Structural constant

Here, are the structure constants for the Lie group defined by the set of the noncommuting matrices appearing in Eq. (94) and which also appear both in the Lagrangean and in the Sclu odinger equation. We further define the covaiiant derivative by... 

The values for the D sodium line of the atomic and structural constants and of the bond refractions, as determined by the author, are collected in Tables XI,2A and XI,2B respectively. 

Parameter k of Equation (4.10) is an expression of the breadth of the Gaussian distribution of the cumulative micropore volume IF over the normalized work of adsorption sfifi, and is therefore determined by the pore structure. Thus B also (cf. Equation (4.13)) is characteristic of the pore structure of the adsorbent, and has accordingly been termed the structural constant of the adsorbent. ... 

The original DR equation is thus a special case of the Dubinin-Astakhov equation, with m = 2 parameter of Equation (4.18) for m = 2 is related to the structural constant B of the DR treatment through the simple expression... 

For a continuous distribution, summation may be replaced by integration and by assuming a Gaussian distribution of size, Stoeckli arrives at a somewhat complicated expression (not given here) which enables the total micropore volume IFo, a structural constant Bq and the spread A of size distribution to be obtained from the isotherm. He suggests that Bq may be related to the radius of gyration of the micropores by the expression... 

These procedures proposed by Dubinin and by Stoeckli arc, as yet, in the pioneer stage. Before they can be regarded as established as a means of evaluating pore size distribution, a wide-ranging study is needed, involving model micropore systems contained in a variety of chemical substances. The relationship between the structural constant B and the actual dimensions of the micropores, together with their distribution, would have to be demonstrated. The micropore volume would need to be evaluated independently from the known structure of the solid, or by the nonane pre-adsorption method, or with the aid of a range of molecular probes. 

The S are the structure constants. From these we form the linear combinations... 

To obtain the Ees we must now integrate the product of p and V. In the atomic region we have a numerical integrals on a radial mesh. In the interstitial we have integrals of products of SSW s. These can always be reduced to expressions involving the structure constants and their energy derivatives, all of which are known [3,4]. 

Following Ham and Segall, the KKR structure constants, D, k,Ej, can be evaluated as the sum of the three series below (for one atom per unit cell lattices)... 

The sums in Eqs. (1) and (2) run, respectively, over the reciprocal space lattice vectors, g, and the real space lattice vectors, r and Vc= a is the unit cell volume. The value of the parameter 11 affects the convergence of both the series (1) and (2). Roughly speaking, increasing ii makes slower the convergence of Eq. (1) and faster that of Eq. (2), and vice versa. Our purpose, here, is to find out, for an arbitrary lattice and a given accuracy, the optimal choice, iiopt > tbal minimises the CPU time needed for the evaluation of the KKR structure constants. This choice turns out to depend on the Bravais lattice and the lattice parameters expressed in dimensionless units, on the... 

The structure constants for Hermitian generators are purely imaginary ... 

Huber, K.P. and Herzberg, G. (1979) Molecular Spectra and Molecular Structure Constants of Diatomic Molecules, Van Nostrand, New York. 

Parameters r, q and q are pure component molecular-structure constants depending on molecular size and external surface areas. For fluids other than water or lower alcohols, q = q. ... 

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