Are natural orbitals useful for generating an efficient expansion of the wave function?

We investigate whether the natural orbitals (NOs) minimize â̂¥Ψ-Φâ̂

Charge transfer, double and bond-breaking excitations with time-dependent density matrix functional theory

Time-dependent density functional theory (TDDFT) in its current adiabatic implementations exhibits three remarkable failures: (a) completely wrong behavior of the excited state surface along a bond-breaking coordinate; (b) lack of doubly excited configurations; (c) much too low charge transfer excitation energies. These TDDFT failure cases are all strikingly exhibited by prototype two-electron systems such as dissociating H2 and HeH+. We find for these systems with time-dependent density matrix functional theory that: (a) Within previously formulated simple adiabatic approximations, the bonding-to- antibonding excited state surface as well as charge transfer excitations are described without problems, but not the double excitations; (b) An adiabatic approximation is formulated in which also the double excitations are fully accounted for. © 2008 The American Physical Society

Avoiding the 4-index transformation in one-body reduced density matrix functional calculations for separable functionals

One of the major computational bottlenecks in one-body reduced density matrix (1RDM) functional theory is the evaluation of approximate 1RDM functionals and their derivatives. The reason is that more advanced approximate functionals are almost exclusively defined in the natural orbital basis, so a 4-index transformation of the two-electron integrals appears to be unavoidable. I will show that this is not the case and that so-called separable functionals can be evaluated much more efficiently, i.e. only at cubic cost in the basis size. Since most approximate functionals are actually separable, this new algorithm is an important development to make 1RDM functional theory calculations feasible for large electronic systems

Reduced Density Matrix Functional Theory (RDMFT) and Linear Response Time-Dependent RDMFT (TD-RDMFT)

Recent advances in reduced density matrix functional theory (RDMFT) and linear response time-dependent reduced density matrix functional theory (TD-RDMFT) are reviewed. In particular, we present various approaches to develop approximate density matrix functionals which have been employed in RDMFT. We discuss the properties and performance of most available density matrix functionals. Progress in the development of functionals has been paralleled by formulation of novel RDMFT-based methods for predicting properties of molecular systems and solids. We give an overview of these methods. The time-dependent extension, TD-RDMFT, is a relatively new theory still awaiting practical and generally useful functionals which would work within the adiabatic approximation. In this chapter we concentrate on the formulation of TD-RDMFT response equations and various adiabatic approximations. None of the adiabatic approximations is fully satisfactory, so we also discuss a phase-dependent exten- sion to TD-RDMFT employing the concept of phase-including-natural-spinorbitals (PINOs). We focus on applications of the linear response formulations to two-electron systems, for which the (almost) exact functional is known

Aufbau derived from a unified treatment of occupation numbers in Hartree-Fock, Kohn-Sham and Natural Orbital theories with the Karush-Kuhn-Tucker conditions for the inequality constraints ni≤1 and ni≥0

In the major independent particle models of electronic structure theory-Hartree-Fock, Kohn-Sham (KS), and natural orbital (NO) theories-occupations are constrained to 0 and 1 or to the interval [0,1]. We carry out a constrained optimization of the orbitals and occupation numbers with application of the usual equality constraints

Failure of time-dependent density functional theory for excited state surfaces in case of homolytic bond dissociation

Adiabatic time-dependent density functional theory (ATDDFT) has much too low excitation energies at long bond length in (dissociating) electron pair bonds. This easily escapes attention partly due to the occurrence of the problems at slightly longer distances than the equilibrium geometry, and partly due to fortuitous error cancellation between wrong (too high) DFT ground state energies being added to wrong (too low) ATDDFT excitation energies to obtain the excited state E vs. R curves. © 2008 Elsevier B.V. All rights reserved

The adiabatic approximation in time-dependent density matrix functional theory: Response properties from phase-including natural orbitals

The adiabatic approximation is problematic in time-dependent density matrix functional theory. With pure density matrix functionals (invariant under phase change of the natural orbitals) it leads to lack of response in the occupation numbers, hence wrong frequency dependent responses, in particular α (ω→0) ≠

Response calculations with an independent particle system with an exact one-particle density matrix

We use the natural orbitals to define an independent particle system, from which the exact one-particle density matrix can be obtained with an ensemble of degenerate determinantal ground states. Also defining explicit phases for the orbitals, and admitting functionals that are dependent on those phases, time-dependent equations for the orbitals and occupation numbers are obtained from an action principle. The wrong polarizability and lack of double excitations of straightforward adiabatic time-dependent density matrix functional theory are then corrected, and the important symmetry χ(ω)=