Excited State Optimizations and Frequencies

216 Exploring Chemistry with Electronic Structure Methods 

The first job step computes the energies of the three lowest excited states. The second job step uses its results to begin the optimization by including the Read option to the CIS keyword, Geom=Check, and Guess=Read (and of course the commands to name and save the checkpoint file). The Freq keyword computes the frequencies at the optimized structure. 

Here is the stationary point found by the optimization, in its standard orientation  

Unfortunately, the frequency job finds an imaginary frequency, indicating that this structure is not a minimum. Here are the displacements corresponding to this frequency  

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Geometry optimizations and frequency calculations for systems in an excited state are also possible using Gaussian s Cl-Singles feature. We will do so in stipes first, the excited state of interest is located via an energy calculation, then an optimization is performed, starting from that point, and finally frequencies are calculated at the optimized geometry. 

The excited-state optimized structures and the computed absorption and emission frequencies of stilbene were calculated [2]. The stilbene orbitals and the Si and S2 energy profiles for both isomers of stilbene are shown in Figure 3.2. 

The CIS wave function is found by solving for the coefficients 0. Since analytic gradients of CIS energies are available, one can then optimize the geometry of each excited state and also calculate its vibrational frequencies. CIS excited-state geometries and vibrational frequencies are more accurate than CIS vertical excitation energies [J. E. Stanton et al., / Chem. Phys., 103,4160 (1995)]. 

A number of types of calculations can be performed. These include optimization of geometry, transition structure optimization, frequency calculation, and IRC calculation. It is also possible to compute electronic excited states using the TDDFT method. Solvation effects can be included using the COSMO method. Electric fields and point charges may be included in the calculation. Relativistic density functional calculations can be run using the ZORA method or the Pauli Hamiltonian. The program authors recommend using the ZORA method. 

Figure 13. Schematic sketch of a reactive NeNePo control experiment. Control is achieved through two time- and frequency-shifted photodetachment laser pulses employing an anion excited state (M ) for intermediate wavepacket propagation. The wavepacket is finally prepared on the neutral potential energy surface in a region that corresponds to enhanced reactivity of the system. The aim of the experiment and theory is to find optimal composite pulses, based on the concept of the intermediate target outlined in Section III.A, that accomplish such a reactive activation of M . Detection is performed by ionization of the potential reaction products of MO to the cationic state (not shown in the graphic).

The two-state approximation is of course an idealization, and a possibility that all the transitions can be driven by the laser imposes significant limits on the Rabi frequency and the duration of the pulse. Namely, the Rabi frequency cannot be too strong in order to avoid the coupling of the laser to the j) — e) transition, which could lead to a slight pumping of the population to the state e). On the other hand, the Rabi frequency cannot be too small as for a small Q the duration of the pulse, required for the complete transfer of the population into the state s), becomes longer and then spontaneous emission can occur during the excitation process. Therefore, the transfer of the population to the state s) cannot be made arbitrarily fast and, in addition, requires a careful estimation of the optimal Rabi frequency, which could be difficult to achieve in a real experimental situation. 

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