Orbital functional theory

This theorem justifies the procedure of Slater and Wood for any version of orbital functional theory. 

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Orbital functional theory 5.2.1 Explicit components of the energy functional... 

The theory is based on an optimized reference state that is a Slater determinant constructed as a normalized antisymmetrized product of N orthonormal spin-indexed orbital functions (r). This is the simplest form of the more general orbital functional theory (OFT) for an iV-electron system. The energy functional E = (4> // < >)is required to be stationary, subject to the orbital orthonormality constraint (i j) = Sij, imposed by introducing a matrix of Lagrange multipliers kj,. The general OEL equations derived above reduce to the UHF equations if correlation energy Ec and the implied correlation potential vc are omitted. The effective Hamiltonian operator is... 

Since the exact ground-state electronic wave function and density can only be approximated for most A-electron systems, a variational theory is needed for the practical case exemplified by an orbital functional theory. As shown in Section 5.1, any rule T 4> defines an orbital functional theory that in principle is exact for ground states. The reference state for any A-electron wave function T determines an orbital energy functional E = Eq + Ec,in which E0 = T + Eh + Ex + V is a sum of explicit orbital functionals, and If is aresidual correlation energy functional. In practice, the combination of exchange and correlation energy is approximated by an orbital functional Exc. 

The Levy construction [222] can be used to prove Hohenberg-Kohn theorems for the ground state of any such theory. It should be noted that any explicit model of the Hohenberg-Kohn functional F[p] implies a corresponding orbital functional theory. The relevant density function p(r) is that constructed from an OFT ground state. This has the orbital decomposition , as postulated by Kohn and Sham [205]. Unlike the density p,, for an exact A-electron wave function T, which cannot be determined for most systems of interest, the OFT ground-state density function is constructed from explicit solutions of the orbital Euler-Lagrange equations, and the theory is self-contained. 

Nesbet, R.K. (2001). Orbital functional theory of linear response and excitation, Int. 

Time-dependent orbital functional theory (TOFT)... 

These concepts, inherent in the TDHF formalism, generalize immediately to orbital functional theory, when electronic correlation energy is included in the model. Given some definition that determines a reference state for any... 

Using the projection-operator formalism of Feshbach [ 115,116], an implicit variational solution for the coefficients cIJiS in can be incorporated into an equivalent partitioned equation for the channel orbital functions. This is a multichannel variant of the logic used to derive the correlation potential operator vc in orbital-functional theory. Define a projection operator Q such that... 

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