60 91 48 v 1 1 7 Se p 20 06 Classical kinetic energy , quantum fluctuation terms and kinetic - energy functionals

Density functional theory is extensively employed for the calculation of atomic and molecular properties. Achieving greater chemical accuracy or computational efficiency is desirable and this has motivated attempts to construct improved kinetic-energy functionals (KEFS) but that is not our aim in this paper. Rather, we aim to obtain expressions for the exact kinetic energy and exact noninteracting kinetic energy that provide a general framework for the development of KEFS. We employ a recently formulated dequantization procedure to obtain the kinetic energy of an N-electron system as the sum of an N-electron classical kinetic energy and an N-electron purely quantum kinetic energy arising from the quantum fluctuations that turn the classical momentum into the quantum one. We show that the N-electron purely quantum kinetic energy can be written as the sum of the (one-electron) Weizsäcker term (TW ) and an (N-1)-electron kinetic correlation term. We further show that TW results from local fluctuations while the kinetic correlation term results from nonlocal ones. We then write the N-electron classical kinetic energy as the sum of the (one-electron) classical kinetic energy (TCl) and another (N-1)-electron kinetic correlation term. For one-electron orbitals we then obtain an expression for the noninteracting kinetic energy as the sum of TCl and TW . The TCl term is seen to be explicitly dependent on the phase of the one-electron orbital and this has implications for the development of accurate orbital-free KEFS. Also, there is a direct connection between TCl and angular momentum and, across a row of the periodic table, the TCl component of the noninteracting kinetic energy will generally increase as Z increases.