Selection Rules for an Electronic Raman Effect in a Situation where the Appropriate Point Group is a Double Group

1968 ◽  
Vol 174 (2) ◽  
pp. 477-478 ◽  
Author(s):  
J. A. Koningstein
Keyword(s):  
Raman Effect ◽  
Point Group ◽  
Selection Rules ◽  
Double Group

New Developments in Raman Spectroscopy with Lasers: Electronic Transitions

1968 ◽  
Vol 22 (5) ◽  
pp. 438-444 ◽  
Author(s):  
J. A. Koningstein
Keyword(s):  
Raman Spectroscopy ◽  
Single Crystals ◽  
Crystal Field ◽  
Raman Spectra ◽  
Raman Effect ◽  
Electronic Transitions ◽  
New Developments ◽  
Selection Rules ◽  
Phonon Spectra ◽  
Host Lattices

A discussion is given of the Raman spectra of single crystals of yttrium gallium garnet (YGaG), of ytterbrium gallium garnet (YbGaG), and of Yb:YGaG. From a comparison of the spectra it has been possible to separate the phonon spectra of the host lattices from that of an electronic Raman effect which occurs between the crystal field levels of the 2F7/2 manifold of Yb3+ in the garnet crystals. Information with respect to the selection rules governing both types of spectra is given.

Matrices and Wave Functions under Double-Group Symmetry

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Time Reversal ◽  
Point Group ◽  
Computational Effort ◽  
Wave Functions ◽  
Group Symmetry ◽  
Time Reversal Symmetry ◽  
Point Group Symmetry ◽  
Matrix Elements ◽  
Double Group

Symmetry is one of the most versatile theoretical tools of physics and chemistry. It provides qualitative insight into the wave functions and properties of systems, and it has also been used successfully to obtain great savings in computational efforts. In the preceding chapter we examined time-reversal symmetry, and now we turn to the more familiar point-group symmetry. We show how relativity requires special consideration and extensions of the concepts developed for the nonrelativistic case, and how time-reversal symmetry and double-group symmetry are connected. Although the techniques that incorporate double-group symmetry presented here are primarily aimed at four-component calculations, they are equally applicable to two-component calculations in which the spin-dependent operators are included at the SCF stage of a calculation. In the preceding chapter, we have shown how the use of time-reversal symmetry can lead to considerable reduction in the number of unique matrix elements that appear in the operator expressions. However, we are also interested in the overall structure of the matrices of the operators. In particular, we are interested in possible block structures, where classes of matrix elements may be set to zero a priori. If the matrices can be cast in block diagonal form, we may save on storage as well as computational effort in solving eigenvalue problems, for example. Matrix blocking will already be effected by the point-group symmetry of the molecule.

scholarly journals A point group approach to selection rules in crystals

2003 ◽  
Vol 45 (8) ◽  
pp. 1440-1450
Author(s):  
V. P. Smirnov ◽  
R. A. Evarestov ◽  
P. Tronc
Keyword(s):  
Point Group ◽  
Group Approach ◽  
Selection Rules

scholarly journals Explicit expressions for totally symmetric spherical functions and symmetry-dependent properties of multipoles

2014 ◽  
Vol 470 (2171) ◽  
pp. 20140435
Author(s):  
Boris Zapol ◽  
Peter Zapol
Keyword(s):  
Point Group ◽  
Product Structure ◽  
Spherical Functions ◽  
Matrix Elements ◽  
Linear Combinations ◽  
Selection Rules ◽  
Charge Distributions ◽  
Symmetry Operators ◽  
Point Groups ◽  
Symmetry Operations

Closed expressions for matrix elements 〈 lm' | A (G)| lm 〉, where | lm 〉 are spherical functions and A (G) is the average of all symmetry operators of point group G, are derived for all point groups (PGs) and then used to obtain linear combinations of spherical functions that are totally symmetric under all symmetry operations of G. In the derivation, we exploit the product structure of the groups. The obtained expressions are used to explore properties of multipoles of symmetric charge distributions. We produce complete lists of selection rules for multipoles Q l and their moments Q lm , as well as of numbers of independent moments in a multipole, for any l and m and for all PGs. Periodicities and other trends in these properties are revealed.

The discovery of the Raman effect

1989 ◽  
Vol 43 (1) ◽  
pp. 1-23 ◽  
Keyword(s):  
Raman Effect ◽  
Rapid Development ◽  
Building Blocks ◽  
Incident Radiation ◽  
100Th Anniversary ◽  
Polyatomic Molecules ◽  
Transparent Medium ◽  
Selection Rules ◽  
Absorption And Emission ◽  
The World

C. V. Raman was born on 7 November 1888. A 100th anniversary • is a milepost, an occasion on which to review the best known of his contributions to science: the recognition that light scattered from a transparent medium includes wavelengths shifted from that of the incident radiation. It was realized from the outset that these shifts were due to an interaction, subtly different from the ordinary processes of absorption and emission, involving exchange of energy between radiation and the molecules of the medium. The discovery was promptly christened the Raman effect by Pringsheim (1), a phrase that caught on immediately and survives today. Its announcement in 1928 drew the attention of scientists around the world and ushered in a period of rapid development that brought the new spectroscopy onto a plateau where it remained, with few changes of substance, for practically a quarter of a century. For most purposes the experimental procedures were easily adapted from tried and true methods already in place for measurement of fluorescence: such instruments were put together from basic building blocks and examples already existed in a number of laboratories. The necessary theory, including selection rules and related symmetry considerations, emerged more gradually and several years elapsed before their framework was firmly in place. To some extent, however, this delay could be attributed to the greater attention now given to polyatomic molecules whose spectra had not been seriously addressed in the older forms of spectroscopy.

Selection Rules in the Raman Effect

Nature ◽  
1929 ◽  
Vol 123 (3107) ◽  
pp. 757-759 ◽  
Author(s):  
F. RASETTI
Keyword(s):  
Raman Effect ◽  
Selection Rules

SELECTION RULES AND TEMPERATURE DEPENDENCE OF THE FIRST-ORDER RAMAN EFFECT IN CRYSTALS

1956 ◽  
Vol 34 (3) ◽  
pp. 312-338 ◽  
Author(s):  
O. Theimer
Keyword(s):  
Temperature Dependence ◽  
Raman Effect ◽  
Scattered Light ◽  
Low Frequency ◽  
Current Theory ◽  
Selection Rules ◽  
First Order ◽  
Non Linear ◽  
Full Symmetry ◽  
Linear Effects

Starting from the most general scattering formulae, the current theory of the Raman effect in crystals is modified in such a way as to remove the well-known discrepancies between theory and experiment concerning the selection rules for calcite and similar crystals. A distinction is made between electrons in delocalized crystal orbitals and electrons in localized atomic or molecular orbitals and it is shown that only the latter produce a Raman scattering in agreement with the unmodified theory. The general formula for the scattering by delocalized electrons is analyzed and it is found that the magnitude of the components [Formula: see text] of the first-order polarizability (qi normal coordinate of the scattering lattice vibration) depends on the wave vectors Q′ and Q″ of incident and scattered light. The wave vector dependence of the first-order polarizability requires selection rules for the first-order Raman effect which do not correspond to the full symmetry of the scattering crystal but only to the symmetry operations of the group of Q = Q′ – Q″ which leave Q unchanged. These modified selection rules are shown to be compatible with experiment. The influence of mechanical anharmonicity and of polarizability derivatives of higher order on the first-order Raman effect is also discussed. It is found that these non-linear effects offer no satisfactory explanation for the great intensity of forbidden lines in the Raman spectrum of some crystals. Concerning temperature effects the non-linear terms in the intensity formulae are found to be of greater importance and are tentatively suggested as being responsible for the anomalous temperature dependence of low frequency external lattice vibrations.

Notizen:Schwingungsspektrum und Kraftfeld von Natriumhexanitrokobaltat

1969 ◽  
Vol 24 (10) ◽  
pp. 1667-1668
Author(s):  
Wolfgang Krasser
Keyword(s):  
Raman Spectrum ◽  
Force Field ◽  
Point Group ◽  
Vibrational Frequencies ◽  
Force Constants ◽  
Selection Rules ◽  
Valence Force ◽  
Valence Force Field ◽  
Infrared Data

Abstract The Raman spectrum of Na3[Co(NO,)8] has been mea-sured in the range from 2000 to 50 cm 1 and the vibrational frequencies and their assignment are compared with infrared data already obtained. The force constants are calculated in the valence force field. With respect to vibrational spectro-scopy the CoN6-octaeder and the N02-group are assumed to be approximately two separate units. The justification of this approximation is discussed on the basis of the Raman spec-trum and the selection rules for the Symmetrie point group S6 of Na3 [Co (N02) 6]. Gefärbte Substanzen mit Absorptionsbanden im kurzwelligen sichtbaren Spektralbereich eignen sich vorzüglich für die Aufnahme des Raman-Spektrums, wenn man einen He —Ne-Laser mit seinem relativ lang-welligen Erregerlicht einsetzt 1 . Ein Molekül mit

Rotational band contours in electronic spectra of large asymmetric top molecules: the 2750 Å system of phenol

1968 ◽  
Vol 307 (1488) ◽  
pp. 97-110 ◽  
Keyword(s):  
Excited State ◽  
Rotational Band ◽  
Point Group ◽  
Resolving Power ◽  
Hydroxyl Group ◽  
Rotational Constants ◽  
Selection Rules ◽  
Electronically Excited ◽  
Band Contour ◽  
Characteristic Features

The rotational band contour of the 0–0 band of phenol at 2750 Å has been recorded experimentally with a resolving power of 300000. The contour contains many characteristic features of which a series dependent on K a has been used to obtain trial sets of rotational constants A', B' and C' in the electronically excited state. The excited state was assumed to be planar. These data together with rotational selection rules were used in an asymmetric rotor band contour computer program and the rotational constants varied until the com­puted contour matched the observed. The contours were matched only by using type B selection rules. The electronic assignment is therefore 1 B 2 – 1 A 1 (using the C 2 v point group) and the excited state rotational constants are : A ' = 0·1773 ± 0·0002 cm -1 ; B ' = 0·08751 ± 0·00006 cm -1 ; C ' = 0·05859 ± 0·00001 cm -1 . These constants reflect an appreciable interaction of the hydroxyl group with the ring in the excited state whereas microwave data have shown very little interaction in the ground state. In particular, there is a slight overall contraction of the molecule along the long in-plane inertial axis from the ground to the excited state in contrast to an expected expansion if there were no hydroxyl group interaction. The origin of the 2750 Å 0–0 band is at 36 348·7 ± 0·2 cm -1 .

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