2560
J . Phys. Chem. 1993,97, 2560-2563
An ab Initio Investigation of the Stationary Points on the Potential Energy Surface for the (C12)2 van der Waals Homodimer Wagner B. De Almeida Departamento de Quimica, ICEx, U.F.M.G.,Pampulha, CP 702, Belo Horizonte, MG,30.161, Brazil Received: September 8, 1992
The ground state potential energy surface for the (C1& homodimer has been examined at the Hartree-Fock and MP2 level of theory employing the 6-31+G* basis set. Three stationary points exhibiting T-shaped, parallel, and linear structures have been located and characterized according to the eigenvalues of the Hessian matrix. Zero-point energy corrections and basis set superposition errors have also been evaluated. The minima that have been found are only slightly different in energy with the T-shaped arrangement predicted to be the global minimum energy structure at both HF/6-31+G* and MP2/6-31+G* levels of theory.
Introduction
IJ
Theoretical and experimental studies of weakly bound molecular complexes have been increasingly reported in the literature. Reviews of the progress achieved so far on the experimental field can be found in refs 1 - 4 and the respective advances in the theoretical approaches in refs 5-1 1. The relatively small binding energies and very flat minima usually reported in studies involving weak molecular associations are the main characteristics of the potential energy surface (PES)for van der Waals complexes, which in many casesexhibit more than onestable minimum energy structure.I2-l9 Molecular clusters trapped in rare-gas solids provide a fascinating conceptual model for the investigation of weak molecular interactions. In the literature of matrix isolation spectroscopy, there is a wealth of information on structures and molecular properties of dimers, trimers, and larger molecular aggregates, mostly obtained by infrared spectroscopy.20 Investigations of dynamics and electronic spectroscopy of such systems are rather scarce. The (02)2 homodimer isolated in Ar2I and (N2)" trapped in Xe22are among the few examples in the literature. The emission and excitation spectra of Cl2 clusters isolated in solid Kr, matrix, and free-standing crystal have been recently reported by Hoffman and A ~ k a r i a nwhere , ~ ~ emission from (Clz)" aggregates could be assigned. In ref 23 the matrix gave evidence for at least two difference aggregate species: one relatively long lived which was suggested most likely to be the (C12)2dimer and one short lived that might be either a larger aggregate, such as a trimer, or a dimer trapped in an unfavourable geometry. Also the long-lived homodimer was suggested to have probably a D 2 d (or parallel) geometry and a T-shaped structure was thought to be less favorable. However, Hoffman and A ~ k a r i a naffirmed ~~ that it was not possible to ascertain the dimer geometry. This work is concerned with the ab initio investigation and characterization of the stationary points present on the PES for the (C12)2 homodimer. The aim of this study is to determine, as accurately as possible, the molecular structure of the long-lived species detected by Hoffman and A ~ k a r i a n .The ~ ~ author is not aware of any other theoretical investigation on the (C12)2system reported so far.
Calculations Following the procedure adopted for the C02-C2H212 and C02-HCN13 complexes, the initial configurations given in Figure 1 were used as starting point in the geometry optimization procedure for the search of stationary points on the PES for the (C12)2 homodimer. A pointwise calculation of the PES,as carried
c1
la
I
I a)
IR
I
I
I
i+
c1
c1
I/
c1
la
I I
*------q a
C )
Cl-
B
c1
R Figure 1. Definition of the intermolecular geometrical parameters R, a, and fl for the three trial stationary points on the PES for the (Cl& homodimer: (a) T-shaped, (b) parallel, (c) linear.
out for the H F 4 1 F binary complex,17has not been done due to
computational limitations. However, the T-shaped, parallel, and linear arrangements are thought as sampling the most relevant areas of the multidimensional PES for the (C12)2 system. Full geometry optimization for each of the three trial structures were performed; the only constraint imposed was to keep the four C1 atoms in the paper plane. The calculations were initially carried out at the Hartree-Fock SCF level with the 6-31+G* basis set24 which contains both d polarization and sp diffuse functions (the standard exponents from ref 24 are used). Then each stationary point located at the Hartree-Fock level was further reoptimized with inclusion of electron correlation effects at the MP2 (MallerPlesset second order perturbation theory)2slevel. Thestationary points located by the gradient technique at the Hartree-Fock and
0022-3654/93/2091-2S60%04.Q0~0 0 1993 American Chemical Society
(C12)2 van der Waals Homodimer
The Journal of Physical Chemistry, Vol. 97, No. 11, 1993 2561
TABLE I: Geometrical Parameters, Rotational Constants (A, & 0, and Energies for the CIz Monomer HF/6-31 +G* 199.3 0.0 0.242831 0.24283 1 -9 18.91 4686 1 3.5712
Rcl-cllf!m Alcm Blcm-I C1cm-l E,,,/ hartrees EZERo/kJmol-'
MP2/6-3 l+G* 201.8 [198.8]" 0.0 0.2367 IO 0.236710 -919.196083 3.2345
RCI
AlcmBlcm
I
C/cm
I
E,,,/hartrees EzERo/kJmol
" Experimental value from ref 42. TABLE II: Geometrical Parameters,' Rotational Constants (A, B, 0, Dipole Moments (Pe),and Energies for the C11 Homodimers HF/6-3 1+G* T-shaped
parallel
linear
199.3 520.6 90.01 89.99 0.121416 0.01 7789 0.01 55 I6 0.0 -1 837.8295 107 -0.364420 0.1018 -0.1470 -0.26262
C,,. 199.3 514.7 180.00 180.00 0.0 0.008772 0.008772 0.0 -1 837.8295354 -0.427432 0.3316 -0.4280 -0.09583
T-shaped
parallel
linear
202.0 365.1 1 12.0 162.4 0.246426 0.0205 IO 0.018934 0.2036 -1838.3947968 -6.90769 0.9026 -6.00509
201.8 404.5 109.3 70.72 0.137440 0.028472 0.023586 0.00001 -1838.3944198 -5.33502
c2r
199.3 462.1 91.15 179.6 0.242815 0.014372 0.013569 0.05 13 EI,,/hartrees -1 837.8296699 AEIkJ mol-' -0.781 874 AEZERo/kJmol-' 0.1805 AEBssE/kJ mol-' 0.0420 AE + AEZERo -0.60137
symmetry R C ICl/pm RlPm aldeg Pldeg Alcm I Blcm I C/cm I
Pc/D E,,,/hartrees AEIkJ mol I AEZERo/kJmol-' AE AELERo
+
D2h
e,,. 201.8 376.9 180.00 180.00 0.0 0.01 2831 0.012831 0.0 -1838.3931831 -2.6701 3
For definition of R , a,and 6 see Figure 1.
MP2 level of theory were characterized according to the eigenvalues of the Hessian matrix26evaluated analytically. If all eigenvalues are positive the stationary point is a true minimum energy structure and the occurrence of one negative eigenvalue characterizes a first-order transition-state structure. In case the molecular system exhibits n imaginary frequencies it is called a nth-order transition state. Due to the shortage of computer resources, MP2/6-3 1+G* harmonic frequency calculation was performed only for the T-shaped dimer. All calculations have been done with the ab initio package Gaussian-88.27
Results and Discussion The results of the HF/6-31+G1 and MP2/6-31+G* calculations for the monomeric and dimeric systems are given respectively in Tables I and 11. Rotational constant values are quoted in order to supply the spectroscopic data for these species.
The intramolecular bond distance C1-C1 practically does not vary upon complexation and the agreement with the experimental monomer bond distance is within 1% of the error. The intermolecular geometrical parameters deserve attention. The HF/ 6-31+G* bond angles a and B deviate very little from the symmetrical values of 90° and 180°, and so the assumption of a Czr, D2h, and Cmrsymmetric configurations is justified at this level of theory. The corresponding MP2/6-3 1+G* angles deviate considerably from the C2,.and D2h values and so quite symmetrydistorted structures are predicted. A similar behavior has been observed for the (HCP)? T-shaped dimer.I6 The molecular dipole moment, induced due to complexation, for the T-shaped dimer is predicted to be substantially higher at the MP2/6-3 1+G* level of theory, which reflects the well-known importance of including electron correlation effects for the calculation of dipole moments. The dipole moment enhancement of 0.2036 D is not negligible at all and so its experimental determination should be encouraged, which could give evidence in favor of the near T-shaped configuration of the (C12)2 homodimer. The stabilization energies given in Table I1 indicate that the near T-shaped homodimer is indeed the lowest minimum energy structure bothat Hartree-Fockand MP2level oftheory. It should be said that as the energy differences between conformations are so small slight deviations from planarity may affect the energy ordering. However, no attempt was made to locate nonplanar stationary points on the PES for the (C12)2 dimer. Basis set superposition error (BSSE) corrections have been evaluated at the HF/6-3 1+G* level using the counterpoise method.28 The effect is differentiated for each stationary point. The 6-31+G* basis set appear to be adequate for the description of the T-shaped structure with a BSSE correction of ~ 5 % . However, for the other two stationary points the effect is quite distinct, with the BSSEcorrections increasing the stabilization energies. The BSSE counterpoise correction method has been addressed many times in the literature.' 1,29-35 Frisch et al.30and Schwenkeand Truhlar" have concluded that counterpoise estimates of basis set superposition error do not provide quantitative information about the basis set deficiencies in studies of hydrogen-bonded complexes and also do not systematically improve the accuracy of the calculations. Their findings may provide an explanation for the undesirable BSSE correction results obtained for the linear and parallel (Cl2)zdimers. It must besaid that Hobza and Zahradnik35 have also examined this BSSE anomaly and have a rather distinct view. They attributed this unexpected increase in the stabilization energy, due to the BSSE correction, to the lack of higher polarization and more diffuse functions and also have said that in this case the full counterpoise should be applied. Unfortunately, a t the present time the use of higher polarized and more diffuse functions is precluded due to the limited amount of computer resources. It is seen from Table I1 that most of the binding characteristics of these systems are due to dispersion effects. It is opportune to say that the dispersion energy contribution to the total intermolecular interaction energy can be considered to be identical to the intersystem correlation energy for large distance^.^^,^^ MP2/ 6-3 1+G* zero-point energy (ZPE) correction was calculated for theT-shaped dimer only, and it is expected that the ZPE correction for the other two stationary points will be around 1 kJ mol-' which would not change the relative MP2 energic order of the three stationary points located on the PES for the (C12)2 homodimer, that is, T-shaped < parallel < linear. Since the ZPE correction would lower the stabilization energy of the near parallel and linear dimers, it is clearly seen that the lowest energy global minimum energy structure on the PES of the (C12)2 homodimer is, at the MP2/6-31+GZ level, undoubtedly the near T-shaped structure with a stabilization energy of -6.91 kJ mol-' and exhibiting a pronounced deviation from a Czr symmetric configuration.
De Almeida
2562 The Journal of Physical Chemistry, Vol. 97, No. 11, 1993
TABLE III: Harmonic Frequencies, we (cm-I), IR Intensities, A (km mol-'), and Raman Activities, A' amu-I), for the C l 2 Monomer
C l r j C 1
;
(A4
112'
I
HF/6-3 1 +G*
I
,365.1 pin
a)
description
WC
A
A'
CI-CI stretching
597.1
0.0
45.6
I
I I
MP2/6-31+G*
0
Cl) 162'
description
wc
A
CI-CI stretching
540.8 [560]"
0.0
\
A'
c1
Experimental value from ref 42.
Tables I11 and IV contain the harmonic frequencies and IR and Raman intensities for the monomeric and dimeric species, respectively. It must be said that Raman intensities depend on the polarizability derivatives which are known to be very sensitive to the basis set used for their evaluation and so the intensities values reported in Tables I11 and IV should be looked at with care. It can be seen that the high-frequency intramolecular fundamental vibrational modes are overestimated compared to experiment at the Hartree-Fock level, while the HF/6-3 1+G* low-frequency intermolecular modes are systematically lower than thecorresponding MP2/6-31+G*values4 Inlightoftheseresults it can be anticipated that the parallel (C12)2 dimer, which exhibits two low imaginary frequencies a t the HF/6-31+G* level, will certainly have all intermolecular frequency values positive at the MP2/6-3 1+G* and so the PES for the (C12)2 homodimer is more likely to exhibit three true minimum energy structures at the correlated level of theory. The MP2/6-3 1+G* intermolecular harmonic frequencies have also been predicted to be consistently higher than the corresponding Hartree-Fock values for other molecular ~omplexes,~6JOJ~.~O and this appears to be a general trend in the harmonic frequency calculations at the MP2 level of theory. Some features in the IR spectrum of the global minimum near T-shaped dimer deserve attention. The Cl-CI stretching mode, which is infrared inactive in the C12 monomer, becomes active upon complexation exhibiting an intensity of 0.69 km mol-' and a frequency shift from the monomer value of -2.9 cm-I at the MP2/6-31+G* level. The enhancement on the intensity of the CI-CI stretching mode seem to bear some relaxation to the deviation from the C2, symmetric structure; the corresponding
c1
;
'J 109'
I b)
/404.5
pin
I
c1
2
c1
Figure 2. MP2/6-31+G* near T-shaped (global minimum) and parallel equilibrium structures on the PES for the (C12)2 homodimer.
HF/6-31+G* intensity value of an almost C2, T-shaped dimer is only 0.01 km mol-' and the frequency shift is -0.5 cm-I. The vdW stretching mode is seen to acquire most of its intensity through correlation effects and so this is an example of the importance of the inclusion of electron correlation for the calculation of low frequency intermolecular fundamental modes of weakly bound molecular associations. Harmonic frequencies do aid in stability determinations, and it is meaningful to use the harmonic frequencies for ZPE corrections. However, it should be kept in mind that as the PES for the (C12)2 homodimer is very flat, exhibiting different minima separated by relatively low barriers, the role of anharmonicity cannot be ignored. Anharmonicity effects will diminish the ZPE correction from the harmonic value and it might change the relative energetic order of the located minima. The two more
TABLE I V Harmonic Frequencies, we (cm-I), IR Intensities, A (km mol-'), and Raman Activities, A'(A4 emu-'), for the Clz Homodimem H F / 6 - 3 I+G* ~~~
~~
~
~
T-shaped descriDtion ~~
we
A
parallel A'
wc
linear
A
A'
~~
CI-CI stretching CI-CI stretching
596.6 596.8
0.0I 0.0
vdW bond stretching bending bending bending bending
8.29 -13.5 9.90 12.7
0.0 0.0 0.0 0.0
Intermolecular Normal Modes 0.17 7.44 0.0 0.63 -13.4 0.0 5.70 -5.48 0.0 3.04 9.4 1 0.0
A
We ~
Intramolecular Normal Modes 55.3 597.1 0.0 39.7 592.2 0.0
~~~
A ~~
0.0 81.4
596.9 597.1
0.0 0.0
0.0 107
0.0 1 5.64 0.0 0.0
7.63 9.07 9.07 14.9 14.9
0.0 0.0 0.0 0.0 0.0
0.18 0.0 0.0
6.18 6.18
MP2/6-31 +G* T-shaped description
WC
~
A
CI-CI stretching CI-CI stretching
Intramolecular Normal Modes 537.9 539.1
0.69 0.03
vdW bond stretching bending bending bending
Intermolecular Normal Modes 50.8 19.5 39.9 45.2
0.23 0.0 0.0 0.02
A'
(Cl2)~van der Waals Homodimer energetic close equilibrium structures on the PES for the (C12)2 homodimer are given in Figure 2 along with the respective MP2/ 6-31+G* values for the intermolecular geometrical parameters R, a,and 8. The MP2/6-31+GS energy difference between the near T-shaped and parallel structures, excluding ZPE correction, is only 1.57 kJ mol-'. This means that a conformational interconversion between these two structures, as has been reported for the C02-.HCN gas-phase ~ o m p l e x , ~might ' be thought as likely to occur. A minimum energy interconversion pathway for the two minimum energy structures on the PES for the H F 4 1 F gas-phase dimer has been calculated in ref 17 and it would also be interesting to calculate the minimum energy path connecting the near T-shaped and parallel (Cl2)Z dimers. In order to carry out such task a pointwise calculation of the PES varying the a and 6 angles should be done. It should, however, be remembered that the present discussion concerns a transition of the trapped dimer in the solid phase. The aforementioned conformational equilibrium is meant to take place in the gas phase.
Conclusions In this study the ground-state PES for the (C12)2 homodimer have been investigated a t HF/6-31 +G* and MP2/6-31+G* level of theory. Three stationary points, one linear and two resembling a T-shaped and parallel configurations, have been located on the PES and have also been characterized by mean of the eigenvalues of the Hessian matrix. The global minimum energy structure on the PES was assigned to a near T-shaped structure which deviates considerably from a C2, symmetric configuration. Also a second equilibrium structure, which resembles a parallel D2h configuration, that is just 1.57 kJ mol-' above the T-shaped global minimum could be found. The near T-shaped geometry appears to minimize more the energy of the dimer than the parallel one, in opposition to the suggestions of Hoffman and A ~ k a r i a n who , ~ ~ hinted that the experimentally assigned dimer could have a parallel geometry. In light of the MP2/6-31+G* results reported in the present study, it appears that the quadrupolar interactions, which favor a T-shaped geometry, are more important for the C12 species in the gas phase than in C12 crystals.43 Using the HF/6-31+G* electric quadrupole moment for the C12 monomer (Qaa = 9.09 C m2) and an expression for the quadrupole-quadrupole interaction between two neutral linear molecules,45which is the leading term in the electrostatic long-range energy for the ( C I Z ) ~ homodimers, the near-T-shaped structure is predicted to be more stable than the parallel one by =OS kJ mol-' equivalent to the a b initio result. From the results of this work, it can be inferred that the long-lived (Cl& dimer observed by Hoffman and A ~ k a r i a ncould ~ ~ be of a near T-shaped geometry and also the short-lived dimer might well be the near-parallel dimer reported in this paper. It has been emphasized that a proper evaluation of the dipole polarizability (needed for the induction energy), of the dipole moment (in the complexes), and of the dispersion energy requires polarization exponents that are much more diffuse that the ones present in standard basis sets such as the 6-31+G*.35 However, inclusion off functions for first-row elements and d functions for hydrogen atoms in conjunction with a treatment of electron correlation, as suggested by Hobza and Z a h r a d ~ ~ iisk ,beyond ~~ our present computer capabilities. Nevertheless, the very small energy differences involved indicate that the (Cl2)Z homodimer has a very shallow PES such that there is a very small energy change to twist one monomer 90° from T-shaped to parallel.
The Journal of Physical Chemistry, Vol. 97, No. 11, 1993 2563
References and Notes ( I ) Sandorfy, C. Top. Curr. Chem. 1984, 120, 42. (2) Dyke, T. R. Top. Curr. Chem. 1984, 120, 86. (3) Legon, A. C.; Millen, D. J. Chem. Reu. 1986, 86, 635. (4) Nesbitt, D. J. Chem. Reu. 1988, 88, 843. (5) Schuster, P.; Zundel, G.; Sandorfy, C. The Hydrogen Bond-Recenr Deuelopments in Theory and Experiments; North Holland: Amsterdam, 1976; Vols. 1-111. (6) Schuster, P. In Intermolecular Interactions f r o m diatomics to bic-polymers: Pullman B., Ed.; Wiley: Chichester, U.K., 1978. (7) Schuster, P. Angew. Chem., Int. Ed. Engl. 1981, 20, 546. (8) van der Avoird, A.; Wormer. P. E. S.; Mulder, F.; Berns, R. M. Top Curr. Chem. 1983, 93, 3. (9) Beyer, A.; Karpfen, A.; Schuster, P. Top. Curr. Chem. 1984, 120, I. (IO) van Lenthe. J. H.; van Duijneveldt-van de Rijdt, J. G. C.; van Duijneveldt, F. B. Ado. Chem. Phys. 1987, 69, 522. (1 I ) Buckingham, A. D.; Fowler, P. W.; Hutson, J. M. Chem. Reu. 1988, 88, 963. (12) De Almeida, W. B. Chem. Phys. 1990, 141, 297. (13) De Almeida, W. B. Chem. Phys. Lett. 1990, 166, 589. (14) De Almeida, W. B.; Hinchliffe, A. Mol. Phys. 1990, 69, 305. ( I 5) De Almeida, W. 8.;Hinchliffe, A.; Craw, J. S.THEOCHEM 1991, 228, 191. ( I 6) Craw, J. S.; De Almeida, W. B. Chem. Phys. Lett. 1991,177, 5 17. (17) De Almeida, W. B.; Barker, D. A,; Hinchliffe, A. J . Chem. Phys., submitted for publication. (18) Barker, D. A.; Hinchliffe, A.; De Almeida, W. B. THEOCHEM, in press. (19) De Almeida, W. B.; Barker, D. A,; Hinchliffe, A. Chem. Phys. Lett. 1992, 194, 477. (20) Ball, D. W., Kafafi, Z. H., Fredin, L., Hauge, R. H., Margrave, J. L., Eds. A Bibliography of Matrix Isolation Spectroscopy; Rice University Press: Houston, 1988. (21) Becker, A. C.; Schurath, U.; Dubost, H.; Galaup, J. P. Chem. Phys. 1988, 125, 321. (22) Kuhle, H.; Bahrdt, J.; Fahling, R.; Schwentner, N.; Wilcke, H. Phys. Rev. B 1985, 31, 4854. (23) Hoffman, G.J.; Apkarian, V. A. J Phys. Chem. 1991, 95, 5372. (24) Clark, T.; Chandrasekhar, J.; Spitznagel, G.W.; Schleyer, P. v. R. J . Comput. Chem. 1983,4, 294. (25) Mdler, C.; Plesset, M. S. Phys. Reo. 1934, 46, 618. (26) Mezey, P. G. Studies in Physical and Theoretical Chemistry, Vol. 53, Potential Energy Hypersurfaces; Elsevier: Amsterdam, 1987. (27) Gaussian-88: Frisch, M. J.; Binkley, J. S.; Schlegel, H. B.; Raghavachari, K.; Melius, C. F.; Martin, R. L.; Stewart, J. J. P.; Bobrowicz, F. W.; Rohlfing, C. M.; Kahn, L. R.; Defrees, D. J.; Seeger, R.; Whiteside, R. A.; Fox,D. J.; Fleuder, E. M.; Pople, J. A. Carnegie-Mellon Quantum Chemistry Publishing Unit, Pittsburg, PA, 1986. (28) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (29) Gutowski, M.;van Lenthe, J. H.; Verbeek, J.;van Duijneveldt, F. B.; Chalasinski, G. Chem. Phys. Lett. 1986, 124, 370. (30) Frisch, M. J.; Del Bene, J. E.; Binkley, J. S.; Schaefer, H. F., Ill. J . Chem. Phys. 1986,84, 2279. (31) Schwenke, D. W.; Truhlar, D. G.J . Chem. Phys. 1985, 82, 2418. (32) Tolosa, S.; Esperilla, J. J.; Espinosa, J.; Olivares Del Valle, F. J. Chem. Phys. 1988, 127, 65. (33) Tsuzuki, S.; Tanabe, K. J . Phys. Chem. 1991, 95, 2272. (34) Schneider, B.; Hobza, P.; Zahradnik, R. Theor. Chim. Acta 1988, 73, 201. (35) Hobza, P.; Zahradnik, R.Chem. Reu. 1988, 88, 71. (36) Collins, J . R.; Gallup, G.A. Chem. Phys. Lett. 1986, 123, 56. (37) Van Lenthe, J. H.; van Duijneveldt-van de Rijdt, J. G. C. M.; van Duijneveldt, F. B. Ado. Chem. Phys. 1987, 69, 521. (38) Gutowski, M.; van Duijneveldt, F. B.; Chalasinski, G.;Piela, L. Mol. Phys. 1987, 61, 233. (39) De Almeida, W. B.; Barker, D. A,; Hinchliffe, A.; Craw, J. S. J. Mol. Struct., submitted for publication. (40) Barker, D. A.; Soscun, H.; Hinchliffe, A.; De Almeida, W. B., submitted for publication. (41) Slanina, Z.; De Almeida, W. B. THEOCHEM 1991, 235, 51. (42) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure IV; Van Nostrand Reinhold: New York, 1979. (43) Williams, D. E.; Hsu, L.-Y. Acta Crystallogr. 1985, A41, 296. (44) Hobza, P.; Zahradnik, R. Studies in Physical and Theoretical Chemistry Vol.3, Weak Intermolecular Interactions in Chemistry and Biology; Elsevier: Amsterdam, 1980. (45) Maitland, G . C.; Rigby, M.; Smith, E. B.; Wakcham, W . A. Intermolecular Forces, Their Origin and Determination; Clarendon Press: Oxford, U.K., 1987; Chapter 2, p 53.
