Nonadiabatic adiabatic process

Chemical processes, such as bond stretching or reactions, can be divided into adiabatic and diabatic processes. Adiabatic processes are those in which the system does not change state throughout the process. Diabatic, or nonadiabatic, processes are those in which a change in the electronic state is part of the process. Diabatic processes usually follow the lowest energy path, changing state as necessary. 

Let us return to the nonadiabatic chemical processes. When a PES has been built, a part of the total Hamiltonian may remain unaccounted for, and this part, acting as a perturbation, induces transitions from the initial to the final state. There are several types of such a perturbation, namely (i) an unaccounted part of the electronic interaction (ii) non-adiabaticity (iii) spin-orbit coupling. 

An adiabatic process is one with no loss or gain of heat to a volume of air. If heat is supplied or withdrawn, the process is diabatic or nonadiabatic. Near the earth s surface, where heat is exchanged between the earth and the air, the processes are diabatic. 

Having suggested that the STIRAP process can be thought of as a special case of an assisted adiabatic process, we now examine another special case of an assisted adiabatic process, namely the composite STIRAP protocol proposed by Torosov and Vitanov [77]. This protocol uses a sequence of an odd number of pairs of delayed pulses (Figure 3.24) with carefully selected phases (listed in Table 3.4) to cancel by destructive interference the nonadiabatic transitions that reduce the efficiency of STIRAP-generated population transfer. We note that this protocol resembles the pulsed incoherent interference control protocol proposed by Shapiro et al. [78]. Torosov and Vitanov show that, for the triad of states illustrated in Figure 3.24, the efficiency of population transfer can be driven arbitrarily close to unity, for example, a deviation from unity of order 10 for the case of resonant excitation with three pairs of pulses. 

Here, the case of free rise in an open mold is analyzed. Because of the very low thermal conductivity of a plastic foam, an adiabatic process will be considered. The nonadiabatic case in a closed mold leads to integral-skin foams. These foams exhibit a mass density gradient, with unfoamed skins in contact with the mold walls (Marciano et al., 1986). 

The concept of adiabacity in e.t. processes has gained importance in recent years, and the question does arise to what extent it may influence the observation of the M.I.R. In principle, the occurence of the M.I.R. is related only to the quadratic form of the activation energy, not to the form of the pre-exponential factor. The M.I.R. should therefore be observed for both adiabatic and nonadiabatic reactions. However, if the observable rate of an adiabatic process is controlled by the solvent relaxation time, the influence of the exponential factor may be negligible [18]. 

See - nonadiabatic (diabatic) process, -> Marcus theory, - Randles, and - Gurney, - adiabatic process (thermodynamics). 

An important factor is the electron coupling between the electrode metal and the redox species or between the two members of the redox couple. If this coupling is strong the reaction is called adiabatic, i.e., no thermal activation is involved. For instance, electrons are already delocalized between the metal and the redox molecule before the electron transfer therefore, in this case no discrete electron transfer occurs [see also -> adiabatic process (quantum mechanics), - nonadiabatic (diabatic) process]. 

However, the treatment of the class of nonadiabatic processes with isolated regions of nonadiabatic behavior differs from the treatment of adiabatic processes in the following (<5) ways. 

If work is now performed under nonadiabatic conditions, the above situation no longer holds. This fact would seem greatly to impair the usefulness of the function E, were it not for the fact that other changes also occur which were absent from the adiabatic process. The question arises whether the function E still remains useful in these altered circumstances. The answer is in the affirmative. 

If now such a process is carried out under nonadiabatic conditions this situation no longer holds, which seems to impair the usefulness of the energy concept. However, other changes now also take place that were absent in the adiabatic process, so as to maintain the viability of the concept of energy. This experience of mankind gives rise to a new assertion, namely, the First Law of Thermodynamics ... 

The discussion in this section assumes adiabatic processes. The question of nonadiabaticity is often discussed but is seldom treated experimentally. The results of attempts to do so suggest that processes with unfavorable intrinsic reactivity and nuclear motion and kinetic-energy change factors can be accelerated by proper choice of ligands or ion-pair reagents that reduce superexchange. "... 

The perturbation theory used by Holstein in his small-polaron model confines its validity to an upper limit for J of around hcoo, which corresponds to a nonadiabatic process. The adiabatic process, for which J > hcoQ, has been studied less extensively. In the high temperature limit, Emin and Holstein [46] arrive at the result that... 

Spin-forbidden reactions are a subset of the broader class of electronically non-adiabatic processes, which involve more than one PES. The fundamental theory of how such processes occur is well understood (7-9), and a very large amount of research is being performed with the aim of elucidating more details in all the areas of nonadiabatic chemistry. It is not possible to present this work here, so I will instead provide an outline of the most important theoretical insights in the... 

Equation (2.2.1) provides a means for determining Q by measuring work for a given process between states 1 and 2, Q may be determined by measuring the work required by the process, and then measuring the work required by any adiabatic process between the same two states. If we want a value for reversible heat transfer, the nonadiabatic process must be reversible however, the value of work for the adiabatic process is independent of reversibility. When state 2 cannot be reached adiabatically from state 1, then instead of measmlng the adiabatic work Wj2, we would measure the adiabatic work for the opposite process (from state 2 to state 1) V 2 - Then (2.1.27) allows us to compute Wj2 by... 

If we want to move from state 1 in Figure 2.8 to states not on the reversible adiabat, then we find experimentally that we must use an irreversible process. However, using an irreversible adiabatic process does not allow us to reach every other state on the diagram. From state 1, we can only reach states above the reversible adiabat by means of some irreversible adiabatic process those states are said to be accessible. To reach states below the line (shaded region in Figure 2.8.), we must use some nonadiabatic process that is, we must transfer heat. This means that a particular asymmetry exists among the states that are accessible using adiabatic processes. 

In 7.1.2 we showed that, for adiabatic processes occurring in closed systems, the combined laws (7.1.11) reduce to a requirement that the system entropy must always increase or remain constant. But if the system can exchange heat with its surroundings, then the entropy may increase, decrease, or remain constant, so for nonadiabatic processes, the entropy no longer serves as an indicator for changes. In this and the... 

We will first consider in detail the collision dynamics of adiabatic processes The nonadiabatic transitions in molecular collisions will be treated later in a more concise form ... 

The dynamical processes can be investigated in two different ways the adiabatic processes, where the system remains in the electronic ground state and the nonadiabatic processes where electronic excitation, ionization or charge transfer occur. Only the ways to study adiabatic phenoma will be described here. 

Any reversible process can be carried out in reverse. Thus, by reversing the reversible nonadiabatic process, it is possible to change the state from B to A by a reversible process with a net flow of heat out of the system and with Aq either negative or zero in each element of the reverse path. In contrast, the absence of an adiabatic path from B to A means that it is impossible to carry out the change A B by a reversible adiabatic process. 

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