Quantum dynamics barrier height

The important criterion thus becomes the ability of the enzyme to distort and thereby reduce barrier width, and not stabilisation of the transition state with concomitant reduction in barrier height (activation energy). We now describe theoretical approaches to enzymatic catalysis that have led to the development of dynamic barrier (width) tunneUing theories for hydrogen transfer. Indeed, enzymatic hydrogen tunnelling can be treated conceptually in a similar way to the well-established quantum theories for electron transfer in proteins. 

Jacobi and Schnepp (1972) and Raich (1972) were the first to develop a quantum-dynamical model for the large-amplitude librations in a-nitro-gen. Their formalism is essentially described in Section IV,C. They first calculated single-molecule mean field states that may be localized as well as delocalized, depending on the height of the rotation barriers from the anisotropic potential. These states were used to construct a basis of exci-tonlike wave functions for the whole crystal. The final step in their calcu-... 

In addition to the thermal studies, researchers have also investigated the two processes using well established experimental dynamical methods [31]. These experiments involve hot hydrogen atoms and therefore sample the potentii energy surface well above the potential barrier height. Several calculations using the LSTH surface have been carried out with modern quantum scattering theory, and one of the... 

In this chapter, we will focus on the development and application of the combined quantum/classical methods. To accomplish this we first provide background on the classical methods used in protein and nucleic acid simulations. In Sect. 2 we review the form and origin of empirical potentials used in biopolymer dynamics, the classical simulation methods, and techniques for evaluating thermodynamic averages as might be important in computing barrier heights for chemical rate processes. Next we describe the basic formalism for mixed quantum/classical simulation methods as well as some of the practical considerations in their development and implementation. This is done in Sect. 3. We conclude in Sect. 4 with an overview of these methods and their potential for chemical studies. 

The spin-boson model can be motivated in terms of the physical problan of a quantum particle (e.g., an electron, muon, or proton) tunneling in an asymmetric double well (Figure 11.4). The relevant energy scales are the asymmetry he, tunneling HAq, and thermal k T, which can be all comparable but are much smaller than the barrier height Eq. Under this circumstance, the dynamics of the quantum particle moving in the double well can be described by what we shall refer to as the subsystem Hamiltonian... 

Some properties of excited merocyanine dyes are compiled in Table 36.6. The most frequently studied is merocyanine 540 (Ml). Ml is readily soluble in alcohols and Hpid membranes, making it attractive for many technical applications and biological activity studies.The solvent polarity has a significant influence on Tf and the related quantum yields. - An intrinsic barrier height of Ej, = 3 kj mol" for isomerization in Sj was determined from dynamical solvation effects on the rate of Ml in polar solvents. Environmental effects on radiative and nonradiative transitions have been studied for mero-cyanines in homogeneous and microheterogeneous systems. ... 

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