Temperature Langevine

Temperature is handled the same way in Langevin dynamics as it its in molecular dynamics. High temperature runs may be used to overcome potential energy barriers. Cooling a system to a low temperature in steps may result in a different stable conformation than would be found by direct geometry optimization. 

This universality is peculiar for the high-temperature approximation, which is valid for //J < 1 only. For sufficiently high temperature the quantum theory confirms the classical Langevin theory result of J-diffusion, also giving xj = 2xE (see Chapter 1). This relation results from the assumed non-adiabaticity of collisions and small change of rotational energy in each of them ... 

Variations on these include running simulations at a variety of temperatures or running Langevin dynamics with a low friction constant to increase the ability to cross barriers at a given temperature (Pastor, W. R. Karplus, M., to be published.). 

We shall now briefly describe the well-known temperature-independent Langevin diamagnetism of closed-shell ions, such as K+ and Cl in KCl and similar Inorganics, such as Si02, AI2O3, and the zeolites, as well as the covalent organic compounds. Since all such... 

The function (a) is known as the Langevin function, after Paul Langevin, French physicist (1872-1946). The magnetic susceptibility of a paramagnetic substance can be expressed as (jim(B/kT). where fim is the magnetic moment, (S the magnetic flux, k the B and T die absolute temperature. 

If the molecular effects of the electric field are irrelevant to microwave heating of solutions, this assumption could be envisaged in the use of operating conditions very far from current conditions. On one hand, it will be necessary to use an electric field of higher amplitude, or to reduce the temperature according to the Langevin function. This last solution is obviously antinomic with conventional chemical kinetics, and the first solution is, currently, technologically impossible. It will, on the other hand, be necessary to avoid reaction media with dielectric loss. The molecular effects of the microwave electric field could, paradoxically, be observed for a medium which is not heated by the action of microwave irradiation. 

Hase s trajectory value for the association rate constant, /cp of 1.04 cm- s maybe used in conjunction with the above Langevin value of the collisional stabilization rate constant to yield a unimolecular dissociation rate constant of 3.75 x 10 ° s and a lifetime of 27 ps. In each case, these values are in excellent agreement with the order of magnitude of lifetimes predicted by Hase s calculations for cr/CHjCl collisions at relative translational energies of 1 kcal mor , rotational temperatures of 300 K, and vibrational energies equal to the zero-point energy of the system. 

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