Nonlocal electron currents

Several other molecular orbital models have been applied to the analysis of VCD spectra, primarily using CNDO wave functions. The nonlocalized molecular orbital model (NMO) is the MO analog of the charge flow models, based on atomic contributions to the dipole moment derivative (38). Currents are restricted to lie along bonds. An additional electronic term is introduced in the MO model that corresponds to s-p rehybridization effects during vibrational motion. 

The time-dependent density functional theory [38] for electronic systems is usually implemented at adiabatic local density approximation (ALDA) when density and single-particle potential are supposed to vary slowly both in time and space. Last years, the current-dependent Kohn-Sham functionals with a current density as a basic variable were introduced to treat the collective motion beyond ALDA (see e.g. [13]). These functionals are robust for a time-dependent linear response problem where the ordinary density functionals become strongly nonlocal. The theory is reformulated in terms of a vector potential for exchange and correlations, depending on the induced current density. So, T-odd variables appear in electronic functionals as well. 

Using pseudopotentials has several major beneficial consequences (i) Only the valence electrons must be treated explicitly, thus the number of equations to be solved [Eqs. (13)] can be reduced drastically (ii) the pseudoorbitals are very smooth near the atomic core, and thus Tout can be reduced drastically and (iii) important relativistic effects of the core electrons of heavy elements such as the 5d elements can be included in nonrelativistic calculations. The major downsides are that the potential v(r) in Eq. (3) must be replaced with a more complicated and computationally expensive nonlocal pseudopotential and, more importantly, that the transferability of the pseudopotential, i.e., its accuracy in different bonding environments, may not be perfect. Developing highly transferable pseudopotentials that can be used at as low an cut as possible is a major current topic of research. 

Computational methods based on multiple scattering theory (MST) are currently formulated only for local potential functions [44]. New formalism may be necessary in order to extend such methods to nonlocal potentials, but this appears to be necessary if electronic self-interaction is to be eliminated systematically. A caveat is... 

The ACID ATj can be plotted as an isosurface similar to the total electron density. However, in contrast to the total electron density, only nonlocal (delocalized) electrons contribute to AT, . For a more detailed analysis of molecular magnetic properties, the current density vectors can be plotted onto the ACID hypersurface. It is important to note that the ACID, as defined earlier, is invariant with respect to the relative orientation of the molecule and the magnetic field. Therefore, the ACID hypersurface is unambiguous even in nonplanar and unsymmetric systems. 

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