J. E. BLOOR, B. R. GILSON,AND D. D. SHILLADY
1238
Theoretical Calculations on Ions and Radicals. 11. SCFMO Calculations on the Excited States of Aromatic Nitriles and the Spin Density
Distributions of the Corresponding Anions
by J. E. Bloor, B. R. Gilson, and D. D. Shillady Cobb Chemical Laboratory, University of Virginia,Charlottesville, Virginia (Received August 1 , 1966)
Semiempirical SCFMO calculations for 12 cyano compounds are reported. By adjusting the resonance integrals for the nitrile triple bond and the carbon-aza nitrogen single bond to the values -2.85 and -2.27 ev, respectively, a satisfactory fit between experiment and theory for both the electronic transition energies and reduction potentials of the neutral mdecules, and the spin densities of the corresponding negative ions was obtained; the spin densities were calculated by the restricted Hartree-Fock perturbation method of part I. Statistical analysis of the relationship between calculated spin densities and experimental coupling constants supports the contention that spin densities calculated by presently used procedures do not warrant the inclusion of extra terms in the McConnell equation for the relationship between experimental proton hyperfine splittings and spin densities. On the other hand, the inclusion of nearest neighbor terms for I4N hyperfine splittings is justified by the calculations and is in accord with recent work of Henning, who demonstrated that a relationship of the type
+
ADN = Q N N ~ P N Q C CCpt ~ i
is of the same order of approximation as the McConnell relationship.
The relationships between theoretically calculated spin densities of radicals and the observed electron spin resonance spectra are of great importance, both from the point of view of assigning hyperfine splitting constants to particular atomic positions and also to our understanding of the mechanism giving rise to the hyperfine There have been many atto relate observed hyperfine splitting constants to calculated spin densities using the simple Huckel molecular orbital (HMO) method or the modification developed by McLachlan4 in which electron correlation effects (as shown by the appearance of negative spin densities) are introduced by a very empirical perturbation procedure. Reports of more sophisticated calculations in which electron correlation effects are introduced explicitly are very few and almost entirely confined to hydrocarbon positive and negative I n part I of this series,s we deThe Journal of Phyeicd Chemistry
scribed such a method in which electron correlation effects were taken into consideration (a) by introducing semiempirical values for repulsion and core integrals in order to calculate the closed-shell selfconsistent field molecular orbitals (SCFMO’s) by the Pariser-Parr-Pople (PPP) method and then (b) carrying out a configuration-interaction (CI) calculation between excited states and the ground state. (1) G. G. Hall and A. T. Amos, “Advances in Atomic and Molecular Physics,” Vol. I, D. R. Bates and E. Estermann, Ed., Academic Press Inc., New York, N. Y., 1965. (2) A. Carrington, Quart. Rev. (London), 17, 67 (1963). (3) L. Salem, “The Molecular Orbital Theory of Conjugated Systems,” W. A. Benjamin, Inc., New York, N. Y., 1966,pp 233-283. (4) A. D.McLachlan, Mol. Phys., 3 , 233 (1961). (5) J. E. Bloor, B. R. GiIson, and P. N. Daykin, J. Phys. Chem., 70, 1457 (1966). (6) L. C. Snyder and A. T. Amos, J. Chem. Phys., 42, 3670 (1965). (7) P. H.Rieger and G. K. Fraenkel, ibid., 37, 2795 (1962).
THEORETICAL CALCULATIONS ON IONS AND RADICALS
IN 8
1239
calculations on cyanobenzenes,la the calculated transition energy for 1,2,4,5tetracyanobenzene was found to be considerably higher (6400 cm-') than the observed value. Our results show that this deviation was due to the value of the resonance integral of the nitrile triple bond, which was considerably different from that used here.
Method General. The details of the PPP SCFMO method have been described many times e l s e ~ h e r e . ~ J I~nJ ~ calculating the closed SCFMO's of the polycyano compound, we have t o choose empirical values for: (1) the one- ((pplpp)) and two-center ((pplqq)) repulsion integrals; (2) the core matrix off -diagonal elements pps between nearest neighbors p and q; and (3) the core matrix diagonal elements, Ipp. For our choice of I,, values, we have used valence-state ionization potentials taken from the tables of Hinze and Jaffe.IE The one-center repulsion integrals were calculated by the Pariser-Parr appro~imation'~ (PPlPP) = I ,
Figure 1. Numbering system used.
(1)
Table I : Parameters in Electron Volts used in Closed-Shell SCFMO Calculations Atom
Valence state
IP
YPP
C(ring) C(cyano) N(amino)d N(aza) N(cyano)
tr.trtr A didir A tr tr tr n2 tr2 tr tr A di2 di x A
11.16 11.19 21.49 14.12 14.18
11.13 11.09 12.34 12.34 12.52
O(methoxyl)d
tr2 tr tr
25.63
15.23
X
The results of this restricted Hartree-Fock (RHF) perturbation method corresponded very closely to the more elaborate "improved unrestricted HartreeFock method" described by Amos' and Snyder,E in which electrons with different spins were allowed to occupy different orbitals. I n the present paper, we present the results of calculations using the RHF perturbation method of part Is on a number of anions of cyano compounds (Figure 1). We have obtained data in order t o provide a basis for discussion of (a) whether it is possible to predict electron spin hyperfine splitting constants using SCFMO parameters chosen to give satisfactory values for other physical properties, e.g., transition energies or reduction potentials, and (b) whether the R H F method gives results at least as good as, and hopefully better than, the simple Huckel-McLachlan treatment previously carried out for a number of cyano compounds.' Ultraviolet spectroscopic measurements on the absorption bands of cyanobenzenes are unusually complete,'-" and these data and also the reduction potential data of Rieger, et UZ.,'~ have made it possible for us to examine whether the successive replacement of hydrogens in the benzene ring by cyano groups is correctly predicted by SCFMO theory. I n previous
- A,
~2
BCX
-2.290 -2.112 -1.980 -2.271 -3,750" -4. OOOb -3.85' -2.000
'
Values used in set 2 a Values used in set 1 calculations. calculations. Recommended final value. * From unpublished work on polysubstituted benzenes, see text.
(8) G.Leandri and D. Spinelli, Boll. Sci. Fac. Chim. Ind. Bologm, 15, 90 (1957). (9) A. Zweig, J. E. Lehnsen, W. G. Hodgson, and W. H. Jura, J . Am. Chem. SOC.,85,3937 (1963). (IO) 0. E. Polansky and M. A. Grossberger, Monatsh. Chem., 94, 647 (1963). (11) P.P. Shorygin, M. A. Geiderikh, and T. I. Ambrush, Rum. J . Phye. Chem., 34, 157 (1960). (12) P. H. Rieger, I. Bernal, W. H. Reinmuth, and G. K. Fraenkel, J . Am. Chem. SOC.,85, 683 (1963). (13) H. E.Popkie and J. B. Moffat, Can. J . Chem., 43,624 (1965). (14) J. E. Bloor, P. N. Daykin, and P. Boltwood, ibid., 42, 121 (1965). (15) For an extensive bibliography, see R. G. Parr, "Quantum Theory of Molecular Electronic Structure," W. A. Benjamin, Inc., New York, N. Y., 1963. (16) J. Hinze and H. H. Jaffe, J . Am. C h m . Soc., 84, 540 (1962).
Volume 71,Number 6 April 1967
J. E. BLOOR, B. R. GILSON, AND D. D. SHILLADY
1240
Table 11: Effect of the Variation of @ON in Benzonitrile Calculations on Spectral Transitions, Spin Densities, and Charge Densities @ON* 8V
-2.942 -3.200 -3.500 -3.750 -3.850 -4.000
-Spectral AEi
4.65 4.65 4.65 4.66 4.66 4.66
transitions,
BV-
f
AEa
f
CM'
P4
b
CrS'
Pa
91
0.0036 0.0028 0.0020 0.0018 0.0017 0.0015
5.39 5.47 5.53 5.59 5.60 5.64
0.73 0.61 0.42 0.35 0.35 0.30
0.1986 0.2122 0.2278 0.2395 0.2437 0.2499
0.2554 0.2743 0.2950 0.3106 0.3162 0.3246
1.1709 1.1924 1.2158 1.2337 1.2401 1.2499
0.1948 0.1763 0.1555 0.1392 0.1332 0,1243
0.2384 0.2145 0.1885 0.1688 0.1616 0.1510
1.3639 1.3296 1.2928 1.2654 1.2558 1.2413
where A , is the electron affnity taken from the tables of ref 16. The two-center repulsion integrals between two a t o m p and q distance r,, A apart were then calculated by the Nishimoto-Mataga (NM) method (eq 2) which we6J7 and others'aJ5J8 have found very successful for semiempirical calculations on other systems 14.397
+ r,, ev = (28.794/(pplpp) + (qqlqq)) ev. 'p'qq)
correlation with experiment would be obtained if a higher value for -PCN was used than that calculated from eq 3. Two sets of calculations for all the cyano compounds of Figure 1 using values of PCN of -3.75 ev (set 1) and -4.0 ev (set 2) were carried out, and the results are summarized in Tables 11-VI. From the statistical analyses (Table IV), it wm found that the regression line obeying the simple McConnelP relationship
= a,,
upH
where a,, For the values of PPq,we have either used the Mulliken magic f o r m ~ l a , eq ' ~ 3, or determined it empirically by fitting it to an observed parameter as discussed below. The
(3) values for parameters used are summarized in Table I. The values for the amino group and the methoxyl group were obtained from unpublished calculations on polyamino- and polymethoxyl-substituted benzenes in which the parameters were adjusted so that the energy of the highest occupied WIO was linearly related to the experimental ionization potentials (usually measured indirectly). Resonance Integral for the Nitrile Group. The value of -2.93 ev for the resonance integral of the nitrile group calculated from eq 3 gave (Table 11) a rather low calculated value for the transition energy of the second ultraviolet transition of benzonitrile, observed at 45,100 cm-', and also a very low value for the spin density of the unpaired electron at the 4 position (Figure 1) in the radical anion derived from that molecule. Since the prime object of the work was to establish whether it was possible to calculate successfully both the electronic transition energies and esr spectra, it was decided to vary PCN in order to see if a better fit with the experimental data could be obtained. The results of our calculations are summarized in Table 11. These demonstrate that a better Ths Journal of Physical Chemistry
=
Q C H ~ P ~
(4)
gave a value for &c" of 26.37 gauss for set 1 and of 25.58 gauss for set 2 with similar correlation coefficients and standard errors (Table IV). For hydrocarbon ions, we have previously obtained6 a value of QmH of 25.99 gauss. To fit the nitrile anions on the same regression line as the hydrocarbon anions, we can estimate by linear interpolation that a value of PCN = -3.85 ev would be suitable; indeed, a calculation on benzonitrile using this value yielded a value of p4 = 0.316 giving a predicted coupling constant of 8.20 gauss compared to the experimental value of 8.40. The second transition energy for this value of PCN was also very close to the experimental value (Table 11). Since it is obvious that calculations with this intermediate value of PCN would fall between the values of our sets 1 and 2, such calculations were not actually carried out for the whole series; however, adoption of this intermediate value is recommended for use in new calculations on nitrile compounds using the other parameters reported here (Table I). In some recent work on the transition energies of aromatic nitriles, Popkie and MoffaP suggested a PCN of -3.5 ev, but this value would give poor results for the esr hyperfine (17) J. E. Bloor and N. Brearley, Can. J . Chem., 43, 1761 (1965); J. E. Bloor, ibid.. 43, 3026 (1965). (18) K. Nishimoto and R. Fujishiro, Bull. Chem. SOC.Japan, 37, 1660 (1964); L. S. Forster and K. Nishimoto, J . Am. C h . Soc., 87, 1459 (1965); K. Nishimoto and L. S. Forster, Theoret. Chim.
Acta, 3, 407 (1965); 4, 155 (1966). (19) R. 8. Mulliken, J. Chim. Phys., 46, 497, 675 (1949). (20) H.M. McConnell, J . Chem. Phye., 24, 764 (1956).
THEORETICAL CALCULATIONS ON IONSAND RADICALS
1241
Table 111: Spin and Charge Densities -Set
Anion of molecule
McLachlsn'
1, BCN = -3.76 evP P
-Set
2, #ON = -4.00evP P
lae=ptiH/
(1) Beneonitrile
0.1152 -0.0171 0.3318 0.1211
0.1089 - 0.0203 0.3106 0.1688
1.0979 1.0040 1.2337 1.2654
0.1057 -0.0165 0.3246 0.1510
1.0977 1.0084 1.2499 1.2413
3.63 0.30 8.42 2.15
(2) o-Dicyanobenzene
- 0.0467
-0.0551 0.1526 0.1211
0.9691 1.1028 1.2163
-0.0591 0.1638 0.1100
0.9681 1.1155 1.2004
0.42 4.13 1.75
0.9566 1.2463 0.9605 1.1904
- 0.0698 0.3138 -0.0827 0.0808
0.9568 1.2526 0.9600 1.1777
1.44 8.29
0.0644
-0.0687 0.3101 0.0805 0.0884
0.0506 0.0914
0.0446 0.1191
1.0478 1.2135
0.0452 0.1095
1.0501 1.1995
1.592 1.808
- 0.0572 0.0594
-0.0674 0.0758
0.9830 1.2919
-0.0691 0.0703
0.9859 1.2810
1.11 1.15
4Cyanopyridineb
0.0768 0.0468 0.1047
0.0547 0.0552 0,1483
1.0005 1.0924 1.3582
0.0607 0.0507 0.1326
1.0036 1.0934 1.3394
1.40 2.62 2.33
4Cyanopyridinec
0.0602 0.0574 0.1068
0.0297 0.0825 0.1663
0.9981 1.1001 1.3695
0.0351 0.0788 0.1488
1.0008 1.1014 1.3506
1.40 2.62 2.33
0.0450 0.0259 0.0579
1.0683 1.0243 1.2644
0.0515 0.0141 0.0577
1.0638 1.0276 1.2709
1.807 0.286 1.047
0.1568 0,0918 m-Dicyanobenzene
p-Dicyanobenzene Tetracyanobensene
-0.0489 0.3220 -0.0888
... ... ...
-
50.08 1.02
4,4'-Dicyanobiphenyl'
0.0629 0.0092 0.0494
0.0583 0.0109 0.0623
1.0651 1.0246 1.2836
0.0599 0.0173 0.0494
1.0645 1.0334 1.2502
1.807 0.286 1.047
Tetracyanoquinodimethane
0.0431 0.0537
0.0552 0.0599
1.0584 1.1569
0.0566 0.0556
1.0602 1.1493
1.44 1.02
Tetracyanoethylene
0.0765
0,0998
1,1801
0.0941
1.1711
1.574
From Table I of ref 7. * Calculation with CUN = a c f 0.6@in the McLachlan method; with BCN(~=)= -2.271 ev in the RHF perturbation method. Calculation with (YN = CUD f 0.50 in the McLachlan method; with BcN(=*) = -2.60 ev in the RHF perturbaCalculation with BCC = 1.944 ev between rings. ' Calculation with all ~ C C= -2.29 ev. tion method.
'
splitting constants (Table 11: p4 = 0.295). The value for the excitation energy of the main absorption band of 1,2,4,5-tetrocyanobenzenewas also predicted to be far too high using this value of ,~?cN.'~ Parameters for Aza Nitrogen. Where the nitrogen is an aza nitrogen, the Mulliken formula, eq 3, gives a value of -2.271 ev for PCN a t a bond distance of 1.34 A. This is considerably different from the value of -2.50 to -2.60 ev used by several previous workers.12*21-2aHowever, on comparing the results using both these values for calculation on 4-cyanopyridine, we find that the first value gives better results for the effect of the aza nitrogen on the excited states of benzonitrile (Table V), and we conclude that
the value of -2.271 ev is more suitable than the more negative values often previously used. Thus, on replacing the C-H in the 4 position of benzonitrile by an aza N, the observed second transition is moved only very slightly by 350 cm-' to higher frequencies. Using P C ~ Nvalue of -3.75 ev, the use of P C - N of ~ ~-2.60 ev predicts a considerable shift to higher frequencies of 1670 cm-', whereas the use of PC-N~~.= -2.27 ev results in a predicted shift of 700 cm-' to higher fre(21) G.Favini, I. Vandoric, and M. Simonetta, Theoret. Chim. Acta, 3 , 45,418 (1965).
(22) F. Peradejordi, C u h k s Phys., 17, 393 (1963). (23) C.Weiss, H.Kovayaahi, and M. Gouterman, J . Mol. Spectry., 16, 415 (1965).
Volums 71, Numbw 6 April 1067
J. E. BLOOR, B. R. GILSON,AND D. D. SHILLADY
1242
Table IV : Statistical Analysis of Relationships between Experimental Hyperfine Splitting Constants and Theoretical Parameters Parameters
Q"
Set 1" Set I* Set 1" Set If Set I' Set 2' Set 2d Set 2" Set 2' Set 2'
21.39 24.33 26.37 18.04 12.13 20.65 23.55 25.58 21.57 14.14
'K
R'
C'
...
16.09
0.594 0.648
... ...
... ... ... ...
...
-9.88
-0.0188 0.282 0.609 0.663
...
... ... ... -13.65 ...
15.15
... ... ... *..
+
...
-0.161 0.194
+
Mean emrb
Standard errorb
Multiple correlationb
No. of data
0.3937 0.4171 0.5912 0.1062 0.1258 0.4120 0.4541 0.5840 0.0925 0.1186
0.5779 0.5872 0.8291 0.1590 0.1829 0.5933 0.6017 0.8498 0.1379 0.1790
0.9856 0.9838 0.9645 0.9608 0.9387 0.9848 0.9829 0.9628 0.9706 0.9414
14 14 14 9 9 14 14 14 9 9
+
From the equation ucH I= (Qc" KAq)p 4-C or aN = QNp RZCoq* C; the latter sum is over all neighbors and is one term only in cyano compounds. * See Table 111, ref 5, for definition. Best line regardless of values of &, K, and C, for carbon-bonded hydrogens. Best line for K = 0, for carbon-bonded hydrogens. " Best line for K = C = 0, for carbon-bonded hydrogens. Best line regardless of values of Q, R, and C,for nitrogens of CEN groups. 'Best line with R = 0, for nitrogens of C=N groups.
Table V : Experimental and Calculated Transition Energies (Set 1 Calculations) -0bad
x
Molecule
value-
101
cm-1
log e
Table VI : Comparison of Polarographic Reduction Potentials with LUMO Energies (Figure 4)
-Calad values-. x 101 cm-1 f
Ella -LUMO energy(polaroSet 1, Set 2, graphic),' p = - 3 . 7 5 @ = -4 ev ev ev
Compound
Benzene Naphthalene (1) Benzonitrile'
(2) o-Dicyanobenzeneb (3) m-Dicyanobenzeneb (4) pDicyanobenzeneb (6) Tetracyanobenzene" (7) pMethoxybenzonitrile (8) pAminobenzonitriled (9) CCyanopyridine' (11) Tetracyanoquinodimethane (12) Tetracyanoethylene"
49.5 32.1 34.7 45.1 36.1 43.1 35.3 43.7 35.6 42.5 35.2 39.1 32.8 40.7 35.2 38.3 45.5 36.9 2.5.3 37.6
...
48.5 32.1 35.1 45.1 37.6 42.8 36.2 44.1 36.5 42.4 36.5 39.7 34.6 40.4 35.4 37.4 45.8 36.2 2.5.2
0.353 0.002 0.256 0.006 0.184 0.003 0.690 0 * 009 0.127 0.000 0.402 0.021 0.601 0.260 0.071 1.740
4.14
40.3
0.873
4.07 2.82 4.01 3.3 3.94 2.56 4.35 3.15 4.18 3.46 4.28 3.04 4.34 3.87 3.46
'
' Sources of experimental data: ref 8. From ref 10. " From From ref 11. " W. M. Moreau and K. W e b , J . Am. ref 9. C h a . Soc., 88, 204 (1966). quencies in much better agreement with theory. The effect of the aza nitrogen in the 4 position on the polarographic reduction potential (AB = 0.71 ev) is also better predicted by the -2.27-e~resonance integral and we think that this value should be considered when planning calculations on aza nitrogen compounds. The Journal of Physical Chemistry
(1) Benzonitrile (2) 0-Dicyanobenzene (3) m-Dicyanobenzene (4) pDicyanobenzene (6) Tetracyanobenzene (7) pMethoxybenzonitrile (8) pAminobenzonitrile (9) 4Cyanopyridine (11) Tetracyanoquinodimethane (12) Tetracyanoethylene
-2.74 -2.12 -2.17 -1.97 -1.02 -2.95 -3.12 -2.03 -0.19
-1.657 -2.040 -1.944 -2.146 -2.673 -1.381 -1.301 -2.120 -3.038
-1.593 -1.955 -1.871 -2.059 -2.567 -1.312 -1.231 -2.059 -2.904
-0.17
-3.875
-3.801
'P. H. Rieger, I. Bernal, W. H. Reinmuth, and G. K. Fraenkel, J . Am. Cha. Soc., 85, 683 (1963).
Electron Spin Densities (a) Proton Splitting Constants. The calculations on the electron spin densities for the nitrile anions derived from the molecules of Figure 1 were carried out using the RHF perturbation method of part Isusing the closedshell SCFMO's of the neutral molecules obtained m described above to calculate the matrix elements using an ALGOL computer program similar to that previously de~cribed.~'Two sets of calculations, one with BCN = -3.75 ev (set 1) and one with PCN = 4.0 ev (set 2), were performed; the results are summarized in Table 111. ~~
~
(24) FORTRAN and ALGOL programs are available from the authors. The ALGOL program is t o be submitted t o the Quantum Chemistry Program Exchange, Bloomington, Ind.
THEORETICAL CALCULATIONS ON IONS AND RADICALS
1243
A statistical analysis of the relationship between the observed proton hyperfine splitting (hfs) constants (upH) and the electron spin density pp at atom p was then carried out using (1) the simple McConnell relationship (eq 4) and an equation relating apHto both spin density and excess charge density (Aqp) upH = (Qc"
+ KAqp)pp
(5)
Two conditions were considered for eq 4: either a finite intercept was allowed or the intercept was arbitrarily assigned to zero. For eq 5, only the form with an added intercept C was used. The results of the analyses are summarized in Table I11 and, for the case of PCN = -3.75 ev (set 1 calculations) and a finite intercept, are shown graphically in Figures 2A and 2B. The scatter in the graphs for calculations of set 2 is very similar, but, of course, the gradients of the graphs are different giving different values for the u--a interaction parameters Qc" and K (Table IV). To place the results for the benzonitriles on the same regression line as the polycyclic hydrocarbons using eq 3 with zero intercept, we would, as already discussed, have to use a value of PCN between the values used for sets 1 and 2. However, the data demonstrate that over this small range the spin densities are linearly related to PCN, so that the calculation using an intermediate PCN value was only carried out for benzonitrile. When we allow a finite intercept, the value of this intercept for the simple McConnell relationship is considerably higher (C = 0.594) than for the case of the hydrocarbons (C = 0.373), lending support to our previous suggestion that the presence of this intercept is due to the operation of some auxiliary factors such as solvent effects or non-nearest-neighbor interactions which are not considered in the derivation of eq 3 and 4 and which are more important for the nitrile anions than for the hydrocarbon anions. The results obtained with eq 5 are not significantly better than those obtained with eq 3. Furthermore, the QcHHand K values obtained (Table IV) are very different from those obtained for polycyclic hydrocarbon ions (Qc" = 24.55, K = -11.52) both in magnitude and, in the case of K, the sign. We now have a positive sign for K in agreement with theoretical prediction^.^^ We feel, however, that this agreement with theory could be fortuitous and should not be given too much significance. It does, however, strengthen considerably our previous contention6 that the spin densities and charge densities calculated from SCFMO wave functions (restricted or unrestricted) are not good enough to be used to test the soundness of equations that include small extra terms added to the simple McConnell relationship, eq 3.
Figure 2A. Comparison of predicted and observed hfs constante using the equation an = 24.33~ 0.648. (Set 1: Q = 24.33; C = 0.648.)
+
!V,#, ,
, * , .,,,,.,,.
I
,
.,
.
I
.
,.,, *
...,
4
N
~2.m
-0.911
1.m
z.9m
y.m
5.m
1.m
0.9m
10.0
RCTURL VRCUE
Figure 2B. Comparison of predicted and observed hfs constants using the equation a= = (21.39 16.09Aq)p 0.594. (Q = 21.39; K = 16.09; C = 0.594.)
+
+
(b) 14N Hyperfine Splitting Constants. It has recently26 been shown that for the hfs constants of (25) J. Higuohi, J . Chem. Phys., 39, 345 (1963). (26) J. C. M. Henning, ibid., 44,2139 (1966).
Volume 71, Number 6 April 1967
J. E. BLOOR, B. R. OILSON,AND D. D. SHILLADY
1244
nitrogen, ApN, the equation for 14N corresponding to the simple McConnell relationship for proton hfs constants is
APN =
QNN~PN
+ QccNC P ~ : i
%r /
(6)
where PN is the electron spin density at nitrogen and p i is the spin density at the nearest neighbor carbon atoms, the sum being over all nearest neighbor carbons C,. It is of interest to investigate whether our SCFMO calculations give for the nitriles reasonable values for the coupling factors and to compare with those of Rieger and Fraenkel‘ for calculations using the Huckel and McLachlan methods; also of interest is whether the addition of the second term does actually produce significant improvement or whether the simple equation
ApN = Q N p ~ is good enough. As suggested for the particular case of nitrile anions in ref 7, the statistical data for these equations are given in Table IV. The most notable improvement of including the extra term as in eq 6 is that the intercept is made very small, although the standard error is also slightly reduced. It seems reasonable, therefore, to include the term involving the adjacent carbon spin density. The value of the U-T parameters are considerably different from those obtained by both the Huckel and McLachlan procedures although the signs of the parameters are the same for all three methods and are in agreement with theory. Since we have no other way of obtaining reliable values of the u-T parameters we cannot assess a t present which of the three methods gives the best U-T parameters. Because of this lack of precision in our knowledge of PT parameters, we did not attempt to estimate the 13Chfs constants. Electronic Transition Energies. The SCFM0 method has been shown to predict successfully at least the first two electronic transitions of many polycyclic hydroc a r b o n ~ ~ ,as ~ ~well * ~as ~ ,the ~ *spin densities of the corresponding negative ions.5 For the cyano compound of Figure 1, we have calculated by the standard CI3vl5method the first two t,ransition enerSCFMO gies and compared them with the experimental data when available. The data are summarized in Table V and expressed graphically for set 1 calculations in Figure 3. To this graph we have also added points for benzene and naphthalene calculated using the parameters of Table I. In general, the agreement between experiment and theory is good, considering the total range of transitions is 25,000 cm-l (from benzene a t 50,000 cm-’ to tetracyanoquinodimethare (TCNQ) at 25,000 cm-l). The only really poor result
+
The Journal of Phyeieal Chmdslry
a4
Figure 3. Comparison of spectral transitions calculated and observed for benzene, naphthalene, and nitriles. Where two transitions are plotted for the same molecule, squares are used for the lower frequency transition and circles for the higher.
was for tetracyanoethylene (TCNE), the main transition of which was predicted to be 2500 cm-’ higher than the observed frequency. It may be that the approximations used in the present calculations are not suitable for TCNE, which is the only compound which does not contain an aromatic ring. Polarographic Reduction Potentials. If we assume there is very little change in the MO’s on adding an electron to a molecule, then we can expect the electron affinity to be given by the energy of the lowest unoccupied MO, E(LU).3 If we assume further that we can either ignore solvent effects or that they can be corrected for by adjusting the regression coefficients, then we might expect E(LU) to be linearly related to electrode reduction potentials measured in DMF. Such relationships are not u n c ~ m m o n . ~The , ~ graph in Figure 4 shows that we have such a case for our E(LU) values.12 The two exceptions on the graph are for TCNE and TCNQ. Since, however, measurements for these two compounds were made in acetonitrile while the others were in DMF, we cannot determine whether the deviations are due t o a poor calculation, as seems likely in the case of TCNE, or due to solvent effect. ~
~
(27),,A. Streitwieser, “Molecular Orbital Theory for Organic Chemists,
John Wiley and Sons, Inc., New York, N. Y..1961, p 176 ff.
THEORETICAL CALCULATIONS ON IONSAND RADICALS
1
1' \
0
Conclusions
Our results on polycyclic hydrocarbons and cyano compounds demonstrate that it is possible to use one set of semiempirical parameters in SCFMO calculsr tions to predict successfully the electronic excited states 'and the electron affinities of the neutral molecules and the spin densities of the radical anions. Moreover, by careful adjustment of the semiempirical
1245
parameters for the heteroatoms, it was found possible to fit results for compounds containing heteroatoms to the same regression lines used for the hydrocarbons. We believe that this procedure of extending systematically calculations on hydrocarbons to compounds containing heteroatoms will prove very fruitful in establishing a set of semiempirical parameters for use in SCFMO calculations of complicated molecules. In the present study, it has led to values of resonance integrals for the carbon-nitrogen bands (a) where the nitrogen is of the aza type ( > N) and (b) where the bond is of the cyano type ( C e N ) , which are bornewhat different from those used previously. Our data on the spin densities of nitrile anions fully substantiate our previous conclusions that SCFMO wave functions are not good enough to warrant using any refinements to the simple McConnell relationship (eq 3) between hfs constants of protons and calculated spin densities, but that for the 14Nhfs it is an improvement (although only slight) to employ an equation (eq 6) in which nearest neighbor effects are included. This result is consistent with the recent work of HenningZ6which demonstrated that eq 6 for 14N hfs constants was of the same degree of approximation as the McConnell equation (eq 3) for proton hfs constants.
Acknowledgments. It is our pleasure to acknowledge financial support from Smith Kline and French Laboratories, Philadelphia, Pa., and also to thank the Computing Center of the University of Virginia for a generous gift of computing time.
VOhm6 71, Number 6
April 1967
