Rao, P Tiruvenganna

Santharam, C V V S N K

English

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POTENTIAL ENERGY CURVES AND DISSOCIATION ENERGY OF THE PO MOLECULEV. V. «. K. K. SANTHAUAM and P. TIRUVENGANNA RAOSpiJCTllOSCOinC L a ROHATCi HIKS, DliVAllTMlilNT OF P H Y SlC S, ANDIUXA X Jn IVEUBITY  W alt AIK{Ucceived March 6, 1962)ABSTRACT. Fi’ftiti llio obhOivod hond-lirnrl sopiiralionn of Uio C '~ X m  sys'liem of ropoi'lcHl by 1 ho nuthoiH (1962). tiitprojarruitc valuoH of y i,/ u iid /•(/ of Iho (J' siatd  havo 1)(U‘M ('utimaU'cf I'lior^'y rurvi's Jinvo boon drawn /or fho X, B and C' lovok o f1*0. Ihobabli' diHHOt iiiiioii |uoduoi,4 ol Uioho siaton havo boon diKou.^Hod TJio diHSooiaUon onor^y of }H) iiioIocuIh u, OHUinalod an 6.8 o.v.A study of tJie sppoti iind of the PO molecule by the authors (1962) excited in a hii,di li'ctiiieiuy (lischarfjjo has led to the analysis and identification of two new doublet aystom.s f>f bands m the ultraviolet region designated as 6^ '—X^Il and The bands of the C'—X  system were observed to bo double double- luNided and were accordingly ascribed to the transition (or “A)—“IT. Neglect­ing what lu’c likely to be small effects arising from A-type doubling, spin splitting and the iulliieiice of D terms, approximate B  values for the vibrational levels of the uppei' r '  state can be obtained from head-head separations. Treatment of the branch formulae givesmk.ad-(Q,Uai=-- (1)where By and BJ' are the effective i?-vallies for the I^li/a and sub-levels, andB ' ' ^ B ’'(\-\-B‘'lA) ... (2)and By" is the true value. Using the true B^' values of the ground state X  ®n and A tlie coupling constant obf-ainod by 8uryanarayana Rao (1958) from the rotational analysis of the y system, the effective By and B"  ^ values are cal­culated according to relations (2). The head-head separations in the intense (0,1), (0, 2), (0, 3), (0, 4) sub-bands and tlie derived values ot according to relation (1) are shov n in Table I.14Potential Energy Curves and Dissociation Energy, etc, 15TABLE IThe head-head separations in the (0,1), (0,2), (0,3), and tho derived values of Bn(0, 4) sub-bandsv', v" R,-Q i ito' -Iti B'oU,1 10 4 0 638 11 9 0.04-10,2 11 2 0.639 10 8 0.6330,3 12 7 0 643 13 4 0.6430,4 13.3 0 642 13.3 0 638From these an approximate valiu' of B'qwas estimated as 0.64 cm“ .^value o l > ' o o b t a i n e d  as 1.58 A IVom the relation = (Herzberg page 180),4.J001x i o - ‘Fjg. 1. Poienl.ial (lurveis ol the X , B  and  C" olectronic HtaiOH of tho B O  mok'cmie.Using the vibrational and rotational constants of the X , B  and C  states, potential energy curves have been drawn adopting the IMorso relation U{r) =  j0o+D<,(l— ro)2. These curves for the X  Hi ground state and tho excited B  ®2(the upper state of the p  system) and G’ (or ®A) states are shown in Fig. 1. For the C' state the value of rol^r^) is used in drawing the potential energy curve. The probable dissociation products are given on the right in Fig. 1.A Jim ill «\tuipf)luiion of tUc* viln’atiomil levels ol the ground state X  gives a value f,71)00 i )u  ^ (7.1 e.v ) tor the djsHoeiiition energy of the PO molecule. The viljrahonal analysis of tlie ji system liy K Dressier (1055) shows tliat the vibra­tional Je\els of the H state coiiveitre very imjikIIv and therefore allow a reliable eslimalioii ol this dissociation energy. The linear oxtrapolaiioii of the vibrational ,.nergv levels of the 11 stale gives 7 / ,  -  - 2t000 un-h Thus the eonvorgencejmiit of the bands ol the B X system is IIOHOO h24000 -  54S00 eni-i or approxi­mately 55000 (‘nr^ above the o" 0 of level.A similar evtrapoliition oi the ^■ibrational levels ol the ('' exeitcd state,nhose spaciijgs rh-erease unilorml>', gives a value for D\  e(pial to 25,2()0\eni“ .^ The com'eigenc(‘ limit ol tlu‘ baiuls of the (J' X  sysieiu is 43050 |-25.3|00— OSSoOdu'h aliove the r" 0 oi AT-lli level.We may now diseuss tlu* jnobable dissociation products ot the X, B ,  and (!* states. Th(‘ at(jm has three bm lying states hS' ground state and the two'^ P metastahle slates The oxygen atom has throe low lying states ■ The ground stall' and the metaslabJo and hS* state.s. The X  ground state may be exjUM.ted to dissoeiat.e into two normal atoms ‘^ 8{P)~\-^1\0). This lowest oomhmation aei'ordmg to Wignei and Witmer’s rules, gives rise toone ' and one II statii with each of the multiplieities 2 and 4. The state helongiiig to this combination ean lie oorielated unambiguously with the observed X -II ground slate of PO. Assuming the validity of noncrossing rule, the state ean 1m‘ corn'luted v\ith the observed lirst excited B state which has been estab­lished by Nandalal Singh (1059) from a detailed rotational analysis. Thus both the 71 and X states dissoi'iate into two normal atoms The second excited A state of PO ma;\' ho assumed to dissociate into an excited P atom in a 4.s orbit and iinexciti'd P^(O) similai to the upper state of the y system of NO.From th(' observed eonvergoneo limit of 55000 cm~^  of the vibrational levels of th<' B slate, ye may therefore estimate the dissociation energy of the PO mole­cule .IS 55000 enr  ^ (G.S e v.) which may be higher than the true value by an amount of about 0.1 c.v. The linear (‘xtrapolated value of the ground state vibiiitional I'liergy levels is 57000 em~h The fact that this is 5 per cent higher than tlie above value can reasonably be attributed to the uncertainty in the extrapolated value ol the ground state.The eomevgenei' limit of the state ivas obtained as 68850 cm“ .^ The dif- ierenee bet ween the couvergence limits ol and B states is ecjual to 14000 ein~^ . This cone.spnnds eitlier to the excitation energy 11370 enr'  ^ of I^) state over the hV ,<tate of the P atom or the exiitation eneigy 15, 870 cm-^ of W  above the ^P ground ,stat(‘ ol 0 atom. Tlius the .-jiatc may dissociate into cither W  (excited / ) -j 7^ (unexcited t)) or ^8 (iinexeitod P) \-^ J) (excited 0) As the linear extra- polati'd  ^able of the T' state will in general be luglier than the true value, the , true convergence limit of the V' state y'ould be less than 68850. So the difference16 C, V. V, S. N. K. Santharam and P. Tiruvenganna Raobetwoon the convergence limits of tlie C" and B  states is expected to be loss than 14000 cm~ .^ Hence the C' state may not possibly dissociate into (unexciteil (excited 0). Further the C  state which should arise from a oi term cannot result from this coml)mation. It may bo icasojuibJe to conclude that the 6" state <lissoeiates into a (excited (unexcited 0). This combi­nation gives rise to 3+(2), X~, 11(3), A(2) and 0 states Aiath lath of multiplicities 2 and 4. The t/' state may therefore be identified as a -i; (oi ‘^ A) state of this combination. The cbfferenee betw^ eeii 14000 cm"^ and 11370 em“  ^ can reasonably be attributed to tlie uncerrainty in the linear extrapolated value of J)'q of the 6" state.Potential Energy Curves and Dissociation Energy, etc. 17A c  K  N O W  b  E  D G iMli: Js: rThe authoi’S wish to exjuess tJieii thanks to l*i of. K 11. Kao for his kind inti rest m this work. One oi the authors ((\ V. \^  S. N. K. Saiitliaram) is grateful to the C.iS.l.R. (Delhi) lor the award of a Itcsearch Foliowsliip.K  E  F  E  K  E  N C E  SDivfisler, K .,  1956, Helv. Phyi>. Aeta , 28, 5(KFli90.Nundalal Kmgli, 1959, Gaa. Jo ur. Phys., 57, 13ti.iSantliaram, C V. V  S. K IC. and Kao, K 3’ , 1992, iH. I ‘Uy{,i,K 168, 553. .Suryanarayamv Kao, 1C., 1958, Can. J  Phya., 86, 1520.

Potential Energy Curves and Dissociation Energy of the Po Molecule

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Potential Energy Curves and Dissociation Energy of the Po Molecule

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