ASO LKAR & MANDE: INTER-NUCLEAR DISTANCE IN DIATOMIC MOLECULES I I I

and intra~roup diatomi c mo lec ul es of group lA , V A,

V IA and V il A eleme nts. (The data o n ha lides,

cha lcol,'!eni cks a nd homonuclear and intra-group

diato mi c molec u les o f the ele me nts of other groups

are too sca nt y to ohtai n separate pl o ts). The va lu es

of III and C for a ll these plots are given in Tab le I . It

T ahle t - The values o r slore 11/ and inlercerl C I'or the ( 1//':,, )11' versus r" r iot s 1'0 1' sever;ll di atolllic molecu les

Molccule III C

IA halides (,() I ± O. I X 4.] 0 ± O.4.'i

IB h;il id cs .'i.% ± 0.4:1 :1.XX ± 0.2')

11 ;\ h;iI id l'.s () .24 ± (U.'i :UX±(UO

Ili A halides ().7X ± O. l .'i 2.3.'i ± D.2()

11113 halides .'i .(,1 ± O.W ] .:1 1 ±O.27

IVA h;ili tb .'i .7() ± OSi ].74 ± 0 ] 7

V A halidcs ().7.'i ± (l.,) I 2.4] ± O.M

II A c hal co~cll id es 4.7:1 ± 0.4] .'i .ll) ± O.4.'i

lil A ch : il co~c ll i d c s (1.7l) ± O.) () O.XX ± 0 ]]

IV 1\ cha\c(l;.!cllides .'i .7(, ± 0.1 7 I'cll) ± 0.2X

V 1\ c ll<llc(l~ l' lli dcs .'i. XX ± 0 27 l .cl6 ± O.2X

IA IHlIlHlIlIICIL' :1I HU;<) ± (1 .1 <) 4.4] ± O . .'i tJ

V A hOIll(llluclc; lI' (l. ] (' ± 0.]] O.]X ± (U7

V I A hOlllollll c lca r 4 ')] ±O. 11 ] .4(l ± 0.11

V il A hOlllo lluclea r 4 .7') ± O. 12 5.07 ± O.2.'i

;lIlel illtra-),'l'Ollp

h:ts hee ll ohserved that a ll these plots arc CJu ite

s lllooth and do no t e xhihit an y apprec iab le scatter.

W e l1l:t y me ntion he re that the va lues of (0,. in the

diatoll1 ic lllolec Ules v iz. Til , LaF, SbF, Sbel , SbBr,

1-11'0, SbTl' are re ported to he uncertain in Re f. I . Ou r plots or ( Ilk.,)''' versus r,. s ugge st that these val ues arc reasonah ly co rrect.

From the p lo t ror II A cha lcogenides (Fi g. I ) we

ha ve e stim:tted the va lu e of re for MgS to be

2.:W:WA. The plot for lil A c halcogen ides (F ig . 2)

giw.<.; th e value or r, eqw tl to 1.8567 A for InO and 2.1 R()t) A lor A ISe. The value or r ,. for S iTe comes

o ut to he 2.2627 A frolll the plot ro r IV A

c halcoge llides (Fi ~. 3). The p lot for VA cha lco­genicle s (F ig . 4) g ives the va lue or r .. eCJ ual to 1.7856

A in SbO. The va lli e or r,. for Rh, o btai ned from the

plot for lA homonuclear diatomic molecul e s is

4 . 1448 A (Fig. 5). The value of r,. for She obta illcd from the plot for V A homonucl e:tr d iatomic

mo lec ules (Fi g . 6 ) come s out to hc 2. :'C)C)l)A.

:Lt, chalcoge:1ides

., CaS :J8aS !

MgS

MgOo SrO

..J

c::f8aO i

BeS ..;

0 BeQ

• value of re eS!imated by th8 authors

1.5 2 ~ h. 6 ~: ____ L-----L--------~

1 re (A')

Fig. I - Plot showing v;lri<ltion hetweell the v,illi es "r ( 1//': ,, )'" and r,. ror II A chalco)!,cll iti cs

III A c halcog eni des

.--~;

-; ;

AISe I IE

'70 ~ 14 r' InO .,.- (l)

x c: I 1\10 GaO -'2_ £12:-i s . 85 i - 010 r '1

.:y r BO • value of r~ J B pstimated hy , 6 ~ ____ ~ ______ ~ _____ t~hf __ 2LJ_t h_o,_s_

1 15 2 25

fi),' . 2 - Plot showill),' variat iOIl het wcell the V; ill ll 'S "I ( I lk" ) 1, '

and r,. I'or III A e h<l l c()~e lli dl's

1.\ 2 IND IA .I PURE & A PPL PH YS, VOL ]l), MARCH 2()() I

I';;' chalcogen:des

2' j r, - ----,-------;--- ...,..-----~,

poSe

15

] PbTe ~SnTe

~ .J

I -; i ~ .. ' - Pi ol silo w ill !.: 1': lri :ll io ll hel wce ll rh e values o/" ( 1/kj l ; :l lld I ~ /"o r IV A ch:il co!..'c iliti es

VA chalcoger:ides

u (')

10 114 ~ OJ

:'{:~ i 2 '1 -O r

'/ '- r " ,. I

-- ; ~, 0 ~-

17 i!-' . -l - 1' 101 , IHlIl' ill !..' v: lr iali oll hel wee ll lile values o/" I I ' " ! I I . I ( I lk ,, ) :1 11<1 r ,. lor \ 1\ C 1;1 CO~e ll l ( L'S

II i s s t ~ lt ed il l ReI. I til ;lt til L' va lues 0 1' r" ill 1< ('; IF , l ~ iF , I~ a r, C; ;I() :IIHI I'S <I re unce rt ~lin . O ur p lo ts

rIll ( 1/(.) '" ; 1 ~;li ll , t r " 11 ~~es ( t il ;iI t ilese va lues ;tre

ql lil L' re; I.'()Il;lh iL' .

60 [·----

55 ~

I , ,0 ~-- -- -- ,--2 :3

• Vil lU'e (If ,;, ~s': '''12 t Bi 0,

~"I~a~~~~~

Fi ~.:; - Pi ol s h{)\vi l1 ~ v: lri :ll ioll hCIIVCCllllil' \;tllIl" "1 1111,, I"

,l lI d r" ror 1/\ IWIlHlI lll cicar di :II(Jllli r 1IIIIk c'u ll"

_ Idu,) 0-; 1-_

~~n12t ~ r h\' 1

_ 1__ __ _ ~j~2:._I ~ ~n'~ __ I

2.

r i C'. () - Pl ot SIH1WIIl C' v:l ri ;lli oll heI WCL: r, llil' vaIUL'-. "I '

( 1;"',, )1 1; alld r" /"m V /\ I Hl l1l0 llucicar dialo illi c IIiOIL'l'I il l"

3 Calculation of the Values 01' r" I'rom Holaliol1:iI

Constants

II i s we ll kn ow ll ' til"l (il e rOi ;t ll o n;iI COII SI <lIII Ii ilnd (il l' int er- nuc lcil r di st"ll cL' r , ;trL' IL'I; ltL'd h\ Illl '

I'ollow in g ex press io n :

. . ( -l )

w ilere II and (' ha ve the i r usual sig llil'i ca ll l 'L', Us i n!-,

the ,,;dues 01' 13,. g i ven ill Re r, I , we h;I\T e;lrli cr

sllow ll '7 [Ilat the diltil o n ro l ;l t io lL tl C{) ll SI;t1l1 n 111

d iat o illi c Illo lec u k s C il l 11L' s vs t e lll~ l l i zL' d \\ 1111 Il l l '

he lp u l' e lcc t ro - lle~ati vi ( y valu es (11' the C (1 I I ~ llI lI L' 1l1

;l lO lll ,' . The dependence or ro tal i(1 ll ;lI l'() ll ~ I ; l l lI , nl

d iato illi c hali des' " 0 11 e l ec t m ll e~;il i \ ' lIy C: III h,'

ex pressed hy [Il e eq uali o ll :

ASOLK A R & M AN DE: INTER-NUCLEA R DISTANCE IN DI ATOM IC I'vIOLECU LES III

log /( = II I log ( 6X / P 2 ) + C ... (5)

where 6.X i :-, the c1il l erence in the eleclronegat i vity val li es () f the c()nstituent at o l1l:-'. T hi s equati on is f() lInd to he ' Ippli ea blc to Illo lecules w ith predomi nantl y i o ni~ character. However, for intra ­group and homonuc lear diat omic molecules7

, the relationship betwee n f3.. and electTonegat i v ity can be ex pressed as:

I · I [Jx"XI1l C ogIJ,. = fJI og , + W

... (6)

since the eleClronegati vit y equali zati on princ iple ' is appli c dl le for such molecule.\. Ou r work has shown') t hat for /I A ilncl TV 13 chal eogen ides . Eq. (5 ) holds good wherea:-,. for lIl A. TV A and VA chalcogenides . Eq . (6 ) is appli cah le. Th e electro-negat i v ity valu es which we hil \'e substituted in Eqs (5) and (6) are on the scale o f Manele ('{ (".,0.". w hich is based on the

effec ti ve nuclear charge obta ined from X-ray spectroscopi c elata . Accordin g to Mulla/~ . this scale is more reliable and al.so is in good correlation wi th P;1l1i i ng· .\ SC; li l'

In the Ci lSl' of M gS. the value of B,. is es timat ed

frolll th e griIJ1h n f I()g /3,. ve rsus Ing (6.XI p C) for II A

c h , li coge ni cl e~ sho\Vn in Fi g. 7"'. It cOllles out to he () . ~ 1)4 Clll ' . Frolll thi s value o f 13, .. rhe value or r,. I hy lI sing Eq. (4) I comes out to be 2.4()()9 A for MgS . As can be easil y seen, there is a very good agreement hetween the v, Iille or r,. obtained for M gS (2. :; 9:;<) A) rrolll ( 1/ /<,.) 1/\ versus r,. graph for II A

chalcogeni des and the value o f r,. obtained from the value of n, es timat ed by us.

In th e CI:-'C 01' In() ilnel A ISe. the values of B,. arc

es tllllilt eci fmlll log n. versus log (JX AXII/ p2) pl() ts rl lr III !\ chaicogenicies (Fi g. R). T he values o f n,. I'm SiT e ami ShO <I re es tilwileci from silll i lar pl ots for IVA ilnel V A chalcogenides (Figs 9 and 10)

respecti ve ly. The v, liues or /J .. for Rb, and Sb, arc

es tima ted from the pl ot or log /3,. versus log (X I~l' )

fllr IA and V A homonuclea r diatomic molecules (Figs I I and I ~ ) respecti ve ly. The va lues o f r,. calculated frolll the cs tilll ilt ed values or B,. for these

':;\ 1 rir'l ",, 111. Ihl' 'c:llin or Ihl' pOi ll l ' I'm l3eO ~ 1I1d l3eS Oil 1111.;

" r"ph 1I1:I Y ~ 1I' p l' ; II ' di '"l1h ill ~. Tl l is po i lll i s hc in ~ di sc lI ss<.:d ill /\ ppl' lId i \ 2.

molecu les using Eq. (4 ) anel th e vidl1 e .~ of r

determined from ( 1Ik ,,)' /\ ve rsus r .. p l o t~ for these

JS

1

' - ---,- ~-~ -! • value 8T 8e

, est 'mated hy beG I

o 1

Bp S U iv:(jO, ~[-3", I l t he authors R"O o \,l

~ I rc g' - 0 .4 I BilO S~aO i

-0.9 ~ I i

·1.I,L---1 - 35 - 3

2 l~a S

IvlgS

1 _ _ -1-_

- 2.5 2

loy (il 'K ,' .1/ 1

I

__ I - 1. '.1 - I

F i ~ . 7 - Plot showing vari al ion hetween Ihe \'~ il li cs or 10" II.. and log (c,x / p C) ror II A ch alc()~<.:nid c,

O.5 ~ , • v a lue of Or. estimated by

o .... 1 r- t he authors . I ",

(!)

cn - f) L ,... -_. I

- 0'1 l_

_l~L _ .1 - 3.5 - 3

ll t/\ chak ogl?nides

I

-25 ,

- .' .-1 c,

Fig. X -- Plot silow in t! variation between Ihe va l l1 e~ Ill'

log 11 .. and log (J X!l X /I / p C ) for II 1/\ cilalcot!e nili L"

---,----, -

: I."

Fig. lJ- Pi ol showin t! var i;lli ll n hL' I \VL'L' nlhl ' ,,; li li L'S II I

lot! 11,. and lot!' (JX .IXfl / P 2 ) ro r I V /\ c h ~ I1 C () .c' C llid l · '

1.14 IND IAN J PURE & APPL PHY S. VOL 3Y. MARCH 2()() I

') I , _~ --, ---,.-----. - 1-~-~--~

I • '1 ,,1,..:(.> 0 1 fI"

, 'il

n::~1 'rno1f..:-; ~ I t'- j . rtU, .... o .-

1," .

~ ;' - OJ, I

I

09

____ . l

B I '.:. r

r' jO 0

, ~ I

1 ._, ____ J

-1

r'i).! . l(l - Pint show in).! v:lr i:l ti ()n hc tIVccnthe val ucs o r log 11,.

:Ind I()).! ( J X.I x" / fI :' ) ror v 1\ cha lc()gcn ides

llloiL:c ul es arc g ive n ill T ,th iL: 2. As can be seen, III

th c case of M gS. InO . ShU ;Ind Sh: there is a c lose 'lgn.:ement bet ween the va lues or r ,. determi ned by

th e,~e two dilTerent meth ods. In the case of Rb"

A ISe and SiTe the values or r,. determined by these

t \vo methods are not rar rrom each other. W e may

menti on here th ;lt in these molecules, except ror

In O. th e va lues or the reduced mass p are reported

to he uncertain ' . Thc dillerences in the values o f r,. oht 'lined hy the two meth ods Illay he attributed to

~ () lll l' l'x tent t o till' uncc rtaint y in the values or p

w hi ch mi ght h<l ve been relkcted in the es timateci

\' ,ilu e .~ or IJ ,. ;lnc! th ose o r k", w hic h in turn may arfec t the v;ilues or r, ..

"

..... - I I ' - -

-] i i I

,'1-, f

If. '1omonucle2r d 2.tonric 1T'·o~ecules

-l

j J I

~I --j -2 o

h~ . II - 1)101 sh" Wl ll g ": lr i ;l t io ll he t WCC Il llt L: valuL:s of l(l ~ Ii ,. :11 )(1 log II) P ' ) I'm 11\ IHl IlIOlll IC/c:lr d ia to illi c

II III IL' l' lI IL' s

-._-r--

I

·-1

-I I

-05 r-

Ol o

- 1 I

J ~' I Sh2

-1_: [... B, ~,;::::i,~O ;:- ~I the authors - 2.5 __ ---L __ ~ __ ___ . ......i __ _

-4 -3 - 2 " tog I>: I/i \

F ig. 12 - P in t showi 11 1,'. v: lriati o ll he l w eL: 11 t h I' \' ;tili l's " I'

log If., and log (X/p 2) "m V!\ hOlllonuc/t: ,II' di:li!)lll i t'

lllo lecul L:s

The spectroscopi call y determineci experil1l L: lll al

values of r" are usuall y reporteci in literature ti P to the acc uracy of 10-5 to I( )"I A units. For compa rin ~ the values of r,. deri ved rrom the es ti mated va lttcs o r

Tah le 2 - V alu es or thc in tc r-nll c lear di stallce I ,. L': IiL'II I,lIeti

1·l'() mthe I'()t' lt ioll .tI C() I)st:lIlt s Ii .. cs ti l1):IIl'd I1\' II'.

and Ihose rrn m the rm ce con stants Mole- /J \, 1',. 1'1'11 11) I',. rrom '\ \'c r :I~I'

clil e (in Clll · ') HI' ( / 11- ,, )1 11 v (lI ll('

( ill A) vc rSl lS 111'1',.

1',. plol r'll,)) ( in A) CIlI II Il)I) '

.\ :lI1d ~

l in A ) MgS 0 2 1:l4 2.4()()() 2.:l<,n() :UII

InO 0 :l2l).'i I .<)OXX I. X.'i(17 1)-:1)

A ISe o l .'i 1:1 2.:1.'iO.'i 2. I X()<J 2 .27

SiTe O. 166:l 2. 0()X4 2.2627 2. 1)-\

ShO O.:l)-\('() 1.7.'iX:I 1.7)-\:) (, I 77

Rh2 ()202 1 4.4:1:24 4 .1 44)-\ -1. 21)

Sh , 0 .0460 2.4 .'i:l1l 2. :1 ()<)() 2 ~ .'

fo rce constant k" w ith th ose nbt,l iI1C<! rl'()1ll (l l ir

es timated va lues or the rotati onal cnlls t,tnt IJ, .. \V('

ha ve g iven in Tab le 2 th e values o r r,. up \I ) r()1II'

pl aces after the dec ill1,ti po inl in tlll'lir.<;J ill sl :l nL'c.

Howevel', since the values or k" ,tre c;ri cuLltL:d rr()1ll

Eq. (2) and the ex perimental va lues o r ( I) . rL:pn rt eci ill

the literature are lip to ri ve pbces arrel' th l' tkc i lll ;ri

po int , it w as fe lt Ing ic; ri 10 li m i t the v,il lIt' .s (l i' S I(l j1I '

II I and intercept C or the ( Ilk,,) '" ve rsu~ r. I ) I () I ~ ('n ly

up tn two places art er th L: dec illlal P(J 11l1. I-:() I' Ihi .s re; tsnn, the ave rage va ltl cs or r,. su~gL: ,s l l'cI 11 \' I I.S

ASOLKA R & MANDE: INTER-NUCLEAR DlSTANCE IN DI ATOMI C MOLECU LES I l."

given in TahiL: 2. arc approx imated up to two places afler the decima l poinl . They are computed by considerin g Ihe ave rage or th e valu es or r,. obtained for each llloiL:culc hy the IWO dillerent meth ods and then rounciin g oil ihe re:;ult s up to two places aner Ihe dec im:ll poin t. II m,IY he menti oned that for most phys ica l a III I cheilli ca l wo rk , Ihi s Illuch accur;lcy (one hundred lh or:ln A) is quite suffi c ient.

4 Conclusioll

T he va lues or the inter-nu clea r distance r , in d iatomic molecules ca n be ca lculated very simply rrolll two Ill et h od~. invok ing force constants and rOI, lli onal C(l l1 s l a n l.~. which y ield matching resull .s. Thi s wo rt-. h rin g~ oul Ihe need or ex perimenl al deler ll1i n;lli oll of r,. in Ihese molecules.

Acknowled).!clllcnt

One o f thc authors (VGA), is very grateful to the Uni versity G rants CO ll1ll1i ss ion, New Delhi, for award ing hl'1 a research fell owship under the Co llege Facu lty Development Programme.

Refercnccs

r11111'/'i(,(/1I IIISlil/ll, III' I '/tl's i, 's /tlllldhoo/;. (McG r;11V Il ill I \'H)~ e,} I . . ; ,.1 cd. 1'17~. pp. 7- 11-:-1 .

(H( ' /tlllld"""k {II I'ill'IfI isi IT {({Id 1,/n·si('s. (eRC I>rcs,. USA). 77 ' h edi li on. 1')%-'17. pp. 1)- 15 .

1 Badger R rv1. .I (flt'lIl e h.".\'. 2 ( 11)]4 ) 12X: :1 ( 11):\5) 71 ().

-1 Her/,herg (;. Mol(,(,III({/' sll('('lm ({IIII /l/olcc llia /' .\' lmcIII/'c - l :

S,,!'elm o(di{/ltllllit' IIltllt'I· III!'s. (I) V,III Noslrand & Co Inc. New Yor~ l. 11)5().

S Mande C 8.: Asolbr V C. I lldillll .I eliI'/' AIII II PIn'.\'. :14 ( 19%)-17 .

(, /\ so l~ ; 11 V c; & ~ll andc C. III di{/l I .I I 'llI'/' A""I Pin'.\'. 15 ( 1<)117) .,:"1)

7 M;ll ld l' C 8: A,o lbr V C. I 'u)(' NOI Amd Sci ' lldill. (,') (f\ )

II I I'JI)I!) ~ .;7.

I-: Sanderson R T. ('f1t 'lIliml Iit'/'iodieill'. (V ;I ll Nosl rand Rei nhold Co), I'J(,() . p .. '7 .

'i Asolbr V (; & M ;11ldc C. I'u)(' Nal Amd Sci IlIliio (under puhlie<lIi (ln l.

III Mandl' C. J)CS hllll l ~h P & Deshlllukh P . .I Ph I'S II . 10 ( 11!77 ) 2:2')';

II M;ll1dl' C. Ch:lllI}padhY<lv<I S. Desh lllukh P t'l rr/ ..

l'IW l/lIl ltl . . ''i I I I)')() I ~"i7 .

12 MuILI), .1. '\1 1/1('111/,, ' tlllel hOIlr/illg. (S pringer-Verl"g. lkrlin. 1 - l c id c lhn.~1. 1')>-1 7. p. (, .

Appcndi x I

The relationship hetwccn r"

and k"

It is well known that the t'orl'l' (1 1 :l ttr:lcli(1I1

between two c harge~ (j l and (h Gin he expressed :1' :

. (A I I )

where r,. is the equilibriulll inter-nll c le,lr c.li stan cl' between the two charges.

By the definiti on o f the foree constant

F=-k"r,. . .. ( /\I. ~I

T hus.

k" ex: Fir,. (A I 3)

substitutin g F frolll Eq. (A 1.1) into Elf. (A 1.3) Wl'

get:

k" ex: (j I (/ ~ I r,. I

.'. k" ex: I / r,.; , . . t 1\ I .-11

thereby

( 1/ k.,) 11\ ex: r,.

( 1Ik,, )"\ = 111 r,. + C

w here 11/ and C have their usua l signifi C< lnce.

Appcndix 2

W e have ob~e r vecl t 11<11 I'm I Ill' 11,\ chalcogenides, equati on:

log B,. = 11/ log (,0,X / p C) + C (/\ :2. I )

is applicabl e; indicat ing that the it A ch,tl c()~e ni d l'~

ex hi bit predominantl y ionic charaCIC!'. H owe vc r. t il l' points for BeO and BeS ex hi hil SO Ill l' sC< II'1l' r t'rPl ll the curve (Fig. 7) . Thi s has led LI S t() check ", il l, til n the bonding scheme in these t\v(j 11l(jIc Cllil'~ j ,

covalent.

13fl INDIAN J PURE & APPL PHYS, VOL 39, MARCH 200 I

We decided to check whether the values of log

(~X I\X/I / p 2 ) for BeO and BeS (shown by ~ in

the graph) get accommodated well on the curve . As can be seen from Fig. 7, whil e the value of log

(~ XAX fI / p .2) for BeS falls very well on the

graph, the point for BeO shows much less scarte r now Thus, it can be assumed that among the IIA chalcogenides, these two molecules seem to exhihit larger covalent character.