amos, molecular physics 1978

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Molecular Physics

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Molecular quadrupole moments,

magnetizability, nuclear magnetic shielding

and spin-rotation tensors of CO2, OCS and

CS2

Roger D. Amos

a

& Maurice R. Battaglia

a

aUniversity Chemical Laboratory, Lensfield Road, Cambridge, CB2 1EW,

U.K.

Available online: 23 Aug 2006

To cite this article: Roger D. Amos & Maurice R. Battaglia (1978): Molecular quadrupole moments,

magnetizability, nuclear magnetic shielding and spin-rotation tensors of CO2, OCS and CS2 , Molecular

Physics, 36:5, 1517-1527

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MOLECULARPHYSICS,1978, VOL. 36, No. 5, 1517-1527

M o l e c u l a r q u a d r u p o l e m o m e n t s , m a g n e t i z a b i l i t y ,n u c l e a r m a g n e t i c s h i e l d i n g a n d s p in - ro t at io n t e n s o r s

o f C 0 2 , O C S a n d C S 2by ROGER D. AMOS and MAURICE R. BATTAGLIA

University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, U.K.(Received 20J a n u a r y 1978)

Ab ini t io calculations have been made of molecular quadrupole moments,the diamagnetic part of the magnetizability and nuclear shielding tensors,and electric field gradients in CO2, OCS and CS2. By combining thesecalculated properties with experimental data, a full analysis of the magnetiza-bility and nuclear magnetic shielding tensors has been obtained for these mole-cules.

1. INTRODUCTIONThe electric moments of molecules provide valuable information about their

ground state charge distribution, and the interaction between molecules in con-densed systems [l]. Although the dipole moments of most simple moleculesare known with great precision [2], there is a paucity of reliable data, experimentalor ab i n i t i o , for the quadrupole moments, 0, of non-dipolar molecules [1, 3].The electronic second moments are comparatively easily evaluated by ab i n l t i otechniques and are simply related to the quadrupole moment and to the dia-magnetic part of the magnetizability tensor Xd. The total magnetizabil ity Xcan be determined by combining Xa with the paramagnetic contribution Xpwhich may be obtained from the rotational g factors [4]. The nuclear magneticshielding tensor g, which is related to the N.M.R. chemical shift, has a dia-magnetic component ga which is readily obtained by ab i n i t i o calculation. Theparamagnetic component a p can be related to the spin-rotat ion tensor C [4-].If the field-gradients produced by the non-spherical electronic charge distribu-tion can be calculated, nuclear quadrupole moments can be found from thenuclear quadrupole coupling constants (e2 Qq) or v i c e -v e r sa [5]. We haveperformed ab i n i t i o MCSCF calculations of 0, Xa, a a and the electric field-gradients for CO2, OCS and CS 2. Using literature values of g, 13C chemicalshifts and nuclear quadrupole moments, we have been able to determine Xp,gP, C and ez Qq for these molecules. The calculated properties are in goodagreement with experimental data.

2. PREVIOUSab i n i t i o STUDIESAs might be expected the most studied of these three molecules is carbon

dioxide. There have been several calculations of the quadrupole momen t ofCO 2 [6-10], the most accurate of which is that by England e t a l . [10] whoM.P. 5 E


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1518 Roger D. Amos and Maur ice R. Battagliaobtained 0 = - 4 . 5 10 -26 e.s.u, using a CI wavefunction. The diamagneticpart of the magnet izability of CO 2 has been calculated by Snyder and Basch [7]and Fischer and Ke mmey [9], thou gh the value for X a quoted in [9] seems tobe in error. McLea n and Yoshimine [11, 12], using an accurate Har tree-Fo ckwavefunction, calculated a dipole moment of 0.985 debye for OCS (-OCS and a quadrupole moment, relative to the cent re of mass, of - 1.48 10 -26 e.s.u.For carbon disulphide Fischer and Kemmey [9] have calculated the quadrupolemome nt, 0 = - 0.818 10 -26 e.s.u., and the diamagnetic part of the magnetiza-bility though, as with CO2, the value quoted for X a seems to be in error.

3. PRESENTab in i t i o RESULTSThe wavefunctions used are of the type called ' pair-replacement MCSCF '

[13], and consist of a relatively small number of configurations obtained bymaking double excitations from the Hartr ee-Foc k fun cti on; with MC SC Fwavefunctions, unlike CI calculations, it is not necessary to include singleexcitations tO achieve accurate values of molecular properties [43]. Only thevalence shell molecular orbitals, corresponding to the cr and 7r bonds in eachmolecule, are correlated. No promotions from the core orbitals are included inthe wavefunction. The usefulness of this type of wavefunction for the calcula-tion of molecular properties is demonstrated in a recent study of hydrogenfluoride [14]. The basis sets used consist of the standard D unn ing [15] 5s3pset of contracted gaussians on carbon and oxygen, and a 5s3p contraction ofVeillard's [16] basis on sulphur. These are augmente d with a set of d functions(ST O-2 G) on each atom. The exponents used for the d functions, which havebeen chosen to minimize the energy, are 1.8 for carbon, 2.5 for oxygen and 2-1for sulphur.The results for various properties of CO2, OCS and CS 2 calculated with theMC SC F wavefunctions are shown in table 1. The b ond lengths used in thesecalculations are: CO2, r c ~ OCS, r c ~ r c s = 1 . 5 5 8 A ;CS2, rCS=l. 554 A. Second moments, magnetizabilities and quadrupolemoments are calculated relative to the centre of mass for each molecule. Noprevious ab in i t i o estimates are available for the majority of these properties.The accuracy of the present calculations should be greater than all previous[6-12] studies, with the exception of the calculation of the quadrupole momentof CO 2 by England e t a l . [10]. An indication of the accuracy of the resultsmay be obtained from the variation of the calculated properties with the sizeof basis set, and type of calculation. In table 2, some representative propertiesof CO 2 are shown, calculated using restricted Har tree-Fock wavefunctionsinstead of MCSCF, and using a reduced basis set with only 5s3p gaussians oneach atom instead of the full 5s3pld basis. The component of the nuclearmagnetic shielding quoted in table 2 shows hardly any variation, and this istrue for all component s of the C, O and S diamagnetic shielding tensors in CO2,OCS and CS 2. Consequently it seems certain that, for the equilibrium geometry,the diamagnetic contributions to the nuclear magnetic shielding tensors havebeen dete rmined with a high degree of precision. On the other hand, thefield gradient at a nucleus (q) is one of the more difficult properties to calculateaccurately. It is apparent from the example in table 2 that this quanti ty variessignificantly, and it is unlikely that the field gradients have been calculated to


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P r o pe rt ie s o f C 0 2 , O C S a n d C S 2

Table 1. Ab ini t io MCSCF properties of COs, OCS and CSs.

1519

COs OCS CSsE - 187"7592 - 510"3498 - 832"8741(x s) 3"077 4"905 6-607(z 2) 25"604 46'765 83"442

3~ZNrN 2 21 "574 41 "574 77"282Xzza -4 3"36 - 69"14 - 93"09Xxxd - 202'05 - 364"03 - 634"38Ozz -4. 57 - 1.36 2"10((rzza)c 284"22 286"69 290"54(axxa)c 439"18 485 "56 533 "41(~zzd)O 414"67 415"09 - -(axx a)o 506"49 540"16 - -(Ozzd)S - - 1061 "52 1061 "48(axxa)s - - 1139"90 1171 "07(q)c - 3"618 -4 "3 30 - 3"990(q)o 4.994 1.926 - -(q)s - - 12.307 6.984

Uni ts : energies in a.u. (1 a.u.~ 4"3598 1 x 10-18joule) ; second mom ent s in 10 -s~ m s ;magnet izabil ities in 10 -s9 joule tesla -s ; quad rupo le mom ent s i n 10 -s6 e.s.u. (10 -s6 e.s .u .~3"336 x 10 4 C m s) ; shie ldings in p.p.m. ; red uce d field gra dients i n 103o m -3.

Tabl e 2. Some selected properties of COs showing the variation of the calculated propertywith size of basis set and type of calculation.SCF 5s3p MCS CF 5s3p SCF 5s3pld MCS CF 5s3pld

(x 2) 3'082 3"091 3"074 3"077(z 2) 26"193 26"041 25"697 25'604(ozza)o 415"34 414"89 414"96 414"67(q)o 6"37 5"81 5"27 4"99Units as in table 1.

bet ter th an 10 per cent , except possibl y for the f ield grad ient at the sulp hurnuclei which , bei ng of larger magni tude, has g reater re la t ive accuracy.

The second mom ent s (x 2 ) and (z 2 ) show comparat ive ly l i tt le var ia t ionwith the type of calculat ion, part i cular ly in the case of (x2). Thi s behav iouralso appl ies to OCS and CS 2 and i t seems probable that the sec ond mo ment s ,fo r the equ i l i b r iu m geometry , are accurate to about 89 per cent. Thi s impliesthat the com pone nts of the d iamagnet iz ab i l i ty

an d

e 2 (1 )

wil l also be d ete rm ine d to abou t 1 per cent , or eve n better in the case of Xz~d.The re i s, however , considerab l y greater u ncer ta in ty associa ted wi th the

5E2

82X,, d = ~za = 2m


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1 52 0 R o g e r D . A m o s a n d M a u r i c e R . B a t t a g li aq u a d r u p o l e m o m e n t w h i c h , f o r a l i n e a r m o l e c u l e , i s

O zz --- Ie l[ ~ Z N r N 2 - - (< z2 ) - -


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P r o p e rt ie s o f C O s , O C S a n d C S 2 1521T h e d i a m a g n e t i c t e r m (X a ) d e p e n d s o n l y o n t h e g r o u n d s t at e w a v e f u n c t i o n ,a n d i s a lw a y s n e g a t i v e , w h i l e t h e p o s i t i v e p a r a m a g n e t i c c o n t r i b u t i o n (X p )r e q u i r e s a s u m m a t i o n o v e r a ll e x c i t e d s t a te s . F o r m o s t c l o se d s h e ll m o l e c u l e st h e d i a m a g n e t i c t e r m d o m i n a t e s . F o r a l i n e a r m o l e c u l e e q u a t i o n ( 4 ) s i m p l i f i e sc o n s i d e r a b l y as t h e r e a r e o n l y t w o i n d e p e n d e n t c o m p o n e n t s o f t h e d i a m a g n e t i cp a r t , e q u a t i o n s ( 1 ) a n d ( 2) , a n d o n l y o n e i n d e p e n d e n t c o m p o n e n t o f t h e p a r a -m a g n e t i c t e r m I


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1522 Roger D. Amos and Maur ice R. BattagliaBuckingham et al . have measured AX for CO 2, - 10 .4+0 .5 [20, 21], andCS2, -28-5 + 0.4 10 -~9 JT -2 [20] from the gas phase Co tton -Mou ton effect.

Pure liquid and dilute solution Cotton-Mouton effect measurements yieldAX =- 2 4+ 2 and A X= -2 7 +3 -2 respectively [22, 23] for CS2.From these values the experimental diamagnetic anisotropies are

CO2 AXd = 158-2 + 0.5 10 -29 JT -2and CS2 AXa = 541 + 2 10 -29 JT -2.It can be seen from table 3 that our calculated values of AX and AXa for CO~and CS 2 are also in good agreement with experimental data. The experimentalmean magnetizabilities 2 are [24] -3 4- 0 (CO2), -53-8 (OCS) and -7 0.1 10 -29 JT -2 (CS2). Considering the level of agreement between calculated andobserved AX and AXd we would expect that our calculated (table 3) meansusceptibilities are accurate to about 1-2 per cent. The 10 per cent difference in2 for OCS is surprisingly large. However, we note that OCS often containstraces of oxygen [25] and that the presence of as little as 0.2 per cent para-magnetic oxygen could explain this discrepancy.The general trends within this series of molecules, i.e. the twofold increasein IX ,a[ and the threefold increase in I x l l , are easily explained. UsingHartree-Fock wavefunctions Malli and Froese [26] have calculated (89 2) forisolated C, O and S atoms to be 1.043 A.2, 1.288 )k2 and 2-724 A 2 respectively.If the crude assumption is made that the electron density of the molecule is justthe sum of the electron densities of the constituent atoms, and also that theatoms are spherical, i.e. (x ~) = (y 2 ) = (z 2) for each atom, then simply addingthe a t o m i c second mome nts as appropriate produces values for (x 2) and (z 2)in the molecules which are in error by only a few per cent. (Thi s is of course thebasis of various semi-empirical schemes [29, 30].) Thus the increase in X, aand X:_a from CO s to CS 2 is due almost entirely to the greater size of the sulphuratom, and, in the case of X a, to the result ing increase in the bond lengths.The diamagnetic contribution to the magnetic anisotropy AXa is proportional to((z ~ ) - (x2)). We see from table 1 that

f z 2 ) - ( x 2 ) ~ ~ Z N r N 2,NSO that the threefold increase in AXa is also simply explained in terms of theincrease in bond lengths and increased number of electrons on going from COsto CS~.To explain the increase in X.p (and hence AX) it is tempting to interpretequation (5) qualitatively, that is, in terms of the relative energies of low lyingunoccupied rr orbitals. However, this approach is known to be dubious in somecases [27], and a rigorous explanation of the increase in X p would require adetailed examination of the transition angular momentum matrix elements forthese molecules.

5. MOLECULARQUADRUPOLE MOMENTSFor a linear molecule there is only one independent component of the

quadrupole moment, Ozz which is given by equation (3). For a dipolar molecule0 is dependent upon the choice of origin. Most experimental determinations


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Proper ties of C02, O C S and C S z 1 5 2 3a r e r e f e r r e d t o t h e c e n t r e o f m a s s , t h o u g h f o r s o m e e x p e r i m e n t s a d i f f e r e n tc h o i c e o f o r i g in is r e q u i r e d [ 39 ]. A l l n u c l e a r a n d e l e c t ro n i c m o m e n t s q u o t e dh e r e ar e r e l at i v e t o t h e c e n t r e o f m a s s . B e c a u s e t h e q u a d r u p o l e m o m e n t is t h ed i f f e re n c e b e t w e e n t e r m s o f n e a r l y e q u a l m a g n i t u d e , t h e n u c l e a r c o n t r i b u t i o n ,E Z N r N 2, a n d t h e a n i s o t r o p y i n t h e e l e c tr o n ic s e c o n d m o m e n t s , ( ( z 2 ) - ( x Z )) ,Nt h i s p r o p e r t y i s d i f f i c u l t t o c a l c u l a t e a c c u r a t e l y a n d c a r e is r e q u i r e d e v e n t od e t e r m i n e t h e s i g n o f 0 [9 ]. I t m i g h t b e p r e d i c t e d f r o m e l e c t r o n e g a t i v i t ya r g u m e n t s ( b a s e d o n a n o p p o s i n g d i p o l e m o d e l f o r 0 ) t h a t t h e q u a d r u p o l em o m e n t s o f t h e s e m o l e c u l e s b e c o m e m o r e p o s i t iy e in t h e d i r e c t io n

0=co~< 0=ocs< 0=cs,.H o w e v e r s i n c e o x y g e n a n d s u l p h u r a r e in f a c t n e g a t i v e l y c h a r g e d i n a ll t h r e em o l e c u l e s , t h is s i m p l e m o d e l w o u l d p r e d i c t t h e w r o n g s i g n f o r C S 2.Tab le 4. Com par i son o f the M C SC F second mo men t s and those ob ta ined f rom a spher ica latom (SA) mo del ( see text ) , in u ni ts of 10 -2o m ~.

CO2 OC S CS2 sA 3.374 5.054 6.734(z ~> 25"604 46"765 83"442

sA 24"948 46"624 84"014E Z N r N 2 21"574 41"574 77"282

-(x2) sA -0"2 97 -0"1 49 -0"1 27


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1524 Roger D. Amos and Maur ice R. Battagliagradient birefringence studies of CO2, Buckingham e t a l . [40] have determined0z z= -4 .3 +0 . 2 -2. e.s.u. The quadrupole moment of OCS is knownaccurately, 0~, =- 0. 79 + 0.01 10 -26 e.s.u., from molecular beam studies [19],and considering the difficulties in calculating a moment as small as this our valueis in reasonable agreement with the experimental result. For CS 2 the quadru-pole moment is much less accurately known, and literature values, both a bi n i t i o and experimental [3, 9], cannot agree on either the sign or the magnitudeof 0. The quadrupole moment can be related to other molecular properties,

0 = - [ e [ g 1 7 7 4 m A X . (7)M p } e lSince g and I are known accurately, the principal uncerta inty (neglectingvibrational effects) in the quadrupole moment arises from the error in AX.A reasonable estimate of AX for CS2, from the data discussed in w4, is - 28.5 _+1.0 10 -29 JT -2. Thi s corresponds to a quadrupo le mo ment

0= =2 .8 + 0"7 x 10 -26 e.s.u.

6. NUCLEARMAGNETIC SHIELDING TENSORSThe discussion of the nuclear magnetic shielding tensors ~ for these mole-

cules parallels that of the magnetizability tensors. The shielding tensors maybe divided into diamagnetic and paramagnetic components [4]

(% A N = ( ~ % , + (% p P)N ,-/~~ (0[ V riN~ 3 ~ - r i ~ r ~ 10)8 f l 'm ~ i t i N 3

L,~ [k)


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P r o p e r t i e s o f C O s , O C S a n d CS 2 1 5 2 5p a r t i c u l a r l y i n t h e c a s e o f ~ E~a. T h i s i s t o b e e x p e c t e d s i n c e t h e m a j o r c o n t r i b u -t i o n t o 6 a c o m e s f r o m t h e c o r e e l e c t r o n s a t t h a t n u c l e u s . T h e m o r e ti g h t l yb o u n d t h e c o r e t h e le s s w i ll b e th e e f f e c t o f c h e m i c a l e n v i r o n m e n t o n t h e d i a -m a g n e t i c s h i e ld i n g . M a l l i a n d F r o e s e [ 2 8 ] h a v e c a lc u l a t e d ~ f o r t h e i s o l a t ed C ,O a n d S a t o m s to b e 2 6 0 . 7, 3 9 5 . 1 a n d 1 0 5 0. 5 p . p . m , r e s p e c t i v e l y , a n d w e s e ef r o m t a b l e 1 t h a t o a a t t h e s u l p h u r n u c l e u s i s c l o s e st to t h a t f o r t h e i s o l a te d a t o m .A l s o , t h e a n i s o t r o p y ( a F l a - - a d ) i s l e a s t f o r s u l p h u r a n d g r e a t e s t f o r c a r b o nw h i c h h a s t h e m o s t d i s t o r te d c h e m i c a l e n v i r o n m e n t i n t h e s e m o l e c ul e s .

A m o r e c o m p l e t e a n a l y s i s o f t h e n u c l e a r m a g n e t i c s h i e l d i n g t e n s o r s a t t h ec a r b o n n u c l e i c o u l d b e m a d e i f i a C N . M . R . i s o t r o p i c s h i f ts w e r e m e a s u r e d ,r e l a ti v e t o s o m e r e f e r e n c e m o l e c u l e w h o s e absolu te s h i e l d i n g i s k n o w n . T h ea b s o l u t e s h i e l d i n g a t t h e l a C n u c l e u s i n C O c a n b e d e t e r m i n e d [ 3 1 - 3 3 ] f r o m ac o m b i n a t i o n o f e x p e r i m e n t a l a n d ab in i t i o d a t a t o b e + 3 . 1 ( + 1 . 6 ) p . p . m .U s i n g l s C c h e m i c a l s h i ft da t a f o r COs [ 33 ], CS~ [ 34 ] and OC S [ 35 ] t oge t he rw i t h o u r M C S C F v a l u e s o f ~ H a n d ~ w e h a v e b e e n a b le t o p r o d u c e a f u lla n a l y s i s o f t h e s h i e l d i n g t e n s o r s i n t h e s e m o l e c u l e s , c f . t a b l e 5. A l s o s h o w n i nt h i s t a b l e is t h e s p i n - r o t a t i o n c o n s t a n t C w h i c h i s s i m p l y r e l a t e d t o e l p,

M p C 1 7 7 ~ ~ Y Z K ( 1 2 )m gN h2 8rrm K~ N rKN'

w h e r e g N i s t h e n u c l e a r g - f a c t o r , o f t h e N t h n u c l e u s , a n d r K i i s t h e d i s t a n c ef r o m t h e K t h n u c l e u s t o t h e s h i e l d e d n u c l e u s .

Tab le 5 . An a ly s is o f n u c lea r m ag n e t i c sh ie ld in g t en so r s an d sp in - r o t a t io n co n s tan t s f o rth e ca r b o n n u c leus in C O2 , OC S a n d C S ~, o b ta in ed u s in g MC SC F v a lu es f o r 6 aan d e x p e r im en ta l i so t r o p ic sh i e ld in g , ~ , i n p .p .m .

C 0 2 O C S C S ~60"9 31 "2 - 8"4oa 387.5 419"3 452"4

~ P - 326"6 - 388"1 - 460.8a a 284"2 286"7 290"5o ct 439"2 485"6 533"4o i~P 0 0 0al p -48 9" 9 - 582"2 - 691 "2o, 284"2 286"7 290"5oi - 50"7 -9 6" 6 - 157"8Ao~ 489"9 582"2 691 "2Aoa -- 155"0 -- 198"9 -- 242"9Ao 334"9 383"3 448"3C (k H z) 5"30 + 0"04 3'16 + 0"03 2"01 + 0"02

F r o m m o l e c u l ar b e a m s t ud i es o f O C S d e L e e u w a n d D y m a n u s [ 19 ] h a v em e a s u r e d A a = 3 72_+ 4 2 p . p . m , a n d C . = 3 .1 __ 0 .2 k H z . P i n e s et a l . [ 3 6 ] h a v ec a lc u la t ed A a = 4 2 5 + _ 1 6 p . p . m . f r o m N . M . R . s t ud i es of s o l id C S2 . F r o mt e m p e r a t u r e a n d f i e ld d e p e n d e n c e s t u d i e s o f t h e s p i n - l a t t ic e r e l a x a t i o n in li q u i dC S 2 S p i e s s et a l . [ 3 7] , u s i n g t h e p o i n t c h a r g e a p p r o x i m a t i o n [ 29 ] f o r a d, c a lc u -l at ed A a = 4 3 8 _ _ 4 4 p . p . m . a n d C ( T h e v a l u e q u o te d b y


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1526 Roger D. Amos and Maur ice R. BattagliaSpiess e t a l . has been divided by 27r to facilitate comparison with our results.)Our calculated results are in good agreement with these experimental values.Reinartz and Dymanus [38] have measured C for the (quadrupolar) aaSnucleus in OCS. Using this data to determine CrxV ( -408 p.p.m. ) we calculate,by adding our MC SC F values of a d,

Ae=329 + 18 p.p.m.5 = 842 + 12 p.p.m.

7. NUCLEARQUADRUPOLE COUPLING CONSTANTSA nucleus with spin I >i 1 will have a quadrupole moment which can interact

with the electric field gradient at that nucleus, producing effects which can beseen in the hyperfine structure of the microwave spectrum, or in N.M.R./N.Q.R. experiments [5]. The calculated values of the reduced electric fieldgradients (q) at the C, O and S nuclei in CO2, OCS and CS 2 are given in table 1.These field gradients may be used to calculate the nuclear quadrupole couplingconstants ( e e O q ) provided values are available for the nuclear quadrupolemome nt Q. For the 170 nucleus the quadrupole moment is known accurately[41], = Q- 0.0263 b (b = barn = 10 -2s mS). By combining the experimental valuefor the a3S nuclear quadrupole coupling constant in OCS [38] with our calculatedvalue of the field gradient, the quadrupole moment of a3S is deduced to be-0 .0 68 b. This result is probably slightly more accurate than a previousestimate, -0.063 b, which was derived by a similar method [42] but using aHar tree-Fock calculation of the field gradient. Using our value for the asSquadrupole moment, and the value of -0-0263 for 170, the nuclear quadrupolecoupling cons tants in CO 2 and CS 2 are pred icted to be 4.6 MH z and 16.5 MHrespectively. Unfortunatel y there is no stable isotope of carbon with 1/> 1,the 11C nucleus has a quadrupole moment, + 0.031 b, but is radioactive and anunsuitable candidate for experiments.

Financial support for this research from the Science Research Council, andhelpful discussions with Professor A. D. Buckingham are gratefully acknow-ledged.N o t e a d de d in p r o o f . - - W e would like to thank Professor W. H. Flygare fordrawing our attention to a microwave Zeeman study of OCS and OCSe [44]

in which similar conclusions are drawn concerning the failure of the point-charge model for the quadrupole moments in these molecules.

REFERENCES[1] BUCKINGHAM, A . D ., 1970, Physical Chemistry : An Advanced Treatise, Vol. IV,edited by H. Eyring, D. Henderson and W. Jost (Academic Press).[2] McCLELLAN,A. L. , 1974, Tables of Experimental Dipole Moments (Rahara).[3] STOGRYN,D. E., and STOGRYN,A. P., 1966, Molec. Phys. , 11, 371.[4] (a) RAMSEY, N. F., 1956, Molecular Beams (Oxford University Press) ; (b) FLYGARE,W. H., 1974, Chem. Rev. , 74, 653.[5] LUCKEN,E. A. C., 1969, Nuclear Quadrupole Coupling Constants (Academic Press).[6] MCLEAN,A. D., 1963,J. chem. Phys . , 38, 1347.[7] SNYDER, L. C., and BASCH, H., 1972, Molecular Wavefunctions an d Properties (Wiley-Interscience).


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Proper ties of C02, O C S and CS2 1527[8] VECULIC,M., OHRN, Y., and SABIN, J., 1973, y. chem. Phys., $9, 3003.[9] FISCHER, C. R., an d KEMMEY, P. J ., 1971 , Molec . Phys . , 22, 1133.[10] ENGLAND, W . B., ROSENBERG, B. J ., FORTUNE, P. J., an d W AH L, A. C., 1976, J . chem.Phys . , 65, 684.

[11] YOSHIMINE,M., and McLEAN, A. D. , 1967 , Int . J . quant. Chem., IS, 313 .[12] McLEAN , A. D., and YOSHIMINE, M ., 1967, J. chem. Phys., 46, 3682.[13] SAUNDERS,V. R. , and GUEST, M . F . , 1974 , At las Sy m po siu m No. 4 , 119.[14] AMOS, R. D. , 1978, Molec . Phys . , 35 , 1765.[15] DUNNING, T. H. , 197 t , J . chem. Phys . , 55, 716.[16] VEILLARD,A ., 1968, Theor. chim. Acta, 12, 405.[17] KERN, C. W ., and MATCHA, R. L ., 1968, J. chem. Phys., 49, 2081.[18] CEDERBERG, . W ., ANDERSON, C. M ., an d RAMSEY, N . F., i96 4, Ph ys . Rev . , 136, A960.[19] DE LEEUW, F. H ., an d DYMANUS, A., 1970, Chem. Phys . Le t t . , 7, 288 ; see also a foot-n o te in J. molec. Spectrose., 48, 427.[20] BUCKINGHAM,A. D . , DISCH, R . L . , and BOGAARD, M . P. (unp ubl ish ed data) .[21] BUCKINGHAM,A. D., PRICHARD, W . H ., an d W HIFFEN, D. H ., 1967, Trans. FaradaySoc., 63, 1057.[22] BATTAGLIA,M. R . , 1978 , Chem. Phys . Le t t . , 54 , 124; see also ref . [45] .[23] BATTAGLIA,M . R . , and RITCHIE, G. L . D. , 1977 , J . chem. Soc . , Faraday Trans . H,7 3 , 209.[24] (a) FOEX, G ., 1957, Tables de C onstantes et D onndes Numeriques, Vol . 7 (Masson) .(b ) Handbook of Physics and Ch emistry, 1 9 7 7 , 5 8 th ed i t i o n ( C h em ica l R u b b e r C o m -p an y Pr e ss ) .[25] Ma th eso n Ga s Da ta Bo o k , 1 9 6 6 , 4 th ed i t i o n ( Ma th eso n C o m p an y ) .[26] MA LLI, G ., a nd FROESE, C., 1967, Int . J . quant. C hem., IS, 99 .[27] BATTAGLIA,M . R . , and RITCHIE, G. L . D. , 1976 , Molec . Phys . , 32, 1481.[28] MA LLI, G. , and FROESE, C., 1967, In t . J . quant. Chem. , lS , 95 .[29] FLYGARE,W. H., and GOODISMAN,J., 1968, J . chem. Phys . , 49, 3122.[30] GIERKE,T . D., and FLYGARE, W . H ., 1972, J . Am. chem. Soc . , 94, 7277.[31] OZIER, I., CRAPO, K . M ., an d RAIVlSEY, N . F. , 1968, J . chem. Phys., 49 , 2314.[32] STEVENS, R. M ., an d KARPLUS, M ., 1968, J . chem. Phys . , 49, 1094.[33] JACKOWSKI, K ., an d RAYNES, W . T ., 1977, Molec . Phys . , 34, 465.[34] ETTINGER,R. , BLUME, P., PATTERSON, A ., an d LAUTERBUR, P. C. , 1960, J . chem. Phys . ,33, 1597.[35] BATTAGLIA,M . R . , COX, T . I . , and MADDEN, P. A . ( to be publ ished ) .[36] PINES, A. , RH IM, W. K. , and WAUGH, J. S., 1971, J . chem. Phys . , 54, 5438.[37] SPIESS, H . W ., SCHWEITZER,D. , HAEBERLEN, U ., an d HAUSSER, K . H ., 1971, J . magn .Reson., 5, 101.[38] REINARTZ,J. M . L. J . , a nd DYMANUS, A., 1974, Ch em. Ph ys . Le t t . , 24, 346.[39] BUCKINGHAM,A. D ., an d LONGUET-HIGGINS, -I . C., 1968, Molec . Phys . , 14, 63.[40] BUCKINGHAM,A. D . , DISCH , R . L . , and DUNMUR, D. A. , 1968 , J . Am. chem. Soc . ,9 0 , 3 1 0 4 .[41] (a) KE LLY, H . P., 1969, Ph ys . Rev . , 180, 55. (b) SCHAEFER, H . F. , KLEMM, R. A. ,

and HARRIS, F. E., 1968, Ph ys . Rev . , 176, 49.[42] (a) ROTHENBERG, S., YOUN G, R. H ., SCHAEFER, H . F., 1970, J . Am. chem. Soc . , 92 ,3243. (b) ROTHENBERG, S., a nd SCHAEFER, H . F ., 1970, J . chem. Phys . , 53, 3015.[43] WAHL, A. C . , and DAS, G. , 1977 , Modern Theoretical Chemistry, Vol . 3 , ed i ted byH. F . Sch ae f e r ( P len u m Pr ess ) .[44] SHOEMAKER,R. L., and FLYGARE, W . H ., 1970, Chem. Phys . , Le t t . , 6 , 576.[45] BATTAGLIA,M . R . , 1978, Non-linear Behaviour of Molecules, Atoms and Ions in Elec-tric, Magnetic or Electromagnetic Fields (Elsevier ). T he co r rec t t rea tme nt o f loca lf ield effec ts leads to Ag = -- 28"5 + 1"0 for CS2.

amos, molecular physics 1978

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