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J . Phys. Chem. 1989, 93, 3056-3062
of d,l and s-orbitals on the metal center in a manner quite analogous to that found from nonrelativistic calculation^^'^ on the corresponding singly occupied orbital l a in C13M with M = Ti, Zr, and Hf. The composition of l a from the quasi-relativistic calculation on CI3Th and C13U allows for a stronger interaction between l a and l b , and we find that D(M-R)QR for all systems in Table VI is larger than the corresponding D(M-R)Fo value. In fact, the bond energies calculated by the quasi-relativistic method are seen to be in close agreement with the experimental bond energies given in Table VI. Further, the quasi-relativistic calculations on C13ThR and C13UR (Table VI) would indicate that actinides, as is the case for early transition metals (Table V), form bonds to hydrogen and alkyls of nearly equal strength.
VI. Concluding Remarks The calculation of the first-order relativistic corrections to bond energies by perturbation theory is based on the nonrelativistic wave function (or density matrix) according to eq 17, and energy corrections due to changes (ApR) in the density matrix induced by relativity enters only to second or higher orders in a2.We have shown in the present and earlier studies*J'*'*that the first-order approach is adequate for calculations of bond energies in compounds containing elements as heavy as gold with Z = 79. The first-order approach is on the other hand not adequate for the heavier actinides where relativistic effects are larger and ApR
as a consequence sizable. In particular, we have found that the contributions to the density from f-type and s-type actinide orbitals are changed considerably by relativity. The contributions to the energy from ApR up to the nth order in a2can in principle be taken into account by resorting to nth-order relativistic perturbation theory based on a Foldy-Wouthuysen transformed Dirac Hamiltonian in which terms up to order n are retained [for a discussion of divergencies and &function contributions see ref 381. In the quasi-relativistic approach presented here, relativistic corrections (ApRvaI)to the valence density are evaluated variationally to all orders with respect to the first-order Foldy-Wouthuysen transformed Dirac Hamiltonian, whereas the influence from higher order terms in the same Hamiltonian are neglected. Calculations on atomic orbital energies for the valence shells of heavy elements indicate that the quasi-relativistic method provides results in better accord with fully relativistic Dirac-Slater results than the first-order theory. Bond energies from quasi-relativistic calculations are further in better agreement with experiment than bond energies based on first-order theory, in the case of actinide compounds.
Acknowledgment. This investigation was supported by the Natural Science and Engineering Research Council of Canada (NSERC) through a travel grant to T.Z. We also thank NATO for an International Collaboration Grant.
The External Heavy Atom Effect: Photophysics of (Dimethylamino)benzonitrile in Cryogenic Rare Gas Matrices Meredith A. Morgan and George C. Pimentel* Laboratory of Chemical Biodynamics, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720 (Received: August 15, 1988; In Final Form: October 25, 1988)
We have investigated the effects of rare gas external heavy atoms on rate constants of spin-forbidden processes of (dimethy1amino)benzonitrile isolated in cryogenic matrices by means of steady-state and time-resolved emission spectroscopy. We interpret the dramatic increase in the phosphorescence yield and the decreases in the fluorescence yield and lifetime and the phosphorescence lifetime in the heavy atom matrices of krypton and xenon in terms of a model in which the rate constant for phosphorescenceincreases 300-fold in xenon compared to argon, while the rate constants for intersystem crossing to the triplet state and nonradiative relaxation from the triplet state increase by factors of less than 5. Measurements in argon matrices doped with heavy atoms indicate that even one heavy atom neighbor has a significant effect on both singlet and triplet lifetimes. We include higher resolution (up to 0.1 nm) emission spectra of (dimethy1amino)benzonitriledetailing vibrational structure which has not previously been observed in the condensd phase. Comparison of the vibrational spacings with a matrix FTIR spectrum indicates that there is distortion of the aromatic ring in the SI state, while the shifts in the 0-0 transitions in acetonitrile matrix indicate that the SI state is somewhat more polar than either the So or T, states.
Introduction Atoms of high nuclear charge are known to increase rates of spin-forbidden processes, both as a component of the solvent (the external heavy atom effect) and as substituents on the molecule of interest itself (the internal heavy atom effect).' Previously, we demonstrated that branching ratios of photochemical reactions in cryogenic rare gas matrices of argon2 or krypton3 can be altered by directing reactants to the triplet state with a heavy atom matrix such as xenon. This work is aimed at quantifying the effects of rare gas external heavy atoms on rates of spin-forbidden processes, by examining the photophysics of (dimethy1amino)benzonitrile (DMABN) in argon, krypton, and xenon matrices. The high intensity and well-resolved features of its fluorescence and phosphorescence make it a suitable subject for a study of the external heavy atom effect. *Author to whom correspondence should be addressed.
0022-3654/89/2093-3056$01 S O / O
DMABN
Heavy atom effects on fluorescence and phosphorescence yields (@f and GP,respectively) and on phosphorescence lifetimes4 ( T ~ have been observed before, but few studies have attempted to determine the effects on individual rate constants. We have measured relative fluorescence and phosphorescence yields and singlet and triplet lifetimes of DMABN isolated in argon, krypton, and xenon, as well as singlet and triplet lifetimes in mixed ar(1) McGlynn, S . P.; Azumi, T.; Kinoshita, M. Molecular Spectroscopy of the Triplet State; Prentice-Hall: Englewood Cliffs, NJ, 1969. (2) Collins, S. T.; Pimentel; G. C. J. Phys. Chem. 1984, 88, 4258. (3) Laursen, S. L.; Pimentel, G.C. J . Phys. Chem., in press. (4) McGlynn, S. P.; Reynolds, M. J.; Daigre, G. W.; Christodoyleas, N. D.J . Phys. Chem. 1962, 66, 2499.
0 1989 American Chemical Society
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Photophysics of (Dimethy1amino)benzonitrile gon:xenon matrices. From these measurements we are able to model the increase in k , (the rate constant for intersystem crossing to the triplet state), k , (the rate constant for phosphorescence), and k,, (the rate constant for nonradiative decay from the triplet state) in these rare gas heavy atom matrices, as well as estimate the effect of a single heavy atom affixed in the vicinity of a chromophoric molecule. DMABN has been the focus of much interest since Lippert et aL5 discovered that it exhibits dual fluorescence in polar roomtemperature solutions. The long-wavelength “anomalous” fluorescence is thought to originate from a state in which the amino methyl groups are twisted from a position syn to the aromatic plane to a position anti, with an accompanying transfer of charge from the amino to the nitrile group! The long-wavelength fluorescence has not been observed in rigid glasses at 80 K,’ where there is insufficient energy to overcome the barrier to formation of the twisted intramolecular charge-transfer state, and is thus not expected in 12 K rare gas matrices. In this paper we include the first phosphorescence spectrum of DMABN exhibiting vibrational structure and the first condensed-phase fluorescence emission and excitation spectra exhibiting this structure. We compare the vibrational spacings with a matrix FTIR spectrum to gain insight into the geometry of DMABN’s “normal” excited states, while comparison of the measured 0-0 transitions with those in a 12 K acetonitrile matrix gives an indication of the relative polarities.
Experimental Section Instruments. Matrices were deposited on a sapphire window cooled by a Displex Model CSW202 (Air Products and Chemicals, Inc.) closed cycle helium refrigerator. The window could be rotated for deposition, emission measurements, and photolysis within the vacuum shroud which was maintained at a pressure of IOd Torr. Calcium fluoride and Suprasil windows were used interchangeably as outer windows. Steady-state emission measurements were made using a Spex Fluorolog 2 (Model 21 2T) spectrofluorometer equipped with a 150-W xenon lamp and single photon counting, interfaced to a DEC PDP LSIl 1 for data acquisition and processing. Approximately 4% of the excitation light was split off to a rhodamine B quantum reference counter to correct for the wavelength dependence of the excitation intensity. Additionally, an identical rhodamine solution was periodically placed in the sample compartment to correct for differences in the sample and quantum reference counter paths. A standardized lamp (Optronic Laboratories) was used to generate a correction for the spectral response of the emission monochromator and photomultiplier tube. The sapphire window was positioned so that excitation was approximately 15” from the normal to the surface, and emission light was collected at 30” from the normal. Steady-state emission spectra were recorded with a 4.0-nm band-pass at the excitation monochromator and a 0.1-4.0-nm band-pass at the emission monochromator. For excitation spectra, the band-pass was 0.2-4.0 nm at the excitation monochromator and 4.0 nm at the emission monochromator. Spectra were taken in 0.1-1.0-nm increments, integrating for 0.25-30 s at each point, depending on the signal intensity and the resolution desired. Wavelength accuracy of the monochromators was determined by use of a mercury pen lamp and was found to be f0.2 nm between 250 and 550 nm. The phosphorescence decay curves were also obtained with the fluorometer. A mechanical shutter was used to cut off the excitation light after steady-state illumination (shutter time
