arXiv subjects

Weitao Yang

Publications and source records attributed to Weitao Yang.

At least 19 recordsLinked to original sources

arXiv2026

libNLPBE: An Open-Source Python Package for Solving the Non-Linear Poisson-Boltzmann Equation

Solvent environments surrounding a solute can significantly alter its chemical properties. These changes become more prominent in electrolyte solutions, where mobile ions largely influence the solute through electrostatic interactions. A theoretical description of these ionic effects will benefit the design of chemistry performed in electrolyte solutions. As a result, the non-linear Poisson-Boltzmann equation (NLPBE) has emerged as an efficient implicit solvent model for electronic structure calculations to address such effects. However, the limited availability of NLPBE solvers for molecular electronic structure calculations greatly hinders theoretical investigation into the ionic effects. To improve accessibility of the NLPBE, we present libNLPBE, an open-source Python library, that solves the NLPBE for molecular systems in combination with density functional calculations, specifically to obtain electrostatic correction terms arising from the electrolyte solution environment for the Fock matrix. The library employs the density fitting (DF) approximation to efficiently calculate solute electrostatic potentials. Furthermore, we develop the modified Damped Inexact Newton Multigrid developed by Holst (mDINMH) method for solving the NLPBE. The mDINMH features a symmetric preconditioner for solving the Newton equation, which enables the use of robust multigrid methods designed for symmetric linear operators. In addition, an algebraic multigrid method has been incorporated into the mDINMH to support a broad range of grid points. We also present a GPU-accelerated version of libNLPBE to leverage parallelization efficiency of GPUs.

physics.chem-ph↗

arXiv2026

Eliminating Delocalization Error through Localized Orbital Scaling Correction with Orbital Relaxation from Linear Response

Despite the great success that Kohn-Sham density functional theory (KS-DFT) has achieved, the delocalization error remains a major challenge for commonly used density functional approximations (DFAs), resulting in systematic errors in ionization energies, electron affinities, band structures, and charge distributions. A recently developed localized orbital scaling correction (LOSC) method, namely linear response LOSC (lrLOSC), addresses these challenges by incorporating a functional correction that includes the screening effect and orbital localization within the LOSC framework. The method has been shown to provide accurate descriptions of bulk systems and core-level binding energies in small molecular systems. In this work, we extend the applicability of lrLOSC to a broader range of molecular systems, spanning various sizes, with a focus on the corrections to valence orbital energies and total energies. To enable the calculation of large chemical systems, we developed an efficient implementation of lrLOSC with computational costs comparable to standard KS-DFT calculations. Numerical results show that, while screening provides modest improvements for small molecules, it becomes critical for achieving high accuracy in larger molecules, from linear to three-dimensional systems. With the screening effect well captured in a unified way, lrLOSC provides accurate descriptions for a wide range of chemical systems, including organic molecular systems of varying sizes and transition-metal oxide complexes, establishing it as a powerful tool for enhancing the reliability of computational simulations of chemical systems.

physics.chem-ph↗

arXiv2026

Excited States from Quasiparticle Hamiltonian Based on Density Functional Theory

Recent advances in occupancy extrapolation (OE) show that potential of orbital-occupation based energy functions can describe electronic excitations. Here, the OE method in the particle-hole channel is extended to an effective quasiparticle Hamiltonian, enabling a multi-configurational description beyond single-determinant OE and $Δ$SCF. The method performs comparably to the Bethe-Salpeter equation for valence singlet and charge-transfer excitations, and better for valence triplet and Rydberg states, supporting its accuracy and broad applicability.

physics.chem-ph↗

arXiv2026

PyGSC: A Python tool for correcting Kohn-Sham orbital energies by mitigating the delocalization error of density functional approximations

Density functional approximations (DFAs) suffer from delocalization error, which limits their accuracy in predicting electron affinities (EAs), ionization potentials (IPs), and quasiparticle energies. In this work, we present a theoretical refinement of the quasiparticle energies from density functional theory (QE-DFT) method by improving the perturbative expression for the exchange-correlation potential, leading to a more consistent description of molecular systems. We further develop an open-source Python program, PyGSC, built upon the PySCF library, which implements the modified QE-DFT framework. Benchmark tests on main-group atoms and G2/97 molecules demonstrate that the modified QE-DFT method outperforms the original DFAs, with third-order corrections achieving mean absolute deviations below 0.3 eV for EA and IP predictions. Application to dipole-bound states of DNA/RNA nucleobases further validates the superiority of the QE-DFT approach over original DFAs, offering an efficient and accurate approach for predicting electronic properties in large molecular systems.

physics.chem-ph↗

arXiv2026

Occupancy Extrapolation: Reaching Many Excited Electronic States from Ground State Calculations

The $Δ$SCF DFT approach defines the system energy as a function of orbital occupancy. Inspired by Landau Fermi liquid theory, we develop an occupancy extrapolation (OE) method that captures excited-state energies via a Taylor expansion of the energy with respect to occupation fluctuation from a reference state. OE retains the physics of $Δ$SCF while offering a physical interpretation of excitation energies as sums of quasiparticle energies and their generalized screened interactions. It yields accurate valence, Rydberg, and charge-transfer excitation energies at $O(N^3)$ cost, avoids separate SCF calculations for each excited state, and enables efficient large-scale excited-state simulations from ground-state calculations.

physics.chem-ph↗

arXiv2026

olLOSC: Unified and efficient density functional approximation to correct delocalization error in molecules and periodic materials

Density functional theory (DFT) is the most promising method for calculating quantum properties of molecules and materials at moderate and large scales. However, commonly used density functional approximations (DFAs) have systematic delocalization error, as demonstrated by underestimated band gaps, over-delocalized charges, and energy level misalignment at interfaces, which limits its quantitative prediction. Extensive efforts, such as the $GW$ approximation to many-body perturbation theory, system-specific tuning of DFA parameters, and correction functionals have been developed to address delocalization error. However, an accurate, efficient, and unified solution to describe total energy, charge density and band structure for both finite systems and materials is still not available. Building on the linear-response localized orbital scaling correction (lrLOSC), we introduce olLOSC: a localized orbital scaling correction with curvature calculated by orbital-free electronic linear response. olLOSC has comparable accuracy to lrLOSC, but is much more computationally efficient. olLOSC corrects delocalization error - especially underestimated gaps, but also the total energy - both in molecules and in materials with small and moderate band gaps, within the same orbital-free approximation. Critically, with a a unified approximation, olLOSC opens the path for robust and efficient DFT applications across molecules, materials, and interfaces.

physics.chem-ph↗

arXiv2026

Derivative Discontinuity in Many-Body Perturbation Theory and Chemical Potentials in Random Phase Approximation

We derive analytical expressions for chemical potentials within the random phase approximation (RPA), equivalently the $GW$ energy functional evaluated using non interacting Green's functions ($G_s$). The chemical potential is obtained using two formally equivalent approaches: a direct derivative of the total energy with respect to particle number, and a functional derivative via the chain rule through $G_s$, both validated with finite difference benchmarks. We show that the functional derivative of the $GW$ correlation energy$\unicode{x2013}$i.e., the $GW$ correlation self energy$\unicode{x2013}$exhibits a discontinuity at integer particle numbers with finite jumps. This resolves the apparent inconsistency between accurate $GW$ quasiparticle energies and the large delocalization errors observed in RPA total energies, as standard $GW$ self energies neglect this nonanalytic behavior. Our results suggest that derivative discontinuities are a fundamental feature of correlation energy functionals, analogous to the known discontinuity in the exact exchange correlation energy.

physics.chem-ph↗

arXiv2026

Velocity Gauge for Oscillator Strength in $Δ$SCF theory

Delta self-consistent-field ($Δ$SCF) theory is widely used for electronic excitation energy calculations. However, calculating the corresponding oscillator strengths is challenging. The corresponding many-electron wavefunctions are not directly accessible. Both the ground-state and the excited-state wave functions from $Δ$SCF are described by reference Kohn-Sham (KS) single-determinant wavefunctions for the fictitious non-interacting systems. The non-orthogonality between the ground and excited Kohn-Sham determinants from two different SCF calculations leads to unphysically origin-dependent transition properties, such as transition dipole moment and length-gauge oscillator strength. Including nuclei contribution in the perturbation is theoretically rigorous, but its effectiveness is only limited to neutral systems, as we show theoretically and numerically. While several other practical approaches have been proposed to tackle the non-orthogonality problem and yield reasonable results, inevitably the determinant of the ground state or the excited state is changed, as well as the density matrix. In this work, we explore the use of the velocity gauge to compute oscillator strength within $Δ$SCF theory. We demonstrate that the velocity gauge is capable of naturally accounting for the non-orthogonality of $Δ$SCF KS wavefunctions and offering origin-independent predictions without any additional correction schemes to the KS wavefunctions. Compared to the length-gauge results obtained via symmetric orthogonalization, velocity gauge can offer comparable results. Furthermore, the adoption of spin-purified singlet excitation energy in the velocity-gauge transition dipole moment significantly enhances the overall performance of the velocity gauge for $Δ$SCF oscillator strength predictions on conjugated chromophores.

physics.chem-ph↗

arXiv2025

LibppRPA: An Open-Source Library for Particle-Particle Random Phase Approximation

The accurate description of electron correlation and excitation energies remains a fundamental challenge in quantum chemistry. The particle-particle random phase approximation (ppRPA) has emerged as a promising method for capturing a broad range of excited-state properties. However, the implementation of ppRPA has been largely limited to in-house software, restricting its accessibility and usability. In this work, we present LibppRPA, an open-source and lightweight Python library designed for efficient and flexible ppRPA calculations of (1) electronic excitation energy and its associated analytical gradients and (2) the ground state correlation energy, and its associated analytical gradients. LibppRPA enables seamless integration with existing quantum chemistry packages, such as PySCF, by utilizing occupation numbers, molecular orbital coefficients, and three-center electron repulsion integrals. We implement both direct diagonalization and the iterative Davidson algorithm for solving the ppRPA equations, as well as active-space approximations, allowing users to balance accuracy and computational efficiency. We demonstrate the performance of LibppRPA through benchmark calculations on singlet-triplet gaps, double excitations, charge-transfer excitations, and valence/Rydberg excitations, showcasing its reliability across diverse molecular systems. The library provides a robust platform for studying electronic excitations and offers new opportunities for future developments in electronic structure theory.

physics.chem-ph↗

arXiv2025

Correcting Delocalization Error in Materials with Localized Orbitals and Linear-Response Screening

Delocalization error prevents density functional theory (DFT) from reaching its full potential, causing problems like systematically underestimated band gaps and misaligned energy levels at interfaces. We introduce lrLOSC to correct delocalization error in materials over a wide range of band gaps. We predict eleven materials' fundamental gaps to within 0.22 eV, while offering a nonzero total energy correction; molecular properties are improved with a parallel implementation of the same theory [J. Phys. Chem. Lett. 16, 2492 (2025)]. lrLOSC is an essential step toward modeling molecules, materials, and their interfaces within the same DFT framework.

cond-mat.mtrl-sci↗

arXiv2025

Wannier Functions Dually Localized in Space and Energy

The construction of Wannier functions from Bloch orbitals offers a unitary freedom that can be exploited to yield Wannier functions with advantageous properties. Minimizing the spatial variance is a well-known choice; another, previously proposed for Wannier functions constructed from the occupied Bloch manifold, minimizes a weighted sum of spatial and energy variance. Departing from all previous work, we extend dual localization to include both valence and conduction bands together. Near the Fermi energy, these dually localized Wannier functions yield frontier (bonding and antibonding) orbitals in bulk silicon and molecular ethylene, as well as $d$-orbital character in metallic copper. Because they are both localized and retain information about the orbital energy spectrum, dually localized Wannier functions are well suited to orbital-dependent methods that associate Wannier functions with specific energy ranges. They naturally induce fractional occupations, allowing for corrections to the DFA total energy.

cond-mat.mtrl-sci↗

arXiv2025

Large-Scale Contextual Market Equilibrium Computation through Deep Learning

Market equilibrium is one of the most fundamental solution concepts in economics and social optimization analysis. Existing works on market equilibrium computation primarily focus on settings with relatively few buyers. Motivated by this, our paper investigates the computation of market equilibrium in scenarios with a large-scale buyer population, where buyers and goods are represented by their contexts. Building on this realistic and generalized contextual market model, we introduce MarketFCNet, a deep learning-based method for approximating market equilibrium. We start by parameterizing the allocation of each good to each buyer using a neural network, which depends solely on the context of the buyer and the good. Next, we propose an efficient method to unbiasedly estimate the loss function of the training algorithm, enabling us to optimize the network parameters through gradient. To evaluate the approximated solution, we propose a metric called Nash Gap, which quantifies the deviation of the given allocation and price pair from the market equilibrium. Experimental results indicate that MarketFCNet delivers competitive performance and significantly lower running times compared to existing methods as the market scale expands, demonstrating the potential of deep learning-based methods to accelerate the approximation of large-scale contextual market equilibrium.

cs.GT↗

arXiv2025

NepoIP/MM: Towards Accurate Biomolecular Simulation with a Machine Learning/Molecular Mechanics Model Incorporating Polarization Effects

Machine learning force fields offer the ability to simulate biomolecules with quantum mechanical accuracy while significantly reducing computational costs, attracting growing attention in biophysics. Meanwhile, leveraging the efficiency of molecular mechanics in modeling solvent molecules and long-range interactions, a hybrid machine learning/molecular mechanics (ML/MM) model offers a more realistic approach to describing complex biomolecular systems in solution. However, multiscale models with electrostatic embedding require accounting for the polarization of the ML region induced by the MM environment. To address this, we adapt the state-of-the-art NequIP architecture into a polarizable machine learning force field, NepoIP, enabling the modeling of polarization effects based on the external electrostatic potential. We found that the nanosecond MD simulations based on NepoIP/MM are stable for the periodic solvated dipeptide system and the converged sampling shows excellent agreement with the reference QM/MM level. Moreover, we show that a single NepoIP model can be transferable across different MM force fields, as well as extremely different MM environment of water and proteins, laying the foundation for developing a general machine learning biomolecular force field to be used in ML/MM with electrostatic embedding.

physics.chem-ph↗

arXiv2024

Accurate and Efficient Prediction of Double Excitation Energies Using the Particle-Particle Random Phase Approximation

Double excitations are crucial to understanding numerous chemical, physical, and biological processes, but accurately predicting them remains a challenge. In this work, we explore the particle-particle random phase approximation (ppRPA) as an efficient and accurate approach for computing double excitation energies. We benchmark ppRPA using various exchange-correlation functionals for 21 molecular systems and two point defect systems. Our results show that ppRPA with functionals containing appropriate amounts of exact exchange provides accuracy comparable to high-level wave function methods such as CCSDT and CASPT2, with significantly reduced computational cost. Furthermore, we demonstrate the use of ppRPA starting from an excited ($N-2$)-electron state calculated by $Δ$SCF for the first time, as well as its application to double excitations in bulk periodic systems. These findings suggest that ppRPA is a promising tool for the efficient calculation of double and partial double excitation energies in both molecular and bulk systems.

physics.chem-ph↗

arXiv2024

Fractional Charges, Linear Conditions and Chemical Potentials for Excited States in $ΔSCF$ Theory

To describe excited states, the electron density alone being insufficient, we use the noninteracting reference density matrix $γ_{s}({\bf x},{\bf x}')$ based on the recently established foundation for the $ΔSCF$ theory, in which ground and excited state energies and densities are obtained from the minimum and stationary solutions of the same functional. We now extend the theory to fractional charges. Based on the exact properties of degeneracy and size consistency, we show that the exact energy functional for fractional charges, expressed as a linear combination of the $γ_{s}$ of an $N-$electron and that of an $\left(N+1\right)-$electron excited state, is a straight line interpolating the energies at integers. We introduce the concepts of excited-state chemical potentials to describe the slopes of these linear lines. Numerical calculations reveal the excited-state delocalization error with common approximate functionals but good performance of corrected functionals on the proven linear conditions.

physics.chem-ph↗

arXiv2024

Orbital Energies Are Chemical Potentials in Ground-State Density Functional Theory and Excited-State $Δ$SCF Theory

We prove the general chemical potential theorem: the noninteracting one-electron orbital energies in DFT ground states and $Δ$SCF excited states are corresponding chemical potentials of electron addition or removal, from an $N$-particle ground or excited state to an $(N\pm1)$-particle ground or excited state. This greatly extends the previous ground state results. Combining with the recently developed exact linear conditions for fractional charges in excited states, where the slopes of the linear lines are defined as the excited-state chemical potentials, our result establish the physical meaning of orbital energies as approximation to the corresponding excited-state ionization potentials and electron affinities, for both ground and excited states of a molecule or a bulk system. To examine the quality of this approximation we demonstrate numerically significant delocalization error in commonly used functionals and excellent agreement in functionals correcting the delocalization error.

physics.chem-ph↗

arXiv2024

Particle-Particle Random Phase Approximation for Predicting Correlated Excited States of Point Defects

The particle-particle random phase approximation (ppRPA) within the hole-hole channel was recently proposed as an efficient tool for computing excitation energies of point defects in solids [J. Phys. Chem. Lett. 2024, 15, 2757-2764]. In this work, we investigate the application of ppRPA within the particle-particle channel for predicting correlated excited states of point defects, including the carbon-vacancy (VC) in diamond, the oxygen-vacancy (VO) in magnesium oxide (MgO), and the carbon dimer defect (C$_{\text{B}}$C$_{\text{N}}$) in two-dimensional hexagonal boron nitride (h-BN). Starting from a density functional theory calculation of the ($N-2$)-electron ground state, vertical excitation energies of the $N$-electron system are obtained as the differences between the two-electron addition energies. We show that active-space ppRPA with the B3LYP functional yields accurate excitation energies, with errors mostly smaller than 0.1 eV for tested systems compared to available experimental values. We further develop a natural transition orbital scheme within ppRPA, which provides insights into the multireference character of defect states. This study, together with our previous work, establishes ppRPA as a low-cost and accurate method for investigating excited-state properties of point defect systems.

physics.chem-ph↗

arXiv2024

Accurate Prediction of Core Level Binding Energies from Ground-State Density Functional Calculations: The Importance of Localization and Screening

A new method for predicting core level binding energies (CLBEs) is developed by both localizing the core-level states and describing the screening effect. CLBEs contain important information about the electronic structure, elemental chemistry, and chemical environment of molecules and materials. Theoretical study of CLBEs can provide insights for analyzing and interpreting the experimental results obtained from the X-ray photoelectron spectroscopy, in which the overlapping of signals is very common. The localization of core-level holes is important for the theoretical calculation of CLBEs. Predicting CLBEs from commonly used density functional approximations (DFAs) is challenging, because conventional DFAs often produce delocalized core-level states, especially when degenerate core-level states exist. In this work, we combine the localization procedure from the localized orbital scaling correction method and the curvature matrix generalized from the exact second-order correction method that contains the screening effect, and the resulting approach can accurately predict CLBEs from ground-state density functional calculations.

physics.chem-ph↗