Doorway states

Aromatic alcohol clusters have been well-studied, also for methodical reasons. The UV chromophore can be exploited for sensitive detection of the IR spectrum [35, 36, 120, 179]. Time-domain experiments become possible [21], which show that the initial energy flow out of the O—H stretching mode occurs primarily via C—H stretching and bending doorway states. Like in the case of carboxylic acid dimers [245], the role of the hydrogen bond is to shift the O—H stretching mode closer to these doorway states and thus to accelerate the initial energy flow. 

Although most of the reported gas-phase experiments do not investigate the temporal evolution of alcohol clusters explicitly, the frequency-domain spectral information can nevertheless be translated into the time domain, making use of some elementary and robust relationships between spectral and dynamical features [289]. According to this, the 10-fs period of the hydrogen-bonded O—H oscillator is modulated and damped by a series of other phenomena. Energy flow into doorway states is certainly slower than for aliphatic C—H bonds [290] but on a time scale of a few picoseconds, energy will nevertheless have... 

One way to conciliate all these findings is to assume that the A adiabatic state is the only one responsible of the EP process, acting as the doorway state. However, because there are important S — If vibronic couplings among the A,B and B states, the rovibrational states are mixed, thus sharing the absorption intensity and also the EP lifetimes. 

The above relations define the conditions for concurrent control of population and energy transfers between all of the states of the system that are connected by dipole allowed transitions. It is unlikely that a situation that complicated will ever be encountered. In the n-state molecule language, typically, not all pairs of states of the molecule are connected with nonzero transition dipole moments. In the skeleton spectrum language, there is usually only a small subset of dipole coupled doorway states. In both cases, of course, when only some pairs of states are coupled with nonzero transition dipole moments, the appropriate control conditions are simplified. 

The importance of the vibron model lies in the fact that it is the doorway state of the optical absorption. (The two-particle states have no oscillator strength, since we cannot create vibrations in the ground state.) Indeed, the creation of vibrations is subsequent to an electronic excitation of a molecule, in the approximation where the absorbing dipole is the sum of molecular dipoles (with the appropriate phase), which is the approximation of weak intermolecular forces. 

The method of building up the remainder of the basis set is reminiscent of the rules followed by Rhodes and coworkers to build up their spectroscopic basis set. The doorway state /i), the one carrying the entire interaction with 1/0), is defined by... 

Problem 9.2. Consider the model where the doorway state s is coupled to two different continua. R and L (see Fig. 9.4). 

In the procedure (Appendix 9B) to evaluate the lineshape (9.40) we use the representation defined by the states 1/) that diagonalize the Hamiltonian in the ( 5), /> ) subspace. Of course any basis can be used for a mathematical analysis. It was important and useful to state the physical problem in terms of the zero-order states 5) and ]/) because an important attribute of the model was that in the latter representation the ground state g) is coupled by the radiation field only to the state 5), which therefore has the status of a doorway state. This state is also referred to as a resonance state, a name used for the spectral feature associated with an underlying picture of a discrete zero-order state embedded in and coupled to a continuous manifold of such states. 

In Section 9.3 we have used this truncated dressed state picture to discuss photoabsorption and subsequent relaxation in a model described by a zero-order basis that includes the following states a molecular ground state with one photon of frequency atomic spectroscopy, however, in molecular spectroscopy applications it has to be generalized in an essential way—by accounting also for molecular nuclear motions. In the following section we make this generalization before turning to consider effects due to interaction with the thermal environment. 

To proceed further, we now assume that, because of Franck-Condon factors, only a> can combine in absorption from the initial state g. That is, a> is an absorption doorway state.29 (The assumption that only a few out of many S, vibrational levels have any appreciable dipole-induced transition probability to or from any given S0 vibrational level is a good approximation for a large number of molecules.) This, with the definition of the fiHm and Eqs. (3.1), gives nlg = (xnag and fi2g = PHag- We also assume, for similar reasons, that either a> or i>> combines in emission with the final state /> (i.e., a> or f > is a doorway state in emission to / . If a> is the emission doorway state,... 

Several useful relations, derived entirely from the orthonormality of the a s, can be obtained for these modulation depths. In doing so, it is convenient to make a distinction between band types, since the general characteristics of the My((Ou) are different for y = a (identical absorption and emission doorway states) as opposed to y a (different absorption and emission doorway states). 

The nature of the initially prepared state is of paramount importance in determining (1) the subsequent IVR dynamics of a species and (2) the way in which the dynamics is manifest in time-resolved and time-integrated fluorescence. The theoretical picture, reviewed in Section III B of the manifestations of IVR in time-resolved fluorescence relies on the assumption that single zero-order states act as doorway states in optical transitions from and to... 

Quasi-statistical complexes in chemical reactions have been discussed by George and Ross (1972). Depending on the extent of statistical averaging, they proposed a classification of experimental results into the categories direct interaction, doorway states (a concept borrowed from nuclear physics), partial statistical complex and complete statistical complex. They stressed that symmetric product angular distributions are indicative of complex formation, but these are neither necessary nor sufficient evidence rather, they indicated that the observations necessary for a complete statistical complex are symmetric angular distributions velocity spectrum peaked near the centre-of-mass velocity and statistical isotope distribution. 

Figure 1.3 A bandhead occurs in the ft-branch of red-degraded (B < B") BaO AlE+ — Xl + bands that appear in the Ba + N2O chemiluminescence spectrum. The low-J lines in the ft branch are arranged toward higher frequency as J increases, pile up near the bandhead, and then move toward lower-frequency as J increases beyond Jh = (3B — B")/]2(B" — B ). The returning ft-branch crosses the band origin and overlays the P-branch. The top spectrum is recorded at 0.2 Torr and the (t/ = 1, v" — 2) band contains two spikes, which are ft(44) and P(46) lines that originate from an a3II(u = 0) A1 +(u = 1) J = 45 doorway state (see Section 6.5.5). In the bottom spectrum, recorded at 24 Torr, the spikes are absent due to collision induced rotational relaxation (from Field, 1976).

In Section 7.8 the possibility of predissociation of isolated lines was mentioned. This is usually called accidental predissociation and can be interpreted as perturbation of a nominally bound rotational level by a predissociated level that lies nearby in energy for this value of J. This type of predissociation should more generally be called indirect predissociation, since the predissociation takes place through an intermediate state (or doorway state, see Section 9.2). 

There are many useful tools to help focus attention on specifiable parts of the behavior of a many-body system, and many of these were listed in Section 9.1.4. The concepts of bright state, doorway state, and dark state, the experimental tools of state-selective excitation and detection, and the analysis tools of wavepackets and survival and transfer probabilities, can provide insights into the causes, preferred pathways, and possibilities for control of intramolecular dynamics. 

This two-state quantum beat example is identical to the doorway mediated non-radiative decay problem frequently encountered in polyatomic molecule Intramolecular Vibrational Redistribution (IVR), Inter-System Crossing (ISC), Internal Conversion (IC), and compound anticrossings. There is a single, narrow bright state. It couples to a single, broad, and dark doorway state. The width of the doorway state is determined by the rate of its Fermi Golden Rule decay into a quasi-continuum of dark states. 

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