Configurational averages

The ASR provides an alternative means for configuration averaging which is not... 

Pi()2i )2i, )i2, 3. ..) and Pf are projection operators on a specific state k. For the purpose of configuration averaging the previous theorem for uncorrelated disorder still holds good with Mid replaced by... 

For the electronic structure calculations in a disordered system, f is chosen to be the Green function (zI-H( n )) where H is the Hamiltonian of the system and n are the random site occupation variables. According to ASF configuration averaged density of states (DOS) is given by ... 

This prescription transforms the effective Hamiltonian to a tridiagonal form and thus leads directly to a continued fraction representation for the configuration averaged Green function matrix element = [G i]at,. This algorithm is usually continued... 

EFFECTIVE PAIR INTERACTIONS IN RANDOM ALLOYS BY DIRECT CONFIGURATIONAL AVERAGING... 

If one is dealing with a randomly disordered alloy it is straightforward to perform the necessary configuration average [9]. In the case of one atom per unit cell one ends up with the following expression for the photo current... 

After we obtained the self-consistent electronic structure of the magnetic multilayers we calculated the non-local conductivity by evaluating the quantum mechanical linear response of the current to the electric field using an approach developed by Kubo and Greenwood. In this approach the conductivity is obtained from a configurational average of two one-electron Green functions ... 

Here is the p-th spatial component of the electronic current operator j and. .. )conf. denotes the atomic configuration average for a disordered alloy. 

With a computer program that evaluates r as a function of time for a given U(r) we can use the ergodic hypothesis (which states that the time average over a long time is equal to the configuration average) and write... 

Equations (8.44) and (8.45) guarantee convergence to a canonical distribution only in the case of fixed B. Because B varies (i.e., the method uses information from momenta sampled in the past in determining the vector B), the evolution is not strictly Markovian. As a consequence, the correlations introduced can lead to the accumulation of systematic errors in the determination of configuration averages [77], However, these correlations can be broken if the update of B is not done each step, but with a lower updating frequency. This is analogous to other approximately Markovian procedures employed in MC simulations (e.g., update of the maximum displacements allowed for individual atoms [78]). 

A useful view of averages can be expressed via the PDT. The configurational average of the quantity F is... 

The bond additivity approximation (BAA) appears to work for polymers dissolved in isotropically polarizable nonpolar solvents. However in the gas phase, BAA has been shown to be incorrect by Ward and coworkers (11). It has been speculated that the solvent provides a symmetrical environment in which local electric fields at a given bond caused by adjoining bonds, are cancelled by fields due to solvent molecules. Thus assuming the correctness of the RIS and BAA models, the configurational average over all internal degrees of freedom r is given by... 

The configurational average in eqn (10) can also be performed (8) with eqn (1). In table III we present the results of our calculations (8) of eqn (10) for poly(p-nitrostyrene) versus the tacticity of the polymer. No experimental EFSHG results have been reported for... 

Configurational averaging - solid solutions and grossly non-stoichiometric oxides... 

Figure 11.13 (a) Enthalpy, (b) entropy and (c) Gibbs energy of mixing of MnO-MgO at 1000 K, all calculated using the configurational averaging technique. 

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