Goel, R K

Nitish, Sanyal K

Pandey, A N

IACS Institutional Repository

Jndian J . Phya, 50, 05Q-UG7 (1970)Intramolecular force fields and vibrational amplitudes of some octahedral system^Nttish K. Sanyal, R K Goel* and A. N Pandey**Dapnrtmmit of Phyaics, Uviverfiity of Oorakhpnr,Gorakhpur 273001{Racfrived 29 December 1975)TIkj MOVFF, MUBI '^F and GVFF foico fioldn arc employed to computer the force constants for sonK; octahedral systems viz., AgBI’+On (*^ —^ Ba2-f, 1. B -  Li^, Na+, K+), Z^F«2-; WF«, | OrCNHa), I^ h , j Co(NH3)„]»-'and lNi(NH3)6 l“+ using euTj-ent vibrational data Moreover, mean amplitudes for these systems have also been computed at temperatu t^ s^ ;T --  0°K, 298.15‘’K and 500°K along with Coriolis coupling constants The results a"o u.se.d to study tjie inflnenm^  of cations on the relativi> stability of tho c3i,omical bonds m the pro>sent systems as well as in tlw^  isooloctronio series T)io results have been found to 1 k‘. in good agree­ment with th(» values rciiortwl in literature.1. I ntroddotionTn recent years, motlified V(U'sion of the conventional force fields have played an important role in understanding the intramoleculav forces in octohetlral systems. Howevej’, modified orbital valence fm'ce field (MOVFF) and modified Urey- Bradley force field (MUBFF) involving six and soV(m XJ^ i-f'auicters Jiavc not been thoroughly investigated. In order to examine their usefulness in understanding the stability of t)\c chemical bonds in different onviTonments. tho MOA^FF, MTTBFF and GVFF force fields have been emploj^cd to compute the force constants, lii addition, tho moan amplitudes of vibration and. Coriolis constants for F i«xF ,«  typo have also boon calculated T)\o octahedral systems under pT’eaent study include in four different environments (viz., Ba,Li‘^ ,^ BajjNa*'*', andSr^Na'i t ), ZilV“- , WF„, (Cr(KH.d«?^, fCofNHald^  ^ and [Ni(NHa)„?' The vibra­tional 'spectra of these systems have '^ocently bcmi studied by Be Hair et al (1974) (lOg*^ "), Toth & Bates (1974) (Z^ Fg® ), McBowell and Asp^ey (1973) (WFg), Schmidt & Muller (1974) [{0 »’(NH3)J»-i and (Co(NH3)„]3+l and Muller eJ al (1974) fNi(NH.,)J“-' Tho obseJ’A'od vibrational fT-oqu<mcies have betm interpreted assuming octalmdral symmetry. Th.c computed results are used to st\idy tho stability of the chemical bonds in d.ifferent environments and. in the isoelectroiiic series* On leave fiom Department of Physios, D. N, College, Meerut, U.P.•* Present Address : Department of Physics, Meerut College, Meerut, U,P,6592 Method of ComputationT)i(^  poH-sosKing ootalirdral symmotry givo riRe to six fimclaiiK j^italvihratioaR wliioh (listrihiitod among different apocioR as follows—-v/vib — fAmong iln-S(‘ vihvations and Vr f^ )^ ar<^, Raman ar,iiV(^ , andintVa”(^ d aotiA^ c^  whiU^  v„(/ott) inaotivo in liotli Tlio ijuictivo isp(‘,nniitod as binary (;ombinal ion bands or (lan bo computed with tho holi) of th(‘ 1‘olation 1^5 V ^ ’'« cases who ’^<i ajiy particular froquonoy has not boon rci-portod, wo ha\’(‘ bo’Towod it from similar systmns (T)(- Hair ef al I974).Wilson’s (1955) !FC matrix nudhod A\as omployod to oaloulato tho force oons- laiits m tho MOVb^F, MUBFF and GVFF models. Tho moan amplitudes of vilp'ation \\ovo evaluated at tompc r^aturo.s T — 0"K, 298 15°K and 500°K using ^y '^'in’s secular equation (1998), | HG  ^ -AA’ | — 0, whore the symbols iiave t]ion‘ usual mi^anings and G matrix (elements and the analytical (expression fo3‘mean amplitudes of vibration uero taken from literature [Cyv i^n (1968), Raana- swamy & Mutliusubramaniani (1971). Sanyal r/a/ (1974)] Tho two dimensional (upiations occurnug ui/,it spocu'.s \\'or(^  s»)lved by Muller’s Z,-mat''ix method |Mull(‘r & F(‘a !0(;k (1968). Muller (1908) and Peacock Miillor (1908)J Tho C C O  have been evaluabxl by following Meal & polo (1956) Thc^  moliMmlaj cons­tants liave lioeu ealeulat(Hl for the skeletons ol hexamine nudal eompli^xeis using point, mass mod(d.660 Nitish K. Sanyal, R. K. Goel and A. N. Pandey4. R esults and B isousrionTJui table 1 presents the vibrational froipumeies used in the pjusont com­putationThe tables 2-4 list tho results of the computed force constants employing MOV'^FF, MUBFF and GVFF force fields respoctiv(dy The j'osults of mean amplitude.s of vibration are presented in tabkv 6The MOVFF and MUBFF employ bond slrtdching force constant K, angli" bonding forci*^  tjoustant D{H) and interaction constants F, F', k, h and (j Tho GVT'F mod(‘] incdiuh^ s /,- bond stretching constant, angle bending constant, and the following ii^teractioji constants Srr and /Vr wliich ri^presiuit cis- and trans­bond stretching interactions «'(‘.spoctivoly, and angle iKjndinginteractions TJk  ^ force constants in GVFF and moan amplitudes, computed by otJier wo’ kcrs h,ave also been included in tho ta>>le.s 4 and 6 rcspexitivcly for c(un- parJson. Tt is obvious from the tables that values a,i’o in good agreement with tl^ oKo reporteh earlio?,Intramolecular force fields 661Ic8-+='8cn^ 3  —^ ■«W<DPhM■p 1SOHopCJ<1Po 1ccErCw«3 17i 7^ *-lOo o:C-J CO :£>O«T1 IM(MCO U3 1—1-l-l1, CO t’ 7lfMooi '  = S  2-t ^  CO r-4hJ IT4 {P, CO <McSSiSH7i 7^Jvoo 25L- ^-1 1  - Hl- I-- inO. .2  Sp  wo a — M ^  "2  4  S S  gis. s.Si £i ^662 Nitiah K . Sanyal, Table 2.R . K . Goel and A. N. Pandey MOVFF constants (in mdyn/A)Sywinm K D F F' k hHaJJIOf, 2.021 pMl 0 444 0.002 0.144 0.157baaNalOf, 2,840 0 579 0,506 -0.002 0.049 0.095ba^KJO j^ 2 027 0 051 0.472 0.055 0 128 0.145HroNaK^ t^ 2 912 0.K47 0.484 0 143 0.250 0 2307.rP,2- 2 son 0 408 0.223 0.202 0 033 0.204WFo(,.d" 4 242 -0.100 0 518 0.010 0.350 0 118WFo(oi,)f^ 4 411 -0.120 0 502 0.019 0.345 0.127rCi-(NHah?' 1 io:i 0.277 0.223 0.068 0.1J2 0,072rCo(NH,)oP' 1.209 0.434 0,204 <U02 0.183 0.140(Ni(NH3)6f^ 0.431 0.043 0.230 -0.011 -0.001 0,00811—-Ohaorvnrl tVe((uonpy, b—HarinoiiiR IVoquwicyTal)lc 3 MUBFF constants (in mdyn/A)tSysfcom K 77 F F' k h fjBa.LilO,, 3 082 0 331 0 312 0.070 0 209 0.004 0.0393 28S 0.270 0.377 -^ 0.130 0.119 -0.023 0 042Na^KIOt. 3 142 0,305 0.320 -0.091 0.198 -O.OlO 0.035iSi'aNalOi, 3.678 0 395 0.298 -0.044 0.337 0.010 0.033ZvF^~ 2 833 0.179 0.000 0.038 0,759 0.007 -0.013WFc(vd« 5.019 -0.075 0.300 -0.209 0.453 -0.002 -0.0G4WFo(w/F 5 284 -0.080 0.317 -0.220 0.451 -0.072 -  0 000I(V(NHo)cT' 1.342 0.131 0 159 0.003 0.193 -0.001 0.013rC!()(NH3) i 1 405 0.207 0.198 0 035 0.263 0.032 0.014rNi(NH3),F' 0 634 0.000 0.173 -0.075 0.049 -0.035 -0.005fl.—OljHprvod froquonoy, b—Harmonic frequencyIn oMtir to study the influence of cations on the relative stability of the chemical bonds, it is useful to see the trend in the bond stretching force cons­tants. The regular variation in the force constaiit K  observed for periodates (Parvoz Ahmed et al 1974) is not observed in the case o f perovskites here A compansoji of the bond iStretching force constant K  from the table 2 shows that K  is smalloT- for Ba^LilOe than BagNaTO .^ Tlie trend in pe '^ovskites can be explained as follows, Tn the ordered pe^ovskite structure of the compounds,Irdramotecutar force fields 6630<l^'T isStJHtH tot o  !£5® oo  o1 II I  e it tCQ lo :zr tM oTtt 2  o  O Io o  © g © ©*© ==5 sJgs' § ©  SS <M ©O ® dCO Tj © TS*Q ^© C0 © *©1^4 oi 04 © 1 ©® o  ”® ® d ® d ® © ffj © ,-,-K Mi- l  .© o©d© lO= s  Io2 CO CO^  to d- n  Otto -rt*d d*  ^00 ©© d oO r Heo CO ^  o  I_-!3O o COo O e %t thJefl 1**9 r*h3&pq n PQ O? N s=©§co;z:S? CO O '2 2 ” ^-H ^© (^  © o  ©^©©di>-_^| ^ I-; l ; "® «M C It to 1 ° © C{<- 1^ I-' ^ S‘1 F-l O=^ d d ©d-i l l® S©oo "d®.WPCi B  § § ©1 sQ oa lp >> so  C ,Is *W ^i sH t,9  cho;©^ PM4i .2  acd o9 f-‘¥ ■ =3 l lo1.13E iPi tt^ a § ^ 1 :  OJ ^C o fi© ffi ^c > “6 6 4 Nitish K. Saiiyal, R. K. Goal and A. N. PandeyoV(‘j'y oxygon i>s jouiod liuoarly |jy ojio raonovalout cation ajid ono T’ + ion. Sinoo tjio ionic radiuM of Li * is smaiior t]ian tlic Na ^  ion thoreforo Li+ ion AvoakenH tho j7 i_ ()2 - moro than tJio Na* ion and thisi offoct in ti ajiHlatofl in stretching force constant On similar grounds wo should expect an oven liighor A^ aluo of K  in (uiso of Baj,KfO„ liocaiisc K"* has la»gce' ionic radius but this trend is not followed, ft may ho duo to tlu^  indication of the hroadoning of lines and hands in the spectra of these compounds and some amount of <lisorde,r of tjie Ba^+ and K+ ions whose .ladii I.S5A and 1 33A respectively, hocau,se nearl^ '^  erpial ionic radii of B a-‘ and K* also tend to disto.rt tho ,structure Avhich under ideal conditions will have 12 coordination .sitc^ s for Ba‘^ ’ and 0 foi K ' The larger K value for Sr^NalO^ than Ba^NaJOn can lie imdorstood m t(\rnis of cell dimcuisioiis iSr- *' lia.y smaller ionic radius tJian Ba^' and the coll constant of Sr„NaIOg (8.2oA)(De Hair d al 1974) IS also .smallej- IJian Ba^NaTOg (8 38A)(l)cHair d al J974) On account of these two (lifferenoes, I-O distance is smaller m Sr^NalOg than in BuoNaJOg Avhich iiuiroases the value of K. Similar ohsiUA a^tiojis have hcen mach; hy He Hair d al (1974) oil tJio basis oj simi)J<^  LJBFF studies The stridchiug fom^ constants in MUBFF and G\'‘FF (fcahloiS 3 and 4 ri'.sjiectivoly) also Jollow IJic similai trend TJu^  bending and iiiUu’action forces ciOiistantiS in threi^  models do not, show regulai' t,i’(uid with tJxo change m the lonii; radius of tlie inonoA’^ alent cation and sonu' cons- tautrS aie. also almost eipial therefore these have not been discussedit is iiiteriiSting to study the relative stability ol the ehemical bc>nds m iso- eleetroiiic seruss. For tins purpf>se wc hav(  ^ tlu’ee S(d,s of isoi'Jcctroiue stu'ie.s viz.(i)— lOg^ *-- (3 7b) and TeO„« - (4 12) (Paiidey d al 1973), (n) M V "  (3.03), KbFg- (3 70) (Sluwma d a l 1074) and NoFg (4 79) (LaBonville 1972), and (lii) -  TaF,.- (3 02) (Pandey d al ]973)and WFg (5.20) wlu^ ro the values iii poi’entlu'Ses a^ ’e tluj st,r(dchiiig bond force constants (OVFF) in mdyii/A From a compiwison ol tlu^ sii values, it is found that in case ol octahedral, VI oxidation State iS iiio.rc) stable Stabli- than lh(‘. VII oxidation state., while in case of hexafluoroauiojis higher oxidation state is more stalile The stability of higher oxidation State in casi*. of hcxajialoanious liave been reiiorti'd in btei'aturo (LaYbinville 1972) The ionic radii ol the (;entral atoms and bojidwl distances ni case of hexiifluoroanions also support this trend.A comparison of stretching lorce constants of 10g*^ - and ZrFg^ *^ with their res­pective di-and tri-oxides and fluorides viz. T(VTT)Og"  ^ (r^ ®^ 3.70) I(V)0i,~5.10) (Parvex Alrmed d al 1974) and Zr(TV) (d« 3.028), Zr (HT)F.» (fP 4.10) (Hange d al 1973), Zr(II)Fjj (fP 3 54)) (Hange el al 1973), (tho A^ alues m ptu'onthoscs aie stretching force constants in mdyn/A and number of non-bonding electrons of the central atoms) slums that low'er oxidation State to be associated witli a higher force constant. In case of fluorides, the crystal field stabilisation energies for configurations, — 0 Hg', — 5 Dq aaid =  OPgf also support the above conolusioiis except in case of ZrFa-Intramotecutar force fields (565A compari^ son of Htrotchiiig for(;o oou'^ iaait K (/r) (Tables 2, 3 & 4) among hf,xammiiio comploxos of bivalent anil trivalent first ro\\- traiisition inoials s1t,om^s that tlie strength of the metal ligand bond vanes in tlicro'ir'der Co—N >  C)r—>J> Ni— TJio stability of the chemical bombs can also bo undoisloocl in terms of 10 D(jl A^ 'alnes for metal ions and ligand group Tlio values (IFiggis 1900) are 24, 22 and 11 respectively m units of cm foi’ thc^  configuration Co '^, O''®'and Ni® ' vhicli are in accordance with tin? calculated vivlues of lovco constants.Coriolis couiilijig constant (O.C.C) are proSent<<Ml in table 5 Figiu'o 1 rc.- presents tlio vai'iatioji of Ejga (/im) with the ratio of masses ol thecentral and ligand atoms which is in agroi'iiiont with the ti'eud roportisl by Muller (1968).10 2 A 3 0 4 0 3 0 6 0  70  BO 9.0 10 0t’lg. 1 VaiiaUoix ol Cunolis couiiliug cuuatant fgj with the iiiaKs lutio {inr(uiy) of ceiitml and ligand aiuiUH.The mean amplitudes of vibration for bounded as ivell as for non-bonded distances li.sted in the tabic 0 at temiioratures; 7 ' -  O'^ IC, 7' - 298.10'K and 2' =  5(K)°K show usual variation It is also notixl that the mean amiditude values for the bonded distances show opposite trend than tlic corresponding strotcli- ing force constants as cxpocitxl Fx’om ilic comparison of the mean amplitudeTable 5 Coriolis eoiiplnig constants of ocitahodral sysiom.sSystemCoriolis coupling constants ('j3 ii.iUl r/UI VlOo'*- 0.201 0 290 7.932ZrFe“- 0.294 0.206 4.801WFo 0.171 0.329 9 077lCr(NH3)ell i^ 0.394 0.10(1 3 053LCo(NH.,)er' 0.307 0.133 3.160LNi(Nl-lJoP' 0 309 0.131 3 147values ill case ol' isoolectronic series bonded distances at room temperature viz. (i) IO ,‘ - (O.0442I ) .  TeO,*- (O.O433A) (Pandoy el (d 1973), (ii) Z r!’,*- (0 0474), N1)F,- (O.O437I )  (Sharma et al 1974), MoF, (0.0400A) (Cyvin 1968) aaid (iii) TaF,"Table 0 Mean amplitudes of vibration (m A)666 Nitish t .  Sanyal, U, K , Goel and A. N. PandeySyHlem O’K 290.15^K 500"KX -Y 0.0429 0.0419 0.0503Y—Yj7(u,i 0.0720 0.0800 0.0944Y-Yzo,, 0.0579 0.0008 0.068113 12-NulOg x - y 0.0423 0.0441 0.0492Y—Y^ 7,oi t 0.0714 0.0797 0 0932Y-Y7„„, 0.0070 0.0604 0.0679Da^ AvlOu X -Y 0.0-128 0.0447 0.0500Y-Y,nort 0.0720 0.0800 0.0944Y—Y lojift 0.0578 0.0007 0.0683SiaNalOt, X -Y 0.0415 0 0130 0.0476Y—y allot t 0.0701 0.0775 0.0901Y-Yio„„ 0.0550 0.0577 0.0641Z i iv - X-Y 0.0442 0.0474 0 054.5Y~Ya,io,t 0.0843 0 1091 0.1340Y-Yiony 0.0552 0.0587 0.0668X -Y 0 0371 0.0384(0.038_b0 003)* (0.0383)**0 0423Y— y B/(ort 0.0709 0.1084(0.101 ±0.005)* (0.104)**0,1315Y—Y tong 0.0601 0.0618(0.066±0.011)*(0.0516)**0.0572wr,(aid'^ X -Y 0.0307 0.0378(0.0377±0.0004)**0.0415Y-Yahon 0.0758 0.1050(0.100±0.005)**0.1290Y-Yiong 0.0495 0.0611(0.0509±0.0003)**0.0562X -Y 0.0538 0.0603 0 0711Y —Y^  iliort 0.0958 0.1194 0.1468Y~Ytano 0.0080 0.0773 0.0919LCo(NH3)dP' X -Y 0.0521 0.0579 0.0680Y-YB,or^ 0.0895 0.1072 0.1296Y-Yip„, 0.0057 0.0735 0.0806LNi(NHa)uf^ X -Y 0.0040 0.0810 0.0098Y-Y.„„y, 0.1<»77 0.1470 0.1835Y-Ytong 0.0839 0.1105 0 1373a—Olisoi'vud frequency, b-Harmoiiic froquomiy,♦-Kiiperinujiital liom Scqi & Wcip (1000). **-frum Mo Dowoll Jt Asiiruy (1U73).Ini/ramolecular force fields 667(0 043BA) (Flharma ft at 1074), WFj, (0 0385A) (Oyviji 1968) (vahu‘s in parontlu^wos aro moan amplitndoK), ii found that th( y^ show oppo^.o trond thoji tjiio conu s^- ponding Rtrctohing force constants. 'From this it is concluded that in casev oi’ hexafliioT’oanions stronger bonds liavo .'smalloj- ni(‘,an ampliird(\‘^ . Rimilai’ trt^ nd has also boon noted in litoratnro.BEFEEENCE8Cyvin S J. 1968 Molcnilnr Vibrations antJ Mean Sqvme Amplitudes, Elncvinr. Am l^nrclam.Dd Hair J Th. W., Corsmit A F. & TJlaeso (! 1974 .7. Tnorg Ntivl Chem 36, 913,Figgis B, N, 1966 Tntrodurfton ’^ to hiijand Fields (Iniprscipncc Publisliors, Now York)Haiigo R H., Margrave .T. L, & Hiistir, J. W. 197,3 High. Temp, Sci, 5, 89.La Bonvillo P., Ferraro ,T. K , Wall M. C. & Basile L. JT. 1972 Coord. Chem 7?nw. 7, 2,17 McDowell R. S, & Aaprey L. B. 1973 J. Mol. Spectroscopy 48. 254,Meal J H & Polo S. R, 1956 J. Chem Phys 24, 1119, 1126.Muller A. 1968 Z. Phys Chem 238, 116 Mullor A. & Peacock C. .1 1968 Moh Phys. 14, 393Muller A., Schmidt K. H. &, Vandi'iiih C. 1974 Spectrochim. Acta 80A, 6.11.Pandey A. N., Sharma D. K. & Dubhsh A, K, 1973 Spectroscopy Letters 6, 401.Poaconk 0. J, &, Muller A 1968 .7 MoJ. Spectroscopy 26, 4.54.Parvoz Ahmed, Dixit L. & Sanyal Nitish K. 1974, hid. .7. Pure Appl Phys. 12, 489, Ramaswamy K. & Muiliuaubramaniam P. 1971 ln.d. J. Phys. 45, 477.Sanyal N. K , Yerma D. N. & Dixit L. 1974 Cure. Sci. 48, 508.Schmidt K. H & Muller A 1974 J Mol. Struct 22, 343.Soip II. M. & Smp R. 1966 Acta Chem. Scand. 20, 2698.,Sharma D K , Pandoy A. N (loci R K 1974 Ind. J. Pure Appl. Phys. 12, 455.Tooth L M. & Bates ,T B, 1974 SpectrocJnm Acta BOA 1096.Wilson E. B (,7r). Dcciii.s ,1. C). & Cross P. C 10.15, Molecular Pi7>rrt^ 'oj?<9, MoGraw-HilI Now York.

Intramolecular Force Fields and Vibrational  Amplitudes of some Octahedral Systems

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Intramolecular Force Fields and Vibrational Amplitudes of some Octahedral Systems

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