Nuclear Magnetic Resonance Coupling Constants and Electronic Structure in Molecules Thomas J. Venanzi College of New Rochelle New Rochelle, N Y 10801 As is well known, the results obtained from nuclear magnetic resonance (NMR) experiments are invaluable tools in deducing iniormnrim wnccrning the electronic itruvturv t r l ' mdecule, 111. He,idrs rntw>uriny the chemical shift, NlII1 cxperimenta call bt, utdizrd i n determine the s p i ~ ~ - s pct,uin pl& constants between atoms in molecules; constants which can give insights into the electronic structure of the bonds between the two nuclei involved in the coupling. In fact, the sign and magnitude of the coupling constant can give us a of thcelectron density around the given nuclei. T o understand the sensitivity of the coupling constant to the electronic structure of the bond, various theoretical calculations of the coupling constants have been done (2,3,4,5). Theoreticallv. one can decomnose the couolina constant into ..
involved. Even more interesting, the coupling constants are sensitive to the oresence of anv lone airs. A brief descriition of the the& of NMR spin-spin coupling constants will be presented. The nature of the three types of coupling mechanisms contributing to the overall spin-spin coudinr constant is reviewed. In addition, we will present the resilts for two different types of coupling constants in molecules: (1) coupling between two carbon atoms (carbon-carbon coupling), neither of which contains a lone pair of electrons and (2) coupling between a carbon atom and a nitrogen atom (carbon-nitroeen cou~line). one of which contains a lone nan . of electrons. ?he results will demonstrate the sensitivity of the coupling constant to both the electronic character of the bond and the lone pair. They also will illustrate the complex relationship between the coupling constants and the % s character of the bonds and lone pairs. Finally, concluding remarks concerning the relations hi^ between the cou~lina constants and the &ctronic struct& of the coupled atoms will be made. Theorv
Besides the direct magnetic interaction between two s~inni1.anuclei. A andB, the nuclei can interact indirectly as ;resultbf magnetic intbactions between the nuclei and the
144
Journal of Chemical Education
molecular electrons. These so-called indirect nuclear spin-spin counline interactions result from three tvDes of cou~lina . meihanTsms ( 6 ) : (1)The Fermi contact interaction between the spin of the electron and the nuclear spin. In this case the electron spm interacts with the spin on nucleus A. The resulting "perturbed" electron then interacts with the spin of the other nucleus, nucleus B. The reverse process, the interaction of the electron spin with nucleus B etc., also contributes to the contact interaction. If the electron has zero probability at either nucleus, the Fermi contact interaction is zero. Since an s electron has a non-zero probability at the nucleus, the contact term d e ~ e n don s the urohabihtv deusitv of the s electrons. The strengih of this intkraction meascred by the Fermi contact term, Jfg. ( 2 ) The interaction between the magnetic dipole of the spinning nucleus and the magnetic field arising from the orbital motion of the electron. In this case, the magnetic field C ~ U X Y by ~ tht url~iti~l inotim ~11t he t'Itt.tr(m internitc with the magnctlc dipole ~t the >pinning mlcleus A. 'l'he re>ulti~i:! .'I,, --r t~~d ~ e d "elvctnm then inter3,.r, \r ith rhr, rn.~~nclic ~ I I I ~ of the other spinning nucleus, nucleus B. As & the ~ i r m i contact case. the reverse nrocess also contributes to the mechanism. If the average angular momentum of the electron is zero, the magnetic field due to the orbital motion is zero. Thus, the presence of only s electrons (average angular momentum = zero) means that the orbital interaction is zero. The strength of this interaction is measured by the orbital term, .A
A~
~
~
~
~~
~
~
~
J!h
(3) The interaction between the magnetic dipole of the spinning nucleus and the magnetic dipole of the spinning electron.In this case, the magnetic dipole of the electron interacts with the magnetic dipole of the spinning nucleus A. The resulting "perturbed" electron then interacts with the other nucleus, nucleus B. As in the previous two cases, the reverse process also contributes to the interaction. Like the orbital term,this term is also zero for s electron interactions. The strength of this interaction is measured bv the soindipolar t&m, The total coupling constant, which is a measure of the total
a:.
P
interaction, is simply the sum of the three contributions mentioned above, While the total coupling constant can be determined both experimentally and theoretically, the individual contributions can be identified only by theoretical calculations. Early theoretical calculations (2) dealt with coupling constants between hvdroeen atoms or between atoms such as carbon and a neighboring hydrogen atom. Since there are n o p orbitals on the hvdroeen . " atom. the onlv contribution to the total couoline constant would he from thk contact term. Recently, calculations have been done for coupling constants between atoms other than hydrogen ( 3 , 4 , 5 ) One . of the main features of these calculations has been the determination of the "non-contact" terms, J f Band JigDB. The actual calculation of J I B (r = FC, 0,or SD) proceeds through the computation of the following two integrals'
.
u
In relationship (21, h is Planck's constant, N is the number of electrons in the molecule, X ? is the molecular orbital corresponding to the ith electron, X:is the perturbed orbital due to the electronic interaction with nucleus A, and hb represents the interaction operator for nucleus B. The differential d r indicates that the integral is evaluated over three-dimensional space as well as over the spin. Finally, the two integrals in eqn. (2) guarantee that both interaction processes (as explained in the above description of the mechanisms) are taken into account when computing JAR. The molecular orbital X ? is usuallv obtained as a snin orbital appearing in an unperturbed Hartree-Fock determinantal wavefunction (7). The various X? are linear comhinations of the atomic orbitals 4,)
where the C: are determined by optimizing the unperturbed Hartree-Fock energy. The perturbed molecular orhitals X : are obtained as solutions to a "perturbation" equation in h i , the interaction operator for nucleus A. In general, Xi are linear combinations of atomic orbitals,
where the C&are the actual parameters determined from the solutions to the perturbation equation in hi.. Both C t and Cfj are coefficients (or numbers) whose magnitudes yield information about "how much" of a particular atomic orbital 4, is in the particular molecular orbital Xi. The interaction operators h i and h;i are different for each of the coupling mechanisms. Their mathematical form, although quite complicated, contains the various physical parameters corrspoqding to the mechanism of interest. Thus, J i B ,as repesented by the integrals in eqn. (2) reflects, in mathematical form, the physical description of the indirect spin-spin coupling mechanisms mentioned at the beginning of this section. If the forms for X ? and X t . as eiven bv eons. over the atomic orbitals, i.e. C$C!,
S$*hhiih d r
(5)
For the Fermi contact interaction, only integrals involving s orbitals will he non-zero; on the other hand, only integrals involving orbitals other than s orbitals will contrihute to the orbital and spin-dipolar terms.
'
The second integral in eqn. (2)is just the complex conjugate of the first integral.
Although ab initio evaluations of J;n in the present formalism are possible for small system^^ the co;responding evaluation on a semi-empirical level is possible for both small and large systems. (8) In a semi-empirical approach the basic equation for J;LB (see eqn. (2)) is utilized subiect to a series of approximations. One of the most successful semi-empirical methods for the calculation of the spin-spin coupling constants is the INDO (intermediate neglect of differential overlap) approximation. In this semi-empirical theory, the approach is relatively simple and rapidly convergent. The various approximations include: (1) The use of only the atomic orbitals of the valence shell for calculation of the coefficients CPj, C:,, the energy E, and the coupling constants JAB. (2) The overlap hetween two different atomic orbitals ip, and $, (i f j ) , the so-called "differential overlap," is set equal t o zero when normalizing the molecular orbitals XP.Obviously, this approximation is crucial to the determination of the unperturbed coefficients C.: (3) Most two electron integrals are neglected with the exeeptmn of integrals of the following form, S S W ) $;(2) l h z d,(lidj(z) d ~ l d ~ ~ (6.3) and SSipXI) $ 3 ) 1 I r $,(l)ip;(2) ~ d-iid.rz (6b) where i and j represent, in the above integrals, orbitals on the same atom (so-called one-center two-electron integrals), and the indices 1 and 2 refer to the electrons. The second integral (6b) is retained despite the approximation made in (2). This is one reason the term "intermediate neglect of differential overlap" is used to describe this particular method. The values for ( 6 4 and (6b) are found by a set of approximations determined by the types of atoms involved. (4) Finally, one electron integrals involving only one atomic orbital are approximated by atomic data or are treated as least-squares determined data. One-electron integrals involving two different atomie orbitals are usually zero by symmetry. One-electron integrals involving two different orbitals on two different atoms (so-called two-center one~electronintegrals) are assumed proportional to the over la^ between the two orbitals with the ~ r o ~ a r t i o n a l iconstant tv
mi
same atom (one-center one-electron integrals) are retained.
When dealing with Row I1 elements we note that, in the INDO approximation, the only atomic orbitals involved in the calculation of J i g will be the valence 2s and 2p orbitals. The Fermi contact term will he related to one-center one-electron integrals over the valence 2s orbitals since the probability amplitude of the valence 2p orbitalis zero at the nucleus. On theother hand, the orbitaJ k d spin-dipolar terms will depend on the presence of the valence 2p orbitals. In the calculation of the contact term Jig the one-center integral (see eqn. ( 5 ) ) is treated as a value determined by a least-squares fit, while in the calculation of J f Band Jig the one-center one-electron integral is treated as another least-squares determined parameter. Both parameters are obtained by fitting the theoretically determined INDO results to the experimental results of the total coupling constants. Thus, the three contributions to the total coupling constant can he computed using the INDO semi-empirical method. With this scheme coupling constants can be determined between anv two nuclei in a eiven molecule. However, the most interesting nuclear spin-sGin coupling constants are those between two atoms which are directly bonded, the socalled one-bond constants, 'J:$". When INDO calculations are done on various one-bond constants, it is found that the sign and magnitude of the one-bond constant depend on (1) the type of bond involved (single,double, or triple) and ( 2 ) the of lone pairs on the atoms involved. To illustrate these two effects the results of the INDO calculations on different types of bonding situations will he considered. Two general cases will be presented, namely,
aital
(1) Carbon-Carbon coupling, an example of bonding between atoms with no lane pairs, and (2) Carbon~nitrogencoupling, an example of bonding between atoms with one lone pair involved. Volume 59
Number 2
February 1982
145
Relationship Between Coupling Constants and Bonding Structure A. Carbon-Carbon Coupling (CC coupling)
Since the nuclear spin of Carhon-12 is zero, spin-spin cou-
.d i n e constants are r e ~ o r t e dfor Carbon-13. INDO results for
CC coupling constants are numerous ( 3 , 4 , 9 ) and illustrate some of the general relationships between structure and the one-bond coupling constants. In Table 1INDO values for ' J & ' J @ , and @' $I are given for some single, double, and triple bonded systems. In the last column of Table 1the experimental values of ' @ E are ~ given. The correlation between the theoretically determined '@8tu1 and ' J @ is generally very good considering the fact that the one-electron integrals in eqn. (5) are treated as least-squares determined parameters. 'EE is the From the results in Tahle 1, one can see that J dominant term in every case. Also, the contact term is positive and increases in magnitude as one goes from single to multiple honds. The orbital and spin-dipolar terms are much smaller than the contact term, hut they do make a noticeahle contribution to coupling constants between multiply honded constants. The sign and magnitude of the coupling constant are, in general, similar to the sign and magnitude of the contact term. Table 1. Calculated Values for Jcc (in Hz) in Carbon Compounds
TJ;:
IJ
36.8
-2 3
11
35 6
34 6
38.5
-2.2
1.1
37.4
44.2
30.5
-0.8
1.1
30.8
29.8
31.7
-1.8
1.2
31.1
33.7
66.0
-2.6
0.6
84.0
56.5
64.3
-12.8
1.6
53.1
57.0
Ethylene (&HI)
70.6
-18.6
3.9
55.9
67.6
Acetylene
140.8
8.3
172.7
171.5
Molecule Smgle Bonds Ethane
' ~ g' J F ~ a
J
A
IC?Hd ,-. ",
Tolueneb (CeHsCHi
Cyclobutane (CIHB)
Neopentane (CSHW)
Acetonitrile (CHzCN) 6.
Multiple Bonds
Benzene (CSHB)
23.6
(C2H21 Experimental valuesare taken from the corresponding table in Ref. ( Q . a me C O U ~ ~~onstamreferstothe ~ I I ~ imeraction betweenthe memy1carbon andme henry1 carbon.
Table 2. Relationship between Carbon-Carbon Coupling Constants and % s Character as Determined lrom the Bonding
Ethane (CsHs)
Toluene
36.8
35.6
25.0
25.0
625.0
38.5
37.4
33.3
25.0
832.3
31.7
31.1
25.0
25.0
625.0
(C~HSCH~
Cyclobutane
(CsHsI
Ethylene
70.6
55.9
33.3
33.3
1000.0
140.8
172.7
50.0
50.0
2500.0
(C~HI)
Acetylene (CsHd
146
Journal of Chemical Education
The contact term itself is proportional to the amount of s electron density in the sigma (a) bond. In a rough way, the amount of s electron density in the a bond is related to bond hybridizations, whether the hybrids are determined from simple structural considerations or from the INDO method itself. To illustrate the relationship between IJFS and the % s character in a 0 bond consider the results in Tahle 2. The % s character is found from a simple hybrid bonding model where carhon singly-bonded is spQybridized and 25% s in character, carhon doubly-bonded is sp2 hybridized and 33.3% s in character, and carbon triply-bonded is sp hybridized and 50% s in character. From the results in Tahle 2, one sees that as the nroduct % s r n i % s r i m increases the contact term 'JKF
lm'
reLt&nship between the total"coup1ing constant and the % s character in the single bond. From the above considerations we see that the total coupling constants can be related to the % s characters in the bonding hybrids by a simple linear relationship cc - a(%sc(d(%scd +b
1ptd
(7)
where a , the slope, and b, the intercept, are determined by a least-squares fit. In the case of carhon-carbon single bonds Schulman and Newton (4) determined, using the % s characters as determined by the INDO method, a value of a = 0.0621 Hz and b = -10.2 Hz. The advantage of a relations hi^ likr tvln. I T ! is i t - prc~licti\.~ wlue I I I d~.tt.rtni~ting ~~~ui)liny , ~ ~ n i ~ t ~ ~irun t i t , . h ~ l ~ r i d t ~ ~ t111 ~ it11;u m s .rr-zmd i r i. i o t e r t - ~ i ~ ~ c to note that the hationship of ~ c h u l m &and Newton prey diets a neeative lJ%tal for an interaction between two carbon atoms wh& the product % sccl) % sccz) is less than 160. This tvoe of bond, which is almost entirelv v in character, is found i n t h e bridgehead bond of bicyclohitine and its derivatives. Thus, the relationship predicts a negative value for the coupling constant between the two bridgehead carbons in these Exuerimental results on bicvclohutane derivmolecules (9). atives (10) have indeed yielded negative values for these couuling constants. However, eqn. (7) holds to a lesser extent ~Fkewise,i t is not correct to generalize the relationship between coupling constants and the % s character to coupling constants between atoms with lone pairs. This will be seen in the next section. B. Carbon-Nitrogen Coupling (CN coupling)
The coupling constants reported for carbon-nitrogen bonds involve 'CC5N counline. . . Theoretical calculations of CN coupling constants are less numerous ( 5 ) than similar computations of CC coupling constants. In Tahle 3 INDO values for 'JFk, 1J&, IJZg, and 'J;F' are given for some single, double. and t r i ~ l ebonded svstems. From the last two columns in Table 3 one sees that the& is fairly good agreement between 'J&P1 and l~Ff.2 As can he seen from Table 3 certain results for CN coupling constants are similar to those for the CC case. First, as in the case of CC coupling, ' J F c predominates in all the singlebonded cases. Second, ' J Oand ' J S Dare uniformly small in all carhon-nitrogen single-bonded coupling constants. Finally, ~
~
In both the CC coupling case and the CN coupling case there are certain coupling constants for which the agreement between the iNDO results and theexperimental results is only fair (the CC coupling constants in acetonitrile and ethylene, and the CN coupling constants in methylamine and aniline).Although this result may be partly due to the limitations of the least-squares method, it is important to point out that despite the many approximations made in applying this method to coupling constants the sign of the coupling constant is correctly predicted in each of the systems listed in Tables 1 and 3. Also, in only one case (methylamine)is there a serious discrepancy between the INDO result and the experimental result. For a discussion of the limitations of the INDO method see References (4) and ( 5 )
Table 3. Calculated Values for JCN(in Hz) in Nitrogen-Containing Carbon Compounds Molecule A. Single Bonds Methylamine (CHaNHi Methyl ismyanidea (CHJNC) Aniline (CsHsNH2) Pyrrole ICH4NH) Tetramethyl ammonium ion [N(CHdnlt B. Multiple Bonds Pyridine IC5HsN) Pyridinium Ion iCsHsNHt) Acetonitrile (CHsCN) Benzyl Cyanide iCrH&NI , . " . Methyl lsocyanideb ICH-NCl
r J Fc.C
'Jd
J
' J F
'J3
Table 4. Relationship between Carbon-Nitrogen Coupling Constants and % s Character in the Bonded Atoms and in the Lone Pair as Determined from Hybridization % s
-2.7
0.2
-0.1
-2.6
-4.5
-11.9
0.2
-0.1
-11.8
-10.7
-8.0
0.4
-0.1
-7.7
-11.4
-14.8
0.9
-13.9
-13.0
-5.9
01
00 -0.1
-5.9
(5.8)
T h e c o u m q constant refers tothe interaction between the niiroqenand the directly bonded methyl carbon. "he coupling constant refers to the interaction between the nitrogen and the directly bonded " e n d carbon atom.
and CN cases, i.e.
< IIJo~SD(dauble)l < IIJo.SD(triple)l (8) l'Jo~SD(single)l Thus, as might be expected, with increasing i~ character in the bonds, the magnitude of the orbital and spin-dipolar terms increases. However, there are important differences between the two cases. In all the CC cases the contact term dominates; in the CN case this is not always true. Also, in the CC case the contact term is always positive and increases as one goes from single to double to triple honds. In the CN case the contact term is negative in most of the single bonded cases (since the maenetoevric ratios of Carbon-13 and Nitroeen-15 are ODpozte insign this is the most likely behavior) gut has varying sinns and maenitudes as one eoes to m u l t i ~ l ehonds. The reason for these new effects seems to be the of a lone pair of electrons with s character on either the nitrogen or carbon atom. To illustrate this "lone pair" effect there is listed the theoretically determined in Tahle 4 the values of '@$I, the % s c and % S N in the o hond, the product % s c % SN,and the % S N (or, in the case of methyl isocyanide, % sc) in the lone pair. The % s characters of the bonding and lone pair electrons are determined, as in the CC case, by considerations of a simple model of lone pair and bonding hybrids. (See discussion above.) As can be seen from Tahle 4 the honds break down into two general types: (I)CN honds where there is either no lone pair (tetramethvl ammonium ion. methvl isocvanide-sinele bond. and the pyridinium ion) or a lone pair with no s character (uvrrole. ~ l a n a rmethvlamine. ~ l a n a raniline). and (2) CN bdnds whkre the lone'pair has Home s character (pyridine, methvlamine. aniline, acetonitrile. and the methvl isocvanide triplebond). For Type (1) bonds the results are &mil&to the case of CC coupling in that ' J F Cis the predominant contribution to 'flow. Likewise, ' J E ~ ,and '@fitalare linearly related to the product % s c % s~ in a manner analogous t o eqn. (7). However, for Type (2) bonds the effect of a lone pair with s character works in an opposite manner to the effect of a bond
Molecule
'J::,
Tetramethyl ammonium ion [N(CHs)d+ Methyl Isocyanidesingle bond CHZNC Pyridinium ion (CsH,NHt) Pyrrole' (CIHW) Methylamineplanar ICHsNHs) Methylamineactual (CHsNHi Aniline planar (CeHsNHi Aniline actual ICaHsNHd Pyridine ICsHsN) Acetonitrile (CKCN) Methyl Isocyanidetriple bond 1CHxNCI
-5.9
"JTO"' n,
% sc % SN lin bond1 lin bond1
% sc % s"
(lone oairl
The nitrogen atom in pyrrole in sp2 hybridized
with s character. For example, if one computes the CN bond coupling constant in the "theoretically" constructed planar methvlamine and nlanar aniline (where the lone uair will be pure p in character) and then computes the same coupling constants in the actual methvlamine and aniline molecules contact term becomes more positive. As the amount of s character in the lone pair increases, the effect is more dramatic. Pyridine has a small negative value for 'JES, whereas pyrrole, which has a similar value of % s c % s~ in the o bond as pyridine, has a large negative value. The difference lies in the fact that the % s character in the lone pair in pyridine is 33.3 (in pyridine, the lone pair can be pictured-as having electron density in the plane of the molecule), while the % s character in thelone in pyrrole is zero (in pyrrole, the lone pair can he pictured as being perpendicular to the plane of the molecule and, thus, purep in character). The effect of the s character in the lone pair is to make the contact term more oositive. In the last two molecules in Tahle 4. CHqNC (methvl and N=C sigma hond very iarge and shhuld'lead to large negative values for the contact term, the amount of s character in the lone pair is also very large, a t least 50%. This large amount of s character in the lone pair outweighs the bond contribution to the contact term. Thus, the N=C and C=N coupling constants in acetonitrile and methyl isocyanide are positive in value. In passing, it should be mentioned that an INDO calculation of the % s character in the lone pair in methyl isocyanide indicates a value of about 70%, a value much higher than the 50% predicted from our simple hybridized model. This would greatly explain the very high positive value of 'J&for the triple bond in methyl isocyanide. Volume 59
Number 2
February 1982
147
Thus, these foregoing examples illustrate the presence of a "lone nair" effect-an effect which operates in a manner oppositeLtothe "bond" effect. Finally, it must he pointed out that if one calculates coupling constants between two atoms A and B where there is more than one lone pair present various new effects may he encountered. For example, interference and additive effects between the lone pairs arise. As an example of this case, the interested reader is referred to (11)where model calculations have been done on the NN coupling constants of hydrazine (NH2NH2).In this case there is a lone pair present on each of the coupled nitrogen atoms. Concluslons From the results in the section on the relationship between coupling constants and honding structure certain conclusions can be drawn concerning directly-bonded coupling constants between atoms A and B; where A and B have either no lone pairs or just one lone pair. (1) For single bonds between the two atoms, the Fermi contact term makes the predominant contribution to
LIT@? -
(2) (a) If there is no lone pair present on either of the two dirrrtly < u.~pledatinn>,thew is a linear rel3rim-nip IL tww11 r h t niilgnifudt~uithevonrncrterm and the prtnlu8.1 ;,', FI, in the ihond. As the s character increases. the contact term increases. Furthermore, if the hond in q"estion is a single hond. the magnitude of the total coupline constant is also lineahy relate; to the product % SA % & inihe hond. If the s character increases in the single hond, the total coupling constant increases in magnitude. (h) If a lone pair with s character is present on one of the directly coupled atoms, the contact term is dependent not only % in the u hond but also on the % s on the product % s ~ SB character in the lone pair. The two effects, the "bond" effect and the "lone pair" effect, operate in opposing directions. In the case of CN coupling, the hond effect makes the contact term more negative while the lone pair effect makes the contact term more positive. (c) If a lone pair with zeros character is present on one of the coupled atoms, the results are the same as those in conclusion (2) (a). (3) The orbital and spin-dipolar terms make a significant contribution to coupling constants between atoms multiply ~
~
'9
148
Journal of Chemical Education
bonded. They make the major contribution to the total coupling constant only in certain cases where a lone pair with s character is present on one of the coupled atoms. The relationship between the three coupling mechanisms and the electronic structure of the bonded atoms serves as a simple illustration of how theory can be utilized to gain insight into chemical ohenomena. In this article it has been shown that a relatively simple semi-empirical theory can be utilized to yield results which are in fairly good agreement with experimental results; results which can then be used to gain insieht into the electronic structure of molecules. Also, it has been shown that, given a molecule with a known honding structure, the coupling constants can be predicted. For example, coupling constants between carbon atoms singlybonded by u bonds of predominantly p character would have negative coupling constants. Such a prediction which is verified in the case of bicyclobutane and its derivatives could be extended to any carhon-carbon coupling constant involving bridgehead carbons (such as terpenes, etc.). On the other hand. the determination of the coupling . constant for a eiven molecule can help elucidate the bonding between atoms in a molecule. For examole. coupline . . small negative " . " constants or positive coupling constants between carbon and nitrogen atoms mav indicate the presence of a lone oair with s character. ~ u i h a result yieids valuable information about the nature of the electronic structure of molecules. Thus, the relationship between a rather complicated phenomenon as snin-suin couplinr . - and the broad topic of electronic structure in moiecules illustrates to the student the usefulness of chemical theory in understanding the connection between structure and properties. Literature Cited
(2) Bli~zard,A. C. and Ssn1ry.D. P.J. Chrm Phya., 65,950 11971).
(4) Schu1man.J. M. and Newton, M.O., J. Amei Chem Sac ,96.6285 l19741. 161 Schulman. J. M. andVenan8i.T. J..J. Amer. Chrm Soc .9R. 4701 119761. R ~N F.. phys. ~ R~ U . , S I~, S Oii953). S ~ . Pl1ar.F. L.. J. CHEM. EDOC.,55,2 (197.8). Pople, J. A. and Ueveridge, D. L., "Approximate Molecular Orbital Theory: McGrsw~Hil1,NewYark. 1 9 7 1 , ~57. . Schulman, J. M. and Venanri,T. J., TeliohadionLefi , IS, 14fil (1976). Pmnermtz,M.,Fink. R.. and Gray, G. A..J. Amer Chrm. Suc., 98,291 (1976). Schulman, J. M.. Ruggio. J., and Yenanzi, T J., J. Amer Chem Sac.. 99, 2045 (lY77).
