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 Multiplicity, Parity and Angular Momentum of a Cooper Pair in Unconventional Superconductors of D4h Symmetry: Sr2RuO4 and Fe-Pnictide Materials

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1435
Author(s):  
Victor G. Yarzhemsky
Keyword(s):  
Angular Momentum ◽  
Cooper Pair ◽  
Point Group ◽  
Group Symmetry ◽  
Cooper Pairs ◽  
Group Approach ◽  
Angular Momentum Projection ◽  
Space Group ◽  
Unconventional Superconductors ◽  
Even Pairs

Sr2RuO4 and Fe-pnictide superconductors belong to the same point group symmetry D4h. Many experimental data confirm odd pairs in Sr2RuO4 and even pairs in Fe-pnictides, but opposite conclusions also exist. Recent NMR results of Pustogow et al., which revealed even Cooper pairs in Sr2RuO4, require reconsideration of symmetry treatment of its SOP (superconducting order parameter). In the present work making use of the Mackey–Bradley theorem on symmetrized squares, a group theoretical investigation of possible pairing states in D4h symmetry is performed. It is obtained for I4/mmm , i.e., space group of Sr2RuO4, that triplet pairs with even spatial parts are possible in kz direction and in points M and Y. For the two latter cases pairing of equivalent electrons with nonzero total momentum is proposed. In P4/nmm space group of Fe- pnictides in point M, even and odd pairs are possible for singlet and triplet cases. It it shown that even and odd chiral states with angular momentum projection m=±1 have nodes in vertical planes, but Eg is nodal , whereas Eu is nodeless in the basal plane. It is also shown that the widely accepted assertion that the parity of angular momentum value is directly connected with the spatial parity of a pair is not valid in a space-group approach to the wavefunction of a Cooper pair.

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.

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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