Wavefunction excited state

H. Nakatsuji, Chem. Phys. Lett., S9, 362 (1978). Cluster Expansion of the Wavefunctions. Excited States. 

In words, equation (Al.6.89) is saying that the second-order wavefunction is obtained by propagating the initial wavefunction on the ground-state surface until time t", at which time it is excited up to the excited state, upon which it evolves until it is returned to the ground state at time t, where it propagates until time t. NRT stands for non-resonant tenn it is obtained by and cOj -f-> -cOg, and its physical interpretation is... 

For separable initial states the single excitation terms can be set to zero at all times at this level of approximation. Eqs. (32),(33),(34) together with the CSP equations and with the ansatz (31) for the total wavefunction are the working equations for the approach. This form, without further extension, is valid only for short time-domains (typically, a few picoseconds at most). For large times, higher correlations, i.e. interactions between different singly and doubly excited states must be included. 

We will find an excitation which goes from a totally symmetric representation into a different one as a shortcut for determining the symmetry of each excited state. For benzene s point group, this totally symmetric representation is Ajg. We ll use the wavefunction coefficients section of the excited state output, along with the listing of the molecular orbitals from the population analysis ... 

In the limit of infinite atom separations, or if we switch off the Coulomb repui. sion between two electrons, all four wavefunctions have the same energy. But they correspond to different eigenvalues of the electron spin operator the first combination describes the singlet electronic ground state, and the other three combinations give an approximate description of the components of the first triplet excited state. 

I don t mean that such a wavefunction is necessarily very accurate you saw a minute ago that the LCAO treatment of dihydrogen is rather poor. I mean that, in principle, a Slater determinant has the correct spatial and spin symmetry to represent an electronic state. It very often happens that we have to take combinations of Slater determinants in order to make progress for example, the first excited states of dihydrogen caimot be represented adequately by a single Slater determinant such as... 

A more general way to treat systems having an odd number of electrons, and certain electronically excited states of other systems, is to let the individual HF orbitals become singly occupied, as in Figure 6.3. In standard HF theory, we constrain the wavefunction so that every HF orbital is doubly occupied. The idea of unrestricted Hartree-Fock (UHF) theory is to allow the a and yS electrons to have different spatial wavefunctions. In the LCAO variant of UHF theory, we seek LCAO coefficients for the a spin and yS spin orbitals separately. These are determined from coupled matrix eigenvalue problems that are very similar to the closed-shell case. 

I mentioned the Brillouin theorem in earlier chapters if rpQ is a closed-shell HF wavefunction and represents a singly excited state, then... 

Excited-state wavefunction analyses arc carried out in the framework of the Intermediate Neglect of Differential Overlap/Single Configuration Interaction (INDO/ SCI) technique to characterize the properties of the photogenerated electron-hole pairs. The SCI wavefunction writes ... 

Regarding the emission properties, AM I/Cl calculations, performed on a cluster containing three stilbene molecules separated by 4 A, show that the main lattice deformations take place on the central unit in the lowest excited state. It is therefore reasonable to assume that the wavefunction of the relaxed electron-hole pair extends at most over three interacting chains. The results further demonstrate that the weak coupling calculated between the ground state and the lowest excited state evolves in a way veiy similar to that reported for cofacial dimers. 

The proposed scenario is mainly based on the molecular approach, which considers conjugated polymer films as an ensemble of short (molecular) segments. The main point in the model is that the nature of the electronic state is molecular, i.e. described by localized wavefunctions and discrete energy levels. In spite of the success of this model, in which disorder plays a fundamental role, the description of the basic intrachain properties remains unsatisfactory. The nature of the lowest excited state in m-LPPP is still elusive. Extrinsic dissociation mechanisms (such as charge transfer at accepting impurities) are not clearly distinguished from intrinsic ones, and the question of intrachain versus interchain charge separation is not yet answered. 

In general, the first excited state (i.e. the final state for a fundamental transition) is described by a wavefunction pt which has the same symmetry as the normal coordinate (Appendix). The normal coordinate is a mathematical description of the normal mode of vibration. 

For nondegenerate vibrations all symmetry operations change Qj into 1 times itself. Hence Q/ is unchanged by all symmetry operations. In other words, Q and consequently y(O) behave as totally symmetric functions (i.e. the function is independent of symmetry). However, the wavefunction of the first excited state 3(1) has the same symmetry as Qj. For example, the wavefunction of a totally symmetric vibration (e.g. Qi of C02) is itself a totally symmetric function. 

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