Valence bond excitation

Because electrons are much lighter than nuclei, they move much faster. The intrinsic temporal regime for valence bond electron dynamics is the few femtosecond to several hundred attosecond timescale. Therefore, efficient and accurate control of electron dynamics requires extreme precision regarding the control field. Commonly attosecond techniques are considered to be the appropriate tools for efficient manipulation of electron motions [61-63, 111, 112]. However, attosecond pulses in the XUV region are not suited for efficient valence bond excitation (see Section 6.1). Here we demonstrate that ultrafast electron dynamics are controlled efficiently on the sub-10 as timescale employing a pair of femtosecond laser pulses with a temporal separation controllable down to zeptosecond precision [8]. 

Looking ahead, coherent laser pulses covering the complete spectral range of valence bond excitation from the UV to the IR spectral region are becoming available (see, e.g., [119]), and we expect SPODS to increase in importance in coherently controlled photochemistry with applications ranging from reaction control within molecules up to discrimination between different molecules in a mixture and laser-based quantum information technologies. 

For this reason, there has been much work on empirical potentials suitable for use on a wide range of systems. These take a sensible functional form with parameters fitted to reproduce available data. Many different potentials, known as molecular mechanics (MM) potentials, have been developed for ground-state organic and biochemical systems [58-60], They have the advantages of simplicity, and are transferable between systems, but do suffer firom inaccuracies and rigidity—no reactions are possible. Schemes have been developed to correct for these deficiencies. The empirical valence bond (EVB) method of Warshel [61,62], and the molecular mechanics-valence bond (MMVB) of Bemardi et al. [63,64] try to extend MM to include excited-state effects and reactions. The MMVB Hamiltonian is parameterized against CASSCF calculations, and is thus particularly suited to photochemistry. 

The other aspect of a conical intersection that we have tried to emphasize is that there is a relationship between the valence bond structures associated with the ground state or the excited state and the position of the surface crossing. In any mechanistic study this is also very interesting because it provides information that can be used to think intuitively about mechanisms. We will try to emphasize this point of view in the rationalization of all the examples we will look at. 

Table 2.4 shows a comparison of the experimental and PPP-MO calculated electronic spectral data for azobenzene and the three isomeric monoamino derivatives. It is noteworthy that the ortho isomer is observed to be most bathochromic, while the para isomer is least bathoch-romic. From a consideration of the principles of the application of the valence-bond approach to colour described in the previous section, it might have been expected that the ortho and para isomers would be most bathochromic with the meta isomer least bathochromic. In contrast, the data contained in Table 2.4 demonstrate that the PPP-MO method is capable of correctly accounting for the relative bathochromicities of the amino isomers. It is clear, at least in this case, that the valence-bond method is inferior to the molecular orbital approach. An explanation for the failure of the valence-bond method to predict the order of bathochromicities of the o-, m- and p-aminoazobenzenes emerges from a consideration of the changes in 7r-electron charge densities on excitation calculated by the PPP-MO method, as illustrated in Figure 2.14. 

The effect of substituents on colour in substituted anthraquinones may be rationalised using the valence-bond (resonance) approach, in the same way as has been presented previously for a series of azo dyes (see Chapter 2 for details). For the purpose of explaining the colour of the dyes, it is assumed that the ground electronic state of the dye most closely resembles the most stable resonance forms, the normal Kekule-type structures, and that the first excited state of the dye more closely resembles the less stable, charge-separated forms. Some relevant resonance forms for anthraquinones 52, 52c, 52d and 52f are illustrated in Figure 4.3. The ground state of the parent compound 52 is assumed to resemble closely structures such as I, while charge-separated forms, such as structure II, are assumed to make a major contribution to the first excited state. Structure II is clearly unstable due to the carbocationic centre. In the case of aminoanthraquinones 52c and 52d, donation of the lone pair from the... 

Consider a diatomic molecule A2 in which there is a single a bond. Excitation of an electron to the a state gives rise to an absorption at 15,000 cm-1. The binding energy of an electron in the valence shell of atom A is -9.5 eV. 

Simonetta and Heilbronner (1964) recently carried out calculations by the valence bond (VB) method for some simple cations, and compared the results obtained by this method, inter alia, with the results of Colpa and collaborators (1963) and of Koutecky and Paldus (1963). In the case of the proton addition complexes of mesitylene and cyclohepta-triene, the electron excitation energies calculated by the VB method agree very well with experiments, and also agree to a good approximation with the results of Cl calculations. The calculations also successfully reproduce the electron density of the cycloheptatriene cation. In this, a perturbation calculation allowed for the AO s adjoining the —CHg—CH2-lihkage. 

We discuss all of the key features of our current CASVB methodology for modem valence bond calculations on ground and excited states. The CASVB strategy may be used to generate compact representations of CASSCF wavefunctions or, alternatively, to perform the fully-variational optimization of various general types ofVB wavefunction. We report also a new application, namely to the fourteen % electrons of a planar dimethylenecyclobu-tadiene chain with three rings. 

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. 

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