Second excited

Second-order effects include experiments designed to clock chemical reactions, pioneered by Zewail and coworkers [25]. The experiments are shown schematically in figure Al.6.10. An initial 100-150 fs pulse moves population from the bound ground state to the dissociative first excited state in ICN. A second pulse, time delayed from the first then moves population from the first excited state to the second excited state, which is also dissociative. By noting the frequency of light absorbed from tlie second pulse, Zewail can estimate the distance between the two excited-state surfaces and thus infer the motion of the initially prepared wavepacket on the first excited state (figure Al.6.10 ). 

CN] —> I + CN. Wavepacket moves and spreads in time, with its centre evolving about 5 A in 200 fs. Wavepacket dynamics refers to motion on the intennediate potential energy surface B. Reprinted from Williams S O and lime D G 1988 J. Phys. Chem.. 92 6648. (c) Calculated FTS signal (total fluorescence from state C) as a fiinction of the time delay between the first excitation pulse (A B) and the second excitation pulse (B -> C). Reprinted from Williams S O and Imre D G, as above. 

The second excitation mechanism, impact scattering, involves a short range interaction between the electron and the molecule (put simply, a collision) which scatters the electrons over a wide range of angles. The usefiil feature of impact scattering is that all vibrations may be excited and not only the dipole active ones. As in Raman spectroscopy, the electron may also take an amount of energy hv away from excited molecules and leave the surface with an energy equal to Eq + hv. 

It was shown above that the normal two-level system (ground to excited state) will not produce lasing but that a three-level system (ground to excited state to second excited state) can enable lasing. Some laser systems utilize four- or even five-level systems, but all need at least one of the excited-state energy levels to have a relatively long lifetime to build up an inverted population. 

Fig. 1. Schematic energy-level diagram for a dye molecule. Electronic states Sq = ground singlet state = first excited singlet state S2 = second excited singlet state Tj = first excited triplet state T2 = second excited triplet state EVS = excited vibrational states. Transitions A = absorption excited states ...

The first two predicted and observed excited states match up easily, and there is reasonable agreement between the two energies (especially for the second excited state). We also identify the fifth predicted excited state with the third observed peak, based on the identical symmetry and its relative oscillator strength with respect to the other predicted excited states it is the strongest state seen here, just as the observed A[ peak has the greatest relative area. 

The red line follows the progress of the reaction path. First, a butadiene compound b excited into its first excited state (either the cis or trans form may be used—we will be considering the cis conformation). What we have illustrated as the lower excited state is a singlet state, resulting from a single excitation from the HOMO to the LUMO of the n system. The second excited state is a Ag state, corresponding to a double excitation from HOMO to LUMO. The ordering of these two excited states is not completely known, but internal conversion from the By state to the Ag state i.s known to occur almost immediately (within femtoseconds). 

This proof shows that any approximate wave function will have an energy above or equal to the exact ground-state energy. There is a related theorem, known as MacDonald s Theorem, which states that the nth root of a set of secular equations (e.g. a Cl matrix) is an upper limit to the n — l)th excited exact state, within the given symmetry subclass. In other words, the lowest root obtained by diagonalizing a Cl matrix is an upper limit to the lowest exact wave functions, the 2nd root is an upper limit to the exact energy of the first excited state, the 3rd root is an upper limit to the exact second excited state and so on. 

The electronic spectrum of imidazole was studied at the CASSCF and CASPT2 levels [96JPC6484]. In the gas phase the first and second excited singlet... 

For large interchain separations (8 A < R < 30 A), the LCAO coefficients of a given molecular orbital are localized on a single chain, as intuitively expected. The lowest excited state of these dimers results from a destructive interaction of the two intrachain transition dipole moments, whereas a constructive interaction prevails for the second excited stale. This result is fully consistent with the molcc-... 

Studies of actinide photochemistry are always dominated by the reactions that photochemically reduce the uranyl, U(VI), species. Almost any UV-visible light will excite the uranyl species such that the long-lived, 10-lt seconds, excited-state species will react with most reductants, and the quantum yield for this reduction of UQ22+ to U02+ is very near unity (8). Because of the continued high level of interest in uranyl photochemistry and the similarities in the actinyl species, one wonders why aqueous plutonium photochemistry was not investigated earlier. 

Figure 5. Dependence of photon Figure 6. The Zeeman sub-levels of the ground state return per Watt of laser power on second excited state, and the effects of optical...

Table 2. Energies and symmetries of the second excited stales of nonaltemant hydrocarbons...

The orbital arrangement for pentalene shown in Fig. 2 serves to indicate how close the second excited state is to the first excited state when two more electrons are placed in the nonbonding orbital to form the dianion. The very small (E2 — E1) values for fulvalene and hepta-fulvalene are realized from the orbital arrangements shown in Fig. 4 in both molecules the two lowest excited states ( 3 and 211) have the same energy in the Huckel picture. 

The symmetry of the most soft distortion in the lowest excited state is given by the direct product of the symmetry of the first excited state (shown in Table 1) and that of the second excited state (shown in Table 2). These symmetries are b3g(R ) for 1 and VII 2(1 ) for XVII and IV- hi (z) for XXI and XXIII, and fli(z) for XXII. The symmetries of the lowest excited states are then predicted to be Cj, Q, and C2 , respectively. It should be noted that despite the strong vibronic coupling with the second excited state, the first excited state of sesqui-fulvalene (XXII) does not undergo a symmetry reduction. 

Following this argument, in the first- and second-excited states, the electrons are placed in the Is and 2s orbitals. The antisymmetric spatial wave function has the lower energy, so that the first-excited state Pi(l, 2) is a triplet state. 

The decay of benzene from the S2 state under collision-free condition has also been studied. J. P. Reilly and co-worker studied the nanosecond UV laser induced multiphoton ionization/fragmentation processes. The rate equation model was used for the simulation and the lifetime of the second excited singlet state was estimated to be 20 ps.19 More recently the... 

Another explanation has been offered to explain the large proportion of cyclobutane derivatives produced by low-energy sensitizers, especially for the anthracene derivatives.<17) This is that energy transfer to diene occurs from the second excited triplet state of the sensitizer rather than the first. Experiments using a large number of anthracene derivatives as sensitizers... 

Energy for second excited triplet. b Energy for lowest excited triplet. 

Figure 3 Type I and type II photooxidation processes with a porphyrin sensitizer illustrated with a modified Jablonski diagram. (S0 = ground singlet state, Si = first excited singlet state, S2 = second excited singlet state, T,i— ground triplet state, Ti = first excited triplet state, i.s.c. — intersystem crossing.)...

Fig. 4. Physical significance of calculations of the potential energy gradient at the starting nuclear geometry. From left to right, negative slope, positive slope, and a calculation for the second excited state...

The formation of thietanes from thiones and olefins has been less exploited for synthetic purposes than the corresponding oxetane-forming reaction. It should be remarked that thiocarbonyl compounds very often undergo efficient photoreactions from the second excited singlet state S2 U4). One interesting synthetic application is found in the photochemical preparation of quinolines from N-thioamides (4.84)498). The primary photochemical step is assumed to be the intramolecular thietane formation. 

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