Study of the rotational splitting of UF6 molecule

83

JournalofMolecularStructure,142(1986)83--85 ElsevierSciencePublisbersB.V.,Amsterdam -Printed in TheNetherlands

STUDY OF TBR ROTATIORAL SPWTTIRG

M. Gi&csi,

2s. Gul&i

OF UP6 MXlK!ULB

and v. Toga

Institute of Isotopic and Molecular Technology, 3400-Cluj-5, POB 700(Romani.a)

The fine rotational structure of UF molecule is analised using the octahedral invariant tensor operator 4 rmalism. It is shown that the rotational splitting can be successfully described for P(l'7)manifold using invariant tensor operator combinations up to sixth order.

The fine rotational structure of the hard spherical top molecules XI6 can be described (ref.1) using the eigenvalue spectrum of the octahedral invariant tensor operator combinations up to sixth order :

T =

c ( T4cos\9

+

!@sin\Q )

where 6 is a global coupling constant, the ‘Q angle take values between 0 and q,

and the fourth ( T4 ) and sixth ( T6 ) rank terms are given by :

(2)

The f

irreductible tensorial operators ( q = k,k-1, ... -k+l,-k ) are

sets of 2k + 1 operators which are transformed in the rotational groups R3 as :

(3)

The a:*9(o< p1) term represents the irreductible representation of the rotational operator R(&p?j') from R3 , and m,

are the Euler angles. P@$ Using Xq.(ll we have the possibility to analyse if the studied molecule's 6 rotational splitting can be described with T4 and T tensor operator combi-

nations. To determine the rotational splitting one caculates the eigenvalue spectrum of the tensorial operator as given in Eq.(l) and compares it with the experimental values. The tensor operator's matrix elements can be easily obtained as :

0022-2860/66/$03.50 01986 ElsevierSciencePub1ishersB.V.

84

LJ M’\ %\

J M,

= (-ljJ-’

I_;,

f ;,

(4)

(JllTk\\J)

are the Wigner 3j simbols and (J\\l?\\J) is the reduced where ( .* * . * . ) matrix element,which for a given J does not depend on M and M'. J and M denote the quantumnumbers of the total angular momentumand its projection on the quantificationaxis respectively. The fit parametersdeductioncan be made by a root-mean-squere procedure using a numericalminimizationprogram. The presentedprocedurefor studyingthe rotationalsplittingof the hard sphericaltop moleculeshas been successfullyused for describingthe rotational patternsof the SF6 molecule (ref.1 and ref.2).In this paper we try to apply it to the UF6 molecule. The obtainedresults are presentedby the P(17) manifoldof UP6, measured by Aldridge et al (ref.3).In Fig.la we present the meaouredspectrumand in Pig.lb the deduced theoreticalresult which describeit. The conclusionof our analysisis that the rotationalsplitting,in the case of UF6 as well, can be accuratelydeterminedusing the eigenvaluespectrumof the octahedral invarianttensor operatorcombinationsup to the sixth rank. In the given example for the P(17) manifold the descriptionis acceptable good for y =oCT/6 and o(= 0.069

E

b

Fig.

1.

(a)

The

measured

I’(

17) manifoldfor 1Jp6molecule.(b) The proper

portion ‘Q 6 [0,7/Y] of the T/C eigenvaluespectrawhich describefor J = 17 the measureddata.

85

1 2 3

W.G. Harter and C.Y. Patterson,Jour. Math. Phys., 20 (1979) 1453 C.W. Pattersonand W.G. Harter, Jour. Chem. Phys., 66 (1977) 4886 J.P. Aldridge,H. Filip, K. Fox, H. Galbraith,R.S. McDowelland D.F. Smith, PreprintLA-UR-76-858(1976).work presentedat the Lasers for Isotope Separationconference,april 13-14, 1976.