In this paper we present a unified treatment of non-radiative decay processes in large molecules which involve either electronic relaxation between two electronic states or unimolecular rearrangeme...

The energy gap law for radiationless transitions in large molecules

An LCAO-MO-SCF-CI model along the lines introduced by Del Bene and Jaffe is developed that is capable of reproducing the better identified observed spectra of nitrogen heterocycles with a rms error of ∼ 1000 cm−1. The model is applied to the spectra of pyrrole, benzene, pyridine, the diazines, symmetric triazine and symmetric tetrazine. The benzene and pyridine spectra are reproduced nearly exactly. The band observed in pyrrole at ∼ 6.5 eV is calculated as two bands at ∼ 6.5 eV, but they are assigned π→σ
* and not π→π. No evidence is found for the low lying 1
B
2g
 in pyrazine, reported at ∼ 30400 cm−1 in pure crystals. The lowest excited singlet of sym. triazine is calculated as 1
E″ (n→π
*), not 1
A″2 (n→π), in agreement with a recent interpretation of Fischer and Small. Several bands are reassigned, and the electronic nature of the transitions discussed. Naphthalene and quinoxaline are examined to insure that no large drift of results are met with molecules of other sizes. Comparison of eigenvalues with molecular ionization potentials is made. Here the numerical agreement appears satisfactory for the first few ionization potentials only.

An intermediate neglect of differential overlap technique for spectroscopy: Pyrrole and the azines

Interaction of orbitals through space and through bonds

In this paper we consider a theory for intramolecular radiationless transitions in an isolated molecule. The Born–Oppenheimer zero‐order excited states are not pure in view of configuration interaction between nearly degenerate zero‐order states, leading to the broadening of the excited state, the line shape being Lorentzian. The optically excited state can be described in terms of a superposition of molecular eigenstates, and the resulting wavefunction exhibits an exponential nonradiative decay. The linewidth and the radiationless lifetime are expressed in terms of a single molecular parameter, that is the square of the interaction energy between the zero‐order state and the manifold of all vibronic states located within one energy unit around that state. The validity criteria for the occurrence of an unimolecular radiationless transition and for exponential decay in an isolated molecule are derived. Provided that the density of vibrational states is large enough (i.e., exceeds the reciprocal of the interaction matrix element) radiationless transitions are expected to take place. The gross effects of molecular structure on the relevant molecular parameters are discussed.

Intramolecular Radiationless Transitions

We present a unified expression for surface-enhanced Raman spectroscopy (SERS). The expression contains a product of three resonance denominators, representing the surface plasmon resonance, the metal-molecule charge-transfer resonance at the Fermi energy, and an allowed molecular resonance. This latter resonance is that from which intensity is borrowed for charge transfer, and when the molecular resonance is active it is responsible for surface-enhanced resonance Raman spectroscopy. We examine this expression in various limits, to explore the relative contribution or each resonance. First, we look at the situation in which only the surface plasmon resonance is active and examine the various contributions to the Raman signal, including the surface selection rules. Then we examine additional contributions from charge-transfer or molecular resonances. We show that the three resonances are not totally independent, since they are linked by a product of four matrix elements in the numerator. These linked matrix elements provide comprehensive selection rules for SERS. One involves a harmonic oscillator in the observed normal mode. This is the same mode which appears in the vibronic coupling operator linking one of the states of the allowed molecular resonance to the charge-transfer state. The charge-transfer transition moment is linked to the surface plasmon resonance by the requirement that the transition dipole moment be polarized along the direction of maximum amplitude of the field produced by the plasmon (i.e., perpendicular to the metal surface). We show that these selection rules govern the observed SERS spectral intensities and apply these to the observed spectra of several molecules. We also suggest a quantitative measure of the degree to which charge transfer contributes to the overall SERS enhancement.

/pdf/a-unified-approach-to-surface-enhanced-raman-spectroscopy-531y8etpir.pdf

I.G. Ross

Papers

Electronic states of azabenzenes: A critical review

The planar vibrations of naphthalene

Spectrum of azulene: Part II. The 7000-A and 3500-A absorption systems

Spectrum of azulene

Band contour analyses of the spectra of asymmetric rotor molecules: Part III. The 3200-Å absorption of napthalene