J. Phys. Chem. 1981, 85, 2760-2765
2760
The Naphthalene-Butadiene Exciplex. An Extended Huckel Treatment Davld F. Eaton' and David A. Pensak Central Research and Development Department, E. I. du Ponf de Nemours and Company, Wlhnington,Delaware 19898 (Received: March 24, 1981; In Fhal Form: June 1, 1981)
Excited states of the supermolecule naphthalenebutadiene (N-B) have been calculated with a modified extended Huckel formalism. Several shallow minima have been located on the lowest excited state potential surface which correspond to weakly bound exciplex geometric configurations in which s-cis-Bor s-trans-B lie over regions of N. The electronic character of the exciplex minima is best described as a mixture of excitation resonance (N*-.Bo No-B*) and charge transfer in which excitation resonance is dominant. The theoretical results are correlated with experimental data from the literature and mechanistic implications are discussed.
-
Introduction Intervention of excited state complexes (exciplexes) during bimolecular photochemical or photophysical events is a well-documented phenomenon. Such events can be conceptually visualized by study of the potential energy surfaces traversed by the system and by examination of the interactions among relevant molecular orbitals (MO's) of the reacting partners at critical positions on the state surfaces. The electronic description of the system at potential minima on the surfaces provides insight into the factors which contribute to stability and/or reactivity on a fundamental level. The quenching of singlet excited state aromatics by olefins or dienes is a prototypal exciplex-mediated radiationless decay process. In the case of quenching of singlet naphthalene (N*) by dienes (D) evidence indicates that weakly bound exciplexes (N-.D)* mediate the acceleration of naphthalene radiationless decay during the quenching act. Experimental correlations of rate constants for overall quenching for a series of dienes with diene ionization potential (log k, vs. I ) have led to the contention that charge-transfer (CTP interactions, in the sense N-.-D+, represent the most important contribution to exciplex stabilization.lV2 Hammond3 has argued that although CT can be important, it need not be. Excitation resonance (ER) and/or vibronic mixing can dominate in some systems. An appropriate wave function, *E*, for the exciplex (N--D)* is given by eq 1 in which contributions from *E* = ~ X N...*DO b X p...p CXN-...D+ + dX(N...D)* (1) localized excitation configurations (N*--Do and N0--D*), CT (N--.D+) and vibrationally excited ground states (N-.D)t are weighted by the coefficients a, b, c, and d in the total description of E*. The relative magnitude of the coefficients dictates the nature of the dominant contributions to the stabilization of E*. In this paper we present the results of a series of extended Huckel calculations (EHT) on the electronic states of the system naphthalene-butadiene as a realistic model for N-D exciplexe~.~ Our aim is to provide a theoretical estimate of the relative importance of CT and ER in the stabilization of N-D exciplexes and then to apply the computational results to suggest plausible electronic mechanisms for this exciplex-mediated radiationless decay process. Additionally, we suggest that the use of relatively simple and available theoretical approaches such as EHT for the study of complex photophysical events is a valuable tool which can provide considerable insight into the nature of electronic interactions in model systems which closely 'Contribution No. 2850. 0022-3654/81/2085-2760$01.25/0
TABLE I: Bond Lengthsu for N and B Geometries Used in EHT Calculations species
N
bondb
C1-C2 2 '-3 '
c,-c, C,-C10 C -H
B
C11-C12
c
12-c,3
C-H B (short)d
CI 1-c,2 c12-c13
C-H
bond length: A
1.381 (1.365) 1.41 7 (1.404) 1.424(1.425) 1.414 (1.393) 1.09 1.341 1.411 1.09 1.344 1.344 1.09
a Calculated by M M 1 (ref 7). See Figure 1 for numbering. Literature value (crystal data) in parentheses. See text for use of B geometries with short internal bond.
resemble true experimental ensembles.
Results Methods and Approach. We have used the EHT program of Hoffmann5 modified to include two-centered repulsions per Anderson.6 Geometries of naphthalene (N) and butadiene (B) were generated by using an Allinger force-field minimization (MM1) process.' Geometrical parameters are listed in Table I. In addition to s-cis-and s-trans-B geometries in which normal ground-state bond distances were used, we have also performed several calculations in which the B bond distances were artifically varied to correspond to the situation that would obtain if substantial excited-state character resided in B. That is, we have shortened the internal C-C bond and slightly lengthened the terminal distance (Table I). In this way we hoped to accentuate the effects of ER contributions to exciplex stabilization, if any. Electronic states of the system N-B were interrogated by construction of a supermolecule (Figure 1) composed (1) Rehm. D.; Weller, A. Isr. J. Chem. 1970, 8, 259. (2) Evans, T.R. J. Am. Chem. SOC.1971,93, 2081. (3) Labianca, D.A.; Taylor, G. N.; Hammond, G. S. J. Am. Chem. Sac. 1972,94,3679. Taylor, G. N.; Hammond, G. S. Ibid. 1972,94,3684,3687. (4) A preliminary report has appeared: Eaton, D. F.; Pensak, D. A. J. Am. Chem. SOC.1978,100, 7428. (5)FORTICON-8, QCPE 1977, NO. 344. (6) Anderson, A. B. J. Chern. Phys. 1975,62, 1187. (7)Allinger, N.L. Adu. Phys. Org. Chem. 1976, 13, 1. (QCPE 318, 1976, N o 344.)
0 1981 American Chemical Society
Naphthalene-Butadiene Exciplex
The Journal of Physical Chemistry, Vol. 85, No. 79, 1981 2761
r
E (OW I-
I I
I
I
I
-9
/'
-10
-1 1
'I I
-12
I
Flgurs 1. Coordinate system and atom numbering used in EHT calculations. Shown for c-B approaching N from above In a coplanar sense. Parameters are as follows: r, interplanar dlstance; d , displacement of B along long axis of N; p , displacement of B along short axis (fusion bond) of N. All In A from origin.
of N and B in a particular orientation. The supermolecule N-B consists of 70 electrons in 35 MO's. Virtual orbitals are numbered 1-35 inclusive; MO's 3 6 7 0 are doubly occupied in the ground state. The four formal excited states of the system (N*-D0, N0-D* repfesent the two possible ER contributors and N+-D-, N--.D' the two possible CT states) were prepared by promotion of an electron from the appropriate occupied MO to the appropriate empty MO. Energies were minimized as a function of r, d , and p (Figure 1) for each electronic configuration, using the geometry optimization programs of the TRIBBLEsystem.8 Contributions from charge and/or electronic mixing to the nature of state minima were determined from the total EHT output at those geometries. Computations were performed on a Digital Equipment Corporation VAX11/780 computer. The specific programs used in this work will shortly be submitted to the Quantum Chemistry Program Exchange (Bloomington, Indiana). Ground State. Interations of MO's. The ground states of both Ne-t-B and Ne-c-B s stems are repulsive for separations less than about 3.6 for all values of d and p . At separations r > 4.5 A we find no electronic interactions between N and B subunits. That is, MO's are localized and characteristic of that subunit. For separations r < 4.5 A interactions among N and B MO's become increasingly significant. This is illustrated in Figure 2 for Nw-B; results for Ne-t-B are discussed separately below. Symmetry notations for the various MO's are given for the separated species (N point group Da;c-B point group C ,) and for the supermolecule N-c-B treated as a C,species. The mixing of MO's is more clearly seen by reference to schematic MO coefficient diagrams as a function of interplanar separation (Figure 3). Figure 2 shows that the frontier orbitals (MO's 34-37) interact pairwise. The ground-state doubly occupied orbitals of the same symmetry, localized at large separations as the N-localized HOMO (MO 36) and the c-B-localized HOMO (MO 37), interact at separations below 4.5 A to stabilize MO 37 and destabilized MO 36. Similarly, the unoccupied LUMO's mix to stabilize MO 35 and destabilize MO 34. This is precisely what would be predicted by simple frontier orbital theory. From Figure 3 it is clear that the interactions between N and c-B are bonding for MO's 37 and 35 and antibonding for MO's 36 and 34. Since the total destabilization of MO 36 is greater than
-13
-14
Figure 2. MO diagram for c-B approaching N from above (cf. Figure 1) showing parentage of localized MO's (r = m) and extent of mixing as a function of separation. Only C,, MO levels are indicated; symmetry deslgnations and MO numbering are given.
K
(8)Pensak, D. A., manuscript in preparation.
Flgure 3. Diagrammatic representation of MO mixing during approach of c-B to N as in Figure 1 and 2: white = positive coefficient, black = negative.
the stabilization of MO 37 at very short separations r < 3 8,(see r = 2.5 A interaction in Figure 2), the overall result of interaction for the ground state is destabilizing. The results presented above (and in Figures 2 and 3) also indicate that electronic excitations which remove electron density from a destabilized, antibonding MO (e.g., MO 36) and deposit it in a stabilized, bonding MO (e.g., MO 35) will result in an overall state stabilization in the region of MO mixing (r < 4.5 A). The situation for N-t-B was found to be qualtiatively similar but the magnitude of MO mixing is less than that found for c-B. Figure 4 illulstrates the interactions calculated for t-B with N. The major difference compared to c-B is that LUMO (MO 35) is N localized at large r.g
The Journal of Physical Chemistry, Vol. 85, No. 79, 1981
2782
r
SSX
Eaton and Pensak
r m 3;
w
-12.501
-
0.6
Figure 4. Representationof MO mixing and energy level shifts on approach of t-B to N from above (geometry 2 of Table 11). Only the HOMO-HOMO and LUMO-LUMO interactions have been shown: white = posltive coefficient, black = negative.
0.80 -
w
0.40 -
4 43 3.0 - r (
3a1
4 4D
Flgure 5. Calculated energies for the N-c-6 electronic states as a function of interplaner separation, r. Geometry as in Figure 1 and entry 5 of Table 11: d = 2.51 A, p = 0. Symbols refer to calculated points; (0) GS, ground state; (0)E,, excitation MO 36 35); (a)E2,3,MO 37 35; (A)E3.2: MO 36 34; (0) E,, MO 37 34.
-
---+
3.0
3.5 I
4.0 I
4,s I
+
the N long axis). The lowest excited state El (excitation MO 36 35) is weakly bound minimizing at r = 2.92 A, d = 2.51 at an energy 0.25 eV (5.8 kcal/mol) below that of the separated configuration N*-.c-B. For large values of r, this state exhibits substantial charge transfer (0.966 e- at r = 5 A) which indicates that Elcorresponds at large r to the localized configuration N+-c-B- (see footnote 9). However, at the minimum charge transfer is calculated to be nearly absent with only 0.070 e- excess on c-B. Excited state E2(excitation MO 37 35) correlates at large r with the localized configuration N*.-c-Bo. In the region r 4 A E2 is very slightly repulsive (AI3 = 0.02 eV) and very close in energy to the next highest state E, (excitation MO 36 34; N0-c-B* at large separations). Extensive state mixing occurs in this region and surface crossing is attempted, but avoidedlO since the state symmetries are the same (A”). E2 is bonding in the region 3.0 A < r < 3.6 A. State E3 is slightly binding in the region of avoided crossing but repulsive at shorter r. The highest lying state E4 (excitation MO 37 34; N--.c-B+ at large r ) is repulsive for all r < 5 A. Figure 6 shows a similar surface projection for the system (N-t-B)*. In this geometrical configuration the exciplex minimum occurs at r = 3.06 A,d = 2.74 A, p = 0, at an energy 0.06 eV (1.4 kcal/mol) below the separated configuration N*-t-B0. No attempted surface crossings occur in this system for any states. At the minimum the degree of CT is 0.212 e- (excess on t-B), a larger degree of CT than found for c-B. Geometries of Quenching. Other potential geometries for quenching were examined. Table I1 lists the geometrical parameters obtained for all stable minima discovered and the stabilization energies obtained. Effects of Bond Shortening in B. As a model for exciplex geometry in which substantial ER contributions
-
-
0-0.10*
41
0 ‘2.5
-
0.60 -
0.20
0-
-
-
3.30,;
7
-
--
3.70 -
--tt
0.2
Figure 6. Calculated energies for the N 4 - 6 electronic states as a function of interplanar separation, r . Geometry as in entry 2 of Table 11; d = 2.74 A, p = 0. Symbols refer to calculated points: (0) OS, ground state; (0)E,, excitation MO 36 35; (W) E*, MO 38 34; (A)Ea, MO 37 -+ 35; (0) E,, MO 37 34.
-
3.50
-
-,(a+
4.00390
0.4
+
--+
Excited States. Figure 5 shows a projection of the potential energy surfaces Ebt (r,d,p) for c-B approaching N from above in a restricted coplanar fashion in a region near the terminus of the naphthalene ring, i.e., d N 2.5 A ( the approximate distance from the 9,lO-fusion bond to the 2,3-bond region) and p = 0 (no offset from the center of (9) Our major disappointment in this work is the failure of EHT to accurately order the MO’s of the N-c-B system. Although EHT correctly places the N-localizedHOMO above HOMO of c-B, it incorrectly places LUMO(N) above LUMO(c-B). This ordering makes the ionic state N+.-c-k- the lowest ionic state so that our calculations do not reflect experimentin predicting the direction of charge transfer. However, we believe that our procedure accurately reflects the electronic interactions which OCCUI in the Ne-B exciplex. This failure did not occur with the N-4-B system whose MO’s were realistically,if not accurately,ordered by the EHT procedure.
-
(10) Salem, L.; Leforestier,C.; Segal, G.; Wetmore, R. J.Am. Chem. SOC. 1976, 97, 479.
The Journal of Physical Chemistry, Vol. 85, No. 19, 1981
Naphthalene-Butadiene Exciplex
TABLE 111: Calculated C,(p,) Wave Function Coefficients for N - . B at r = 5 A and at Exciplex Minima
TABLE 11: Exciplex Stabilization Energies for (Naphthalene-Butadiene)*
Representotionb
Geometrya
AE,,(eV)'
1.
1.02
'
5, 2
- 0.04
0
3. 0.25 2.96 2.32
4. 0.29 3.22 5
2.51 2.92 (2.50 2.91 le
+0.465 -0.308 t0.005 0
0
35
36
c.0
a
0 0
+0.397 + 0.269 -0.010 0 0
0 -0.434 +0.654
r = 2.9 + 0 . 2 5 6 -0.359 -0.203 +0.227 + 0.095 -0.047 -0.305 -0.217 t 0 . 4 6 9 +0.429
-0.17
s - C i s Diened
-r
C.
G:%
2. 2.74 3.06 0 (269 2.99 0)'
-d
34
37
r= 5 8
L
3.11
coeff for Moa
geometryb atomC
s-Trans Diene
d
2763
-0.10
t 0.243
a Refer t o Figure 1. d = distance ( A ) along Np long axis;p = distance along Np short axis; r = interplanar separation. b Planar projection o f approximate orientaExciplex stabilization energy relative tion at minimum. p = 0. e Using short to separated entities Np* and Bu. B geometry; see text.
0 -0.339 -0.573
t 0.368
+0.162
-0.358 - 0.242 + 0.243 + 0.361 + 0.222 +0.110 - 0.143 -0.218
+ 0.181
+ 0.230 + 0.148 - 0.047 -0.111 + 0.225 - 0.254 + 0.370 -0.417
r = 3.06 Be +0.371 -0.201 -0.242 -0.166 -0.255 + 0.274 + 0.314 t 0.541 -0.392 - 0 . 3 6 8 +0.244 -0,391 +0.271 + 0 . 5 3 1 -0.385
-0.25 (-0.36)'
0 0
+0.113 - 0.092 -0.182 + 0.508 + 0.331 -0.324 - 0.523
For HOMO'S and LUMO's only, see Figures 3 and 4. As given in Table 11. Numbering as in Figure 1; for d = 2.51 A , p = 0. t-B (geometry 2), C,, dangles. e d = 2.74A,p=O. a
would be manifested, we examined systems in which the internal C-C bond of B was shortened, and the terminal C-C double bond slightly lengthened, relative to groundstate values (Table I). Our purpose was to artificially generate an exciplex structure which would correspond in a minimal sense to that expected for an electronic structure heavily weighted toward the ER configuration N0--B*,and then to examine the effect of the geometry change on the stabilization energy. A priori, one would expect that any geometrical change in any one of the molecular subunits away from the ground-state minimum energy would destabilize all the states of the system unless some special electronic factors were at work. Two systems were examined by using the altered B geometries: N w - B at d = 2.5 A (geometry 5 of Table 11) and N.4-B at d = 2.70 A (geometry 2 of Table 11). Minimization of the El geometries with respect to separation r provided greater final stabilization, at similar final geometry, when the altered geometry was used. N-c-B minimized at d = 2.50 A, r = 2.91 A, p = 0 and afforded 0.36 eV (8.3 kcal/mol) stabilization compared to 0.25 eV for the initial c-B geometry. Similarly, N.4-B minimized at d = 2.69 A, r = 2.99 A, p = 0, AE = 0.12 eV (2.8 kcal/mol) compared to 0.06 eV previously. The results are included in Table I1 for comparative purposes. Overlap Populations. Exciplex stabilization is reflected in positive overlap between N and B subunits in the excited states El at the minima. For Ne-c-B positive overlap populations between carbon atoms C1(4)Nand C14(11? (0.027) and atoms C2(3)N and Cl?(l,)B(0.005) confirm the binding interactions at the minimum and suggests a preference for N-B 1,4 photoaddition which is experimentally observed (see Discussion). The N-4-B El minimum exhibits similar positive overlap, but the "dangling" B terminus (C14Bsee geometry 2 of Table 11) precludes product formation from this geometry without prior s-t s-c interconversion. Calculated overlap populations are C4N-C11B = 0.019; C3N-C;2B = 0.004; and C2N-C13B= 0.005 (see Figure 1 for numbering; to generate the t-B geometry perform a 180" rotation of the terminal CI3-Cl4 bond around the internal C12-C13 bond).
-
TABLE IV: Electronic Descriptiona of Exciplex Minima: qex= a ( N * . * . B ot) b ( N " . * . B * + ) c(N+.*.B'). geometry
a
b
C
N*.*t-B( 2 ) b N...c-B (5)'
0.50 0.55
0.36 0.38
0.14 0.07
a Factored so that a + b + c = 1.0. Table 11. Geometry 5 o f Table 11.
* Geometry 2 of
Exciplex Wave Functions. MO mixing of N and B subunits at separations r < 4.5 A ensures that state wave functions will be described by mixtures of localized state functions. Calculated wave function coefficients are listed in Table I11 for the N w - B and N-4-B exciplexes. We have chosen to dissect calculated wave functions at the El exciplex minima into localized state contributions by weighting NO, Bo (HOMO) and N*, B* (LUMO)coefficients until a good match with calculated coefficients is found. Ionic state contributions are included by factoring the calculated degree of electron transfer at the minimum into the weighting procedure. Table IV summarizes the results of this analysis; coefficients in the state expansion are normalized on a percent contribution basis ( a + b + c = 1). The analysis indicates that the El minima are best described as predominantly ER states with only small contributions from CT. Discussion We have used EHT calculations to examine the excited states of N-mB. We present several major conclusions to be discussed in more detail below: (1)The N-B exciplexes exhibit little preference among potential geometric configurations for quenching. (2) Only a small degree of charge transfer contributes to the electronic description of the exciplexes at the minima. Excitation resonance dominates.
2764
Eaton and Pensak
The Journal of Physical Chemistry, Vol. 85, No. 19, 1981
(3) Calculated geometries and energetics can be correlated with qualitative experimental trends. Exciplex Binding and Geometry. Our results indicate that a large variety of geometrical configurations provide a degree of weak binding between N and B subunits in the exciplex (Table 11). However, the calculations predict the N-B excited state potential surface to be quite soft. Almost any geometry of approach of B to N* will result in a stabilizing interaction. This result was predicted by Salem“ using a frontier orbital perturbation analysis and is quantitatively confirmed by our results. The apparent freedom to explore various geometries on a vast potential surface with many shallow minima would, in our view, enchance the probability that an N*.-Bo encounter will result in quenching. Geometrical excursions on the E (r,d,p)surface can be accompanied by relaxations in the B geometry to further stabilize the exciplex (e.g., the shortening of the B internal C-C formal single bond, or s-trans to s-cis interconversion), or to promote radiationless decay via product formation (e.g., 1,4 photoaddition). Electronic Description of the Exciplex. The two exciplex minima calculated in detail were found to be described by a high degree of electronic mixing between N and B subunits. Dissection of the mixing into ER and CT contributions (Table IV) showed that only a small degree of CT (7 and 14%)could be ascribed to the El minima but that a substantial mixing of N0-B* character (-35%) was required in order to adequately describe the state functions. Importantly, the N*-B0 character of the exciplex was substantially reduced (50-60%) at the minima compared to large separations. This result indicates that the exciplex stabilization arises from a combination of ER and CT which is apparently heavily weighted, for this system, toward ER rather than CT. The small degree of CT calculated suggests that interpretation of experimental results designed to probe CT may be misleading. Experimentally, it is clearly difficult to assess contributions from ER to observed rate constants for quenching. A series of papers by Weiss and co-worke d 2implicates a change in mechanism, from CT- to ERdominated quenching, in the interaction of phosphines and amines with a graduated series of excited aromatics, and elegantly illustrates the difficulties attendant on establishing ER contributions to quenching phenomena. We suggest that experimental techniques in use today overemphasize the correlations of quenching rate data with parameters which probe ionic (CT) contributions to exciplex interactions. Solvent effects and oxidation or ionization potential data are capable of detecting small ionic effects; the reliance by photochemists on these kinds of techniques ensures a mechanistic interpretation weighted toward ionic contributions to the exclusion of other possibilities. Mechanism of Quenching. Theory and Experiment. The results presented here indicate that significant electronic interactions between N* and an approaching Bo occur at substantial nonbonding separations. We view the general quenching process as proceeding by virtue of the extensive excitation resonance which is manifested as the species approach one another. The variety of potential minima revealed by our calculations suggest that, regardless of the orientation of the initial approach of N and B subunits, extensive electronic mixing will occur to impart (11) Salem, L.,quoted in Cooke, R. S., Ph.D. Thesis, California Institute of Technology, 1969, p 69. (12) Marcondes, M.E.R.; Toscano, V. G.; Weiss, R. G. J.Am. Chern. Soc. 1975,97,4485. J. Photochem. 1979, 10, 315.
considerable B* character to the incipient exciplex. Mixing short-lived B* ~haracter’~ into the initial, pure N* state will accelerate overall radiationless processes in the exciplex. We suspect, based on the broad, shallow minima calculated, that prompt radiationless decay can occur from many geometrical orientations, and that final minimized geometries of the kind we predict may rarely be attained by the (N.-B)* system. This view is consonant with experimental results. Quina14has shown that the fluorescence of intramolecular models for N-diene quenching, e.g., a- and P-1, exhibit very
@@ 1
large degrees of “quenching” of the N-localized emission relative to comparable intermolecular systems. No geometrical constraints on the intramolecular quenching process appear to exist in 1,in spite of the indications from molecular models that 1 can only attain one or two plausible quenching geometries, rather than many, with ease. Our resulta confirm that many geometrical configurations can provide small, but potentially significant electronic mixing. Further, the variety of configurations available for interaction ensure that even constrained systems can experience sufficient electronic perturbation to cause efficient quenching. Steric effects on quenching should therefore be minor. A variety of congestion-free configurations will provide weak binding but substantial electronic mixing, allowing quenching partners to eschew sterically unfavorable, but electronically attractive geometries. Experimental results provide support for this interpretati~n.~J~ Yang and co-workers” have reported that product formation can accompany quenching of N* by dienes. The nature of the 1,4-addition product formed is entirely consistent with the overlap population analysis of the most stable exciplex calculated by us. Limiting quantum yields for adduct formation are generally small (0.01-0.4)16which suggests that substantial radiationless decay of the exciplex precedes localization in the bonding minimum leading to product formation. This is consistent with our view that several exciplex geometries can be explored, and lead to efficient radiationless decay to ground state, rather than channeling only effective collisions into a favored geometry leading to product. The importance of CT in exciplex stabilization is reflected in the dipole moment of the exciplex. Using our calculated interchromophoric distances (r)and the calculated degree of CT ( a ) ,we derive dipole momenta, p = aer (e = 4.80 X statcoulomb) for the N w - B and N.4-B exciplexes of 0.99 and 3.0 D, respectively. Interestingly, we find the larger dipole moment, and the larger degree of CT, for the less stabilized exciplex. For exciplexes which are known from experiment to be quite polar, much larger dipole moments have been determined by examination of exciplex emission shifts as a function of solvent dielectric constant.16 Taylor“ has (13) Dienes are nonfluorescentand possess broad, usually structureless, high extinction, absorption features. These data imply that SIof dienes is short lived and experiences rapid (
