Acta Physica Aeademiae Scieraiarum Hungaricae, Tomus 48 (2--3), pp. 197--201 (1980)

DISSOCIATION ENERGY OF Si 2 MOLECULE*

By

T. V. I~AMAKRISHNA RAO and R. RAMAKRXSHNA REDDY

DEPARTMENT OF PHYSICS, S.V. UHIVEHSITY POST-CRADUATE CENTRE ANAHTAPUR 515 003, A.P. INDIA

(Received in revised form 20. XI I . 1979)

The t rue po ten t ia l energy curves have been construeted for the different eleetronic s t s tes of the Si i mulecule by the me thods of LAXSn~AN and RAo as well as MOnSE. The dlssociation energy for the ground s ta te of the Si s molecules has been es t imated to be 3.28 eV by the method of curve f i t t ing using the three pa ramete r LIPPINCOTr potent ia l function. The es t imated D eis in good agreement wi th the mass spec t romet ¡ va]ue 3.25 ~ 0.22 eV as well as GAYDON'S value 3.35 ~= 0.2 eV.

lntroducfion

The spectrum of the Si~ molecule is of interest for a va ¡ of reasons. One would expect the Si 2 and C 2 molecules to be reIated and the similaritŸ and differences in their spectra are of interest from the point of view of the theory of electronic structure of diatomic molecules. DouoI~s [1] first found two band systems of the Si~ molecule and designated them as 3~--an and a~_3~. VEwiA and WARsoP [2] investigated three band systems of Si z in absorption using flash photolysis teehnique. Two of the band systems at 320 and 210 nm are new, whereas the third is an extension of the a~--aE system observed by Dou6I~S in emission. VER~A and WARSOI" [2] have pointed out that it is not definŸ whether the ground state of Si 2 is the a~v~- t state or not because of the low-lying triplet states. Some of the bands of C~ ate not yet known and a]so Si~ has r resemb]ance with the Cz moleeule. The theoretical knowledge of the Si 2 may be useful to understand the spectrum of the C z molecule. Keeping this aim in mind, the authors took up the esti- mation of the dissociation energy of the Siz molecule. A knowledge of the exact value of the dissociation energy of diatomic molecules is of fundamental importance for thermochemistry and it is often of interest in astrophysics. The dissociation energy of Si~ has been estimated by various methods, bu t the values reported show a lack of agreement with one another. VvRMA and WARSOI, [2] have reported the value of D e to be 3.0 ~- 0.2 eV. Mass spectro- scopic studies have yielded 3.25 -}- 0.22 eV. GAYDON [3] has recommended the

* Paper presented a t the Nat ional Conferenee on Molecular Spectroscopy, held a t Annamala i Univers i ty , 1 6 - - 1 8 t h Augus t 1979, India .

6 A ~ P k ~ ~ A ~ ~ H~,n~~~~~ 48, 1980

198 T. V. RAMAKRISHNA RAO tmd R. RAMAKRISHNA REDDY

va lue 3.35 -;- 0.2 eV. T h e inves t iga t ion deals wi th the es t imat ion of disso- c iat ion energy of Si 2 moleeule b y f i t t ing the LIPPINCOTT fune t ion wi th the t rue po ten t i a l energy eurve using the molecu la r cons tan t s r e p o r t e d b y VERMA

and WARSOr [21.

The me thod of curve f i t t ing

The tu rn ing poin ts for different e leet ronic s ta tes of the Si 2 molecule a te ca lcula ted using the m e t h o d of LAKSH~A~ and RAO [4]. The p resen t m e t h o d [4] was successfully ver i f ied in a n u m b e r of cases [4, 5, 6, 7, 8]. CHAKRABORTY and PAr~ [9] suggested t h a t this m e t h o d is considered as reliable and accura te wi th less m a t h e m a t i e a l eomputa t ions . The tu rn ing points as ob ta ined b y LAXSH~aAN and l~Ao's [4] m e t hod for di f ferent eleetronic s ta tes of Si z a te g iven in Table I a long wi th those ob ta ined b y the MORSE [10] m e t h o d for com- par i son purpose .

The t rue po ten t i a l energy curves ( R K R V ) have been used to es t imate the dissoeiat ion energies of d ia tomic molecules in a n u m b e r of tases b y f i t t ing

Table I The tzue potential energy curves for different electronic states of Si~ molecule

u + To (cm-')

Te----0 254.98 761.92

1264.83 1763.68 2258.50 2749.28 3236.02

Tt=24582.64 24717.80 24985.14

Te=30768.77 3O998.58 31449.28 31888.08

Te=46762.21 46986.93 47426.63 47853.33

rm~(=m) r~q l~esent method [

0.2179 0.2135 0.2106 0.2083 0.2064 0.2048 0.2033

0.2574 0.2514

0.2283 0.2242 0.2217

0.2276 0.2232 0.2204

MOS~E Present method

X 3 ~ ; s tate

0.2180 0.2317 0.2135 0.2374 0.2106 0.2416 0.2083 0.2451 0.2064 0.2482 0.2048 0.2512 0.2033 0.2539

H3~~ - state

0.2574 0.2763 0.2515 0.2843

K 3 ~ ~ s ta te

0.2282 0.2428

0.2240 0.2496 0.2213 0.2449

N3~~ state

0.2276 0.2423 0.2234 0.2489 0.2207 0.2541

~)

MoRs~

0.2317 0.2374 0.2416 0.2451

0.2483 0.2512 0.2539

0.2763 0.2845

0.2427 0.2494 0.2545

0.2423 0.2491 0.2544

Acta Physica Academiae Sdemiarum Htmgarieae 48, 1980

DISSOCIATION ENERGY OF Si z MOLECULI 1 9 9

a potential function with the RKRV curves. In the present investigation i t was found tha t the LXrPIr~COTT potential function [11] gives the best f i t with

V - VRKRV an average percentage deviation less than 0.05 in the value of

for the ground state of Si 2 molecule. The LIrrIr~COTT function as modified by STEELr [11] is

U ( r ) = D e l 1 - e x p { - - n ( r -- re)2 2r } ] X

in which

De

F 2 F 2 Cr176 �9 a - - , n - - - - , where b = 1 . 0 6 5 and F =

1 + 5 F re(ab)2 6B2 4

The RKRV turning points are used in the above expression and for a particular value of D e, the energy values U(r) are compared with U. This is repeated for different values of De in steps of 0.06 eV and the value for which

Table II

Comparison of the observed and calculated energy values

�9 U (nm) (cm- 1) Da -~ 3.22 eV De = 3,28 eV De = 3.34 eV

254.9

761.9

1264.8

1763.6

2258.5

2749.2

3236.0

254.9

761.9

1264.8

1763.6

2258.5

2749.2

3236.0

244.9

740.6

1226.8

1727.0

2220.6

2701.8

3174.7

260.5

757.5

1256.7

1758.2

2247.8

2720.4

3211.6

0,089

249.6

754.9

1250.4

1760.3

2263.3

2753.8

3235.8

265.5

772.1

1280.9

1792.0

2291.1

2772.7

3273.4

0.053

254.3

769.1

1273.9

1793.5

2306.0

2805.7

3296.8

27O.6

786.7

1305.1

1825.8

2334.3

2825.1

3335.1

0.167

0.2317

0.2374

0.2415

0.2451

0.2483

0.2512

0.2539

0.2179

0.2135

0.2106

0.2083

0.2064

0.2048

0.2033

Average

deviation

%

6* ~4r Physi�91 ~4cademiae Sr Hurtgarir 48, 1980

2 0 0 T . V . RAMAKRISHNA R A 0 and R, RAMAKRISHNA R E D D Y

the best f i t t ing of the energy values is achieved is taken to be accurate disso- ciation energy of the molecule. Such a procedure has been employed for the ground states of TiO [121, SO, SeO and TeO [13], BiO and BiS [141 and P+ [15] molecules. The resuhs of these calculations in the case of the ground state of Si I which are necessary for comparison ate given in Table II.

Results and discussion

The RKRV turuing points agree well with those of Morts~. [10] for the ground state, as the deviation between the experimental value of ~t (0.0013 cm -1) and that calculated from the Pekeris relation ~ (0.001279 cm -1) is negligible. The resuhs of Table II show tha t the best fitting of the energy values is achieved for D e = 3.28 -4- 0.18 eV, since the average percentage deviation in this case is minimum. This value is significant because it has been estimated by using the true potential energy curves based on experimental data. This is in very good agreement with the mass spectroscopic value 3.25 ~ 0.22 eV and also with GXYDON's [3] recommended value 3.35 + 0.2 eV. The above resuhs support the view tha t the electronic state 31~- is the ground state of the Si 2 molecule. As has been pointed out by VERMA and WiRsOr [2], there is not sufficient evidente to assign the N3L~-g state to any electrouic configuration. The D e value for this state is not determined in the present study.

Using the same LXPPINCOTT function [11] the estimated dissociation energies for H and K states are 9,100 and 5,200 cm -1, respectively. With these valucs the dissociation products in the upper and lower states ate deter- mined as follows

D›191 4- Te = D› (XSL'-i) + EA.

Therefore EA : 7,183 cm - i which is in good agreement with the value of 6,300 cm -1, the atomic excitation of iD 2 for Si atom. The Birge--Sponer extrapolation gives the dissociation limits of 33,700 and 39,500 cm -1 for H and K states, respectively.

Thus D~ (H3I~)= 3 3 , 7 0 0 - 24,583 = 9,117 cm -1, which is in good agreement with the curve fitting value of 9,100 cm -i .

�9 3 - - Similarly, De(K I ¡ ) : 39,500 -- 30,768 : 8,732 cm-i , which is compar- able with the value of 5,200 cm - i obtained by eurve fitt ing method. STEELZ et al [16] concluded, based on a large number of computations on different molecules, that no single potential function is suitable to represent adequately all the states of the same molecule. The authors ate of the opiuion tha t the conclusion drawn by STEEL~ et al is quite applicable to the K state of Si 2 molecule. The atomic excitation corresponding to the K state is obtained as

8,732 -4- 30,768 - - 26,500 = 13,000 cm -i .

Ae~ Phy1~ Aeademiae Seien~ª Hungarir 48, 198~

DISSOCIATION ENERGY OF Si I MOLECUI~ 2 0 1

This v a l u e is in c lose a g r e e m e n t w i t h t h e a t o m i c e x c i t a t i o n o f 1S 0 for S i a t o m .

Thus t h e m o l e c u l e ge t s d i s s o c i a t e in t h e u p p e r a n d ] o w e r s t a t e s as

S i ( a P ) - [ - S i (aP) in t h e Xal~-g s t a t e ,

Si(a D + Si(1D~J in t h e Hal-~-, s t a t e ,

S i (aP) -}- Si(IS0) i n t h e K 3 I ~ " s t a t e .

A c k n o w l e d g e m e n t

The authors wish to express their thanks to Prof. S. V. J. LA~SHMAN and Prof. S. V. SUBIt&HltANYAM for thcir intercst in the present work.

REFERENCES

1. A. E. DOUr Can. J. Phys. 33, 810, 1955. 2. R. D. VVRMA and P. A. WAEsoP, Can. J. Phys., 41, 152, 1963. 3. A. G. GAYDON, Dissociation Energies, Chapman and Hall Ltd. London, 1968. 4. S. V. J. LAKSHMAN and T. V. RXMAKmSHNA I~AO, J. Phys. B4, 269, 1971. 5. T. V. RAMAKmSHNA RAO and S. V. J. LAKSHMAN, Physica, 56, 322, 1971. 6. T. V. HAMAKmSHNA RAO and S. V. J. LAKSHMAN, J. Quant. Spectro. Radiat. Transfcr,

12, 1063, 1972. 7. T. V. RAMAKIUSHNA HAO and R. RAMAKRISHNA REDDY, Physica C, 95, 412, 1978. 8. T. V. HAMAKRXSHNA RAO and R. RAr~AKRXSHNA REDDY, Curr. Sci, 48, 95, 1979. 9. B. CHAKRABORTY and Y. K. PAN, Applied. Spectro. Rey. 7, 283, 1973.

10. P. M. MO~SE, Phys. Rey., 34, 57, 1929. 11. D. STEEL~., Spectrochim. Acta, 19, 411, 1963. 12. S. V. J. LAKSHMAN, T. V. RAMAKRISHNA I~AO and G. T. •AIDU, CI~tT. Sci., 47, 7, 1978. 13. S. V. J. LAKSHMAN, T. V. HAMAKRISHNA RAO and G. T. NAIDU, Ind. J. Pure and Appl.

Physics, 15, 834, 1977. 14. B. P. A$THANA, V. S. KUSHAWAHA and K. P. R. NAIR, Acta Physica Polonica A, 42, 739,

1972. 15. T. V. RAM*KmSHNA RAO and R. RAMAKRISHINA REDDY, Proc. Indian Acad. Sci A, 8 8 ,

257, 1979. 16. D. STEELE, E. H. LIPPINCOTT and J. T. VANDERSLICE, Rey. Mod. Phys., ~4, 239, 1962.

, 4 ~ PhyJiea Aeademiwa Sr rum H.,~aricae 48, 1980