Transverse Exchange Energy

Table 5.5. Transverse exchange energies ( j) and its Breit approximation (Ej ) from RHF- [68] and RLDA-calculations [36]. Also the total correction is given (all energies are in...

Transverse exchange energies ( j) for closed subshell atoms Selfconsistent ROPM, RLDA and B88-RGGA results in comparison with perturbative RHF values (Coulomb gauge for j in the case of RHF — all energies in Hartree [172]). 

The kernels with two transverse exchanges in Fig. 4.4 give the following contribution to the energy shift in the scattering approximation... 

Fig. 4.1. Relativistic correction factor for the EDA exchange energy density longitudinal contribution (B.54), transverse contribution (B.55) and total correction -I- J...

Table 4.1 Exchange-only ground-state energies from ROPM and RHF calculations for noble gas atoms Coulomb (C) and Coulomb-Breit (C + B) limit in comparison with complete transverse exchange (C + T) (Engel et al. 1998a). For the RHF approximation the energy difference with respect to the ROPM is given, AE = tot(RHF) — tot(ROPM), providing results from (a) finite-differences calculations (Dyall et al. 1989) and (b) a basis-set expansion (Ishikawa and Koc 1994). All energies in mHartree. uext and c as in Ishikawa and Koc (1994).

The curvature coupling elements are thus simply off-diagonal matrix elements of the unprojected force constant matrix in the basis of eigenvectors of the projected force constant matrix. The classical notion that a trajectory will overshoot the path and climb the wall if the path curves on the way down the hill is a reflection of this curvature coupling. Climbing the wall in a transverse direction is tantamount to exchanging energy between the reaction path and the transverse vibration. 

Exchange-only ionization potentials of neutral atoms calculated from ground state energy differences For the ROPM the selfconsistent inclusion of the transverse exchange (C-fT) is compared with complete neglect of (C). The RGGA data have been obtained by the relativistic extension of the Becke parameterization [37] (all energies in mHartree [172]). 

E = exchange energy Ep = Fermi energy Eh = transverse Hall electric field Ej = energy of crystal field level E , = magnetoelastic energy... 

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