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Exchange function

Boron Removal. Boron [7440-42-8] is occasionaHy present in water suppHes at an unacceptable level. It cannot be removed with the standard anion-exchange resins unless the water is deionized. Selective removal is possible by using an anion exchanger functionalized with /V-methy1g1ucamine [6284-40-8]. This resin is in limited commercial supply. The borate form of conventional strong base anion exchangers is used in some nuclear reactors to adjust the concentration of boron in water used as a moderator. The resin releases boron as the water temperature rises. [Pg.386]

The turboexpander in combination with a compressor and a heat exchanger functions as a heat pump and is analyzed as follows In Fig. 29-44 consider the compressor and aftercooler as an isothermal compressor operating at To with an efficiency and assume the working fluid to be a perfect gas. Further, consider the removal of a quantity of heat by the tumoexpander at an average low temperature Ti-This requires that it dehver shaft work equal to Q. Now, make the reasonable assumption that one-tenth of the temperature drop in the expander is used for the temperature difference in the heat exchanger. If the expander efficiency is and this efficiency is mul-... [Pg.2519]

Local exchange and correlation functionals involve only the values of the electron spin densities. Slater and Xa are well-known local exchange functionals, and the local spin density treatment of Vosko, Wilk and Nusair (VWN) is a widely-used local correlation functional. [Pg.119]

All three terms are again functionals of the electron density, and functionals defining the two components on the right side of Equation 57 are termed exchange functionals and correlation functionals, respectively. Both components can be of two distinct types local functionals depend on only the electron density p, while gradient-corrected functionals depend on both p and its gradient, Vp. ... [Pg.273]

We ll now take a brief look at some sample functionals. The local exchange functional is virtually always defined as follows ... [Pg.273]

Becke formulated the following gradient-corrected exchange functional based on the LDA exchange functional in 1988, which is now in wide use ... [Pg.273]

In an analogous way to the exchange functional we examined earlier, a local correlation functional may also be improved by adding a gradient correction. [Pg.274]

Pure DFT methods are defined by pairing an exchange functional with a correlation functional. For example, the well-known BLYP functional pairs Becke s gradient-corrected exchange functional with the gradient-corrected correlation functional of Lee, Yang and Parr. [Pg.275]

Gaussian98 gives a choice of six exchange functionals and seven correlation functionals, together with a number of so-called hybrid functionals. These latter... [Pg.227]

Perdew and Wang have proposed an exchange functional similar to B88 to be used in connection with the PW91 correlation functional given below (eq. (6.30)). [Pg.185]

A gas is to be cooled from 190°F to 105°F with partial condensation taking place. The dew point is 120°F. The cooling water enters at 90°F and leaves at 110°F. Figure 10-37 illustrates the basic exchanger functions. [Pg.74]

Nevertheless, despite all the new resins primarily designed for specialist market niches, for the most part we are primarily concerned with a limited number of standard resin types that provide common exchange functions for general industrial and institutional boiler plant processes such as ... [Pg.346]

D Integrated Total Systems with Micro Mixing and Micro Heat Exchange Functions... [Pg.405]

As this acid cleavage releases considerable heat, the apparatus used needs efficient heat exchange units [64]. Selectivity of the hydroperoxide cleavage is affected if temperature rises in an undesired manner. For this reason, not the technical 65-90 wt.-% solutions, but rather strongly diluted ones (e.g. below 10%) are employed. In the first case, a sudden loss of the heat exchange function could result in an temperature increase from 50 to 500 °C within seconds. [Pg.539]

Inserting equation (6-14) into equation (6-12) retrieves the p4/3 dependence of the exchange energy indicated in equation (3-5). This exchange functional is frequently called Slater exchange and is abbreviated by S. No such explicit expression is known for the correlation part, ec. However, highly accurate numerical quantum Monte-Carlo simulations of the homogeneous electron gas are available from the work of Ceperly and Alder, 1980. [Pg.88]

For the function F two main classes of realizations have been put forward (see in particular Adamo, di Matteo, and Barone, 1999). The first one is based on a GGA exchange functional developed by Becke, 1988b. As outlined above, this functional is abbreviated simply as B (sometimes one also finds B88)... [Pg.94]

Functionals which are related to this approach include among others the recent FT97 functional of Filatov and Thiel, 1997, the PW91 exchange functional (Perdew, 1991, and Burke, Perdew, and Wang, 1998) and the CAM(A) and CAM(B) functionals developed by Handy and coworkers (Laming, Termath, and Handy, 1993). [Pg.94]

The second class of GGA exchange functionals use for F a rational function of the reduced density gradient. Prominent representatives are the early functionals by Becke, 1986 (B86) and Perdew, 1986 (P), the functional by Lacks and Gordon, 1993 (LG) or the recent implementation of Perdew, Burke, and Emzerhof, 1996 (PBE). As an example, we explicitly write down F of Perdew s 1986 exchange functional, which, just as for the more recent PBE functional, is free of semiempirical parameters ... [Pg.94]

The corresponding gradient-corrected correlation functionals have even more complicated analytical forms and cannot be understood by simple physically motivated reasonings. We therefore refrain from giving their explicit expressions and limit ourselves to a more qualitative discussion of the most popular functionals. Among the most widely used choices is the correlation counterpart of the 1986 Perdew exchange functional, usually termed P or P86. This functional employs an empirical parameter, which was fitted to the... [Pg.94]

We have repeatedly indicated that usually the exchange contributions are significantly larger in absolute numbers than the corresponding correlation effects. Therefore, an accurate expression for the exchange functional in particular is a prerequisite for obtaining meaningful results from density functional theory. However, we have seen in Chapters 1 and 5 that the... [Pg.95]


See other pages where Exchange function is mentioned: [Pg.2183]    [Pg.390]    [Pg.154]    [Pg.502]    [Pg.504]    [Pg.566]    [Pg.293]    [Pg.382]    [Pg.262]    [Pg.501]    [Pg.240]    [Pg.119]    [Pg.119]    [Pg.274]    [Pg.228]    [Pg.229]    [Pg.404]    [Pg.6]    [Pg.341]    [Pg.405]    [Pg.409]    [Pg.541]    [Pg.36]    [Pg.234]    [Pg.88]    [Pg.93]    [Pg.95]    [Pg.96]    [Pg.98]   
See also in sourсe #XX -- [ Pg.3 , Pg.26 ]




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Approximate exchange functionals

Are Molecular Exchange-correlation Functionals Transferable to Crystals

B3-LYP exchange-correlation functional

B3-LYP exchange-correlation functional calculating structural parameters

B3-LYP exchange-correlation functional in determination of vibrational spectra

B3-LYP exchange-correlation functional reliability of calculated relative energies

B3LYP exchange-correlation functional

B88 exchange functional

B97, exchange-correlation functionals calculating structural parameters

B97, exchange-correlation functionals heterocycles

Basis functions exchange correlation

Becke 88 exchange functional

Becke exchange functionals

Bond lengths exchange-correlation functionals

Classification of Exchange-Correlation Functionals

Cooling heat exchange function

Correlation function exchange

Density Functionals of Exchange Energy

Density Functionals of Exchange-Correlation Energy

Density exchange-correlation functionals

Density functional differential exchange

Density functional theory Hartree-Fock exchange

Density functional theory Hartree-Fock-Slater exchange

Density functional theory exact exchange potential

Density functional theory exchange-correlation

Density functional theory exchange-correlation energy

Density functional theory exchange-correlation functionals

Density functional theory exchange-correlation holes

Density functionals Perdew-Wang-91 exchange-correlation

Dirac exchange energy functional

Dirac exchange functional

Electronic structure methods exchange-correlation functional

Exact exchange energy density functional

Exact exchange energy density functional from Fock operator

Exact exchange functionals

Exact exchange orbital functionals

Exchange and Correlation Energy Functionals

Exchange correlation functional

Exchange correlation functionals, local

Exchange correlation functionals, local density approximations

Exchange correlation functionals, local theory

Exchange correlation functionals, local with experimental data

Exchange energy functional

Exchange energy functional relativistic

Exchange functional

Exchange functionals

Exchange functionals

Exchange operator wave function calculations, functionals

Exchange resins functional groups

Exchange-correlation energy functional

Exchange-correlation energy functional gradient-corrected

Exchange-correlation energy functional hybrid

Exchange-correlation energy functionals

Exchange-correlation energy, density functionals

Exchange-correlation functional generalized gradient approximation

Exchange-correlation functional local density approximation

Exchange-correlation functional, for

Exchange-correlation functional, in density

Exchange-correlation functional/potential

Exchange-correlation functionals

Exchange-correlation hole functions

Exchange-correlation relativistic energy functional

Exchange-correlation relativistic functionals

Exchange-density functionals

Exchange-energy density functional, theory

Exchange-energy functionals

Exchange—correlation density functional

Excitation energy exchange-correlation functional

Explicit Relativistic Exchange-Correlation Functionals

Fock exchange functional

Functional group exchanges

Functional group exchanges definition

Functionalized Ion Exchange Membrane in Electrodialysis

Functionalized polar group exchange

Generalized gradient approximations exchange correlation functionals

Global hybrid exchange functionals

Gradient-corrected exchange-correlation functional

Halogen-lithium exchange reactions functionalized compounds

Hartree-Fock exchange function

Histidine Hydrogen Exchange for Analysis of Protein Folding, Structure, and Function

Hohenberg-Kohn theorems exchange correlation functional energy

Hybrid exchange functionals

Hydroxide exchange membranes functional groups

Ion Exchange functional groups

Ion exchange function

Kohn-Sham theory exchange-correlation energy functional

LDA and GGA Exchange Functionals

LDA exchange functional

Local exchange functional

Local exchange functional nonrelativistic

Local exchange functional relativistic corrections

Local gradient-corrected exchange-correlation functional

Local spin-density approximations hybrid exchange functionals

Local-scaling density functional theory exchange energy

Long-range corrected exchange-correlation functional

Mixing exchange functionals

Nonlocal exchange functional

OPTimized exchange density function

Orbital-Dependent Exchange-Correlation Functional

Orbital-functional response theory, exchange-only

Perdew-Wang exchange functional

Perdew-Wang-91 exchange-correlation functional

Power exchange function

Proton exchange membrane fuel cells functions

Relativistic exchange-correlation functional

Response time as a function of the thermal driving force for an idealized heat exchanger at different hold-up values

Search for Functional Group Exchanges GRX

Self exchange-correlation function

Semi-empirical Orbital-Dependent Exchange-Correlation Functionals

Slater exchange functions

Statistical exchange functional

The Pair Density. Orbital-dependent Exchange-correlation Functionals

The Power Exchange Function

The Quest for Approximate Exchange-Correlation Functionals

The Structures and Functions of Ion-Exchange Membranes

The exchange-correlation functional

Time-dependent density functional theory exact exchange

Vosko local exchange correlation function

Wave functions exchange-correlation holes

Xa exchange functional

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