Librational Energy Research Articles

Spectroscopic study of conformational dynamics of 1,1′-binaphthyl in a jet

Analysis of the fluorescence excitation spectrum of 1,1′-binaphthyl in a jet shows that in the origin region there are four transitions, in an energy range of 150 cm−1, which strongly overlap through the occurrence of strong progressions in a torsional mode. The four transitions can be described in terms of excitations to levels of an interchange-equivalent naphthalene dimer in a trans and cis configuration. The dimer splittings are 50 and 63 cm−1 for 1,1′-binaphthyl-h14 and 50 and 57 cm−1 for 1,1′-binaphthyl-d14. The Franck–Condon envelope of the librational progressions indicates that the potential energy surface for states of A and B symmetry are different, which implies that the interplanar angle in each of the four excited states is different. From the intensities in the A and B progressions it is further deduced that for the origin transitions the transition moment in each subunit is oriented in the naphthalene plane at an angle of ∼50° with respect to the long axis. From the Franck–Condon envelope in the librational progressions it is further deduced that the change in torsional angle on optical excitation to the B-potential energy surface is ∼12° to the trans and 6° to the cis side. From this a maximum (state dependent) barrier of 150 cm−1 is calculated. It is further shown that, near the intense false origin, numerous modes appear which are induced through vibrational mixing. This Fermi-resonance effect is most obvious in perdeutero binaphthyl, where the vibronically induced intensity in the region of the most intense false origin is smeared out over many modes. The emission spectrum of the molecule can be interpreted by assuming that in 1,1′-binaphthyl very efficient vibrational relaxation occurs through conversion of vibrational into librational energy with molecular rotations providing the matching energy. It is also suggested that, after vibronic excitation, vibrational relaxation occurs into the energetically most stable structure. Finally, the observed red shift of the binaphthyl fluorescence in solution must be due to solvent stabilization of the excited molecule in a structure which is more planar than the one observed in the isolated molecule.

Phonon-defect interaction in KCl-CN

Interactions of phonons with tunneling and librational energy states of CN - in a KCl host lattice are probed by Brillouin scattering. Results for two concentrations, n CN = 1.6 × 10 19 cm -3 and 5.9 × 10 19 cm -3, are compared with pure KCl.

Neutron scattering studies of(CN)−defects in KBr

We have studied both the librational and the tunneling excitations of ${(\mathrm{CN})}^{\ensuremath{-}}$ ions in a KBr matrix through the interaction of these modes with the acoustic phonons of the KBr host. From our measurements on a sample containing 0.00034 mole fraction of KCN in KBr, we find the ${A}_{1g}\ensuremath{-}{T}_{2g}$ tunnel splitting to be 0.28 \ifmmode\pm\else\textpm\fi{} 0.05 meV (2.3 \ifmmode\pm\else\textpm\fi{} 0.4 ${\mathrm{cm}}^{\ensuremath{-}1}$). From measurements on a more concentrated system, 0.0045 mole fraction of KCN in KBr, the ${A}_{1g}\ensuremath{-}{E}_{g}$ librational excitation energy is found to be 1.6 \ifmmode\pm\else\textpm\fi{} 0.1 meV (13.0 \ifmmode\pm\else\textpm\fi{} 1.0 ${\mathrm{cm}}^{\ensuremath{-}1}$). These values are consistent with the results of optical measurements.

Electrostatic model for the rotational potential in ammonium halides

An electrostatic model for the rotational potential of an ammonium tetrahedron in a cubic field is proposed. The rotational potential can be written as a rapidly converging series of kubic rotator functions. The NX4 ion, where X is hydrogen or deuterium, performs small angular motions about the minimum of the potential in both the ordered and disordered states, giving rise to librational energy levels. The anharmonic portion of the energy levels, both from the kinetic and potential energies, accounts for good agreement with infrared absorption data in NH4Cl, ND4Cl, NH4Br, and ND4Br. We use a one parameter fit to these data and then compute the potential barriers for rotations about threefold and fourfold axes of the tetrahedron. The difference between the transition temperatures for ND4Cl and NH4Cl is also explained.

First Excited Librational States for 〈100〉‐, 〈110〉‐, and 〈111〉‐Type Paraelectric Defects in Cubic Crystals

AbstractFirst excited librational eigenstates and energy eigenvalues are deduced in the tunneling approximation and listed for 〈100〉‐, 〈110〉‐, and 〈111〉‐oriented paraelectric defects sites of cubic symmetry. These supplement the existing listings for the librational ground states.

Theory of Activated Radiationless Processes: Orientation Relaxation of Polar Molecules

A first-principles theoretical expression for the rate of a thermally activated process is derived. The treatment is specialized to the orientation relaxation of dipolar molecules, which is viewed as a radiationless transition between electronic states corresponding to the dipole in discrete orientations. The dipolar electronic states are calculated in the Born-Oppenheimer approximation and the associated adiabatic potential-energy surfaces are taken to be displaced, undistorted harmonic potentials. Transitions between the different electronic states arise through the nonadiabatic kinetic-energy operator associated with the librational degree of freedom of the reorienting dipole. The explicit expression for the transition rate is calculated to first order by evaluating the integral over the time-correlation function of the Kubo representation of the rate constant in the strong-coupling limit using the method of steepest descent. It is shown that the transition rate is actually a sum of five contributions arising from phonon scattering processes in which 0, ±1, ±2 quantum changes take place in the librational degree of freedom of the dipole. When kT is large compared with a quantum of librational energy, the expression for the transition rate simplifies to the functional form of the Arrhenius equation in which the pre-exponential factor and the activation energy are given in terms of specific molecular properties. The theory is applied to a quantitative treatment of the relaxation of dipolar impurities in ionic crystals. The dielectric behavior of polar organic molecules in liquids is also qualitatively examined, and the explicit dependence of the relaxation time on the molecular dimensions in a homologous series of compounds is obtained. Even though the theory is specialized to dipolar relaxation, the basic expressions are generally applicable to any thermally activated process involving the migration of ions or atoms, e.g., ionic conductivity, mobility, viscous flow, and diffusion.

Minimization of polypeptide energy. VII. Second derivatives and statistical weights of energy minima for deca-L-alanine.

The matrix of second derivatives of 21 apparent local energy minima of deca-L-alanine has been computed. The results show that all these conformations are true local energy minima and, therefore, potentially stable conformations for this peptide. Calculations of the relative statistical weights of these conformations confirm earlier theoretical considerations on the importance of the librational free energy of stable conformations of peptides. As predicted earlier, the relative statistical weights of the local energy minima do not always fall in the same order as the relative energies.

Energy Evolution in Pd2H below 1°K

Energy evolution below 1°K has been observed in β-phase palladium hydride (formal composition Pd2H). The rate of evolution was strongly temperature-dependent below 0.1°K, but became temperature-independent between 0.1° and 1.0°K. It depended upon previous specimen history and was greatly reduced by annealing of the specimen below 50°K. For specimens kept below 1°K, the rate of energy production at a given temperature diminished with a half-life of about 8 h. The results are explained semiquantitatively as a (spectroscopically forbidden) nuclear-spin conversion in quasi-molecular PdH4 units left behind in small concentrations when the lattice is cooled through the rotational transition (at 55°K) of β-palladium hydride. The temperature-dependence below 0.1°K appears to result from limitation in the rate at which the lattice can remove the change in librational energy associated with the conversion process.