Conjugated Radicals. 1II.l Calculations of Electronic Spectra of

1249

CONJUGATED RADICALS

Conjugated Radicals. 1II.l Calculations of Electronic Spectra of Alternant Odd Radicals of the Allyl, Benzyl, and Phenalenyl Types by P. &rsky and R. Zahradnik

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Institute of Physical Chemistry, Czechoslovak Academy of Sciences, Prague, Czechoslovakia (Received February 6, 1969)

The results of the LCI-SCF study of odd polyene radicals, odd a,w-diphenylpolyene radicals, benzyl radical, and benzo derivatives, and phenalenyl radical and benzo and naphtho derivatives are presented. Experimental data on the electronic spectra are still rather poor and in some cases even not very reliable. These radicals are "little colored" in comparison with the radical ions of a similar size and having the same number of r-electrons (e.g., the pair 1-naphthylmethylradical and naphthalene radical anion) due t o the fact that the position of the first band of radical anions is connected with an unnatural N + V gap in the HMO scheme, whereas that of neutral radicals is connected with a natural gap (which is considerablygreater than an unnatural gap for systems of similar siae). First-order CI does not change this situation substantially.

Natural radicals studied in this paper belong to the odd alternant systems without a cycle or with a cycle (I odd 1or I odd 2 according to our classification21a).

Methods, Compounds, and Results Methods and procedures were exactly the same as described in part I s 3 We considered an interaction of the ground state (G) with 40 singly excited configurations (of types A, B, C,, and C,), or, for smaller systems (e.g., pentadienyl, benzyl), with all singly excited configurations. Calculations were carried out by the L C I S C F (Longuet-Higgins and Pople) method. Systems 2 and 18 were also calculated by the L C I S C F (Roothaan) method. The following systems were studied: odd polyenes (1-6),4 odd a,w-diphenylpolyenes (7-11),4 benzyl (12), 1-naphthylmethyl (13), 2-naphthylmethyl (14), 1-anthrylmethyl (15), 2-anH&= (CH-CH ),,-H 1, n = 1 2, n 3, n 4, n 5, n 6, n

= =

7I"\**/ \

/,.(

2 3 4

5

n = l

n=2

d

n =5

r \P

L) L.)

LJ'.J

17

20

15

p, f'\

18

21

Discussion Comparison of Theoretical and Experimental Data. Experimental data for allyl given by several authors are available in l i t e r a t ~ r e . ~ -These ~~ data differ from each other rather considerably: Ohnishi, Sugimoto, and Nitta5 reported absorption maximum at 236 mp;

n = 3 n =4

&6 14

16

19

CH=CH),+Ph 7, 8, 9, 10, 11,

= 10

13

12

-CH2

= =

Ph&'H;Lt(

thrylmethyl (16), 9-anthrylmethyl (17), phenalenyl (18), benzophenalenyl (19), dibenzophenalenyl (20), and benzo [cd]pyrenyl(21). I n order to obtain as complete a knowledge of the properties of the studied systems as possible, calculations were also carried out for systems for which no experimental data are available a t present. Great reactivity of these radicals is a reason why the experimental studies proceed rather slowly. Data on electronic spectra are available in the literature for six of the systems studied: 1, 12, 13, 14, 17, and 18. Theoretical electronic spectra of systems 1-11 are drawn schematically in Figure 1. Experimental and theoretical (LCI-SCF) data for arylmethyl radicals 12-14 are given in Figures 2 and 3. Finally, results of calculations for the phenalenyls together with the experimental data for 18 are presented schematically in Figure 4.

I

(1) Part 11: R. Zahradnik and P. 6&rsky, J. Phys. Chem., 74,1240 (1970). (2) R.Zahradnik and J. Michl, Collect. Czech. Chem. Commun., 30,515 (1965). (3) R. Zahradnik and P. Gbrsky, J.Phys. Chem., 74,1235 (1970). (4) In the polyenic part of molecule, all-trans configuration was con-

sidered. (5) S. Ohnishi, et al., J. Chem. Phys., 39, 2647 (1963). (6) T. Shida and W. H. Hamill, J . Amer. Chem. Soc.,

88, 6371 (1966). (7) C. L.Currie and D. A. Ramsay, J. Chem. Phys., 45,488 (1966). (8) D.M.Bodily and M. Dole, ibid., 44,2821 (1966). (9) E.J. Burrell, Jr., and P. K. Bhattacharyya, J. Phys. Chem., 71, 774 (1967). (10) A. B. Callear and H. K. Lee, Trans. Faraday Soc., 64, 308 (1968).

Volume 7.4, Number 6 March 19,1970

P. CARSKYAND R. ZAHRADN~K

1250

(CH,-CH)&H, -1 -2

@ell etd 25

4 4 8

L

Porter and Stmchan" W a n d Mker" RipocbM

8

I

n= 2

0 -1 -2

I

lot "I

\

I

w

I

\

I

\

0-

n=3


-1 -2 -

t

3

0-

n= 4

-1 -

-2 -

t i

0

0 -1

0-

-2

n-5

-2 -1

5 1 5

1

I

I Moria''

Berthier3"' Berthier 3', j ' Berthier 3''j'k Hnchlijfe d ai3"i'e4n

0

0

-1

-1

-2

-2

40

e Mor1

I

30

20

10

30

20

10

0

5 (kK)

Figure 1. LCI-SCF prediction of electronic spectra of odd polyenes 1-6 and odd a,@-diphenylpolyenes 7-11. Allowed transitions are indicated by vertical lines, forbidden ones by wavy lines with arrows; f stands for the oscillator strengths.

Shida and HamilP recorded absorption band of amethylallyl with a maximum a t 500 mp; Currie and Ramsay7 recorded absorption maximum of allyl at 408 mp; Bodily and Doles measured the absorption spectrum of allyl in the region 230-270 mp with a maximum a t 258 mp, and Burrell and B h a t t a ~ h a r y y afound ~ in the region 290-380 mp a maximum at 310 mp. According to the recent measurement by Callear and Lee,l0 allyl exhibits an absorption in the region of 222-249 mp with maxima a t 224, 225, 227, and 229 mp. For theoretical data, cf. ref 11-16. Our LCI-SCF calculation (configurations G, A(l + 2), B(2 + 3), C,(1 + 3), and Cg(1--t 3) were taken into account) results in a first strongly forbidden electronic transition a t 423 mp (this differs by only about 0.8 kK from the band position reported by Currie and Ramsay), and a second (allowed) transition at 197 mp, the value of which is different by approximately 6.5 kK from the maximum given by Callear and Lee. Evidently, it is questionable how reasonable the n-electron approximation is in so small a molecule as allyl. Without any doubt, a-levels lie between the The Journal of Physical Chemistry

Figure 2. Experimental and theoretical spectral data for 12 (for details see text). Arrows and solid curve indicate the positions of experimentally found maxima. Calculated electronic transitions are indicated by vertical lines (forbidden transitions by wavy lines with arrows). Dotted lines and curve represent LCI results for the benzyl cation35and electronic spectrum of the dimethylbenzyl cation,a5 respectively. Explanation: V B calculation, bHMO with first-order CI treatment, cFE-MO; dfirst-order CI, oscillator strengths are not given, "Huckel M0'8, 'Longuet-Higgins and Pople MO's, U S C F - M O , method ~ ~ ~ of composite system (benzene and methylene group), iLCI, different MO's for each configuration, 2LCI,ground state, 3 A-type, 3 B-type, 9 %type, and 9 Cg-type configurations, nRoothaan MO's, Rbicentricrepulsion integrals calculated according to Pariser and Parr, and Obicentric repulsion integrals calculated according to Mataga and Nishimoto.

n-levels; nevertheless we believe that owing to the interaction between degenerate configurations A and B (first order CI, cf. Figure 5), the calculated excitation energy of the first transition is reasonable and lower than the energies of the T + u* and u --+ a* transitions, which, moreover, should be weak. Benzyl has been studied intensively both experimentally17-26 and theoretically.12"4*27-32 The LCI(11) W.Moffitt, Proc. Roy. SOC.,A218,486 (1953). (12) H.C.Longuet-Higgins and J. A. Pople, Proc. Phys. SOC.,A68, 591 (1955). (13) G.Berthier, J . Chim. Phys., 52,141 (1955). (14) H.Brion, R.Lefebvre, and C. Moser, ibid., 54,363 (1957). (15) D.M. Hirst and J. W. Linnett, J . Chem. Soc., 1035 (1962). (16) J. W.Linnett and 0. Sovers, Discussions Faraday SOC.,35, 58 (1963).

CONJUQATED RADICALS I

I

I

1251 I

I

I

‘

I

I

i

c,

M-3 1 cp

___-----

1

c, (4-3)

(4-93)

//

ui

‘50 I

Ill

I T I

I 1

40

I

I

I

I t

I

I

I

I

I

‘

+ E(2-4)

30 I

I

fDownloaded by CENTRAL MICHIGAN UNIV on September 15, 2015 | http://pubs.acs.org Publication Date: March 1, 1970 | doi: 10.1021/j100701a015

A(1-Q)

/-

I

It

-

‘1t

LC I

01

ev Figure 3. Comparison of experimental and theoretical spectral data of 13 and 14. Intensities of the experimentally found maxima in the visible88 and ultraviolets4 regions are drawn in independent arbitrary units. LCI data are indicated below by vertical lines (forbidden transitions by wavy lines with arrows).

SCF

t

12

log f

log& 4

0

3

1

2

2

1

3

‘1t

SCF

LC I

0‘ Figure 5. SCF and LCI excitation energies in allyl (1) and benzyl (12) radicals.

0

4

0

3

1

2

2

1

3

0

50

40

30

20

10

40

30

20

dkK:

Figure 4. LCI-SCF prediction of electronic spectra of 18-21 (-). Arrows indicate the experimental data of 18 (for details see text). Allowed calculated transitions are indicated by vertical lines (forbidden by wavy lines with arrows); fstanda for the calculated oscillator strengths. For comparison, experimental and theoretical data for the cations corresponding to 18, 19, and 22 are added ( . . . . .), cf. R. Zahradnik, M. TichQ, P. Hochmann, and D. H. Reid, J . Phys. Chem., 71, 3040 (1967).

.

(17) G.Porter and E. Strachan, Spectrochim. Acta, 12,299 (1958). (18) G. Grajacar and S. Leach, Compt. Rend., 252, 1014 (1961). (19) H.Schihr and J. Kusjakow, Spectrochim. Acta, 17, 356 (1961). (20) A. T.Watts and S. Walker, J . Chem. Soc., 4323 (1962). (21) B. Brocklehurst and M. I. Savadatti, Nature, 212, 1231 (1966). (22) G. Porter and M. I. Savadatti, Spectrochim. Acta, 22, 803 (1966). (23) J. Ripoche, Compt. Rend., 262,30 (1966). (24) J. Ripoche, Spectrochhn. Acta, 23A, 1003 (1967). (25) C. L. Angell, E. Hedaya, and D. McLeod, Jr., J . Amer. Chem. Soc., 89,4214 (1967). (26) P. M. Johnson and A. C. Albrecht, J . Chem. Phys., 48, 851 (1968)). (27) W.Bingel, Z . Naturforach., loa,462 (1965). (28) Y. Mori, Bull. Chem. SOC.Japan, 34,1031, 1035 (1961). (29) C.Bertheuil, Compt. Rend., 256,5097 (1963). (30) J. Baudet and G. Berthier, J . Chhn. Phys., 60, 1161 (1963). (31) G. Berthier, “Molecular Orbitals in Chemistry, Physics, and Biology,” P. 0. Lowdin and B. Pullman, Ed., Academic Press, New York, N. Y., 1964. (32) A. Hinchliffe, R. E. Stainbank, and M. A. Ali, Theoret. Chim. Acta, 5, 96 (1966). Volume 74,Number 6 March 19, 1970

P. CARSKY AND R. ZAHRADN~K

1252 Table I : LCI-SCF Spectral Characteristics (Doublet-Doublet Transitions) Transition

Allyl Pentadienyl 1,3-Diphenylallyl


Benzyl

a-Naphthylmethyl

1 2 1 2 3 1 2 3 4 5 1 2 3 4 5 6 7 1 2 3 4 5 6 7

8 Phenalenyl

9 10 1 2

a

4 5 6 7 8 9 10 11 12

G, kK

X, mp

I

23.65 50.81 16.48 29.28 40.91 17.89 25.44 25.44 26.83 29.40 22.75 23.21 34.90 35.41 43.63 47.52 48.00 17.50 24.30 29.29 32.52 33.79 33.85 37.83 42.00 44.56 45.57 19.21 19.89 24.67 28.16 32.13 32.28 32.31 40.18 42.67 44.52 45.49 46.97

422.9 196.8 606.9 341.5 244.4 559.0 393.2 393.2 372.7 340.1 439.5 430.8 286.5 282.4 229.2 210.4 208.4 571.5 411.6 341.4 307.5 296.0 295.4 264.3 238.2 224.4 219.4 520.6 502.7 405.3 355.1 311.2 309.8 309.5 248.9 234.4 224.6 219.8 212.9

0 0.382 0 0 0.711 0 0 0 0 1.177 0 0 0 0.056 0.309 0 0 0 0 0 0.154 0.159 0 0 0 0.148 0.136 0 0 0.001 0 0.297 0.278 0.010 0 0.003 0 0 0

. I .

-0.418

... ...

-0.144 .,. .,.

...

...

0.071

... ... ...

-1.253 -0.510

... ... ... ... ...

-0.812 -0.798

... ... ...

-0.831 -0.868 -3.892

...

-2.893 -3.692 -0.528 -0.556 -1.987

...

-2.512 -3.173 -1.427

*..

SCF theory accounts for both the band at 22 kK and the intense band a t 32 kK. The absorption curve presented in Figure 2 was recorded by Porter and Savadatti,22who produced benzyl by photolysis of toluene a t 77°K. This result agrees well with the one reported recently by Johnson and Albrecht.26 Results of other experimental and theoretical studies are given in Figure 2 in which also the experimental and theoretical data for the benzyl cation are presented for comparison. Arrows mean the positions of the O+O transitions in the first (and in one case also the second) band of the benzyl radical which was generated under various conditions (by photolysis6 of toluene in glass a t 77"K,17 by a discharge in toluene vapor (emission),20 by photolysis of toluene in different glasses a t 88°K (fluore~cence),~~ and by flash ") Experimental pyrolysis of benzylbromide in DCCCUO. data agree fairly well with each other and also the The Journal of Physical Chemistry

-Weights

lot3 I

A A A A A A A A A A A A Cp A A

cp Ca A A A A

A A Cp

c, A c, B B B A B

B A

cp

CB

c, A

Ca

(1+2) (142) (243) (1 + 3) (243) (7+8) (6+8) (5+8) (448) (748) (244) (344) ( 3 + 5) (3+4) (2-4) ( 3 4 5) ( 3 4 6) (5+6) ( 4 + 6) (3+6) (546) ( 4 4 6) (246) ( 4 4 8) (4+7) (346) ( 5 4 7) (749) (748) ( 7 + 10) (4 7) (749) (7+8) (3+7) ( 4 + lo) ( 4 + 8) ( 4 4 9) (3+7) (5 + 8)

50; 50; 45.5; 41.8; 49.1; 44.3; 37.3; 37 * 3; 33.9; 48.2; 40.4; 43.1; 53.5; 44.8; 44.1; 28.8; 34 * 3; 39.1; 37.6; 24.6; 34.6; 34.5; 19.5; 33 * 7; 39.9; 39.6; 79.9; 42.9; 45.0; 45.9; 48.5; 42.8; 41.1; 31.9; 82.9; 22.1; 27.5; 28.1; 35.5;

B B B B B B B B

(2 4 3) 50 ( 2 4 3) 50 ( 3 + 4 ) 45.5 ( 3 4 5 ) 41.8; ( 3 + 4 ) 49.1 ( 8 4 9 ) 44.3 ( 8 4 10) 37.3 ( 8 4 11) 37.3 B ( 8 4 12) 33.9; B ( 8 4 9) 48.2 B ( 4 4 6 ) 40.4; B ( 4 + 5 ) 43.1 A ( 1 + 4 ) 16.0; B ( 4 4 5) 44.8 B ( 4 4 6 ) 44.1; A ( l + 4 ) 18.7; C, ( 2 4 5 ) 34.3 B ( 6 + 7) 39.1 B ( 6 + 8 ) 37.6; B ( 6 4 9) 24.6; B ( 6 + 7) 34.6 B ( 6 4 8) 34.5 B ( 6 + 10) 19.5; Cp ( 5 + 8 ) 10.0; C, ( 5 4 8 ) 39.9; B ( 6 4 9 ) 39.6; A ( 3 4 6 ) 2.5; A ( 5 4 7) 42.6; A (6- 7) 44.9; A (4-7) 45.8; B ( 7 4 10) 48.5; A ( 5 + 7 ) 41.7; A ( 6 + 7) 40.9; B ( 7 + 11) 31.8; Cg ( 6 + 8 ) 5.8; Cjj ( 6 4 10) 20.4; C, (5 + 10) 25.7; B ( 7 + 11) 28.1 C, (6 + 9) 35.4;

Cp ( 2 + 4) 14.8

Cp ( 7 + 9 ) Cjj (3-

5)

22.0 6.6

B

( 4 4 7 ) 16.0

C,

( 3 4 5 ) 6.2 (4- 7) 18.7

B

Cp ( 5 + 7 ) 4.5 Cp ( 5 + 7) 18.9 Cjj Cjj Cp C, B

Cp Cp C, Cp

( 5 4 7) (4+7) (4-8) ( 5 + 7) (649) ( 6 4 7) ( 5 + 7) ( 5 + 7) ( 6 + 9) ( 6 + 7) (5+7) (5-c 9) (549) (448) (449)

C,

( 6 4 8 ) 13.2

A A A Cp

A A

15.8 10.0 8.0 3.6 2.5 3.1 3.4 2.0 1.0 3.5 3.2 8.7 2.3 14.0 14.7

agreement of theory with experiment for the first two bands is reasonable. Evident discrepancy occurs at the third band; at present it is difficult to decide whether the reason is a trouble of a general nature which manifests itself in the short-wavelength region by a rather poor agreement (effect of neglect of doubly excited configurations?), or if u -+ a* and a + u* transitions are "wedged" in between the R --t a* transitions similarly as in allyl. Results of calculations reproduce well the positions of the 0 + 0 transitions in the fiTst bands of naphthylmethyl radicals reported by Watts and Walker,33who measured emission in the visible region after discharge in 1- and 2-methylnaphthalene vapor (Figure 3). Absorption spectra in the ultraviolet region were mea(33) A. T. Watts and S. Walker, Trana. Faraday Boo., 60,484 (1964). (34) G. Porter and E. Strachan, ibid., 54,1595 (1958).

CONJUGATED RADICALS

1253

Table I1 : LCI-SCF Spectral Characteristics (Quartet-Quartet Transitions)" Transition

Allyl (Energy of QI is 3.051 eV) Pentadienyl (Energy of Q1 is 2,122 eV)


1,3-Diphenylallyl (Energy of Q1 is 2.925 eV)

Benzyl (Energy of Q1 is 2.552 eV)

a-Naphthylmethyl (Energy of QI is 2,225 eV)

Phenalenyl (Energy of Q1 is 3.155 eV)

A, mp

f

log f

...

...

...

...

...

*..

...

...

1 2 3

10.97 36.64 40.26

...

0 0.525 0

... ...

...

912 273 248

1 2 3 4 5 6 7 8

2.64 5.32 9.30 9.31 10.27 13.97 14.01 26.46

3786 1879 1075 1074 974 716 714 378

1 2 3 4 5 6

11.41 11.90 18.82 24.74 26.56 43.41

...

877 840 531 404 376 230

...

1 2 3 4 5 6 7 8

9.62 11.51 12.86 15.57 17.27 24.90 27.41 29.78

1040 869 778 642 579 401 365 336

,..

...

...

1 2 3 4 5 6 7 8 9 10 11 12 13 14

6.06 6.34 7.20 9.11 11.83 12.17 15.14 15.50 21.31 24.31 30.33 32.37 34.53 35.84

1649 1578 1389 1098 845 82 1 660 645 469 411 330 309 290 279

0 0 0 0.001 0 0.003 0 0 0.010 0.051 0.131 0.049 0.023 0.248

...

...

...

...

.*.

8,

kK

...

...

-0.280

...

*..

,..

0 0 0 0 0 0 0 0.80

,,.

,..

0 0 0,001 0 0 0.338

...

0 0 0 0

0 0 0.080 0.318

.,. ,

.

I

...

... ... ... -0.097 ... ...

...

-3.08

...

... -0.472

*..

... ... ... ... ... ...

-1.096 -0.498

...

...

... ...

-3.054

...

-2.592

... ...

-2.022 -1.293 -0.884 -1.309 -1.646 -0.605

Weight-

Q (1 - 3 )

7

100

88.5; 50, 50, 88.5; 52.4; 46.0; 38.1; 36.6; 36.5; 46.2; 39.0; 39.0; 50.0; 78.2; 44.3; 76.5; 49.9; 44.3; 46.6; 49.9; 79.8; 28.0; 69.6; 32.2; 48.4; 25.0; 40.4; 31.4; 35.9; 29.9; 35.2; 38.4; 38.8; 42.8; 24.2; 47.8; 43.9; 48.4; 34.3; 40.2; 26.6; 37.6; 38.6; 39.6;

Q (1-5) Q ( 2 4 5) Q ( 2 + 5) Q (2-4) Q ( 5 + 11) Q (6 11) Q ( 5 + 11) Q (7 + 10) Q (7 11) Q (7 12) Q (7 11) Q (7 + 10) Q (7- 12) Q (2- 6) Q(346) Q (3+5) Q (3-6) Q (3- 7) Q ( 2 + 7) Q(347) Q ( 4 + 8) Q ( 5 - 8) Q (5-7) Q (5+9) Q (5-8) Q (4- 9) Q (4 + 10) Q ( 4 - 9) Q (5+9) Q (5+9) Q (4+9) Q ( 4 + 8) Q(548) Q (6- 8) Q (5+8) Q (5+8) Q (6 10) Q (5 + 10) Q (3-9) Q (6 + 11) Q (3 + 10) Q (3+9) Q ( 6 + 11) Q (3 + 10)

-

---

-

11.5 50 50 11.5 20.2; 46.0 29.7; 36.6 36.5 46.2 39.0 39.0 50.0 16.0; 44.3 16.8 49.9 44.3 46.6 49.9 9.3; 28.0 9.1 32.2 48.4 25.0 40.4 31.4 35.9 26.3; 29.6; 32.8; 36.8; 36.3; 23.6; 18.0; 41.0; 43.1; 31.9; 39.8; 26.2; 34.4; 36.5; 35.0;

Q (6 + 10) 20.2 Q (6 + 10) 29.7

Q (1-7)

5.1

Q (3-9)

6.5

Q (6-8) Q (6-8) Q ( 6 + 9) Q (6 10) Q (4-9) Q (5- 9) Q (6 - 9 ) Q (5 10) Q ( 6 + 10) Q (4 11) Q ( 4 4 10) Q ( 3 4 9) Q (4 + 11) Q ( 3 + 10) Q ( 3 + 9)

-

-

23.2 17.0 7.9 5.7 8.2 21.6 16.7 7.1 3.3 8.0 9.2 13.9 10.4 12.6 11.1

In contrast to the ground (doublet) state the lowest quartet cannot be described by one dominating configuration. The composition of the latter is given a t each system in the first line above the first quartet-quartet transition.

sured by Porter and Strachana4by photolysis of 1and 2-methylnaphthalenes a t 77°K. A more thorough comparison of theory with experiment requires further experimental information about the short-wavelength region. It was found recentlys5 that probably 9-anthrylmethyl radical was formed besides or instead of the expected 9-anthrylmethyl cation when 9-chloromethylanthracene Was treated with aluminum chloride in

methylene chloride. This possibility was supported both by esr and electronic spectra (first and second bands: exptl, 15.0 and 22.5 kK; LCI-SCF, 14.5 and 22.5 kK). For isomers 15 and 16, theory predicts two weak or forbidden bands in the visible region and a strong band in the ultraviolet region as the (35) R. Zahradntk, A. Krohn, J. Panoti, and D. gnobl, Collect. Czech. Chem, Commun., tobe published.

Volume 74, Number 13 March 19, 1970

P. CARSKY AND R.


1254 third band (predicted positions of maxima of 15: 14.6, 23.8, and 26.6 kK; and those of 16: 14.6, 23.0, and 25.6 kK). Results of the L C I S C F calculations for systems 18-21 are given in Figure 4. Very few experimental data are available in the literature: according to ref 36 and 37, the solution containing 18 is yellow and blue, respectively, and Reidas reported the first band at 613 mb. These results are indicated by arrows in Figure 4. The first allowed theoretical transition (LCI) lies at 25 kK and that corresponds to a yellow color of solution. Clearly, a thorough experimental study becomes very topical. When Roothaan MO’s were used, practically the same SCF and L C I S C F results were obtained. This was demonstrated with systems 2 and 18. Similarity and differences in the electronic spectra of radicals and corresponding ions (formed by an abstraction or addition of one electron) were analyzed by Longuet-Higgins and Pople:12 first band of radicals is always shifted bathochromically with respect to the first band of ions owing to first-order CI. It is worth mentioning (Figures 2 and 4) that this difference is rather small (about 3 kK) and that two or three first transitions in the radicals are forbidden. In contrast to radicals, mixing of configurations is unimportant for the long-wave transitions in the corresponding ions (cf. e.g., data on arylmethyl cations86). First-order perturbation treatment (in the HMO framework) indicates a negligible effect of inductively acting substituents on the first band of radicals (a

The Journal of Physical Chemistry

ZAHRADN~K

band arising from the transition from the ground into the state described by the configurations A(m - 1 + m) and B(m + m l), where m denotes the singly occupied MO in the ground state). In contrast to it we expect a considerable effect in radical ions of benzenoid hydrocarbons. A parallelism appears in the behavior of the pairs odd alternant radical-alternant even hydrocarbon and odd alternant ion-radical ion of the alternant even hydrocarbon. Compositionof the LCI Wave Functions. In Tables I and I1 we present the weights of configurations in the LCI wave functions of several systems, particularly of those studied experimentally. Most of the transitions in the visible and ultraviolet regions arise from excitation into states that are formed by an interaction between degenerate configurations. Position of the longest wave-length band is nearly always connected with the transitions m - 1 --+ m and m +m 1; however, in benzyl, this band is connected with the transitions 2 + 4 and 4 + 6 (Figure 5).89

+

+

(36) P.B. Sogo, M. Nakazaki, and M. Calvin, J . Chem. Phys., 26 1343 (1957). (37) D.H.Reid, Chem. Ind. (London), 1504 (1956). (38) D. H.Reid, Quart. Rev., 19,274 (1965). (39) NOTEADDEDIN PROOF.Recently three papers were pub-

lished which are closely related to the problems studied. PPP-type calculations on allyl and pentadienyl were carried out by T. Amos and M. Woodward, J . Chem. Phys., 50, 119 (1969). Doublet electronic states of the benzyl radical were studied by means of the Roothaan SCF procedure combined with configuration interaction by J. C. Schug and D. H. Phillips, J . Chem. Phys., 49, 3734 (1968),and by Yu.A. Kruglyak, Theoret. Chim. Acta, 15,374(1969).

Conjugated Radicals. 1II.l Calculations of Electronic Spectra of

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