Dependence Of Electronic Transition Moment Research Articles

Chemical enhancement effects on protoporphyrin IX surface‐enhanced Raman spectra: Metal substrate dependence and a vibronic theory analysis

AbstractSurface‐enhanced Raman spectra (SERS) of protoporphyrin IX (PPIX) and analogous metal‐containing PPIX compounds excited at 785 nm exhibit robust, strongly enhanced (~5 × 109) spectra that are highly dependent on the nanostructured metal (Au or Ag). Although the relative intensities of the 785‐nm SERS vibrational spectral features are very similar for all observed PPIX‐based compounds, the relative intensities are dramatically different on Au and Ag SERS substrates. Time‐dependent density functional theory (TDDFT) calculations are carried out for Au2/Ag2–PPIX complexes to understand the origins of this chemical enhancement contribution to the observed SERS spectra. The observed metal dependence of the SERS spectra in the heme ring stretching region (1,500–1,620 cm−1) are reproduced by calculated resonance Raman intensities due to low‐lying metal (σ) to molecule (π*) charge transfer excitations of the metal dimer–PPIX complexes when the metal dimer is near a porphyrin ring Cβ position. The nuclear coordinate dependence of electronic transition moments is essential for capturing the effects of these CT excitations. A simple method for determining the importance of the transition moment normal mode dependence relative to Franck–Condon factors (A term) is described and implemented. The consequences of this vibronic analysis for the observation of overtone/combination bands in SERS spectra are discussed.

Nuclear coordinate dependence of electronic transition moments involving torsional modes: the Franck–Condon/symmetry forbidden m03+ band in the allowed S 1←S 0 transition of toluene

A novel theory of vibronic intensity borrowing by large-amplitude vibrations was developed in a form to modify the conventional Herzberg–Teller theory. The ingredients are: (1) Crude Born–Oppenheimer wavefuntions (CBO Wf’s) at more-than-one (2×2×3=12) conformations were used as building blocks of the adiabatic BO Wf. (2) The latter was made to belong to the molecular symmetry group ( G 12) by Fourier-series expansion terminated at the low (ninth) order. (3) The non-Born–Oppenheimer effect was shown to be less significant. The experimental observation of the subtitle was successfully interpreted with this formalism, endorsing the previous assertion by Walker et al. [J. Chem. Phys. 102 (1995) 8718].

Simulation of Non-Condon Enhancement and Interference Effects in the Resonance Raman Intensities of Metalloporphyrins

The room-temperature resonance Raman (RR) spectra of nickel(II) porphine have been simulated for excitation within the Q-band optical transition, taking into account both coordinate-independent (Condon) as well as coordinate-dependent (non-Condon) contributions to the Raman scattering amplitude of each vibration. Computation of scattering intensities for all three classes of Raman-active modes (polarized, depolarized, and inversely polarized) observed in metalloporphyrin spectra was made possible in this fashion. Vibronic parameters were evaluated at the INDO level from the dependence of electronic transition moments and transition energies upon nuclear coordinates; the transform theory of RR scattering was then applied to compute the relative intensities of vibrational modes. The calculated enhancement patterns are in excellent agreement with experimental results. Three vibrational modes of b1g symmetry (ν10, ν11, and ν16) are identified as being the primary Jahn−Teller distortion coordinates: a substantial fraction of the total internal-mode reorganization energy for S0 − S1 photoexcitation is predicted to arise from symmetry-lowering. Interference between Condon and non-Condon scattering amplitudes is found to be a major determinant of the intensities of several polarized vibrations as well as those depolarized modes which are Jahn−Teller active. The dependence of scattering intensity on excitation wavelength for such modes is correctly predicted, indicating that the relative amplitudes and phasing of Condon and non-Condon contributions for each vibration are reliably determined.

The origin of off-resonance Raman intensity

This paper re-examines methods originally proposed in a paper by Berg and Robinson for the calculation of absolute Raman cross sections, on and far off resonance. In contrast to previous theories of the Raman effect, the concept of polarizability derivatives is hidden: The Franck–Condon effect is the dominant factor in determining Raman cross sections. When sums over the vibrational fine structure are carried out and only a single electronic transition is used, large differences in calculated scattering cross sections occur when using Raman formulas related by various transformations. This is in agreement with conclusions in the earlier paper. However, resonance Raman intensity is not very sensitive to the various methods discussed in the paper. When the sums are extended over more than a single electronic state or when the nuclear dependence of electronic transition moments is taken into account, interference effects found in the Berg–Robinson paper can be subdued, shifted, or eliminated. The need for precise off-resonance Raman excitation spectra of simple gas phase diatomic molecules is stressed.

Nuclear Coordinate dependence of electronic transition moments in orbitally forbidden transitions: A new interpretation of deuterium isotope effects

The nuclear coordinate dependence of electronic transtion moments has been investigated for the purpose of finding new interpretations of deuterium isotope effects on spectral intensities and radiative decay rates in orbitally forbidden electronic transitions. By using “AO following nuclei” wavefunctions as the building block for the electronic wavefunction in the adiabatic BO vibronic wavefunction, the spin-free hamiltonian is diagonalized to generate eigenfunctions and eigen-energies. It is found that the electronic transtion moments based on these eigenfunctions show dependences upon the vibrational modes which are not directly involved in vibronic coupling. This leads to interpretations of the deuterium isotope effects in T 1 → S 0 radiative transitions of aromatic hydrocarbons and S 0 → S 1 absorption in pyrazine which are not based on the conventional Herzberg—Teller or non-BO coupling.

Light emission of electron impact excited hydrogen molecules and the dependence of electronic transition moment on internuclear distance

By studying the intensity of light emitted by hydrogen molecules, which have been excited by keV electrons, the dependence of the electronic transition moment on internuclear distance can be determined over a wide region. Experimentally it was found for the Werner band system that the quantity ``transition energy times electronic transition moment'' is a constant between 0.6 and 1.6 Å as predicted by theory. Several vibrational bands exhibit strong intensity perturbations, especially the 3 → ν″ progression.

Potential Curves and R Dependence of Electronic Transition Moments from Molecular Continuum–Continuum Emission Spectra. I. Theory

A procedure is developed for analyzing the oscillatory structure observed in the continuum–continuum emission of diatomic molecules when the upper state is attractive and the lower state repulsive. Given the potential curve of the lower state and the positions of the diffuse maxima and minima, the procedure uniquely determines the potential curve of the upper state. A simple semiclassical method is presented for deriving both the upper-state potential and the R dependence of the electronic transition moment from the measured relative intensity distribution. Criteria for the applicability of this method are presented and discussed.