Within the framework of zero-temperature Fock-space density-functional theory (DFT), we prove that the Gateaux functional derivative of the universal density functional, deltaF(lambda)[rho]/deltarho(r)(rho=rho0), at ground-state densities with arbitrary normalizations ((rho(0)(r))=n is an element of R+) and an electron-electron interaction strength lambda, is uniquely defined, but is discontinuous when the number of electrons n becomes an integer, thus providing a mathematically rigorous confirmation for the \"derivative discontinuity\" initially discovered by Perdew et al. [Phys. Rev. Lett. 49, 1691 (1982)]. However, the functional derivative of the exchange-correlation functional is continuous with respect to the number of electrons in Fock space; i.e., there is no \"derivative discontinuity\" for the exchange-correlation functional at an integer electron number. For a ground-state density rho(0,n)(nu,lambda)(r) of an external potential nu(r), we show that deltaF(lambda)[rho]/deltarho(r)\(nu,lambda)(rho=rho0,n)=mu(SM)(n)-nu(r), where the constant mu(SM)(n) is given by the following chain of dependences: rho(0,n)(nu,lambda)(r) bar right arrow [nu] bar right arrow E-0(nu,lambda)(n) bar right arrow mu(SM)(n) = partial derivativeE(0nu,lambda)(k)/partial derivativek\(k=n). Here [nu] is the class of the external potential nu(r) up to a real constant, and mu(SM)(n) is the chemical potential defined according to statistical mechanics. At an integer electron number N, we find that there is no freedom of adding an arbitrary constant to the value of the chemical potential mu(SM)(N), whose exact value is generally not the popular preference of the negative of Mulliken\’s electronegativity, - 1/2 (I+A), where I and A are the first ionization potential and the first electron affinity, respectively. In addition, for any external potential converging to the same constant at infinity in all directions, we resolve that mu(SM)(N) =-I. Finally, the equality mu(DFT)=mu(SM)(n) is rigorously derived via an alternative route. where mu(DFT) is the Lagrangian multiplier used to constrain the normalization of the density in the traditional DFT approach.

}, keywords = {CORRECT ASYMPTOTIC-BEHAVIOR, ELECTRONIC SYSTEMS, EXCHANGE-CORRELATION FUNCTIONALS, EXCITATION-ENERGIES, EXTENDED KOOPMANS, GROUND-STATE ENERGIES, HOMOGENEOUS FUNCTIONALS, INTERACTING, KINETIC-ENERGY, KOHN-SHAM EIGENVALUE, OCCUPATION NUMBERS, THEOREM}, isbn = {1050-2947}, url = {The lack, of accurate transferable local pseudopotentials represents one of the remaining, barriers to the. general application of orbital-free density functional theory (OF-DFT, a linear scaling technique). Here we report a method to generate high quality ab initio local pseudopotentials (LPS\’s) for use in condensed matter DFT calculations. We exploit the first Hohenberg-Kohn theorem, which states that the external potential is, one-to-one mapped to the ground-state electron density. By employing a scheme for inverting the Kohn-Sham (KS) equations due to Wang and Parr, we iteratively solve for the KS effective potential v(eff)(KS)(r) until it reproduces a target density. From v(eff)(KS)(r) we derive a global LPS for the entire system. This global LPS is then further decomposed to obtain an atom-centered LPS. We show that LPS\’s,derived from bulk environments are substantially more transferable than those derived from atoms alone. In KS-DFT tests on Si, we show that this bulk-derived LPS can reproduce accurately phase orderings predicted by nonlocal pseudopotentials for both metallic and semiconducting phases. We then tested this LPS in OF-DFT calculations on Si crystals, where we demonstrate that this bulk-derived LPS (BLPS), combined with a linear-response-based kinetic energy density functional with a density-dependent kernel, correctly predicts a diamond structure ground state for Si in an OF-DFT calculation. Other bulk properties, such as defect formation energies and transition pressures are also presented as tests of this BLPS. This approach for deriving LPS\’s isolates much of the remaining error in OF-DFT to the kinetic energy density functional, providing means to test new functionals as they become available.

}, keywords = {CORRECT ASYMPTOTIC-BEHAVIOR, ELECTRONIC-STRUCTURE CALCULATIONS, ENERGY-DENSITY FUNCTIONALS, EXCHANGE-CORRELATION POTENTIALS, GROUND-STATE GEOMETRIES, INITIO MOLECULAR-DYNAMICS, KINETIC-ENERGY, NORM-CONSERVING PSEUDOPOTENTIALS, THOMAS-FERMI APPROXIMATION, WAVE-FUNCTIONS}, isbn = {1098-0121}, url = {