Finding the electrons in atomic wavefunctions

An orbital refers to a one-electron wavefunction, and more specifically to the spatial part of a one-electron spin-orbital. Electronic orbitals are often associated with the simple Hartree-Fock (HP) approximation, a single-configuration approximation to the complex 

Discovering Chemistry With Natural Bond Orbitals, First Edition. Frank Weinhold and Clark R. Landis. 2012 John Wiley Sons, Inc. Published 2012 by John Wiley Sons, Inc. 

Mathematically, the single-configuration Fhf wavefunction is expressed as a Slater determinant (antisymmetrized product) of the occupied spin-orbitals. In this hmit, only the chosen N occupied spin-orbitals contribute to description of the A-electron system, whereas an infinite number of remaining virtual spin-orbitals are ignored. This crude HF-t3fpe (or molecular orbital) description of the true many-electron P(ri, T2,. .., r v) exerts a powerful hold on chemical pedagogy, but is often seriously defective in quantitative terms. 

Fortunately, the rigorous measurement theory of many-electron quantum mechanics justifies essential retention of orhital-type conceptions and their applications in bonding theory. As originally formulated by J. von Neumann in his Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, NJ, 1955), the fundamental object underlying quanta measurement of a pure-state iV-electron system is the density matrix F  

Husimi (Proc. Phys. Math. Soc. Jpn. 22,264,1940) subsequently showed that analogous measurable properties of smaller sufisystems of the iV-electron system are expressed most rigorously in terms of corresponding /rth-order reduced density matrices 

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