J. Phys. Chem. 1990,94, 5589-5592 of the first hyperpolarizabilities become reliable. The values for the dipole polarizabilities for HCP are as expected considerably larger by a factor of about 2 compared to those for HCN.5J3*i7 However, the very high value obtained for the high values for the /3 tensor compared to the corresponding HCN values were unexpected and suggest that further calculations on molecules containing heavier atoms than the first two periods, i.e., second row and higher, will yield interesting results.
Conclusions The geometry optimization results support the conclusion of Amos et al.' that accurate geometries can be obtained at the MP2 level if the basis set is made large enough. However, we also find that equivalent results may obtained using the coupled cluster CCD level but with a smaller basis set. Both methods also produce the experimental vibration frequencies with an accuracy of less than 5%. The results also support the conclusions of Simundiras ~~
(17)
~~
Jam",
C. J.; Fowler, P. W. J . Chem. Phys. 1986,85, 3432.
5589
et a1.I0 on the importance of including a set o f f basis functions in order to get accurate values for bending frequencies in bonded systems. The calculations on the polarizabilities and the first hyperpolarizabilities show that although the dipolar polarizabilities can be predicted with an accuracy of 1&15%, using only two sets of carefully chosen diffuse functions, the first hyperpolarizability tensor is far more sensitive to the number of diffuse functions and reliable values can only be obtained by using a set of more than 4D sets of functions. The exponents of these D functions can be obtained from the innermost D function by applying a reduction factor of 0.5 for successive exponents. Acknowledgment. This research was supported by the Naval Air Systems Command through Contract MDA 9003-86-C-0245. The author thanks the very supportive University of Tennessee Computing Center staff, especially Sue Smith for implementing the GAUSSIANM program on the IBM 3090/200 and for the allocation of an extensive amount of computer time and of disk space. Registry No. Phosphaethyne, 6829-52-3.
Ab Initio Calculations on the Geometries and Stablllties of Acetylene Complexest Jianguo Yu,* Sbujun Su, and John E. Bloor Department of Chemistry, The University of Tennessee, Knoxville, Tennessee 37996- I600 (Received: November IO, 1989; In Final Form: January 22, 1990)
Structures of four different molecular complexes of acetylene, (C2H2I2,(C2H2)3, (C2H2)+ and (CZHZ)~. have been studied at both the Hartree-Fock and the M0ller-Plesset perturbation (MP2) levels. For the dimer a T-shaped structure of Cb symmetry is found to be the most stable, for (C2H2)3 a "twisted" C3, structure is favored, and for (C2H2),two structures have the same interaction energies. The one with S, symmetry seems to be more experimentally favored. For ( C Z H ~ a) ~ , nonplanar structure is predicted to be most stable. The results show that all the acetylene complexes larger than the dimer which were studied show a preference for multiple T-type hydrogen bonding.
I. Introduction The structure and properties of weakly bound molecular complexes have gained more and more attention in recent years, both theoretical and experimental. Complexes of acetylene are one of the key systems in determining the geometries and stabilities of these complexes. For the acetylene dimer, the simplest acetylene cluster, Pendley and Ewing' reported five bands using long-path low-temperature Fourier transform infrared spectroscopy. Although their spectra do not allow a complete determination of the complex's structure, the band shapes are consistent with the staggered parallel structure (S-shaped) proposed by Sakai et al.* This structure is depicted in Figure la. Miller et aL3 discussed several possible interpretations of the three main peaks observed in the infrared spectrum of the dimer and suggested that there exists more than one stable dimer structure. A second paper by Fischer et al.' showed that the bands in the IR spectra of acetylene have rather different pressure dependencies and may be associated with different cluster sizes. Recently, Bryant et al? provided the evidence for two dimer structures and assigned one to the S-shaped one (Figure la) with C , symmetry. Although the free-jet infrared absorption spectroscopy study of Ohshima et a1.6 was interpreted as evidence for an acetylene dimer complex, which is a hydrogen-bonded T-shaped structure with C , symmetry (Figure lb), the radio-frequency, microwave, and IR spectra obtained by Muenter et a1.7 were used Pttscntcd at the International Conference in Honor of Professor John A. Pople, Oct 16-19, !989, Center for Computational Quantum Chemistry, University of Georgia, Athens, GA.
0022-3654/90/2094-5589$02.50/0
to conclude that the T-shaped acetylene dimer appears not to have C, symmetry. Fraser-8 presented model calculations to interpret the large C-H stretching vibrational dependencies of the interconversion tunneling splittings and the corresponding infrared vibrational tunneling state selection rules in the acetylene dimer. For the larger sizes of acetylene cluster, Prichard et al? proposed a trimer geometry with D3,, or C3,symmetry (see Figure 2a.b) based on the infrared vibration rotation spectra. Bryant et a1.I0 conducted a rotational analysis for the infrared spectra of the acetylene tetramer and found that a puckered ring structure of S, symmetry (see Figure 3a) is consistent with the experimental data. There have been a number of previous theoretical investigations of acetylene clusters; Sakai et aL2 calculated the intermolecular
-
(1) Pendlcy, R. D.; Ewing, G. F. J. Chem. Phys. 1983, 78, 3531. (2) Sakai, K.; Koide, A,; Kihara, T. Chcm. Phys. L r r . 1977, 47, 416. (3) Miller, R. E.; Vohralik, P. F.; Watts, R. 0. J. Chem. Phys. 1984,80,
5453.
(4) Fischer, G.; Miller, R.E.; Vohralik, P. F.; Watts, R.0.J. Chem.Phys. 1985, 83, 1471. (5) Bryant, G. W.; Eggers, D. F.;Watts, R. 0. J. Chem. Soc., Faraday Trans. 2 1988,84, 1443. (6) Oshima, Y.;Matsumoto, Y.;Takami, M.Chem. Phys. Lett. 1988, 147, 1.
(7) Prichard, D. G.; Nandi, R.N.; Mucnter, J. S. J . Chem. Phys. 1988, 89, 115. ( 8 ) Fraser, G. T. J. Chcm. Phys. 1989, 90,2097. ( 9 ) Prichard, D.; Mucnter, J. S.; Howard, B. J. Chem. Phys. Leu. 1987, 135. 9. (IO) Bryant, G. W.; Eggers, D. F.; Watt, R. 0. Chem. Phys. Lrr. 1988, IS!, 309.
0 1990 American Chemical Society
Yu et al.
5590 The Journal of Physical Chemistry, Vol. 94, No. 14, 1990 (b) (a)
H-$FC*
H-C
1"
H
TABLE I Geometries of Acetylene and Its DimeP method configuration L. A HF/3-21G monomer 1.1875 1.1884 ( r , ) T-shaped I . 1880 (ra)
I
P
C--t-l
H
MP2/6-31G*
Figure 1. Two possible structures for (CZH& (a) S-shpaed structure with C, symmetry and (b) T-shaped structure with C, symmetry.
S-shaped monomer T-shaped
1.1880 1.2180 1.2170 (rl) 1.2171 (r3)
S-shaped
1.2170 1.2026 (1)
exptb
RPU.A 1.0509 1.0513 (r,) 1.0525 (r4) 1.0507 (rs) 1.0512 1.0660 1.0665 (r2) 1.0684 (r4) 1.0659 (rs) 1.0662 1.0621 (2)
'For r , , r2, r3, r4, and rs, see Figure Ib. bReference 14.
I
I
TABLE 11: Effect of Restraint on tbe Distance of tbe Center of Mass and Energy (AE) of Acetylene Dimer kcal/mol AE, dimer method R, A 6, deg T-shaped HF/3-21G restrained 4.5096 1.6 unrestrained 4.5097 1.6 2.2 MP2/6-31G* restrained 4.3178 unrestrained 4.3222 2.2 S-shaped HF/3-21G restrained 4.3851 42.1 1.1 unrestrained 4.3820 42.0 1.1 1.6 MP2/6-31G* restrained 4.2243 41.7 1.6 unrestrained 4.2229 41.8
recently, Bone et a].,', using MP2 ab initio calculations, found that the global minimum of the acetylene trimer is of C3hsymmetry. In the present work a consistent set of ab initio methods were employed to calculate the geometries and stabilities for acetylene dimer, trimer, tetramer, and pentamer.
6
11. Computational Details
potential for acetylene and found the S-shaped and T-shaped dimers have deep potential minima with the S-shaped being by far the deepest. Using a b initio calculations at the M~ller-Plemet second-order (MP2) level with a DZP basis set, Alberts et al." located the minima on the potential energy surfaces of the acetylene dimer and trimer complexes and predicted a T-shaped structure for the dimer and a C3hstructure for the trimer. More
First, the geometry of the acetylene monomer in dimer complexes was checked. Calculations at the HF/3-21G and MP2/ 6-31G* levels were used to optimize geometries of the S-shaped and T-shaped dimers both with and without relaxing all geometrical parameters in the systems, including that of acetylene monomer. It was found that the geometry of acetylene monomer in these complexes was almost identical with its isolated configuration (Table I) and that either with or without relaxing the geometry of C2H2monomer the geometries of the complexes and the interaction energies did not change very much (Table 11). Therefore, in all following calculations, the geometric parameters of the acetylene molecule in its complexes were restricted to the values that were optimized at the corresponding theoretical levels. Four levels of a b initio calculations, HF/3-21G, HF/6-31G*, MP2/3-21G, and MP2/6-31G*, were performed to optimize the S-and T-shaped structures for acetylene dimers. Among all of the four levels, two levels that do not include the electronic correlation, HF/3-21G and HF/6-3 IC*, yielded longer distances of the hydrogen bond and smaller interaction energies compared to those calculated with the MP2 model. The electronic correlation must be included for such weakly bound complexes as acetylene clusters. It should be pointed out that the MP2/3-21G produced satisfactory results compared to that from the MP2/6-3 lG* procedure but was less time-consuming. Therefore, for the trimers (C,H,), and tetramers (CZH2)4both the HF/3-21G and MP2/ 3-21G models were used in obtaining their optimized geometries, and then the MP3/6-311G** method was employed to calculate the interaction energies. For the pentamers (CzH& only the HF/3-2 1G calculations were carried out to optimize the geometries. All calculations were conducted on the IBM-3090 at UTCC using the GAUSSIAN 86 program.I3
(1 1) Alberts, 1. L.; Rowlands, T. W.; Handy, N. C. J . G e m . Phys. 1988, 88, 381 1.
(12) Bone, G. R. A.; Murray, C. W.; Amos, R. D.; Handy, N. C. Chem. Phys. Lett. 1989, 161, 166.
Figure 3. Three possible structures for (C2H2)4: (a) S4,(b) C,h, and (c) D3h.
The Journal of Physical Chemistry, Vol. 94, No. 14, 1990 5591
Geometries and Stabilities of C2H2Complexes TABLE III: Optimized Geometries and Interaction Energies ( A E )
for Dimers -
~
I
~~
u,
dimer method T-shaped HF/3-21G MP3/6-31 1GS*//HF/3-21G HF/6-3 IG* MP2/3-2lG MP2/6-31G* MP3/6-311G**//MP2/631G*
expt
R, A 0, deg kcal/mol 4.5096 1.6 1.5 4.6188 1.3 4.3245 2.0 4.3 178 2.2 1.5 4.41 4.3851
S-shaped HFJ3-21'3 MP3/6-31 lG**//HF/3-21G HF/6-3 IG* MF2/3-21G MP2/6-31GS MP3/6-31 IG**//MP2/631G*
expt
t
+
t t
t
t
42.1
+ +
+
++++
1.1 1.3
1.o
1.4 1.6 1.3
54.7
I eFigure 5. Plot of A,?? vs 8. TABLE I V Optimized Geometries and Interaction Energies for Tri"
geometry Cqr
c
b
d
Figure 4. Twisted "top" structure. e
111. Results and Discussion A. Dimers. In our calculations, the T-shaped structure was
more stable than the S-shaped form at all of the four levels of calculation shown in Table 111. At the highest level of calculation (MP3/6-31 IG**//MP2/6-31G*) the interaction energy AE for the T- and S-shaped structure was 1.5 and 1.3 kcal/mol, respectively. This indicates that even though there might exist two hydrogen bonds of A type, Le., between a hydrogen on one acetylene monomer and the A bond on the other, in the S-shaped dimer, it is less stable than the T-shpaed form in which there exists only one hydrogen bond of A type. Alberts et al." claimed the S-shaped structure to be the transition state. Experimentally, it was shown that the T-shaped hydrogen plays a key role in forming larger size of acetylene clusters. This T-shaped structure was found to be C, symmetry a t all of four levels. Since Muenter et al.' experimentally predicted a preferred structure with twisted "top" about its center of mass by 27O (see Figure 4), we calculated the change in the interaction energy AE with the change of the angle shown in Figure 5 and found the T-shaped dimer of C , symmetry to be more stable. Our results are well in agreement with the experimental data of Ohshima et aL6 and those of Albert et al." B. Trimers. We tried to optimize the D3hconfiguration for the acetylene trimer but failed to obtain the geometry shown in Figure 2a. On the basis of the analysis of the stabilities of acetylene dimer structure, we assumed that there should exist three distorted T-type hydrogen bonds in the trimer of C3, symmetry. Besides C3@we also proposed and optimized several other possible configurations for (C2H2)3 (Figure 3c-f). The optimized geometries and the interaction energies are shown in Table IV. Among the optimized structures, the one with c 3 h symmetry (Figure 3b) was found to be the most stable, which is not surprising, because of three "distorted" hydrogen bonds of T type while others have (13) Frisch. M.; Binkley, J. S.;Schlegel, H. B.; Raghavachari, K.;Martin, R.;Stewart, J. J. P.; Bobrawicz, F.; Defrees, D.; Secger, R.;Whiteside, R.; Fox, D.; Fluder, E.; Pople, J. A. Gaussian 86 (IBM 3090) Version;Carnegie-Mellon Quantum Chemistry Publishing Unit: Pittsburgh, PA, 1984. (14) Baldacci, A.; Ghersetti, S.;Hurlock, S.C.; Rao, K. N. J. Mol. Srrucr. 1976. 59, 116.
t
&+++
4.4095 43.4 4.3292 40.0 4.2124 41.9 4.12
+
f
method
R, A
8, deg 46.9 49.1
HF/3-21G 4.474 MP2/34.335 21G expt 4.354 40.0 HFJ3-21G 2.904 123.9 MP2/32.658 123.9 21G HF/3-21G 2.831 2.851 (RJ MP2/32.658 1.635 ( R , ) 21G HF/3-21G 2.881 M$2/32.660 21G HF/3-21G 2.879 M$2/32.659 21G
hE,b
kcal/mol
kcal/mol
4.6 5.9
4.5
2.9 3.9
2.9
3.3 4.3
3.3
3.1 4.0
3.0
3.1 4.0
3.0
'For c, d, e, and f, see Figure 2. bMP3/6-31G*//MP2/3-21G,
only two. It was found in this work that the interaction energy for a hydrogen bond of T type is about 1.53 kcal/mol at the MP3/6-31 lG**//MP2/3-21G level. Even though the total interaction energies AE in the other four trimers all are close to the sum of two single hydrogen bonds and the AE for the trimer with c 3 h symmetry is a bit less than the sum of three single H bonds, the latter is still much more favored than all others. We believe that the acetylene monomers tend to aggregate via the hydrogen bonds. To reach the maximum number of the hydrogen bonds, therefore, the trimer has to be twisted to accommodate three hydrogen bonds. It should be pointed out that the degree of twisted angle has little effect on the interaction energy; thus, a twisted H bond (- 1.49 kcal/mol) is almost identical with a hydrogen bond of the exact T type (- 1.53 kcal/mol) in terms of the interaction energy. Bone et a1.I2 obtained similar results in which the c 3 h trimer of acetylene is the most stable among all trimers. C. Tetramers. The expected structure for a tetramer of acetylene is a planar configuration with C4! symmetry, based on the preceding discussion on dimers and trimers in which it was found that the more T-shaped hydrogen bonds formed between acetylenes, the more stable are the complexes. However, Bryant et a1.I0 experimentally predicted a geometry of S4symmetry for the acetylene tetramer (Figure 3a). The structure has the molecular centers of 2.78 A from the S, axis, and they are alternately 0.89 A above and below a plane that contains the cluster center of mass and is perpendicular to the rotation axis. All four molecules are tilted 28O with respect to this plane. Although the hydrogen bonds are twisted, this S,symmetry makes the tetramer more stable because it reduces the repulsion among its member monomers. We optimized both the C4, (Figure 3b) and S4 structures and found that both have the same interaction energy at both HF/3-21G and MP2/3-21G levels. The results are shown
5592
The Journal of Physical Chemistry, Vol. 94, No. 14. 1990
Yu et a].
TABLE V Optimized Geometries and Interaction Energies for TetnmeP geometry c4h
S4
D3h
method HF/3-21G MP2/3-21G MP3/6-31 lG**// MP2/3-21G HF/3-21G MP2/3-21G MP3/6-31 IG*+// MP2/3-21G expt HF/3-21G MP2/3-21G MP3/6-31 lG**// MP2/3-2 1G
R,A
e
AE. Q,
6
4.449 4.237 3.107 88.7 2.977 88.6 2.78 2.940 2.673
9.0 0.351 9.0 0.337 28
kcal/mol 7.0 9.3 7.6 7.0 9.3 7.6
0.89 4.0 5.5 4.6
‘0 is the twisted angle and the tilted angle (in deg); 6 is the value above and below the plane containing the center of mass.
in Table V. For the tetramer of C, symmetry, the interaction among the four monomers shortens the distance between two opposite acetylenes from 4.325 A in the T-shaped dimer alone to 4.237 A in the C4, tetramer. Also, the interaction energy is increased to about 1.9 kcal/mol per H bond at the MP2/631 lG**//MP2/3-21G level accordingly. For the tetramer of S4 symmetry, we found about 1 O of distortion for the hydrogen bond of T type and similar distances between two neighboring acetylene molecules as those in the C4*tetramer. This leads to a distance of 2.97 A between the molecular centers of mass and the S4axis in our calculation, which is fairly close to the experimental value of 2.78 A. Our calculations thus support the rather strange S4 structure found experimentally’0 for the acetylene tetramer. We would like to point out that since the interaction energies in C4h symmetry are almost identical with those in S4symmetry at all levels of theories, it is likely to identify a tetramer of C, symmetry experimently. Besides C4h and S4symmetries, we also optimized a tetramer structure with DJhsymmetry. Because all of the hydrogen bonds were formed between each of three in-plane acetylene molecules and the r bond of a fourth out-of-plane one and only have three H bonds, the interaction is weaker than that in c4h and S4 structures. D. Penfamers. Two structures in this cluster were optimized at the HF/3-21G level; one is a planar ring (Figure 6b) and the other a nonplanar structure (Figure 6a). The interaction energies are 8.58 and 8.64 kcal/mol, respectively. For the planar pentamer, the interacting energy for each H bond is 1.72 kcal/mol, lower
Figure 6. Two possible structures for (C2HJ5: (a) nonplanar ring and (b) planar ring with c 5 h symmetry.
than that of 1.75 kcal/mol in the planar tetramer. This is not surprising due to the little distortion (-go) of the T-type H bond in the planar pentamer. The value of 1.72 kcal/mol is higher than that of the T-shaped dimer (1.60 kcal/mol). The nonplanar pentamer is a little more stable than the planar one, although the T-shaped H bond is more twisted than the planar one but the nonplanar pentamer has lower repulsive energy. We expect that our results concerning structures and stability of pentamers can contribute to experimental chemistry to determine those structures. IV. Conclusion According to the calculations at both the Hartree-Fock and MP2 levels, the T-shaped dimer with C, symmetry is the most stable one of all dimer structures investigated. The larger complexes tend to form as many T-type H bonds as possible. For the trimer the most stable form is that of C3h symmetry with three twisted T-type H bonds, agreeing with experimental results, but the tetramers with C4h and S4symmetry have almost the same stability. The calculated geometry of the tetramer with S4symmetry agrees with that deduced from experiment.’O The geometries of both the planar and nonplanar pentamers have been optimized, and it is hoped that the calculated results will help experimental chemists in determining the actual structure of the pentamers. Acknowledgment. This research was supported in part by the Naval Air Systems Command through Contract MDA 900386-C-0245. The authors thank the very supportive University of Tennessee Computing Center staff. Dr. S.Su is grateful to the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science (Grant R01-1025-95), for financial support of this work. Registry NO. (CzH2)2, 26875-73-0; (C2H2)3, 31014-03-6; (C2H2)4. 91981-03-2; (C2H2)5. 127354-22-7.
