Mean amplitudes of vibration for mixed halides of phosphorus and arsenic

158

Journal of Molecular Siriicttire Elsevier Publishing Company, Amsterdam. Printed in the Netherlands

Mean amplitudes of vibration for mixed halides of phosphor

and arsenic

fn another article’ of this issue we have coruscated the force constants of some mixed halides of phosphorus and arsenic. These force constants have been used to calculate mean amplitudes of vibration2 in these compounds. The mean amplitudes of vibration for pyramidal XYzZ molecules have been studied previously in some few works, which are summarized elsewhere2. In particular it should be mentioned that Nagarajan et al. 3 have calculated the mean amplitudes

for some of the molecules also treated in the present work, but using

a less accurate method. TABLE

1

MEANML-ES

OF

VIBRATION

Temperamre(“Kj

PF&l

0 298

PF,Br

0 298

PFJ PC&F

0

298 0 298

PCI,Bf PC&I

PBr,F PBr,CI P&J P&Cl PX,Br AsCf,Br AsBr,CI

29: 0 298 0 298 0 298 0 298 0 298 0 298 0 298 0 298

IN

A wrr~

XY

0.0410 0.0418 0.0411 0.0419 0.04f2 0.0420 0.0443 0.0485 0.0458 0.0507 0.0462 0.0513 0.0425 0.0491 0.0441 0.0519 0.0450 0.0535 0.0458 0.0573 0.0459 0.0574 0.0431 0.0510 0.0396 0.0522

J. &&I. Structure,2 (1968) 158460

0.0434 0.0470 0.0406 0.0459 0.0406 0.0471' 0.0415 O-0424 0.0431 0.0502 0.0443 0.0543 0.0418 0.0427 0.0466 0.0520 0.0445 0.0546 0.0469 0.0524 0.0452 0.0539 0.0393 0.0515 0.043l 0.0510

0.0600 0.0674 0.0611 0.0695 0.0623 0.0717 0.0628 0.0903 0.0609 0.0840 0.0618 0.0864 0.0548 O.fOOl 0.0552 0.1006 0.0517 0.0876 0.0527 0.1141 0.0520 0.1110 0.066f 0.0992 0.0585 0.1144

0.0638 0.0812 0.0630 0.0870 0.0685 0.x053 0.0630 0.0792 0.0612 0.0989 0.0613 0.1051 0.0623 0.0849 0.0591 0.0920 0.0541 0.1063 0.0613 0.1056 0.0517 0.0971 0.0643 0.1101 0.0632

0.1062

SHORT

COMMUNI&ATIONS

TABLE

2

159

MEAN-SQUARE AMPLITUDES OF VIBRATION (AT 298 “K) IN AZ UNITS, AND THEIR RELATION TO THE RECIPROCAL AVERAGE ELECIXONEGATIVITIES

PF,CI PF,Br PFJ PCIpF PCI,Br Pclg

0.001747 0.001756

PBr,F PBr,Cl

0.001823

0.002210

0.001764 0.001798

0.002218 0.002352 0.002570 0.002632

0.002520 0.002948 0.002411 0.002694

0.002704

0.312 0.350

0.002862

PBrJ

0.002746

A representative given below.

set of distance deviations

0.002905

d=

&“),

for the four types of distances

is

S,’

D1&*

2*S,’ sinA + S,’ cask,

r* =

0.375 0.385 0.396

0.002981 0.003279 0.003295

PI,CI PI,Br

r = 2-3(s,‘+

0.273 0.278 0.280 0.300 0.341 0.358

0.002107

= pr, +rd+

RDpr

sinB

Here Si and S,” denote the appropriate coordinates4 of the A’ and A” species,

respectively,

and

D 12 =

[R2+D2-2RD

cosB]*,

p = R-DcosB,

7 = D-RcosB

For explanations of the other symbols, refer to some of the cited works’*4. For

the mean-square IXY 2

=

IYY 2 = Da2

amplitudes



=

of vibration

Iyz2

=

I,,’

+(Zrl’+ZI1”),

2Z,,’ sin2A+2*Z,,’ + (RD)’

p(Z14’+Z12”)

from the above equations:

= = Z22’

sin2A+Z,,’

4p2&‘+ZJ+2pr

+ (2RD)*r

one obtains

&%f2

cos2A

z2g

sinB

Z,,‘sinB++RD(&_+

+Z2,“)sin2B

These equations are consistent with those given by Venkateswarlu et al.’ for the same quantities. The calculated mean amplitudes of vibration (Z) are given in Table 1. It is of interest to note that the mean amplitudes for P-Y (Y = halogen) decrease with increasing sum of electronegativities for the halogen atoms, xxi. Specifically there exists a nearly linear relationship between Zry2and the reciprocal values of cXi; cf. Table 2. This feature may be interpreted by means of the simple formula derived by Miille@*’ as a consequence of the reported relationship between fpy

J. Mol.Srrucrwe,

2 (1968) 158-160

160

SHORT

COMMUNICATIONS

and the ‘sum of electronegativities’.

Miiller6*’ also draws attention to the close connection between mean-square amplitudes of vibration and the reciprocal values of the corresponding stretching force constants. Jnstitute of Theoretical Chemistry, Technical University of Norway, Trondheim (Norway) Institute of Inorganic Chemistry, University of Giittingen (Germany)

I.

ELVEBREDD

B, Vrzr S. J. A.

CYVIN

MILLER

B.

-BS

A. MULLER, B.K~REBs,I.ELvEBREDD, B. VIZIAND S. 3. CYW, J. Mol. Structure, 2 (1968)149. S. 3. Cm, Molecular Vibrations and Mean Square Amplitudes, Universitetsforlaget, Oslo, 1968. G_ NAGARAJAN. I. R. DURIG AND A. Miiti.~~, Mowtsh. Chem., 98 (19&7) 1545_ S. J.Cnm,J. BRUNVOLL, B. N. CYVIN,I.ELVEBREDD AND G. HAGEN, Mol. Phys., 12 (1968) in press. 5 K. VENKATTSWARLUAND K.V.RAJALAKSHMI, Proc. Indian Acad. S&A61 (1965)255. 6 A. MUELLER, Nuturwissensch., 53 (1966) 701. 7 A. M~~LLER,Z_P!J~S.Chern., in press.

1 2 3 4

Received February I9th, 1968 J. Mof. Structure, 2 (1968) 158-I 60

Mean amplitudes of vibration of difluorodiazinc Introduction Difiuorodiazine has been subjected to many investigations since Bauer’ for the first time (1947) reported an electron-diffraction study of the molecule. The IR spectrum of NzF2 (cis and trans) was first reported by Sanborn’ (1960), who also caloulated a complete force field. King and Overend 3 reinvestigated the rn spectrum and also reported for the first time the Raman spectrum of cis-N,F2. A work on the microwave spectrum of c&N2F2 is due to Kuczkowski and Wiison4. In the present work a refined force field was produced for the N2F, molecules, and wasused tocalculate the meanamphtudesof vibration.Thework was initiated by the modem electron-diffraction investigation of Bohn and Baue?, who reported seemingly doubtful mean amplitudes of vibration. Structural parameters The structural data used as equilibrium parameters in the present calculations were taken from Bohn and Bauer’. The rotational constants (in cm-“) cal-

culated from these data are: .T.Mot. Structure, 2

(1968’) 160-163