Ensemble approach, suitability

Here Tq are coordinates in a reference volume Vq and r = potential energy of Ar crystals has been computed [288] as well as lattice constants, thermal expansion coefficients, and isotope effects in other Lennard-Jones solids. In Fig. 4 we show the kinetic and potential energy of an Ar crystal in the canonical ensemble versus temperature for different values of P we note that in the classical hmit (P = 1) the low temperature specific heat does not decrease to zero however, with increasing P values the quantum limit is approached. In Fig. 5 the isotope effect on the lattice constant (at / = 0) in a Lennard-Jones system with parameters suitable for Ne atoms is presented, and a comparison with experimental data is made. Please note that in a classical system no isotope effect can be observed, x "" and the deviations between simulations and experiments are mainly caused by non-optimized potential parameters. 

An avenue that has received exploration is the development of equations for evolution of probability-density functions. If, for example, attention is restricted entirely to particular, fixed values of x and t, then the variable whose value may be represented by v becomes a random variable instead of a random function, and its statistics are described by a probability-density function. The probability-density function for v may be denoted by P(v where P(v) dv is the probability that the random variable lies in the range dv about the value v. By definition P(v) > 0, and P(v) dv = 1, One approach to obtaining an equation of evolution for P(v) is to introduce the ensemble average of a fine-grained density, as described by O Brien in [27], for example another is formally to perform suitable integrations in... 

Lj M-R/Lj M-R bond enthalpies within a homologous series of compounds or predicting enthalpies of reactions interconnecting members of the series. Converting such relative bond enthalpies to an absolute scale is less straightforward, however, and requires a judiciously chosen anchor point" (an accurate estimate of D(Lj M-X)). Rigorously absolute values of D(Lj M-R) are accessible via one-electron sequences as shown in Equations 5-10, provided suitable Lj M/Lj M-R/Lj M-X ensembles are available. This approach has recently been applied to an actinide(III)/(IV) and a lanth-... 

An ensemble dynamics approach has been described by Im et al., suitable for deciphering solid-state NMR observables of membrane proteins. Various computational methods for determining transmembrane helix orientations are discussed, and the distributions of VpuTM (from HIV-1) and WALP23 (a synthetic peptide) orientations from solid-state NMR and... 

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