Excited states of benzene

The UHF option allows only the lowest state of a given multiplicity to be requested. Thus, for example, you could explore the lowest Triplet excited state of benzene with the UHF option, but could not ask for calculations on an excited singlet state. This is because the UHF option in HyperChem does not allow arbitrary orbital occupations (possibly leading to an excited single determinant of different spatial symmetry than the lowest determinant of the same multiplicity), nor does it perform a Configuration Interaction (Cl) calculation that allows a multitude of states to be described. 

The excited states of benzene exemplify the importance of the following points in any theoretical study of excited states ... 

Woodruff and coworkers65 produced triplet states for several carotenoid pigments by pulse radiolysing benzene solution of the carotenoids with higher concentration of naphthalene. The initially produced excited states of benzenes (both singlet and triplet) are... 

In contrast to borazine, the three corresponding excited singlet states of benzene have a much wider spread of absorbing wavelengths and exhibit easily distinguished vibrational fine structure. Many photolysis experiments have been performed using laser lines tuned to selective excite a particular vibrational level of a particular excited state of benzene. Such experiments are more difficult with borazine. The triplet states of benzene have been located experimentally and quantum yields for fluorescence and phosphorescence at various wavelengths and pressure conditions have been determined. 

In an early application to butadiene [16], and later to the ground and excited states of benzene [17], Berry analyzed MO-based wavefunctions using valence bond concepts, simply by considering the overlaps with nonorthogonal VB structures. Somewhat closer than this to a CASVB type of approach, are the procedures employed by Linnett and coworkers, in which small Cl wavefunctions were transformed (exactly) to nonorthogonal representations [18-20]. The main limitation in their case was on the size of systems that may be treated (the authors considered no more than four-electron systems), both because this non-linear transformation must exist, and because it must be possible to obtain it with reasonable effort. 

The lowest excited states of benzene are actually of B2u and Bi symmetry, and they can be reached directly by neither one-photon nor two-photon purely electronic transitions (the 0-0 band at energy Eq-o. the origin of the transition, is absent from the spectra). However, excitation into these states can be obtained through vibronic coupling (VC), if a vibrational mode of an appropriate symmetry is coupled to the electronic transition. The IPA or 2PA spectra can then show a series of narrow peaks shifted from the 0-0 band... 

Insofar as the latter process docs not involve any orbital reoptimization for any particular state, it provides a wave function that is roughly equivalent in quality only to an HF wave function for the ground state. Of course, this may still be useful for a number of purposes. CIS results for six excited states of benzene are included in Table 14.2, as are results from other levels of theory that will be discussed later. The CIS results are qualitatively useful, insofar as the states are correctly ordered, and the error is fairly systematic - all states are predicted to be too high in energy by an average of 0.7 eV. The worst prediction is for the lowest excited state, which is known to have significant dynamical electron correlation, and is therefore challenging for the CIS method. 

Table 14.2 Energies (eV) for singlet excited states of benzene relative to the Aig, ground state as predicted by various methods ...

Table 14.2 includes RPA results for the six excited states of benzene already discussed in the context of CIS. The more complete RPA formalism does improve the results for those cases where CIS is most in error, but the net improvement in mean absolute error over all six states is only 0.1 eV in this case. 

Table 14.2 includes TDDFT results from the pure BPW91 and hybrid B3LYP functionals for the six excited states of benzene previously discussed for CIS and RPA methods. The pure functional is better for the most highly correlated Biu state, but the mean absolute error for the two methods over all six states is equivalent. The improved quality of the TDDFT results compared to CIS or RPA is substantial. 

Perhaps the best-known photoaddition reaction of benzene is that with chlorine to produce hexachlorocyclohexane (3.37). of which one steroisomer is widely used as an active component in insecticides. However, this reaction does not involve the excited state of benzene chlorine absorbs light and cleaves homolytically to give chlorine atoms, which then attack the ground state of benzene, leading to overall addition. 

In 1995, we decided to stop further research on this topic because it seemed a philosophical idea that engages primarily theoreticians with little or no impact on experimental chemistry. That this was a premature decision became obvious at the end of 1995, when we learned from Haas and Zilberg31 about the frequency exaltation of the bond alternating vibrational mode in the l B2U excited state of benzene. This created a link of the purely theoretical notion to an experimental probe. The synthesis of Siegel s distorted benzene32,33 demonstrated that a ground state cyclohexatriene has been finally achieved and that this may be a case where 7r-dis-tortivity is at work. This was followed by a demon-... 

Scheme 34. b2U Modes of Benzene and Their Frequencies in the Ground and B2u Excited States of Benzene (Refs 227, 232, and 233)... 

The addition of benzene to 2,3-dihydropyran was examined in the presence of cyclopropyl bromide [177] in an attempt to determine the nature of the excited state of benzene responsible for the formation of the ortho adduct [11,12], The absorption of the bromide at 254 nm was taken into account (90% of the radiation was absorbed by benzene) and a decrease of the rate of formation of 50% in the heavy-atom solvent was observed. Cyclopropyl bromide also quenched the fluorescence of benzene (kq = 3.82 X 10s L/mol 1 /s ). These data are interpreted as enhanced intersystem crossing of Si benzene and the necessary involvement of the Si state in formation of the ortho cycloadduct. 

The molecular orbitals of benzene are schematically represented in Fig. 3. The first excited state of benzene cannot be described by one electron configuration, due to the degeneracy of the highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs). The Si state of benzene (B2u) can be represented as 4>24>4 - 4>35 and the S2 or state (Biu) as 4>24>5 - 4)3(t,4-... 

The spin-coupled method has now been applied to a large number of aromatic systems benzene and naphthalene azobenzenes, such as pyridine, pyridazine, pyrimidine and pyrazine five-membered rings, such as furan, pyrrole, thiophen, and thiazole and inorganic heterocycles, such as borazine ( inorganic benzene ) and boroxine, for which we find little evidence of aromaticity. Structural formulae are collected in Fig. 1. For all of these molecules we have included the effects of electron correlation for the Jt electrons but not for the a framework. This a-n separation is an approximation whose utility rests upon the chemistry of aromatic systems — to abandon it would be to ignore this entire body of experience. Furthermore, very extensive calculations [4] have demonstrated that rc-electron only correlation affords an excellent description of ground and excited states of benzene. 

The aim of this exercise is to compare the bonding features of the ground versus first excited states of benzene, with a method different from that of the preceding exercise. The bond index for an r—s bond will be taken as the probability of finding a spin alternation from r to s in the wave function. Thus, the r—s bond index can be estimated by summing up the squares of the coefficients of the determinants displaying an r-s spin alternation, in the wave function of the state under consideration. 

TABLE 7.Ans.l Indices for the r—s Bond in the Ground and Excited States of Benzene... 

With this method, we clarified the electronic structures of the ground and excited states of benzene, butadiene, methane, and hydrogen molecules [1,2]. We also applied the method to valence excited states of polyenes [3] and then-cations [4]. In previous studies, we put our focus on the formalism of CASVB and its applicability to molecules in their equilibrium structures. 

Fig. 3. CAS VB description for the ground and singlet excited states of benzene.

Christiansen O, Koch H, Halkier A, Jprgensen P, Helgaker T, Sanchez de Meras A (1996) Large-scale calculations of excitation energies in coupled-cluster theory The singlet excited states of benzene. J Chem Phys 105 6921-6939. 

Scavenging Studies. The solvent excited states produced by radiolysis of aromatic liquids could be produced directly, or formed, via charge neutralisation of solvent ions. The low oscillator strengths of the first and second excited states of benzene, toluene and p-xylene preclude direct excitation into these states. However, the third excited state could be excited with a yield as high as unity. 

---