Mechanisms That Interchange Axial and Equatorial Atoms in Fluxional Processes: Illustration of the Berry Pseudorotation, the Turnstile, and the Lever Mechanisms via Animation of Transition State Normal Vibrational Modes

2006 ◽  
Vol 83 (2) ◽  
pp. 336 ◽  
Author(s):  
Marion E. Cass ◽  
King Kuok Hii ◽  
Henry S. Rzepa
Keyword(s):  
Transition State ◽  
Vibrational Modes ◽  
Normal Vibrational Modes

Temperature dependence of the normal vibrational modes of hcp Zr

1978 ◽  
Vol 18 (6) ◽  
pp. 2632-2642 ◽  
Author(s):  
C. Stassis ◽  
J. Zarestky ◽  
D. Arch ◽  
O. D. McMasters ◽  
B. N. Harmon
Keyword(s):  
Temperature Dependence ◽  
Vibrational Modes ◽  
Normal Vibrational Modes

Vibrational Total Energy Distributions in Terms of Symmetry Coordinates, Forces and Momenta

1980 ◽  
Vol 35 (4) ◽  
pp. 464-465
Author(s):  
Alain J. P. Alix ◽  
Erling Rytter
Keyword(s):  
Total Energy ◽  
Polyatomic Molecules ◽  
Vibrational Modes ◽  
Energy Distributions ◽  
Symmetry Coordinates ◽  
Generalized Symmetry ◽  
Normal Vibrational Modes

Abstract The fundamental definitions of the Total Energy and of the Vibrational Total Energy Distributions are presented in details in terms of either symmetry coordinates, or generalised symmetry forces, or generalized symmetry coordinates. This, give now a uniform tool for physicists and chemists in the field of characterisation of the normal vibrational modes of polyatomic molecules.

Energy distributions of neutrons scattered from solid C60 by the beryllium detector method

1995 ◽  
Vol 73 (11-12) ◽  
pp. 763-771 ◽  
Author(s):  
J.R. D. Copley ◽  
D. A. Neumann ◽  
W. A. Kamitakahara
Keyword(s):  
Energy Range ◽  
First Principles ◽  
Spectroscopic Data ◽  
Vibrational Modes ◽  
First Principles Calculations ◽  
Energy Distributions ◽  
Gaussian Functions ◽  
Detector Method ◽  
Normal Vibrational Modes ◽  
Rich Spectrum

We measured the energy distribution of neutrons scattered from polycrystalline C60, using a high-resolution filter-analyzer spectrometer. In the energy range 30–90 meV (242–726 cm−1) we observed a rich spectrum that we fitted to a sum of 15 Gaussian functions, each of which is assigned to one or a set of several degenerate normal vibrational modes of the C60 molecule. We also observed two broad features in the energy range from 90–130 meV (726–1049 cm−1). Our results are generally in excellent agreement with published spectroscopic data. Detailed comparisons with the results of several first-principles calculations suggest that present-day theories can predict the internal vibrational frequencies of C60 rather well, at least in the 30–90 meV range of energies.

Normal vibrational modes in benzil crystals

2002 ◽  
Vol 44 (2) ◽  
pp. 373-378 ◽  
Author(s):  
M. A. Ivanov ◽  
V. A. Kimasov ◽  
Yu. F. Markov
Keyword(s):  
Vibrational Modes ◽  
Normal Vibrational Modes

scholarly journals Popular Integration Grids Can Result in Large Errors in DFT-Computed Free Energies

2019 ◽  
Author(s):  
Andrea N. Bootsma ◽  
Steven Wheeler
Keyword(s):  
Transition State ◽  
Molecular Orientation ◽  
Density Functional ◽  
Low Frequency ◽  
Basis Sets ◽  
Vibrational Modes ◽  
Free Energies ◽  
Functional Theory ◽  
Stereoselective Reactions ◽  
Transition State Structures

Density functional theory (DFT) has emerged as a powerful tool for analyzing (bio-)organic and organometallic systems and proved remarkably accurate in computing the small free energy differences that underpin many chemical phenomena (e.g. regio- and stereoselective reactions). We show that the lack of rotational invariance of popular DFT integration grids reveals large uncertainties in computed free energies for some isomerizations, torsional barriers, and regio- and stereoselective reactions. The result is that predictions based on DFT-computed free energies for systems with very low-frequency vibrational modes can change qualitatively depending on molecular orientation. For example, for a metal-free propargylation of benzaldehyde, predicted enantioselectivities based on B97-D/def2-TZVP free energies using a popular pruned (75,302) integration grid can vary from 62:38 to 99:1 by simply rotating the transition state structures. Relative free energies for the regiocontrolling transition state structures for an Ir-catalyzed C–H functionalization reaction computed using M06/6-31G(d,p)/LANL2DZ and the same grid can vary by more than 5 kcal/mol, resulting in predicted regioselectivities that range anywhere from 14:86 to >99:1. Errors of these magnitudes occur for different functionals and basis sets, are potentially widespread among modern applications of DFT, and can be reduced by using much denser integration grids than commonly employed.<br>

Electronic Potentials of Normal Vibrational Modes in SbSI Crystals

2002 ◽  
Vol 274 (1) ◽  
pp. 1-15 ◽  
Author(s):  
A. Audzijonis ◽  
L. Žigas ◽  
J. Narušis ◽  
R. Žaltauskas ◽  
L. Audzijonienė
Keyword(s):  
Vibrational Modes ◽  
Normal Vibrational Modes
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