Electronic Structure Calculations Of Solids Research Articles

Quantum embedding theories to simulate condensed systems on quantum computers.

Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties that are more complex than tractable at present on classical architectures. Here, we discuss computational frameworks to carry out electronic structure calculations of solids on noisy intermediate-scale quantum computers using embedding theories, and we give examples for a specific class of materials, that is, solid materials hosting spin defects. These are promising systems to build future quantum technologies, such as quantum computers, quantum sensors and quantum communication devices. Although quantum simulations on quantum architectures are in their infancy, promising results for realistic systems appear to be within reach.

Electron capture nuclear decay rate under compression in a confined environment

We have calculated the effect of compressing the radioactive atoms in the crystal lattice environments on their electron capture nuclear decay rates. The electronic structure calculations of solids using the density functional techniques have been used to calculate the change of electron density at the nuclei and the corresponding change of electron capture nuclear decay rate of the radioactive atoms confined to the interstitial spaces of different crystal lattices. The effects of finite nuclear size and vacuum polarization were considered in the calculations. It has been found that the calculations significantly underpredict the experimentally measured increase of electron capture nuclear decay rate under compression. The increase of decay rate due to compression-induced quantum anti-Zeno effect is generally believed to be very small because of very short duration of initial nonexponential decay time for the nuclear decays. However, this effect could be observable for the electron capture nuclear decay of $$^{\mathrm {163}}$$ Ho, because of its very low decay energy. Moreover, certain models of quantum measurement indicate much longer initial nonexponential decay time and the corresponding implication on the increase of decay rate under compression is still not known. It is important to understand the large discrepancy between the measured and calculated increase of electron capture nuclear decay rate under compression and the associated role of quantum anti-Zeno effect because of their possible implications in various astrophysical and geophysical calculations.

Dealing with the exponential wall in electronic structure calculations.

An alternative to the density functional theory is the use of wavefunction based electronic structure calculations for solids. In order to perform them, the Exponential Wall (EW) problem has to be resolved. It is caused by an exponential increase of the number of configurations with increasing electron number N. There are different routes one may follow. One is to characterize a many-electron wavefunction by a vector in Liouville space with a cumulant metric rather than in Hilbert space. This removes the EW problem. Another is to model the solid by an impurity or fragment embedded in a bath which is treated at a much lower level than the former. This is the case in the Density Matrix Embedding Theory (DMET) or the Density Embedding Theory (DET). The latter two are closely related to a Schmidt decomposition of a system and to the determination of the associated entanglement. We show here the connection between the two approaches. It turns out that the DMET (or DET) has an identical active space as a previously used Local Ansatz, based on a projection and partitioning approach. Yet, the EW problem is resolved differently in the two cases. By studying a H10 ring, these differences are analyzed with the help of the method of increments.

SCDM-k: Localized orbitals for solids via selected columns of the density matrix

The recently developed selected columns of the density matrix (SCDM) method (Damle et al. 2015, [16]) is a simple, robust, efficient and highly parallelizable method for constructing localized orbitals from a set of delocalized Kohn–Sham orbitals for insulators and semiconductors with Γ point sampling of the Brillouin zone. In this work we generalize the SCDM method to Kohn–Sham density functional theory calculations with k-point sampling of the Brillouin zone, which is needed for more general electronic structure calculations for solids. We demonstrate that our new method, called SCDM-k, is by construction gauge independent and a natural way to describe localized orbitals. SCDM-k computes localized orbitals without the use of an optimization procedure, and thus does not suffer from the possibility of being trapped in a local minimum. Furthermore, the computational complexity of using SCDM-k to construct orthogonal and localized orbitals scales as O(Nlog⁡N) where N is the total number of k-points in the Brillouin zone. SCDM-k is therefore efficient even when a large number of k-points are used for Brillouin zone sampling. We demonstrate the numerical performance of SCDM-k using systems with model potentials in two and three dimensions.

Domain overlap matrices from plane-wave-based methods of electronic structure calculation.

Plane waves are one of the most popular and efficient basis sets for electronic structure calculations of solids; however, their delocalized nature makes it difficult to employ for them classical orbital-based methods of chemical bonding analysis. The quantum chemical topology approach, introducing chemical concepts via partitioning of real space into chemically meaningful domains, has no difficulties with plane-wave-based basis sets. Many popular tools employed within this approach, for instance delocalization indices, need overlap integrals over these domains-the elements of the so called domain overlap matrices. This article reports an efficient algorithm for evaluation of domain overlap matrix elements for plane-wave-based calculations as well as evaluation of its implementation for one of the most popular projector augmented wave (PAW) methods on the small set of simple and complex solids. The stability of the obtained results with respect to PAW calculation parameters has been investigated, and the comparison of the results with the results from other calculation methods has also been made.

Relativistic LMTO method for systems of light elements

This paper reviews the theoretical background of an approximate treatment of relativistic effects within the tight-binding (TB) linear muffin-tin orbital (LMTO) method for ab-initio electronic structure calculations of solids. The formalism employs two-component spinors and an orbital basis set of the scalar-relativistic approximation. The developed theory is applied to selected metallic systems and its results are compared to those of a fully relativistic TB-LMTO method.

Electronic Structure Calculations of Solids with a Similarity-Transformed Hamiltonian

A new wavefunction-based method of electronic band structure calculation of solids is proposed based on the transcorrelated (TC) method. In the TC method, a Jastrow–Slater-type correlated wavefunction is used as a trial function. Similarity transformation of the Hamiltonian with respect to the Jastrow correlation function is utilized to derive Hartree–Fock (HF)-like self-consistent-field (SCF) equations, which determine the one-body wavefunctions in the Slater determinant and their orbital energies. Since the electron correlation is taken into account, the method could be a practical tool for band structure calculation of solids where the HF method fails even qualitatively. The single-particle energy dispersion of the electron gas shows no singularity at the Fermi surface due to the screening effect incorporated in the TC method. It is also demonstrated that this method significantly reduces the band gaps of Si, C, and SiC when compared with their corresponding Hartree–Fock values.

Method of increments for excitations in correlated electron systems

The method of increments has been invaluable for electronic structure calculations of solids based in wavefunctions, i.e., quantum chemical techniques. While it is well documented for ground-state calculations we want to give here a coherent description when it is applied to the computation of excitations of weakly and strongly correlated electron systems. Previous applications can be viewed as special cases of the general scheme.

Density fitting of Coulomb integrals in electronic structure calculations of solids

A density fitting approach to Coulomb integrals is formulated for infinite systems with translational periodicity. Demands for Coulomb integrals scale linearly with regard to the number of unit cells, thereby opening the possibility of highly effective evaluation of the Coulomb part of electronic structure calculations in the solid state. The problem of the inverse of the Coulomb matrix in the $\ensuremath{\Gamma}$ point of the momentum space is solved analytically. As a byproduct, self-reproducibility of the overlap matrix (a feature not having a molecular analogue, with fundamental consequences for Coulomb tail cancellation) is revealed.

Future Trends in Modeling Electron Energy Loss Near-Edge Structure (ELNES)

The increasing availability of fast, multiprocessor high performance computing facilities has revolutionized iterative electronic structure calculations of solids, particularly for those systems possessing little or no symmetry. This combined with the semi-commercial dissemination of well-supported software packages for the calculation of both occupied and unoccupied electronic states at high levels of approximation has opened up the possibilities for more routine modeling and understanding of electron energy loss near-edge structure (ELNES) data obtained in the TEM/STEM, and hence the elucidation of chemical bonding in solids at high spatial resolution.The two modeling approaches presented and compared here involve ab-initio band structure calculations based on the full linear augmented plane wave (FLAPW - WIEN97) approach, and full multiple scattering (MS) clusterbased methods. We have performed a systematic study of transition metal carbides and nitrides and compared the modeling results with high resolution EELS data.

ELECTRONIC STRUCTURE OF SOLIDS IN THE SELF-INTERACTION CORRECTED LOCAL-SPIN-DENSITY APPROXIMATION

An ab-initio implementation of self-interaction corrections (SIC) within local spin density (LSD) electronic structure calculations of solids is presented. The linear-muffin-tin orbital method is used in the tight-binding representation and with the atomic spheres approximation. The variational minimum of the SIC-LSD energy functional is found by the steepest descent method, i.e., no matrix diagonalizations are involved. Special care is taken to secure stability with respect to unitarian mixing of electron states. Applied to the transition metal monoxides and La 2 CuO 4 the SIC-LSD significantly improves the desription in comparison to LSD.

Electronic structure of epitaxial interfaces

Metal-semiconductor (Schottky barrier) and semiconductor-semiconductor (heterojunction) interfaces show rectifying barrier heights and band offsets, which are two key quantities required to optimize the performance of a device. A large number of models and empirical theories have been put forward by various workers in the field during the last 50 years. But a proper understanding of the microscopic origin of these quantities is still missing. In this article, our focus is mainly to present a unified framework for first principles investigation of the electronic structure of epitaxial interfaces, in which one of the constituents is a semiconductor. LMTO method is now a well established tool for self-consistent electronic structure calculations of solids within LDA. Such calculations, when performed on supercell geometries, are quite successful in predicting a wide range of interface specific electronic properties accurately and efficiently. We describe here the basic formalism of this LMTO-supercell approach in its various levels of sophistication and apply it to investigate the electronic structure of A- and B-type NiSi2/Si(111) interface as a prototype metal-semiconductor system, and CaF2/Si(111) interface as a prototype insulator-semiconductor system. These are a few of the most ideal lattice matched epitaxial interfaces whose atomic and electronic structures have been extensively studied using a wide range of experimental probes. We give here a glimpse of these experimental results and discuss the success as well as limitations of LDA calculations to achieve accuracies useful for the device physicists.

Hartree-Fock band-structure calculations with the linear muffin-tin-orbital method: Application to C, Si, Ge, and alpha -Sn.

A general formalism is presented for electronic structure calculations of solids in the Hartree-Fock approximation based on the linear muffin-tin-orbital (LMTO) method. The nonlocal exchange operator is evaluated in the basis of tight-binding muffin-tin orbitals with the atomic-sphere approximation. Since the LMTO minimal basis set by construction is orthogonal to the core states and fairly complete, well-converged calculations are obtained even for high-Z materials. The frozen-core approximation is used and relativistic effects are incorporated through the scalar relativistic approximation. No assumption of a weak pseudopotential is needed, and electronic states of high-angular-momentum character are treated straightforwardly. The method is applied to diamond, Si, Ge, and \ensuremath{\alpha}-Sn, for which the Hartree-Fock band structures and cohesive energies are presented and compared to the results of local-density calculations, to experiments, and, for C and Si, to previous Hartree-Fock calculations.