J. Phys. Chem. 1995,99, 12115-12124
12115
Infrared Spectral Properties of the Naphthalene Cation: Radiative Cooling Kinetics Experiments and Density Functional Calculations Yen-Peng Ho, Yu-Chuan Yang, Stephen J. Klippenstein,* and Robert C. Dunbar" Chemistv Department, Case Westem Reserve University, Cleveland, Ohio 44106-7078 Received: April 21, 1995; In Final Form: June 5, 1 9 9 P
Time-resolved photodissociation thermometry and density functional theory have been applied to the study of the infrared (IR) spectral properties of the naphthalene cation. The radiative cooling rate of isolated gasphase naphthalene ions was measured directly using a thermometric approach based on time-resolved photodissociation (TRPD). Two-photon excitation of the ion at a wavelength of 355 nm was used for TRPD rate measurements at various cooling times after formation of the ions (by multiphoton ionization at 193 nm). The observed dissociation rates were calibrated against a previous experimentally determined rateenergy curve as a thermometric probe, providing cooling curves for initially hot ions. Radiative cooling time constants were observed to be 0.9 s (CloHgf) and 1.9 s (CloDs+). For comparison with these experimental results, the IR absorption intensities were calculated using nonlocal density functional theory (DFT) implementing Becke's three-parameter functional for incorporating exchange and correlation effects. A DunningLluzinaga valence double-5 basis set with a single set of d-polarization functions on the C atoms was employed. Both the observed cooling curves and the DFT calculations provide strong support for the absolute IR intensities reported from direct absorption measurements in Szczepanski, J.; Roser, D.; Personette, W.; Eyring, M.; Pellow, R.; Vala, M. J. Phys. Chem. 1992, 96, 7876. Increased accuracy of nonlocal DFT, even when employing moderate-sized basis sets, as compared with Hartree-Fock calculations is suggested by the better agreement with experimental observations of the absolute IR intensities for cationic naphthalene and for a sample series of organic molecules.
IR transitions in these two studies. There is also some
I. Introduction Polycyclic aromatic hydrocarbons (PAHs) have often served as leading examples for understanding spectroscopic and photophysical phenomena in larger molecules and are central to our growing knowledge of such properties for cations. Accurate understanding of the radiative properties of PAHs is also of fundamental importance to the modeling of the interstellar environment. These molecules are currently considered to provide a plausible explanation for a number of unidentified infrared (IR) interstellar emission bands.'$2 In the origin regions of these emissions there is a high flux of ionizing ultraviolet r a d i a t i ~ n ,so ~ that the PAH systems are expected to exist predominantly in cationic form. Unfortunately the determination of IR spectroscopic properties of cations is substantially more difficult than that for neutrals, owing to the difficulty of establishing high concentrations of well-characterized ions. Recently two separate groups have begun detailed experimental investigations of the IR absorption properties of these cations, using low-temperature matrix techniques to achieve useful concentrations of ions in solid-phase environment^.^-'^ In particular, Vala and co-workers have recently reported frequencies and absolute intensities for a variety of matrixisolated cationic specie^^-^ including the naphthalene ~ a t i o n . ~ Meanwhile, Allamandola and co-workers have also reported IR frequencies and absolute absorption intensities for matrixisolated naphthalene cationsg and very recently for other PAHs.'O Although these studies agree in many respects, the current difficulty of such techniques for quantitative IR characterization is strikingly pointed out by the disagreement of a factor of 50 in the absolute intensities assigned to the naphthalene cation @
Abstract published in Advance ACS Abstracts, July 15, 1995.
0022-3654/95/2099-12115$09.00/0
disagreement among the spectral assignments. As the discordant results of these two absorption-spectroscopic studies suggest, it is hard in practice to quantitate such difficult molecular species via direct optical absorption intensity measurements. A fundamentally different approach to this question is provided through cooling measurements. The kinetics of cooling of an isolated cation by infrared fluorescence emission is governed by the same IR transition intensities as IR absorptions, but the cooling rate can be measured without any of the absolute calibration uncertainties which make it hard to quantitate absorption experiments with confidence. The IR radiative cooling rate of internally hot cations gives a highly reliable absolute calibration number for the overall IR intensity of the molecule, which, when combined with the more detailed relative intensity information for individual modes coming from absorption measurements,resolves the absolute spectral properties in an entirely satisfactory way. At the same time, quantum-chemical calculations can fill in the gaps in experimental information in a usefully complementary way. The further goal of being able to calculate the spectral properties of such big molecules in an absolute and confident fashion is still rather distant, but new methods and more capable computers are bringing this closer. At the current stage of progress, it is very useful to do both experiments and calculations in parallel, with close interaction between them at every point. In this article, the techniques developed in our laboratory for measuring cooling kinetics of isolated gas-phase ions are applied to the naphthalene ion in close combination with new quantumchemical calculations of the spectral properties. The experimental strategy for measuring ion cooling kinetics exploits the strong dependence of ion unimolecular dissociation rates on internal energy. Time-resolved photodissociation (TRPD) is 0 1995 American Chemical Society
Ho et al.
12116 J. Phys. Chem., Vol. 99, No. 32, 1995 used to measure these dissociation rates in this “thermometric” context. The photodissociation rate constant is observed as a function of cooling time for an initially hot sample of naphthalene cations.I1-l7 The comparison of the observed dissociation rate constants, calibrated against a previous experimental determination of the rate-energy curve,18-zzprovides a view of the decreasing internal energy (or alternatively temperature) as a function of cooling time.1’,13.’6%z3 Corresponding simulated cooling curves may be generated directly from computed IR absorption intensities via a Boltzmann average over the emission and absorption rates for each of the modes.23 Comparing the observed and estimated cooling curves then provides a global test of the absolute accuracy of the set of IR absorption intensities used. This in turn may validate the accuracy of a computed IR intensity set or may provide a guide to adjustment or parametrization of the intensity computations. Finally, the calibration of absolute IR intensities derived in this way gives a basis for validating or correcting the more uncertain absolute calibrations of absorption-intensity experiments. Previous ab initio quantum chemical calculations of the IR spectral properties of the naphthalene cation at the HartreeFock (HF) levelz4 have proven to be of considerable utility in the interpretation of the spectral observations. However, the HF-predicted absolute intensities for the naphthalene cation were in overall terms a factor of 6 greater than the larger of the two experimentally observed sets of values, and this would not seem to be a useful level of theory for such calculations on the naphthalene cation. Nonlocal density functional theory (DFT) provides a useful alternative quantum-chemical approach which has been shown for many properties to provide results which are of similar accuracy to those obtained in multireference configuration interaction treatment^.^^ The computational requirements for nonlocal DFT calculations depend on the particular implementation but are at worst only modestly greater than corresponding HF level calculations. Thus, DFT should provide a useful approach for proceeding beyond HF for molecules such as the polycyclic aromatic hydrocarbons. There have been a wide variety of tests of the validity of DFT for properties such as molecular binding energies and vibrational f r e q u e n c i e ~ .However, ~~ there have been relatively few studies of its prediction capab es for the IR i n t e n s i t i e ~ ; ~ the ~ -most ~~ detailed such examinations are studies by Fan and Ziegler26and by Dobbs and D i ~ o of n ~the~ IR intensities for a series of small organic molecules. These studies suggest that nonlocal DFT does indeed provide improved estimates for the IR absorption intensities, particularly when basis sets of triple-5 or higher quality are employed. Here, nonlocal DFT calculations of the IR spectral properties of the naphthalene cation have been performed with the hope of obtaining a more meaningful theoretical reference for the spectral interpretation and particularly of the absolute intensities. Unfortunately, the relatively large size of the polycyclic aromatic hydrocarbons restricts these calculations to basis sets of at best double-
