SPECTRA OF PERFLUORO-2,1,3-BENZOSELENADIAZOLEANIONRADICAL
1281
responding to an equivalent conductance of 68 ohm-' responding to an activation energy of 38 kcal/mole valid cm2 equiv-1.21 With the arrangement of the S042below the transition temperature is not justified. The ions on a face-centered cubic lattice,22this is in essence activation energy for conduction in the disordered another case of anti-fluorite type of crystal AB2 with high-temperature structure is likely to be very much disordered and mobile B ions (Li). However, this lower than in the essentially ordered one below the structure forms here not in a diffuse but in a Jirst-order transition temperature for Xa2S which may be estitransition from the monoclinic low-temperature phase mated to be approximately 1000" (cf., e.g., the very small temperature dependence of the c o n d u ~ t i v i t y ~ ~a t 575" with an entropy change AS,, of approximately 8 cal/deg mole. Together with the very low entropy in the disordered high-temperature form of solid AgI of fusion, 2.7, the high value of AS,, is taken to reflect above 145"). the disordering and mobilizing of the lithium ions in However, in the transition regions of these substances, a rapid increase in conductivity must occur the cubic structure. I n addition, the relatively high similar in extent to, but more gradual than, the (isoheat capacity of this phase, 52 cal/deg mole, as comthermal) one in AgI. Its start seems to have been pared with 46 for the liquid, further suggests that the disordering process is not completed at, but, continues observed in SrC12 near 700", corresponding to the unusually high activation energy of 70 kcal/mole.20 above, the transition temperature as it does in K2S. This rapid rise is, however, not expected to lead to as impossibly high a K value, a t the melting point, as that (19) "Landolt-Bornstein Tabellen," Vol. 11, 6th ed, 1959, p 237. (20) E. Barsis and A. Taylor, J. Chem. Phys., 45, 1154 (1966). cited above for Na2S. One of the highest ionic conOlder literature is cited there. ductivities of a solid measured, beside that of AgI, (21) A. Kvist and A. LundBn, 2.Naturforsch., 20a, 235 (1965). K = 2.5 ohm-' cm-I, seems to be that recently obtained (22) T . Forland and J. Krogh-Moe, Acta Chem. Scand., 11, 565 for cubic Li2S04near its melting point, K = 2.6, cor(1957).
Electronic and Electron Spin Resonance Spectra of the Perfluoro-2,1,3-benzoselenadiazole Anion Radical' by J. Fajer, B. H. J. Bielski, Departments of Nuclear Engineering and Chemistry, Brookhaven National Laboratory, Upton, New York 11973
and R. H. Felton Department of Chemistry, Brandeis University, Waltham, Massachusetts
02164
(Received September 26, 1967)
The electronic absorption and electron spin resonance (esr) spectra of the perfluoro-2,1,3-benzoselenadiazole radical anion are presented. Results of a semiempirical self-consistent field-molecular orbital (SCF-MO) study of the molecule and the isologs, 2,1,3-benzoselenadiazole and 2,1,3-benaothiadiazole,are assessed by comparison of calculated and experimental esr and electronic spectra of the radicals. Similar comparisons were made of the neutral species. I t is concluded that a p-orbital model satisfactorily describes the pertinent experimental data.
Introduction Examples of nitrogen or oxygen aromatic heterocyclic radical anions are well known; less familiar are anions in which the heteroatom is sulfur or selenium. The increasing i n t e r e s P 4 shown in the electronic properties of 2,1,3-benzoselenadiazole (I), 2,1,3-benzothiadiazole (11),and their derivative anions prompts us to report on similar properties of the perfluoro-2,1 ,&benzoselenadiazole (111) anion.
One source of interest in these molecules is the possible interaction of empty d orbitals with the r-electron (1) This work was performed under the auspices of the U. S. Atomic Energy Commission. (2) E. T. Strom and G . A. Russell, J . Amer. Chem. SOC.,87, 3326 (1965). (3) N. M. Atherton, J. N. Ockwell, and R. Deitz, J . Chem. Soc., A, 771 (1967). (4) J. Fajer, J. Phys. Chem., 69, 1773 (1965).
Volume 72,Number .I April 1968
J. FAJER,B. H. J. BIELSKI, AND R. H. FELTON
1282 system. Previous s t ~ d i e s ~ofJ , I, ~ 11, and the radical anions were carried out within the framework of the Huckel molecular-orbital theory, and, therefore, the conclusion that d orbitals were not needed was necessarily qualitative. We have applied a more sophisticated treatment of electronic structure, uiz., selfconsistent field-molecular-orbital theory, to these molecules. Rather than make arbitrary and untested assumptions as to the nature of the d-p interactions, we employed a basis set which included only the 3p orbital of sulfur and the 4p orbital of selenium. Parameters relating to these orbitals are well characterized and may be chosen a priori from atomic spectral data or theoretical investigations of related molecules. I n addition, an extensive configuration interaction treatment was performed for both closed- and open-shell molecules to ascertain if the customary neglect of doubly excited states was justified. With reasonable choices for parameters we not only find good agreement between calculated and experimental electronic spectra, but also note that the SCFIS10 treatment predicts spin-density distributions generally in accord with those observed.
A, mp Figure 1. Sodium reduction of I11 in tetrahydrofuran: 1, absorption spectrum of starting material; 6, final product. ( E is in liters per mole centimeter.)
A
10
I. M = Se: X = H 11; M = S;’X = H 111, M = Se; X = F
Experimental Section Samples of I11 were prepared by the reaction of selenous acid with tetrafluoro-o-phenylenediaminea and were sublimed twice. Anal. Calcd for C6F4N2Se: C, 28.26; N, 11.07; F, 30.01 Found: C, 28.26; N, 10.99; F, 29.80 (Galbraith Laboratories, Knoxville, Tenn.). The infrared spectrum was consistent with that reported’ for I (with allowances for the C F instead of CH absorptions). The anion was prepared at room temperature by sodium or potassium reduction of I11 dissolved in tetrahydrofuran. Optical absorption measurements and extinction coefficients were obtained as previously d e ~ c r i b e d . ~Electron spin resonance spectra were measured on a Varian V4500 spectrometer equipped with a 9-in. magnet and 100-kc field modulation.
Experimental Results Compound I11 reacts with sodium in tetrahydrofuran to yield reddish solutions. Representative absorption spectra, at various stages of reduction, are displayed in Figure 1. The successive spectra develop through well defined isosbestic points as the reaction proceeds, suggesting formation of a single new species. Oxidation of the product by exposure to dry air regenerates SO-%% of the original spectrum. The esr spectrum The Journal of Phusical Chemistry
I
7
Figure 2. (a) Electron spin resopance spectrum of 111.in tetrahydrofuran; (b) computer-simulated spectrum.
of the radical obtained by potassium reduction is shown in Figure 2a. Analysis of the observed 39-line spectrum yields the following isotropic hyperfine splitting constants: U F = 3.56 and 4.34 G for the two sets of two equivalent fluorine atoms, and U N = 6.08 G for the two equivalent nitrogen atoms. A computersimulated spectrum employing the above values is shown in Figure 2b. The line-shape function for (5) N. K . Ray and P. T. Narasimhan, Theoret. Chim. Acta, 5 , 401
(1966). (6) We are indebted to M. W. Buxton of Imperial Smelting Corp. for a sample of the diamine. (7) V. A. Pazdyshev, Z. V. Todres-Selektor, and L. 8. Efros, J . Cen. Chem USSR, 30, 2533 (1960).
1283
SPECTRA OF PERFLUORO-2,1,3-BENZOSELENADIAZOLE ANIONRADICAL individual hyperfine lines was Lorentzian with a halfwidth of 0.62 G. We were unable to detect splitting due to either the potassium gegenion or the Se7?(770 natural abundance). These extra transitions may contribute to the rather broad line widths. Similar reduction of I in tetrahydrofuran yielded esr spectra essentially equivalent to those obtained earlier.
SCF-MO Calculations A . Method. The SCF-MO’s for closed-shell molecules were obtained by the method of Pariser and Parr,S and Pople (PPP),g For the open-shelled doublets, the method of Adams and Lykos’O was employed. This latter treatment is an extension of the PPP approximations to Roothaan’s SCF theory of open shells.11 Our computational scheme apparently differs from recent calculations’z of aromatic anions, in that excitation energies here are related to one-electron energies of the SCF-MO’s via Roothaan’s open-shell Fock operator.
F
=
H
+ 2 J T - KT + 2(MT - KO)
(1)
I n eq 1, H is the one-electron operator; J T and KT are the total Coulomb and exchange operators, respectively; K O is the exchange operator for the half-filled shell; and MT is an exchange coupling operator. As a result, excitation energies (relative to the ground-state energy) differ slightly from those derived by LonguetHiggins and P0p1e.l~ Table I gives these energies for Table I : Excitation Energies of Singly Excited Radical States“ Energy
State 2x1
em
2XZ
en
2x3
en
2X4
en F11;
a el
Jlli
- €k + ‘ / a J m m f 3 / ~ K k m - Jkm - ern + ‘/ZJrnm + a / a K r n n - Jmn - €k f K m n K m k 2 K k n - Jkn - Ck + 2 K m n 2 K m k - Jkn
and Kilt are Coulomb and exchange integrals
for MO’s 1 and 1’.
unique half-filled shell, and n,o, . . . are virtual orbitals. The Slater-determinant notation is familiar. Excited states of the type 2x4were allowed to interact with the ground state, and configurational-interaction matrix elements among the excited states were reduced by utilizing the diagonality of F in the SCF-MO basis. I n addition, we corrected spin densities after configuration interaction in a nonperturbative manner, thereby involving all excited states of appropriate symmetry. This differs from the customary procedurelZ of using only configurations 2x4. As a check, the total spin density was computed. I n all instances the total was 1.0000. Furthermore, the computer program developed has the additional flexibility of allowing the incorporation of doubly excited states in both closed- and open-shell computations. For closed-shell electronic spectra, one has the option of including the five di~tinguishablel~ types of double excitations with configuration interaction not only between them and the ground or singly excited states, but also among the doubly excited states themselves. For the open-shell molecules the (presumably) four lowest doubly excited states could be included for configuration-interaction calculations. I n this case no interaction among doubly excited states was considered. This neglect is inconsistent; nevertheless, for the molecules considered here, doubly excited states had little effect upon the predicted electronic spectra. The four types of configurations were generated from the excitations: 2k + 2n, m n, and k -+ n, and two doublets arising from k -+ n and m-+ 0 . B. Parameters. The same set of parameters was used for both neutral and radical forms of a given molecule. Table I1 lists the needed parameters. There for the Hth atom of core charge, Z, I, is the valencestate ionization potential of a PR electron, and 7, is the monocentric electron repulsion integral. For selenium, parameters were obtained from the paper of Hinze and Jaff6.16 Fluorine values were obtained from different sources.16 Other one-center integrals are conventional choices with the exception of I, = -9.6 eV. This value is a member of the parameter set,‘? -+
the following excited states.
‘x3 ’ ~ 4=
= 2-”’{
‘x1
= 14161*
2XZ
=
Id161*
*
14161-. . 4 k 6 k 4 n I
* *
9
9
- 14161 . Bk4rndnl]
4k‘$rn6nl
*
-
6-”’{ 214141. .4&4nl
/@I61*
dkdrn6rnl
@k+rn6n/
- ldJ161. . $k+rndnlI
(2)
@k&’$rn(
(3)
where the ground state is ‘XO =
I$161* a
*
I n referring to individual orbitals, the indices 1, 2,
, ,
.,
k relate to filled orbitals (in the ground state), m is the
(8) R. Pariser and R. G. Parr, J. Chem. Phys., 21, 466 (1953). (9) J. A. Pople, Trans. Faraday Soc., 50, 901 (1954). (10) 0. W.Adams and P. G. Lykos, J . Chem. Phys., 34, 1444 (1961). (11) C. C.J. Roothaan, Rev. Mod. Phys., 32, 179 (1960). (12) A. Hinchliffe, Theoret. Chim. Acta, 5, 208 (1966);A. Hinchliffe, R. Stainbank, and M. Ali, ibid., 5, 95 (1966). (13) H.C.Longuet-Higgins and J. Pople, Proc. Phys. Soc., 68A, 591 (1965). (14) J. Murre11 and K. L. McEwen, J. Chem. Phys., 25, 1143 (1956); H.Ito and Y. I’Haya, Theoret. Chim. Acta, 2, 247 (1964). (15) J. Hinze and H. H. Jaff6, J. Phys. Chem., 67, 1501 (1963). (16) L. Oleari, L. Di Sipio, and G. De Miohelis, Mol. Phys., 10, 97 (1966). (17) K.Nishirnoto, Theoret. Chim. Acta, 7, 207 (1967).
Volume 72, Number 4
April 1968
J. FAJER, B. H. J. BIELSKI,AND R. H. FELTON
1284
ficulty resides in the (probably) erroneous assumption that
Table I1 : Semiempirical Parameters (eV) Atom
C N Se S
F
Y
2
9.4915' 12. 12b 11.15' 9.90E 16. 70e
1 1 2 2 2
I
-9.6" -14. 12b -23.85' -22.Sd -35. 36s
B @OF
aF = QFPC (4) holds rather than the theoretically expected form
= -1.75
osea = -1.10 @SN = -1.68
as =
Reference 17. C. Weiss, H. Kobayashi, and 11.1. Gouterman, J . Mol. Spectrosc., 16, 415 (1965). Reference 15. M. Bielefeld and D. D. Fitts, J. Amer. Chem. Soc., 88,4804 (1966). a Reference 16. a
used here, that included variable core resonance integrals Prv and bicentric repulsion integrals ypv. Bicentric repulsion integrals were calculated according to the recently proposed scheme17which treats vertical correlation in an approximate manner by assigning electrons alternately above and below the molecular plane. Different formulas are then used for upper-upper and upper-lower interactions. For the electrons "associated" with selenium or sulfur, we simply averaged the results of the two formulas. Core resonance integrals PCNand PCC were calculated by the variable method." The only parameters which then had to be judiciously guessed were &N, and PCF. The integrals P s e ~and PSN were calculated from an overlap approximation
P
= PoS(r)
where S ( r ) is the overlap of 2pa orbitals centered on carbons a distance r apart, and -2.48 eV < Po < -2.39 eV. (We arbitrarily chose the 2pn-2pn overlap integral here since there are at present insufficient data to allow the determination of a Po appropriate to NS or NSe interactions.) The value of PCF was allowed to vary between -1.75 and -2.5 eV. The crystal structures of I and I1 are known.'* The geometry of I11 was approximated by using the atomic positions of I and a C F bond distance of 1.30 A.
Results and Discussion
aH = -27p, aH
= -27p,
-1
(A) 2 . 8 ~ ~ ~ ~ (B)
where pr is the carbon spin density and E , = 1 - P, is the excess charge at carbon atom ~1 having a charge density P,. A similar McConnell relation for aN was employed12 ax = - 2 1 ~ ~ Determination of
aF
is quite approximate.
The Journal of Physical Chemistry
The dif-
+
(5)
QFCPC
Equation 5 reflects the splitting contributions from 2pn spin on fluorine. Since little is knownlg with regard to parameters in eq 5, we use, instead, eq 4 with Q F = 50 10 G.19v20 The computed hyperfine splitting constants are displayed in Table 111. Included there are spin densities before and after configuration interaction (CI). The latter spin densities were used in the McConnell relations, and charge densities did not include the minor effects of CI. The assignment of the hydrogen hyperfine splitting constants agrees with previous results.233 The assignment of aF values is quite reasonable, in view of the obser~ation'~ that substitution of weakly electronwithdrawing groups in radicals already containing strongly electron-attracting groups does not greatly perturb the spin density ; however, this assignment is not to be regarded as definitive because of the aforementioned difficulties in relating coupling constants and spin densities. ~
~~~
Table 111: Spin-Density Distributions and Coupling Constants (G) hloleode
I
I1
Position
-Spin No CI
denaity-
CI
1 4
0.203 0.115
0.270 0.119
5
0.091
0.061
1 4
0.242 0.092
0.295 0.104
5
0.066
0.049
a (calcd)
a (exptl)
5.67 3.21 3.01 1.65 1.61
5.79"
(A) (B) (A) (B)
6.19 2.81 2.67 1.32 1.28
5 . Ha
(A) (B) (A) (B)
2.59
2.48 1.65
1.59
IIIb
1 4 5
0.208 0.103 0.085
0.252 0.116 0.065
5.29 5.8 A 0 . 6 3.25 f 0 . 3
6.08 4.34 3.56
IIIc
1 4 5
0.208 0.103 0.085
0.291 0.103 0.061
6.11 5.15 js 0 . 5 3.05 rt 0 . 3
6.08 4.34 3.56
Hydrogen hyperfine splittings were computed using
two relations suggested by Hinchliffe,12Le.
QFFPF
Reference 3. Number of excited states, 13. ' Number of excited states, 67.
(18) V. Luzzati, Acta Cryat., 4, 193 (1951). (19) M.Kaplan, J. R. Bolton, and G. Fraenkel, J . Chem. Phys., 42, 955 (1966). (20) A. Carrington, A. Hudson, and H. C . Longuet-Higgins, Mol. Phys., 9 , 377 (1966).
SPECTRA OF PERFLUORO-2,1,3-BENZOSELENADIAZOLEANIONRADICAL
1285
~
Table I V : Bond Orders
--
Molecule
I
I1
a
Reference 18.
Table V:
distance, 1 Exptla
--Interatomic SCF-MO
Bond
...
1-2 3-9 4-9 4-5 5-6 8-9
1.296 1.461 1.356 1.458 1.467
1-2 3-9 4-9 4-5 5-6 8-9
1.305 1.457 1.357 1.451 1.457
Neutral species---
*..
SCF-MO
1.83 1.30 1.42 1.30 1.42 1.46
0.1868 0.8596 0.3138 0.8961 0.3526 0.2773
1.60 1.34 1.46 1.29 1.46 1.41
0.2982 0.8131 0.3321 0.8886 0.3682 0.3321
-Radical Interatomio distance,
(SCF-M0)-
1
HMO~
...
...
...
1.329 1.431 1.384 1,420 1.451
0.0981 0.6848 0.4760 0.7399 0.5399 0.3697
...
0.579 0.548 0.566 0.723 0.603 0.528
Bond order
0.1960 0.6396 0.4830 0.7529 0.5331 0.4484
1.336 1.430 1.381 1.421 1.436
Huckel calculations of ref 5.
Charge Densities Atom-
I
Molecule
I I*I1 I1 ( HPYIO)Q 11.I11 111.a
Bond order
I
-
1
2
4
1.269 1.505 1,265 1.272 1.499 1.277 1.520
1.931 1.969 1,834 1.437 1,913 1.933 1.971
1,025 1.137 1.020 1,010 1.107 1.040 1.138
5
0,950 1.051 0.962 1.005 1.066 0.788 1.062
7
9
0.790 0.818 0.836 0.994 0.872 0.960 0.833
10
1.985 1.979
11
1,984 1.978
Reference 5.
Large nitrogen and C(5) spin-density alterations are caused by CI. Increasing the number of excited states generally improves the agreement with experiment. We find that spin densities calculated from neutral molecule R40’s are quite bad. Bond distances of I, 11, and their anions are compared with experimental interatomic distances in Table IV. The bond order-bond distance relations used werez1
rcc = 1.517 - 0.18P,, rCN = 1.451
-
1.18P,,
with P,, the total mobile bond order between atoms p and v. Formation of the radical tends to remove the strongly alternating character of the neutral molecule while decreasing the bond order between the heteroatoms. This latter point may be the reason why we have not been able to form stable dinegative ions. The charge densities listed in Table V show that nitrogen atoms possess considerable excess charge in both neutral and radical forms, indicating that a variable self-consistent electronegativity featurez2 might be useful in future studies of these or related molecules. The observation that selenium or sulfur atoms carry a slight positive charge while the fluorine atoms are
essentially neutral increases our confidence in the one electron parameters of these atoms. Indeed, the ground-state properties are parameter insensitive. Included in Tables IV and V for comparison are results of an HMO treatment5 of benzothiadiazole. One observes from the bond orders that the simple theory imparts more aromatic character to the molecule than the experimental bond distances warrant. Also, the charge density on the sulfur atom is low, particularly in view of the higher charge densities (1.628 or 1.844) obtained with differsnt Huckel parameters.2 Tables VI and VI1 contain the computed transition energies and oscillator strengths for neutral and radical species, respectively. The first column gives results obtained when only a few (12-27) singly excited states are used; the third column shows the effect of inclusion of many (60-70) configurations, both singly and doubly excited. Columns two and four give the principal configurations ( 2 10%) constituting the excited state. It is clear that the number of excited states exerts a (21) K. Nishimoto and L. S. Forster, Theoret. Chim. Acta, 4, 155 (1966). (22) R. D. Brown and M. L. Heffernan, Trans. Faraday Soc., 54,767 (1958). Volume 78, Number
4 April
1968
J. FAJER,B. H. J. BIELSKI,AND R. H. FELTON
1286
t t t J & tm mt mt
m,m,
v v v v
v-v
s N
3
h
m
t ,
v
h h h h
; h H ; h ; h
Y
The Journal of Physical Chemistry
U Y
c-4
H
Y Y U
SPECTRA OF PERFLUORO-2,1,3-BENZOSELENADIAZOLEANIONRADICAL
ww43
1287
w
? @ ? ?? m 3 *
- m m
o¶
m
m- m- w- 7-i- mi mo m * m w o
??"???
0 0 0 0 0 0
v v v v v v
3 H
H
H H
Volume 72, Number 4 April 1968
1288 moderate influence upon the energies, and in the case of neutral molecules, doubly excited states are needed to decrease the intensity of the lowest z-polarized (long axis) band relative to that of the first y-polarized band. The predicted radical spectra of the selenium compounds possess the general features of the observed spectra, particularly with regard to the intensity distribution. Transition energies are somewhat low, with the discrepancy increasing as more excited states are added to the CI basis. A striking effect was noticed when y s was set a t 11.90 eV.23 Then the one-electron energy c4 increased by about 1 eV, causing an inversion in the ordering of the fourth and fifth states of 11.- and, simultaneously, an impressive decrease in the energy of the strongly allowed z-polarized transition. The other states were only mildly altered. This inversion occurred for y s > 11.0 eV and was not present in the neutral molecule. The reason for the change in e4 could be traced back to the large alteration in the nitrogen atom coefficient for this RIO. Apparently, the set of linear equations constituting the open-shell Fock Hamiltonian is not well poised with respect to this eigenvector; other MO’s did not display substantial variations. The essential point of the calculation is not the accuracy which we deem acceptable, but rather the sensitivity of the computation to: (a) parameters, and (b) amount of CI. With regard to point a, the effect of increasing ye has been noted ; in addition, a dramatic change occurred when I C was set equal to the PariserParr value of -11.22 eV. Then neutral electronic spectra were clearly incorrect, since two strong absorptions appeared at about 30,000 cm-l, instead of the observed single absorption. This feature was present irrespective of mild variations in other parameters. Conversely, fixing ICand varying PCF,PSeN, or PSN had little effect. Point b indicates an unsatisfactory feature of the present theory, Le., the neglect of highly energetic configurat,ions is not theoretically or
The Journal of Phusical Chemistry
J. FAJER, B. H. J. RIELSKI,AND R. H. FELTON computationally justified. This is particularly so when one is dealing with molecules of low symmetry. Our experience leads us to agree with the conclusion of EvlethZ4that the conventional parameters should be readjusted to account for extensive CI. It is doubtful whether such features as inclusion of non-nearest neighbor p’s, penetration integrals, or self-consistent electronegativity will alter the above remark. If it is possible to obtain a rationalization of pertinent experimental results using only a p-orbital basis, what is the role of sulfur and selenium d orbitals? The two d orbitals which are symmetric and antisymmetric with respect to reflection in the vertical plane will mix with .rr orbitals. It is possible that higher excited states at ca. 45,000 cm-l will be shifted some 4000-8000 cm-1.25 However, there is no unique manner of estimating the additional atomic integrals needed. For this reason we do not believe that, at present, the SCF-RIIO theory is capable of unambiguously demonstrating d-orbital participation. One needs a completely nonempirical theory. This remark is exemplified by considering the anomalously low energies of the strongly allowed z-polarized transitions of I1 - and I11 * - (at energies 37,010 and 35,470 crn-l, respectively). The orbitals involved are just those whose one-electron energies are sensitive to y s or 7 s e . Clearly no conclusion regarding d-orbital participation is justified until one is certain that values of ys, yeB, YSN, and YSeN are correctly chosen. With this one exception (which is not the case for I -) a p-orbital model is satisfactory.
-
Acknowledgments. We are indebted to Dr. D. C. Borg for the use of his esr simulation program, EPRSYN, and to Mrs. V. H. Wilson for her aid with the experiments. (23) M. Bielefeld and D. D. Fitts, J . Amer. Chem. Soc., 88, 4804 (1966). (24) E.M.Evleth, J. Chem. Phys., 46, 4151 (1967). (25) Shifts of this order were found by Bielefeld and Fittsza when
d orbitals were included in the basis set of thiophene.
