Long‐range asymptotic behavior of ground‐state wave functions, one‐matrices, and pair densities

Alchemical insights into approximately quadratic energies of iso-electronic atoms

Accurate quantum mechanics based predictions of property trends are so important for material design and discovery that even inexpensive approximate methods are valuable. We use the alchemical integral transform to study multi-electron atoms and to gain a better understanding of the approximately quadratic behavior of energy differences between iso-electronic atoms in their nuclear charges. Based on this, we arrive at the following simple analytical estimate of energy differences between any two iso-electronic atoms, ΔE≈-(1+2γNe-1)ΔZZ̄. Here, γ ≈ 0.3766 ± 0.0020 Ha corresponds to an empirical constant, and Ne, ΔZ, and Z̄, respectively, to electron number, nuclear charge difference, and average. We compare the formula's predictive accuracy using experimental numbers and non-relativistic, numerical results obtained via density functional theory (pbe0) for the entire periodic table up to Radon. A detailed discussion of the atomic helium-series is included.

From Fredholm to Schrödinger via Eikonal: A New Formalism for Revealing Unknown Properties of Natural Orbitals

Previously unknown properties of the natural orbitals (NOs) pertaining to singlet states (with natural parity, if present) of electronic systems with even numbers of electrons are revealed upon the demonstration that, at the limit of n → ∞, the NO ψ_n(r⃗) with the nth largest occupation number ν_n approaches the solution ψ̃_n(r⃗) of the zero-energy Schrödinger equation that reads T̂([ρ₂(r⃗, r⃗)]^-1/8 ψ̃_n(r⃗)) - (π²/ṽ_n)^1/4 [ρ₂(r⃗, r⃗)]^1/4 ([ρ₂(r⃗, r⃗)]^-1/8 ψ̃_n(r⃗)) = 0 (where T̂ is the kinetic energy operator), whereas ν_n approaches ν̃_n. The resulting formalism, in which the "on-top" two-electron density ρ₂(r⃗, r⃗) solely controls the asymptotic behavior of both ψ_n(r⃗) and ν_n at the limit of the latter becoming infinitesimally small, produces surprisingly accurate values of both quantities even for small n. It opens entirely new vistas in the elucidation of their properties, including single-line derivations of the power laws governing the asymptotic decays of ν_n and ⟨ψ_n(r⃗)|T̂|ψ_n(r⃗)⟩ with n, some of which have been obtained previously with tedious algebra and arcane mathematical arguments. These laws imply a very unfavorable asymptotics of the truncation error in the total energy computed with finite numbers of natural orbitals that severely affects the accuracy of certain quantum-chemical approaches such as the density matrix functional theory. The new formalism is also shown to provide a complete and accurate elucidation of both the observed order (according to decreasing magnitudes of the respective occupation numbers) and the shapes of the natural orbitals pertaining to the ¹Σ_g⁺ ground state of the H₂ molecule. In light of these examples of its versatility, the above Schrödinger equation is expected to have its predictive and interpretive powers harnessed in many facets of the electronic structure theory.

Daylight-White-Emitting and Abnormal Thermal Antiquenching Phosphors Based on a Layered Host SrIn2(P2O7)2

Single-phase white-emission phosphors possess a judicious usage potential in phosphor-converted white-light-emitting diodes (WLEDs). Recently, numerous efforts have been made toward the development of new patterns of white-emitting phosphors that achieve excellent quantum yield, superior thermal stability, and applaudable cost effectiveness of WLEDs. Finding suitable single-component white phosphor hosts to provide an ideal local environment for activators remains urgent. Inspired by the original discovery of the promising host MgIn₂(P₂O₇)₂ (MIP) and its structural dependence on alkali-metal cations, we synthesized a brand-new phosphor host, SrIn₂(P₂O₇)₂ (SIP), via the traditional solid-state reaction. Its crystal structure was determined using an ab initio analysis and the Rietveld method. It belongs to a monoclinic unit cell with the space group C2/c. Besides, SIP exhibits a special layered three-dimensional framework in which the monolayer [SrO₁₀]_∞ was surrounded by a bilayer [In₂P₄O₁₄]_∞ made of the InO₆ octahedra and P₂O₇ groups. A series of pure SIP:Tm³⁺,Dy³⁺ phosphors with tunable blue-white-yellow emission were prepared by adjusting the dopant concentration and utilizing the Tm³⁺-Dy³⁺ energy transfer. The daylight-white-emitting phosphor SIP:0.01Tm³⁺,0.04Dy³⁺ (the correlated color temperature is 4448 K) exhibits an abnormal thermal antiquenching property, and the emission intensity of 423 K reaches 103.7% of the initial value at 300 K. On the basis of the temperature-dependent lattice evolution and microenvironment analysis, the reduction of β and lattice distortion can lead to lower asymmetry of the activators and benefit the compensation of trapped-electron thermal activation. In this work, an integration study was carried out on the crystal structure of the new matrix, the occupation of the luminescent center, the interaction of different activators in the host, and the distortion degree of the local structure for the activators, which is of great practical sense for producing a novel single-matrix white phosphor possessing superior thermal endurance for UV-light-stimulated WLEDs.

Singling Out Dynamic and Nondynamic Correlation

The correlation part of the pair density is separated into two components, one of them being predominant at short electronic ranges and the other at long ranges. The analysis of the intracular part of these components permits to classify molecular systems according to the prevailing correlation: dynamic or nondynamic. The study of the long-range asymptotics reveals the key component of the pair density that is responsible for the description of London dispersion forces and a universal decay with the interelectronic distance. The natural range-separation, the identification of the dispersion forces, and the kind of predominant correlation type that arise from this analysis are expected to be important assets in the development of new electronic structure methods in wave function, density, and reduced density-matrix functional theories.

Exploration of near the origin and the asymptotic behaviors of the Kohn-Sham kinetic energy density for two-dimensional quantum dot systems with parabolic confinement

The behaviors of the positive definite Kohn-Sham kinetic energy density near the origin and at the asymptotic region play a major role in designing meta-generalized gradient approximations (meta-GGAs) for exchange in low-dimensional quantum systems. It is shown that near the origin of the parabolic quantum dot, the Kohn-Sham kinetic energy differs from its von Weizsäcker counterpart due to the p orbital contributions, whereas in the asymptotic region, the difference between the above two kinetic energy densities goes as ∼ρ(r)r². All these behaviors have been explored using the two-dimensional isotropic quantum harmonic oscillator as a test case. Several meta-GGA ingredients are then studied by making use of the above findings. Also, the asymptotic conditions for the exchange energy density and the potential at the meta-GGA level are proposed using the corresponding behaviors of the two kinetic energy densities.

Revised M06-L functional for improved accuracy on chemical reaction barrier heights, noncovalent interactions, and solid-state physics

We present the revM06-L functional, which we designed by optimizing against a larger database than had been used for Minnesota 2006 local functional (M06-L) and by using smoothness restraints. The optimization strategy reduced the number of parameters from 34 to 31 because we removed some large terms that increased the required size of the quadrature grid and the number of self-consistent-field iterations. The mean unsigned error (MUE) of revM06-L on 422 chemical energies is 3.07 kcal/mol, which is improved from 3.57 kcal/mol calculated by M06-L. The MUE of revM06-L for the chemical reaction barrier height database (BH76) is 1.98 kcal/mol, which is improved by more than a factor of 2 with respect to the M06-L functional. The revM06-L functional gives the best result among local functionals tested for the noncovalent interaction database (NC51), with an MUE of only 0.36 kcal/mol, and the MUE of revM06-L for the solid-state lattice constant database (LC17) is half that for M06-L. The revM06-L functional also yields smoother potential curves, and it predicts more-accurate results than M06-L for seven out of eight diversified test sets not used for parameterization. We conclude that the revM06-L functional is well suited for a broad range of applications in chemistry and condensed-matter physics.

Construction of exchange-correlation functionals through interpolation between the non-interacting and the strong-correlation limit

Drawing on the adiabatic connection of density functional theory, exchange-correlation functionals of Kohn-Sham density functional theory are constructed which interpolate between the extreme limits of the electron-electron interaction strength. The first limit is the non-interacting one, where there is only exchange. The second limit is the strong correlated one, characterized as the minimum of the electron-electron repulsion energy. The exchange-correlation energy in the strong-correlation limit is approximated through a model for the exchange-correlation hole that is referred to as nonlocal-radius model [L. O. Wagner and P. Gori-Giorgi, Phys. Rev. A 90, 052512 (2014)]. Using the non-interacting and strong-correlated extremes, various interpolation schemes are presented that yield new approximations to the adiabatic connection and thus to the exchange-correlation energy. Some of them rely on empiricism while others do not. Several of the proposed approximations yield the exact exchange-correlation energy for one-electron systems where local and semi-local approximations often fail badly. Other proposed approximations generalize existing global hybrids by using a fraction of the exchange-correlation energy in the strong-correlation limit to replace an equal fraction of the semi-local approximation to the exchange-correlation energy in the strong-correlation limit. The performance of the proposed approximations is evaluated for molecular atomization energies, total atomic energies, and ionization potentials.

Calculating the Lifetimes of Metastable States with Complex Density Functional Theory

Among other applications, complex absorbing potentials (CAPs) have proven to be useful tools in the theory of metastable states. They facilitate the conversion of unbound states of a finite lifetime into normalized bound states with a complex energy. Adding CAPs to a conventional Hamiltonian turns it into a non-Hermitian operator. Recently, we introduced a complex density functional theory (CODFT) that extends the Kohn-Sham method to the realm of non-Hermitian systems. Here, we combine CAPs with CODFT and present the first application of CODFT to metastable systems. In particular, we consider the negative ions of the beryllium atom and the nitrogen molecule. Using conventional exchange-correlation functionals as functionals of a complex density, the resonance positions and the resonance lifetimes are obtained, and they are in line with the findings of other studies.

Correlation effects in molecular conductors

The source-sink potential (SSP) model introduced previously [F. Goyer, M. Ernzerhof, and M. Zhuang, J. Chem. Phys. 126, 144104 (2007)] enables one to eliminate the semi-infinite contacts in molecular electronic devices (MEDs) in favor of complex potentials. SSP has originally been derived for independent electrons and extended to interacting two-electron systems subsequently [A. Goker, F. Goyer, and M. Ernzerhof, J. Chem. Phys. 129, 194901 (2008)]. Here we generalize SSP to N-electron systems and consider the impact of electron correlation on the transmission probability. In our correlated method for molecular conductors, the molecular part of the Hückel Hamiltonian of the original SSP is replaced by the Hubbard Hamiltonian. For the contacts, however, the single-electron picture is retained and they are assumed to be spin polarized. Using our method, we study electron transmission in molecular wires, cross-conjugated chains, as well as aromatic systems. We find that, for realistic values of the electron-electron repulsion parameter, correlation effects modify the transmission probability quantitatively, the qualitative features remain. However, we find subtle new effects in correlated MEDs, such as Coulomb drag, that are absent in uncorrelated systems.

Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density

We construct improved quantum Monte Carlo estimators for the spherically and system-averaged electron pair density (i.e., the probability density of finding two electrons separated by a relative distance u), also known as the spherically averaged electron position intracule density I(u), using the general zero-variance zero-bias principle for observables, introduced by Assaraf and Caffarel. The calculation of I(u) is made vastly more efficient by replacing the average of the local delta-function operator by the average of a smooth nonlocal operator that has several orders of magnitude smaller variance. These new estimators also reduce the systematic error (or bias) of the intracule density due to the approximate trial wave function. Used in combination with the optimization of an increasing number of parameters in trial Jastrow-Slater wave functions, they allow one to obtain well converged correlated intracule densities for atoms and molecules. These ideas can be applied to calculating any pair-correlation function in classical or quantum Monte Carlo calculations.

Exact Kohn-Sham versus Hartree-Fock in momentum space: Examples of two-fermion systems

The question of how density functional theory (DFT) compares with Hartree-Fock (HF) for the computation of momentum-space properties is addressed in relation to systems for which (near) exact Kohn-Sham (KS) and HF one-electron matrices are known. This makes it possible to objectively compare HF and exact KS and hence to assess the potential of DFT for momentum-space studies. The systems considered are the Moshinsky [Am. J. Phys. 36, 52 (1968)] atom, Hooke's atom, and light two-electron ions, for which expressions for correlated density matrices or momentum densities have been derived in closed form. The results obtained show that it is necessary to make a distinction between true and approximate DFTs.

Continuum states from time-dependent density functional theory

Linear response time-dependent density functional theory is used to study low-lying electronic continuum states of targets that can bind an extra electron. Exact formulas to extract scattering amplitudes from the susceptibility are derived in one dimension. A single-pole approximation for scattering phase shifts in three dimensions is shown to be more accurate than static exchange for singlet electron-He(+) scattering.