J. B. Page

Energetics of large fullerenes : balls, tubes, and capsules

First-principles calculations were performed to compare the energies of 29 different fullerene structures, with mass number from 60 to 240, and of eight nonhelical graphite tubes of different radii. A quantity called the planarity, which indicates the completeness of the π-bonding, is the single most important parameter determining the energetics of these structures. Empirical equations were constructed for the energies of nonhelical tubes and for those fullerene structures that may be described as balls or capsules. For a given mass number, bail-shaped fullerenes are energetically favored over capsular (tube-like) fullerenes.

First-order resonance Raman profile lineshapes from optical absorption lineshapes — a consistency test of standard theoretical assumptions

Abstract It is pointed out that an exact relation holds between the lineshapes of optical absorption and first-order resonance Raman profiles under commonly-used theoretical assumptions. This relation is utilized to predict profile lineshapes from measured absorption data for β-carotene and cyanocobalamin and the results are compared with measured profiles.

On the separation of resonance Raman scattering into orders in the time correlator theory

A detailed study is carried out of the separation of resonance Raman scattering into orders within the time‐correlator formulation of Hizhnyakov and Tehver (HT). This formulation is exact for a multimode system at all temperatures and for all electron–phonon coupling strengths within well‐defined ’’standard assumptions.’’ As in any Raman theory, the full m‐phonon Raman scattering involves the electron–phonon coupling to infinite order, owing to virtual phonon transitions accompanying the m real final state phonon transitions. The HT separation into orders is seen to correspond to a particularly convenient grouping of the contributions, such that the full m‐phonon scattering is expressed as a power series in explicit orders of the electron–phonon coupling, but with each term of the series also containing factors involving the electron–phonon coupling implicitly to infinite order. Each term of this series except the first vanishes for T→ 0, with the result that the (explicitly) mth order scattering and the ...

Temperature effects in the time‐correlator theory of resonance Raman scattering

Within well‐defined ‘‘standard’’ assumptions and the time‐correlator theory’s separation of resonance Raman (RR) scattering into orders, previously discussed exact relations allow one to calculate mth‐order RR profile line shapes directly from optical absorption data at T≠0 K. At T=0 K, the mth‐order profiles are identical with the full m‐phonon profiles, which are the experimentally measured quantities, while for T≠0 K, the m‐phonon profiles include higher‐order corrections due to processes which freeze out at T=0 K and which involve virtual phonon excitation–deexcitation in all Franck–Condon active modes. In this paper we show that for one‐phonon scattering from a large class of multimode systems, the correction due to a thermally populated mode is small if (1) the mode’s frequency is small compared with the smallest resolvable width in the optical absorption and/or (2) the mode’s electron–phonon coupling is weak. For the multimode system β‐carotene in isopentane at T=123 and 298 K, the sum of correctio...

General theory of vibrational mode mixing and frequency shifts in resonance raman scattering

Abstract A general formalism is given for treating vibrational mode mixing, frequency shifts, and atomic equilibrium position shifts under electronic excitation in resonance Raman scattering. The theory is exact for first-order scattering at T = 0 K for all linear and quadratic electron-phonon coupling strengths. Numerical results illustrating mode mixing are presented.

Inclusion of frequency shifts with electronic excitation in the calculation of multiple‐order resonance Raman profile line shapes from optical absorption data

A previously discussed exact relation which allows one to compute first‐order resonance Raman intensity profile line shapes directly from optical absorption data within well‐defined assumptions is generalized to approximately include vibrational frequency shifts with electronic excitation and is extended to profiles of higher order. For a large class of optical absorption line shapes and sufficiently small frequency shifts and temperatures, the generalization is found to be quite simple. We demonstrate its usefulness and the importance of including frequency shifts by using optical absorption data to compute first‐, second‐, and third‐order profile line shapes for the KClO4:MnO−4 impurity system and comparing the results with measured profiles.

Resonance Raman scattering study of azulene. II. Nonzero temperature multimode model calculations

In a recent paper (Az I), well‐structured T=300 K resonance Raman (RR) profiles for the 1400, 1260, 900, and 2×825 cm−1 lines of azulene in CS2 and for the 825 cm−1 line of azulene in methanol were reported. Previously developed transform techniques were used to (1) compute RR profile line shapes directly from measured optical absorption spectra, and (2) extract ratios of Stokes loss parameters from the line shape scale factors. The transform analysis indicated that (1) our model assumptions (adiabatic and Condon approximations, harmonic phonons, atomic equilibrium position shifts, and small vibrational frequency shifts upon excitation to a single electronic state) are basically correct allowing forminor modifications, and (2) any deviations from these assumptions are likely to be larger for the 900 cm−1 mode and smaller for the 1400 and 1260 cm−1 modes. In this paper (Az II), we report model calculations of the optical absorption spectra, RR profile line shapes, and relative RR intensities. In these calc...

T ≠ 0 K Multimode modeling of optical absorption spectra and resonance Raman profiles

Abstract We discuss the superiority of the time-correlator approach over conventional sum-over-states methods for exact multimode modeling of T ≠ 0 K optical absorption and resonance Raman profiles. Numerical illustrations of thermal broadening are given, and a short-time approximation is shown to be very convenient for modeling this effect.

Jahn-Teller distortions in solid C20 and other fullerene structures

Abstract We have used first principles molecular dynamics to determine the energies of Jahn-Teller distortions in a variety of neutral and negatively charged fullerene structures. We find that smaller structures have larger Jahn-Teller distortion energies. Solid C 28 and solid C 20 , which have covalent bonds connecting the individual fullerene balls, are found to have energies which are much lower than the energies of their molecular components. The charged state of solid C 20 is found to have a total distortion energy which is about six times larger than that of C − 60 .

Resonance Raman scattering study of azulene. I. Experiment and theoretical analysis via transform techniques

Room temperature resonance Raman (RR) profiles for the 1400, 1260, 900 and 2×825 cm−1 lines of azulene in CS2 and for the 825 cm−1 line in methanol are reported. These profiles display pronounced multimode interference effects within the measured spectral range (570–720 nm). Using previously developed transform techniques, we analyze our RR data by calculating profile line shapes directly from our measured optical absorption data. The calculated and measured profile line shapes are in good agreement for all of the modes studied. These results are consistent with the model assumptions upon which the transform analysis rests. To further test our model assumptions, we extract ratios of the RR Stokes loss parameters from the scale factors of our profile line shape fits. RR Stokes loss parameters estimated from these ratios are found to be in good correlation with published 2K emission intensity ratios. However, their correlation with published 4K absorption intensity ratios indicates the presence of some inte...