First-principles approach

Ultrasonic Spectroscopy. Information on size distribution maybe obtained from the attenuation of sound waves traveling through a particle dispersion. Two distinct approaches are being used to extract particle size data from the attenuation spectmm an empirical approach based on the Bouguer-Lambert-Beerlaw (63) and a more fundamental or first-principle approach (64—66). The first-principle approach implies that no caHbration is required, but certain physical constants of both phases, ie, speed of sound, density, thermal coefficient of expansion, heat capacity, thermal conductivity. 

Psichogios, D. C., and Ungar, L. H., A hybrid neural network-first principles approach to process modeling. AIChEJ. 38, 1499 (1992). 

The key attribute of flows in micro devices is their laminar character, which stands in contrast to the mostly turbulent flows in macroscopic process equipment. Owing to this feature, micro flows are a priori much more accessible to a model description than macro flows and can be described by first-principle approaches without any further assumptions. In contrast, for the simulation of turbulent flows usually a number of semi-heuristic models are applied, and in many situations it is not clear which description is most adequate for the problem under investigation. As a result, it stands to reason to assume that a rational design of micro reactors... 

Lichtner, PC. and Biino, G.G. (1992) A first principles approach to supergene enrichment of a porphyry copper protoore. 1 Cu-Fe-S subsystem. Geochim. Cosmochim. Acta, 3987-4013. 

Herrmann C, Reiher M (2007) First-Principles Approach to Vibrational Spectroscopy of Biomolecules. 268 85-132 Higson SPJ, see Davis F (2005) 255 97-124... 

Palacios JJ, Perez-Jimenez AJ, Louis E, SanFabian E, Verges JA (2002) First-principles approach to electrical transport in atomic-scale nanostructures. Phys Rev B 66(3) 035322... 

First law of thermodynamics, 24 645-648 First limiting amino acid, 2 601 First-order irreversible chemical kinetics, 25 286-287, 292-293 First-principle approach, in particle size measurement, 13 153 First sale doctrine, 7 793 Fischer, Emil, 16 768 Fischer carbene reaction, 24 35-36 Fischer esterification, 10 499 Fischer formula, 4 697 Fischer-Indole synthesis, 9 288 Fischer lock and key hypothesis, 24 38 Fischer-Tropsch (FT) synthesis, 6 791, 827 12 431... 

Calculations of chemical shielding and EFG parameters for crystalline materials have become a valuable tool for the interpretation of solid-state NMR data. With the advent of powerful computational resources and methods that allow calculations to be performed within a reasonable time, quantum chemical first-principles approaches are nowadays feasible and of very great applicability to NMR. Former studies dealt with the prediction of chemical shifts and other NMR parameters from... 

Let us start with first-principles approach in the particular case of immobile particles (low temperatures). An infinite set of equations for many-point densities pm,m = Pm,m r m r m> t), where f m = n,..., rm (below a symbol f lm denotes the vector fj omitted in a set r m) could be derived by summing recombination and generation contributions which yields ... 

Clusters of still heavier homologues of carbon offer the prospect of studying the transition to metallic behavior, which is reached with lead in the bulk. This line of study has already been started experimentally [79]. Theory lags behind considerably here, obviously because of the steeply increasing computational effort of first-principles approaches. Nevertheless, a few studies in this direction have started to appear, for example by Wang et al. [80], who looked at Ge, n<21, within a TB model. Direct comparisons with experiment are still lacking, though. 

First principles approaches are important as they avoid many of the pitfalls associated with using parameterized descriptions of the interatomic interactions. Additionally, simulation of chemical reactivity, reactions and reaction kinetics really requires electronic structure calculations [108]. However, such calculations were traditionally limited in applicability to rather simplistic models. Developments in density functional theory are now broadening the scope of what is viable. Car-Parrinello first principles molecular dynamics are now being applied to real zeolite models [109,110], and the combined use of classical and quantum mechanical methods allows quantum chemical methods to be applied to cluster models embedded in a simpler description of the zeoUte cluster environment [105,111]. 

In the direct design approach, a desired supersaturation profile that falls between the solubility curve and the metastable limit of the system is followed based on feedback control of the concentration measurement. This is in contrast to the traditional first-principles approach, where a desired temperature profile or antisolvent addition rate profile is followed over time such as shown in Fig. 14. For a cooling crystallization, the direct design approach follows a setpoint profile that is solution concentration vs. temperature (or solvent-antisolvent ratio) as opposed to temperature (or addition rate) vs. time. Because the desired crystallizer temperature is determined from an in-situ solution concentration measurement, the batch time is not fixed. 

Fig. 14 Schematic block diagrams of the temperature (7) vs. time (t) profile from first principles approach (A) and of concentration (C) vs. temperature (7) profile from direct design (B).

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