7662
Equivalence of the Energy Gaps AI (1,2) and AE (1,2) between Corresponding Bands in the Photoelectron ( I ) and Electronic Absorption ( E ) Spectra of SpiroC4.41nonatetraene. An Amusing Consequence of Spiroconjugation C. Batich, E. Heilbronner,* Erika Rommel, M. F. Semmelhack, and J. S. Foos Contribution from the Physikalisch-chemisches Institut der Universitat Basel, CH-4056 Basel, Switzerland, and the Department of Chemistry, Cornell University, Zthaca, New York 14850. Received June 8, 1974
Abstract: Correlation of the photoelectron (PE) spectra of spiro[4,4]nonatetraene (l),spiro[4.4]nona-l,3,7-triene(2), spiro[4.4]nona-1,3,6-triene(3), and spiro[4.4]nona-1,3-diene(4) yields the assignment of the first three bands at 7.99, 9.22, and 10.55 eV in the PE spectrum of 1 (symmetry D2d) to ionization processes in which the photoelectron vacates the molecular orbitals la2(a), lbl(T), and 7e(n), respectively. The difference A1(1,2) = 1.23 eV between the positions of the first two PE bands of 1 is equal, within the limits of error, to the difference AE (1,2) = 1.2 to 1.3 eV between the first two bands 8e(x*) laz(x) and 8 e ( ~ * ) lbl(.rr) in the electronic absorption spectrum of I. It is shown that this correspondence is the consequence of spiroconjugation between two identical alternant subsystems in a molecule of D2d symmetry, e.g., in 1.
-
+
Orbital diagrams such as the one shown in Figure 1 (see column a ) seem to suggest that the difference A1(1,2) = I ( 2 ) - Z(1) between the second and first ionization potentials of a closed shell molecule M should match exactly the difference AE (1,2) = E (2,- 1) - E (1 ,- 1) between the excitation energies corresponding to the second and first bands in the electronic spectrum of M. More generally (see column b of Figure l ) , the difference
between the (vertical) ionization potentials I ( r ) , which according to M(xo)
-
‘ E ( Y ,k ) =
- E(Xo) = -
E($k)
-
Jrk
+
(1)
AZ(i, j ) = Z(i) - Z ( i )
I(?)
singly excited singlet and triplet configurations of M , we have
M+($;‘)+ e-
(2 )
2Krk
(8) 3 E ( r ,k ) = E(3X,R) - E(Xo) = E(bk) -
E($,.)
-
J,.k
where stands for the orbital energy of $r and where Jrk (the Coulomb integral) and K r k (the exchange integral) have their usual meaning, Le.
correspond to the ejection of an electron from one or the other of two nondegenerate orbitals $ r ( r = i or J ) , might naively be expected to equal
(3 1
h ~ ( i , j=) ~ ( j , k -) ~ ( i , k )
where E ( r , k ) ( r = i or j ) stands for the electronic excitation energy
of the neutral, closed shell molecule M. (In ( 2 ) and (4),xo = ( $ I ) ~,. , (#,)2 , . is the ground state configuration of M and xrk S= ( $ 1 ) 2 . . . ( i c r ) l . . . ($.n)’($k)’ a singly excited configuration obtained by promoting an electron from $r to # k . ) However, from the well-known matrix elements of the Hamiltonian for the ground and singly excited states of a closed shell molecule M,I it is immediately obvious that the expected equality I
A E ( i , j ) = AZ(i, j )
(5)
will generally not be true. If =
Ih4. . . d r b r . . . zhniinl
(6)
is the SCF single Slater-determinant wave function of the ground state and i x k
1 {I = ->T
-
$,&j
. . . d&,.- . . b&,l- + -
Idid1
-
f
. dk$y-
$nznr}
(7) Journal of the American Chemical Society
z(r) =
(4)
E ( Y , k ) = E ( X ; ) - E( X O )
xo
Assuming the validity of Koopmans’ theorem, i.e.
/
96:25
/
-€($J
* (10)
it follows from (3), (4),and (8) that A ’ E ( i ,j ) = AI({, j ) 3-
(J{k
-
Jjk)
A 3 E ( i , j ) = AZ(i,j)
+
+ 2(Kjk - Ki,) (11) (Jtk- J,k) (12)
As can be seen from (1 1) the relationship 5 applied to singlet-singlet transitions will be true only if (J,k - J,k) 2(K,k - K l k ) = 0, which is generally not the case.3 Indeed, the sign and the size of A l E ( i J ) - A Z ( i , j ) depends critically on the shape of the orbitals $,, $, and # k . Haselbach and his coworker^^^^ have given rules for the qualitative prediction of this difference, rules which can be applied, e.g., for the assessment of “through-space’’ and “throughbond” interactions5 between localized (or semilocalized) orbitals. It will be shown that in certain spiro-conjugated systems,‘j e.g., in spiro[4.4]nonatetraene ( I ) , J!k - J,k and KJh - K , k should be zero in a first approximation, due to the prevailing symmetry and (almost) pairing properties of selected bonding ($,, $ J ) and virtual ( $ k ) orbitals. Thus this class of compounds will yield examples where the naive ex-
December 1 I , 1974
+
7663
E(1,-1) or E(i,k) UJ, or
W,
W2
W,
or
(b)
(a)
6
7
8
9
10
11
12
13
14
15
16
17
18
6
7
8
9
10
11
12
13
14
15
16
17
18
6
7
8
9
10
11 --
12
13
_ M_
15
16
17
18
10
11
12
13
15
16
17
18
Figure 1. Level scheme for ionization and electronic transitions in the framework of an independent electron treatment.
pectation expressed by ( 5 ) is exceptionally fulfilled.
I. The Photoelectron Spectrum of Spiro[4.4]nonatetraene (117
Figure 2 shows the photoelectron spectra of 1 and its diand tetrahydro derivatives 2, 3, and 4. The corresponding
2
1
5
4
6
3
a
7
9
10
ionization potentials of 1, and those of the reference compounds 2 (spir0[4.4lnona-1,3,7-triene),~,~ 3 (spiro[4.4]nona-1,3,6-triene), 4 (spir0[4.4]nona-l,3-diene),~~~ 5 (spir0[4.4Jnon-l-ene),~~6 . (cyclopentane), 7 (cyclopenr tene), I I 8 (cyclopentadiene),’ l b , I 2 9 (spiro[4.3]hepta-1,3~ ’ ~ 10 (spiro[4.3]octa-1,3diene = “ h o m o f ~ l v e n e ” ) , ~ and diene)I0 a r e given in Table I. These potentials refer to the
__
~
..
Table I. Photoelectron Spectraa --R
7-
Compd
1st
band 2nd
7
3rd
1 2 3 4 5 6
7 . 9 9 ;8.17; 8.32 9.22 10.55 8 . 2 5 ;8 . 4 2 9.03; 9 . 2 0 : 9.37 10.36 8 . 2 7 ; 8.44 9 . 2 5 ; 9.45 10.50 8.10; 8.38 10.30 8.86d
7 8
9.20 K60 8.15 8.38d
9
10
10.75 9.45 10.12d
12.71
u
onset
11.7b 11.4 11.5 11 .o 10.65d 10.5 10.9 11.2 e 10.8d
All ionization potentials are given in eV. Italic values are the most intense component(s) of the band. Band correlated with orbital 6e(u); see text. Both components of same intensity. Values taken from ref. 10. e Band at 10.90 eV correlated with Walsh-orbital’ 12ai ( u ) ; band at 11.90 eV correlated with orbital 7b2(u). Corresponding orbital mainly of Walsh-type, centered on cyclopropane f
moiety. position of the corresponding band maximum or to the highest intensity fine-structure component and are thus close to the vertical ionization potential Iv,J. All spectra have been recorded on a modified PS-15 spectrometer (Perkin-Elmer Ltd., Beaconsfield, England).
6
7
8
9
14
Figure 2. Photoelectron spectra.
It is known’4 that 1 rearranges to indene 11 by a unimolecular process a t 65’ with t 112 = 65 min, and also on irradiation, direct (Pyrex filter) or sensitized (thiaxanthenone). Therefore one might have expected that the reaction
1
11
occurs also under the conditions prevailing in the inlet system and/or the target chamber of the photoelectron specHeilbronner, et al.
/
Spectra of Spiro(4.4/nonatetraene
7664 trometer. The photoelectron spectrum of 11 has been described by Eland and Danby.I5 O u r own spectrum of l l confirms their data within +0.02 eV, i.e., 8.12, 8.95, and 10.30 eV for the first three T bands. These fine-structured bands are intense and sharp, the 0 0 vibrational component being the most prominent. As can be seen from Figure 2 there is no indication of these bands in the photoelectron spectrum of 1. Recordings taken a t different times and from two independently prepared samples of 1 yield exactly the same spectrum, i.e., the one shown in Figure 2. The photoelectron spectroscopic evidence for spiroconjugation has been first described by Schweig and his coworkers. I n a series of papers they investigated the photoelectron
-
la,(n)
lb,W
7e (IT)
If the basis orbitals an are assigned an orbital energy ( ~ , l X l a , ) = A , and if the interaction matrix elements (resonance integrals) are ( x , l ~ l a b ) = ( a l J ~ I a d ) = B , ( r r , l X ( T c ) = -(aalXl.lrd) = -(?rdXIXc) = (KdXITd) = b , then the energies of the LCBO orbitals in eq 15 are
€ ( f a , ( n ) )= A, - B - 2b < ( l h j ( n ) ) = A, - B
€(7e(7r)) = A,
+
+
2b
(16)
B
The lowest unoccupied (antibondingj molecular orbitals have to be written in terms of the antibonding basis orbitals a n * of energy A , * . They form the degenerate set spectra of tetravinylmethane (12, X C),I6 tetravinylsilane (12, X Si),I7 9,9’-spirobifluorene (13, X = C), 9,9’spirobi(9-silafluorene) (13, X Si),I8 and 1,l’-spirobiindene ( 14).19 11. Simple Molecular Orbital Model for
Spiro[4.4]nonatetraene (1) As a basis for the discussion of the photoelectron and electronic spectra of 1 we construct a simple MO model for 1 following the rules given by Simmons and Fukunaga6d and by Hoffmann, Imamura, and Zeiss.6b The 62 electrons of 1 (symmetry D2d) occupy the following set of bonding molecular orbitals 8xal + 1x-a, + l x b , + 7 x b 2 + 7 x e (13) The three highest occupied orbitals laz(a), l b l ( a ) , and 7e(.rr) of local a symmetry are best visualized as h e a r combinations of either the la;(a) or the 2 b i ( ~ orbitals ) of the two spiro-connected cyclopentadiene moieties of individual C 2 symmetry. To avoid confusion of the orbital labels we have marked the orbitals of 8 ( C 2 ) with a dot, e.g., a2 belongs to the irreducible representation A2 of Cz,, and a2 to the representation Az of D2d. Note that 2 b j ( ~ )is a “true” a orbital of 8 while I b j ( a ) is best described as a pseudo-a orbital of the bridging methylene group. Because of the high symmetry of 1 a Z D O linear combination of bond orbitals will be sufficient for our purposes. The numbering and the relative phases of the basis .rr orbitals 1 71, = + @J (14) (e.g.. n = a , p = 1, u = 2 ) and thus of the atomic 2p orbitals
cbr are shown in the following diagram and Newman projection: 1
a
8e(i7*)
1
=
:yzbr:
+
=
yZ(T,*
iab*
7rb*
+
7r,*
-
7r,+
-1-
Td*)
(17) - a,*)
Had we used the traditional conventions of HMO theory [Le., all Coulomb integrals equal a; resonance integrals equal 0 if 1 , u = 1.2; 3,4; 6,7; 8,9; if 1 , u = 2,3; 7,8 use n p and for the homoconjugative interactions, m p if = 1,6; 4,9; and - m p if fi,u = 1,9; 4,6; note that m < n < I ] then the orbital energies associated with the highest occupied bonding orbitals would be ~
E(la,(n)) =
€(lb,(n)) =
(Y
CY
- (2m
+
+ n
( 2 n ~- vz
