B u l l . Soc . Chim. B e l g . v o l . 86/n" 7 / 1 9 7 7

MOLECULBB FORQ PULD S f U D Y OF SOME XY5Z TYW YOLECXJU8 BY KINETIC CONS'PANB METHOD.

S. Y o h a

Department of Physics, Preaidency C o l l e g , Madras 600005, India. Received 17/2/77 - Accepted 26/5/77

ABSTKAC'P I ~ 1 1 the quadratic po ten t ia l energy constants of fin f l52 tm molecules have h e n evaluated using Wilson's F-G matrix method, On the b-ia Of a

conetraints and ce r t a in simplifying considerations are employed in solving the problem. The values of molecular po ten t i a l conetente, obtained on the baeie of kine t ic constants a r e found to be reasonable.

MTRODUCTION : meqwncy assignments r e l a t ing t o OsOF5 and ReOF5 have been recent ly made by Holloway e t al(1). revised by them. of th i s type of molecules, i t h a been found that tbe a w e t r y coordinatee(2) may be modified. coordinates a l l the quadratic po ten t ia l energy constants of t h e e molecules and a l so SF5C1 and WF5C1 molecules have been evaluated afresh.

The new s e t of conatants viz., molecular k ine t i c Wn8ttU1tS appear t o be of baeic significance in the study of molecular vibrationa. T b impontanca of molecular k ine t ic constants i n molecular vibration8 has been demonstrated by Thirugnanasambandam and Mohan for the various molecular types(3-7). Several authorstl l-17) u t i l i m d t h i e concept in evaluating the molecular constants of di f fe ren t types or moleculee. Such i n i t i a l s tud ies were na tura l ly confined t o 2 X 2 and 3 X 3 vibra t iona l probleme.

The purpose of the present paper is t o exanina yer another molecular tYpe v ie , 61 2, type involving 4 I V problems, on t he bas i s of the new procedure

Basically, the procedure adopted here is the well-known Wilson's F-G matrix method(l8) and the force f i e l d employed is the G.Q.V.F.F. The two-fold procedure is adopted here i n solving the problem. provided by the physical meanid of the redundancy cons t ra in ts r e l a t i n g t o t h e po ten t ia l energy constants. The second om is r e l a t e d to the u t i l i z a t i o n of k ine t i c constants t o l i n k the concerned F matrix elements (3-17) i n solving thn secular equation in an eaey mmero The po ten t i a l energg conatants evaluated i n f i v e molecules have l e d to in t e re s t ing

r e s u l t s in t b s e cases. These results a m very encour&ng inaemuch as they not only confirm well es tab l i shed a p e c t e of the problem but a l s o give rise freeh r e s u l t s of 8ignific-W.

s e t of symmetry coordinateso The k ine t i c COnfjtats, the redundancy

Further, the assignments r e l a t i n g t o IOP5 have been In an attempt t o evaluate

O&he bas is of

the po ten t i a l energy conetants

such a revised a r t of e w t r y

5

The first one is

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TBEOBETICAL C O N 6 I l W A T I O N S i Group t heo re t i ca l considerattone show that these M P type of molecules belong8 t o C4v symmetry poseeaein5 4 A + 2B + 1 B + '(E vibra t ions . 5

1 1 2

- 532 -

where AD is the change in the X-Z bond, Ad i e the change in the X-Y5 bond, Ar between jth and kth X-Y bond8,AP jth X-Y bond and kth X-Z bond anddLjr is the change in the eagle between the j th X-Y bond and kth X-Y5 bond.

is the change in the jth X-Y bond, A 4 i e the change in the angle jk i e the change in the angle between the

The moat general quadratic polzantial energy function ha8 been conaidered and the F matrix elements have been obtained. Making urn of the redundancy cons t ra in te , the F matrix element8 may be reduced t o the following condensed f orme. A 1 Type: '11 = 'D

'22 'd Fjj - fr +2frr + fir pW =2e2(f , + i c(a + rk 1 + f '

PP 2 72(fp + re

F12 fDd

'13 'Dr F14 = & f D K

'23 fdr

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1.

2.

3.

4.

5. 6.

7.

8 .

9.

10.

11.

12.

13 *

14.

15.

16.

17.

18.

19 20.

21.

22.

23 o

24.

X-2 atretching

X-Y stretching 5 x-Y st re tching

YXY bending

YXY5 bending

YI[z bending

I[z/ lcy5 interact ion

U/XY interaction

XY5/XY interaction

XY/ adjacent interact ion lcy

XY/ opposite 1(y internction

YAY/ opposite Y n interact ion

YiCi5/adjacent Y W 5 interact ion

YXY /opposite YXY5 interact ion

Y U / opposite YSZ interact ion

YLY/ adjacent YXY interact ion

YM/ adjacent YAZ interact ion

XZ/ Yn interaction

a/ YitY interaction

W5/ YXY interaction

XYs/ Y1(y5 interaction

W/ adjacent YW interact ion

XY/ adjacent YLY5 in teract ion

a/ oppoeite YUy5 interact ion

5

5

5

kD - present

kd - present

k, - present

k i - present

k, - present

k p - present

kDd - -sent

kDr - ZBPO

kdr - zero

Gr - present

k& - present

k{f - present

k,- present

k L - present

k' - present

kSa - present

kjp - present

H

- absent

% - present

k d j - absent

kda - present

k;j - present

k& - preseat

k;& - present

......................................................................... 16THOD OR K U E T I C COBSTAN'P.6:*

T b G matrix element8 are obtained on tb ba8is of Wilson'e mthod(l8). T b evaluation of kinet ic conatante is baaed on Wil8On'S expression for the k h t i c energy of the vibrating molecule,

where the kinet ic energy matrix elements K i j - (GTj ). 'The erpreaaione for ths individual valenm kinet ic constants mag be

w 2F = S K k

obtained from the author on request.

- 534 -

Making use of the mlevan t G matrix e l e m n t e , the k ine t i c constante are obtained for these molecules. The determination of eymmetry po ten t i a l energy constants, involved in the secular equation, from the ni v ibra t iona l frequencies alone has been a mathematically underdatermined problem 80 far. attempt to evaluate a l l the symmetry po ten t i a l energy constants assoc ia ted with a problem of order n 7 1 should involve the incorporation of a t l e a s t ni(ni - 1) /2 addi t iona l data o ther than ni rrequencies. The study of k i n e t i c constante(3-11) provide8 the requi red number of addi t iona l data through the symmetry k ine t i c constante and the corresponding symmetry force constants.

Therefore any genuine

The K ' s are t h e l i n e a r combinations of the re levant k i n e t i c constants. This method was successfu l ly appl ied in the e iap le 2 X 2 end 3 L 3 problems, It may be, w i t h advantage, extended t o the molecules charac te r i sed by v ibra t iona l problems of higher order. In the present inves t iga t ion , 4 Y 4 problem is aeeociated with A1 a n d E species.

spec ies The addi t iona l cons t ra in ts ueed in A1 species and in

F: spec ies on account of the study of k ine t i c constants ar83

Al SDeCie8: E SDeCiee:

F12 - ( '12 1922 IF22 - ( K89 IK99 )p99

p23 = ( '23 /K33 IF33 p9 10 = ( 99 10 4 0 10 IF10 10

'14 ( '14 "44 "44 F8 11 = ( K8 11 4 1 11 )P11 11

F24 - ( K24 /K44 >EM F9 11 = ( 99 11 4 1 11 )P11 11

P34 - ( Kw /Kw IFlclr F1o 11 = ( IClO 1141 11 IF11 11

'13 ( '13 " 5 3 "33 ' 8 10 ( '8 10 I K l 0 10 "10 10

Thus one is l e f t with four unknowns and four frequencies. involved in the A1 species andE speciee a re e a s i l y

&SULlb WD DISCUSSION: Results r e l a t i n g t o f i v e l a s Z type molecules a re discussed here. s t r u c t u r a l parameters and v ibra t iona l rrepuenciee u e d in evalua t ing the po ten t i a l constants of tb molecule8 a m given in t ab le 1. Table 2 gives the k i n e t i c constants whereas t ab le 3 deals with the po ten t i a l energy constants of these molecules as obtained here. Tbe comparison of the present s e t of po ten t i a l constante with the e a r l i e r authors are brought out i n t ab le 4. A s expected, the k ine t i c constants of them molecules group themselves i n t o three categories(3-11) 1.

2.

The equations evaluated.

The

The algebraic sum of the bond angle in t e rac t ion k i n e t i c constants i n any molecule vanishes.

Again sum of the bending and angle-angle in t e rac t ion k ine t i c cons tan ts a l s o vanishes. These two sets of complementary k i n e t i c constants

- 5 3 5 -

D A ( x - 2 ) 2.00

r i n A (X-Y) 1.56

d i n A (L-Y) 1.56 a - P - r ’ i n d e g 90

A1 Tsper

$1 834

33 599

d4

$5

37

703 2 J

404

B Type: 1

624

J6 . 396

504

B2 Type:

E TJPe: $8 916

579 9 J

442 5 0

51 270

1 s85

1.86

1-75 90

927.3

680.4

640.2

362.9

647

30 7

310

710 3

372.2

343

204.8

2.260

1.826

1.826 90

743

704

243

390

640

182

3 77

671

278

302

228

1.761 1.92

1.92 90

989.6

737.6

643

309

652

243

334

713

260

365

125

l.P 1.76

1.76 90

926.6

716.4

644

280.5

a4

210

332

700.6

263

367

164

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4.6020

2.7857

2.7717

0.7943

0.8161

0.9558

0.6881

0.0000

0.0000

0.0000

0.3831

-0.4000

-0.0922

-0.2118

-0.4845

-0.1837

-0.2228

abeent

-0.3441

0.0000

0.lW

0.1916

0.2355

-0.2355

2.4769

2.9015

3.1724

0.9734

0.9486

0.7809

0.2123

0.0000

0.0000

0.0423

0.0669

-0 5791 -0.0670

-0.2443

-0.1887

-0.1290

-0.0499

abeent

-0.1093

0.0000

0.1298

0.1512

0.1395

-0.1395

5.2216

2 9622

3.1028

0.9596

0.9301

1.1067

0.3550

0.0000

0.0000

-0.0004

0 0512

-0 5652

-0.0477

-0.2367

-0.965

-0.1181

-0 1443

absent

-0.1779

0.0000

0.0952

0.1174

0.1281

-0.1281

2.5135

2 9538

3.5187

1.1677

1.0941

1.0183

0.1696

0.0000

0.0000

0.0002

-0 3693

-0.7734

-0.0504

-0.4062

-0.2683

4.1282

-0.1165

absent

-0.0850

0.0000

0.1009

0.1428

0.1332

-0.1332

2.5155

2.9560

2.9558

0.8863

0.7342

0.6765

0.1680

0.0000

0.0000

0.0001

0.1991

-0.4920

-0.0497

-0.1923

-0.2777

-0.0839

-0.0764

absent

-0.0839

0.0000

0.0996

0.0995

0.0953

-0 0953

- 537 -

3.8793 6.2069

4.8190

0 3934

0.6640

1.0859

1.5332

0.0000

0.0000

-0.7051

0.6227

-0.0377

0.3535

-0.0976

-0.6301 -0.0884 -0.Z%55

0.0000

-0.4903

0.0000

0.2628

0.0922

0.5316

-0.5316

7.2742

5.0742

4.4097

0.2417

0.4131

0.2520

0.3713

0.0000

0.0000

4*2375

0.0653

-0,0892

-0.0036

-0.1337

0.0123 -0.0367 -0.0123

0.0000

-0.0477

0.0000

0.0567

0.0430

0.2307

-0.2307

3.0717

6.0850

4.7235

0.3497

0.1725

0.2629

0.7292

0.0000

0.0000

0.0997

0 0638

-0.1‘489

0.0427

-0.0669

4.1776 -0.0513 -0.0384

0.0000

-0.0326

0.0000

0.0175

0.0510

0.0960

-0.0960

8.5477 5.5-

4.7505

0.1845

0.1896

0.3167

0.3197

0.0000

0.0000

-0 + 0287

-0.0464

-0.0283

0.0843

-0.0134

-0.1246 -0.0187

-0 0772

0.0000

-0.0264

0.0000

0.0315

0.0209

0 0390

-0 - 0390

8.1964

5.2164

4.6699

0.1518

0.2212

0 3020

0.2965

0.0000

0.0000

0.0275

0. 0304

0.0025

0.0743

-0.0737

-0.1528 -0.0121

-0.0478

0.0000

-0.0835

0.OOOO

0.0991

0.0144

0.0921

4 0921

- 538 -

TABU 4

f D

'd

f r f

f

f

f D r

fdr

* rr

*D

f d

fd

f d

3.8793

6.2069

4 8 1 9

0.3934

0.6640

1.0859

0.0000

0.0000

-0.3051 0.6227

0.4330

0.2628

0.0000

-0.2321

3.120

5.072

4.682

0.450

0.493

0.926

0.zm

0.080

- -

0 336

0.406

- -

7.2N2

5.OR2

4.4097

0.2417

0.4131

0.2520

0.0000

0.0000

-0.2373

0.0653

0.0464

0.0567

0.0000

-0.0551

6-99 4.60

4.42

0.20

0.55

0.44

0.00

- 0.00

0.18

- - - -

3.0717

6.0850

4.7235

0.997

0.1725

0.2629

0.0000

0.0000

0.0997

0.0638

0.0293

0.0175

0.0000

-0.057

2.6600

5.4600

4.6260

0.3793

0.2699

0.3538

0.0000 - - - - -

4.0203

0.1821

- 539 -

3. The remaining k ine t i c constante involving s t r e t ch ing and bond-bond in t e rac t ions via. , supplementary k ine t i c constants doeon't vanish when t h e i r algebraic aum is added.

Apart from the general behaviour of k ine t i c constants the following observations may be made from table 2. 1. The bond-bond in te rac t ion k ine t i c constant8 kDr and kbr (i.e, i n t e rac t ion

between a bond and a bond i n a plane perpendicular t o tlls bond) takes zero values for a l l the molecules under inveetigation.

2. The behaviour of k ine t i c constante r e l a t i n g t o the in te rac t ion betWeen th bond and t lm adjacent bond krr is a l so in l i n e w i t h the previous observation except in IOF molecule.

a bond and an angle in a plane perpendicular t o the bond) i s absent. and k:& assume aame values in

magnitude.

kDpc and qa with the previous observation with respec t t o octehedral 'Ly6

molecule s( 7).

5 3. The bond-angle in t e rac t ion k ine t i c conetants(i .e, i n t e rac t ion between

4. The in te rac t ion k ine t i c conatants k&

5. The in te rac t ion k ine t i c constants k i . , k, , khoL , k ' , , kva , k'/p

6. T b observations r e l a t ing t o zero and abeent k i n e t i c constante agree assume negative sirpl I n a11 the cases atudied hsre.

-om the t a b l e 3, the following observations may be made. 1. In all the cases the equator ia l s t r e t ch ing po ten t i a l constants(X-P)

are smaller than th corresponding axial a t re tch ing po ten t i a l conatants (X-F5 1.

2. The in te rac t ion poten t ia l constants fm, fb, fD{ and fa{ aeaume zero value8 in a l l the cases.

3e fa, f), , fJp , rDa and 4. It i s pleasing t o note the same sign for both the k i n e t i c conetante and

are a l l uniquely negative in a l l the case8

the poten t ia l constants with respect t o the in t e rac t ion constante (YXYd opposite YW5 in te rac t ion , YXY/ adjacent YXY in te rac t ion , 5 YXY/ adjacent Y E 4 in te rac t ion , XZ/YW5 i n t e rac t ion and W/ oppoaite YXY5 in te rac t ion) f o r a l l the molecules etudied here.

5. The s t re tch ing poten t ia l constants f&or a l l the cases are in the

Comparing the present s e t of values with those of e a r l i e r authors, it mag be found that both f,, and f d value8 assume higher values i n the present investigation r e l a t i n g t o IOB5, WF5C1 and SF5Cl. h i w y eyltematic ae t a of all t h e independent po ten t i a l constants are available fo r the f i r s t time.

CONCLUSION : Uti l iz ing a fresh s e t of symmetry coordinate8 and taking advantam of k ine t i c constants and redundant ammetry coordinates it has been possible t o evaluate a l l tae independent po ten t ia l constants r e l a t i n g t o f i v e XY t o obtain a l l the independent po ten t i a l constants.

expected range.(s-cl, 1-0, UT-c1, Re4 and 0e-0)

It may be added t h a t a

molecules. A l l the molecules have been s tudied here f o r w first tFme The r e e u l t s r e l a t i n g t o

5

- 540 -

a l l these molecules shor qua l i t a t ive ly s i m i l a r behaviours cha rao te r i s t i c of this type of molecules. here seem t o be reasonable. v i t a l importance because of their de f in i t e r o l e s with respec t t o the v ibra t iona l s t ruc tu re of the molecular type under study. Been tha t the k ine t i c constants do play a fundamental r o l e in molecular dynamics and a recognition of the same leads t o systematic sets of molecular constnnts.

The values of the poten t ia l constants obtained The i n t e rac t ion eorce constants seem t o be of

It may be

REFEBNCES: J. H. Holloway, H. S e l i g end 8. H. Clnassen, J.Chem.Phys, 9, 4305 (19f l ) 3: K., Venkateswarlu and K. Sathiandan, Opt. and Spectroec, 11, 24 (1961)

3. P. Thirugnannsambandam and S. Mohan, J.Chem.Phy5, 61, 470 (1974) 4. P. Thiruynanasambondam and S. Yohan, Indian J. Pure & Appl. Phys,

12, 206 (1974); 13, 398 (1975) 5. P. Thirugnanaeambaniam and S. Yohan, Indian J. Phys, 49, 808 (1975)

J. Annamalai Univ. (in pres s ) 6. P. Thirugnannsmbandam and S. Yohan, Pramana, 8, 40 (1977) 7. P. Thirugnnnegambandam and S. Mohan, Bull.Soc.Chim.E!elgee, 84, 987 (1975)

8. P. Thirugnamsambandam and S. Mohan, Indian J. Phys, Jan 1977 ( i n press ) 9* P. Thiruganasambandm and G.J.Srtdvaaan, J.Chem.Phys, 50, 2467 (1969) 10. P. Thirugnanasambandam and N . Karunanidhi, Indian J. Phys,49, 658 (1975)

50, 527 (1976) 11. S. Mohan, B u l l . Soc.Chim. Belges, 85, 535 (1976) 12. N.K.Sanya1, L i D i d t , ~.R.Pandey, H.S.Singh &B.P.Singh, Indian J. Pure &

13. N.Y.Sanya1, P.Ahmad and L . D i x i t , i b i d , 12, 155 (1974) 14. N.K.Sanya1, P.Ahmad and C.D.Pandey, i b i d 12, 437 (1974) 15. N.K.Sanya1, D.N. Verma and L. D i X i t , i b i d , 13, 273, (1975) 16. N.X.donya1, L . D i x i t , B.H.Subramanyam and A.N.Pandey, Indian J. P h p ,

47, 37 (1973) 17. a.a.Srivastava, A.K.Dublish, ~ . N . P a ~ d e y and A.K.Yithal,

18. ~.B.Wilson, Jr, J .C.~ec ius and P.C. Cr088, lYolecuar v ibra t ions '

19. D.F.Smith and G.Y.Begum, J. Chem.Phys, 43, 2001 (1965) 20. .A.J.Kale and K.SathiWdm, Spctrochim Acta, 26A, 1337 (1970) 21. L.g.Sutton(Ed), Chem.Soc,(London), Spec.Pub1. 11, (19%)

Appl. Phys, 10, 493 (1972)

Z.Naturforsch, 27a, 1213 (1972)

McGraw H i l l co, (1955)

* * . * * * * * * * *

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