Ground-state structures and vibrational frequencies are calculated for complexes of the nitrate anion with one and two water molecules at the ab initio Hartree–Fock level with a basis set including diffuse and polarization functions. Two local minimum geometries are found for each complex. Calculations of the electronically excited states at the CIS level are then used to find the forces on each of the atoms upon vertical excitation to the two lowest-lying (near-degenerate) strongly allowed electronic transitions. These forces are converted to gradients of the excited-state potential surfaces along the ground-state normal modes and compared with the parameters obtained previously from empirical simulations of the experimental resonance Raman intensities of NO3− in dilute aqueous solution. The calculations on two-water clusters agree well with the experimental excited-state geometry changes along the totally symmetric N–O stretch. The calculations underestimate the frequency splitting of the antisymmetric stretching vibration (degenerate in the isolated D3h ion) and the resonance Raman intensity in this mode, suggesting that bulk solvent polarization enhances the asymmetry of the local environment for NO3− in water. Comparison of the ground-state vibrational frequency splitting of the antisymmetric stretch with the corresponding values for the nitrate ion in salts having known crystal structures suggests that the rms difference among the three N–O bond lengths for nitrate anion in water probably exceeds 0.01 Å.
Quantitative analysis of resonance Raman scattering cross sections, together with charge-transfer absorption and emission spectra, can provide detailed information about the changes in nuclear equilibrium geometry undergone by both the electron donor and acceptor and the surrounding solvent in photoinduced charge-transfer processes. The molecular parameters that determine absorption and fluorescence band shapes and resonance Raman cross sections are summarized, and methods for extracting those parameters through spectral modeling are reviewed with emphasis on charge-transfer systems. Applications to the determination of molecular and solvent reorganization parameters to several organic intra- and intermolecular charge-transfer transitions are then presented, and prospects for further development of the technique are discussed.
Resonance Raman intensities of p-nitroaniline, a prototypical “push–pull” chromophore with a large first hyperpolarizability (β), have been measured in dilute solution in five solvents having a wide range of polarities (cyclohexane, 1,4-dioxane, dichloromethane, acetonitrile, and methanol) at excitation wavelengths spanning the strong near-ultraviolet charge-transfer absorption band. The absolute Raman excitation profiles and absorption spectra are simulated using time-dependent wave packet propagation techniques to determine the excited-state geometry changes along the five or six principal Raman-active vibrations as well as estimates of the solvent reorganization energies. The total vibrational reorganization energy decreases and the solvent reorganization energy increases with increasing solvent polarity in all solvents except methanol, where specific hydrogen-bonding interactions may be important. The dimensionless normal coordinate geometry changes obtained from the resonance Raman analysis are converted to actual bond length and bond angle changes with the aid of normal mode coefficients from a ground-state density functional theory calculation. The geometry changes upon electronic excitation involve predominantly the Cphenyl–Nnitro, N–O, and phenyl C2–C3 bond lengths, with little involvement of the amino group. Nonresonant Raman spectra in 1,4-dioxane, dichloromethane, ethyl acetate, acetone, acetonitrile, and methanol show only a very small solvent dependence of the vibrational frequencies. This suggests that changing the solvent affects the excited state more than the ground state, calling into question two-state models that treat the ground and charge-transfer excited states as linear combinations of neutral and zwitterionic basis states with solvent dependent coefficients.
Quantum sum rules impose limits on the hyperpolarizability, beta. A survey of the largest second-order molecular susceptibilities finds what appears to be a universal gap between the experimental results and the fundamental limits. In this work, we use theory, linear spectroscopy, Raman spectroscopy, and measured values of beta (using hyper-Rayleigh scattering and Stark Spectroscopy) to show that this gap is due to an unfavorable arrangement of excited state energies. The question of whether this result is a universal property of a quantum system or a matter of present paradigms for making molecules is discussed.
The coupling between nuclear vibrations and electronic excitations (electron-phonon coupling) in semiconductor nanocrystals influences many photophysical processes in these materials. While electron-phonon coupling in CdSe nanocrystals has been studied both experimentally and theoretically for more than 20 years, there remains little agreement about its magnitude and size dependence. This Perspective summarizes key literature results, suggests reasons for their disagreement, and proposes approaches to better determine this important quantity.
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