Indexing from first principles

Similar to structure solution from first principles, the ab initio indexing implies that no prior knowledge about symmetry and approximate unit cell dimensions of the crystal lattice exists. Indexing from first principles, therefore, usually means that Miller indices are assigned based strictly on the relationships between the observed Bragg angles. 

Accurate indexing from first principles rests on the four cornerstones ... 

All three computer codes (TREOR, DICVOL, and ITO) have been extensively tested by hundreds of researchers. They have undergone multiple revisions by both the original developers and experienced crystallographers, and therefore, are quite reliable, provided adequate quality powder diffraction data are employed. As already noted above, the following are the keys to successful indexing from first principles precision, precision, and precision. 

Seco, J., Luque, F.J., and Barril, X. (2009) Binding site detection and druggability index from first principle. Journal of Medicinal Chemistry, 52, 2363-2371. 

Although all functions can be differentiated from first principles, using equation (4.4), this can be a rather long-winded process in practice. In this chapter, we deal with the differentiation of more complicated functions with the aid of a set of rules, all of which may be derived from the defining relation (4.4). In many cases, however, we simply need to learn what the derivative of a particular function is, or how to go about differentiating a certain class of function. For example, we learn that the derivative of y —f x) — sin x is cos x, but that the derivative of y = j(x) = cos x is —sin x. Similarly, we can differentiate any function of the type y =/fx) = x" by remembering the rule that we reduce the index of x by 1, and multiply the result by n that is ... 

The microphysics in the field generation and particle acceleration described here is clearly beyond the reach of the magneto hydrodynamic approximation. A parameter study utilizing a PIC code working from first principles is necessary to fully understand the interdependence between the relative bulk Lorentz factors of the colliding plasma shells, the power law index of the non-thermal electron population, eb and in a broader sense the detailed evolution and structure in collisionless shocks. 

From the change in optical constants of the film covered surface compared to the bare surface, one can calculate from first principles the thickness and refractive index of the film using the equations derived by Drude. The sensitivity of the measurement is dependent primarily on the differences in refractive index of the solution and film, and the film and substrate. 

The molar refraction of a substance, a product of its refractive index, molecular weight, and density, m be assumed to be a fimdamental physical property of materials (1). Furthermore, the molar refraction may be treated (as established by Denbigh) as the sum of the bond refractions that make up the molecule (6). These two postulates make possible, the calculation of the refractive indices of polymers almost from first principles (7,8). Two useful relations for the molar refraction, R, are provided here (1) The Lorentz-Lorentz equation... 

The second step is to find good estimates of the rate parameters. The rate parameters can be obtained from collision theory, transition state theory, as well as first principles calculations such as DFT Calorimetric measurements of heats of adsorption is possible for the surface intermediates with a gas phase precursor. Otherwise, the surface energetic must be estimated. As we have mentioned earlier, the computational cost of DFT is overriding its utility and accuracy in the present-day capabilities. Eventually, the parameter space must be constructed with two major constraints. The first constraint requires the consistency with the thermodynamics and the second constraint requires that the macroscopic rate data can be reproduced. Unity bond index-quadratic exponential potential (UBI-QEP) method of Shustorovich (1986, 1998) offers a relatively accurate and affordable estimation of the surface energetics. 

According to the systematic nomenclature these substances were first named l-f-triazolo[d] pyrimidines in compliance with the general principles of the Ring Index/ More recent papers and Chemical Abstracts indexes use the term i -triazolo[4,5-d]pyrimidine (147) in accord with the lUPAC nomenclature. The numbering of substituents when using the last-mentioned name is different from that of the 8-aza analogs. For the formulas of oxygen and sulfur derivatives names derived from the lactim or thiolactim form are almost exclusively in use (in common with the purine derivatives). These derivatives are thus described as hydroxy and mercapto derivatives, respectively. The name 1,2,3,4,6-pentaazaindene is used only rarely for this system. 

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