Coherent states molecular systems

Modem photochemistry (IR, UV or VIS) is induced by coherent or incoherent radiative excitation processes [4, 5, 6 and 7]. The first step within a photochemical process is of course a preparation step within our conceptual framework, in which time-dependent states are generated that possibly show IVR. In an ideal scenario, energy from a laser would be deposited in a spatially localized, large amplitude vibrational motion of the reacting molecular system, which would then possibly lead to the cleavage of selected chemical bonds. This is basically the central idea behind the concepts for a mode selective chemistry , introduced in the late 1970s [127], and has continuously received much attention [10, 117. 122. 128. 129. 130. 131. 132. 133. 134... 

Segal D, Nitzan A, Davis WB, Wasielewski MR, Ratner MA (2000) Electron transfer rates in bridged molecular systems 2. A steady-state analysis of coherent tunneling and thermal transitions. J Phys Chem B 104( 16) 3817—3829... 

This general feature of the stochastic scheme may cause convergence problems. For example, consider a situation in which the molecular system is predominately in a single state, say pu. Although the expectation values of the population P2 = trp22 and the corresponding coherences are zero, there are the same number of random walkers in these states which need to cancel... 

The scheme we employ uses a Cartesian laboratory system of coordinates which avoids the spurious small kinetic and Coriolis energy terms that arise when center of mass coordinates are used. However, the overall translational and rotational degrees of freedom are still present. The unconstrained coupled dynamics of all participating electrons and atomic nuclei is considered explicitly. The particles move under the influence of the instantaneous forces derived from the Coulombic potentials of the system Hamiltonian and the time-dependent system wave function. The time-dependent variational principle is used to derive the dynamical equations for a given form of time-dependent system wave function. The choice of wave function ansatz and of sets of atomic basis functions are the limiting approximations of the method. Wave function parameters, such as molecular orbital coefficients, z,(f), average nuclear positions and momenta, and Pfe(0, etc., carry the time dependence and serve as the dynamical variables of the method. Therefore, the parameterization of the system wave function is important, and we have found that wave functions expressed as generalized coherent states are particularly useful. A minimal implementation of the method [16,17] employs a wave function of the form ... 

In Ref. [4] we have studied an intense chirped pulse excitation of a molecule coupled with a dissipative environment taking into account electronic coherence effects. We considered a two state electronic system with relaxation treated as diffusion on electronic potential energy surfaces with respect to the generalized coordinate a. We solved numerically equations for the density matrix of a molecular system under the action of chirped pulses of carrier frequency a> with temporal variation of phase [Pg.131]

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 1993, the first ultrafast vibrational echo experiments on condensed matter systems were performed using a free electron laser as the source of temporally short, tunable infrared pulses (11). Recently, the development of Ti sapphire laser-based optical parametric amplifier (OPA) systems has made it possible to produce the necessary pulses to perform vibrational echoes using a tabletop experimental system (12,13). The development and application of ultrafast, IR vibrational echoes and other IR coherent pulse sequences are providing a new approach to the study of the mechanical states of molecules in complex molecular systems such as liquids, glasses, and proteins (14-20). While the spin echo, the photon echo, and the vibrational echo are, in many respects, the same type of experiment, the term vibrational echo is used to distinguish IR experiments on vibrations from radio frequency experiments on spins or vis/UV experiments on electronic states. In this chapter, recent vibrational echo experiments on liquids, glasses, and proteins will be described. 

The demand for efficient numerical methods in biological solid-state NMR may be explained not only by the interest in studying larger and more complex molecular systems, but also by the fact that most of the nuclear spin interactions are anisotropic (i.e., dependent on the orientation of the molecule relative to the external magnetic field) which complicates the NMR spectra as well as the transfers of polarization and coherence... 

From the results in the last section it is clear that for particular applied radiative frequencies or frequency multiples, close to resonance with particular molecular states, each molecular tensor will be dominated by certain terms in the summation of states as a result of their diminished denominators—a principle that also applies to all other multiphoton interactions. This invites the possibility of excluding, in the sum over molecular states, certain states that much less significantly contribute. Then it is expedient to replace the infinite sum over all molecular states by a sum over a finite set—this is the technique employed by computational molecular modelers, their results often producing excellent theoretical data. In the pursuit of analytical results for near-resonance behavior, it is often defensible to further limit the sum over states and consider just the ground and one electronically excited state. Indeed, the literature is replete with calculations based on two-level approximations to simplify the optical properties of complex molecular systems. On the other hand, the coherence features that arise through adoption of the celebrated Bloch equations are limited to exact two-level systems and are rarely applicable to the optical response of complex molecular media. 

Whereas coherence can persist up to the nanosecond range for atomic and molecular systems exposed to dilute gaseous environments, the situation is radically different in liquids and solids. Interactions with neighbouring atoms, with phonons in crystalline materials and with conduction electrons in metals, shift the coherence times down by several orders of magnitude, and local quantum superpositions are usually not observable. Intermediate cases are the electronic states used as qubits in the form of superconducting islands introduced by Y. Nakamura et al. [4]. The latest reports [5] show coherence times up to 10 s for these objects, which would allow time for operations of a quantum computer. The decoherence mechanisms in such circuits have been discussed theoretically by Burkhard et al. [6],... 

In the case of coherent laser light, the pulses are characterized by well-defined phase relationships and slowly varying amplitudes (Haken, 1970). Such quasi-classical light pulses have spectral and temporal distributions that are also strictly related by a Fourier transformation, and are hence usually refered to as Fourier-transform-limited. They are required in the typical experiments of coherent optical spectroscopy, such as optical nutation, free induction decay, or photon echoes (Brewer, 1977). Here, the theoretical treatments generally adopt a semiclassical procedure, using a density matrix or Bloch formalism to describe the molecular system subject to a pulsed or continuous classical optical field, which generates a macroscopic sample polarization. In principle, a fully quantal description is possible if one represents the state of the field by the coherent or quasi-classical state vectors (Glauber, 1965 Freed and Villaeys, 1978). For our purpose, however. 

Only for a coherent excitation (i.e., for AE F) can one expect time dependence of the emission spectrum. The vibrational redistribution corresponds here to the time evolution (coherence loss) of the initially prepared, nonstationary s> state (Trie, 1976 Mukamel, 1978). Initial, narrow-band s>-> 3 emission would decay and the broad-band l - g emission would build up at the time scale of fi/F. To our knowledge, such a behavior has never been evidenced in a convincing way. The reason for it may lie in the choice of molecular systems, which has so far been limited to aromatic molecules with no or small substituents. In such molecules, the coupling... 

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