264 research outputs found
Are natural orbitals useful for generating an efficient expansion of the wave function?
We investigate whether the natural orbitals (NOs) minimize â̂¥Ψ-Φâ̂
One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures
In this review we provide a rigorous and self-contained presentation of
one-body reduced density-matrix (1RDM) functional theory. We do so for the case
of a finite basis set, where density-functional theory (DFT) implicitly becomes
a 1RDM functional theory. To avoid non-uniqueness issues we consider the case
of fermionic and bosonic systems at elevated temperature and variable particle
number, i.e, a grand-canonical ensemble. For the fermionic case the Fock space
is finite-dimensional due to the Pauli principle and we can provide a rigorous
1RDM functional theory relatively straightforwardly. For the bosonic case,
where arbitrarily many particles can occupy a single state, the Fock space is
infinite-dimensional and mathematical subtleties (not every hermitian
Hamiltonian is self-adjoint, expectation values can become infinite, and not
every self-adjoint Hamiltonian has a Gibbs state) make it necessary to impose
restrictions on the allowed Hamiltonians and external non-local potentials. For
simple conditions on the interaction of the bosons a rigorous 1RDM functional
theory can be established, where we exploit the fact that due to the finite
one-particle space all 1RDMs are finite-dimensional. We also discuss the
problems arising from 1RDM functional theory as well as DFT formulated for an
infinite-dimensional one-particle space.Comment: 55 pages, 7 figure
Compact two-electron wave function for bond dissociation and Van der Waals interactions: A natural amplitude assessment
Electron correlations in molecules can be divided in short range dynamical
correlations, long range Van der Waals type interactions and near degeneracy
static correlations. In this work we analyze for a one-dimensional model of a
two-electron system how these three types of correlations can be incorporated
in a simple wave function of restricted functional form consisting of an
orbital product multiplied by a single correlation function
depending on the interelectronic distance . Since the three types of
correlations mentioned lead to different signatures in terms of the natural
orbital (NO) amplitudes in two-electron systems we make an analysis of the wave
function in terms of the NO amplitudes for a model system of a diatomic
molecule. In our numerical implementation we fully optimize the orbitals and
the correlation function on a spatial grid without restrictions on their
functional form. Due to this particular form of the wave function, we can prove
that none of the amplitudes vanishes and moreover that it displays a distinct
sign pattern and a series of avoided crossings as a function of the bond
distance in agreement with the exact solution. This shows that the wave
function Ansatz correctly incorporates the long range Van der Waals
interactions. We further show that the approximate wave function gives an
excellent binding curve and is able to describe static correlations. We show
that in order to do this the correlation function needs to diverge
for large at large internuclear distances while for shorter bond
distances it increases as a function of to a maximum value after which
it decays exponentially. We further give a physical interpretation of this
behavior.Comment: 16 pages, 13 figure
Functional Derivative of the Zero Point Energy Functional from the Strong Interaction Limit of Density Functional Theory
We derive an explicit expression for the functional derivative of the
subleading term in the strong interaction limit expansion of the generalized
Levy--Lieb functional for the special case of two electrons in one dimension.
The expression is derived from the zero point energy (ZPE) functional, which is
valid if the quantum state reduces to strongly correlated electrons in the
strong coupling limit. The explicit expression is confirmed numerically and
respects the relevant sum-rule. We also show that the ZPE potential is able to
generate a bond mid-point peak for homo-nuclear dissociation and is properly of
purely kinetic origin. Unfortunately, the ZPE diverges for Coulomb systems,
whereas the exact peaks should be finite.Comment: 12 pages, 7 figure
Response calculations based on an independent particle system with the exact one-particle density matrix: polarizabilities
Recently, we have demonstrated that the problems finding a suitable adiabatic
approximation in time-dependent one-body reduced density matrix functional
theory can be remedied by introducing an additional degree of freedom to
describe the system: the phase of the natural orbitals [Phys. Rev. Lett. 105,
013002 (2010), J. Chem. Phys. 133, 174119 (2010)]. In this article we will show
in detail how the frequency-dependent response equations give the proper static
limit (), including the perturbation in the chemical potential,
which is required in static response theory to ensure the correct number of
particles. Additionally we show results for the polarizability for H and
compare the performance of two different two-electron functionals: the
phase-including L\"owdin-Shull functional and the density matrix form of the
L\"owdin-Shull functional.Comment: 10 pages, 6 figure
Implications of the unitary invariance and symmetry restrictions on the development of proper approximate one-body reduced density matrix functionals
In many of the approximate functionals in one-body reduced density matrix
(1RDM) functional theory, the approximate two-body reduced density matrix
(2RDM) in the natural orbital representation only depends on the natural
occupation numbers. In Phys. Rev. A 92, 012520 (2015) Wang and Knowles
initialised a discussion of to what extent this simplification is valid, by
introducing two different H geometries with identical natural occupation
numbers, but different 2RDMs. Gritsenko has argued that this feature is due
symmetry [Phys. Rev. A 97, 026501 (2018)]. This work aims to contribute to the
discussion on the following points: 1) one should rather speak of
symmetry-restricted variants of the universal functional, than saying that the
universal functional is symmetry dependent; 2) the unitary invariance of
degenerate NOs can lead to large deviations in the 2RDM elements, especially
the phase of the NOs; 3) symmetry-restricted functionals are constructed for
the H geometries considered by Wang and Knowles, whose structure could
serve as guide in the construction of approximate 1RDM functionals.Comment: 15 pages, 3 figures, 3 table
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
Exchange-correlation functionals from the strongly-interacting limit of DFT: Applications to model chemical systems
We study model one-dimensional chemical systems (representative of their
three-dimensional counterparts) using the strictly-correlated electrons (SCE)
functional, which, by construction, becomes asymptotically exact in the limit
of infinite coupling strength. The SCE functional has a highly non-local
dependence on the density and is able to capture strong correlation within
Kohn- Sham theory without introducing any symmetry breaking. Chemical systems,
however, are not close enough to the strong-interaction limit so that, while
ionization energies and the stretched H2 molecule are accurately described,
total energies are in general way too low. A correction based on the exact next
leading order in the expansion at infinite coupling strength of the
Hohenberg-Kohn functional largely improves the results.Comment: 9 pages, 6 figures. Submitted to PCCP's Themed Collection on Density
Functional Theory and its Application
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