Explicitly orbital-dependent approximations to the exchange-correlation energy functional of density functional theory typically not only depend on the single-particle Kohn-Sham orbitals but also on their occupation numbers in the ground state Slater determinant. The variational calculation of the corresponding exchange-correlation potentials with the Optimized Effective Potential (OEP) method therefore also requires a variation of the occupation numbers with respect to a variation in the effective single-particle potential, which is usually not taken into account. Here it is shown under which circumstances this procedure is justified.
We introduce a novel energy functional for ground-state electronic-structure calculations. Its fundamental variables are the natural spin-orbitals of the implied singlet many-body wave function and their joint occupation probabilities. The functional derives from a sequence of controlled approximations to the two-particle density matrix. Algebraic scaling of computational cost with electron number is obtainable in general, and Hartree-Fock scaling in the seniority-zero version of the theory. Results obtained with the latter version for saturated small molecular systems are compared with those …
We report equations of motion for the occupation numbers of natural spin orbitals and show that adiabatic extensions of common functionals employed in ground-state reduced-density-matrix-functional theory have the shortcoming of leading always to occupation numbers which are independent of time. We illustrate the exact time-dependence of the natural spin orbitals and occupation numbers for the case of electron-ion scattering and for atoms in strong laser fields. In the latter case, we observe strong variations of the occupation numbers in time.
The breaking of orbital degeneracy on a transition metal cation and the resulting unequal electronic occupations of these orbitals provide a powerful lever over electron density and spin ordering in metal oxides. Here, we show how to dynamically modulate the orbital populations on Mn atoms at ferroelectric/manganite interfaces by switching the ferroelectric polarization. The change in orbital occupation can be as large as 10\%, greatly exceeding that of bulk manganites. This flippable orbital splitting is in large part controlled by the propagation of ferroelectric polar displacements into the…
The breaking of orbital degeneracy on a transition metal cation and the resulting unequal electronic occupations of these orbitals provide a powerful lever over electron density and spin ordering inmetal oxides. Here, we use ab initio calculations to show that reversibly modulating the orbital populations on Mn atoms can be achieved at ferroelectric/manganite interfaces by the presence of ferroelectric polarization on the nanoscale. The change in orbital occupation can be as large as 10%, greatly exceeding that of bulk manganites. This reversible orbital splitting is in large part controlled b…
Orbital occupation selects structural dimensionality in binary transition-metal oxides
Sichuan Normal University（四川师范大学）；Renmin University of China（中国人民大学）；University of Chinese Academy of Sciences（中国科学院大学）；University of Electronic Science and Technology of China（电子科技大学）
In contrast to the original Kohn-Sham (KS) formalism, we propose a density functional theory (DFT) with fractional orbital occupations for the study of ground states of many-electron systems, wherein strong static correlation is shown to be described. Even at the simplest level represented by the local density approximation (LDA), our resulting DFT-LDA is shown to improve upon KS-LDA for multi-reference systems, such as dissociation of H2 and N2, and twisted ethylene, while performing similarly to KS-LDA for single-reference systems, such as reaction energies and equilibrium geometries. Becaus…
We have performed x-ray linear and circular magnetic dichroism experiments at the Mn L2,3-edge of the La0.7Sr0.3MnO3 ultra thin films. Our measurements show that the antiferromagnetic (AF) insulating phase is stabilized by the interfacial rearrangement of the Mn 3d orbitals, despite the relevant magnetostriction anisotropic effect on the double-exchange ferromagnetic (FM) metallic phase. As a consequence, the Mn atomic magnetic moment orientation and how it reacts to strain differ in the FM and AF phases. In some cases a FM insulating (FMI) phase adds to the AF and FM. Its peculiar magnetic pr…
We present the results of an LDA and LDA+U band structure study of the monoclinic and the corundum phases of V2O3 and argue that the most prominent (spin 1/2) models used to describe the semiconductor metal transition are not valid. Contrary to the generally accepted assumptions we find that the large on site Coulomb and exchange interactions result in a total local spin of 1 rather than 1/2 and especially an orbital occupation which removes the orbital degeneracies and the freedom for orbital ordering. The calculated exchange interaction parameters lead to a magnetic structure consistent with…
Using Co-L_(2,3) and O-K x-ray absorption spectroscopy, we reveal that the charge ordering in La_(1.5)Sr_(0.5)CoO4 involves high spin (S=3/2) Co^2+ and low spin (S=0) Co^3+ ions. This provides evidence for the spin blockade phenomenon as a source for the extremely insulating nature of the La_(2-x)Sr_(x)CoO4 series. The associated e_g^2 and e_g^0 orbital occupation accounts for the large contrast in the Co-O bond lengths, and in turn, the high charge ordering temperature. Yet, the low magnetic ordering temperature is naturally explained by the presence of the non-magnetic (S=0) Co^3+ ions. From…
Fractional occupation numbers can produce open-shell degeneracy in density functional theory. We develop the corresponding perturbation theory by requiring that a differentiable map connects the initial and perturbed states. The degenerate state connects to a single perturbed state which extremizes, but does not necessarily minimize or maximize, the energy with respect to occupation numbers. Using a system of three electrons in a harmonic oscillator potential, we relate the counterintuitive sign of first-order occupation numbers to eigenvalues of the electron-electron interaction Hessian.
We propose hybrid schemes incorporating exact exchange into thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)] for an improved description of nonlocal exchange effects. With a few simple modifications, global and range-separated hybrid functionals in Kohn-Sham density functional theory (KS-DFT) can be combined seamlessly with TAO-DFT. In comparison with global hybrid functionals in KS-DFT, the resulting global hybrid functionals in TAO-DFT yield promising performance for systems with strong static correlation effects (e.g., the dis…
The occupation of d-orbitals controls the magnitude and anisotropy of the inter-atomic electron transfer in transition metal oxides and hence exerts a key influence on their chemical bonding and physical properties. Atomic-scale modulations of the orbital occupation at surfaces and interfaces are believed to be responsible for massive variations of the magnetic and transport properties, but could thus far not be probed in a quantitative manner. Here we show that it is possible to derive quantitative, spatially resolved orbital polarization profiles from soft x-ray reflectivity data, without re…
The strong boundary normalized condition of wavefunction for fully occupied semicore 3d orbitals leads the linear response DFT+U on such metal oxide to have an insurmountable obstacle in Hubbard U determination. We treated the orbital self-energy and orbital relaxation as components of eigenvalues with respective orbital occupation number that follows the Fermi-Dirac distribution. By self-consistently solving the second partial deviation of total energy based on the most simple local density formalism with Hubbard U correction, we found the local density exchange-correlation potential function…
First-principles density functional theory calculations have been performed to understand the electronic structure and orbital polarization of LaNiO$_3$ with a reduced coordination and under strain. From the slab calculation to simulate [001] surface, it is found that $d_{3z^2-r^2}$ orbital occupation is significantly enhanced relative to $d_{x^2-y^2}$ occupation owing to the reduced coordination along the perpendicular direction to the sample plane. Furthermore, the sign of the orbital polarization does not change under external strain. The results are discussed in comparison to the bulk and …
Finite-temperature adiabatic-connection reduced density-matrix functional theory: a unified framework for i-DMFT and TAO-DFT
Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Department of Applied Physics, Nanjing University of Science and Technology（南京理工大学应用物理系）
Magnetic anisotropies of ferromagnetic thin films are induced by epitaxial strain from the substrate via strain-induced anisotropy in the orbital magnetic moment and that in the spatial distribution of spin-polarized electrons. However, the preferential orbital occupation in ferromagnetic metallic La$_{1-x}$Sr$_x$MnO$_3$ (LSMO) thin films studied by x-ray linear dichroism (XLD) has always been found out-of-plane for both tensile and compressive epitaxial strain and hence irrespective of the magnetic anisotropy. In order to resolve this mystery, we directly probed the preferential orbital occup…
We extend the recently proposed thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)] to generalized-gradient approximation (GGA) exchange-correlation density functionals. Relative to our previous TAO-LDA (i.e., the local density approximation to TAO-DFT), the resulting TAO-GGAs are significantly superior for a wide range of applications, such as thermochemistry, kinetics, and reaction energies. For noncovalent interactions, TAO-GGAs with empirical dispersion corrections are shown to yield excellent performance. Due to their computati…
Manipulating the orbital occupation of valence electrons via epitaxial strain in an effort to induce new functional properties requires considerations of how changes in the local bonding environment affect the band structure at the Fermi level. Using synchrotron radiation to measure the x-ray linear dichroism of epitaxially strained films of the correlated oxide CaFeO3, we demonstrate that the orbital polarization of the Fe valence electrons is opposite from conventional understanding. Although the energetic ordering of the Fe 3d orbitals is confirmed by multiplet ligand field theory analysis …
Phenomenological orbital-polarization (OP) terms have been repeatedly introduced in the single-particle equations of spin-density-functional theory, in order to improve the description of orbital magnetic moments in systems containing transition metal ions. Here we show that these ad hoc corrections can be interpreted as approximations to the exchange-correlation vector potential A_xc of current-density-functional theory (CDFT). This connection provides additional information on both approaches: Phenomenological OP terms are connected to first-principles theory, leading to a rationale for thei…
A combination of $^{19}$F magic angle spinning (MAS) nuclear magnetic resonance (NMR) and density functional theory (DFT) were used to study the ordering of F atoms in Pb$_2$Ti$_4$O$_9$F$_2$. This analysis revealed that F atoms predominantly occupy two of the six available inequivalent sites in a ratio of 73:27. DFT-based calculations explained the preference of F occupation on these sites and quantitatively reproduced the experimental occupation ratio, independent of the choice of functional. We concluded that the Pb atom's 6$s^2$ lone pair may play a role ($\sim$0.1 eV/f.u.) in determining t…
In all archetypical reported (001)-oriented perovskite heterostructures, it has been deduced that the preferential occupation of two-dimensional electron gases is in-plane $d_\textrm{xy}$ state. In sharp contrast to this, the investigated electronic structure of a spinel-perovskite heterostructure $γ$-Al$_2$O$_3$/SrTiO$_3$ by resonant soft X-ray linear dichroism, demonstrates that the preferential occupation is out-of-plane $d_\textrm{xz}$/$d_\textrm{yz}$ states for interfacial electrons. Moreover, the impact of strain further corroborates that this anomalous orbital structure can be linked to…
Open-system density functional theory may be formulated in terms of ensemble averages arising from interaction with a bath. The system is allowed to exchange particles with the bath and the states in the ensemble average are those corresponding to integer numbers of particles. The weights in the ensemble average are typically equated with time-averaged values of the occupation numbers of the various states comprising the open system. As a result, there are two constraints on the occupation numbers: (1) Their sum must be unity so that the ensemble average is a probability function and (2) The s…
We present first-principles studies on the orbital states of the layered perovskites Ca$_{2-x}$Sr$_x$RuO$_4$. The crossover from antiferromagnetic (AF) Mott insulator for $x < 0.2$ to nearly ferromagnetic (FM) metal at $x=0.5$ is characterized by the systematic change of the $xy$ orbital occupation. For the AF side ($x < 0.2$), we present firm evidence for the $xy$ ferro-orbital ordering. It is found that the degeneracy of $t_{2g}$ (or $e_g$) states is lifted robustly due to the two-dimensional (2D) crystal-structure, even without the Jahn-Teller distortion of RuO$_6$. This effect dominates, a…
Fractional occupation numbers can be used in density functional theory to create a symmetric Kohn-Sham potential, resulting in orbitals with degenerate eigenvalues. We develop the corresponding perturbation theory and apply it to a system of $N_d$ degenerate electrons in a harmonic oscillator potential. The order-by-order expansions of both the fractional occupation numbers and unitary transformations within the degenerate subspace are determined by the requirement that a differentiable map exists connecting the initial and perturbed states. Using the X$α$ exchange-correlation (XC) functional,…
We present evidence of strain-induced modulation of electron correlation effects and increased orbital anisotropy in the rutile phase of epitaxial VO$_2$/TiO$_2$ films from hard x-ray photoelectron spectroscopy and soft V L-edge x-ray absorption spectroscopy, respectively. By using the U(1) slave spin formalism, we further argue that the observed anisotropic correlation effects can be understood by a model of orbital selective Mott transition at a filling that is non-integer, but close to the half-filling. Because the overlaps of wave functions between $d$ orbitals are modified by the strain, …
In approximate Kohn-Sham density-functional theory, self-interaction manifests itself as the dependence of the energy of an orbital on its fractional occupation. This unphysical behavior translates into qualitative and quantitative errors that pervade many fundamental aspects of density-functional predictions. Here, we first examine self-interaction in terms of the discrepancy between total and partial electron removal energies, and then highlight the importance of imposing the generalized Koopmans' condition -- that identifies orbital energies as opposite total electron removal energies -- to…
The determination of spectral properties from first principles can provide powerful connections between microscopic theoretical predictions and experimental data, but requires complex electronic-structure formulations that fall outside the domain of applicability of common approaches, such as density-functional theory. We show here that Koopmans-compliant functionals, constructed to enforce piecewise linearity in energy functionals with respect to fractional occupations - i.e. with respect to charged excitations - provide molecular photoemission spectra and momentum maps of Dyson orbitals that…
We report the first wholly non-empirical generalized gradient approximation, non-interacting free energy functional for orbital-free density functional theory and use that new functional to provide forces for finite-temperature molecular dynamics simulations in the warm dense matter (WDM) regime The new functional provides good-to-excellent agreement with reference Kohn-Sham calculations under WDM conditions at a minuscule fraction of the computational cost of corresponding orbital-based simulations.
The unequal electronic occupation of localized orbitals (orbital polarization), and associated lowering of symmetry and degeneracy, play an important role in the properties of transition metal oxides. Here, we examine systematically the underlying origin of orbital polarization, taking as exemplar the 3$d$ manifold of Co$^{2+}$ in a variety of spin, orbital and structural phases in the double perovskite La$_2$CoTiO$_6$ and the (001) superlattice (LaCoO$_3$)$_1$+(LaTiO$_3$)$_1$ systems. Superlattices are of specific interest due to the large experimentally observed orbital polarization of their…
