Radiationless vibrational relaxation

Alternatively, the molecule could cross from S, into an excited vibrational level of T,. Such an event is known as intersystem crossing (ISC). After the radiationless vibrational relaxation R3, the molecule finds itself at the lowest vibrational level of T,. From here, the molecule might undergo a second intersystem crossing to S0, followed by the radiationless relaxation R4. All processes mentioned so far simply convert light into heat. 

Another form of radiationless relaxation is internal conversion, in which a molecule in the ground vibrational level of an excited electronic state passes directly into a high vibrational energy level of a lower energy electronic state of the same spin state. By a combination of internal conversions and vibrational relaxations, a molecule in an excited electronic state may return to the ground electronic state without emitting a photon. A related form of radiationless relaxation is external conversion in which excess energy is transferred to the solvent or another component in the sample matrix. 

Fig. 11. (a) Diagram of energy levels for a polyatomic molecule. Optical transition occurs from the ground state Ag to the excited electronic state Ai. Aj, are the vibrational sublevels of the optically forbidden electronic state A2. Arrows indicate vibrational relaxation (VR) in the states Ai and Aj, and radiationless transition (RLT). (b) Crossing of the terms Ai and Aj. Reorganization energy E, is indicated. 

Because of the dense spectrum of the highest vibrational sublevels and their rapid vibrational relaxation in the A2 state, this radiationless transition (RLT) is irreversible and thus it may be characterized by a rate constant k. The irreversibility condition formulated by Bixon and Jortner [1968] reads... 

The radiationless transition between two states of same spin is called internal conversion, the one occuring with inversion of spin being termed intersystem crossing. In both processes the excess energy is liberated as heat. All these transitions between different electronic states are customarily preceded by vibrational relaxation, i.e. the deactivation from a higher vibronie level to the v0-level of the same electronic state (Fig. 5). 

The absorption of electromagnetic radiation by molecular species in solution in the UV/visible region is followed by relaxation from excited electronic states to the ground state mostly by a combination of radiationless processes. Vibrational relaxation, where the excess energy is rapidly dis-... 

In the radiative transition shown, most of the energy is removed from the system by photon emission, whereas for the radiationless transition the sum of the electronic energy and vibrational energy is constant and energy is subsequently removed from the system by vibrational relaxation to v = 0 of f2, with the solvent acting as an energy sink. 

The theory of radiationless transition considers the transition to occur in two steps (i) horizontal transition from one energy state to the other at the isocnergetic point, for the two combining states and (ii) vibrational relaxation of the lower energy state. The step (i) is the rate determining step. The rate constant is given by the theory of Robinson and Frosch as,... 

Techniques have now been developed to study decay rates in pico-second ranges such as vibrational relaxation and radiationless transitions (t = 10-12 — 10, s) by using high intensity laser pulses (see Section 10.4). 

Suppose that absorption promotes a molecule from the ground electronic state, S0, to a vibra-tionally and rotationally excited level of the excited electronic state S, (Figure 18-13). Usually, the first process after absorption is vibrational relaxation to the lowest vibrational level of Sj. In this radiationless transition, labeled R, in Figure 18-13, vibrational energy is transferred to other molecules (solvent, for example) through collisions, not by emission of a photon. The net effect is to convert part of the energy of the absorbed photon into heat spread through the entire medium. 

Figure 18-13 Physical processes that can occur after a molecule absorbs an ultraviolet or visible photon. S0 is the ground electronic state. S, and T, are the lowest excited singlet and triplet electronic states. Straight arrows represent processes involving photons, and wavy arrows are radiationless transitions. R denotes vibrational relaxation. Absorption could terminate in any of the vibrational levels of S,. not just the one shown. Fluorescence and phosphorescence can terminate in any of the vibrational levels of Sq.

The next two chapters are devoted to ultrafast radiationless transitions. In Chapter 5, the generalized linear response theory is used to treat the non-equilibrium dynamics of molecular systems. This method, based on the density matrix method, can also be used to calculate the transient spectroscopic signals that are often monitored experimentally. As an application of the method, the authors present the study of the interfadal photo-induced electron transfer in dye-sensitized solar cell as observed by transient absorption spectroscopy. Chapter 6 uses the density matrix method to discuss important processes that occur in the bacterial photosynthetic reaction center, which has congested electronic structure within 200-1500cm 1 and weak interactions between these electronic states. Therefore, this biological system is an ideal system to examine theoretical models (memory effect, coherence effect, vibrational relaxation, etc.) and techniques (generalized linear response theory, Forster-Dexter theory, Marcus theory, internal conversion theory, etc.) for treating ultrafast radiationless transition phenomena. 

In condensed media and liquid phase, the excess vibrational energy is typically released to the surrounding medium on a very fast timescale and therefore not observable by steady-state methods. Following the vibrational relaxation, the molecule returns to its electronic ground state. This occurs upon emission of a photon or via radiationless transitions. Radiationless transitions should be divided into two general classes [90] ... 

Observable effects in the quenching of fluorescence are usually the result of competition between radiation and bimolecular collisional deactivation of electronic energy, since vibrational relaxation is normally so rapid, especially in condensed phases, that emission derives almost entirely from the ground vibrational level of the upper electronic state. The simplest excitation-deactivation scheme, which does not allow for intramolecular radiationless... 

It is clear that a number of questions need to be answered. Why, in the condensed phase, is the intersystem crossing between two nn states so efficient What is the explanation of the conflict between the linewidth studies of Dym and Hochstrasser and the lifetime studies of Rentzepis and Busch, with respect to the vibrationally excited levels It was in an attempt to provide some answers to these questions that Hochstrasser, Lutz and Scott 43 carried out picosecond experiments on the dynamics of triplet state formation. In benzene solution the build up of the triplet state had a lifetime of 30 5 psec, but this could only be considered as a lower limit of the intersystem crossing rate since vibrational relaxation also contributed to the radiationless transition to the triplet state. The rate of triplet state build-up was found to be solvent-dependent. 

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