|
||||||||
The one-electron equation for orbitals embedded in frozen electron density (Eqs. 20-21 in [Wesolowski and Warshel, J. Phys. Chem, 97 (1993) 8050]) in its exact and approximated version is solved for an analytically solvable model system. The system is used to discuss the role of the embedding potential in preventing the collapse of a variationally obtained electron density onto the nucleus in the case when the frozen density is chosen to be that of the innermost shell. The approximated potential obtained from the second-order gradient expansion for the kinetic energy prevents such a collapse almost perfectly but this results from partial compensation of flaws of its components. It is also shown that that the quality of a semi-local approximation to the kinetic-energy functional, a quantity needed in orbital-free methods, is not related to the quality of the non-additive kinetic energy potential - a key component of the effective embedding potential in one-electron equations for embedded orbitals. |
|
||||||||
The effective embedding potential introduced by Wesolowski and Warshel [J. Phys. Chem., 97 (1993) 8050] depends on two electron densities: that of the environment (nĀ B ) and that of the investigated embedded subsystem (nĀ A ). In this work, we analyze this potential for pairs nĀ A Ā and nĀ B , for which it can be obtained analytically. The obtained potentials are used to illustrate the challenges in taking into account the Pauli exclusion principle. |
|
||||||||
The effective embedding potential introduced by Wesolowski and Warshel [J. Phys. Chem., 97 (1993) 8050] depends on two electron densities: that of the environment (n B ) and that of the investigated embedded subsystem (n A ). In this work, we analyze this potential for pairs n A and n B , for which it can be obtained analytically. The obtained potentials are used to illustrate the challenges in taking into account the Pauli exclusion principle. |