Electron excitation probability approximation

Eq. (21), which directly reflects the non-Born-Oppenheimer dynamics of the system. Assuming that the system is initially prepared at x = 3 in the diabatic state /2), the corresponding initial distribution pg mainly overlaps with orbits A and C, since at x = 3 these orbits do occupy the state /2). Similarly, excitation of /i) mainly overlaps with orbits of type B, which at x = 3 occupy the state /i) (see Fig. 32). In a first approximation, the electronic population probability P t) may therefore be calculated by including these orbits in the... 

In the case of direct vibrational excitation, the vibrational transition probability is given by p, where are the intermediate and ground vibrational states, respectively, and is the vibrational transition moment. The electronic transition probability out of the intermediate state is < n < e ng e > n>, where are the excited and ground electronic states, respectively, and is the electronic dipole moment operator and vibrational state in the upper electronic state. Applying the Born-Oppenheimer approximation, where the nuclear electronic motion are separated, S can be presented as... 

An electronically excited molecule may, under some conditions, absorb another quantum and be raised to a higher excited state. Usually the population of excited species is so low that the probability of this occurrence is very slight. However, in recent years the technique of flash photolysis has been developed, which allows us to investigate the absorption properties of excited states. An extremely high intensity laser, which has approximately one million times the power of a conventional spectroscopic lamp, is turned on for a tiny fraction of a second, and a large population of excited species is produced. Immediately after this photolysis flash is turned off, a low-power spectroscopic flash may be turned on and the absorption spectrum of the already-excited system determined. By varying the delay between photolysis and spectroscopic flashes, much can be learned about the absorption and lifetime of singlet and triplet excited states. 

Formula for the Probability of Electron Excitation in the MO LCAO Approximation... 

Fig. 4. Distributions of integral probabilities of electron excitations to the energy ranges of [5n, 5(n + 1)] eV in fl decay of (a) LiT, (b) LiOT, (c) CH3T, (d) C2H3T, (e) C2H5T, (f) C3H7T, (g) NH2-C2HT, and (h) NH2-C2H4T in the SCF approximation.

We have calculated the data presented in the table in collaboration with G. V. Smeloy (Kaplan et al., 1983, 1985). In the MO LCAO approximation we have used the same bases of atomic functions as in calculations of the excitation probabilities of the corresponding molecules (see Section III,B,1). Allowing for electron correlation, calculations of the number of Cl configurations and the atomic bases were the same as those given in Section III,B,2. 

The probability for resonance transfer of electronic excitation decreases as the distance between the two molecules increases. If chlorophyll molecules were uniformly distributed in three dimensions in the lamellar membranes of chloroplasts (Fig. 1-10), they would have acenter-to-center spacing of approximately 2 nm, an intermolecular distance over which resonance transfer of excitation can readily occur (resonance transfer is effective up to about 10 nm for chlorophyll). Thus both the spectral properties of chlorophyll and its spacing in the lamellar membranes of chloroplasts are conducive to an efficient migration of excitation from molecule to molecule by resonance transfer. 

In recent years, there have been many attempts to combine the best of both worlds. Continuum solvent models (reaction field and variations thereof) are very popular now in quantum chemistry but they do not solve all problems, since the environment is treated in a static mean-field approximation. The Car-Parrinello method has found its way into chemistry and it is probably the most rigorous of the methods presently feasible. However, its computational cost allows only the study of systems of a few dozen atoms for periods of a few dozen picoseconds. Semiempirical cluster calculations on chromophores in solvent structures obtained from classical Monte Carlo calculations are discussed in the contribution of Coutinho and Canuto in this volume. In the present article, we describe our attempts with so-called hybrid or quantum-mechanical/molecular-mechanical (QM/MM) methods. These concentrate on the part of the system which is of primary interest (the reactants or the electronically excited solute, say) and treat it by semiempirical quantum chemistry. The rest of the system (solvent, surface, outer part of enzyme) is described by a classical force field. With this, we hope to incorporate the essential influence of the in itself uninteresting environment on the dynamics of the primary system. The approach lacks the rigour of the Car-Parrinello scheme but it allows us to surround a primary system of up to a few dozen atoms by an environment of several ten thousand atoms and run the whole system for several hundred thousand time steps which is equivalent to several hundred picoseconds. 

We solve the dme-dependent relativistic Dirac-equation for complicated ion-atom systems iti the Diiac-Fock-Slater approximation including the many-electron effects by means of an inclusive probability description. Various gas-gas and gas-solid target collision systems are discussed. We find the dominant effect in the observed excitation probability of inner shells to be a reladvisdc dynamic coupling of various levels which in a non-reladvisdc descripdon is zero. The effect of excitation and transfer during the passage within the solid allows us to understand the gas-solid target systems. An ab-inido calculation of K MO X-rays is presented for the system Cl" on Ar. 

In the late 1980s, this three-electron excitation was cited by other researchers as a heuristic case to argue that, "as far as we can tell, a multiply excited state such as 3p is virtually inaccessible by single-photon absorption." Yet, small-size (for reasons of economy) SSA calculations show that the state-specific HF result, which is of course obtained from an independent electron model with no electron correlation, produces nonzero values for the probabilities of the three transitions. Furthermore, the order of magnitude of the HF transition probabilities is the same as that from computations that include some part of electron correlation. Specifically, the results of the SSA calculations for the oscillator strengths, using only approximate wavefunctions for the oS, are ... 

The probability for single electron excitations depends on the kinematics of the incident electron and the transition probability (Celotta and Huebner, 1979). Within the approximation of fast collisions this transition probability is described by the dipole matrix element of the initial and final state of the target. Summing up over all possible excitations with AE the energy distribution of fast inelastically scattered electrons is obtained. 

The spectral function actually selected diagonal matrix elements Ann ( ) in a suitable one-electron basis representation - may exhibit well-defined structures reflecting the existence of highly probable one-electron excitations. Due to the Coulomb interaction, we cannot assign each excitation to an independent particle (electron or hole) added to the system with the excitation energy. Nonetheless, some of these structures can be explained approximately in terms of a particle-like behaviour, so having a quasiparticle (QP) peak. Where a second peak is required we may have what is called a satellite. 

The probability of exciting an electron from an initial state x r, to a final state can be described in terms of the X-ray absorption cross section, a, which is defined as the number of electrons excited per unit time divided by the number of incident photons per unit time per unit area [152]. By applying Fermi s golden rule and using the dipole approximation, can be written as... 

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