Laud, B B

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POTENTIAL ENERGY CURVES AND DISSOCIATION ENERGIES OF SOME DIATOMIC MOLECULESB. B. LAUD aSI) D. R. KALSULKARD epa r tm en t  o f  P h y sic s , Marathw aoa  U n iv e r s it y .A uranoabad , M a ha ra sh tra , I n d ia .(Received October 30, 1907)ABSTRACT. Tho potential energy curves have been constructed for the 3 kno-wn states of VO, using Lippinoott’s as well as Morse’s potential function. The comparison of tho most probable transitions predicted from the two sots of curves with the available intensity data for the yellow-green and the infra-red systems of VO reveal Lippincott’s function to bo closer to tho true potential function. The function has further been useil to calculate the dissocin- tion energies of some diatomic molecules.P O T E N T I A L  E N E R G Y  C U R V E S  Though Morse’s (1929) expression for the potential energy o f a molecule is, by far, the most commonly employed, the one developed by Lippincott (1953), viz.,... (1)promises to be valuable (Lippincott 1953; Laud 1962). A good potential energy function, besides satisfying the requisite criteria at extreme limits, viz. at r—>0, r =  r, and oo, must not be away from actual curve in the intermediate positions. The intermediate behaviour of a function may be judged by a comparative study of the most probable transitions obtained from the curves on the basis o f the Franck-Condon principle and those lying on the Condon parabola obtained ex­perimentally. In the present note, the quantitative intensity data on the Yellow- green system of VO, obtained by the present authors and those on the infra-red system of the same molecule obtained by Keenan and Schroeder (1952), have been brought to bear on the graphical results obtained from Lippincott’s expres­sion with a view to examine the function from this point o f view.The potential energy curves have been constructed for tho throe states o f VO, viz., the ground state, the upper state of the infra-red system, and the upper state o f the well-known yellow-green system. The values o f tho constants and r, corresponding to the lower and the upper states o f the yellow-green system have been given by lagerqvist and Selin (1967); and for the upper state of the infra-red system were obtained by Keenan and Schroeder (1962). However, for this state was not available in the literature. This wa>s obtained by using the relation =  constant which, for the different electronic states of the same molecule, is found to hold fairly well. The values o f the constant for* Present address : Pancham Khemra j College, Sawantadi, Maharastra, India.60Potential Energy Curves o f Diatomic Molecules 6 1the lower and the upper states o f the yellow-green system obtained from this relations are :Lower state : 4058.48, Upper state : 4047.40Using the mean value of those i.e. 4052.94 as the value of the constant, for the upper state o f the infra-red system comes out to be 1.660-4®. Using this value of and the other relevant constants, presented in table I, potential energy curves have been constructed for the three states of VO molecule (fig. 1). We have also constructed potential energy curves for the same three states using Morse function for a comparative study (fig. 2).Xl0840302010GROUND STATERED INFRARED SYSTEM UPPER STaTJ^ j, - - ; ! ' . :  YELLOW GREEN SYSTEM UPPER st a t e//! /.w--------------V . :  7. \ •------r* ; V 6: V . - 5->• ’ • V * 4v^o•1'^• ii V  ;f II Int\  ^ -?----------- 1 V., I  7\-----------1 V, 5r ------- /  V., - 4J5±.V - IV - o0 1 2 3 4Fig. 1. Potential energy curves (Lippineott function)Table 1 ConstantsState Wg WgXg AuthorLower 1011.56 4.97 1.689 Lagerqvist and Selin, (1957).Upper (Infra-red system) 908.2 6.0 1.650* Keenan and Schrooder, (1952).Upper (Yellow-green system) 865.9 6.6 1.672 Lagerqvist and Selin, (1957).• This value was obtained by the procedure explained above.52 B. B. Lavd and D. B. KalsvlharX i oFig. 2. Potentiftl em'rgy c.urvcvM (Morse' funrtion)In table 2, we give some of the most probable tnisitions of the yellow-green system predicted from the two sets of curves and those obtained by the present authors in the spectral study of VO molecule. In table 3, we present similar sets of values for the infra-red system of VO, the experimental values given there being those of Keenan and Sclirocder (1952).Table 2Some of the most probable transitions : Yellow-green systemExporimontal Lippincott Morse(0,0) (0.0) (0,0)(1.0) (1.0) (1.0)(2,2) (2.1) (2.0)(3.2) (3.2) (3,0)(4.4) (4,4) (4,1)(5.5) (5,5) (0,1)(6,5) (6.5) (0.2)Table 3Some o f the most probable transitions, Infra-red systemPotential Energy Curvets of Diatomic Molecules 53Exporimontal LippiiK'ott M(>reo(0.0) (0,0) (O.0)(0.1) (0.1) (o.a)(1,0) (1,0) (1.0)(1.2) (1,2) (1.3)(2.0) (2.0) (2.0)(3.1) (3.1) (3,0)(5,3) (5,3) (3.1)The tables reveal clearly that the Lippincott’s expression gives a better fit with experimental values than Morse’s. Hence, wc have enough justification to assume Lippincott’s function to be closer to the true potential function.D T S S O C T A T I O N  E N E R G I E SThere have been some controversies about the dissociation energies of VO, TiO and ZrO.Mahanti (1935) has found the value 6.3 e.v. for the dissociation energy of VO by linear extrapolation analytically. Herzberg (1950) supports this value; while Gaydon (1947) favours 5 .5±1 e.v., obtained by graphical extrapolation.Christy (1929) has given 6.9 e.v. as the dissociation energy o f TiO. Gaydon (1947) favours 5 .5±1 e.v. Recently Brewer (1953) has found the value to bo 6.94 e.v.For ZrO, the values suggested so far are : (1) 7.8 e.v. (Herzberg, 1950) and 6.5T1.5e.v. (Gaydon, 1947).A correct estimate o f dissociation energy can be made if the exact molecular potential is known. As has been indicated above, Lippincott’s function is in all respects closer to the true potential function. Using this function in Schrodinger equation, the following relation is obtained.H^(ergs/molecule) Ke(Q4iirHiiWfXelZh)—1 /fe‘ (2)We used this relation to compute the dissociation energies o f VO, TiO and ZrO, constants used being those given by Lagerqvist and Selin (1957) for VO and Lowater (1929; 1932) for the other two molecules. The dissociation energies5 4 B. B. Lavd and D .  R. Kalsulharthus found arc given in table 4 along with those obtained from tho similar rela­tion arising from Morse function, viz. =  We^ jiWeXe.Table 4Dissociation energies in e.v.Molociile Lippinoott MorsoVO 4.99 6.38TiO 5.35 6.83ZrO 0.18 7.78It will be observed that the values obtained by using Lippincott’s expression are about 21 %  loss than those obtained from Morse function and arc closer to  those estimated by Gaydon. However, for VO and TiO, Gaydon has suggested the same value, viz. 5.6 e.v., while, the one calculated above for VO is lower than that for TiO. It may be mentioned here that Merrill (1940), from his study o f astrophysical data, observed that the dissociation energy o f VO should be loss than that o f TiO. The above results conform tio this conclusion.R E F E R E N C E SBntwor E., 19i33, Ghcm. Bev., 52, 1.Christy A.. 1.92!), Phyx. Rpv., 88, 701.CaydoTi A. G., 1047, Disweiation encrgir.n and Spectra of dialomir moleculex, Chapman & Hull, London.Horzborg G.. 1959, Molecular Spectra, and Moleeulnr Slruciure, Vol. I, Van Noslrand & Company, Now York.Koenau P. C. and Sc.hroodor L. W., 1952, Axtrophys. .J., 115, 82.Lagorqvist A. and Soliu L. E., 1957, Arh. Fys., 12, 553.Laud B. B., 1962, Indian J. Phys., 86, 639.Lippincott E. R., 1953, J. Ohem. Phys., 21, 2070.Lowator F., 1929, Proa. Phys. 8oc. London, 41, 557.1932, Proc. Phys. Soe. London, 44, 51.Mahanti P. C., 1935. Proc. Phys. Soe. London, 47. 433.Morrill P. W., 1940, Spectra of Long Period Variable Stars. Univorsily of Chicago Prosp. Morse P. M., 1929, Phys. Bev., 84, 57.

Potential Energy Curves and Dissociation Energies of Some Diatomic Molecules

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Potential Energy Curves and Dissociation Energies of Some Diatomic Molecules

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