Energy coupling, degree

If the wave functions of individual species are separable (Born-Oppenheimer approximation), and if there is a weak energy coupling between the system of long-lived, chemically reacting particles with other degrees of freedom, the total probability distribution function p(t, r, v, e) of the system can be separated ... 

Figure 3. Effect of the degree of energy coupling, measured as respiratory control with ADP (R.C.adp), on the energy-dependent (respiratory chain linked) accumulation of iron (A) and calcium (B) in respiratory state 1 (in the absence of Viyo) and state 4 (with 3.3 mM succinate as the substrate, %). Rat liver mitochondria (31).

For the case of two strongly coupled degrees of freedom (2D biasing), 9, and 02, one can also compute the two dimensional free energy surface W along 0, and 02 and choose proportional and opposite to as in equation (15). In this case the expression for is a 2D truncated Fourier expansion ... 

The possible causes for these swelling in the mitochondrial depended on the chain length and degree of unsaturation. This potential is similar to the features used to disrupt the energy coupling processes in cellular (Pressman Lardy, 1956). 

This canonical behavior of the system particles is not accounted for by standard Newtonian dynamics (where the system energy is considered to be a constant of motion). In order to perform molecular dynamics (MD) simulations of the system under the influence of thermal fluctuations, the coupling of the system to the heat bath is required. This is provided by a thermostat, i.e., by extending the equations of motion by additional heat-bath coupling degrees of freedom [75]. The introduction of thermostats into the dynamics is a notorious problem in MD and it cannot be considered to be solved satisfactorily to date [76]. In order to take into consideration the stochastic nature of any particle trajectory in the heat bath, a typical approach is to introduce random forces into the dynamics. These forces represent the collisions of system and heat-bath particles on the basis of the fluctuation-dissipation theorem. 

In recent years, these methods have been greatly expanded and have reached a degree of reliability where they now offer some of the most accurate tools for studying excited and ionized states. In particular, the use of time-dependent variational principles have allowed the much more rigorous development of equations for energy differences and nonlinear response properties [81]. In addition, the extension of the EOM theory to include coupled-cluster reference fiuictioiis [ ] now allows one to compute excitation and ionization energies using some of the most accurate ab initio tools. 

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