Electron density asymptotic behavior

Glossman, M. D., L. C. Baibas, A. Rubio, and I. A. Alonso. 1994. Nonlocal Exchange and Kinetic Energy Density Functionals with Correct Asymptotic Behavior for Electronic Systems. Int. I. Q. Chem. 49, 171. 

Glossman, M. D., Baibas, L. C., Rubio, A. and Alonso, J. A. Nonlocal exchange and kinetic energy density functionals with correct asymptotic behavior for electronic systems, Int.J. Quantum ( hem., 49 (1994), 171-184... 

This is known as the ionization potential theorem. Equation 7.7 between max and ionization potential I can also be obtained alternatively by looking at the asymptotic behavior of the density of a many-electron system. For atoms and molecules, the asymptotic decay of the density is given as [6-11]... 

Since momentum densities are unfamiliar to many. Section II outlines the connection between the position and momentum space representations of wavefunctions and reduced-density matrices, and the connections among one-electron density matrices, densities, and other functions such as the reciprocal form factor. General properties of momentum densities, including symmetry, expansion methods, asymptotic behavior, and moments, are described in... 

DPT schemes, which allow to calculate the electron affinities of atoms are based on the exact [59,60] and generalized (local) [61,62] exchange self-interaction-corrected (SIC) density functionals, treating the correlation separately in some approximation. Having better asymptotic behavior than GGA s, like in the improved SIC-LSD methods, one should obtain more... 

Density Functional Theory (DFT) has become a powerful tool for ab-initio electronic structure calculations of atoms, molecules and solids [1, 2, 3]. The success of DFT relies on the availability of accurate approximations for the exchange-correlation (xc) energy functional Exc or, equivalently, for the xc potential vxc. Though these quantities are not known exactly, a number of properties of the exact xc potential vxc(r) are well-known and may serve as valuable criteria for the investigation of approximate xc functionals. In this contribution, we want to focus on one particular property, namely the asymptotic behavior of the xc potential For finite systems, the exact xc potential vxc(r) is known to decrease like — 1/r as r —oo, reflecting also the proper cancellation of spurious self-interaction effects induced by the Hartree potential. 

Becke, D.A. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 1988, 38, 3098-100 Lee, C.T., Yang, T., Parr, R.C. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron-density, Phys. Rev. B, 1988, 37, 785-9. 

It is also known that in a finite many-electron system, the true exchange potential Vx(r) and exchange energy density e (r) have the following asymptotic behavior [45,137] ... 

It is instructive and helpful for assessing the correctness of the numerical apparatus to investigate the asymptotic behavior of the leptonic coalescence density P R). In the limit R 00 the ground-state HH system dissociates into separated H(1 s) and H( 1 s) atoms. In this case the electron and positron densities are spatially separated and do not overlap. Necessarily, lim/ oo P R) = 0. 

The long-range tail of each function has exponential dependence, making it easier to match the correct asymptotic behavior of the electron density. The electron-nucleus cusp condition is readily satisfied by STO functions. 

Hoffmann-Ostenhof, M. Hoffmann-Ostenhof, T. Schrodinger inequalities and asymptotic behavior of the electron density of atoms and molecules. Phys. Rev. A 1977, 16, 1782-1785. 

Nagy, A. AmoviUi, C. Electron-electron cusp condition and asymptotic behavior for the Pauli potential in pair density functional theory. J. Chem. Phys. 2008,128, 114115. 

The addition of this term to the TF and TFD energy density functionals improves the behavior oi the calculated electron density. The density is no longer infinite at the nucleus, and the asymptotic behavior far from the nucleus is greatly improved. Another benefit from using this gradient correction is that molecules are now stable entities with respect to the separated atoms the nonbinding theorems (whether or not atoms will bind together to form a... 

A. D. Becke, Phys. Rev. A, 38, 3098 (1988). Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. C. Lee, W. Yang, and R. G. Parr, Phys, Rev, B, 37, 785 (1988). Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. 

---