DNA cyclization and looping in the wormlike limit: Normal modes and the validity of the harmonic approximation

The intersystem crossing rates of uracil and thymine molecules in interaction with the heat bath were studied by means of the ab initio methods. The rates were calculated employing the time-dependent approach based on the correlation function. The normal modes of the singlet and triplet electronic states were related by the Duschinsky transformation. The correlation function was calculated using the Condon approximation for the spin-orbit matrix element and harmonic approximation for the nuclear motion. The excess vibrational energy in the initial singlet excited electronic state decreases the rate of the triplet formation in uracil and thymine. This decrease is more pronounced for uracil. Also, it was found that the change of the adiabatic energy gap can significantly modify the rate of the triplet formation.

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Revisiting an old concept: the coupled oscillator model for VCD. Part 1: the generalised coupled oscillator mechanism and its intrinsic connection to the strength of VCD signals

Physical Chemistry Chemical Physics ◽

10.1039/c6cp01282e ◽

2016 ◽

Vol 18 (31) ◽

pp. 21202-21212 ◽

Cited By ~ 20

Author(s):

Valentin Paul Nicu

Keyword(s):

Harmonic Approximation ◽

Normal Modes ◽

Oscillator Model ◽

Coupled Oscillator ◽

Intrinsic Connection ◽

Coupled Oscillator Model

This work reports the development of a generalised coupled oscillator expression for VCD that is exact within the harmonic approximation and is applicable to all types of normal modes, regardless whether the considered molecule is symmetric or asymmetric.

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Exotic Spectra and Lattice Vibrations of Ice X Using the DFT Method

Molecules ◽

10.3390/molecules23112780 ◽

2018 ◽

Vol 23 (11) ◽

pp. 2780 ◽

Cited By ~ 4

Author(s):

Lu Jiang ◽

Shu-Kai Yao ◽

Kai Zhang ◽

Ze-Ren Wang ◽

Hui-Wen Luo ◽

...

Keyword(s):

Vibrational Spectrum ◽

Inelastic Neutron Scattering ◽

Harmonic Approximation ◽

Normal Modes ◽

Dft Method ◽

Inelastic Neutron ◽

Lattice Vibrations ◽

Ideal Crystal ◽

Two Peaks ◽

Ice Phase

A typical vibrational spectrum in the ice phase has four separate bands: Translation, libration, bending, and stretching. Ice X, the final ice phase under high pressure, shows an exotic vibrational spectrum. Based on harmonic approximation, an ideal crystal of ice X has one peak, at 998 cm−1, for Raman scattering and two peaks, at 450 cm−1 and 1507 cm−1, for infrared absorption in this work. These three characteristic peaks are indicators of the phase transition between ice VII and VIII and ice X. Despite many experimental and theoretical works on ice X, only this study has clearly indicated these characteristic peaks in the region of the IR band. The phonon density of states shows quite different features than ice VIII, which could be verified by inelastic neutron scattering in the future. The dynamic processes of 15 vibrational normal modes are discussed and the typical hydrogen bonds are missing.

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Debye–Waller factor and the Lindemann parameter of some hexagonal close-packed metals

Canadian Journal of Physics ◽

10.1139/p80-055 ◽

1980 ◽

Vol 58 (3) ◽

pp. 384-387 ◽

Cited By ~ 3

Author(s):

A. Ramanand ◽

R. Ramji Rao

Keyword(s):

Distribution Function ◽

Harmonic Approximation ◽

Normal Modes ◽

Waller Factor ◽

Hexagonal Close Packed ◽

Debye Waller Factor ◽

Anisotropic Temperature ◽

Modes Of Vibration ◽

The Mean ◽

Temperature Factors

The Debye–Waller factor has been calculated as a function of temperature for the four hexagonal close-packed (hcp) metals cobalt, ruthenium, erbium, and scandium, using a lattice-dynamical model to evaluate the normal mode frequencies and eigenvectors in the harmonic approximation. The calculation of the anisotropic temperature factors for these metals requires a knowledge of the eigenvectors for the various normal modes of vibration. The frequency distribution function is also used to calculate the mean-square amplitude of displacement of the atoms, in the cubic approximation. The first and second negative moments of the distribution function are used to calculate the low- and high-temperature limits of [Formula: see text], respectively. The value of the Lindemann parameter obtained from the present calculations is consistent with the value quoted by Gschneidner.

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Introduction To Liquids

Chemical Dynamics in Condensed Phases ◽

10.1093/oso/9780198529798.003.0010 ◽

2006 ◽

Author(s):

Abraham Nitzan

Keyword(s):

Small Amplitude ◽

Large Scale ◽

Liquid Metals ◽

Harmonic Approximation ◽

Classical Mechanics ◽

Normal Modes ◽

Equilibrium Structure ◽

Ideal Gas ◽

Starting Point ◽

Basic Concepts

The statistical mechanics of atomic motion in gases and solids have convenient starting points. For gases it is the ideal gas limit where intermolecular interactions are disregarded. In solids, the equilibrium structure is pre-determined, the dynamics at normal temperature is characterized by small amplitude motions about this structure and the starting point for the description of such motions is the harmonic approximation that makes it possible to describe the system in terms of noninteracting normal modes (phonons). Liquids are considerably more difficult to describe on the atomic/molecular level: their densities are of the same order as those of the corresponding solids, however, they lack symmetry and rigidity and, with time, their particles execute large-scale motions. Expansion about a noninteracting particle picture is therefore not an option for liquids. On the other hand, with the exclusion of low molecular mass liquids such as hydrogen and helium, and of liquid metals where some properties are dominated by the conduction electrons, classical mechanics usually provides a reasonable approximation for liquids at and above room temperature. For such systems concepts from probability theory (see Section 1.1.1) will be seen to be quite useful. This chapter introduces the reader to basic concepts in the theory of classical liquids. It should be emphasized that the theory itself is general and can be applied to classical solids and gases as well, as exemplified by the derivation of the virial expansion is Section 5.6 below. We shall limit ourselves only to concepts and methods needed for the rest of our discussion of dynamical processes in such environments.

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Investigation of the spin-forbidden process in thymine

Hemijska industrija ◽

10.2298/hemind110924079e ◽

2012 ◽

Vol 66 (2) ◽

pp. 165-170

Author(s):

Mihajlo Etinski

Keyword(s):

Correlation Function ◽

Energy Gap ◽

Harmonic Approximation ◽

Normal Modes ◽

Electronic States ◽

Nuclear Motion ◽

Intersystem Crossing ◽

Condon Approximation ◽

Adiabatic Energy ◽

Mode Mixing

The intersystem crossing rate from the lowest singlet to the lowest triplet state of thymine was studied by means of the ab initio methods. The rate was calculated employing the time-dependent approach based on the correlation function. The normal modes of the singlet and triplet electronic states are related by the Duschinsky transformation, i. e. by rotation and translation. The correlation function was calculated using the Condon approximation for the spin-orbit matrix element and harmonic approximation for the nuclear motion. The intersystem crossing rate strongly depends on the singlet-triplet adiabatic energy gap and on the normal mode mixing.

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Anharmonic interactions in alkali halides. I

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1965.0179 ◽

1965 ◽

Vol 287 (1409) ◽

pp. 259-280 ◽

Cited By ~ 94

Keyword(s):

Optical Constants ◽

Sodium Iodide ◽

Harmonic Approximation ◽

Normal Modes ◽

Alkali Halides ◽

Temperature Dependent ◽

Spectral Functions ◽

Modes Of Vibration ◽

Longitudinal Optic ◽

Anharmonic Interactions

Calculations of the Griineisen parameters of individual modes of vibration, of the average Griineisen parameter, and of the temperature dependence of the elastic constants, of sodium iodide and potassium bromide have given reasonable agreement with experiment. The model used was a shell model, obtained from experimental measurements of the dispersion curves, extended in a simple way to include the anharmonicity. Calculations have also been made of the spectral functions of some of the normal modes propagating in the [111] direction. These show qualitative agreement with experiment in that the longitudinal optic modes are particularly temperature dependent. The results are used to discuss the validity and usefulness of a quasi-harmonic approximation in which the frequencies are those measured experimentally. The optical constants and the reflectivity of the crystals have also been calculated and are compared with experiment.

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