J . Am. Chem. SOC. 1992, 114, 511-516
51 1
Analysis of Electron Donor-Acceptor Complexes: H3N*F2, H3NC12,and H3NClF I. R~eggen*and T . Dah1 Contribution from the Institute of Mathematical and Physical Sciences, University of Tromso, 9000 Tromso, Norway. Received March 5, 1991
Abstract: An extended geminal model has been applied to study the electron donor-acceptor complexes H3N*F2,H3N.CI2,
and H,N.CIF. By adopting a [9s, 6p, 2d/7s, 4p, 2d/4s, 2p] contracted Gaussian-type basis set, the equilibrium N-X (X = nearest halogen atom) distances are predicted to be 2.76 8, (H,N.F,), 2.57 A (H,N.CI,), and 2.30 8, (H3N-C1F). The predicted binding energies are 6.8 kJ/mol (H3N.F,), 24.6 kJ/mol (H3N.C1,), and 45.1 kJ/mol (H3N.C1F). An energy decomposition analysis demonstrates the similarity between these three complexes. The Coulombic interaction between the distorted monomers is found to be the main origin of the intermolecular interaction. A decomposition of the Coulombic term into electrostatic and inductive terms shows that the latter is approximately 4 times larger than the former for all the three complexes.
I. Introduction Molecular complexes between amines and halogens belong to the class of complexes called charge-transfer complexes or electron donor-acceptor complexes. A general theory for charge-transfer complexes was formulated in 1952 by Mulliken.' According to this theory, the ground state wave function has the form
h
= a$o(D,A)
+ bh(D+-A-)
where a >> b, #(D,A) is the properly antisymmetrized no-bond wave function, and $(D+-A-) represents transfer of an electron from the donor, D, to the acceptor, A. There is also an excited state
= a*+'(D+-A-) - b*+,(D,A) where a* = a and b* = b. This theory successfully explained many spectroscopic results. Mulliken also used the theory to predict the geometry of several types of charge-transfer complexes, among them the aminehalogen c o m p l e x e ~ . ~Crystal .~ structures determined by Hassel and co-workers and by other g r o ~ p s were, ~ . ~ however, not in agreement with these predictions. For complexes between lone-pair electron donors and halogens or other halogen-containing acceptors, the crystal structures showed that the geometry obeys quite simple rules and that the relative orientation of the partner molecules is very similar to that observed for hydrogen bonds. The discrepancies between Mulliken's predictions and the crystal structures were among the reasons why it was argued and later generally accepted that it is not sufficient to consider only the charge-transfer interaction when describing the properties of the complexes and that in many complexes this interaction is not the dominant contribution to the ground-state stabilization.6 The relative importance of the various contributions to this stabilization has been the subject of some dispute.' A number of quantum mechanical works on charge-transfer complexes have been made in order to describe the nature of the intermolecular interactions. Morokuma and Kitaura* tried to separate the contributions from electrostatic, polarization, exchange, dispersion, and charge-transfer interactions. The sum of these contributions was, however, different from the calculated ~~~
~
~~~~~~
( I ) Mulliken, S. R. J . Am. Chem. SOC.1952, 74, 811. (2) Mulliken, S. R. J . Am. Chem. SOC.1950, 72, 600. (3) Reid, C.; Mulliken, R. S. J . A m , Chem. SOC.1954, 76, 3869. (4) Hassel, 0.;Ramming, C. Q. Reo. 1962, 16, I . (5) Prout, C. K.; Kamenar, B. In Molecular Complexes; Foster, R., Ed.;
Elek: London, 1973; Vol. I , Chapter 3. (6) Hanna, M. W.; Lippert, J. L. In Molecular Complexes; Foster, R., Ed.; Elek: London, 1973; Vol. 1, Chapter I . (7) Mulliken, R. S.; Person, W . B. J . Am. Chem. SOC.1969, 91, 3409. (8) Morokuma, K.; Kitaura, K. In Molecular Interactions; Ratajczak, H., Orville-Thomas, W. J., Eds.; Wiley, New York, 1980; Vol. 1, Chapter 2.
0002-7863/92/1514-511$03.00/0
total energy, and an additional "mixing" term had to be added to account for this difference. In several works, attempts have been made to elucidate the similarity between charge-transfer and hydrogen bonds.8-'0 The results seem to disagree somewhat. Recently, a method of natural bond orbital analysis (NBO)"-" has been proposed for the study of intermolecular interactions. Compared with the Morokuma-Kitaura analysis, the NBO method leads to an alternative definition of the charge-transfer energy based on a different treatment of intermolecular overlap between filled and unfilled orbitals. The Morokuma-Kitaura approach and N B O analysis yield very different results for the chargetransfer energy, thereby illustrating some of the difficulties related to the charge-transfer concept. The minimum energy N- - -halogen charge-transfer bond distances obtained by the quantum mechanical calculations are in general much longer than those found in the X-ray crystal s t r u ~ t u r e s . ~ ~ It ~ ~has ~ ~been ~ ~ ' suggested ~~'~ that these differences are due to effects of the crystal forces in the X-ray structures.1° Only two gas-phase structures of complexes between these kinds of molecules have been published. In the electron diffraction structure of the trimethylamine-bromine complex,20and extremely short N- - -Br bond and an unexpected orientation of the bromine molecule were observed. These results indicate that this complex is of a completely different type than ordinary charge-transfer complexes. In the microwave structure of the trimethylaminetrifluoroiodomethane complex,2' the geometry of the chargetransfer bond is very close to that observed for similar complexes in the crystalline state. There are therefore no strong arguments for expecting a considerably longer charge-transfer bond distance in the gas phase than in the crystalline state. The purpose of this work is 3-fold: ( 1 ) to demonstrate that accurate quantum chemical calculations on the complexes H3N-F2, H3N.CI2, and H,N.CIF yield nitrogen- --halogen bond distances which are considerably shorter than the equilibrium distances obtained in previous calculations; (2) to analyze the differences (9) Kollman, P.; Allen, L. C. Chem. Reo. 1972, 72, 283. (10) Kollman, P.; Dearing, A,; Kochanski, E. J . Phys. Chem. 1982, 86, 1607. (11) Foster, J. P.; Weinhold, F. J . Am. Chem. SOC.1980, 102, 7211. (12) Weinstock, R. B. Ph.D. Thesis, University of Wisconsin-Madison. Weinstock, R. B.; Weinhold, F. University of Wisconsin Theoretical Chemistry Institute Report WIS-TCI-661, 1981. (13) Reed, A. E.; Weinhold, F. J . Chem. Phys. 1983, 78, 4066. (14) Reed, A. E.; Weinstock, R. B.; Weinhold, F. J . Chem. Phys. 1985, 83. ~. . 735. ~(15) Curtiss, L. A.; Pochatko, D. J.; Reed, A. E.; Weinhold, F. J . Chem. Phys. 1985, 82, 2619. (16) Reed, A. E.; Weinhold, F.; Curtiss, L. A,; Pochatko, D. J. J . Chem. Phys. 1986, 84, 5687. (17) Reed, A. E.; Curtiss, L. A,; Weinhold, F.Chem. Reo. 1988, 88, 899. (18) Lucchese, R. R.; Schaefer, H. F. J . Am. Chem. SOC.1975, 97,7205. (19) Umeyama, H.; Morokuma, K.; Yamabe, S . J . Am. Chem. SOC.1977, 99, 330. ( 2 0 ) Shibata, S.; Iwata, J. J. J . Chem. Sor., Perkin Trans. 2 1985, 9. (21) Legon, A. C.; Millen, D. J.; Rogers, S. C. Chem. Commun. 1975, 580.
0 1992 American Chemical Society
R~leggenand Dah1
512 J . Am. Chem. SOC.,Vol. 114, No. 2, 1992 and the similarities of the bonding in these complexes; (3) on the basis of this analysis to suggest the characteristic features of electron donor-acceptor complexes. The theoretical framework for our analysis is the extended geminal models developed by R ~ e g g e n . ~These ~ - ~ ~models are size-extensive, they can be applied for any intersystem distances, and they have a conceptual structure which facilitates interpretation. In particular, the energy decomposition scheme formulated within this framework shall be used to study the origin and the character of the interaction between the subsystems of the complexes in question. The structure of the paper is as follows: In section I1 we give a brief description of the theoretical framework. Section 111 is devoted to computational details. In section IV we present the results and our analysis. 11. Theoretical Framework In the works by Rraeggen and c c ~ w o r k e r s ~there ~ * ~is~a, detailed ~~ description of the theoretical approach adopted in this work. In this section we therefore give only the key ideas and the formulas required for the presentation of the results in section IV. If the general extended geminal modelZ2is truncated at the double-pair correction level, we have the following ansatz for the electronic wave function of a closed-shell 2N-electron system:
In eq 1 (PAPS' denotes the APSG function, Le., the antisymmetric product of strongly orthogonal geminals, PK represents a single-pair correction term, and 9, represents a double-pair correction term. The energy can formally be evaluated within the framework of the method of moments: EEXG = ( @APSCIH@EXG)
= EAPSG +
N
N
C EK + C
