Born correction

This is close, but not equal to the tin-foil Born-corrected energy 1... 

Free energy of hydration studies of simple cations have shown that the Born correction predicts only about half the correction expected, based on molecular simulations with different cutoff radii.The orientational polarizability of water in the vicinity of a simple cation has been studied to assess the conditions under which Born-like behavior can be expected. 

Pack R T and Hirschfelder J O 1970 Energy corrections to the Born-Oppenheimer approximation. The best adiabatic approximation J. Chem. Phys. 52 521-34... 

A. rather complex procedure is used to determine the Born radii a values of which. calculated for each atom in the molecule that carries a charge or a partial charge. T Born radius of an afom (more correctly considered to be an effective Born radii corresponds to the radius that would return the electrostatic energy of the system accordi to the Bom equation if all other atoms in the molecule were uncharged (i.e. if the other ato only acted to define the dielectric boundary between the solute and the solvent). In Sti force field implementation, atomic radii from the OPLS force field are assigned to ec... 

The following points may be borne in mind while selecting the correct rating of the fuses ... 

A very simple version of this approach was used in early applications. An alchemical charging calculation was done using a distance-based cutoff for electrostatic interactions, either with a finite or a periodic model. Then a cut-off correction equal to the Born free energy, Eq. (38), was added, with the spherical radius taken to be = R. This is a convenient but ill-defined approximation, because the system with a cutoff is not equivalent to a spherical charge of radius R. A more rigorous cutoff correction was derived recently that is applicable to sufficiently homogeneous systems [54] but appears to be impractical for macromolecules in solution. 

In most climates the wet bulb temperature is well below the dry bulb temperature and there is an advantage in using water or evaporative cooling for larger plant. These options need to be investigated and compared. The present concern over spray-borne diseases may indicate a preference for air cooling in the vicinity of institutions but correct maintenance of water cooling towers and evaporative condensers will permit their use elsewhere. Table 10.2, based on the tentative temperature differences of 15 K and 12 K... 

Comprehensive application data should be made available for all marketed packaged units, to allow designers or sales engineers to make the correct selections for their purposes. However, it should be borne in mind that manufacturers or sales outlets are frequently not aware of all the parameters of an installation, and the interpretation of catalogue data has many pitfalls. 

In equation (2) Rq is the equivalent capillary radius calculated from the bed hydraulic radius (l7), Rp is the particle radius, and the exponential, fxinction contains, in addition the Boltzman constant and temperature, the total energy of interaction between the particle and capillary wall force fields. The particle streamline velocity Vp(r) contains a correction for the wall effect (l8). A similar expression for results with the exception that for the marker the van der Waals attraction and Born repulsion terms as well as the wall effect are considered to be negligible (3 ). 

How important the breakdown of the Born-Oppenheimer approximation is in limiting our ability to carry out ab initio simulations of chemical reactivity at metal surfaces is the central topic of this review. Stated more provocatively, do we have the correct theoretical picture of heterogeneous catalysis. This review will restrict itself to a consideration of experiments that have begun to shed light on this important question. The reader is directed to other recent review articles, where aspects of this field of research not mentioned in this article are more fully addressed.10-16... 

If we are correct in our assumption that the electrophilic substitution of aromatic species involves such a complexes as intermediates—and it has proved possible actually to isolate them in the course of some such substitutions (p. 136)—then what we commonly refer to as aromatic substitution really involves initial addition followed by subsequent elimination. How this basic theory is borne out in the common electrophilic substitution reactions of benzene will now be considered. 

Ruland and Smarsly [9,84,240] can analyze their recorded data in the classical Born approximation, but have to correct for the special geometry of the grazing incidence experiment. They propose not to carry out the necessary corrections in a... 

The Born-Bethe approximation for low-energy electrons requires correction for two reasons. First, the integrals defining the total oscillator strength and the... 

Theory doesn t tell us what initial Li a star has, only what depletion it suffers. An accurate estimate of the initial Li abundance is therefore a pre-requisite before observations and models can be compared. The Sun is a unique exception, where we know the present abundance, A(Li) = 1.1 0.1 (where A(Li)= log[AT(Li)/AT(H)] + 12) and the initial abundance of A(Li)= 3.34 is obtained from meteorites. For recently born stars, the initial Li abundance is estimated from photospheric measurements in young T-Tauri stars, or from the hotter F stars of slightly older clusters, where theory suggests that no Li depletion can yet have taken place. Results vary from 3.0 < A(Li) < 3.4, somewhat dependent on assumed atmospheres, NLTE corrections and TeS scales [23,33]. It is of course quite possible that the initial Li, like Fe abundances in the solar neighbourhood, shows some cosmic scatter. Present observations certainly cannot rule this out, leading to about a 0.2 dex systematic uncertainty when comparing observations with Li depletion predictions. 

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