Pandey, A N

Verma, U P

English

IACS Institutional Repository

i",d,an J. l'hy •. 548, 520-522 (1980) Pseudo-exact force constants for [Mg (NHs)6]H U P Verma, A N Pandey Imd V KUDlar· Moleculo.l' Speotl'()SCopy Rosuaroh Labora.t.ory, j)epa .. tment of PhysICs, Meerut Colloge, Moorut·250001 Recolved II July 1978 AbstrElct! The normM coun.lllmto ana.lYfi1R has b('uu lJOl'fOl'med 1'01' thu cum-l)ll1x [Mg(NH.;t)eJoH hltVlIlg ILll uctu.hodral fl'l1.lllUWul'k I:ltructw'(" HAcen1.1y J'UpOl ted lHot,opw ~hlftl3 have beGn ut3t:ld to dtltel'llllllO thl' psoud~-exu.('1, furco ('II11Ht,autB anrl mOllon arul)htud(l~ of vlbrat.lon w1th the help of point mass mouel (PlIiM). ps"utiu·exo.ct force OOll.9tant. dl'" to ·'lIig/"Mg iBot,,~c shlfts aro aJao employed to dl'ltOl'llllne tho mellon mnplltud()1:1 of vlbl'a(,lOn EL~ ruuID tam-puraturl'. \. 1. Introduction Iteccntly, l'lu~ (l976) ba~ >ltudwd the lI1ft-med I1nd RamaH Hpel'tru of mallY HubR1,itu1,od magnosium chloride hexa·I1111111111oS. and IllPIIHured th" fL"oQU(111("Y Klutts f01' all activo VIbratIOnal handH Ho haH also lIlpo,-j,pd tho Vlbl'uti()JHLI frllqllell!nij8 amI I~otol}ic ~Iuft>l for MgL.2t- (L = NH., ND3) Thercfo]"{l it, was (}Oll"Idorod worthwhile to coml'ut,o t,he p",mdo-oxacL f01"cO COllAt,llnt8 for thIA cOllllllex u>ling point Jlla~" J1Iodel III conJunctlOll with iH01,0})1" shiHs <lata PHlludo-nXllct, forcn constants thus obtaultld havo heon uHed to cllleuJlll.p the moan amplitudes ot vlbl'af,ioJl aL foom j,£llnperatul"t' UHHlg L matl"lx method 1U(1Im amphl,udcs of vibratlOll am also reported Ilt T = D, 2!J~'15 I1lld 500 l{ 2. Theoretical consideration Tho octllhedral X Yo type system bolongs to symmetry glOUp, 0", and the HIX vllHatwllallUodeR 1:\1'(' classifiod according to symmot,ry type aA follow, : l'Vi~. ~ Al,+Eg+2.li\,,+F~u+F2'" whom IJ I1nd u represent goratic and ungllrade modcs that m'o Raman I1lld infrared l1etiv(, l"flMpectivoly But tho mod" Ji'2u i~ inactIve in both and iA d"terminerl wit, II t,he help of WIi~Oll'R relation V5 = V2V6' Jf ttL!) bmary combinatIOn is not permitted. J"01"CO cOllstant pllmmet,erH aJ'C ovaluated, a""uming (NH~) group aR a point 1111 .. "" and taluIIg lllto account, tho iHotoplC shIfts, using the Aocular detorlllinant~ (WIl"oll ct al l!J5Ii) I U.Ji'- ilft' I ~ O. These "ymmetrized force eOllstants havll • Dopartment of PhY""'" M.M College, J\1odin"gllJ.'·201204 li20 Pseudo-exact force mnstant, for rMg (Nllg )o]21 521 been usod to (waluat,,, th" elrmentA of matrix uHing the Cy1'm'H (I !l61!) ~('{'\lla,l' dotnminal1ts I~a-l-AEI ~~fi 111011gwit,h I~F--AAEI =0 III l,hpi!' ll~1Htl l1otationH, 3. Results and Discussion We have omploYlld hoavy fttOill Aub~t,ituti()n (24Mg/26Mg Rlld 14N/JoN) and H/D Rubst,it,utiol\ tllChlliquCA fo)' t.he dutol'lIlillat,ion 01 JlHcudo-exact, fOJ're ('on~tantK (Tab]o 1). ]rOI''''' llol1HtalltA ob1.uinod by heavy atOl1l ~ubsj,itutioll teellluqur "T(' In excelleut agreonll1nt II'lt,h each othllr but H/D HubstitutlOn teohUlfjllc yiddA values slightly highul' than tho~o dlHl to lWlwy at,om Aubstitution techlllquc. Howovpl', it IR reported in \heratoUl(, (Dunran and MiIIR ][164, l'halmJ' 1971, McDowell an(i (1 .. ldhlat.t, 1971. MeDowcll PI (ll 1972: Mohan and Mlillm' 1072) I,IUI,t, heavy al,om ~UhRt.it.\ItlOn t.l1ehniqul' ywldH beLt.or rCR1Ilt.R owing to the small fnlquoncy shUtK l'ompaccd t,o H/D HubHt,it,utlOn 1,(l('.hniqlw We ha,vc. therefor!', \l~od p~e\ld()·exa(lt JOJ'ne eOllHtant,>/ obtained OIL UKlllg 24Mg/2°Mg i~ot()pil' Rhifis III t.lw dot,lH'lIl11wtIOIl of I)(oan amplit.lllim, of vibrn.tioll OJ,t room tl'lIlpel'al,url' (IMU_N -~ O'095!),,t IN ... N --- (1·140H A 1'01 Jllll'ar. and IN"' N ~~ 0·1151 A 1'01 nOll-ItiOtopw 81ult FOI'Ct-l ( ·Ollf.ltttllt, RID A 8ymmeif"IJ jorce cot/stant,o; 1'\,(.'1 •• ) 1·1~G 1 126 1·14!J ~',,(E.) tHi92 o Ml7 11·0(l~ F3J(]l~1 I,} o·~n2j:0·02;1 U'~66-L (1·04" (j 934 :lIHH7 F",(1<',,,) - 0·2.i1.J.IH'!12 ·-O·~J!) .I-11ol9!1 --0·:102.1 (I·OIlS 1i\4(f!\'J) 0124:1-0·010 1I112JO·]l3 0·11i2./ 0·04·1 1".,-. (F'2(,) n·os!! II nsn (I·O~1 F",(F",) 0·(l8!! II·OHQ [H191 H. I "tflrnal J?' ('t' {'o'n!Jlfmts f, U·K:16 (HUn /1·861 fir O·O~R O'08H U·()UO f'rr - IJ.U66 -0046 -0·072 f'rlr-f'''ra: - 0 120 -0·109 -0·151 fll -f\.'a 0·106 0'101 0'122 fa:Q-f"1ll 0·(109 0·006 ()·Olb fr/lo:l-fa ll / 0'0(19 0·006 0·015 522 U P Verma A N Pandey and V Kumar line",r) Th" lU"",n amphtudoR of vibrat']Oll at l' = 0, 298·15 and 500 I{ evaluated uMmg L approximation ml1thod (Table 2) fairly agl'ee with t,heAo values and t,hHrofol'o point. maAR model nan be Huccl1sHfulIy employed in t,ho caso of Buch ('()mp)exeA. Table 2, f>.leoted meo.n ampiJtud." (1) for I "Mg(14NH.),l'· J)1r~ta.nc(} 'I'~ OK ~9S'15K 000 Ii ______ __ M _______ Mg.N (J'071H 0'0894(0·0909) O'IOf)6 N N (Lllloo.r) 0,0972 0·1470 (0·1409) 01871 N .N(non. linear) 0,0860 0·1151(0 IInl) o 1434 Valuef,! in ( Rhlft'R ) m'o calculated mnn@: psonrlo-oxfl.rt iOl'clj con~t,B.nt~ ~l' 2~ Mg/2ijMg \ i AcknowledglDent 'I'wo of tlw a,ut.hOl'H (AN!' ILJl<i VJ() 11l'e t·h .. nkf\:t) to uce N('w l)eUu i'o1 fiuun";,,! a~slStmlC(~. UPV iH t.lutnkfn! to CSIH. New Delhi 101 Itwurrlmg HPn",]' f .. lloIl'Mhi}! References Plus R 1976 Spectroch,m, Acta 32A 26:1 WilRon (JI') E 13, DeclUR ~T C and CJ'UBA P C }!l55 Molecular Vi(n''''1DIIN, Me-Gr(J1J', Nf.1') )'ork C.vVJIl S __ I 1968 '.ll1olccular V't1l1'ntio'118 {HId Mean Ampht.'Ud{~s', El8('v1~r Pub Co, Am8ir'rdam Dunc.an .J L and MIll. I M 1964 Spectroc/VI1n Acta 20A 52:l Thakur H N 1971 ,J. Mol. Sf>'uct, 7, 315 McDowoll R S and Goldblatt. M 1971 [nary Ohem, 10, 625 McDowell R S, AMprey L B a.nd HOF~kmFl L (J 1972 J. Olt-pm. jJhYR. 56, !H7!! Mo],,,n Nand Mullor A 11172 .J Mol. 81'cctry 42. 20:l 

Pseudo-Exact Force Constants for [Mg (NH3)6]2+

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Pseudo-Exact Force Constants for [Mg (NH3)6]2+

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