Non-adiabatic relaxation

The closer two particles pass, the greater is their interaction. Still, AJ/J may turn out to be less than 1 even in the case of face to face collision. In this limit collisions are weak, y 1 and the model of the correlated process fits the situation well. If close impacts produce a strong effect, then the influence of more distant paths is negligible, and the process approaches the non-correlated limit y 0. 

From a mathematical perspective either of the two cases (correlated or non-correlated) considerably simplifies the situation [26]. Thus, it is not surprising that all non-adiabatic theories of rotational and orientational relaxation in gases are subdivided into two classes according to the type of collisions. Sack s model A [26], referred to as Langevin model in subsequent papers, falls into the first class (correlated or weak collisions process) [29, 30, 12]. The second class includes Gordon s extended diffusion model [8], [22] and Sack s model B [26], later considered as a non-correlated or strong collision process [29, 31, 32], 

Though these are alternative models, they are both particular cases of the non-adiabatic impact theory of angular momentum relaxation in gases. Thus, we prefer to call them models of weak and strong collisions , as is usually done in analogous problems [13, 33], 

It is easily seen that impact non-adiabatic relaxation of angular momentum proceeds exponentially in the Keilson-Storer approximation. Let us dwell upon some particular cases. 

In the case of weak collisions, the moment changes in small steps AJ (1 — y)J J, and the process is considered as diffusion in J-space. Formally, this means that the function /(z) of width [(1 — y2)d]i is narrow relative to P(J,J, x). At t To the latter may be expanded at the point J up to terms of second-order with respect to (/ — /). Then at the limit y - 1, to — 0 with tj finite, the Feller equations turn into a Fokker-Planck equation 

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In the Keilson-Storer model of J-diffusion, non-adiabatic relaxation is assumed to extend to the whole energy spectrum of a rotator. Actually, for large J the relaxation becomes adiabatic. The considerable difference between the times appears in the adiabatic limit since xe = 00, while xj is defined by m-diffusion according to Eq. (1.12). As is seen from Eq. (1.5) and Eq. (1.6), both J- and m-diffusion are just approximations which hold for low- and high-excited rotational levels, respectively. In general 0 < xj/xE < 1 + y. 

Factorization of the impact operator (5.1) greatly reduces the computational effort required in any variant of IOS [197]. When the inequality (5.43) holds, this factorization is acceptable but only for purely non-adiabatic relaxation as is J-diffusion. Though N2-Ar collisions are mostly non-adiabatic, it would still be better to account for adiabatic-ity, which becomes more significant the higher the rotational quantum number j. 

Keilson-Storer kernel 17-19 Fourier transform 18 Gaussian distribution 18 impact theory 102. /-diffusion model 199 non-adiabatic relaxation 19-23 parameter T 22, 48 Q-branch band shape 116-22 Keilson-Storer model definition of kernel 201 general kinetic equation 118 one-dimensional 15 weak collision limit 108 kinetic equations 128 appendix 273-4 Markovian simplification 96 Kubo, spectral narrowing 152... 

Both simulations stress that the relaxation rate for the adsorption energy into the lattice is slow, 1—4 ps, and that energy relaxation into e-h pairs, omitted in these molecular dynamics simulations, is likely to be of the same order of magnitude or perhaps even larger. The non-adiabatic relaxation rate is estimated to also be 1 ps from the vibrational damping rate of the parallel mode for H adsorbed on Cu(lll) [150]. The excitation of e-h pairs accompanying H adsorption on Cu has... 

Figure 3. Photoexcitation (up) and non-adiabatic relaxation (down) solvent responses (Eq. 1)...

VT relaxation in molecular collisions with atoms and radicals can be illustrated by relaxation of vibrationally excited N2 on atomic oxygen (Andreev Nikitin, 1976 see Fig. 2-35). The interval between degenerated electronic terms grows when an atom approaches the molecule. When the energy interval becomes equal to avibrational quantum, non-adiabatic relaxation (the so-called vibronic transition, Fig. 2-35) can take place. The temperature dependence of this relaxation is not significant, and typical rate coefficients are high lO -lO cm /s. Sometimes, as in the case of relaxation on alkaline atoms, the non-adiabatic VT-relaxation rate coefficients reach those of gas-kinetic collisions, that is, about 10 ° cm /s. 

Initial and final Me-N2 energy terms cross an ionic term (Fig. 2-36), which leads to a fast non-adiabatic relaxation transition (Bjerre Nikitirr, 1967). The maximum cross sections of such relaxation processes are presented in Table 2-25. 

Table 2-25. Maximum Cross Sections of Non-Adiabatic Relaxation of Electronically Excited Sodium Atoms...

In this chapter, the theoretical tools introduced in Chaps. 2 and 4 are applied to the study of the non-adiabatic relaxation dynamics of pyrazine after ultraviolet... 

More recently, theoretical studies using on-the-fly trajectory surface hopping (TSH) simulations based on time-dependent density functional theory (TDDFT) electronic structure calculations [39, 41] suggested an important participation of the dark Au(nn ) and B2g(mr ) states in the non-adiabatic relaxation dynamics after excitation to the bright state. 

Abstract In this review we discuss the theory and application of methods of excited state quantum chemistry to excited states of transition metal complexes. We review important works in the field and, in more detail, discuss our own studies of electronic spectroscopy and reactive photochemistry. These include binary metal carbonyl photodissociation and subsequent non-adiabatic relaxation, Jahn-Teller and pseudo-Jahn-Teller effects, photoisomerization of transition metal complexes, and coupled cluster response theory for electronic spectroscopy. We aim to give the general reader an idea of what is possible from modem state-of-the-art computational techniques applied to transition metal systems. 

This list of contributions to this field in recent years is far from exhaustive, for a more in-depth discussion we direct the reader to the following reviews [30, 44, 71 ]. We now present in more detail aspects of the ongoing work in our group in this field. This is in order to further illustrate to the reader the type of chemistry and photo-induced effects that can be investigated using state-of-the-art computational methods on transition metal complexes and also complement the type of work already discussed above. The work presented below covers some of the salient aspects in theoretical study of the photochemistry of transition metal complexes, namely photodissociation, photoisomerization, non-adiabatic relaxation, Jahn-Teller and pseudo-Jahn-Teller effects, and the accurate analysis of electronic spectra of various transition metal complexes. 

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