J. Phys. Chem. 1989, 93, 4441-4447 TABLE 111: Comparative Raman Assignments for N,N,N’,N’-Tetramethylbenzidineand N,N,”,N’-Tetramethyl-p-phenylenediamine in the Ground (So) and Triplet (TI) States‘
TMB-h TI 1605 1593
TMPD-H TI 1623 1573
Sn
1540
1508
1360 1290 1218 1165
1441 1380’ 1360 1219 (1162) 957 942
Sn
1450
1479}
950
1435
1345 1217 1155
1170 1156
945
930
iii Wavenumbers in cm-I.
assianmentsb 8a 8a + d(N-ring) 19a 6(CH3) d(N-ring) u(inter-ring) 9a p(CH3) 18a d(NC2)
:y; ) 6a + As(NC2)
= stretch; 6, A = in-plane distortions; p
= rocking.
variations of band activity in the same way as for the radical cation state.2 For example, 19a and 18a are symmetry-forbidden in the case of TMPD but lead to intense signals in the TMB spectra. However, besides these discrepancies, close similarities are noticed concerning the - N ( a l k ~ l )vibrations ~ (resonance activity of various 6,p(CH3/C2H5) modes) and of d(NC2);high IP(N-ring) frequency with respect to the ground-state value; notable resemblance with the radical cation spectra, which clearly indicate that comparable iminium configurations occur in both cases. This is in favor of a planar, quinoidal structure for T I TMPD as for TI TMB. The
4441
‘io .q
/
\
T i TMPD
alternative nonplanar model proposedl for TI TMPD is thus definitely rejected. According to the discussion of the Raman assignment,’ the strong band observed around 1500 cm-’ for this species is likely to correspond to the ring mode 8a, coupled to the vs(N-ring) stretching. On this basis, the assignments of TI TMB and TI TMPD are compared in Table 111. The important frequency decrease noted for modes 8a and 9a in TMPD on going from the ground state to the triplet state (90 and 47 cm-l, respectively) contrasts with the quasi-intensitivity observed in the case of TMB. This reflects a much stronger antibonding character on the ring skeleton in the former compound, where the charge is confined in a smaller space. In conclusion, two aspects of the structure of TI TMB have been evidenced from this Raman investigation: (i) an analogy with the structure of TI biphenyl regarding the quinoidal configuration of the C6H5-C6HSframework and the significant double-bond character of the inter-ring bond, and (ii) a manifest similarity with TI TMPD concerning the iminium character of the -N(alkyl)2 groups due to a conjugation of the unpaired electrons with the nitrogen lone pairs of electrons. This double aspect of the triplet structure is remarkably comparable to the double resemblance found for the TMB‘+ structure with the biphenyl and TMPD radical cations, respectively. The analogy between the triplet and radical cation structures is still supported by various vibrational features. The reducing nature of TI TMB can be understood on this basis. Registry No. TMB, 366-29-0;TEB, 6860-63-5; D,, 7782-39-0.
Singlet Adiabatic States of Solvated PRODAN: A Semiempirical Molecular Orbital Study Predrag Ilich* and Franklyn G. Prendergast Department of Biochemistry and Molecular Biology, Mayo Foundation, Rochester, Minnesota 55905 (Received: July 5. 1988; In Final Form: December 2, 1988)
X-ray structural analysis depicts PRODAN (6-propionyl-2-(dimethylamino)naphthalene)as a planar system with four molecules stacked in a unit cell of a moncclinic crystal. AMI semiempirical calculationspredict planar conformationfor isolated PRODAN with rotational barriers 0.03 kcal/mol for the propionyl and 0.33 kcal/mol for the amino group, and AHf = 6.74kcal/mol. Adiabatic INDO/S-CI calculations suggest antiquinoidal distortion as the likely ring structural change in the lowest excited singlet state. Twisting of the dimethylaminogroup at position 2 induces, in comparison with either 1- or 3-substituted analogues, strong molecular orbital (MO) localization in the former derivative and occurrence of a highly polar excited singlet state. Decrease of the charge density on nitrogen atom, induced by specific electrostatic interactions with the surrounding medium, promotes the MO with strong N(2py) character into the HOMO level. The transition to that state, determined within the {T*,T] n(N) singlet manifold, is shifted strongly to the red, and the electric dipole moment of the lowest excited state is quadrupled. These predictions are corroborated by the strong emission shifts PRODAN and chromophores of similar structure and topology of substitution exhibit in media of different polarity and viscosity.
-
Introduction Introduced by Weber et a1.I as a sensitive fluorescent probe of the electrostatic character of its environment, PRODAN (Figure 1) has been utilized in protein and more recently in lipid research.2 Substitution of H4 by cyclohexanoic acid appears to offer a definite advantage for site selection by the label in studies of the heme pocket in ap~myoglobin.~A chemical variant, 6-acryloyl-2-(dimethylamino)naphthalene,ACRYLODAN, introduced by Prendergast et al.,4 covalently binds to protein -SH ( I ) Weber, G.; Farris, F. J. Biochemistry 1979, 18, 3075. (2) Chong, P. L . 4 . Biochemistry 1988, 27, 399. ( 3 ) Cowley, D. Nature 1986, 319, 14.
group^,^ providing a combination of the essential spectroscopic characteristics of the propionylaminonaphthalene moiety with a high specificity of labeling. Both compounds are representative of a wide class of chromophores given by the general formula Gl-R-G2, where R is a conjugated ring with [4n 21 atoms or valence electrons and are typical organic functional groups. Most commonly encountered pairs, dialkylamine and aldehyde or dialkylamine and nitrile, provide centers of different local electron density, usually
+
(4) Prendergast, F. G.; Meyers, M.; Carlson, G. L., Iida, S.;Potter, J. D. J . Biol. Chem. 1983, 258, 7541. ( 5 ) Friedman, M.; Kruhl, L. H.; Cavins, J. F. J . Biol. Chem. 1970, 245, 3868.
0022-3654/89/2093-444l$01.50/00 1989 American Chemical Society
4442
Ilich and Prendergast
The Journal of Physical Chemistry, Vol. 93, No. 11, 1989
FABLE I: The PRODAN Crystal Parameters As Determined by X-ray Analysis space group cell parameters a b c
V
antipodally positioned on the ring. Chromophores of this class fluoresce in two wavelength domains, separated by as much as 60 n n 6 A structural determinant for the low-energy emission is the existence of a sterically unhindered exonuclear amino group, as has been shown by Grabowski and co-workers,6-10in a series of comparative structure-solvatochromism studies. Embedding requirements for the red emission are steric freedom for the amino group and a proximity of charged solvent molecules. Solvatodynamic restrictions (at low temperature, for example), on the other hand, favor a high-energy fluorescence, as has been shown by Rettig and co-workers" and others.12 Lippert introduced the term "dual fluorescence" for this phen~menon;'~ however, it was not before the use of the pump-probe, time-resolved absorptionlo and optically delayed, total emission spectrum measurement^'^ that two discernible fluorescent states were observed in some of these chromophores. Early electronic structure calculations on this class of chromophores were either limited to r*,rstates" or, if r*+n transitions were included, no significant conformational changes of the excited chromophore were considered.I6 Several recent theoretical models have ad hoc included the twisted substituent amino group, perhaps guided by ideas and experimental results of GrabowskL6 Indeed, ~emiempirical~~"-'~ and few ab initio20 MO calculations show a significant charge localization in the excited twisted amino group; however, in neither case could ordering of states account for the postulated optical transition. Addition of a medium in the form of a continuous dielectric brought no substantial improvements to those calculation^.'^ We started by first analyzing the M O structure of the levels around the optical gap and considering what possible structural changes might be induced upon electron excitation. It appears that a specific sequence of ring deformations and twisting of the terminal amino group lowers the energy of the low excited singlet (6) Grabowski, Z. R.; Rotkiewicz, M.; Siemiarczuk, A,; Cowley, D.; Baumann, W. Nouv. J. Chim. 1979, 3, 443. (7) Grabowski, Z. R.: Dobkowski, J.; Kuehnle, W. J. Mol. Struct. 1984, 114, 93. (8) Grabowski, 2. R.; Dobkowski, J. Pure Appl. Chem. 1983, 55, 245. (9) Lipinski, J.; Chojnacki, H.; Grabowski, Z. R.; Rotkiewicz, K. Chem. Phys. Letr. 1980, 70, 449. ( I O ) Ruliere, C . ;Grabowski, 2. R.; Dobkowski, J. Chem. Phys. Lett. 1987, 137. 408. ( I I ) Rettig, W. J. Phys. Chem. 1982, 86, 1970. (12) Heisel, F.; Miehe, J. A , ; Szemik, A. W. Chem. Phys. Left. 1987, 138, 121. (13) Lippert, E.; Lueder, W.; Boss, H. In Advances in Molecular Spectroscopy; Mangin, A,, Ed.; Pergamon Press: Oxford, UK, 1962; p 443. (14) Gilabert, E.; Lapouyade, R.; Ruliere. C. Chem. Phys. Letf. 1988, 138, 121. (15) Khalil, 0. S.;Meeks, J. L.; McGlynn, S. P. J . Am. Chem. Sot. 1973, 95, 5876. (16) Lewis, F.; Holman, B. J. Phys. Chem. 1980, 84, 2326. (17) Nowak, W.; Adamczak, P.; Balterm. A,: Sygula, A . J . Mo1. Sfruct. (THEOCHEM)1986, 139, 13.
(18) Dobkowski, J.; Kirkor-Kaminska, E.: Koput, J.: Semiarczuk, A. J. Luminesc. 1982, 27, 339. (19) LeFemina, J. P.; Duke, C. B.; Paton, A. J . Chem. Phys. 1987, 87, 2151.
(20) Bonacic-Koutecky, V.: Michl, J. J. Am. Chem. Sor. 1985, 107, 176.
6.199 f 12 8, 12.401 f 7 A 14.824 f 6 8, 1235 f 4 8,'
P
90" 98.76'
Y
01
(Y
Figure 1. PRODAN: IUPAC labeling and orientation of the molecule in our calculations.
P2,lc monoclinic
1.222 g/cm3 density 4 formula/unit cell sample characteristics transparent colorless prismatic crystals of approximate size 0.1 X 0.2 X 0.4 mm. Twinning in all (five) examined crystals reduced precision in the final cell parameters
state. Furthermore. the existence of several different domains in a molecule (aromatic core, carbonyl group, diametrically positioned amino group) implies local diversity of short- and intermediate-range interactions with the embedding medium. Explicit evaluation of these interactions, even within a crude, one-electron formalism, does indeed establish two distinctly different sets of electronic states in the low excited singlet: (a) high-energy { ~ * ,line r j state of a planar molecule embedded in a weakly interacting medium and (b) low-energy (r*,n)state of twisted conformation, and surrounded by solvent molecules with strong local charge densities. This is admittedly a simplified scheme, limited to certain singlet states. However, it seems to account for the major observed spectroscopic data of several of these chromophores in solution phase. Methods
Semiempirical methods M N D 0 / 3 , MNDO, and AMI were used in essentially their original forms to calculate the ground-state molecular electronic structure. Electronic transitions were calculated by a variant of the INDO/S method, employing the one-center parameters of Zerner and Ridley.2' Mataga-Nishimoto repulsion integrals22 and the standard ur and ~ ioverlap r parameters2I were used for single excited configuration mixing. Mixing in a selected small set of double excited configurations (from a total of 2 403 830), using the Ohno-Klopman repulsion integral^^^,*^ and setting (rrand sr overlap parameters closer to 1.O and 0.5, respectively, appeared to produce energy positions and oscillator strengths closer to the solution-phase absorption envelope of PRODAN (see Figure 3). Canonical configuration interaction (CI) states were calculated after successive preselections from a subset of single and double excited configurations, by using the perturbation expansion criteria of Boys." In experimental runs 600 configuration interaction states were calculated from a preselected set of up to 65000 configurations. However, extreme demands on memory allocation and time of execution forced us to routinely diagonalize 200-300 CI states, preselected from 5000-10 000 configurations. Larger CI sizes and inclusion of double excited configurations were shown to decrease transition energies and to level oscillator strengths of all calculated bands. Calculations were performed on Digital Equipment Corp. computers VAX-8600, VAX-l1/780, VAX11/750, and microVAX I1 running the VMS operating system. Results
Ground-State Properties. The PRODAN crystal geometry was determined at the X-ray analysis facilities of the University of Illinois. The structure was solved by direct phase retrieval from patterns of Mo K a I , Ka2, and Ka, radiation scattered off a molecular crystal mounted on an Enraft-Nonius CAD4 automated (21) Ridley, J.; Zerner, M. Theoret. Chim. Acta (Berlin) 1972, 32, 11 I . (22) Mataga. N.; Nishimoto, K. Z. Phys. Chem. 1952, 13, 140. (23) Ohno, K. Theoret. Chim. Acta (Bedin) 1964, 2, 219. (24) Klopman, G. H. J. A m . Chem. SOC.1964, 86, 4550. (25) Bernal, M. J. M.; Boys, S.F. Philos. Trans. R . Sot. (London) 1952, A245, 139.
The Journal of Physical Chemistry, Vol. 93, No. 11, 1989 4443
Singlet Adiabatic States of Solvated PRODAN TABLE 11: Z Matrix of the PRODAN Crystal Structure Parameters connectivity bond length, bond angle, dihedral angle,
atom H
A
dee,
C C C
1.084 1.365 1.495 1.211 1.501 1.084 1.073 1.517 1.101 1.101 1.101 1.409 1.084 1.365 1.084 1.408 1.417 1.084 1.367 1.418 1.084 1.372 1.084 1.41 1 1.387 1.429 1.101 1.101 1.101 1.439 1.101 1.101 1.101
122.0 123.3 120.2 119.0 109.0 112.0 114.5 107.0 111.0 1 10.0 118.9 121.0 120.9 120.0 121.2 122.3 1 15.0 121.7 118.6 123.0 121.0 121.0 121.2 119.8 121.9 111.0 116.0 117.0 120.0 110.0 111.0 114.0
0 C
H H C
H H H C
H C
H C C
H C C
H C
H C N C
H H H
C H H H
chain
den 1(a)
1 .o 179.9 -0.2 -57.0 53.0 175.9 -174.0 57.0 -55.0 -1 80.0 -179.0 1.6 177.0 -0.7 -179.1 -7.0 178.3 -1.4 180.0 1.7 178.0 -1 .o -178.6 173.0 -171.0 -40.0 76.0 1.2 -168.0 56.0 -56.0
2(b) 3(c) 4 4 6 6 6 9 9 9 3 3 13 15 15 17 18 18 20 21 21 23 23 20 26 27 27 27 26 31 31 31
l(a) 2(b) 3 3 4 4 4 6 6 6 2 3 3 13 13 15 17 17 18 20 20 21 21 21 20 26 26 26 20 26 26 26
l(a) 2 2 3 3 3 4 4 4 1 2 2 3 3 13 15 15 17 18 18 20 20 23 18 20 20 20 18 20 20 20
’P
“
E
I
W
n
U
a
Figure 2. Molecular packing in a unit cell.
TABLE 111 Comparison of Calculated Heats of Formation and Rotational Barriers of the 2-Dimethylamino and 6-Propionyl Group in Geometrically Unrestricted PRODAN
property A HI. .. kcal ,/mol amino group plan perp barrier, kcal/mol propyl group plan perp barrier, kcal/mol
-
MIND0/3
method MNDO
AMI
28.509 -3.224
3.386 -8.724
6.735 +0.327
-0.845
-4.662
+0.029
IO
K-axis diffractometer. A total of 2966 intensity data were collected over 21.49 h of scanning in the u/8 mode. The most important of the structure determination data are summarized in Table I. X-ray structure parameters along with arbitrary atom labeling are given in Table I1 in the form of a Z matrix, suitable as input parameters for M O calculations. The molecule is planar in the crystal phase. The C2-N,’ bond of 1.378 A as well as the C2-Nl’-C2/ and C2-NI’-C{ angles close to 120’ are decisive for a flat amino group strongly conjugated with the naphthalene ring. The propionyl mend shows a bonding pattern typical of a contracted, partially conjugated (aryl)C-C=O fragment. Four molecules per unit cell are coplanar skew-stacked and create a fishbone pattern (Figure 2 ) . The extent of molecular pair interactions and collective charge transfer effects is unknown. However, that these nonbonding interactions are dependent on crystal packing is suggested by apparent variants of PRODAN crystals. Depending on whether the crystals are grown from a tetrahydrofuran (THF)-methylene chloride solution or from solutions in other solvents, they can be variably colored, from pale yellow to deep orange. Emission yield and color were also reported to vary in these sample^.^^.^' No data on geometry and conformation of isolated PRODAN molecules, either in vapor phase or embedded in a noble-gas matrix, (26) Ludington, K. T. Ph.D. Thesis, University of Illinois, UrbanaChampaign, IL, 1986. (27) (a) Marriott, G. J. Ph.D. Thesis, University of Illinois, UrbanaChampaign, IL, 1987. (b) Marriott, G. J. Max-Planck Institute of Biophysical Chemistry Goettingen, FRG, personal communication, 1987.
have been reported. We employed MIND0/328 MND0,29and AM1 30 semiempirical M O methods to calculate the ground-state properties of an isolated molecule. M I N D 0 / 3 was least satisfactory: the AH, was high and the geometries of the substituent groups (short bonds, 120’ angles, indicating strong conjugation with the naphthalene ring) were inconsistent with the perpendicular conformation. Perpendicular rather than planar conformation was more stable by M N D O calculations (Table 111). Several aryl-substituted molecules such as nitrobenzene and benzaldehyde, experimentally known to be planar, are also assigned a perpendicular conformation by MNDO calculations. This recognized deficiency of MNDO to overestimate nuclear-nuclear repulsion of nonbonded groups has been corrected in the AMI method.30 Indeed, at the expense of introducing a more elaborate core-repulsion empirical function, the nonbonding interaction between the dimethylamino group and the adjacent atoms in the naphthalene ring are lowered by 13.1 kcal/mol, and PRODAN is predicted to be planar. It is interesting to note that MNDO method, employed in recent ground-state calculations of PRODAN, is claimed to predict a planar conformation.” No data are given for the PRODAN molecule; however, it appears that the longer C-N bond (>1.41 A after optimization) Nowak et al. (28) Bingham, R. C.; Dewar, M. J. S.; Lo, D. H. J . Am. Chem. Sor. 1975, 97, 1285. (29) Dewar, M. J. S.; Thiel, W. J . Am. Chem. SOC. 1977, 99, 4899. (30) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J . Am. Chem. SOC.1985, 107, 3902.
4444
The Journal of Physical Chemistry, Vol. 93, No. 11, 1989
used in their work may have caused a decrease in calculated repulsion energies between the naphthyl HI-Cl-C2-C3-H3 and the atoms in the dimethylamino group. Two effects, an incorrect geometry parameter and a deficiency inherent in the method, may thus have canceled each other, yielding what is likely to be a true conformation. In our calculations, heats of formation, somewhat lower by M N D O than by the AM1 method, could be further slightly lowered by increasing the iteration criteria by 1 or 2 orders of magnitude (and increasing the number of self-consistent field (SCF) iterations by another 500-800), but contrary to the conclusion of Boyd et al.,' we have not observed significant energy or geometry changes in repeated calculations at different levels of precision. In view of our results, the results of previous MNDO and AM1 calculations on amino- and carboxy-substituted benzene and naphthalene, and the results of ab initio calculations on smaller systems,32we conclude that isolated PRODAN is, as in the crystal state, a planar molecule, with AHf in the range 3-4 kcal/mol. The 1 14-cm-' rotation barrier for the amino group is apparently lower than expected for a similar barrier in substituted benzenes and certainly much lower than in acyclic conjugated systems. The electron distribution in PRODAN and geometry parameters indicate a flattened but weakly conjugated amino group that can rotate around the C,-N1 bond with little energy penalty. Had larger changes in the bonding type been involved, e g , when going from a flat, strongly conjugated amino group attached by a short bond to the aromatic ring to a pyramidal, trialkyl-type substituted ammonia, the barrier would be 4-5 kcal/mol higher. Electronic Transitions. Adiabatic States. Little is actually known about the PRODAN low singlet domain. Conventional methods failed to yield a vapor-phase sample,27and no band assignment has been reported. The closest approximation is afforded by the absorption spectrum of the chromophore dissolved in an inert solvent (Figure 3, top). For comparison INDO/SCISD results for planar, crystal structure PRODAN are given. The transition lines are convoluted with Gaussians with the total areas proportional to the oscillator strengths (Figure 3, bottom). The valence-shell MOs around the optical gap are approximately similar to the analogous orbitals in naphthalene. This is truer for the lowest virtual orbitals (hereafter denoted as the LUMO layer) which, although vertically shifted, display a general LCAO MO pattern of the parental b2,, b3,, bl,, a,, and b,, symmetry. The HOMO layer is more complex; the naphthalene x HOMO is split into two highest T orbitals of approximate a, symmetry and, furthermore, a new orbital of strongly localized oxygen 2py,xcharacter is intercalated into the layer, forming a pseudodegenerate pair, less than 1000 cm-' apart, with an orbital of approximate a(b3,) character. The latter orbital has a strong nitrogen 2p, character but no localized, nitrogen 2 ~ , orbital ,~ is apparent in the MOs scheme of the crystal structure PRODAN. CI calculations, including all valence-shell single excited configurations and double excited configurations of the HOMO, LUMO layer, indicate IO transitions in the absorption domain given in Figure 3, top. The first broad absorption band with the maximum at 3 5 6 nm has been of principal spectroscopic interest, and according to our calculations it is dominated by a pair of x-polarized transitions (4t = - 1 9 O and -14O, respectively) positioned at 365 and 355 nm. The twinning is induced by the fact that two highest occupied MOs in PRODAN are of the same, naphthalene (a,) HOMO parentage, and we label these transitions as 'Lb 'A, and 'L'b 'A,, respectively. The position of the transversal, 'La 'Al calculated band varies with the number of interpolated transitions, from 258 to 270 nm. In view of the positions of 'La 'Al transitions in hexacenes3' and the absorption band of the solution phase, presumably of the same character, centered at 277 nm (Figure 3, top) this energy is too high. A prominent calculated
- -
-
-
Ilich and Prendergast I
WAVELEYGTH
[nml
Figure 3. Top: absorption spectra of PRODAN dissolved in (a) perfluorohexane and (b) a mixture of 35% (v/v) perfluorohexane and 65% heptafluorobutanol. Absorbances of the two spectra are not quantitatively related. Bottom: INDO/S CISD transition wavelengths and oscillator strengths for the first IO transitions in PRODAN. The plotted line intensities are slightly nonlinear and enveloped in Gaussians with total areas proportional to oscillator strengths.
transition at 250 nm is predominantly x-polarized (@t = 12O), and an ad hoc conclusion would be that the longitudinal 'Bb 'Al transition precedes the transversal B-A counterpart in the PRODAN singlet manifold. Closer analysis shows that most ring orbitals participating in this transition make nearly symmetric products with the y vector; however, mixing in the orbital with a large N(2p,) coefficient sufficiently perturbs the transition electron density34to create an electric dipole observable with a strong x component. (In view of this, one may question whether this state should continue to be labeled 'Ba,) The next transition, positioned at 232 nm and nearly collinear with the long axis (@t = 4') displays all the MOs characteristic of a true 'Bb ]Al line state. Spacing between calculated transitions into Lb, La, Bb, and B, states is larger than implied by the gross absorption features of solvated PRODAN, a fact caused principally by interpolation of several nonsymmetric transitions. Neither of those bands fits into the Platt-Murre11 classification ~ c h e m e ,and ~ ~while , ~ ~ certain of those bands are predicted to have considerable line strengths, their spectroscopic presence is yet to be proven. Certain features in the absorption spectrum, on the other hand, may be caused by molecular Rydberg transitions, not accounted for in our valence-shell calculations. Rydberg transitions have been observed at low energies in several alkyl-substituted aryl amine^,^^-^' and while pure Rydberg bands are unlikely to be observed in the solution-phase spectra, mixed Rydberg-valence transitions may be responsible for strong solvent shifts. If a configuration selection is strongly biased toward {a*] n ( 0 ) configurations, a very weak transition at 388 nm, predominantly x-polarized, is indicated. Linear dichroism measurements of the absorption spectra of PRODAN crystals2' indicate pre+-
-
-
(34) Callis, P. R.; Scott, T. W.; Albrecht, A. C. J . Chem. Phys. 1983, 78, 16.
(31) Boyd, D. B.; Smith, D. W.; Stewart. J. J . P.; Wimmer, E. In Science and Engineering and CRAYSupercomputers; Aldag, J. Ed.; CRAY Research: Minneapolis, MN, 1987; pp 195-21 2. (32) Hehre, W. J.; Radom, L.; von R a p e Schlayer, P.; Pople, J. A. A b inirio Molecular Orbital Theory: Wiley: New York. 1987. Chapter 7. (33) Platt, J. R J . Chem. Phys. 1949, 17, 484.
(35) Murrell, J. N . The Theory of the Electronic Spectra of Organic Molecules; Wiley: New York, 1963; pp 97-98. (36) Ilich, P., Can J . Spectrosc. 1987, 32, 19. (37) Fuke, J.; Nagakura, S.J . Mol. Spectrosc. 1977, 64, 139. (38) Muto, Y . ;Nakato, Y . ;Tsubomura, H . Chem. Phys. Left. 1971, 9, 597.
Singlet Adiabatic States of Solvated PRODAN
The Journal of Physical Chemistry, Vol. 93, No. 11, 1989 4445 TABLE IV: Approximate Symmetries and Corresponding Hartree-Fock Spectral Values (hartrees) of Molecular Orbitals of the Crystal Structure PRODAN (Middle Column), Antiquinoidally Distorted Crystal Structure (Left Column), and Crystal Structure with a Perpendicularly Twisted Dimethylamino Group
I Figure 4. Ring distortions leading to lower excited singlet energies; indicated structural changes are grossly exaggerated.
dominantly longitudinal polarization of a band in the lowest absorption domain, but no details are discernible from these spectra. Our calculations strongly suggest that all transitions in this domain are longitudinally polarized, and consequently anisotropy measurements of rigidly embedded PRODAN samples may be of little value in band analysis. Solvent shifts may provide additional indirect evidence (Figure 3, top). The asymmetric changes that the first band exhibits when the 0-H character of the medium is increased does suggest more than a single band in this domain. The issue here, however, has not been the (T*) n ( 0 ) but rather a ( T * } n(N) line, as implied by Stark effect measurements made by Huang and L ~ m b a r d iby , ~ the ~ dielectric loss measurements of Weisenborn,40by solvatochromic measurements described by Lippert,13 K o ~ o w e r G , ~r~a b ~ w s k i , ~and * ~ -Meech,42 ~ and by the transient absorption measurements of Ruliere et a1.I0 Early semiempirical calculations of M O ionization energies in nitroaniline, employing the Del B e ~ ~ e - J a f fversion e ~ ~ of CNDO/S method, predicted the low-lying states to be completely determined within the ( T } M O layer of benzene parentage.I5 Variations of the C=N bond length and the C-C=N bond angle in the calculations of p-(dimethylamino)benzonitrile,I6 employing the Krogh-Jespersen-Ratner variant of the INDO/S method,44 resulted in level shifts, and {.*) n(N)(nitrile) was indicated as the lowest singlet transition.16 N o possibilities for ring-structure changes or twisted conformations have been entertained in these theoretical studies. A twisted amino group, the hallmark of the postulated “new state” in electronically excited aminoaryl chrom0phores,4~does appear to introduce a highly polar excited state as demonstrated in recent CNDO/S calculations of PRODAN17 and di1nethy1anilines.l~ Inconsistent with the postulated model, however, is the fact that the calculated (r*) n(N) configurations are of much higher energy than the optical gap. Effects of environment, strongly suggested by solvatochromic fluorescence emission shifts, were theoretically considered within the formalism of Amos-Burrows theory46but never explicitly evaluated in MO caIculation~.~~~~J~ We start by considering what possible transition drives the molecule into the excited state and what is, symmetrically and energetically, the most probable adiabatic structure in that state. Calculated line strengths are highest for the C(2p,) .*,a configurations. The primary one-photon absorption in PRODAN is completely defined by this semiempirical valence-shell M O formalism, within the Hartree-Fock (HF) states of predominant naphthalene (?r*,n) character. The analogous energy impact causes the C-C bond elongation and virtual disappearance of the 65 kcal/mol twisting barrier in ethene.47 The same pattern would require changes in at least two bonds in naphthalene, if the overall ring geometry is to be preserved. This would amount to a resonance between 55 experimentally indistinguishable tautomers. A more likely scenario would include redistribution of the electron excitation energy within the whole ring and dissipation through a sequence of transitory minima on a potential energy surface of
LUMo
5
-
- 004
MO
e
-
-
-.44
j n
-
-
Huang, K.-T.; Lombardi, J. J. Chem. Phys. 1971, 55, 4072. Weisenborn, P. C. M.; Varma, C. A. G. 0.;De Haas, M. P.; WarM. Chem. Phys. Lett. 1986, 129, 562. See, for a review: Kosower, E. M. Acc. Chem. Res. 1982, 15, 259. Meech, S.R.; O’Connor, D. V.; Phillips, D. J . Chem. Soc., Faraday Trans. 2 1983, 79, 1563. (43) (44) (45) 911. (46) (47)
Del Bene, J.; Jaffe, H. H. J . Chem. Phys. 1968, 48, 1807. Krogh-Jespersen, K.; Ratner, M. J . Chem. Phys. 1976, 65, 1305. See,for a review: Rettig, W. Angew. Chem., Int. Ed. Engl. 1986, 25, Amos, T. A,; Burrows, B. L. Adu. Quantum Chem. 1973, 7 , 289. Merer, A. J.; Mullikan, R. S.Chem. Reu. 1969, 69, 639.
W Figure 5. Cartesian product (absolute values) of HOMO-LUMO molecular orbitals of PRODAN with antiquinoidally distorted ring and with twisted dimethylamino group.
the excited state. A structure with an elongated Ch-Cl and C3-C4 pair of bonds and a slightly twisted C,, C2 (dimethylamino) C3 fragment is the one that is at lower energy than the primary excited adiabatic state. The tautomer is possibly resonant with the approximately symmetrical antiquinoid counterpart obtained by elongation of a pair of C5-C4a and C7-cS bonds and twisting of the C5, c6 (1-propionyl), C7 fragment around the c6, c8, axis, thus creating a symmetrical scheme analogous to photoassociation of two 2-substituted allyl fragments to a 1,3-butadiyne (Figure 4). In this process, the M O with strongly localized oxygen 2pY, character for the planar, crystal structure PRODAN evolves into a pair of states of a predominant T character, while a second HOMO orbital acquires strong N 2p, character. It is interesting to note that while the MOs 40 and 41 (see Table IV), evolved from the n ( 0 ) state and now apparently of the naphthalene ring a type, are not of DZhsymmetry parentage. Rather, they correspond to a two-dimensional representation of the approximate S4symmetry group induced by disrotatory twisting of the antipodal allyl fragments in the PRODAN molecule. The optical gap is significantly reduced in this resonant structure. However, within the INDO/S formalism, this particular resonant structure is not distinctly favored over other possible tautomeric variants of the excited PRODAN. Elongation of any C-C or C-heteroatom bond decreases the orbital overlap, particularly the 2p, component. This is not closely paralleled by changes in two-electron integrals which are empirical quantities in INDO/S. One consequence is that the lower virtual part of the H F spectrum becomes contracted, HOMO and LUMO energies become more negative and the configurations determining the optical gap are necessarily of lower energy. What distinguishes the tautomer on Figure 4 and makes it energetically more favorable to other tautomers is the next step, which includes twisting of the dialkylamino group with respect
4446
The Journal of Physical Chemistry, Vol. 93, No. 11, 1989 1
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Figure 6. Radial distribution of distances between molecular centers of charges for the simulated water ensemble.
Figure 7. Ordering of the two highest occupied MO and the lowest excited-state dipole lengths for (i) the crystal structure PRODAN in a medium of low polarity (left) and (ii) an antiquinoidally distorted, twisted PRODAN surrounded by water charges, which induce a decrease in the charge density on nitrogen atom (right). Indicated state symmetries are very approximate, and no actual level crossing occurs.
to the plane of the Cl, C2, C, pro-allylic fragment. The highest occupied and lowest unoccupied valence orbitals have a node on the naphthyl-amino bridging carbon atom and relatively large amplitudes on C l and C 3 ,the terminal atoms of the pro-allylic fragment (Figure 5). As a consequence, the nitrogen group of highly surface active materials do not point to significant bulk-state the 2-amino derivative acquires a more localized character than distortions of the water s t r u c t ~ r e . ~ ~ ~ ~ ~ in either the 1- or 3-amino analogue. In this sequence of events, Of the three major energy summands in the Hartree-Fockassuming all other factors are invariant, the emission blue edge Roothaan-Hall expression, the nuclear repulsion between the will be set at a lower value in the case of 6-propionyl-2-(dichromophore and water atoms is the largest. Within the Condon methy1amino)naphthalene than for the 5-propionyl-l-(diapproximation this term is canceled when energies of two electronic methylamino) analogue. states are subtracted. Two-center electron repulsion terms, derived Apparently the sole twisting of the amino group, which is the from atomic ionizations and electron affinities, are carefully adpivotal argument in the twisted intramolecular charge-transfer justed to account for the electron correlation and weak nonormodel,45cannot be the first adiabatic structural charge (i) because thogonality of INDO/S atomic orbitals and are further scaled21 there is no experimental or theoretical evidence that low singlet to reproduce electronic transition energies of conjugated cyclic excitation is limited to the amino group region, causing an imhydrocarbons. An ad hoc inclusion of these terms into a full mediate electron redistribution in the C2-N,' orbital domain, and supermolecular Hamiltonian is unjustified for it would result in (ii) because such change is by itself energetically unfavorable for an effective overrepresentati~n~~ of the specific, limited interit increases the optical gap by more than 2500 cm-'. Only a molecular interaction. If the chromophore is considered only, then combination of antiquinoid distortion of the ring and twisting of two-electron integrals should be corrected for the electron density the amino group creates a low-energy excited singlet. changes caused by atomic and bond charges of proximal water The final directing factor is extramolecular; a strong electromolecules. A simple perturbative estimate shows that these static interaction with atomic charges of the surrounding discrete corrections are small, for the HOMO-LUMO energies in PROmolecular environment could significantly perturb the composition DAN and a water molecule differ by more than 80000 cm-'. of configurations determining the optical gap by reordering MOs Evaluation of the interaction through a correction to the onein the HOMO layer. particle, two-center attraction terms provides a crude first estimate Molecular Environment. The environment was created by of the possible intermolecular effects. In this way, the waterdynamically equilibrating4* 241 water molecules contained within PRODAN penetration integrals are evaluated within the Slater a deformable spherical stochastic boundary.49 Embedding was type function (STF) basis and no additional parameters are inachieved by tumbling the PRODAN molecule within this droplet troduced. Ordering of the MOs in the HOMO layer apparently in a pseudorandom way. The extent of the immediate environdepends, within our electrostatic interaction model, on a field ment, 1.9-3.9 A, was determined from the radial distribution of acting on the nitrogen group. If a particular embedding is achieved pair distances calculated for the dynamically simulated water (equivalent to a shift of 0.085 au in the nitrogen hi, elements) the droplet we used for embedding (Figure 6). highest orbital becomes the n ( N ( 2 ~ , , ~ )orbital ) of approximate The lower bound, about two-thirds of the sum of the van der Waals radii, is also in accord with the shortest e ~ p e r i m e n t a l l y ~ ~ ~ ~a,' symmetry parentage. The electric dipole moment of the first excited singlet is quadrupled ( k = 16-19 D) with respect to the determined solute-water atom pair distance. Extending the upper crystal structure PRODAN (Figure 7). boundary smoothed fluctations of the electric potential, as well If the field is scaled down or a different solvent embedding as of transition energy shifts, but apparently introduced no configuration is achieved, inducing smaller shifts in the electron qualitative changes in the interaction picture.52 The pseudodensity on the nitrogen group, the H O M O orbital is of C(2p,) random embeddings created a variety of transition energy shifts character, and the several lowest excited singlet states have electric and transition and state moment changes. However, the sample dipole moment in the range 2-5 D. This electrostatic interaction proved statistically insufficient to represent pseudodistribution of model therefore points to two essential effects: (i) the solvent the inhomogeneity sites of PRODAN in water.52 It should be electrostatic field has to be strong and locally specific and (ii) once noted that, by this method of embedding, no bulk-state distortions a particular arrangement of chromophore-solvent molecules has of the water cluster due to discontinuity on the water-PRODAN been attained the chromophore has to be trapped in a certain interface are accounted for. While this may appear to be a serious energy minimum, allowing the emission from an adiabatic state conceptual error, it should be recalled that the majority of excreated by distortion of the naphthalene ring and a twisting of perimental measurements of water structure at interfaces with the attached amino group. The latter effect appears to be correlated with the hydrodynamic control that the solvent exerts on (48) Brooks, 9. R.; Bruccoler, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S . ; Karplus, M . J . Compuf. Chem. 1983, 5 , 187. (49) Brooks, C. L., 111,. Karplus, M . J . Chem. Phys. 1983, 79, 6312. (50) Soper, A . K.; Phillips, M . G. Chem. Phys. 1986, 107, 47. (51) Narten, A . H. J . Chem. Phys. 1972, 56, 5681. (52) Ilich, P.: Haydock, C.; Prendergast, F. G. Chem. Phys. Lett., in press.
(53) Hawkins, R. K.; Eggelstaff, P. A. Clays Clay Miner. 1980, 28, 19. (54) Steytlef, D. C.; Dore, J. C.; Wright, C. J. Mol. Phys. 1983,48, 1031. (55) Claverie, P. In Intermolecular Interactions: From Diafomics to Biopolymers, Pullman, B., Ed.; Wiley: Chichester, UK, 1978; pp 63-305.
J . Phys. Chem. 1989, 93, 4441-4451 the low-energy emission as has been observed in p-( 1-perhydropyridiny1)benzonitrile at different temperatures.]'
Conclusion By extensive semiempirical ground-state calculations of PRODAN (6-propionyl-2-(dimethylamino)naphthalene)we predict that the molecule has a planar conformation, which is in accordance with the X-ray crystal structure data. We established a sequence of plausible structural, conformational, and electronic density distribution changes in the lowest singlet excited state. This scheme posits that the electronically excited chromophore first undergoes a structural change indicating a quasi-separation of a 2-(dimethylamino)allyl fragment. Twisting of the amino group, the conformational requirement identified by solvatochromic measurements6 and indicated by recent ~emiempirical,'~ and model ab initio calculations,20occurs in the second step, promoting a differentiation of a high occupied M O into a localized orbital with strong N(2pJ character and roughly quadrupling the electric dipole moment of that state. When the chromophore is embedded in a particular way into a shell of discrete water molecule atomic charges, the localized M O with a strong nitrogen 2p,, coefficient is promoted into the HOMO level and the highly polar lowest excited state becomes defined by [ T * ) n(N) electronic state manifold. If excited-state PRODAN is locked in this conformation long enough on a radiative time scale, its emission will be red shifted approximately 50 nm. If, on the other hand, the local electrostatic potential of the medium around the
-
4447
nitrogen atom is of lower magnitude, the polarity of the lowest excited singlet state in the twisted PRODAN is significantly reduced and the line strength to that state becomes negligible. The next lowest transition, in that case, is of higher energy and a predominant ( T * , T ] naphthalene ring character, characteristic of the planar, crystal structure PRODAN. This scheme, arrived at without additional parametrization beyond that inherent in the semiempirical method employed, appears to fully agree with the direction and magnitude of the emission shifts observed in PRODAN in media of different local polarity and viscosity. It further suggests a pattern of adiabatic changes that may occur in a low singlet manifold of a wide class of disubstituted aryl chromophores. Acknowledgment. We are thankful to Prof. M. C. Zerner (University of Florida, Gainesville, FL) for the INDO/S program, Dr. C. Haydock (Mayo Foundation, Rochester, MN) for useful discussions and coordinates of water clusters, to Dr. G. J. Marriott (Max-Planck Institute of Biophysical Chemistry, Goettingen, FRG) for experimental data, and to J. M. Smidt, P. H. Hart, and L. Wilkin for superb typing of the manuscript. P.I. thanks Prof. P. R. Callis (Montana State University, Bozeman, MT) for help with early INDO/S calculations and Dr. T. Zivkovic (Texas A&M University at Galveston, Galveston, TX) for a critical reading of the manuscript. This work was supported by N I H Grant G M 34847. Registry No. PRODAN, 70504-01-7,
Electrostatic Properties of L-Alanine from X-ray Diffraction at 23 K and ab Initlo Caicuiations Riccardo Destro,* Riccardo Bianchi, and Gabriele Morosi Dipartimento di Chimica Fisica ed Elettrochimica, e Centro CNR, Universita' di Milano. Via Golgi 19, Milano 201 33, Italy (Received: June 16, 1988; In Final Form: January 9, 1989)
Maps of the electrostatic potential of L-alanine have been derived from single-crystal X-ray diffraction data collected at 23 (1) K and interpreted with a multipole (pseudoatoms) formalism. In the crystal, minima in the potential of virtually identical magnitudes are observed near both oxygen atoms, in spite of their different environments. For an isolated, zwitterionic molecule constructed by assembling the pseudoatoms, a single minimum of -500 (42) kJ mol-] 1el-l is obtained. Its position, which differs from those of the minima in the crystal, is at 1.15 A from an oxygen atom-the one that forms two hydrogen bonds in the crystal structure-and along the line connecting, in the crystal, the oxygen and hydrogen atoms involved in the shortest hydrogen bond. Theoretical maps of the electrostatic potential, calculated by self-consistent field molecular orbital (SCF MO) ab initio methods with four different basis sets, have been compared with those derived from the experiment. In the region of the carboxylate group the best agreement is obtained with maps computed with the largest basis set here employed, of double-{ plus polarization quality (6-3 lG**). From various multipole models adopted to analyze the X-ray data, values of 12.7 (7)-13.1 (7) D are derived for 1 ~ 1 ,the magnitude of the molecular dipole moment of L-alanine in the solid state, to be compared with literature values, 12.3-17.0 D, of solution measurements. For an isolated molecule of the amino acid, the theoretical estimates of lpl with our basis sets are in the range 12.0-12.9 D. Atomic electric field gradients (EFG) have also been derived from the results of the X-ray diffraction experiment, and the corresponding asymmetry parameters 17 and quadrupole coupling constants (QCC) e2qQ/hevaluated. Those of the N atom (7 = 0.3 (l), and QCC in the range 1.I (2)-2.5 (2) MHz, depending on the model employed for the least-squares refinement of the X-ray data) are in substantial agreement with literature NQR determinations of TJ = 0.26 and QCC = 1.205 MHz. Comparison with reported spectroscopic results shows that the positive sign of the quadrupole constant and the orientation of the EFG tensor at this atom are correctly determined by our procedure. Negative signs are obtained for the QCCs of both oxygen atoms, whose EFG tensors have the largest component V, parallel, within loo, to the corresponding C-0 bond. For the oxygen atom involved in two hydrogen bonds, we determine QCC = -8.1 (5) MHz and TJ = 0.42 (9); for the other, which forms a single hydrogen bond, QCC = -6.8 ( 5 ) MHz and TJ = 0.8 (1). In the absence of 170quadrupole resonance estimates, for these quantities comparison has been made with reported data of hydrogen-bonded systems involving carboxylate groups. It is found that the values predicted by our experimental derivation for the two oxygen atoms agree with such literature data within our estimated standard deviations. Theoretical EFG tensors have also been evaluated at the SCF level with the same four basis sets employed for the calculation of the electrostatic potential; similarities and differences with respect to the X-ray derived results are discussed.
Introduction Electronic charge density, molecular dipole moment, electrostatic potential, and electric field gradients are some of the properties of molecular crystals that can be evaluated by a suitable
treatment of X-ray diffraction data.l-s This method has been extensively applied, Over the Past 15 Years, to derive the first of (1) Stewart,
R. F.J . Chem. Phys. 1972, 57, 1664-1668.
0022-3654/89/2093-4447$0l.50/00 1989 American Chemical Society
