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J . Phys. Chem. 1989, 93. 1784-1793
How would the FOCO method perform in calculations on bond-breaking processes? It is known that the second-order energy diverges for such cases, and so does the second-order Hylleraas functional. However, surprisingly enough, the FOCOs determined for nonequilibrium geometries constitute as good basis set for higher orders MBPT/CC calculations as they do for the equilibrium structure. This was illustrated numerically in our previous paper. I The present paper focuses exclusively on the total energy. It is our future goal to apply the FOCO method to study various molecular properties. There is evidence that the method performs well for properties related to the interaction with the electric field.23 Work is in progress to apply FOCOs to study weak intermolecular interactions. The present calculation have been performed on a SCS-40 computer, at the University of Arizona Computer Center. The Gaussian integrals were calculated with a vectorized version of the MOLECULEprogram by Almlof,20and the MBPT/CC calculations were performed with the PROPAGATOR program system.2’ (19) Pople, J. A.; Binkley, J . S. Mol. Phys. 1975, 29, 599. (20) Almlof, J.; Faegri, K., Jr.; Kussell, K. J. Comput. Chem. 1982, 3, 385. (21) The PROPAGATOR program consists of the molecule integral program of J. Almlof, GRNMG, that does SCF calculations and integral transformation of G.Purvis and MBPT/CC for many-body perturbation theory calculations, written by R. J. Bartlett, G . D. Purvis, Y. Lee, S. J. Cole, and R. Harrison. (22) Bender, C. F.; Davidson, E. R. Phys. Reu. 1969, 183, 23. (23) Adamowicz, L.; Bartlett, R. J.; Sadlej, A. J. J. Chem. Phys. 1988, 88, 5149.
Conclusion Very accurate MBPT and coupled-cluster calculations are presented for three polyatomic 10-electron systems, which provide more than 95% of the electronic correlation energy. It is significant that the results have been obtained with conventional Gaussian basis sets, without resorting to explicitly correlated functions, which some believe to be the only functions capable of reproducing the correlation energy to such accuracy. However, the computer time requirements for the highest levels of the MBPT/CC implementations mandate that the number of active correlation orbitals be reduced to the minimum, thereby allowing the calculations to be performed in a realistic time span. The present FOCO procedure, we believe, provides an efficient contraction scheme for virtual orbitals that have emerged from the S C F calculations. In the current implementation of the FOCO method, after correlation orbitals are generated, we perform a full four-index transformation of the two-electron integrals to initiate the MPBT/CC calculation. It is, however, possible to assume that FOCOs are new Gaussian-contracted orbitals and evaluate molecular integrals directly by using them as basis functions. This approach would be especially beneficial when a large number of S C F virtual orbitals are reduced to a relatively small numbers of FOCOs. Work in this direction is in progress. Furthermore, we plan to extend our FOCO procedure to UHF-type zero-order functions. This will allow us to study open-shell radicals and anions. Also, we shall soon present applications of the FOCO procedure to larger systems with over 50 electrons.
Electron Donor-Acceptor Complexes. 2. Evaluation of the Criteria for Ground-State Stability of Weak bw-aw Complexes Using Semiempirical Energy Surfaces William A. Glauser, Douglas J. Raber,* and Brian Stevens Department of Chemistry, University of South Florida, Tampa, Florida 33620 (Received: May 16, 1988)
Semiempirical (MNDO and AM 1) quantum-mechanical calculations augmented by dispersion calculations are used to probe the gas-phase, ground-state behavior of weak br-ar donor-acceptor complexes in both electron donor-acceptor (EDA) complex and exciplex geometries. Computed binding energies are in good agreement with experimental vapor-phase data. The extent to which these calculations accord with the predictions of conformational stability advanced by the orbital correlation scheme is taken as a qualitative measure of the degree of charge transfer in the ground state. Computations reveal little intrinsic difference between EDA complex versus exciplex ground-state stabilities in the gas phase, where it appears that charge-transfer interactions may sometimes be overshadowed by classical long-range interactions, which are less sensitive to conformational changes. Calculated dipole moments and frontier orbital perturbation energies confirm this behavior. The distinction most likely arises in solution due to the dielectric and cage-compression effects of the solvent, which create suitable conditions for charge transfer to occur. The role of configuration interaction in the supermolecule formalism is evaluated and discussed.
Introduction Investigations into molecular complexation provide a fertile testing ground for theoretical descriptions of condensed matter, solvation, phase transitions, and biological molecular recognition. Excited molecular complexes have been implicated as intermediates in collisional electron and energy transfer processes,’ and it has been suggestedZthat reversible complexation may lower the activation barrier to subsequent irreversible thermal chemical reaction. Molecular complexation is predicated upon a delicate balance between short-range (quantal) and long-range (classical) intermolecular forces. At one extreme are weakly bound van der Waals complexes, characterized by loose, nonspecific association and primary stabilized by long-range dispersion interaction^.^ At the ( I ) Masuhara, H.; Mataga, N . Acc. Chem. Res. 1981, 14, 312. (2) Mulliken, R. S. J. Am. Chem. SOC.1952, 74, 811.
0022-3654/89/2093-1784$01.50/0
other extreme are hydrogen-bonded complexes that exhibit relatively strong, specific and highly directional binding of a primarily electrostatic nature.4” At intermediate strengths lie donor-acceptor complexes that receive stabilization from charge-transfer (CT) interactions as well as from electrostatic and dispersion A donor-acceptor complex results from an association between closed-shell molecules with definite stoichiometry (usually 1 :1) in which the concentration exceeds that expected for a van der Waals complex.* The charge-transfer stabilization is ostensibly (3) Margenau, H.; Kestner, N. R. Theory of Intermolecular Forces, 2nd ed.; Pergamon Press: New York, 1971. (4) Morokuma, K. J. Chem. Phys. 1971, 55, 1236. (5) Morokuma, K. Acc. Chem. Res. 1977, 10, 294. (6) Morokuma, K.; Kitaura, K. In Molecular Interactions; Ratajczak, H., Orville-Thomas, W. J., Eds.; Wiley: New York, 1980; p 21. ( 7 ) Lathan, W. A,; Pack, G . R.; Morokuma, K. J . Am. Chem. SOC.1975, 97, 6624.
0 1989 American Chemical Society
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premised on the concept that frontier orbital symmetries of donor and acceptor in the point group of the complex provide a theoretical basis for distinguishing geometries that give rise to EDA vs exciplex behavior. Thus the spectroscopicbehavior of the system could be dictated by the relative orientation, in addition to the identity, of the molecular components. Although the phenomenon of charge transfer is both necessary and sufficient to explain the unique spectral features associated with EDA comple~es?~ energy decomposition analyses reveal that charge-transfer alone is not sufficient to account for observed ground-state b e h a v i ~ r . ~For - ~ very weak complexes, it may not even be a necessary construct. In contrast, charge-transfer interactions almost exclusively dictate the energetics and preferred orientation in the excited (CT) state. The orbital correlation scheme is thus able to make strong predictions regarding aspects of the excited-state behavior (isomerizationzs and intermolecular electron transfer) of EDA complexes and exciplexes. This is in \kkgs,cT = a\k(D,A) b\k(D+-A-) marked contrast to the situation encountered in the ground state where the strength of the predictions is expected to vary with the strength of the charge-transfer interaction. Although this scheme where a >> b in the ground state and b >> a in the excited state. is conceptually based on the overlap and orientation principle," In valence-bond terminology these states correspond to a no-bond the selection rules deduced rely only on the availability of totally and a dative resonance structure, respectively. The "no-overlap" symmetric singly excited CT states and are thus independent of state refers to a situation wherein component molecules interact the approximations used in calculating the wave function. For classically (physically) through long-range electrostatic and pothis reason, the orbital correlation scheme provides a useful larization forces only. By contrast, the covalent state refers to theoretical framework and heuristic device for testing the relative a situation wherein component molecules have interacted quantum importance of charge transfer in determining ground-state bemechanically (chemically) such that orbital overlap and charge havior. Therefore the degree to which the orbital correlation delocalization have occurred. scheme is followed is a measure of the degree of charge transfer. Spectroscopic processes are generally treated as strictly uniIn the limit of strong ground-state interaction, the orbital cormolecular phenomena, but under certain conditions absorption relation scheme should be a reliable a priori indicator of and emission processes attributable to molecular complexation ground-state stability as a function of conformation. This concan be observed.l2 Indeed, modern interest in molecular comjecture will be investigated in a forthcoming paper. plexation originated with the observation by Benesi and Hildebrand The charge-transfer theory of EDA complexes is a vapor-phase of a new absorption band when benzene and iodine were m i ~ e d . ' ~ 9 ' ~ theory8 and is thus particularly well suited to computational study. As a matter of definition, bimolecular absorption defines EDA Theoretical testing is essential because experimental studies in complexes, whereas bimolecular emission to a dissociated ground solution phase, static vapor phase, or even supersonic molecular state defines e ~ c i p 1 e x e s . l ~These ~ ' ~ two broad categories have beamsz9s30are presently incapable of determining the precise generally been considered to be mutually exclusive.l2 A corollary orientations adopted in weak molecular complexes. For this reason to this classification scheme states that the identity of the molecular many computational studies have been carried out on donorcomponents comprising the system uniquely determines which type with a view toward acceptor complexes over the past 2 of complex is formed. This point of view is cast into doubt, estimating geometries, binding energies, and C T band locations. however, by the observations of Itoh et al. of an intram~lecular'~ High-quality ab initio calculations are prohibitively expensive for donor-acceptor system that exhibits an emission characteristic all but the smallest bn-an systems, so recourse has been made of both an exciplex and an excited EDA complex and an analogous to semiempirical methods. Unfortunately, most of these studies intermolecularls system that behaves as an exciplex at high temare deficient in one or more of the following ways: (i) They are peratures and an EDA complex at low temperatures. In addition based upon methods now considered obsolete. (ii) They are limited to this implied excited-state isomerism, the appearance of multiple in scope to a small number of systems and thus not able to make CT absorption bands has suggested the possibility of multiple generalizations. (iii) Arbitrary parameters have been employed conformations in ground state EDA c o m p l e ~ e s . This ~ ~ ~line ~ ~of to ensure an important contribution by charge transfer. (iv) They evidence led Stevensz1-z6to propose an orbital correlation scheme have calculated stabilities by using only the charge-transfer component. (v) They have neglected dispersion. (vi) They have used experimental (solid state) intramolecular and intermolecular (8) Mulliken, R. S.; Person, W. B. Molecular Complexes, A Lecture and geometries. These difficulties suggest a reexamination of previous Reprint Volume; Wiley: New York, 1969. results, but the advent of newer and more theoretically sound (9) Del Re, G. Gazz. Chim. Ital. 1983, 113, 695. (10) Mulliken, R. S. J . Am. Chem. SOC.1950, 72, 600. computational methods make it essential.
a consequence of the relatively low ionization potential of the donor together with the high electron affinity of the acceptor. Donor-acceptor complexes have been classified into six categoriess that reflect the nature of both the donor (n, bn, ba) and acceptor (an, aa) molecular orbitals involved in the transfer of charge density. Semantically it is useful to distinguish the term charge transfer, which denotes a static transfer of charge density from donor to acceptor, from that of electron transfer, which indicates a dynamic transfer of an electron to afford an ion pair.g Mulliken's two-state modelz-lOJ'advanced during the early 1950s provided a unifying theoretical framework for understanding the spectroscopic and ground-state behavior of donor-acceptor complexes. In this quantum-mechanical formulation, the ground (\k@)and excited (CT) state (\kcT) wave functions are described by a linear combination of a no-overlap state \k(D,A) and a covalent state \k(D+-A-):
+
( I 1) Mulliken, R. S. R e d . Trau. Chim. Pays-Bas 1956, 75, 845. (12) Turro, N . J. Modern Molecular Photochemistry; Benjamin-Cummings: Menlo Park, CA, 1978; pp 135-146. (13) Benesi, H. A,; Hildebrand, J. H. J . Am. Chem. SOC.1948, 70,2382. (14) Benesi, H. A,; Hildebrand, J. H. J . Am. Chem. SOC.1949,71,2703. (15) Birks, J. B. In The Exciplex; Gordon, M., Ware, W. R., Eds.; Academic Press: London, 1975; Chapter 3. (16) Stevens, B. In Aduances in Photochemistry; Pitts, J. N., Jr., Hammond, G . s., Noyes, W. A,, Jr., Eds.; Wiley-Interscience: New York, 1971; Vol. 8, Chapter 4. (17) Itoh, M.; Mimura, T.; Usui, H.; Okamoto, T. J . Am. Chem. SOC. 1973, 95, 4388. (18) Itoh, M.; Mimura, T. Chem. Phys. Lett. 1974, 24, 551. (19) Holder, D. D.; Thompson, C. C. J . Chem. SOC.,Chem. Commun. 1972, 227. (20) Mobley, M. J.; Rieckhoff, K. E.; Voigt, E. M. J. Phys. Chem. 1978, 82, 2005. (21) Stevens, B. J . Phys. Chem. 1984, 88, 702. (22) Stevens, B. Tetrahedron Lett. 1984, 25, 1863. (23) Stevens, B. Chem. fhys. Lett. 1984, 107, 235.
(24) Stevens, B. Chem. Phys. 1984, 90, 1. (25) Stevens, B. Mol. Phys. 1985, 55, 589. (26) Stevens, B. Chem. Phys. 1985, 100, 193. (27) Hanna, M. W.; Lippert, J. L. In Molecular Complexes; Foster, R., Ed.; Elek Science: London, 1973; Vol. 1; Chapter 1 . (28) Okajima, S.; Lim, B. T.; Lim, E. C. Chem. fhys. Lett. 1985,122.82. (29) Castella, M.; Tramer, A,; Piuzzi, F. Chem. Phys. Lett. 1986, 129, 105. (30) Castella, M.; Tramer, A.; Puzzi, F. Chem. Phys. Lett. 1986, 129, 112. (31) Iwata, S.; Tanaka, J.; Nagakura, S. J. Am. Chem. SOC.1966,88,894. (32) Kuroda, H.; Amano, T.; Ikemoto, I.; Akamatu, H. J . Am. Chem. Soc. 1967, 89, 6056. (33) Chesnut, D. B.; Moseley, R. W. Theor. Chim. Acta 1969, 13, 230. (34) Lippert, J. L.; Hanna, M. W.; Trotter, P. J. J . Am. Chem. SOC.1969, 91, 4035. (35) Chesnut, D. B.; Wormer, P. E. S. Theor. Chim. Acta 1971,20,250. (36) Mo, 0.;Yanez, M.; Fernandez-Alonso,J. I. J. Phys. Chem. 1975, 79, 137. (37) Yan, J. M.; Liu, J. K. Acta Chim. Sin. 1984, 42, 639.
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Recently we have evaluated MND038 as a computational tool for probing the energetics and conformational preferences of weak, nonpolar donor-acceptor complexes, and we concluded that it provides a satisfactory account of the nondispersion portion of the interaction energy.39 Other investigator^^,^^ have presented evidence that the dispersion component may be satisfactorily modeled using the nonempirical atom-atom scheme developed by Huiszoon and M ~ l d e r . ~Finally, ~ the third-generation semiempirical method AM143gives a more realistic account of nonbonded repulsions than M N D O and should provide an improved description of the nondispersion portion of the intermolecular interaction energy. We present herein a comprehensive computational study of the ground states of several ba-a* donor-acceptor complexes using the above semiempirical methods. We have made no prior assumptions except those inherent in the methods themselves. The primary objectives of the present study can be summarized by the following questions: (i) Does there exist any intrinsic energy difference between the gas-phase geometries of EDA complexes and exciplexes? (ii) Does the computational method adopted in this study provide quantitatively accurate values for the binding energies and equilibrium intermolecular distances? Our previous study39dealt largely with dimeric systems (for which there is a paucity of experimental data relating to stoichiometric 1:l complexes, and it was therefore limited to comparisons with ab initio data) and was only able to demonstrate the qualitative reliability of our approach. (iii) Can one relate computational results to the large body of experimental data that has been accumulated from solution-phase studies? (iv) Do the currently existing criteria for classification of donor-acceptor complexes suffice to explain gas-phase behavior? (v) Do supermolecule calculations at the self-consistent field (SCF) level adequately describe the chargetransfer interaction? It is a tacit assumption of the supermolecule a p p r ~ a c hthat ~ . ~the charge-transfer component is implicitly included in the total SCF intermolecular interaction energy as indeed are the electrostatic, polarization, and exchange repulsion cont r i b u t i o n ~ . ~ .A~ ,serious ~ ~ question then arises in connection with the significance of configurationally interacted (CI) supermolecular wave functions. In particular, what role is played by C I with excited C T configurations in the supermolecule approach if charge transfer is presumably already included at the SCF level of theory? The weak br-ax systems chosen for study are comprised of aromatic hydrocarbon donors (benzene, naphthalene, anthracene, and pyrene) in conjunction with benzoquinone (BQ), tetracyanoethylene (TCNE), and tetracyanobenzene (TCNB) as acceptors. Because there exists much greater variability in donor strengths than in acceptor strengths, the charge-transfer character of the complex is largely a function of donor strength. Donor molecules were unsubstituted to minimize steric ( u ) effects as well as electrostatic (dipole) interactions. Furthermore, electron-donating substituents, such as methoxy, or amine groups, would successively increase the donor strength of a given aromatic nucleus and result instead in the formation of moderate to strong br-ar complexes. Many of these weak donor-acceptor complexes have been studied experimentally,8s20thus affording a basis for comparison with computational results. Finally, the complexes chosen for study encompass the entire range of possible orbital correlations (all combinations of donor and acceptor frontier orbital symmetries) and thus offer a broad spectrum of potential charge transfer. (38) Dewar, M. J. S.; Thiel, W. J. Am. Chem. SOC. 1977, 99, 4899. (39) Glauser, W. A,; Raber, D. J.; Stevens, B. J. Comput. Chem. 1988, 9, 538. (40) Pawliszyn, J.; Szczesniak, M. M.; Scheiner, S . J. Phys. Chem. 1984, 88, 1726. (41) Bhanuprakash, K.; Kulkami, G. V.; Chandra, A. K. J. Comput. Chem. 1986, 7, 731. (42) Huiszoon, C.; Mulder, F. Mol. Phys. 1979, 38, 1497. (43) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J. A m . Chem. SOC.1985, 107, 3902. (44) Smit, P. H.; Derissen, J. L.; van Duijneveldt, F. B. Mol. Phys. 1979, 37, 50 1,
Glauser et ai. Details of the Computations Computations were carried out at the single-determinant S C F level using the LCAO-MO approximation. The supermolecule approach5s6was employed throughout in which a single atomic orbital (AO) basis set spans the entire complex, and thus the supermolecular orbitals (SMO) are constructed directly from these AOs (LCAO-SMO) without the intermediacy of MOs localized on either molecular component. The energy was variationally minimized. Whereas perturbational methods are particularly well suited for describing the long-range part of the intermolecular potential, variational techniques are better suited for calculating the short- and intermediate-range comp0nents,4~which are more relevant to the complexation process. All donor and acceptor monomers chosen for study each have at least DZhsymmetry, ensuring that the resulting donor-acceptor complexes can possess C2, symmetry. For construction of the intermolecular orbital correlations that provided the impetus for the present work, high symmetry of the complex is necessary. Three basic structural types offer the possibility of C, symmetry: perpendicular (T-shaped), coplanar, or cofacial ( ~ a n d w i c h ) We .~~ have found46that closed correlations, which are obtained when all four frontier R MOs of both donor and acceptor belong to different symmetry species of the C,, point group, are afforded only in cofacial geometries. Nevertheless, cofacial geometries are predicted to be the most stable by Mulliken's overlap and orientation principle" and are also observed in crystal structures of EDA c~mplexes.~' Cofacial complexes whose individual molecular components possess DZhsymmetry could have C2,, C,, or Cl symmetry, but the last case was excluded from study because all MOs have the same symmetry label and no meaningful correlations can be made. For C,, geometries the molecular planes are parallel and the principal rotation axes of the component molecules are coincident, whereas in C, geometries the principal axes are noncoincident. C, structures can exist in only two isomeric forms that differ by a 90' rotation about the principal axis. C, structures, on the other hand, can exist in an infinite number of isomeric forms that differ only by a relative translation of one component with respect to the other along either of the minor axes. To reduce the problem to a manageable size, we have limited our investigation to only one C2, and one C, isomer for each donor-acceptor combination studied as shown in Figures 1 and 2. S C F interaction energies were computed as the difference in energy between each donor-acceptor complex and the sum of the geometry-optimized isolated subunits. A potential energy profile was generated for a prescribed geometry by varying the intermolecular separation in increments of 0.10 8, in the region above 4.0 8, and in increments of 0.05 8, for distances less than 4.0 8,. The frontier orbital component of the S C F interaction energy (AEfm0)was evaluated in accordance with the 4+4 orbital app r ~ x i m a t i o n ~by~ subtracting -~~ the energies of the two highest occupied orbitals of the donor and r$-2) from the energies of the corresponding intermolecular orbitals (JiDand JiDt). We use the term IMO (intermolecular orbital) to denote a frontier valence S M O that has appreciable density in the intermolecular region. These orbitals would describe any covalent intermolecular bonding. The relevant IMOs are identified by their symmetry and topological correspondence to the donor HOMOS in the isolated subunit. Dispersion energies (Edisp) were calculated by using an atomatom potential that approximates the first term of the multipole expansion given by second-order perturbation theory.48 This represents the long-range portion of the interaction: Edisp= x x A i j r i i 6 i
i
(45) Hirschfelder, J. 0.;Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley: New York, 1954. (46) Glauser, W. A,; Stevens, B., unpublished results. (47) Mayoh, B.; Prout, C. K. J. Chem. Soc., Faraday Trans. 2 1972,68, 1072. (48) London, F. 2. Phys. 1930, 63, 245
The Journal of Physical Chemistry, Vol. 93, No. 5, 1989 1787
Electron Donor-Acceptor Complexes
n
0
Figure 1. Structures of C,, complexes: (a) benzene-BQ; (b) naphthalene-BQ; (c) anthracene-BQ; (d) pyrene-BQ; (e) benzene-TCNE; (f) naphthalene-TCNE; (g) anthracene-TCNE; (h) pyrene-TCNE; (i) benzene-TCNB; (j)naphthalene-TCNB; (k) anthracene-TCNB; (I) pyrene-TCNB.
Subscripts i and j refer to atoms belonging to the donor and acceptor, respectively. The Aij are atom-atom parameters derived by Huiszoon and M ~ l d e that r ~ ~were obtained through a fit to anisotropic ab initio multipole dispersion energies,49and rij is the distance between atoms i andj. Although the individual pairwise interactions are isotropic, Edis is sensitive to orientation of the molecular components via ri,.lo MNDO calculations at the S C F level were carried out by using a Harris 800D computer. We redimensioned the standard source codeso951to accommodate a maximum of 100 atoms and 300 basis orbitalss2 In the calculation of a complex, the subunits were held planar but were otherwise allowed to fully relax within the indicated symmetry constraints. The input geometries were those of the optimized isolated monomers. The C I contribution to the total interaction energy was computed as the difference between the S C F energy of the complex and the S C F energy augmented by a 4x4 CI calculation. Such a CI calculation spans the two highest occupied and the two lowest unoccupied IMOs of the complex and thus accesses most low-lying (singly and doubly excited) C T states of the complex. All microstates generated by permuting the electron occupation between these orbitals are allowed to mix with the reference ground state. MNDO-CI, AMI, and AM1-CI calculations were carried out by using the standard AMPAC source code,53which was implemented on an IBM 3081 computer. Because geometry optimizations using CI wave functions are prohibitively expensive, MNDO-CI and AM 1-CI calculations were done at fixed geometries that were obtained through MNDO-SCF and AM 1-SCF optimization calculations, respectively. The total interaction energy is defined as the sum of three terms: Etot = ESCF + + ECl The notation that we will use to define the level of computation is illustrated for MNDO. MNDO-SCF, MNDO-SCF/D, and MNDO-SCF/D/CI refer to computations that include the first term, the first two terms, and all three terms, respectively.
Results Computations at the MNDO-SCF level yielded potential energy curves of striking uniformity for both C , and C,complexes. The results are summarized in Table I. All complexes yielded predominantly repulsive curves with shallow minima in the vicinity (49) Mulder, F.; van Dijk, G.; Huiszoon, C. Mol. Phys. 1979, 38, 577. (50) Thiel, W. QCPE 1979, 11, 379.
(51) Thiel, W. Harris implementation of MNDO, unpublished modifications. ( 5 2 ) Rodriguez, W. M.S. Thesis, University of South Florida, Tampa, FL, 1986. (53) Stewart, J. J. P. QCPE 1985, 51, 523.
TABLE I: Calculated MNDO-SCF Interaction Energiesec (kcal mo1-I)
acceptor
benzene
BQ TCNE TCNB
2.09 (1.26) 1.87 (1.72) 2.60 (2.39)
donor naphthalene anthracene 2.77 (2.62) 3.30 (2.57) 2.76 (2.55) 3.49 (2.61) 3.46 (3.31) 4.79 (4.07)
pyrene 4.09 (3.77) 3.69 (3.47) 5.08 (4.21)
" A positive sign indicates that the complex is higher in energy than the separated monomers. *Values for C, structures in parentheses following those of the corresponding C , structure. cEvaluated at calculated (MNDO-SCF/D) equilibrium intermolecular separation (see Tables I1 and 111).
TABLE 11: Calculated MNDO-SCF/D Interaction Energies" (kcal mol-') and Equilibrium Intermolecular Distancesb (angstroms) for Czu Complexes
acceptor BQ TCNE TCNB
benzene
donor naphthalene anthracene
pyrene
-2.90 (3.85) -4.22 (3.80) -4.98 (3.75) -5.68 (3.75) -3.38 (3.80) -4.88 (3.75) -5.74 (3.70) -6.89 (3.70) -3.93 (3.80) -6.03 (3.80) -7.42 (3.75) -8.43 (3.70)
' A negative sign indicates that the complex is lower in energy than the separated monomers. In parentheses following the interaction energy.
TABLE 111: Calculated MNDO-SCF/D Interaction Energies" (kcal mol-') and Equilibrium Intermolecular Distancesb (angstroms) for C, Complexes
acceptor BQ TCNE TCNB
donor naphthalene anthracene pyrene -2.42 (3.95)) -3.93 (3.80) -4.20 (3.80) -5.29 (3.75) -3.09 (3.80) -4.56 (3.75) -4.82 (3.75) -6.41 (3.70) -3.80 (3.80) -5.68 (3.80) -6.25 (3.75) -7.93 (3.75) benzene
" A negative sign indicates that the complex is lower in energy than the separated monomers. In parentheses following the interaction energy.
of 5.2 A and highly repulsive interaction energies in the vicinity of 3.5 A. More importantly, for any given system, the C , isomer is systematically more repulsive than the corresponding C,isomer. The displacement between these two curves is typically about 0.4 kcal mol-'. Since no curve exhibited a minimum in the physically relevant region between 3.0 and 4.0 A, no meaningful comparison could be made between the relative stabilities of the CZuand C, geometries. Illustrative examples of this behavior are depicted in Figure 3.
1788 The Journal of Physical Chemistry, Vol. 93, No. 5, 1989
Glauser et al.
Figure 2. Structures of C, complexes: (a) benzene-BQ; (b) naphthalene-BQ; (c) anthracene-BQ; (d) pyrene-BQ; (e) benzene-TCNE; (f) naphthalene-TCNE; (8) anthracene-TCNE; (h) pyrene-TCNE; (i) benzene-TCNB; 6)naphthalene-TCNB; (k) anthracene-TCNB; (1) pyrene-TCNB. TABLE IV: Calculated AMI-SCF/D Interaction Energies (kcal mol-')"' donor
acceptor BQ
TCNE TCNB
naphthalene anthracene pyrene -6.29 (-5.90) -7.52 (-6.24) -8.03 (-7.57) -4.38 (-3.73) -5.20 (-4.70) -7.42 (-6.89) -8.68 (-7.30) -10.28 (-9.42) -5.86 (-5.60) -8.74 (-8.18) -10.87 (-8.96) -12.54 (-11.36) benzene
Q Anegative sign indicates that the complex is lower in energy than the separated monomers. bThe intermolecularseparation was not optimized. A single AM1 calculation was made at the MNDO-SCF/D optimized distance. c Values for C, structures in parentheses following those of the corresponding C2"structures.
Realistic treatments of weak intermolecular interactions must include dispersion (intermolecular correlation), which is formally unaccounted for at the S C F level of t h e ~ r y . When ~ , ~ an atomatom potential was used to include dispersion, minima in the energy surfaces were found. This permitted the necessary comparisons to be made, and the results are summarized in Tables I1 and 111. All systems exhibited potential wells (ca. 3-9 kcal mol-') with minima located in the vicinity of 3.75 A. In contrast to the results obtained at the S C F level (without dispersion), the C, isomers are more attractive than their C, counterparts although the differences in their interaction energies are small. The largest energy difference, observed for the anthracene-TCNB system, was only 1.2 kcal mol-]. However, it is not clear that these energy differences are actually significant relative to the inherent uncertainty of the computations. Moreover, we did not carry out full-geometry optimizations with dispersion to verify that each C, structure is a minimum on the potential energy surface. Consequently our calculated energy differences between the C, and C, structures might only be approximate. For a series of acceptors with a common donor, stability of the complexes increased in the following order: BQ C TCNE < TCNB. This behavior is illustrated in Figure 4 for naphthalene
complexes possessing C, symmetry. For a series of donors with a common acceptor, stability of the complexes increased in the following order: benzene C naphthalene C anthracene C pyrene. This behavior is illustrated in Figure 5 for T C N E complexes possessing C,, symmetry. Trends identical with those seen in Figures 4 and 5 are observed for the corresponding C, complexes. Single-point AM 1-SCF/D calculations were performed for intermolecular distances optimized with MNDO-SCF/D calculations (Table IV). Once again the C,, and C,structures are virtually isoenergetic. The trends in stability observed for variations in both the donor and acceptor series are also the same as found with MNDO. Quantitatively, S C F interaction energies given by AM 1 are less repulsive than MNDO values by 2-4 kcal mol-'. The next hierarchical level of analysis focused on the occupied frontier A MOs of the donor. It was conjectured that the HOMOs of the donor and acceptor subunits would transform into the four highest occupied IMOs of the complex. In most instances the two highest occupied IMOs ($D and $w) do in fact originate from the two HOMOS of the donor. However, the next two lower lying IMOs are generally not of acceptor HOMO parentage, originating instead from lower lying A MOs of the donor. The dissection of the S C F interaction energy to determine the frontier orbital component affords the results listed in Table V. Every structure exhibits a substantially negative AEfmo For any given acceptor, frontier orbital interaction energies suggest decreasing stability of the complex in going from smaller donors (benzene) to larger donors (pyrene). This is identical with the trend observed for S C F calculations (Table I) but is opposite to the trend observed for SCF/D calculations (Tables 11-IV). The A& ,, values have been extracted directly from SCF calculations, so their agreement is reasonable. On the other hand, dispersion energies are calculated outside of the quantum-mechanical framework and cannot therefore be related to specific orbital
TABLE V: Calculated Frontier Orbital Interaction Energiesec (kcal mol-') in All-Valence Electron MNDO-SCF Supermolecule Calculation
donor acceDtor BQ
TCNE TCNB
benzene -8.35 (-7.56) -17.26 (-15.40)
-19.91 (-18.3ij
naohthalene -7.53 (-7.36) -13.51 (-12.67) -16.56 (-15.2ij
anthracene
Dvrene
-6.96 (-6.27) -10.84 (-9.301 -13.30 (-10.96)
-3.51 (-3.63)
a ,
-10.97 (-10.01) -15.17 (-13.56j
" A negative sign indicates that the two highest occupied frontier IMOs of the complex are lower in energy than the two highest HOMOs of the donor from which they derive. bEnergies evaluated at the calculated equilibrium intermolecular distance (see Tables I1 and 111). 'Values for C, structures in parentheses following those of the corresponding C , structures.
The Journal of Physical Chemistry, Vol. 93, No. 5. 1989 1789
Electron Donor-Acceptor Complexes
2 001
I ,
I
3.54
4.00
5.00
4.50
5.50
6.00
Intermolecular Distance [AI
3.0
3.5
4.0
4.5
5.0
Intermolecular Distance (AI Figure 5. Potential energy curves depicting MNDO-SCF/D interaction energies for C,,complexes of TCNE with a series of donors: benzeneTCNE (squares);naphthalene-TCNE (diamonds);anthracene-TCNE (circles); pyrene-TCNE (triangles).
(4
4
2 00
I
TABLE VI: Calculated MNDO-SCF Dipole Moments‘.* (debye) donor acceptor benzene naphthalene anthracene pyrene BQ 0.055 (0.085) 0.080 (0.135) 0.094 (0.252) 0.080 (0.112) TCNE 0.094 (0.254) 0.124 (0.383) 0.135 (0.650) 0.163 (0.510) TCNB 0.089 (0.238) 0.132 (0.420) 0.151 (0.823) 0.189 (0.543)
I
1.50E 0
u Tc1
“Values for C, structures in parentheses following those of the corresponding C,, structure. Evaluated at calculated (MNDO-SCF/D) equilibrium intermolecular separation (see Tables I1 and 111).
y 1.00. r
0 7
L
W W e
.500
-.501 35
4.5
40
55
5.0
60
Intermolecular Distance [AI (b) Figure 3. Potential energy curves depicting MNDO-SCF interaction
energies for C, (triangles) and C, (circles) structures of the (a) benzene-BQ and (b) anthracene-TCNE complexes. 2 00
1
Q
4
E 0
-1.00m
1 V I
-2,oo-
z L m
-3.001
1 - 1-70 0 30
35
4 0
45
50
Intermolecular Distance (AI Figure 4. Potential energy curves depicting MNDO-SCF/D interaction energies for C, complexes of naphthalene with a series of acceptors: naphthalene-BQ (squares);naphthalene-TCNE (circles); naphthaleneTCNB (triangles).
interactions. Therefore SCF/D trends need not parallel those of the frontier-orbital component. For any given donor, the acceptor trends demonstrate complete agreement between frontier orbital and SCF/D interaction energies and partial agreement between frontier orbital and S C F interaction energies. Nevertheless the tenuous relationship that exists between frontier orbital and SCF/D interaction energies suggests that AEf,, values may not be reliable predictors of the absolute or relative stability of a given complex. Finally, the acceptor trends given by frontier orbital interaction energies parallel that of the expected charge-transfer interaction, whereas the donor trends run opposite. The highest level of analysis involves the use of CI wave functions. At the equilibrium distance given by S C F / D calculations, no significant CI stabilization by C T states was found for any of the 24 structures studied. The same result was obtained when these calculations were repeated by using the AMI Hamiltonian. The magnitude of the CI matrix elements depend sensitively upon the extent of orbital overlap between donor HOMOS and acceptor LUMOs, but Slater-type orbitals (STOs) with single exponents, which are used in M N D O and AM1 basis sets, generally underestimate intermolecular overlap integrals.31 Therefore we simulated the effects of increased overlap by artificially shortening the intermolecular separation. MNDO and AMI calculations that were performed for intermolecular distances as short as 2.0 A still yielded negligible CI stabilization energies. At still closer distances, orbital crossings occur that invalidate the original frontier orbital patterns upon which the C T excited states are built. Throughout, all CI matrix elements between singly excited states and the ground state are identically zero. Dipole moments for the various systems range from 0.1 to 0.8 D and are listed in Table VI. In general, for any series of complexes with a common donor or acceptor, dipole moments increase with increasing acceptor or donor strength. Whereas the molecular components in C, structures possess only out-of-plane dipolar components, those for C, structures additionally have in-plane components, and this is reflected by their larger calculated dipole moments.
1790 The Journal of Physical Chemistry, Vol. 93, No. 5, 1989
Glauser et al.
TABLE VII: Predicted Behavior of C h Complexes Based upon Donor-Acceotor Frontier Orbital Correlations"
donor acceptor benzene naphthalene anthracene pyrene dual, EDA dual, EDA dual, EDA BQ dual, EDA anti, EDA TCNE anti, EDA syn, exciplex anti, EDA TCNB syn, exciplex anti, EDA syn, exciplex syn, exciplex "Adapted from ref 26.
Discussion Analysis of S C F I D Results. ( a ) Correspondence with Experiment. Calculations at the S C F / D level refer to isolated complexes (vide infra) and thus afford a basis for comparison with experimental measurements in the vapor phase. In a strict sense, our computations model a single, motionless system at 0 K, whereas experimentally observable quantities refer to a statistical average over the thermally populated vibrational, rotational, and translational states of an ensemble of systems. The inherent neglect of zero-point vibrational energies and thermal effects introduces errors into the calculated binding energies, but these errors essentially cancel when comparing different geometries of the same complex54and should not invalidate comparisons with experimental binding energies obtained at reasonably low temperatures. On this basis, our quantum-mechanically calculated binding energies correspond to the thermodynamically measured change in internal energy that attends complexation (AU). At ambient temperature, experimental AH values are generally larger than AU values by 0.5 kcal mol-'. Computational studies must necessarily evaluate a very limited number of geometries, and our analysis is limited to the energetically more favorable cofacial geometries (and specifically C, complexes that differ little in energy from the C, analogues). In the only investigation relevant to the present Hanazaki has reported vapor-phase binding energies of 6.0 and 7.1 kcal mol-' for the benzene-TCNE and naphthalene-TCNE systems, respectively. The respective calculated interaction energies are 44% and 31% too small when MNDO is used (see Table 11). The AM1 results of 5.2 and 7.4 kcal mol-' (Table IV) for these two complexes are both within 13% of the experimental values. Previous semiempirical calculations at the INDO level using a variational supermolecule approach4] showed an even greater tendency to underestimate binding energies. On the other hand, ab initio calculations of the same sort generally overestimate binding energies.40~41~5s Considering the inherent uncertainty in the measurement of weak-complex stabilities, we conclude that AM l binding energies agree quantitatively with experiment whereas MNDO results agree only qualitatively. Experimental measurements of the equilibrium intermolecular distances are not generally available in the gas-phase or solution. Crystal structures of weak b r - a r complexes generally exhibit intermolecular distances of 3.3 A, which is slightly less than the interplanar van der Waals distance of 3.4 8,observed in graphite! Because gas-phase complexes are looser than their condensedphase counterparts (vide infra), slightly larger distances are expected in the gas phase. Our calculated MNDO-SCF/D equilibrium intermolecular distances (3.75-A mean value for the 24 structures studied) are in good agreement with this expectation. ( b ) Correspondence with Theory. The major assumption underlying the orbital correlation scheme is that charge-transfer interactions will always be present to confer nominal stability upon a complex in a given geometry if no symmetry-imposed prohibitions can be found.21-26The major result of the orbital correlation scheme is that donor-acceptor systems existing in C, conformations are necessarily predicted to be EDA complexes, whereas C,, conformations may be classified as EDA complexes or as exciplexes depending upon the orbital symmetries. All donor-acceptor pairs are in principle capable of EDA complex behavior, whereas (54) Scheiner, S.; Szczesniak, M. M. Znt. J . Quanfum Chem., Quantum Biol. Symp. 1984, 11, 201. (55) Watanabe, Y.; Kashiwagi, H. f n t . J . Quantum Chem. 1983, 23, 1739.
30
40
35
50
45
Intermolecular Distance
(Ai
(a) 2
ooy 9
-6
Olpi
30
I
35
40
45
Intermolecular Distance
50
(A)
(b) Figure 6. Potential energy curves depicting MNDO-SCF/D interaction energies for the C,, (triangles) and C, (circles) structures of the (a) benzene-TCNB and (b) naphthalene-TCNE complexes.
only those in a restricted class are capable of exciplex behavior. A marked preference for C, symmetry is therefore expected only for systems such as benzene-TCNB, anthracene-TCNB, pyrene-TCNB, and naphthalene-TCNE that are nominal exciplexes in C , symmetry. On this basis, the S C F and SCF/D results are not in accord with the orbital correlation scheme (Table VJI), which further implies that the degree of charge transfer in the ground state of these weak complexes is negligible. This behavior is illustrated for the benzene-TCNB and the naphthalene-TCNE systems in Figure 6. These results are corroborated by the frontier orbital interaction energies (Table V), which also exhibit no difference between C2, and C, structures for the four systems predicted by the orbital correlation scheme to show differential stability. Our calculations uniformly show an increase in stability with decreasing ionization potential of the donor, which accords with the basic tenets of charge-transfer theory. Hanna et a1.27*34 and Claverie et suggested, however, that the increase in donor polarizability and strength of the long-range induction interaction attending a decrease in ionization potential might by themselves ~
~
( 5 6 ) Malrieu, J . P.; Claverie, P. J Chim Phys. 1968, 65, 735
Electron Donor-Acceptor Complexes suffice to account for enhanced stabilities of the complex. Our results uniformly show C, structures to be slightly more repulsive than the corresponding C,structures at the S C F level of theory, a consequence of increased overlap between filled orbitals of donor and acceptor. When the dispersion component is included (SCF/D), C, structures become slightly more stable than their C, counterparts because the interatomic distances, upon which dispersion sensitively depends, are smaller at any given interplanar distance. It remains to be shown that the isotropy of the cofacial interaction energies actually results from the near absence of charge transfer and not from counterbalancing anisotropies in other interaction components. All long-range (electrostatic, polarization, and dispersion) and short-range (exchange repulsion and charge transfer) interaction components are anisotropic to some extent when nonspherical molecular charge distributions are considered. However, the degree of interaction anisotropy varies considerably according to the following general ranking: electrostatic > charge transfer > exchange repulsion > polarization > dispersion. However, in the nonpolar complexes studied herein, the leading electrostatic interaction term is the relatively weak quandrupole-quadrupole term, so charge-transfer interactions should be the most anisotropic. Even if the electrostatic interactions were significant, they would parallel those of charge transfer. The electrostatic term favors a cofacial arrangement in which a negative lobe of the donor quadrupole faces a positive lobe of an acceptor q u a d r ~ p o l e .Charge-transfer ~~ interactions also favor a cofacial arrangement (to maximize s--A overlap), but one that is more restrictive. The directional nature of the charge-transfer interaction reflects an intimate connection with orbital symmetry and a quadratic dependence on orbital overlap.34 Because orientational preferences are often dictated by the most anisotropic component of the interaction energy, the preferred orientation should in general be the one that maximizes the charge-transfer i n t e r a ~ t i o n Such . ~ ~ anisotropy has been observed in semiempirical calculations of analogous excited-state complexes (e.g., naphthalene-TCNE), where the charge-transfer interaction predominates.46 It follows that if charge-transfer stabilization were present to any significant degree for the ground-state complexes, then the calculated total interaction energies should have been highly anisotropic. On this basis, our present results strongly suggest that charge-transfer stabilization is negligible for weak b s - a s complexes in the gas phase. Influence of the Medium. ( a ) CT Band Intensities. The intensity of a C T band is larger in solution than in the vapor phase,s7 but magnitude intensification cannot be accounted for quantitatively by theories based on dielectric effects alone.58 H a n a ~ a k has i ~ ~attributed the intensification of the lowest lying C T band in T C N E complexes to increased ground-state charge-transfer interaction in the liquid, which implies that gas-phase complexes exhibit weaker and less specific binding than their liquid-phase counterparts. Our present computational results, which indicate little preferential orientation and negligible charge transfer in the gas phase, are consistent with this explanation. We suggest that gas-phase complexes of the kind we have investigated are bound through relatively isotropic long-range interactions and should formally be classified as van der Waals complexes instead of donor-acceptor complexes. Because only a small fraction of the many orientations that are energetically accessible offer the requisite overlap to bring about optical C T transitions, gas-phase C T bands lose intensity.60 ( b ) Dispersion. Seminal ab initio studies carried out for small model systems have established that dispersion interactions cannot be neglected in quantitatively accounting for the stability of nonpolar donor-acceptor c~mplexes,~~*'"' and these interactions are maximized in orientations that offer largest polarizabilities. (57) Tamres, M. In Molecular Complexes; Foster, R., Ed.; Elek Science: London, 1973; Vol. 1 , Chapter 2. (58) Davis, K. M. C. In Molecular Association; Foster, R., Ed.; Academic Press: London, 1975; Vol. 1, Chapter 3. (59) Hanazaki, 1. J . Phys. Chem. 1972, 76, 1982. (60) Rice, 0. K. Int. J . Quanrum Chem., Symp. No. 2 1968, 219.
The Journal of Physical Chemistry, Vol. 93, No. 5, 1989 1791
Our present results go even further in suggesting that dispersion provides the bulk of the stabilization in these complexes. For complexation occurring in solution, the reactants are solvated donor (DS,) and solvated acceptor (AS,,,), and the product is solvated complex (DAS,,,,). Although dispersion forces are extremely important in the gas phase, they are effectively nullified in solution because the donor-acceptor (&A) dispersion interaction can occur only at the expense of donor-solvent (D-S) and acceptor-solvent (A-S) dispersion interactions8 (vide infra). This interpretation is consistent with experimental enthalpies of complexation, which are systematically greater in the gas phase than in s o l ~ t i o n . ~ ~ ~ ~ Thermodynamic analysis indicates that AHgasis more negative than AHsoln by approximately the AH,,, of the solvent.8s61 The cancellation of dispersion effects in solution provides an explanation for the experimental observation that exciplexes have effectively destabilized ground states in solution despite computational results (Tables 11-IV and Figures 4-6) that indicate a potential well capable of supporting bound states. We conclude that solutionphase behavior will be most appropriately modeled by calculations confined to the S C F level (without dispersion), and these calculations show all 24 structures depicted in Figures 1 and 2 (20 EDA complexes and four exciplexes) to be unstable (Table I). In contrast, we argue that gas-phase complexation must be studied at the SCF/D level, and these calculations show all 24 structures to be stable (Tables I1 and 111). Therefore, in the gas phase, nominal EDA complexes and exciplexes are both expected to demonstrate ground-state stability. The requirement for instability of the exciplex ground state is in full accord with solution-phase spectroscopic data, but the concept of delineating complexes along the line of ground-state stability is clearly less relevant in the gas phase than in solution phase. This conclusion is consistent with the gas-phase observations of Saigusa and Itoh,62963 who have obtained the first spectroscopic evidence of exciplex fluorescence induced from the excitation of a weak, ground-state van der Waals complex precursor. Just as in the case of collisional exciplex formation, the emissive CT state is reached indirectly through the initially populated locally excited (LE) state. Excited EDA complexes possess similar C T emissive states but are accessed directly from absorption in the C T band. More recently, Anner and H a a have ~ ~ postulated ~ the existence of donor-acceptor "van der Waals" complexes in supersonic jet expansions for systems such as anthracene-dimethylaniline or perylene-dimethylaniline, which are formally classified as exciplexes in solution.16 They further interpret excitation wavelength-dependent lifetimes to indicate that some DA pairs are not suitably oriented for charge-transfer interaction on the lowest locally excited surface, which suggests that the Franck-Condon ground state is essentially a van der Waals complex. We conclude that exciplex geometries can be distinguished from EDA complex geometries in the gas phase along the lines of spectroscopic absorption, not ground-state stability. ( c ) Dipole Moments. The measured dipole moment for these weak complexes results from roughly equally weighted contributions from a charge-transfer component and electrostatic induction component. Dipole moments furnish the most sensitive measure of the degree of charge transfer,8 although the absence of experimental vapor-phase dipole moments precludes the quantitative evaluation of our calculated dipole moments. Assuming correspondence between calculated and vapor-phase moments, solution-phase measurements are larger by an order of magnitude (Le., 0.75 vs 0.09 D for benzene-TCNE and 1.28 vs 0.38 D for naphthalene-TCNE). Such trends are consistent with the isotropy of cofacial interaction energies insofar as they both suggest that charge-transfer interactions are relatively unimportant in the gas phase for the type of complex studied herein. In contrast to the stabilization energies, calculated dipole moments are highly anisotropic; moments for C,structures are (61) 935. (62) (63) (64)
Bhowmik, B. B.; Srimani, P. K. Spectrochim. Acta, Part A 1973,29A, Saigusa, H.; Itoh, M. Chem. Phys. Lett. 1984, 106, 391. Saigusa, H.; Itoh, M. J . Chem. Phys. 1984, 81, 5692. Anner, 0.;Haas, Y . Chem. Phys. Lett. 1985, 119, 199.
1792 The Journal of Physical Chemistry, Vol. 93, No. 5, 1989 greater than the corresponding C , structures by a factor of 2-4. The out-of-plane components are of comparable magnitude for both types of structure, and the enhancement noted in C, structures is due to the induction of an in-plane dipole component in the donor molecule by the asymmetrically positioned acceptor. Calculated dipole moments are highly dependent upon geometry. Therefore, when vapor-phase measurements become available, those geometries of a given complex that lead to poor agreement could be eliminated as potential candidates. We suggest that dipole moments will provide a sensitive test for the geometry adopted in a molecular complex. ( d ) Solution-Phase Differential Stability. Computations at the S C F level suggest that both EDA complexes and exciplexes should be unstable in solution. While this is consistent with the current operational definition of exciplexes in solution,I5 such a result contradicts a wealth of experimental evidences,” indicating the existence (hence stability) of EDA complexes in solution, although the actual geometry adopted is largely uncertain. This inconsistency can be explained by invoking the dielectric and compression effects of the solvent that act in concert to enhance the charge-transfer character of the complex. Factors that tend to enhance orbital overlap will likewise enhance the contribution of charge transfer upon complex stability in accord with Mulliken’s suggestion2 that charge-transfer forces will increase rapidly under internal or external pressure. Large separations of charge within molecular electronic distributions that are energetically unfavorable in the gas phase are stabilized in a polar medium through dipolar and other electrostatic interactions. Even in nonpolar solvents, the polarizable medium provides a mean for stabilizing separations of charge through inductive interactions. We therefore propose that the chargetransfer interactions responsible for ground-state stability and orientational anisotropy in solution are not reproduced by S C F computations of the isolated complex, because such calculations are inherently incapable of accounting for the mechanical and dielectric effects of solvent. This further suggests that chargetransfer interactions in EDA complexes exist always in potentia and are manifested phenomenologically when external agencies (Le., solvent) are present to provide the necessary conditions. The actual extent of differential stabilization of EDA complexes vs exciplexes is dependent upon the exact nature of the solvent.6’ Analysis of CI Calculations. ( a ) Role of Locally Excited States. For a calculated interaction energy to be valid, it is essential that all species be computed at the same level of theory. In S C F calculations this is guaranteed by using the same basis set throughout, which is implicitly done in all MNDO and AM1 calculations. At the CI level, the situation is not so clear-cut unless the C I spans the full orbital space. The all-valence-electron calculations for the relatively large complexes investigated herein demands a limited CI, spanning a limited subset of occupied and virtual MOs. Because there are more MOs in the complex than in either component, a given range of CI will entail a more complete CI for the molecular components than for the corresponding complex, a clear violation of the requirement for consistency of computational level. Consistency will be ensured if and only if the same number of orbitals are spanned in the CI calculations of both the complex and the total of the two components. For these reasons our CI calculations have used a larger range of orbitals for the complex (4x4) than for the individual components (2x2). Singly excited states used in CI calculations are of two basic types: charge transfer and local excitation. C T states have no analogue in the isolated molecular components (except for very high energy vacuum states) and are therefore unique to the complex. Therefore, any computed stabilization of the complex gained through C I with C T states represents a contribution to the total energy that is necessarily absent in the molecular components. For all 24 donor-acceptor structures studied, the two highest occupied IMOs were of donor HOMO parentage, and for most the two lowest unoccupied IMOs were of acceptor LUMO parentage. In those cases the four lowest lying singly excited C T states are produced by a 4 x 4 CI calculation without the possibility
Glauser et al. of accidentally including LE states. The effect of CT contributions in the CI calculations of the compounds studied here was relatively small, generally less than 0.5 kcal mol-I. The situation is quite different for LE states. It has often been argued that LE states also have a role in stabilizing the ground states of donor-acceptor complexes of low symmetry.8 However, our computations show no evidence of stabilization resulting from LE contributions to the CI; the calculated values for this component were zero in all cases. For weak complexes of the type studied here, the relative orbital energies of the components are not significantly perturbed by complexation. This is reflected by the lack of change in the energies of the T,T*transitions of the complex vs those of the free components. Therefore, we argue that stabilization of the ground-state complex gained through CI with LE states is offset by a corresponding stabilization of the isolated molecular components that serve as a reference. ( b ) Brillouin’s Theorem. Although first-order excited states may be higher in energy after CI mixing than their zero-order counterparts, the opposite is true for ground states. It is axiomatic that first-order ground states must be more stable than zero-order ground states. Therefore results obtained at the SCF/D/CI level cannot alter our conclusions obtained at the S C F / D level: that all gas-phase complexes studied are uniformly stable. Results at the SCF/CI level may be different. We have argued that S C F calculations (without dispersion) nominally reflect behavior in solution, and repulsive energy surfaces were found at relevant intermolecular separations. Inclusion of CI could result in a calculated net attraction. This conjecture is clearly ruled out, however, by the systematic absence of significant CI stabilization in our present results. The systems studied exhibit vanishing CI matrix elements between singly excited C T states and the ground state. This result is a direct consequence of Brillouin’s theorem, which states that matrix elements will equal zero for the Hamiltonian operator between the Hartree-Fock (HF) determinant (ground state) and all singly excited determinants built from the same orbitals as the ground state.65,66 In the supermolecule approach, the Hartree-Fock determinant is constructed from orbitals of both donor and acceptor parentage. Therefore all singly excited C T states of the complex have been built from orbitals in the H F determinant and are a priori excluded from direct interaction with the ground state. These considerations are applicable to variational calculations that do not approach the Hartree-Fock limit.66 The exclusion of singly excited states does not extend to doubly excited states, which can directly interact with the ground state.67 Moreover, singly, triply, and quadruply excited states can interact indirectly with the ground state through their direct interaction with doubly excited states. Although this “coattail” effect is not necessarily negligible, the role of singly excited CT states in stabilizing the ground state is greatly diminished in supermolecule calculations. Our calculations indicate only small contributions from these allowed components of CI stabilization. This may appear to contradict the premise behind Mulliken’s charge-transfer theory of EDA complexes,2*s-”which ascribes the stability of the ground state to its interaction with low-lying singly excited D’Astates. However, his theory was originally formulated in valence-bond terminology where the donor and acceptor wave functions are computed separately. Under these conditions the dative structures (singly excited C T states) are free to interact directly with the ground state. This has been the traditional approach used by most workers in the field who actually carry out the computations by treating the D+A- state as a perturbation.3’,32*34 We now conclude that much of what appears as first-order (CI level) charge-transfer stabilization in valence-bond treatments is nominally included in the zero-order (SCF level) charge-transfer stabilization in the supermolecule M O treatment. (65) Salem, L. The Molecular Orbital Theory of Conjugated Systems; Benjamin: San Francisco, 1966; pp 53, 376. (66) Schaefer, H . F., 111 The Electronic Structure of Atoms and Molecules; Addison-Wesley: Menlo Park, CA, 1972; p 10. (67) Lowe, J. P. Quantum Chemistry; Academic Press: New York, 1978; p 327.
J . Phys. Chem. 1989, 93, 1793-1799 Conclusions Although the concept of charge transfer is necessary to explain the spectral properties of donor-acceptor complexes, we conclude that the role of charge transfer in determining intrinsic groundstate properties is negligible for weak complexes of the type studied here. It appears that the effects produced by solvent provide a mechanism whereby the role of charge transfer becomes decisive in dictating both stability and preferred orientation. Semiempirical calculations augmented by dispersion calculations afford quantitatively accurate values for the vapor-phase binding energies and qualitatively accurate equilibrium intermolecular separations. It is proposed that S C F and SCF/D level calculations model solution-phase (for inert solvents) and gas-phase complexation behavior, respectively. S C F level supermolecular wave functions adequately account for the ground-state charge-transfer interaction. The currently accepted criterion of distinguishing EDA complex vs exciplex behavior in solution along the lines of spec-
1793
troscopic absorption should apply equally well in the gas phase. However the criterion of ground-state stability does not appear to be as valid in the gas phase as it is in solution.
Acknowledgment. We thank Dr. Kendall N. Houk (University of California, Los Angeles) and Dr. John Yates (University of Pennsylvania) for providing us with copies of the Harris 800 versions of GAUSSIAN-80 and MNDO. We also thank the Center for Scientific Computing of the University of South Florida for use of their facilities and David Ferguson for implementation of the AMPAC program on the IBM 3081 computer. Registry No. Benzene-BQ, 2760-15-8; naphthalene-BQ, 3918-70-5; anthracene-BQ, 3918-71-6; pyrene-BQ, 1939-60-2; benzene-TCNE, 1446-08-8; naphthalene-TCNE, 1223-66-1; anthracene-TCNE, 451744-6; pyrene-TCNE, 2399-97-5; benzene-TCNB, 743 1-46-1; naphthalene-TCNB, 740-98-7; anthracene-TCNB, 747-42-2; pyrene-TCNB, 737 1 - 1 7-7.
Conformational Changes upon Excitation of Dimethylamino Para-Substituted 3H-Indoles. Viscosity and Solvent Effects Michel Bellettte and Gilles Durocher* DPpartement de Chimie, UniversitP de MontrPal, C.P. 6128, Succ. A , MontrPal, Quebec, H 3 C 3J7 Canada (Received: May 27, 1988; In Final Form: August 9, 1988)
Absorption and fluorescence spectra, quantum yields, and lifetimes are studied and compared for two substituted 3H-indole molecules, 2- [p-(dimethylamino)phenyl]-3,3-dimethyl-3H-indole (1) and 5-(dimethylamino)-3,3-dimethyl-2-phenyl-3H-indole (2), in various polar and nonpolar environments. The mirror-image relation between the absorption and the fluorescence spectra has been used together with the theoretical relation between the fluorescence radiative decay constant and the absorption intensity in order to make judgments about any changes of nuclear conformation between the ground and relaxed excited states. Molecule 1 in nonpolar solvents is shown to undergo large conformational changes from a planar form in the ground state to a twisted conformation in the excited state. The absorption spectra of molecule 2, on the other hand, would be explained by contributions of various conformations. The planar conformation of 2 is responsible for the fluorescence emission in all solvents. Contrary to the well-known twisted internal charge-transfer states (TICT), these twisted conformations in the 3H-indoles are not polar (localized excitation) and consequently much less stabilized than the more polar planar geometry (delocalized excitation) in polar environments. Specific (complex and exciplex formations) and unspecific (dielectric enrichment of the solute's solvent shell) associations between these dipolar solutes and the solvent are invoked in order to explain the experimental results, which emphasize the importance of characterizing the local polarity of the probes used in microenvironments. In that respect particular photophysical and spectroscopic parameters have been proposed for each molecule in order that one might follow the micropolarity of heterogeneous systems.
Introduction Time-resolved studies of solvation in polar media have recently been shown to benefit from the time-resolved fluorescence and the time-dependent Stokes shift of specific molecular probes containing the dimethylamino group.',2 The experiments are based on the observation that excitation of a molecular probe to an excited electronic state generally results in a change in the permanent dipole moment. The Franck-Condon principle assures that the formation of the excited state will occur on a time scale much faster than any nuclear rearrangement in the molecule or in the environment. As a result. the excited-state sDecies (FC state) will be formed out of equilibrium as far as the excked-state is concerned. With increasing time, geometry Of the the solvent restructures around the excited dipole, and this results in a lowering of the energy of the excited-state species, which is by a red shift in the fluorescence spectrum, and sometimes in a new excited-state geometry, which is revealed by dual fluorescence. TICT (twisted internal charge transfer) states stabilized in polar solvents are good exampies of the
The very different spectroscopic and photophysical behavior of the para-substituted benzylideneanilines and 3H-indoles depending upon the nature and the position of the electron donor substituents has prompted our research group to study these potential fluorescence probes in more detail.&' The fluorescence decays of the 3H-indoles in nonpolar solvents have been shown to be single exponentials even with the presence of small polar molecule^.^^^ Methods for extracting rate constants in such cases ( 1 ) Simon, J. D. Acc. Chem. Res. 1988, 21, 128. (2) Meech, S. R.; Phillips, D. J . Chem. SOC.,Faraday Trans. 2 1987,83, 1941.
(3) Grabowski, Z . R.; Rotkiewicz, K.; Siemiarczuk, A.; Cowley, D. J.; Bauman, W . Nouu. J , Chim. 1979, 3, 443. Grabowski, 2. R.; Rotkiewicz, K.; Rubaszewska, W.; Kirkor-Kaminska. E. Acra Phys. Pol. 1978, A54,767. Grabowski, Z. R.; Rotkiewicz, K.; Siemiarczuk, A. J . Lumin. 1979, 18/19, 420. Grabowski, Z . R.; Dobkowski, J. Pure Appl. Chem. 1983, 55, 245. (4) Scheuer-Lamalle. B.; Durocher, G. Can. J . Spectrosc. 1976, 21, 165. (5) BelletZte, M.; Scheuer-Lamalle, B.; Baril, L.; Durocher, G . Can. J . Soectrosc. 1977. 22. 31. ( 6 ) BelletZte,'M.; Durocher, G. Can. J . Chem. 1982, 60, 2332. BelletZte, M.: Durocher. G. Can. J . Soecrrosc. 1979. 24. 87. BelletZte. M. ThZse de Doctorat, Universiti de Mohtreal, 1982. ( 7 ) BelletZte, M.; Durocher, G. J . Photochem. 1983, 21, 251. ,
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0022-3654/89/2093-1793$01 S O / O
0 1989 American Chemical Society
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