Donald F. Heller

Theory of vibrational overtone line shapes of polyatomic molecules

We present a general theory for the overtone absorption line shapes of isolated polyatomic molecules. The theory is based on a separation of the molecular vibrational degrees of freedom into: (1) a few relevant CH local modes which interact directly with the radiation field, and (2) the remaining ’’bath’’ modes which induce spectral broadening and determine the line shapes. Line shapes are evaluated using the standard Fano–Zwanzig scattering formalism. A simple yet general model is put forth to illustrate some of the features exhibited by polyatomic line shapes. Specific application is made to benzene. The model adequately accounts for the overtone line shapes recently observed by Bray and Berry. Within its context we are able to understand the observed vibrational state and isotopic dependence of the line shape and to predict line shapes for related but as yet unstudied systems. To our knowledge this is the first dynamical application of local mode theories. We discuss their advantages and the extent to ...

Nonradiative decay processes in benzene

Abstract We investigate the behavior of single vibronic level nonradiative decay rates in benzene and benzene- d 6 . The effects of excitation in a promoting mode which undergoes frequency and geometry changes in the S 1 relaxation (to T 1 or S 0 ) are considered in detail. Calculated relative nonradiative decay rates are compared with experimental values and are used to assign triplet state vibrational frequencies to the ν s , ν 10 and ν 16 vibrations. This comparison also indicates that none of these modes, nor the modes ν 1 and ν 6 , are likely to be the dominant promoting modes for the S 1 → T 1 decay. Some simple expressions are given which provide good estimates of the vibronic state dependence of the non-radiative decay rates. In conjuction with experimental decay rate data, these estimates can aid in guiding spectral assignments of vibronic bands. Simple but general theoretical criteria are derived which are useful in determining those vibrations which are poor (or good) accepting modes. Our previous theory is generalized to consider absolute nonradiative decay rates. The results are used to suggest a possible mechanism for the “channel three” decay process observed by Callomon . Although the numerical applications presented here are to benzene electronic relaxation processes, the theoretical developments also apply to and the calcultions illustrate general features of nonradiative decay in the statistical limit.

Density functional formulation of collisional polarizabilities: Application to homonuclear noble gas diatoms

We apply the general density functional formalism for electron gases in external fields to the specific case of electric susceptibilities of interacting closed shell systems. Computations are presented for the parallel and perpendicular components of the incremental polarizability tensors of He2, Ne2, and Ar2, as functions of internuclear distance. In the case of He2 our results can be compared with recent coupled Hartree−Fock calculations. For all three of the light noble gases we have evaluated the thermal averages of the pair polarizability components which correspond to the second dielectric virial coefficients and low pressure light depolarization ratios: Agreement with experimental data is found to be very good. The dependence of these calculated collision−induced optical properties on interatomic potentials and the long range behavior of the pair polarizability are considered in detail.

Relative rate calculations for intramolecular radiationless transitions

Abstract We present a formulation of relative rate calculations for intramolecular radiationless transitions which includes many of the recent theories in the literature as special cases. Our method, which is closely related to the previous work of Siebrand, allows us to treat simultaneously the effects of anharmonicity (κ), geometry shifts (Δ Q ) and frequency changes (Δω) in all the vibrations of interest. We apply this approach to the S 1 → T 1 intersystem crossing in benzene and argue that the theory can be used to determine bounds for Δω S 1 →T 1 s only if Δ Q s and κs are accurately known. The use of “local” versus “normal” modes of vibration is discussed. We conclude, from our failure to explain the emission cutoff in S 1 , that the representation of vibronic interaction energies as products of “electronic factors” and vibrational overlap integrals is valid only near the origin of the excited singlet.

Molecular overtones as local modes

Abstract The apparent simplicity of polyatomic overtone spectra and the conceptual utility of local modes are considered. The form and basis-set-dependence of the dipole moment operator are discussed and a criterion given for overtone spectra to be well described within a local mode picture. Caution is needed in making dynamical inferences based on agreement between overtone and local mode line positions.

Photodissociation dynamics of small polyatomics: Isolated molecule behavior and collision induced effects

We outline a conceptually simple theoretical approach to the study of photodissociation of small polyatomics at low pressures. In this approach, we employ a realistic Hamiltonian and solve numerically for the ensuing dynamics. Formaldehyde is treated as a prototype, and the results of calculations are given and compared with recent experiments. Several conclusions are drawn about the photodissociation mechanism. In particular, our calculations suggest that the barrier to products lies above the first few vibrational levels of S1. Hence, both the experimentally determined nonradiative decay of S1, and the much slower CO appearance rate, must be collision induced. We expect similar time‐lag behavior to be evinced in other small polyatomics and we suggest that collisional effects often may persist to very low pressure.

Electronically induced IR multiphoton absorption: a direct probe of the quasicontinuum

Abstract Electronic excitation followed by nonradiative decay provides a novel method for directly accessing the vibrational quasicontinuum of polyatomic molecules. From there efficient nonresonant absorption of infrared photons occurs. Quasi-continuum CrO2Cl2 molecules absorb off-resonance radiation with near-resonance efficiency. Some fluence threshold effects persist when absorption originates from the quasicontinuum.

Short range electronic distortion and the density dependent dielectric function of simple gases

Abstract The coefficient defining the density expansion of the dielectric function of a simple gas are expressed as thermal averages of products of two-body adiabatic polarizabilities. To allow this description a superposition form has been introduced for the three -body polarizability: this approximation leads to results which reduce to the well-known Kirkwood, dipole-induced-dipole (DID) theory only when the pair polarizabilities are replaced by their long range (dispersional) form. When non -DID effects are retained, i.e., when ab initio (e.g., Hartree-Fock) pair polarizabilities are used, significant corrections are found, but the triplet contributions are still small except at very high densities and pressures. In particular, we evaluate the second and third dielectric virial coefficients for room temperature helium, and compare our calculated values with those obtained in recent DID treatments. The marked differences found in the resulting density dependence of the Clausius-Mossotti function, and the relative insensitivity to the choice of interaction potential, are discussed in terms of short range electronic distortion.

Density functional theory of interacting closed shell systems. II. The determination of charge densities and the Hellman–Feynman theorem

The density functional formalism and the additive density approximation are used to obtain the nonadditive contribution to the electron density of a set of closed shell atoms in the absence of external fields. It is shown that due to the additive density approximation, the Hellman–Feynman theorem is violated when the force on the nucleus is examined. The reason for this violation is discussed.

The role of accepting modes in the theory of nonradiative transitions

Abstract We treat explicitly the role of geometry and frequency changes in the nonradiative decay of individual vibrational levels in isolated large molecules, and present new results appropriate to the case of small effective energy gaps.