Electronic Structure of T Systems Part Ill. Applications in Spectroscopy and Chemical Reactivity Marye Anne Fox and F. A. Matsen University of Texas at Austin, Austin, TX 78712
In the orecedine articles in this series (1),we have oresented a new view uf the rlectronic structure of r systems that combines the best featuresof Huckel and valence bond theory (2). I t employs electronic structure diagrams, energy spectra that are linear functions of fractional valence bond character. We show here that electronic structure diagrams make more accurate predictions of spectral properties and chemical reactivity for simple a systems than do either Huckel molecular orbital or valence bond theory alone. In this paper we treat absorption and photoelectron spectra and spin density distribution in radicals and discuss a number of problems regarding chemical reactivity: geometrical isomeriention, sterrochemistrv of hiradical and carhene additions, topolom of pericyclic reactions, and a state-specific photoreaction. We find for many a systems that good agreement with experiment is obtained for a fractional valence bond character between 0.3 and 0.5. Spectroscopy Polyene Absorption Spectra The state enereies hvdrocarhons can be used . . of coniueated , to predict absorption spectra and the process can he generalized for long-chain polyenes. This prediction is accomplished by calculating the transition energies rrquired for promotion of an elecrron from a filled tusuallv hondina! orbital to a vacant MO. Since Hiickel theory ailows a prediction of the enereies of these orbitals.. a general formula will relate the .. length of a polyene to its lowest energy tmnsition. By indurtion, we see that the orbital enewies - of ethylene and hutadiene ohe; the formula u
-
MO
A0
T k f o r k = 1,2,. . .M
tr = +Zp cos
M+l
a general formula derived by Coulson for energies in M-atom linear polyenes (3).Since in the ground state the orbitals are doubly occupied, we can easily identify the highest occupied molecular orbital (HOMO, k = MI2) and the lowest unoccupied molecular orbital (LUMO, k = M/2 1) between which the lowest energy electronic transition occurs. The frequency of the longest wavelength absorption is given, therefore, by
+
h v ~ ( M=) r(HOM0) - r(LUM0) = 2p
[-
(S) + (=)I msr
cow
Mk+l
T
= -48 sin 2M+1
Thus, we see that Hiickel theory predicts that, as the length of a polyene increases, the transition energy will disappear; i.e., that long polyenes should he black. Not only are polyenes not hlack but the spectrum levels off a t 18,000 cm-' (-550 nm) (4). The shift to longer wavelength in absorption upon increasing the length of a conjugated system can he illustrated by comparing the electronic structure diagrams of ethylene (Fig. 1) and butadiene (Fig. 2). At the Huckel extreme a t the left side of the diagram, the energy difference between the ground and excited state decreases, ultimately, with longer and longer ?rsystems, approaching zero. At the VB extreme a t the right, the separation between ground and excited states for all polyenes remains constant a t I -28, the electron repulsion parameter. Clearly, the valence bond prediction is also in error, for i t requires that all polyenes exhibit the same ahsorption spectrum. If, however, one mixes valence bond character into the Hiickel MO's.. i.e.. . between the left and rieht extremes of the correlation diagram, hettrr correspondence with experiment is observed than with eithvr rxtreme model alone. Thus, the transition energies will he a sum of the conrril~utionof thr Huckel HO!vlO-LUMOrnerev seuaration and some fraction of the repulsion parameter I:'
-
hv(M) = (1 - X ) ~ Y H B ~ + L ~TI I Fractional valence bond character therrt'ore intrnducrs electron reoulsion into Huckel statesand exr~lainsnhv- the . o d v.ene absorption spectra level off a t a non-zero transition enerm. Thus. near the center of the electronic structure diagrams, where fractional electron repulsion is included, we resolve the auestion of whv are not black. Indeed, . oolvenes . with x = 0.3?. hv(M) - hvnaa.~ I - hunucrer we quantitatively reproduce both the lowest energy transition of butadiene and the transition energy for an infinitely long polyene. An alternate interpretation is based on the Pierl's instability (2). X
0
X
Figure 1. Linear correlation diagram for ethylene.
I
=
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FRACTIONAL VALENCE BOND CHARACTER Figure 2. Linear corrleation diagram for butadiene.
(Ew-EM)+
(EM+-EM]
+a
- I("28)MORE DNIC
STATES
0
0
I
FRACTIONAL VALENCE BOND CHARACTER Figure 3. Ionization energies for butadiene (C4He
-
C Hec).
Photoelectron Spectroscopy Photoelectron spectra can also he predicted with our graphical approach. Photoelectron spectroscopy (PES) (5) provides a method for the determination of the energy I(k) required to form an ion M+(k) in an electronicstate k from the ground state of the parent molecule M, i.e., the energy required to remove an electron to the vacuum. Koopman's theorem, which is used routinely to related MO energies to PES, states that
I(k) = -4k) where c(k) is the energy of the kth occupied orbital in M. This association has been used to assign values for a and 0. Koopman's theorem is based on several assumptions. Among these are the neglect of (1)the difference in electron repulsion in the neutral molecule and in the ion and (2) configuration 552
Journal of Chemical Education
interaction among the several molecular orbital states. However, since the cation formed by ionization normally will have a lower electron density than its neutral precursor, electron repulsion is generally greater in the parent molecule than in the related cation. This suggests that I(k) obtained by Koopman's theorem may somewhat overestimate real ionization energies.' In Figure 3, we have plotted the differences between the cationic state energies and the molecular ground state of hutadiene. T o the latter, we have added a, the energy required to remove an electron from an isolated carbon atom. The Koopman's ionization energies are thus given on the extreme left of the figure. As these MO states correlate with VB states (i.e., as we move to the right of this figure), lower ionization energies are predicted, as is in fact observed in many conju-
'
Nevertheless, Koopman's theorem often gives good, albeit sometimestoo large, estimates of ionization potentials for many conjugated systems.
gated hydrocarbons. This figure also correctly predicts that the degeneracy in the third state of the ion is partially removed. I t should he noted that exactly the same considerations a o ~ l vto the radical anion e neutral conversion. Since the pa;tkle-hole relationship (c.f., pairing theorem in alternant hvdrocarhons ( 6 ) )aoolies. Fieure 3 would be exactlv suoerimposahle (save fo; v e k i c z displacement caused b; increased electron repulsion) on the corresponding electron detachment from radical anions. Such states, which can be studied by spectroscopic techniques, are of fundamental importance in studies of anion photochemistry (7).
a
Many examples of excited-state, sudden polarization in unsymmetrical homopolar systems are known (8).
S-cis, s-trans-hexatriene provides an interesting example of sudden polarization effected by rotation about the central bond. On rotation, the system is separated into two allyl fragmentri denoted A1 and Az. Each has an MO configuration $12$z and Huckel energy of +2.8@. However $Z = 0,so no
Polarization Effects on Absorption Spectra Effect of Electronegatiuity. If we convert ethylene into a heterodiatomic system by increasing the electronegativity of atom B relative to atom A (by an amount 6 ) (e.g., convert ethylene to formaldehyde), the energy levels of ethylene are perturbed, qualitatively, as shown in Figure 4. On the left side are the ethylene levels taken from the center of Figure 1.Note that the excited singlet states S1 and Sp correlate with the ionic (albeit nonpolarized) and states A--B+ A+-BAs the electroneeativitv of B increases with respect to A, (i.e., as we I move to the right in Fig. 4) these ionic states are split. The INCREASING ELECTRONEGATIVITY covalent and triplet Figure 4, Increasing stabilization of a rwitterionic state of ethylene. states are effected only slightly, however. In an electronic excitation in less-polarized olefins (i.e., further to the left of Fig. 4), the transition occurs from a state which is largely covalent to one which is largely ionic.
-
(m) (m).
I
-
(8)
h"
A-B +A+-B-
These transitions have relevance in photosynthesis and photoelectrochemical cells. At high polarization (i.e., on the right half of the figure) the ground state is ionic, where relative to ethylene, electron transfer from B to A has taken place. In optical transitions in these highly polarized olefins, polarization actually decreases upon excitation. A+-B-
hu
A-B
Both transitions are described as charge transfer transitions. I'olarization of Unsaturated H)drocarbons. A more subtle increase in the elwtroneeativitv of atom H in ethvlene can be accomplished by appripriati substitution a t either carhon atom. If we choose a somewhat polarized olefin (at I in Fig. 4) and if we rotate the two methylene groups relative to each other so that @ approaches 0,we obtain Figure 5. That is, the ground state So (which has substantial character) will be more strongly affected by twisting than any other state. We note that as So crosses S1, the ground state suddenly changes from A=B to A+-B-, a phenomenon that is called audden polarizarion, i.e.. upon twisting, a awalent state is converted to a highly polarized zwitterionic state. This sudden polarization is oftenexperienced in excited state reactions.
DiHEDRAL ANGLE (+)F 5 m 5. Th3efiecl ol inereasingdihebalangle on& state energies of palarked ethylene.
Huckel energy is gained or lost if an electron is transferred from A1 to Ap or vice versa. In consequence, the Huckel ApC and AI+ Ap- are equal to energies for A1 Ap, A1each other and to +2.8P. Since s-cis, s-trans-hexatriene is not symmetrical about its midpoint, it possesses a nonzero (hut extremely small) dipole moment in its ground state. Let us assume that, because of the difference in electron repulsion, the two ends of the dipole moment are oriented to make Az slightly more electron-rich
+
+
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than A1. We can mimic this difference in electron repulsion by adding a small electronegative parameter 6 to A2. (Its precise value is of little significance.) Then the correlation diagrams of AI- Az+, AI' Az', and AI+ Az- are as shown in Figure 6, together with the correlation of the ground and excited states of hexatriene (for which the Hiickel energies are *1.88, f 1.250, and f0.4450). We see that the following reaction is a reasonable one.
+
+
+
This is the mechanism nronosed bv Dauben t o exolain the highly stereospecific p;od;cts in t h e photocycli~ationof trans-3-ethvlidenecvclooctene( 9 ) and in the mechanism for electron transfer in &ion (10). Our a treatment, Figure 4, predicts that increasing alkyl substitution (increased polarization by hyperconjugation) should lead to lower enerm electronic transitions. That this is so is demonstrated in tL table, which lists ultraviolet ahsordion maxima and ionization enereies - within a familv of substituted ethylenes (11). Effect of Heteroatoms. In principle, one might expect that more dramatic shifts would he ohsewed in the n,a* transitions of C-heteroatom double bonds. Unlike the preceding cases, however, substitution of a heteroatom into a a system induces many more quantitative changes than can he conveniently handled by this simple treatment. Clearly, the presence of unshared electrons on the heteroatom will drastically alter the values for a and @ for appropriate elements of the Hiickel matrix and will induce altered sigma frames in such molecules. These effects would tend to move ahsorotion transitions to higher energies, offsetting the trend toward lower transition enereies caused hv.. nolarization alone. For examole. while the lowest energy a,=* transition in ethylene occurs at'161.4 nm, that for formaldehyde
aooroach. like occurs at 155.5 nm (I I ). Note that our -maohical . .. a-CI theory itself, willbe valid ibr pn,hlenls involvin:, a effects only; sperifically, it cannot handle rhanges inducrd t ~ yn effects. The presence of nonhonded electrons does allow for an
Figure 6. The effect of twisting an the energies of the low-lying states of hexabiene
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Journal of Chemical Education
Effect ot Alkyl Substltutlon of *,?re Transition Energles compound Ethylene Propene I-Butme l-Pentene l-Hexene 2-Methylpropene cis
