A note on the force field of Weinstock and Goodman for octahedral hexafluorides and the L matrix method

157

NOTES

11. Ii. NAKAMOTO, “Infrared Spectra of Inorganic and Coordination Compounds.” Wiley, New York, 1963. Vibratiolts.” 1.2. E. BRIGHT WILSON, JR., J. C. DECIUS, AND P. C. CROSS, “Molecular McGraw-Hill, New York, 1955. H. F. SHVRVEIA Department of Chemistry, Queen’s University, Kingston, Canada H. J. BERNSTEIN

Division

of Pure Chemistry, Research Council, Ottnwa, Canada

Xational

Received:

October 29, 1968

A Note on the Force Field of Weinstock and Goodman Octahedral Hexafluorides and the L Matrix Method In an excellent review Weinstock and Goodman

article about vibrational (1) proposed the relation F,r/Fg

proprrt,ies

of octahedral

= --km u(mx + 2m Y),

for

hexafluorides (1)

the secular equat8ion of the for the force constants of species Flu . Wit.h this assumption same species can be solved completely, since it is a two-dimensional species. Weinstock and Goodman (1) derived relation (1) in an indirect way based on a certain approach of forceconstant determinations by Claassen (2). It was also used by Brunvoll to calculate mean amplitudes of vibration for the same types of molecules. These data are included in Cyvin’s book (3). Later it was shown by Cyvin et ~2. (4) that these values agree very well with t,hose obtained from force constants based on experimental Coriolis coupling coefficients. In another paper it was shown by Rliiller (5) t)hat reliable mean amplitudes of vibration and good force constants (for the case ~nx > nl Y) can be calculated for all molecules of the which possess a two-dimensional species cont,aining one stretching and one type SY,, hending mode of vibration, if the following assumption is made: L,, The physical composed of the Here we want equivalent. The model are in the

= 0.

Gll = 2~~ + p,- = (21tnX) Gl? = 4~s

condition

(1) corresponds

+

(ll~f~j,

= 4/nlX ,

Gns = S/LX+ 2~ y = (8/mx) Hence

(2)

meaning of the method is that t,he normal coordinate Q, (v,‘, is entirely symmetry coordinate SZ (angle bending) and not of S1. to show that in the case of octahedral SE76 molecules (1) and (2) are exactly G matrix elements for the t,wo-dimerlsiorl:ll block (F,,,) ill the collsidrred usually adopted symmetry coordinates (3) :

CS) +

(2/u! p)

to F,,/F,,

= -G,JGI,

.

(4)

It has been shown by Peacock and Miiller (6) that (4) is identical wit,h (2). Therefore the special constraint of Weinstock and Goodman (1) for octahedral XI’, molecules is identical with t.he L matrix method of Miiller (51, which can be llsrd in the more general case for

158

NOTES TABLE FORCE CONSTANTS (mdyne/&

Molecule

(Species)

I

FOR TWO-DIMENSIONAL SPECIES IN SOME MOLECTJLES~

41

KS

F22

soz

(Al)

10.41 (10.45)

0.32 (0.40)

0.815 (0.818)

PFI

(E)

4.96 (4.98)

0.21 (0.23)

0.49 (0.489)

so3

(E’)

10.52 (10.76)

OSOl

(Fz)

7.72 (7.78)

GeCl(

(Fz)

2.73 (2.73)

SF6

(Flu)

4.75 (5.79)

SeFs

(PI,)

4.88 (4.86)

TeFe

(Flu)

4.98 (4.96)

-0.30 (-0.46)

0.623 (0.618)

-0.03 (0.09)

0.427 (0.424)

0.13 (0.13)

0.170 (0.170)

-0.74 (-1.11)

1.10 (1.02)

-0.44 (-0.42)

0.64 (0.65)

-0.24 (-0.18)

(0.40)

0.40

a Parenthesized values are from the approximation Liz = 0. The values for the hexafluorides are taken from S. Abramowitz and I. W. Levin, J. Chem. Phys. 44,3353 (1966). molecules of the type SE=, . According to this method the calculation of F and z matrix elements follows easily from the explicit formulas given by Peacock and Miiller (6). In Table I some results of force constants are given (in parentheses), as calculated by the method of Muller (5). They are seen to agree very well with values obtained with the aid of additional experimental data and also included in the table; for citations of literature another paper of Peacock and Mtiller (7) should be consulted. REFERENCES 1. B. WEINSTOCK AND G. L. GOODMAN, Advan. Chem. Phys. 9, 169 (1965). 2. H. H. CLAASSEN, J. Chem. Phys. 30, 968 (1959). 3. S. J. CYVIN, “Molecular Vibrations and Mean Square Amplitudes.” Universitetsforlaget, Oslo, and Elsevier, Amsterdam, 1968. 6. S. J. CYVIN, J. BRUNVOLL, AND A. MUELLER,Acta Chem. &and., 22,2739 (1968). 6. A. MUELLER,Z. Physik. Chem. 238, 116 (1968). 6. C. J. PEACOCK AND A. MUELLER,J. Mol. Spectry. 26,454 (1968). 7. C. J. PEACOCK AND A. MUELLER,Z. Naturforsch. 23a, 1029 (1968). A. MUELLER Institute of Inorganic Chemistry University in GBttingen West Germany

1.59

iYOTES

s. J. CYVIN J. BIIUNVOLL

Institule of Theoretical Chemistry Technical University of Norway Trondheim, Norway Received:

November 6, 1968

Laser-Excited

Raman

Syndiotactic

Spectra

of Polymers:

Polypropylene

The Laser-Raman spectrum of form I (Dz symmetry) of syndiotactic polypropylene was recorded and analyzed. Because of small intramolecular collpling many accidental degeneracies occur for most of the fundamental vibrations. It is suggested that the observed Raman spectrum arises from d modes as predicted by normal coordinate calculations. While the vibrational spectrum of isotactic polypropylene can be considered as satisfactorily understood (I), some more data are needed for a complete understanding of the vibrational spectrum of syndiotactic polypropylene (SPP). It has been predicted (2, 3) and experimentally shown (4-7) that the SPP chain can take up two different conformations according to the physical treatment performed on the substance. We have recorded the Rarnab spectrum of form I of a highly crystalline sample of SPP using a Laser source of 6328 A as the exciting line on a Cary 81 Laser-Raman spectrometer. The spectrum was recorded on a powdered sample enclosed in a glass ampule held against the hemispherical collector lens of the machine. The spectrum is reproduced in Fig. 1 and the observed Raman frequencies are listed in Table I. The observed spectrum exhibits a strong emission in the 135sl-100 cm-l region. WP do not have a reasonable explanation for this feature but suggest

FIG. 1. Laser-excited propylelle.

Raman

spectrum

of form I (DZ symmetry)

of syndiotactic

polg_