arXiv subjects

Min-Ye Zhang

Publications and source records attributed to Min-Ye Zhang.

12 recordsLinked to original sources

arXiv2026

Correlation-consistent Gaussian basis sets for copper solids from material-constrained atomic optimization

Correlation-consistent Gaussian basis sets are central to systematic molecular quantum chemistry, but their direct use in periodic solids is often limited by severe linear dependence from diffuse atomically optimized primitives. This problem is particularly acute for metallic and metal-containing systems, where reliable complete-basis-set (CBS) extrapolation is needed for correlated-wavefunction benchmarks. We introduce material-constrained atomic optimization (MCAO), a basis-set optimization framework that preserves the atomic and correlation-consistent character of Gaussian basis sets while penalizing large overlap-matrix condition numbers in representative solids. As a proof of concept, we generate Dunning-style MCAO-cc-pVXZ basis sets (X = D, T, Q) for Cu with all-electron, scalar-relativistic all-electron, effective core potential (ECP), and pseudopotential treatments. The resulting basis sets remain numerically stable for Cu solids and surfaces while reproducing molecular Cu dimer energetics and plane-wave reference properties of bulk Cu. CBS-extrapolated random-phase approximation calculations further enable a controlled assessment of pseudopotential, relativistic, and basis-set errors in bulk Cu and CO adsorption on Cu(111), providing scalar-relativistic all-electron Gaussian-basis benchmarks for the CO adsorption puzzle.

physics.chem-ph↗

arXiv2026

Efficient Bethe-Salpeter Equation Calculations Based on Numerical Atomic Orbitals and Norm-Conserving Pseudopotentials: Dual-${\boldsymbol k}$-Mesh Strategy

We present an efficient implementation of the Bethe--Salpeter equation (BSE) based on numerical atomic orbitals (NAOs) and norm-conserving pseudopotentials within the ABACUS+LibRPA framework. By exploiting the localized resolution-of-identity (LRI) technique, the screened Coulomb interaction is cast into a real-space, unit-cell-indexed form $W_{μν}(\boldsymbol R)$ that is inherently short-ranged and well localized. This spatial locality enables an efficient Fourier interpolation of the BSE kernel from the coarse $\boldsymbol k$-mesh used in the preceding $GW$ calculation to an arbitrarily dense $\boldsymbol k$-mesh on which the BSE Hamiltonian is assembled and diagonalized, thereby giving rise naturally to a dual-$\boldsymbol k$-mesh workflow. Building on this scheme, we systematically examine the convergence of the absorption spectra with respect to the NAO basis set, the auxiliary basis set, and the $\boldsymbol k$-point sampling. Benchmark calculations for both molecular and periodic systems collectively validate the accuracy of the present implementation and establish the dual-$\boldsymbol k$-mesh strategy as a practical and reliable approach for $GW$+BSE calculations.

cond-mat.mtrl-sci↗

arXiv2026

$G^0W^0$ implementation based on the pseudopotential and numerical-atomic-orbital basis-set framework: Algorithms and benchmarks

The $GW$ method delivers substantially improved accuracy in electronic band structure calculations over conventional Kohn-Sham density functional theory (KS-DFT) by explicitly incorporating the electron self-energy effect beyond mean-field approximations. Despite many existing implementations, a periodic $GW$ implementation within the framework of numerical atomic orbitals (NAO) combined with the pseudopotential (PP) scheme has not been reported. This is urgently needed given the increasing popularity of the NAO-PP framework in KS-DFT calculations and its importance for the development of machine-learning electronic-structure approaches. In this work, we present an efficient NAO-PP-based $G^0W^0$ computational framework by interfacing the first-principles software package ABACUS with LibRPA -- a library for performing low-scaling random-phase approximation and $GW$ calculations based on NAOs. Our approach employs the localized resolution of identity (LRI) technique with a novel compression scheme, significantly improving both computational efficiency and numerical stability. In addition, an analytic treatment of the small-q limit of the microscopic dielectric function reduces the need for dense q-point sampling. Furthermore, we propose a practical strategy to select a suitable KS-DFT pseudopotential prior to $G^0W^0$ calculations by examining the frequency-dependent macroscopic dielectric function. Systematic benchmarks validate the effectiveness of our compression scheme and real-space tensor filtering strategies, demonstrating both high accuracy and significant computational efficiency gains. Comparisons with established $G^0W^0$ implementations show excellent agreement in band structures and band gaps, confirming ABACUS+LibRPA as a reliable and efficient platform for large-scale $G^0W^0$ simulations.

cond-mat.mtrl-sci↗

arXiv2026

Low-scaling \textit{GW} calculations of quasi-particle energies for extended systems within the numerical atomic orbital framework

The many-body perturbation theory within the $GW$ approximation is a widely used method for describing the electronic band structures in real materials. Its application to large-scale systems is, however, impeded by its high computational cost. The rate-limiting steps in a typical $GW$ implementation are the evaluation of the polarization function under the random phase approximation (RPA) and the evaluation of the $GW$ self-energy, both of which have a canonical $O(N^4)$ scaling with $N$ being the system size. The conventional space-time algorithm within the plane-wave basis sets reduces the scaling from $O(N^4)$ to $O(N^3)$, albeit with a large prefactor and increased memory cost. Here, we present a space-time algorithm within the numerical atomic orbital (NAO) basis-set framework, for which the evaluation of the polarization function and self-energy is formally reduced to $O(N^2)$ or better with respect to system size. This is achieved by computing these quantities in real space, where low-scaling algorithms can be formulated by leveraging the localized resolution of identity (LRI) technique. The resulting NAO-based, LRI-enhanced space-time $GW$ algorithm has been implemented in the LibRPA library interfaced with the FHI-aims code package. Benchmark calculations for crystalline solids show that the low-scaling implementation yields quasi-particle energies in close agreement with the conventional $O(N^4)$ k-space formalism previously implemented in FHI-aims. For the systems studied here, the observed overall scaling is substantially reduced relative to the canonical approach, and the low-scaling implementation becomes advantageous already for systems containing fewer than 100 atoms.

cond-mat.mtrl-sci↗

arXiv2026

All-electron Quasiparticle Self-consistent GW for Molecules and Periodic Systems within the Numerical Atomic Orbital Framework

We report an all-electron implementation of the quasiparticle self-consistent GW (QSGW) method for molecular and periodic systems within the framework of numerical atomic orbitals (NAOs), as implemented in the LibRPA software package. Our implementation is based on the space-time formalism, combined with the localized resolution-of-identity approximation to treat two-electron quantities. We found that analytical continuation of the self-energy matrix, in combination with the ``Mode B" QSGW scheme, can yield stable self-consistent quasiparticle energy spectra. Systematic benchmark calculations on molecules and crystalline solids (including typical semiconductors and wide-gap insulators) demonstrate that our NAO-based QSGW scheme yields molecular ionization potentials and quasiparticle band gaps for periodic solids that are consistent with reference results from established implementations. Our work opens the way for large-scale QSGW calculations, taking advantage of the NAO-based low-scaling algorithm previously developed for the G0W0 method.

cond-mat.mtrl-sci↗

arXiv2025

Applying Space-Group Symmetry to Speed up Hybrid-Functional Calculations within the Framework of Numerical Atomic Orbitals

Building upon the efficient implementation of hybrid density functionals (HDFs) for large-scale periodic systems within the framework of numerical atomic orbital bases using the localized resolution of identity (RI) technique, we have developed an algorithm that exploits the space group symmetry in key operation steps of HDF calculations, leading to further improvements in two ways. First, the reduction of $\mathbf{k}$-points in the Brillouin zone can reduce the number of Kohn-Sham equations to be solved. This necessitates the correct implementation of the rotation relation between the density matrices of equivalent $\mathbf{k}$-points within the representation of atomic orbitals. Second, the reduction of the real-space sector can accelerate the construction of the exact-exchange part of the Hamiltonian in real space. We have implemented this algorithm in the ABACUS software interfaced with LibRI, and tested its performance for several types of crystal systems with different symmetries. The expected speed-up is achieved in both aspects: the time of solving the Kohn-Sham equations decreases in proportion with the reduction of $\mathbf{k}$-points, while the construction of the Hamiltonian in real space is sped up by several times, with the degree of acceleration depending on the size and symmetry of the system.

physics.comp-ph↗

arXiv2024

Precision benchmarks for solids: G0W0 calculations with different basis sets

The GW approximation within many-body perturbation theory is the state of the art for computing quasiparticle energies in solids. Typically, Kohn-Sham (KS) eigenvalues and eigenfunctions, obtained from a Density Functional Theory (DFT) calculation are used as a starting point to build the Green's function G and the screened Coulomb interaction W, yielding the one-shot G0W0 selfenergy if no further update of these quantities are made. Multiple implementations exist for both the DFT and the subsequent G0W0 calculation, leading to possible differences in quasiparticle energies. In the present work, the G0W0 quasiparticle energies for states close to the band gap are calculated for six crystalline solids, using four different codes: Abinit, exciting, FHI-aims, and GPAW. This comparison helps to assess the impact of basis-set types (planewaves versus localized orbitals) and the treatment of core and valence electrons (all-electron full potentials versus pseudopotentials). The impact of unoccupied states as well as the algorithms for solving the quasiparticle equation are also briefly discussed. For the KS-DFT band gaps, we observe good agreement between all codes, with differences not exceeding 0.1 eV, while the G0W0 results deviate on the order of 0.1-0.3 eV. Between all-electron codes (FHI-aims and exciting), the agreement is better than 15 meV for KS-DFT and, with one exception, about 0.1 eV for G0W0 band gaps.

cond-mat.mtrl-sci↗

arXiv2024

Temperature-dependent Electronic Spectral Functions from Band-Structure Unfolding

The electronic band structure, describing the periodic dependence of electronic quantum states on lattice momentum in reciprocal space, is a fundamental concept in solid-state physics. However, it's only well-defined for static nuclei. To account for thermodynamic effects, this concept must be generalized by introducing the temperature-dependent spectral function, which characterizes the finite-width distributions of electronic quantum states at each reciprocal vector. Many-body perturbation theory can compute spectral functions and associated observables, but it approximates the dynamics of nuclei and its coupling to the electrons using the harmonic approximation and linear-order electron-phonon coupling elements, respectively. These approximations may fail at elevated temperatures or for mobile atoms. To avoid inaccuracies, the electronic spectral function can be obtained non-perturbatively, capturing higher-order couplings between electrons and vibrational degrees of freedom. This process involves recovering the representation of supercell bands in the first Brillouin zone of the primitive cell, a process known as unfolding. In this contribution, we describe the implementation of the band-structure unfolding technique in the electronic-structure theory package FHI-aims and the updates made since its original development.

cond-mat.mtrl-sci↗

arXiv2024

LibRPA: A Software Package for Low-scaling First-principles Calculations of Random Phase Approximation Electron Correlation Energy Based on Numerical Atomic Orbitals

LibRPA is a software package designed for efficient calculations of random phase approximation (RPA) electron correlation energies from first principles using numerical atomic orbital (NAOs). Leveraging a localized resolution of identity (LRI) technique, LibRPA achieves $O(N^2)$ or better scaling behavior, making it suitable for large-scale calculation of periodic systems. Implemented in C++ and Python with MPI/OpenMP parallelism, LibRPA integrates seamlessly with NAO-based density functional theory (DFT) packages through flexible file-based and API-based interfaces. In this work, we present the theoretical framework, algorithm, software architecture, and installation and usage guide of LibRPA. Performance benchmarks, including the parallel efficiency with respect to the computational resources and the adsorption energy calculations for H$_2$O molecules on graphene, demonstrate its nearly ideal scalability and numerical reliability. LibRPA offers a useful tool for RPA-based calculations for large-scale extended systems.

cond-mat.mtrl-sci↗

arXiv2023

Sub-quadratic scaling real-space random-phase approximation correlation energy calculations for periodic systems with numerical atomic orbitals

The random phase approximation (RPA) as formulated as an orbital-dependent, fifth-rung functional within the density functional theory (DFT) framework offers a promising approach for calculating the ground-state energies and the derived properties of real materials. Its widespread use to large-size, complex materials is however impeded by the significantly increased computational cost, compared to lower-rung functionals. The standard implementation exhibits an $\mathcal{O}(N^4)$-scaling behavior with respect to system size $N$. In this work, we develop a low-scaling RPA algorithm for periodic systems, based on the numerical atomic orbital (NAO) basis-set framework and a localized variant of the resolution of identity (RI) approximation. The rate-determining step for RPA calculations -- the evaluation of non-interacting response function matrix, is reduced from $\mathcal{O}(N^4)$ to $\mathcal{O}(N^2)$ by just exploiting the sparsity of the RI expansion coefficients, resultant from localized RI (LRI) scheme and the strict locality of NAOs. The computational cost of this step can be further reduced to linear scaling if the decay behavior of the Green's function in real space can be further taken into account. Benchmark calculations against existing $\textbf k$-space based implementation confirms the validity and high numerical precision of the present algorithm and implementation. The new RPA algorithm allows us to readily handle three-dimensional, closely-packed solid state materials with over 1000 atoms. The algorithm and numerical techniques developed in this work also have implications for developing low-scaling algorithms for other correlated methods to be applicable to large-scale extended materials.

physics.comp-ph↗

arXiv2020

The influence of high-energy local orbitals and electron-phonon interactions on the band gaps and optical spectra of hexagonal boron nitride

We report $ab$ $initio$ band diagram and optical absorption spectra of hexagonal boron nitride ($h$-BN), focusing on unravelling how the completeness of basis set for $GW$ calculations and how electron-phonon interactions (EPIs) impact on them. The completeness of basis set, an issue which was seldom discussed in previous optical spectra calculations of $h$-BN, is found crucial in providing converged quasiparticle band gaps. In the comparison among three different codes, we demonstrate that by including high-energy local orbitals in the all-electron linearized augmented plane waves based $GW$ calculations, the quasiparticle direct and fundamental indirect band gaps are widened by $\sim$0.2 eV, giving values of 6.81 eV and 6.25 eV respectively at the $GW_0$ level. EPIs, on the other hand, reduce them to 6.62 eV and 6.03 eV respectively at 0 K, and 6.60 eV and 5.98 eV respectively at 300 K. With clamped crystal structure, the first peak of the absorption spectrum is at 6.07 eV, originating from the direct exciton contributed by electron transitions around $K$ in the Brillouin zone. After including the EPIs-renormalized quasiparticles in the Bethe-Salpeter equation, the exciton-phonon coupling shifts the first peak to 5.83 eV at 300 K, lower than the experimental value of $\sim$6.00 eV. This accuracy is acceptable to an $ab$ $initio$ description of excited states with no fitting parameter.

cond-mat.mtrl-sci↗

arXiv2019

Electronic Band Structure of Cuprous and Silver Halides: a Numerically Accurate All-Electron $GW$ Study

Group IB metal halides (CuX and AgX, X=Cl, Br and I) are widely used in optoelectronic devices and photochemical catalysis due to their appropriate optical and electronic properties. First-principles calculations have confronted difficulties in accurately predicting their electronic band structures. Here we study CuX and AgX with many-body perturbation theory in the $GW$ approximation, implemented in the full-potential linearized augmented plane waves (FP-LAPW) framework. Comparing the quasi-particle band structures calculated with the default LAPW basis and the one extended by high-energy local orbitals (HLOs), denoted as LAPW+HLOs, we find that it is crucial to include HLOs to achieve sufficient numerical accuracy in $GW$ calculations of these materials. Using LAPW+HLOs in semi-local density functional approximation based $GW_0$ calculations leads to good agreement between theory and experiment for both band gaps and the splitting between metal (Cu or Ag) $d$ and X-$p$ states. It is indicated that quasi-particle band structures of CuX and AgX are crucially influenced by the numerical accuracy of $GW$ implementations, similar to what was found in ZnO [Jiang, H.; Blaha, P. Phys. Rev. B 2016, 93, 115203]. This work emphasizes the importance of numerical accuracy in the description of unoccupied states for quasi-particle band structure of materials with the $d^{10}$ electronic configuration.

cond-mat.mtrl-sci↗