An efficient k.p method for calculation of total energy and electronic density of states

Optimal basis set for electronic structure calculations in periodic systems

An efficient method for calculating the electronic structure of systems that need a very fine sampling of the Brillouin zone is presented. The method is based on the variational optimization of a "single" (i.e. common to all points in the Brillouin zone) basis set for the expansion of the electronic orbitals. Considerations from k.p-approximation theory help to understand the efficiency of the method. The accuracy and the convergence properties of the method as a function of the optimal basis set size are analysed for a test calculation on a 16-atom Na supercell.

Nuclear-Electronic Orbital Approach to Quantization of Protons in Periodic Electronic Structure Calculations

The nuclear-electronic orbital (NEO) method is a well-established approach for treating nuclei quantum mechanically in molecular systems beyond the usual Born-Oppenheimer approximation. In this work, we present a strategy to implement the NEO method for periodic electronic structure calculations, particularly focused on multicomponent density functional theory (DFT). The NEO-DFT method is implemented in an all-electron electronic structure code, FHI-aims, using a combination of analytical and numerical integration techniques as well as a resolution of the identity scheme to enhance computation…

Compact representation of one-particle wavefunctions and scalar fields obtained from electronic-structure calculations

We present a code-independent compact representation of one-electron wavefunctions and other volumetric data (electron density, electrostatic potential, etc.) produced by electronic-structure calculations. The compactness of the representation insures minimization of digital storage requirements for the computational data, while the code-independence makes the data ready for "big data" analytics. Our approach allows to minimize differences between original and the new representation, and is in principle information-lossless. The procedure for obtaining the wavefunction representation is closel…

Minimal parameter implicit solvent model for ab initio electronic structure calculations

We present an implicit solvent model for ab initio electronic structure calculations which is fully self-consistent and is based on direct solution of the nonhomogeneous Poisson equation. The solute cavity is naturally defined in terms of an isosurface of the electronic density according to the formula of Fattebert and Gygi (J. Comp. Chem. 23, 6 (2002)). While this model depends on only two parameters, we demonstrate that by using appropriate boundary conditions and dispersion-repulsion contributions, solvation energies obtained for an extensive test set including neutral and charged molecules…

Accurate electronic excitations for two alkali-halide systems obtained by density-functional theory and verified by multi-configuration self-consistent field calculations

Use of density-functional theory in a $Δ$self-consistent field framework result in both the ground- and two lowest electronicly excited states of the NaCl and LiCl. The accuracy of this method is confirmed using a multi-configuration self-consistent field method to obtain the same states. The overall good agreement between the calculated ground and excited potential-energy surfaces speaks promising for the computationally simple $Δ$self-consistent field method.

One-way multigrid method in electronic structure calculations

We propose a simple and efficient one-way multigrid method for self-consistent electronic structure calculations based on iterative diagonalization. Total energy calculations are performed on several different levels of grids starting from the coarsest grid, with wave functions transferred to each finer level. The only changes compared to a single grid calculation are interpolation and orthonormalization steps outside the original total energy calculation and required only for transferring between grids. This feature results in a minimal amount of code change, and enables us to employ a sophis…

Ten-million-atom electronic structure calculations on the K computer with a massively parallel order-N theory

A massively parallel order-N electronic structure theory was constructed by an interdisciplinary research between physics, applied mathematics and computer science. (1) A high parallel efficiency with ten-million-atom nanomaterials was realized on the K computer with upto 98,304 processor cores. The mathematical foundation is a novel linear algebraic algorithm for the generalized shifted linear equation. The calculation was carried out by our code ' ELSES ' (www.elses.jp) with modelled (tight-binding-form) systems based on ab initio calculations. (2) A post-calculation analysis method, called …

Many-Body Quantum Calculations for Graphyne for Electronic Devices

Moving beyond traditional 2D materials is now desirable to have switching capabilities (e.g., transistors). Here we propose using graphyne because, as we will show in this letter, obtaining regions of the electronic bandstructure which act as valence and conduction bands, with an apparent bandgap, is found. Here for particular allotropes of graphyne, density of states (DOS) and electronic bandstructure diagrams with E(k) vs k are found for the graphyne allotropes graphyne-1 and graphyne-2 having, respectively, one and two triple C-C carbon-carbon bonds between adjoining benzene rings. The ab i…

An approach to first principles electronic structure calculation by symbolic-numeric computation

This article is an introduction to a new approach to first principles electronic structure calculation. The starting point is the Hartree-Fock-Roothaan equation, in which molecular integrals are approximated by polynomials by way of Taylor expansion with respect to atomic coordinates and other variables. It leads to a set of polynomial equations whose solutions are eigenstate, which is designated as algebraic molecular orbital equation. Symbolic computation, especially, Gröbner bases theory, enables us to rewrite the polynomial equations into more trimmed and tractable forms with identical roo…

Bypassing the energy functional in density functional theory: Direct calculation of electronic energies from conditional probability densities

Density functional calculations can fail for want of an accurate exchange-correlation approximation. The energy can instead be extracted from a sequence of density functional calculations of conditional probabilities (CP-DFT). Simple CP approximations yield usefully accurate results for two-electron ions, the hydrogen dimer, and the uniform gas at all temperatures. CP-DFT has no self-interaction error for one electron, and correctly dissociates H2, both major challenges. For warm dense matter, classical CP-DFT calculations can overcome the convergence problems of Kohn-Sham DFT.

Accuracy and efficiency of modern methods for electronic structure calculation on heavy- and superheavy-element compounds

The methods which are actively used for electronic structure calculations of low-lying states of heavy- and superheavy-element compounds are briefly described. The advantages and disadvantages of calculations with the Dirac-Coulomb-Breit Hamiltonian, Huzinaga-type pseudopotential, shape-consistent Relativistic Effective Core Potential (RECP) and Generalized RECP are discussed. The nonvariational technique of the electronic structure restoration in atomic cores after the RECP calculation of a molecule is presented. The features of some approaches accounting for electron correlation, the configu…

Hybrid preconditioning for iterative diagonalization of ill-conditioned generalized eigenvalue problems in electronic structure calculations

The iterative diagonalization of a sequence of large ill-conditioned generalized eigenvalue problems is a computational bottleneck in quantum mechanical methods employing a nonorthogonal basis for {\em ab initio} electronic structure calculations. We propose a hybrid preconditioning scheme to effectively combine global and locally accelerated preconditioners for rapid iterative diagonalization of such eigenvalue problems. In partition-of-unity finite-element (PUFE) pseudopotential density-functional calculations, employing a nonorthogonal basis, we show that the hybrid preconditioned block ste…

基于VASP的CeO₂态密度计算

Density of States Calculation of CeO$_2$ Based on VASP

本研究基于VASP软件，采用密度泛函理论（DFT）方法对CeO₂的态密度（DOS）进行了详细分析，深入研究了其晶体结构和电子能级分布，为CeO₂在催化和电子材料中的应用提供了理论支持，也为新型CeO₂基材料的设计与开发提供了指导。

Hamiltonian symmetries in auxiliary-field quantum Monte Carlo calculations for electronic structure

We describe how to incorporate symmetries of the Hamiltonian into auxiliary-field quantum Monte Carlo calculations (AFQMC). Focusing on the case of Abelian symmetries, we show that the computational cost of most steps of an AFQMC calculation is reduced by $N_k^{-1}$, where $N_k$ is the number of irreducible representations of the symmetry group. We apply the formalism to a molecular system as well as to several crystalline solids. In the latter case, the lattice translational group provides increasing savings as the number of k points is increased, which is important in enabling calculations t…

Periodic Electronic Structure Calculations With Density Matrix Embedding Theory

We extend density matrix embedding theory to periodic systems, resulting in an electronic band structure method for solid-state materials. The electron correlation can be captured by means of a local impurity model using various choices of wave function methods. The method is able to describe not only the ground-state energy but also the quasiparticle band picture via the real-momentum space implementation. We investigate the performance of periodic DMET in describing the ground-state energy as well as the electronic band structure for one-dimensional solids. Our results show that DMET are in …

Electronic structure and optical properties of quantum crystals from first principles calculations in the Born-Oppenheimer approximation

We develop a formalism to accurately account for the renormalization of electronic structure due to quantum and thermal nuclear motions within the Born-Oppenheimer approximation. We focus on the fundamental energy gap obtained from electronic addition and removal energies from Quantum Monte Carlo calculations in either the canonical or grand canonical ensembles. The formalism applies as well to effective single electron theories such as those based on Density Functional Theory. We show that electronic (Bloch) crystal momentum can be restored by marginalizing the total electron-ion wave functio…

Discrete discontinuous basis projection method for large-scale electronic structure calculations

We present an approach to accelerate real-space electronic structure methods several fold, without loss of accuracy, by reducing the dimension of the discrete eigenproblem that must be solved. To accomplish this, we construct an efficient, systematically improvable, discontinuous basis spanning the occupied subspace and project the real-space Hamiltonian onto the span. In calculations on a range of systems, we find that accurate energies and forces are obtained with 8--25 basis functions per atom, reducing the dimension of the associated real-space eigenproblems by 1--3 orders of magnitude.

电子结构计算中积分计算的高效方法

Efficient methods for computing integrals in electronic structure calculations

本文提出高效方法计算电子结构计算中出现的积分，通过将积分表示为轮廓积分并利用Clenshaw-Curtis求积法进行评估，通过数值实验验证了方法的效率。

FEAST fundamental framework for electronic structure calculations: Reformulation and solution of the muffin-tin problem

In a recent article [1], the FEAST algorithm has been presented as a general purpose eigenvalue solver which is ideally suited for addressing the numerical challenges in electronic structure calculations. Here, FEAST is presented beyond the "black-box" solver as a fundamental modeling framework which can naturally address the original numerical complexity of the electronic structure problem as formulated by Slater in 1937 [2]. The non-linear eigenvalue problem arising from the muffin-tin decomposition of the real-space domain is first derived and then reformulated to be solved exactly within t…

Numerical Analysis of the Multiple Scattering Theory for Electronic Structure Calculations

The multiple scattering theory (MST) is one of the most widely used methods in electronic structure calculations. It features a perfect separation between the atomic configurations and site potentials, and hence provides an efficient way to simulate defected and disordered systems. This work studies the MST methods from a numerical point of view and shows the convergence with respect to the truncation of the angular momentum summations, which is a fundamental approximation parameter for all MST methods. We provide both rigorous analysis and numerical experiments to illustrate the efficiency of…

用于全势电子结构计算的一种间断Galerkin格式

A discontinuous Galerkin scheme for full-potential electronic structure calculations

本文提出一种用于周期系统全势电子结构计算的高效间断Galerkin数值格式，结合原子球与间隙区域的不同基函数，具有系统性的谱收敛速率，并给出了严格的先验误差分析和数值模拟验证。

Implementation of Quantum Machine Learning for Electronic Structure Calculations of Periodic Systems on Quantum Computing Devices

Quantum machine learning algorithms, the extensions of machine learning to quantum regimes, are believed to be more powerful as they leverage the power of quantum properties. Quantum machine learning methods have been employed to solve quantum many-body systems and have demonstrated accurate electronic structure calculations of lattice models, molecular systems, and recently periodic systems. A hybrid approach using restricted Boltzmann machines and a quantum algorithm to obtain the probability distribution that can be optimized classically is a promising method due to its efficiency and ease …

Real-time feedback from iterative electronic structure calculations

Real-time feedback from iterative electronic structure calculations requires to mediate between the inherently unpredictable execution times of the iterative algorithm employed and the necessity to provide data in fixed and short time intervals for real-time rendering. We introduce the concept of a mediator as a component able to deal with infrequent and unpredictable reference data to generate reliable feedback. In the context of real-time quantum chemistry, the mediator takes the form of a surrogate potential that has the same local shape as the first-principles potential and can be evaluate…

Ab initio lifetime correction to scattering states for time-dependent electronic-structure calculations with incomplete basis sets

We propose a method for obtaining effective lifetimes of scattering electronic states for avoiding the artificially confinement of the wave function due to the use of incomplete basis sets in time-dependent electronic-structure calculations of atoms and molecules. In this method, using a fitting procedure, the lifetimes are extracted from the spatial asymptotic decay of the approximate scattering wave functions obtained with a given basis set. The method is based on a rigorous analysis of the complex-energy solutions of the Schr{ö}dinger equation. It gives lifetimes adapted to any given basis …

The MRChem multiresolution analysis code for molecular electronic structure calculations: performance and scaling properties

MRChem is a code for molecular electronic structure calculations, based on a multiwavelet adaptive basis representation. We provide a description of our implementation strategy and several benchmark calculations. Systems comprising more than a thousand orbitals are investigated at the HF level of theory, with an emphasis on scaling properties. With our design, terms which formally scale quadratically with the system size, in effect have a better scaling because of the implicit screening introduced by the inherent adaptivity of the method: all operations are performed to the requested precision…

CP2K：一款电子结构与分子动力学软件包——Quickstep：高效且精准的电子结构计算

CP2K: An Electronic Structure and Molecular Dynamics Software Package -- Quickstep: Efficient and Accurate Electronic Structure Calculations

本综述介绍开源电子结构与分子动力学软件包CP2K的核心能力，重点阐述其基于高斯与平面波方法的密度泛函理论及后Hartree-Fock方法，依托新型算法实现高性能电子结构计算。