Publications

The size-dependent electronic structure of CdTe quantum wires is determined by density functional theory using the local density approximation with band-corrected pseudopotential method. The results of the calculations are then used to assign the size-dependent absorption spectrum of colloidal CdTe quantum wires synthesized by the solution-liquid-solid mechanism. Quantitative agreement between experiment and theory is achieved. The absorption features comprise transitions involving the highest 25-30 valence-band states and lowest 15 conduction-band states. Individual transitions are not resolved; rather, the absorption features consist of clusters of transitions that are determined by the conduction-band energy-level spacings. The sequence, character, and spacing of the conduction-band states are strikingly consistent with the predictions of the simple effective-mass-approximation, particle-in-a-cylinder model. The model is used to calculate the size dependence of the electron effective mass in CdTe quantum wires.

Under pressure, a quasi-two-dimensional electron gas can collapse toward the true two-dimensional (2D) limit. In this limit, the exact exchange-correlation energy per electron has a known finite limit, but general-purpose semilocal approximate density functionals, such as the local density approximation (LDA) and the Perdew-Burke-Ernzerhof generalized gradient approximation (PBE GGA), are known to diverge to minus infinity. Here we consider a model density for a noninteracting electron gas confined to a thickness $L$ by infinite-barrier walls, with a fixed 2D density $1/[\ensuremath{\pi}{({r}_{s}^{\text{2D}})}^{2}]$ and ${r}_{s}^{\text{2D}}=4$ Bohr. We estimate that LDA, PBE, and the strongly constrained and appropriately normed (SCAN) meta-GGA are accurate for the exchange-correlation energy over a wide quasi-2D range, $1.5<L/{r}_{s}^{\text{2D}}<3.85$, but not for smaller $L$. Of these functionals, only SCAN tends to a finite limit when $L$ tends to 0. Since the noninteracting kinetic energy, treated exactly in Kohn-Sham theory, dominates in this limit within a deformable jellium model, all of the general-purpose functionals can estimate the pressure required to achieve any thickness (with SCAN and LDA better than PBE). This pressure vanishes around $L/{r}_{s}^{\text{2D}}=3.85$, where the 3D electron density is roughly that of the valence electrons in metallic potassium, and it reaches about 20 GPa at $L/{r}_{s}^{\text{2D}}=1.5$ and 400 GPa at $L/{r}_{s}^{\text{2D}}=0.6$.

Triangulene and its analogue metal-free magnetic systems have garnered increasing attention since their discovery. Predicting the magnetic coupling and spin-polarization energy with quantitative accuracy is beyond the predictive power of today's density functional theory (DFT) due to their intrinsic multireference character. Herein, we create a benchmark dataset of 25 magnetic systems with nonlocal spin densities, including the triangulene monomer, dimer, and their analogues. We calculate the magnetic coupling (<i>J</i>) and spin-polarization energy (Δ<i>E</i>_spin) of these systems using complete active space self-consistent field (CASSCF) and coupled-cluster methods as high-quality reference values. This reference data is then used to benchmark 22 DFT functionals commonly used in material science. Our results show that, while some functionals consistently correctly predict the qualitative character of the ground state, achieving quantitative accuracy with small relative errors is currently not feasible. PBE0, M06-2X, and MN15 are predicting the correct electronic ground state for all systems investigated here and also have the lowest mean absolute error for predicting both Δ<i>E</i>_spin (0.34, 0.32, and 0.31 eV) and <i>J</i> (11.74, 12.66, and 10.64 meV). They may therefore also serve as starting points for higher-level methods such as the <i>GW</i> or the random phase approximation. As other functionals fail for the prediction of the ground state, they cannot be recommended for metal-free magnetic systems.

The spherical cell, OPW, and APW methods for the determination of the direct hyperfine contact density P F d are compared by means of explicit calculations for lithium metal. Serious deficiencies of the first two methods are discussed. In particular the OPW method is found to converge very slowly for the absolute value of P F d , although it predicts relative changes in P F d due to changes in atomic volume reasonably well. The Fermi level density of states, another quantity which affects the Knight shift, is also considered.

The exchange-correlation energy of a jellium metal surface is analyzed in terms of the wavelength of the fluctuations that contribute to it, using a three-dimensional scheme different from that used by other authors. It is shown that with this scheme there exists an exact limiting form at long wavelengths which includes all many-body correlations and which is independent of the surface density profile. The local-density approximation is formulated as a function of wavelength, and it is shown to be exact at short wavelength. The interpolation scheme between these limits, which was discussed previously, is formulated and checked more completely and used to calculate surface energies.

The Perdew-Zunger (PZ) self-interaction correction (SIC) was designed to correct the one-electron limit of any approximate density functional for the exchange-correlation (xc) energy, while yielding no correction to the exact functional. Unfortunately, it spoils the slowly varying (in space) limits of the uncorrected approximate functionals, where those functionals are right by construction. The right limits can be restored by locally scaling down the energy density of the PZ SIC in many-electron regions, but then a spurious correction to the exact functional would be found unless the self-Hartree and exact self-xc terms of the PZ SIC energy density were expressed in the same gauge. Only the local density approximation satisfies the same-gauge condition for the energy density, which explains why the recent local-scaling SIC is found here to work excellently for atoms and molecules only with this basic approximation and not with the more advanced generalized gradient approximations (GGAs) and meta-GGAs, which lose the Hartree gauge via simplifying integrations by parts. The transformation of energy density that achieves the Hartree gauge for the exact xc functional can also be applied to approximate functionals. Doing so leads to a simple scaled-down self-interaction correction that is typically much more accurate than PZ SIC in tests for many molecular properties (including equilibrium bond lengths). The present work unambiguously shows that the largest errors of PZ SIC applied to standard functionals at three levels of approximation can be removed by restoring their correct slowly varying density limits. It also confirms the relevance of these limits to atoms and molecules.

This dataset contains all VASP inputs and outputs for the paper "Improved Laplacian-level meta-GGA for the weakly-nonlocal solid and liquid metals." For the preprint, see arXiv:2203.09403, and for the reference densities, fitting routines, and analysis scripts, see the Gitlab code repository.\n\nDescription of individual tarballs:\n\n\n\tAE6: 6-molecule set of atomization energies\n\tferro: relaxed geometries and magnetic moments for the ferromagnetic solids Fe, Ni, and Co\n\tintermetallics: formation energies of three intermetallic solids, HfOs, ScPt, and VPt2\n\tLC20: relaxed geometries and equilibrium bulk moduli for the LC20 set of cubic solids. Equilibrium geometries by equation of state fit. Bandgaps for select insulators are included here.\n\tLC20_stress_tensor: same as LC20, but equilibrium geometries found by minimizing forces on unit cell computed with Laplacian-dependent stress tensor\n\tLC23: equilibrium geometries, bulk moduli, and cohesive energies for the LC23 set (LC20 + K, Rb, and Cs) found by equation of state fit. Bandgaps for select insulators are included here.\n\tPt_monovac: monovacancy formation energies for Pt, computed in a few different ways described in the text\n

The band structure of lithium has been calculated by the OPW method using the Seitz potential for the ions and the selfconsistent Hartree potential due to the conduction electrons. Use of the same potential for the 'core state' as for the conduction-electron states is found to be of some importance. A novel method is presented to transform the OPW generalized eigenvalue problem into standard eigenvalue form. The band structure so obtained agrees with previous calculations, particularly that of Rudge (1969). The calculated Fermi surface distortions are less than 4%, while the density of states and optical masses are 1.50 and 1.47 respectively. The direct interband optical conductivity has also been calculated; its overall magnitude is in reasonable agreement with measurements by Mathewson and Myers (1973). The calculation predicts a sharp absorption edge at 3.4 eV, in agreement with the measurement by Hodgson (1966), and in contrast to the much slower rise in the optical conductivity beginning at 2.4 eV reported by Mathewson and Myers.