Polarizability excited state

R. Cammi, L. Frediani, B. Mennucci, K. Ruud, Multiconfigurational self-consistent field linear response for the polarizable continuum model Theory and application to ground and excited-state polarizabilities of para-nitroanUine in solution. J. Chem. Phys. 119, 5818 (2003)... 

Middendorf, T. R., Mazzola, L. T., Lao, K., Steffen, M. A., and Boxer, S. G., 1993, Stark effect (electroabsorption) spectroscopy of photosynthetic reaction centers at 1.5 K Evidence that the special pair has a large excited-state polarizability. Biochim. Biophys. Acta, 1143 223fi234. 

The electrostatic effects associated with the relative orientation of the chromophores show a specific connection with the corresponding electronic excited states and dipole transition moments that can, in turn, be related to changes in the hyperpolarizabilities via summation-over-states (SOS) expressions [1 3]. When the molecules interact, the electronic excited states split. In the case of a collinear arrangement, the intensities (oscillator strengths) are shifted to the red, that is, to the states of lower energies, whereas for a side by side and parallel configuration, the intensities are shifted to the blue. Furthermore, since the excited state polarizabilities are usually larger than the... 

For further details of DFT calculations of excited state polarizabilities and three-photon absorption see [58, 59]. 

Section 4.1.1 reviews second harmonic generation (SHG) for para-nitroaniline (PNA), Section 4.1.2 the polarizability and second hyperpolarizability of nitrogen and benzene, Section 4.1.3 the second hyperpolarizability of Cgo, Section 4.2 the excited state polarizability of pyrimidine and r-tetrazine. Section 4.3 three-photon absorption, and finally, in Section 4.5 the electronic g-tensor and the hyperfine coupling tensor are reviewed as examples of open shell DFT response properties. 

Excited state properties of molecules are often important parameters in different models of interacting systems and chemical reactions. For example, excited state polarizabilities are key quantities in the description of electrochromic and solva-tochromic shifts [99-103]. In gas phase there has been a series of experiments were excited state polarizabilities have been determined from Laser Stark spectroscopy by Hese and coworkers [104-106]. However, in the experiments most often not all the tensor components can be determined uniquely without extra information from either theory or other experiments. 

Calculations of analytic excited state properties for correlated methods have been reported by several groups [107-118]. Excited state dynamic properties from cubic response theory were first obtained by Norman et al. at the SCF level [55] and by Jonsson et al. at the MCSCF [56] level, and in a subsequent study a polarizable continuum model was applied to account for solvation effects [119]. Hattlg et al. presented a general theory for excited state response functions at the CC level using a quasi-energy formulation [120] which was subsequently implemented and applied at the CCSD level [121, 122]. The first ID DFT calculation of dynamic excited state polarizabilities, which we will shortly review here, was presented in [58] for pyrimidine and -tetrazine utilizing the double residue of the cubic response function derived in Section 2.7.3. 

Jonsson et al. review tlie Kohn-Sham density functional theory (DFT) for time-dependent (TD) response functions. They describe the derivation of the working expressions. They also review recent progress in the application of TD-DFT to open shell systems. They reported results on several properties (i) hyperpolarizabilities (e.g. para-nitroaniline, benzene, Cgg fullerene), (ii) excited state polarizabilities (e.g. pyrimidine), (iii) three-photon absorption and (iv) EPR spin Hamiltonian parameters. 

Excited State Polarizabilities. - Jonsson et al.156 have attempted to simulate excited state polarizabilities by means of the optimization of a single determinant ground state. These excited state polarizabilities are given by the double residues of the cubic response functions. The method has been applied to H20, 03, HCHO, C2H4,C4H6, cyclobutadiene, pyridine, pyrazine and s-tetra-zine and the results compared with others obtained from multi-determinant optimized excited states. 

Quadratic response theory in combination with self-consistent field (SCF), MCSCF, and coupled-cluster electronic structure methods have been used for calculation of excitation energies and transition dipole moments between excited electronic states <2000PCP5357>. The excited state polarizabilities for r-tetrazine are given by the double residues of the cubic response functions <1997CPFl(224)201>. 

The residue analysis of the CRF yields different types of excited-state quantities such as three-photon transition matrix elements (three-photon absorption) [27], the two-photon matrix elements between excited states (the cross section for second-order transitions), and the excited-state polarizability (dynamic second-order property). 

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