Running Excited State Calculations

The following Gaussian keywords and options are useful for excited state calculations  

CIS=(Rool=n) Specifies which excited state is to be studied (used for geometry optimizations, population analysis, and other single-state procedures). The default is the first (lowest) excited state (n=l). 

Exploring Chemistry with Electronic Structure Methods 

CIS=(NState =n) Specifies how many excited states are to be predicted. The default is 3. Note that if you are searching for some specific number of excited states, especially in conjunction with spectroscopic data, you will want to set NStales to a somewhat higher number to take into account the forbidden and degenerate states that are very likely to be interspersed within the states you are looking for. 

CIS=50-50 Predicts both singlet and triplet excited states (by default, 

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Finally, run another CASSCF 6,5)/6-31G(d) job to predict the energy of the ground state, using the same strategy as for the excited state. Retrieve the initial guess from the checkpoint file from the excited state calculation. 

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. 

Absorption and photodissociation cross sections are calculated within the classical approach by running swarms of individual trajectories on the excited-state PES. Each trajectory contributes to the cross section with a particular weight PM (to) which represents the distribution of all coordinates and all momenta before the vertical transition from the ground to the excited electronic state. P (to) should be a state-specific, quantum mechanical distribution function which reflects, as closely as possible, the initial quantum state (indicated by the superscript i) of the parent molecule before the electronic excitation. The theory pursued in this chapter is actually a hybrid of quantum and classical mechanics the parent molecule in the electronic ground state is treated quantum mechanically while the dynamics in the dissociative state is described by classical mechanics. 

A different analysis applies to the LR approach (in either Tamm-Dancoff, Random Phase Approximation, or Time-dependent DFT version) where the excitation energies are directly determined as singularities of the frequency-dependent linear response functions of the solvated molecule in the ground state, and thus avoiding explicit calculation of the excited state wave function. In this case, the iterative scheme of the SS approaches is no longer necessary, and the whole spectrum of excitation energies can be obtained in a single run as for isolated systems. 

Langer and Doltsinis [45] have calculated nonadiabatic surface hopping trajectories for 10 different initial configurations sampled from a ground state AIMD runs at 100 K. They later extended their study to a total of 16 trajectories [41, 42], From a mono-exponential fit to the 5) population a lifetime of 1.3 ps is obtained (see Table 10-1 the average transition probability and its standard deviation leads to the interval [0.6...1.1...3.5] ps. Thus methylation appears to result in a slightly longer excited state lifetime. 

Bernu et al. [65] used this method to calculate some excited states of molecular vibrations. Kwon et al. [66] used it to determine the Fermi liquid parameters in the electron gas. Correlation of walks reduced the errors in that calculation by two orders of magnitude. The method is not very stable and more work needs to be done on how to choose the guiding function and analyze the data, but it is a method that, in principle, can calculate a desired part of the spectrum from a single Monte Carlo run. 

However, in addition to the need to run multiple SCF calculations to obtain the electronic energies, Ej, of many excited states, the ASCF approach has a number of undesirable features that severely limit its applicability. First, one encounters the problem of variational collapse. If a molecule possesses no symmetry elements, it is impossible to obtain SCF solutions for any state other than the lowest energy state of a given multiplicity. Second, many excited states cannot be adequately approximated by any single determinant and one must resort to low-spin restricted open-shell approaches which can be difficult to converge. 

Fig. 8. Norm of the excited state. The full line in the lower panel shows the full calculation for the dashed line the Coinmin channel has artificially been closed. The upper plot stems from a run where the transition was only allowed at the asymmetric intersection. The steps are due to the oscillation of the excited state wavepacket.

Figures 15(a) and 15(b) show the calculation results of EEPF and VDF of N2 X, respectively. The calculations were run at Tg = 1200 K, Ne = 5.0 x IQU cm-3 and Te = 2.5 - 4.5 eV. These parameters were chosen to correspond to our experimental results at P = 1.0 Torr and 2 = 60 mm obtained in the experimental apvparatus shown in Fig. 3. It should be repeated that we choose a reduced electric field so that the electron mean energy s) equals (3/2)/cTe when we compare the numerical calculation with the number densities obtained experimentally by OES measurement. Obviously, the EEPF is not like Maxwellian. It has a dip in the range from 2 to 3 eV owing to frequent consumption of electrons with this energy range due to inelastic collisions to make vibrationally excited molecules. Meanwhile, Fig. 15(b) shows that the VDF is also quite far from the Maxwellian distribution. The number density of the vibrational levels shows rapid decrease first, then moderate decrease, and rapid decrease again as the vibrational quantum number increases. This behaviour of the VDF of N2 X state has been frequently reported, and consequently, our model is also considered to be appropriate. If we can assume corona equilibrium of some excited states of N2 molecule, for example, N2 C state, we can calculate the number density of the vibrational levels of the excited state that can be experimentally observed. This indicates that we can verify the appropriateness of the calculated VDF of the N2 X state as shown in Fig. 15(b).

Answer Focusing on the sodium D line at 589.3 run, we can calculate the energy gap as shown. The degeneracies for tiiis transition as 2 1, and the Boltzmann distribution (Equation 5.9) is used to calculate Ihe ratio and percentage of sodium atoms in the excited state at the temperatures given. Even at the highest temperature, less than 1 in 5 sodium atoms is in the excited state. This implies that, in flames, emission signals wiU be too low to be of practical value and that only in plasma will emission be feasible. 

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