Becke-Roussel functional

Neuman, R., Handy, N. C., 1995, Investigations Using the Becke-Roussel Exchange Functional , Chem. Phys. Lett., 252, 19. 

Table III The ratio of approximate to exact exchange energy per electron of a uniform electron gas. For the approximations listed in Tables I and II but not listed here, this ratio is exactly 1. The Becke-Roussel exchange functional is a non-empirical meta-GGA based upon the hydrogen atom.

The jBRX indicates the use of the Becke-Roussel (BR) functional (Becke tmd Roussel 1989) ... 

Meta-GGA functionals incorporate the Laplacian of the electron density and generally depend on the electron kinetic energy density. These features allow a systematic improvement of results for many quantum chemical calculations. We have used the exchange functional BR89 (Becke-Roussel 1989 represented in analytic form) [87,90] and the correlation functional B94 (Becke 1994) [90, 91]. Minnesota functionals tested are M05 [92], M05-2X [93], M06-L [94], M06-HF [95], M06 [96], M06-2X [96], and Ml 1 [97]. Another global hybrid studied is BMK [98]. A hybrid extension of the nonempirical exchange-correlation TPSS (Tao, Perdew, Staroverov, and Scuseria) [99] and functional TPSSh [100] is also examined. 

Proynov E, Gan Z, Kong J (2008) Analytical representation of the Becke-Roussel exchange functional. Chem Phys Lett 455 103-109... 

Another functional form (not a correction) proposed by Becke and Roussel (BR) has the form... 

BR Becke and Roussel s 1989 MGGA exchange functional that includes a dependence on the Laplacian of the density in addition to its gradient. Becke, A. D. and Roussel, M. R. 1989. Phys. Rev. A, 39, 3761. 

In contrast to the gradient expansion of the exchange hole of Perdew [135], the BR functional does not reduce to LSDA in the uniform density limit. To recover this limit approximately, Becke and Roussel multiplied the term t — t ) in Eq. (141) by an adjustment factor of 0.8. At the same time, the BR exchange energy density has the correct — p(r)/2r asymptotic behavior in the r — oo limit. 

Becke and Roussel (BR) functional, 185 Bell, Evans, Polanyi (BEP) principle, 364 Bell correction, tunnelling, 391 Bending energy, in force fields, 11 BLYP function, 188 Boltzman probability function, 374 Bond critical points, electron density analysis, 225... 

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