 0.009 5.01 0 0.076 140 5.01 0 -0.001 0.115 5.01 0 160 -0.001 0.147 5.01 0 0.160 180 0 5.01 140 40 0.016 0.057 5.01 100 80 0.020 -0.030 5.01 60 120 0.004 0.010 160 -0.013 5.01 20 0.126
-
C2H2***N2
4.82 4.82 4.82 4.82 4.82 4.82 4.82 4.64 4.64 4.64 4.64 4.64
0 0 0 0
IO 20 30
0 0 0
IO 20
0 10 20 30 0 0 0
0 -0.002 -0.002 0.000 -0.01 5 -0.024 -0.026
0.199 0.193 0.177 0.153 0.186 0.152 0.111
C2Hz***NCH 180 0 170 0.011 160 0.020 180 0.016 180 0.022
0.590 0.580 0.549 0.561 0.481
For a definition of angles, see Figure I ; 4 = 0" in all cases. Apx and Ap, are the induced dipole components in the axis system shown in Figure I .
the atom with highest atomic number. Acetylene as Proton Acceptor. In all three HCCH/HX complexes (X = F, CI, CN), the equilibrium structure is T-shaped with the H pointing toward the acetylene molecule, forming a hydrogen bond with the r-electron cloud of the We take this configuration to correspond to f12 = 0" (Figure 1). Because of the shape of the r-electron cloud, it is likely that the HX molecule will undergo large-amplitude motions in the plane of the complex, but only small ones out of the plane. For this reason we studied conformations where HX is rotated through
Induced Dipole Moments in Acetylene Complexes
n
a
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3521 TABLE V Calculated Induced Moments for Certain Configurations of C,HV G H ? and C,HV C O P
-
b
Figure 2. Two possible routes for conversion between different conformers of (HCCH),: (a) in-plane; (b) out-of-plane.
up to 30° in-plane, but only 6 O out-of-plane. The measured dipole moment is the component along the u inertial axis, which coincides approximately with the Z axis shown in Figure 1, and since the results in Table 111 show that none of these motions have much effect on Apz, we expect the theoretical calculations at the equilibrium structure to agree well with measurements of the induced dipole. Indeed, the experimental result for the HF complex of 0.65 D obtained by Nelson et a1.16 does agree well with our calculations. However, for the H C N complex, the calculated induced dipole is more sensitive to variations in geometry, and the measured induced dipole will probably be lower than the value calculated for the equilibrium structure. Acerylene us Proton Donor. The complex between acetylene and carbon monoxide is known to be linear, and the circumstantial evidence that the structure is HCCH-CO and not HCCH*+.0C19 has been confirmed by the infrared spectrum of the "CO isotop ~ m e r . ~We ' performed calculations for the rotation of CO about its center of mass and for a cogwheel type motion of both molecules. The results are shown in Table IV. The value of Oo for dZ corresponds to the orientation HCCH-CO; 180°, to HCCH-.OC. In both cases the induced dipole points away from the acetylene. When combined with the dipole of carbon monoxide, it produces in the first case a substantial total dipole of 0.3 D but in the second a much smaller dipole of 0.05 D. Thus, experimental determination of the dipole of this complex could provide confirmatory evidence for the structure. The complex HCCH-NZ is believed to be linear3z with a center-of-mass separation of 4.822 A, and the Buckingham-Fowler model also favors the linear structure. The induced dipole for the linear structure is 0.199 D, but from Table IV we can see that librations of either molecule, especially the acetylene, away from this equilibrium structure are likely to reduce the induced dipole considerably. The linear complex of acetylene with hydrogen cyanide has only recently been detected, and has the structure HCCH-.NCH. Block et ala2'have determined its dipole moment to be 3.42 D in the ground vibrational state, which, when combined with the measured value of the hydrogen cyanide gives an induced dipole of about 0.44 D, in reasonable ageement with our calculated value of 0.590 D, particularly when librations away from the minimum are taken into account. Acerylene Dimer. The equilibrium structure for this complex is T-shaped with C, planar symmetry.22 It is, however, known to undergo large-amplitude in-plane motions and almost certainly rotates like a pair of cogwheels from one T-shaped structure to (31) Muenter, J. S. Personal communication. (32) Muenter, J. S.;Prichard, D. G.; Nandi, R. N.; Howard, B. J. Bull.
Am. Phys. SOC.1988, 33,941. (33) Lovas, F. J. J . Phys. Chem. Ref. Data 1978, 7 , 1445.
RIA
Wdeg
4.38 4.38 4.38 4.38 4.38 4.38 4.38
90 90 80 70 90 45 45
3.292 3.292 3.292 3.292 3.292
90 80 90 80 90
02/deg 4/deg A P X D APYID 4 4 D (C2H2)Z 0
0 0 0 0 90 90 0
IO 10 20 10 45 45
90 90 80 80 90
0 0.059 0.023 0.033 0 -0.078 0
C,H,**.CO, 0 0 0 -0.052 0 -0.054 0 -0.103 10 0
0 0 0 0 0.030 0.078 0
-0.337 -0.320 -0.310 -0.241 -0.316 0 0
0 0 0 0 0
-0.141 -0.140 -0.139 -0.156 -0.142
"See Figure 1 for a definition of angles. Apx, Apy, and Ahz are the dipole components in the axis system shown in Figure 1.
another, following the motion illustrated in Figure 2a. The barrier to this motion is estimatedZZfrom the tunneling splittings to be only 33 cm-l. The most recent a b initio calculation^^^ give an estimate for the barrier of only 20 cm-I, but the calculated value is very sensitive to the quality of the calculation. We calculated the dipole moment for the geometries listed in Table V. The last of the values shown is zero by symmetry. The dipole moment at the equilibrium geometry (0.337 D) is rather high compared with the experimental value of 0.28 D, but if the possibility of cogwheel-like rotation is taken into account, then we can see that the magnitude of the average dipole would be somewhat lower than the equilibrium value of 0.337 D: e, e, 4 BBD
+ +
90
0
0
-0.337
45
45
0
O.Oo0
0
90
0
0.337
Here a positive sign for the induced dipole corresponds to a moment in the direction from molecule 1 to molecule 2. There is also the possibility of an out-of-plane cogwheel motion, illustrated in Figure 2b, and in this case the dipole does not drop quite to zero, because there is no center of symmetry in any intermediate configuration:
+
01 90
e, 0
90
4.337
45
45
90
(0.111)
0
90
90
0.337
+ +
P ~ D
In this case, the dipole moment for the intermediate geometry is perpendicular to the line joining the centers of mass. This is a less favorable path for interconversion between the conformers because the intermediate structure has a much higher energy than it does in the planar case, but motion along this coordinate would also reduce the average dipole moment. We conclude that the values of the dipole moment obtained from our calculations are in goad agreement with the experimental value of 0.28 D.22 AcetylenelCarbon Dioxide. The equilibrium structure for this complex has a planar C, geometry, with the molecules parallel to each other. It is less floppy than any of the other four complexes for which dipoles are known. All our calculations used a center-of-mass separation of 3.292 A. From the results shown in Table V, we see that the dipole varies very little for small changes in the geometry, except in the case where both molecules are (34) Bone, R. G. A.; Handy, N. C. Theor. Chim. Acta, in press.
3522 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991
Le Sueur et al.
TABLE VI: Calculated Induced Moments for Certain Configurations Of CiHv * *AP
RIA
9ideg
AklD
4.04 4.05 4.10 4.17 4.27 4.37 4.48 4.57 4.64 4.66 4.57 3.51
90 80 70
-0.057 -0.050 -0.030 -0.001
60 50 40 30 20 10 0
90 90
0.030 0.057 0.07 1 0.065 0.039 0 -0.035 -0.098
0 -0.023
-0.039 -0.044 -0.034
-0.009 0.028
0.069 0.100 0.113
0 0
"Ap, and AM, are the components of the dipole moment parallel and perpendicular to the axis of the acetylene molecule.
rotated through 10' in the same direction, and even then the change is only about 15%. These values are smaller by 10-1 5% than the experimental value of 0.161 D.23 However, the distributed multipoles of C02 were obtained from the work of Amos et al.29 and are adjusted by Moller-Plesset perturbation theory for the effects of electron correlation. This procedure usually overestimates the electron correlation correction to the moments, which will accordingly be somewhat too small. If uncorrected SCF moments are used, the calculated induced moment is some 10% too large. We conclude that, here too, the electrostatic picture gives a satisfactory account of the induced moment. AcetylenelArgon. The complex between acetylene and argon adopts a T-shaped equilibrium structure, but it undergoes large-amplitude oscillations about this s t r u c t ~ r e . Although ~~*~~ various values for the center-of-mass separation have been proposed, the most reliable is likely to be the value of 4.04 A based on a ground-state microwave spectrum.% The experimental dipole moment is very small, namely 0.027 D, and the calculated value of 0.057 D found for the equilibrium structure is too large by a factor of about 2. In Table VI, R and B gives the position of the argon atom in polar coordinates relative to the center of mass of the acetylene molecule, which is aligned along the z direction. Thus the T-shaped experimental equilibrium structure has R = 4.04 A and B = 90°, while structures with B = ' 0 are linear. Table VI gives calculated dipole moments for a few other configurations close to the equilibrium structure, to give some guidance on the effect of zero-point vibrations. These results suggest that radial zero-point motion would tend to increase, rather than decrease, the average dipole. Larger excursions from the equilibrium geometry could occur, with the argon atom moving over the surface of the acetylene molecule, and while it is unlikely that the linear structure would be stable, a motion of large amplitude is quite possible. Table VI shows some induced dipole moment values calculated for structures in which the argon atom is positioned on an ellipse that coincides approximately with the van der Waals envelope, with a minor axis of 4.04 A and a major axis of 4.66 A. The components of the dipole moment parallel and perpendicular to the acetylene axis are tabulated, and the induced moments are illustrated in Figure 3. The measured dipole is the average component along the a inertial axis (Le., approximately along the line
Figure 3. Induced dipole moment of HCCH-Ar for different positions of the Ar atom relative to the HCCH molecule.
joining the centers of mass), and it is very clear from the figure that this component falls rapidly to zero as the argon atom moves away from the equilibrium geometry. It can be seen that such a motion would reduce the magnitude of the average dipole moment considerably. The experimental resultsz6 show that the lowest frequency vibration is very floppy, with a frequency of 8.9 cm-I, and the root-mean-square value of AB is 20'. If we assume that this vibration is a harmonic oscillation in the angle t9 between the acetylene molecular axis and the center-of-mass vector, we can use the measured root-mean-square value of Ad to obtain the vibrational wave function and perform a vibrational average. The average value of the dipole component along the center-of-mass vector is found in this way to be 0.033 D, which is in satisfactory agreement with the experimental value of 0.027 D.
Conclusions Acetylene is involved in a wide variety of complexes, and the induced moments vary considerably in magnitude. A simple electrostatic model based on distributed multipole moments and distributed polarizabilities gives a satisfactory account of these induced moments. The induced moment calculated a t the equilibrium geometry by using this model is not always in close agreement with the experimental value, but there is no case in which the discrepancy is not readily understandable in terms of librational motions of the complex, which often cause very substantial changes in the magnitude and direction of the induced moment. It is not usually possible to calculate an averaged value of the induced moment without more knowledge of the vibrational motion than is currently available, but an approximate calculation of the vibrationally averaged induced moment for the A+C2H2 complex gives a result in satisfactory agreement with experiment. Acknowledgment. We are grateful to Dr. J. S.Muenter for providing experimental results in advance of publication and for some helpful discussions. C.R.L.S. thanks the SERC for financial support. Supplementary Material Available: Distributed multipole moments and polarizabilities used in these calculations (Tables S1 and S2) (9 pages). Ordering information is given on any current masthead page.
