Publications

Understanding Density-Driven Errors for Reaction Barrier Heights

Delocalization errors, such as charge-transfer and some self-interaction errors, plague computationally efficient and otherwise accurate density functional approximations (DFAs). Evaluating a semilocal DFA non-self-consistently on the Hartree-Fock (HF) density is often recommended as a computationally inexpensive remedy for delocalization errors. For sophisticated meta-GGAs like SCAN, this approach can achieve remarkable accuracy. This HF-DFT (also known as DFA@HF) is often presumed to work, when it significantly improves over the DFA, because the HF density is more accurate than the self-consistent DFA density in those cases. By applying the metrics of density-corrected density functional theory (DFT), we show that HF-DFT works for barrier heights by making a <i>localizing</i> charge-transfer error or density overcorrection, thereby producing a somewhat reliable cancellation of density- and functional-driven errors for the energy. A quantitative analysis of the charge-transfer errors in a few randomly selected transition states confirms this trend. We do not have the exact functional and electron densities that would be needed to evaluate the exact density- and functional-driven errors for the large BH76 database of barrier heights. Instead, we have identified and employed three fully nonlocal proxy functionals (SCAN 50% global hybrid, range-separated hybrid LC-ωPBE, and SCAN-FLOSIC) and their self-consistent proxy densities. These functionals are chosen because they yield reasonably accurate self-consistent barrier heights and because their self-consistent total energies are nearly piecewise linear in fractional electron number─two important points of similarity to the exact functional. We argue that density-driven errors of the energy in a self-consistent density functional calculation are second order in the density error and that large density-driven errors arise primarily from incorrect electron transfers over length scales larger than the diameter of an atom.

Assessing r2SCAN meta-GGA functional for structural parameters, cohesive energy, mechanical modulus and thermophysical properties of 3d, 4d and 5d transition metals

The recent development of the accurate and efficient semilocal density functionals on the third rung of Jacob's ladder of density functional theory such as the revised regularized strongly constrained and appropriately normed (r2SCAN) density functional could enable the rapid and highly reliable prediction of the elasticity and temperature dependence of thermophysical parameters of refractory elements and their intermetallic compounds using quasi-harmonic approximation (QHA). Here, we present a comparative evaluation of the equilibrium cell volumes, cohesive energy, mechanical moduli, and thermophysical properties (Debye temperature and thermal expansion coefficient) for 22 transition metals using semilocal density functionals, including local density approximation (LDA), the Perdew-Burke-Ernzerhof (PBE) and PBEsol generalized gradient approximations (GGA), and the r2SCAN meta-GGA. PBEsol and r2SCAN deliver the same level of accuracies for structural, mechanical and thermophysical properties. Otherwise, PBE and r2SCAN perform better than LDA and PBEsol for calculating cohesive energies of transition metals. Among the tested density functionals, r2SCAN provides an overall well-balanced performance for reliably computing the cell volumes, cohesive energies, mechanical properties, and thermophysical properties of various 3d, 4d, and 5d transition metals using QHA. Therefore, we recommend that r2SCAN could be employed as a workhorse method to evaluate the thermophysical properties of transition metal compounds and alloys in the high throughput workflows.

Higher-order van der Waals coefficients from static multipole polarizability

CSD 2224113: Experimental Crystal Structure Determination

An entry from the Inorganic Crystal Structure Database, the world’s repository for inorganic crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the joint CCDC and FIZ Karlsruhe Access Structures service and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy

The Hohenberg-Kohn theorem is extended to fractional electron number $N$, for an isolated open system described by a statistical mixture. The curve of lowest average energy ${E}_{N}$ versus $N$ is found to be a series of straight line segments with slope discontinuities at integral $N$. As $N$ increases through an integer $M$, the chemical potential and the highest occupied Kohn-Sham orbital energy both jump from ${E}_{M}\ensuremath{-}{E}_{M\ensuremath{-}1}$ to ${E}_{M+1}\ensuremath{-}{E}_{M}$. The exchange-correlation potential $\frac{\ensuremath{\delta}{E}_{\mathrm{xc}}}{\ensuremath{\delta}n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})}$ jumps by the same constant, and $\frac{{\mathrm{lim}}_{r\ensuremath{\rightarrow}\ensuremath{\infty}}\ensuremath{\delta}{E}_{\mathrm{xc}}}{\ensuremath{\delta}n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})}&gt;~0$.

Divergence and accurate resummation of density functional perturbation theory, with applications to atoms and molecules

Toward Improved Semilocal and Nonlocal Density Functionals for Atoms, Molecules, and Solids

Semilocal density functionals construct the exchange-correlation energy density at a point from the electron density and orbitals in the neighborhood of that point. They can be constructed nonempirically, and work best for sp-bonded systems near equilibrium. They increase in sophistication from the local spin density approximation to the generalized gradient approximation to the meta-GGA. For a molecule like CO on a transition metal surface, it appears that only a meta-GGA can give a good simultaneous description of the lattice constant and surface energy of the metal, on the one hand, and the adsorption energy of the molecule on the other [1]. I will discuss two remaining deficiencies of the revised TPSS meta-GGA [2]: its artificial order-of-limits problem, and its need for more information about non-bonded interaction. When electrons are shared over stretched bonds, full nonlocality is needed, and typically empirical parameters are also needed. This suggests that we don’t yet know enough about the full nonlocality of the density functional for the exchange-correlation energy.

van der Waals interaction as a summable asymptotic series

The dynamic multipole polarizabilities and thus the second-order van der Waals coefficients ${C}_{2k}$ of all orders are known exactly for the interaction between two classical spherical conducting shells, each of uniform electron density $\ensuremath{\rho}$ with outer radius $R$ and thickness $t$. The result is ${C}_{2k}=\ensuremath{-}{c}_{k}(t/R)\sqrt{4\ensuremath{\pi}\ensuremath{\rho}}{[{(2R)}^{2}]}^{k}$. The ${c}_{k}$ approach a limiting constant value, so the infinite series for the van der Waals interaction at separation $d$, $\ensuremath{-}{C}_{6}/{d}^{6}\ensuremath{-}{C}_{8}/{d}^{8}\ensuremath{-}\ensuremath{\cdots}$, can be summed analytically, diverging only for $d\ensuremath{\le}2R$. This divergence can be removed without changing the asymptotic series. Real quasispherical objects like nanoclusters, fullerenes, and even atoms can be approximated by this spherical-shell model, with $R$ fixed by the true static dipole polarizability. Once $t/R$ is fixed, all the higher coefficients are determined by just ${C}_{6}$ and ${C}_{8}$. Finally, we compare the exact ${C}_{2k}$ to those from a pair interaction model, which works for solid spheres ($t=R$) but not for fullerenes.

Effect of bridge on energy transfer and photoinduced charge separation in perylene-diimide-naphthalene-bisimide-hexathiophene based donor-bridge-acceptor triads

\nFemtosecond transient absorption spectroscopy is performed to assess bridge effects on energy transfer and charge separation in molecular junctions. A short, conjugated bridge can facilitate charge separation from both donor and acceptor, whereas in longer bridges charge separation only occurs from the excited donor.\n

Correlation Energy of 3D Spin-Polarized Electron Gas: A Single Interpolation Between High- and Low-Density Limits

Meta-generalized gradient approximation: Third rung on the ladder of density functional approximations

On the Jacob’s Ladder of density functional approximations to the exchangecorrelation energy, each higher rung adds another local ingredient which can be used to satisfy further exact constraints. The rst rung is the local density approximation. The second rung or generalized gradient approximation (GGA) adds the gradient of the density. The third rung or meta-GGA further adds the Kohn-Sham orbital kinetic energy density. I will review the nonempirical construction of a recent meta-GGA [1] and its mostly-successful numerical tests for molecules [2,3] and solids [4].

High-density limit of the Perdew-Burke-Ernzerhof generalized gradient approximation and related density functionals

We point out a simplifying but mildly inconsistent assumption of the Perdew-Burke-Ernzerhof (PBE) correlation functional, which should be corrected when evaluating the high-density limit of the PBE energy for nonsinglet systems under uniform density scaling. The discussion also concerns high-density limits of all density functionals that use PBE as an ingredient, including the Tao-Perdew-Staroverov-Scuseria (TPSS) approximation. We revisit the nonrelativistic correlation energies of isoelectronic atomic ions in the limit of infinite nuclear charge and explain small discrepancies between the PBE and TPSS values of these limits existing in the literature.

A SCAN perspective on the puzzle of the α ↔γ phase transition of Ce

Erratum: Tests of a ladder of density functionals for bulk solids and surfaces [Phys. Rev. B<b>69</b>, 075102 (2004)]

Received 8 December 2008DOI:https://doi.org/10.1103/PhysRevB.78.239907©2008 American Physical Society

Density functional theory is straying from the path toward the exact functional

The theorems at the core of density functional theory (DFT) state that the energy of a many-electron system in its ground state is fully defined by its electron density distribution. This connection is made via the exact functional for the energy, which minimizes at the exact density. For years, DFT development focused on energies, implicitly assuming that functionals producing better energies become better approximations of the exact functional. We examined the other side of the coin: the energy-minimizing electron densities for atomic species, as produced by 128 historical and modern DFT functionals. We found that these densities became closer to the exact ones, reflecting theoretical advances, until the early 2000s, when this trend was reversed by unconstrained functionals sacrificing physical rigor for the flexibility of empirical fitting.

Simplified Generalized Gradient Approximation

Versatile van der Waals Density Functional Based on a Meta-Generalized Gradient Approximation

Van der Waals interactions are ubiquitous in different materials yet not always described properly by current theories. Now, researchers have determined how to accurately and efficiently treat long-range Van der Waals interactions together with other chemical bonds, new findings that are important for studies of layered materials.

Symmetry Breaking with the SCAN Density Functional Describes Strong Correlation in the Singlet Carbon Dimer

The SCAN (strongly constrained and appropriately normed) meta-generalized gradient approximation (meta-GGA), which satisfies all 17 exact constraints that a meta-GGA can satisfy, accurately describes equilibrium bonds that are normally correlated. With symmetry breaking, it also accurately describes some sd equilibrium bonds that are strongly correlated. While sp equilibrium bonds are nearly always normally correlated, the C₂ singlet ground state is known from correlated wave function theory to be a rare case of strong correlation in an sp equilibrium bond. Earlier work that calculated atomization energies of the molecular sequence B₂, C₂, O₂, and F₂ in the local spin density approximation (LSDA), the Perdew-Burke-Ernzerhof (PBE) GGA, and the SCAN meta-GGA, without symmetry breaking in the molecule, found that only SCAN was accurate enough to reveal an anomalous under-binding for C₂. This work shows that spin symmetry breaking in singlet C₂, which involves the appearance of net up- and down-spin densities on opposite sides (not ends) of the bond, corrects that underbinding, with a small SCAN atomization-energy error more like that of the other three molecules, suggesting that symmetry breaking with an advanced density functional might reliably describe strong correlation. This article also discusses some general aspects of symmetry breaking and the insights into strong correlation that symmetry breaking can bring. The normally correlated low-lying triplet excited state has the right vertical excitation energy in SCAN but not in LSDA or PBE, where the triplet is a false ground state. Fractional occupation numbers are found only for the symmetry-unbroken singlet and only in LSDA and PBE GGA.