Finite electronic temperature

VandeVondele J, Rothlisberger U, Accelerating Rare Reactive Events by Means of a Finite Electronic Temperature, J Am Chem Soc, 124, 8163-8171 (2002)... 

Given that quantum chemistry calculations directly provide electronic energies, which formally correspond to zero temperature and pressure, ways for connecting to finite, realistic temperature and pressure are needed. One method is first-principles thermodynamics (FPT), the basic concept of which is that the thermodynamically prevailing state of a surface is the one that minimizes the surface free energy, y, subject to external conditions such as temperature and the chemical potentials of the various components of the system ... 

The introduction of a finite particle temperature changes the structure of the longitudinal (in the direction of wave propagation) component of the momentum equation for the electrons, leading to a definite non-negative electron density, as for example, in the case of a Boltzmann electron distribution [38] that is ... 

The ratio of Hp/Hj, intensities, which is a measure of the electron temperature, increased with It was greater with finite bias voltages than when Fb = 0V. 

The impact of a finite gas temperature has been considered (Shkarofsky et al., 1966 Winkler et al, 1990), to allow an energy transfer from the atoms or molecules back to the electrons in elastic collisions at very low electric fields. 

Unsaturated polyester finishes of this type do not need to be stoved to effect crosslinking, but will cure at room temperature once a suitable peroxide initiator cobalt salt activator are added. The system then has a finite pot life and needs to be applied soon after mixing. Such a system is an example of a two-pack system. That is the finish is supplied in two packages to be mixed shortly before use, with obvious limitations. However, polymerisation can also be induced by ultra violet radiation or electron beam exposure when polymerisation occurs almost instantaneously. These techniques are used widely in packaging, particularly cans, for which many other unsaturated polymers, such as unsaturated acrylic resins have been devised. 

Every gas changes into a liquid if the pressure is high enough and the temperature is low enough. The atoms or molecules of a liquid or solid stick together in a finite volume rather than expanding, as a gas does, to fill all available space. This cohesiveness comes from electrical forces of attraction between the negative electron cloud of each atom and the positive nuclei of other atoms. We describe intermolecular forces in Chapter 11. 

As discussed in Sect. 6.2, the electronic states of a paramagnetic ion are determined by the spin Hamiltonian, (6.1). At finite temperamres, the crystal field is modulated because of thermal oscillations of the ligands. This results in spin-lattice relaxation, i.e. transitions between the electronic eigenstates induced by interactions between the ionic spin and the phonons [10, 11, 31, 32]. The spin-lattice relaxation frequency increases with increasing temperature because of the temperature dependence of the population of the phonon states. For high-spin Fe ", the coupling between the spin and the lattice is weak because of the spherical symmetry of the ground state. This... 

From the measured mobilities, certain general systematics can be observed. Of these, the dependences of mobility on temperature and molecular srtucture, which are of obvious importance, will be discussed in the following subsections. In n-alkanes, at and around room temperatures, the electron mobility gradually falls with the carbon number, but it becomes nearly constant at n > 7. One interpretation attributes this to electron scattering by a finite part of the alkane... 

At zero temperature the electrons in a solid occupy the lowest energy levels compatible with the Pauli exclusion principle. The highest energy level occupied at T = 0 is the Fermi level, Ep. For metals the Fermi level and the electrochemical potential are identical at T = 0, since any electron that is added to the system must occupy the Fermi level. At finite temperatures Ep and the electrochemical potential p of the electrons differ by terms of the order of (kT)2, which are typically... 

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