arXiv subjects

Weitao Yang

Publications and source records attributed to Weitao Yang.

At least 37 records · Page 2Linked to original sources

arXiv2024

Chemical Potentials and the One-Electron Hamiltonian of the Second-Order Perturbation Theory from the Functional Derivative Approach

We develop a functional derivative approach to calculate the chemical potentials of the second-order perturbation theory (MP2). In the functional derivative approach, the correlation part of the MP2 chemical potential, which is the derivative of the MP2 correlation energy with respect to the occupation number of frontier orbitals, is obtained from the chain rule via the non-interacting Green's function. First, the MP2 correlation energy is expressed in terms of the non-interacting Green's function and its functional derivative to the non-interacting Green's function is the second-order self-energy. Then the derivative of the non-interacting Green's function to the occupation number is obtained by including the orbital relaxation effect. We show that the MP2 chemical potentials obtained from the functional derivative approach agrees with that obtained from the finite difference approach. The one-electron Hamiltonian, defined as the derivative of the MP2 energy with respect to the one particle density matrix, is also derived using the functional derivative approach, which can be used in the self-consistent calculations of MP2 and double-hybrid density functionals. The developed functional derivative approach is promising for calculating the chemical potentials and the one-electron Hamiltonian of approximate functionals and many-body perturbation approaches dependent explicitly on the non-interacting Green's function.

physics.chem-ph↗

arXiv2024

Foundation for the ΔSCF Approach in Density Functional Theory

We extend ground-state density-functional theory to excited states and provide the theoretical formulation for the widely used $ΔSCF$ method for calculating excited-state energies and densities. As the electron density alone is insufficient to characterize excited states, we formulate excited-state theory using the defining variables of a noninteracting reference system, namely (1) the excitation quantum number $n_{s}$ and the potential $w_{s}(\mathbf{r})$ (excited-state potential-functional theory, $n$PFT), (2) the noninteracting wavefunction $Φ$ ($Φ$-functional theory, $Φ$FT), or (3) the noninteracting one-electron reduced density matrix $γ_{s}(\mathbf{r},\mathbf{r}')$ (density-matrix-functional theory, $γ_{s}$FT). We show the equivalence of these three sets of variables and their corresponding energy functionals. Importantly, the ground and excited-state exchange-correlation energy use the \textit{same} universal functional, regardless of whether $\left(n_{s},w_{s}(\boldsymbol{r})\right)$, $Φ$, or $γ_{s}(\mathbf{r},\mathbf{r}')$ is selected as the fundamental descriptor of the system. We derive the excited-state (generalized) Kohn-Sham equations. The minimum of all three functionals is the ground-state energy and, for ground states, they are all equivalent to the Hohenberg-Kohn-Sham method. The other stationary points of the functionals provide the excited-state energies and electron densities, establishing the foundation for the $ΔSCF$ method.

physics.chem-ph↗

arXiv2024

Accurate Excitation Energies of Point Defects from Fast Particle-Particle Random Approximation Calculations

We present an efficient particle-particle random phase approximation (ppRPA) approach that predicts accurate excitation energies of point defects, including the nitrogen-vacancy (NV$^-$) and the silicon-vacancy (SiV$^0$) centers in diamond and the divacancy center (VV$^0$) in 4H silicon carbide, with errors within 0.2 eV compared with experimental values. Starting from the ($N+2$)-electron ground state calculated with the density functional theory (DFT), the ppRPA excitation energies of the $N$-electron system are calculated as the differences between the two-electron removal energies of the ($N+2$)-electron system. We demonstrate that the ppRPA excitation energies converge rapidly with a few hundred of canonical active-space orbitals. We also show that active-space ppRPA has weak DFT starting-point dependence and is significantly cheaper than the corresponding ground-state DFT calculation. This work establishes ppRPA as an accurate and low-cost tool for investigating excited-state properties of point defects and opens up new opportunities for applications of ppRPA to periodic bulk materials.

physics.chem-ph↗

arXiv2023

Linear Scaling Calculations of Excitation Energies with Active-Space Particle-Particle Random Phase Approximation

We developed an efficient active-space particle-particle random phase approximation (ppRPA) approach to calculate accurate charge-neutral excitation energies of molecular systems. The active-space ppRPA approach constrains both indexes in particle and hole pairs in the ppRPA matrix, which only selects frontier orbitals with dominant contributions to low-lying excitation energies. It employs the truncation in both orbital indexes in the particle-particle and the hole-hole spaces. The resulting matrix, the eigenvalues of which are excitation energies, has a dimension that is independent of the size of the systems. The computational effort for the excitation energy calculation, therefore, scales linearly with system size and is negligible compared with the ground-state calculation of the (N-2)-electron system, where N is the electron number of the molecule. With the active space consisting of 30 occupied and 30 virtual orbitals, the active-space ppRPA approach predicts excitation energies of valence, charge-transfer, Rydberg, double and diradical excitations with the mean absolute errors (MAEs) smaller than 0.03 eV compared with the full-space ppRPA results. As a side product, we also applied the active-space ppRPA approach in the renormalized singles (RS) T-matrix approach. Combining the non-interacting pair approximation that approximates the contribution to the self-energy outside the active space, the active-space $G_{\text{RS}}T_{\text{RS}}$@PBE approach predicts accurate absolute and relative core-level binding energies with the MAE around 1.58 eV and 0.3 eV, respectively. The developed linear scaling calculation of excitation energies is promising for applications to large and complex systems.

physics.chem-ph↗

arXiv2022

Combining Renormalized Singles $GW$ Methods with the Bethe-Salpeter Equation for Accurate Neutral Excitation Energies

We apply the renormalized singles (RS) Green's function in the Bethe-Salpeter equation (BSE)/$GW$ approach to predict accurate neutral excitation energies of molecular systems. The BSE calculations are performed on top of the $G_{\text{RS}}W_{\text{RS}}$ method, which uses the RS Green's function also for the computation of the screened Coulomb interaction $W$. We show that the BSE/$G_{\text{RS}}W_{\text{RS}}$ approach significantly outperforms BSE/$G_0W_0$ for predicting excitation energies of valence, Rydberg and charge transfer (CT) excitations by benchmarking the Truhlar-Gagliardi set, Stein CT set and an atomic Rydberg test set. For the Truhlar-Gagliardi test set, BSE/$G_{\text{RS}}W_{\text{RS}}$ provides comparable accuracy to time-dependent density functional theory (TDDFT) and is slightly better than BSE starting from eigenvalue self-consistent $GW$ (ev$GW$). For the Stein CT test set, BSE/$G_{\text{RS}}W_{\text{RS}}$ significantly outperforms BSE/$G_0W_0$ and TDDFT with the accuracy comparable to BSE/ev$GW$. We also show that BSE/$G_{\text{RS}}W_{\text{RS}}$ predicts Rydberg excitation energies of atomic systems well. Besides the excellent accuracy, BSE/$G_{\text{RS}}W_{\text{RS}}$ largely eliminates the dependence on the choice of the density functional approximation. This work demonstrates that the BSE/$G_{\text{RS}}W_{\text{RS}}$ approach is accurate and efficient for predicting excitation energies for a broad range of systems, which expands the applicability of the BSE/$GW$ approach.

physics.chem-ph↗

arXiv2022

Renormalized Singles with Correlation in $GW$ Green's Function Theory for Accurate Quasiparticle Energies

We apply the renormalized singles with correlation (RSc) Green's function in the $GW$ approximation to calculate accurate quasiparticle (QP) energies and orbitals. The RSc Green's function includes all orders of singles contributions from the associated density functional approximation (DFA) and treats higher order contributions in a perturbative manner. The $G_{\text{RSc}}W_{\text{RSc}}$ method uses the RSc Green's function as the new starting point and calculates the screened interaction with the RSc Green's function. The $G_{\text{RSc}}W_0$ methods fixes the screened interaction at the DFA level. For the calculations of ionization potentials in the GW100 set, $G_{\text{RSc}}W_{\text{RSc}}$ significantly reduces the dependence on the starting point of DFAs used and provides accurate results with the mean absolute error (MAE) of $0.34$ eV comparable to ev$GW$. For the calculations of core-level binding energies in the CORE65 set, $G_{\text{RSc}}W_{\text{RSc}}$ slightly overestimates the results because of underscreening, but $G_{\text{RSc}}W_0$ with GGA functionals provides the optimal accuracy of $0.40$ eV MAE comparable to ev$GW_0$. We also show that $G_{\text{RSc}}W_{\text{RSc}}$ predicts accurate dipole moments of small molecules. These two methods, $G_{\text{RSc}}W_{\text{RSc}}$ and $G_{\text{RSc}}W_0$, are computationally much favorable than any flavor of self-consistent $GW$ methods. Thus, the RSc approach is promising for making $GW$ and other Green's function methods efficient and robust.

physics.chem-ph↗

arXiv2022

Multireference Density Functional Theory for Describing Ground and Excited States with Renormalized Singles

We applied renormalized singles (RS) in the multireference density functional theory (DFT) to calculate accurate energies of ground and excited states. The multireference DFT approach determines the total energy of the $N$-electron system as the sum of the ($N-2$)-electron energy from a density functional approximation (DFA) and the two-electron addition energies from the particle-particle Tamm-Dancoff approximation (ppTDA), naturally including multireference description. The ppTDA@RS-DFA approach uses the RS Hamiltonian capturing all singles contributions in calculating two-electron addition energies, and its total energy is optimized with the optimized effective potential method. It significantly improves the original ppTDA@DFA. For ground states, ppTDA@RS-DFA properly describes dissociation curves tested and the double bond rotation of ethylene. For excited states, ppTDA@RS-DFA provides accurate excitation energies and largely eliminates the DFA dependence. ppTDA@RS-DFA thus provides an efficient multireference approach to systems with static correlation.

physics.chem-ph↗

arXiv2022

Combining Localized Orbital Scaling Correction and Bethe-Salpeter Equation for Accurate Excitation Energies

We applied localized orbital scaling correction (LOSC) in Bethe-Salpeter equation (BSE) to predict accurate excitation energies for molecules. LOSC systematically eliminates the delocalization error in the density functional approximation and is capable of approximating quasiparticle (QP) energies with accuracy similar or better than the $GW$ Green's function approach and with much less computational cost. The QP energies from LOSC instead of commonly used $G_{0}W_{0}$ and ev$GW$ are directly used in BSE. We show that the BSE/LOSC approach greatly outperforms the commonly used BSE/$G_{0}W_{0}$ approach for predicting excitations with different characters. For the calculations for Truhlar-Gagliardi test set containing valence, charge transfer (CT) and Rydberg excitations, BSE/LOSC with the Tamm-Dancoff approximation provides a comparable accuracy to time-dependent density functional theory (TDDFT) and BSE/ev$GW$. For the calculations of Stein CT test set and Rydberg excitations of atoms, BSE/LOSC considerably outperforms both BSE/$G_{0}W_{0}$ and TDDFT approaches with a reduced starting point dependence. BSE/LOSC is thus a promising and efficient approach to calculate excitation energies for molecular systems.

physics.chem-ph↗

arXiv2022

Benchmark of $\boldsymbol{GW}$ Methods for Core-Level Binding Energies

The $GW$ approximation has recently gained increasing attention as a viable method for the computation of deep core-level binding energies as measured by X-ray photoelectron spectroscopy (XPS). We present a comprehensive benchmark study of different $GW$ methodologies (starting-point optimized, partial and full eigenvalue-self-consistent, Hedin shift and renormalized singles) for molecular inner-shell excitations. We demonstrate that all methods yield a unique solution and apply them to the CORE65 benchmark set and ethyl trifluoroacetate. Three $GW$ schemes clearly outperform the other methods for absolute core-level energies with a mean absolute error of 0.3 eV with respect to experiment. These are partial eigenvalue self-consistency, in which the eigenvalues are only updated in the Green's function, single-shot $GW$ calculations based on an optimized hybrid functional starting point and a Hedin shift in the Green's function. While all methods reproduce the experimental relative binding energies well, the eigenvalue self-consistent schemes and the Hedin shift yield with mean errors $<0.2$ eV the best results.

physics.chem-ph↗

arXiv2022

Localized orbital scaling correction for periodic systems

Density functional theory offers accurate structure prediction at acceptable computational cost, but commonly used approximations suffer from delocalization error; this results in inaccurate predictions of quantities such as energy band gaps of finite and bulk systems, energy level alignments, and electron distributions at interfaces. The localized orbital scaling correction (LOSC) was developed to correct delocalization error by using orbitals localized in space and energy. These localized orbitals span both the occupied and unoccupied spaces and can have fractional occupations in order to correct both the total energy and the one-electron energy eigenvalues. We extend the LOSC method to periodic systems, in which the localized orbitals employed are dually localized Wannier functions. In light of the effect of the bulk environment on the electrostatic interaction between localized orbitals, we modify the LOSC energy correction to include a screened Coulomb kernel. For a test set of semiconductors and large-gap insulators, we show that the screened LOSC (sLOSC) method consistently improves the band gap compared to the parent density functional approximation.

cond-mat.mtrl-sci↗

arXiv2021

LibSC: Library for Scaling Correction Methods in Density Functional Theory

In recent years, a series of scaling correction (SC) methods have been developed in the Yang laboratory to reduce and eliminate the delocalization error, which is an intrinsic and systematic error existing in conventional density functional approximations (DFAs) within density functional theory (DFT). Based on extensive numerical results, the SC methods have been demonstrated to be capable of reducing the delocalization error effectively and producing accurate descriptions for many critical and challenging problems, including the fundamental gap, photoemission spectroscopy, charge transfer excitations and polarizability. In the development of SC methods, the SC methods were mainly implemented in the QM4D package that was developed in the Yang laboratory for research development. The heavy dependency on the QM4D package hinders the SC methods from access by researchers for broad applications. In this work, we developed a reliable and efficient implementation , LibSC for the global scaling correction (GSC) method and the localized orbital scaling correction (LOSC) method. LibSC will serve as a light-weight and open-source library that can be easily accessed by the quantum chemistry community. The implementation of LibSC is carefully modularized to provide the essential functionalities for conducting calculations of the SC methods. In addition, LibSC provides simple and consistent interfaces to support multiple popular programing languages, including C, C++ and Python. In addition to the development of the library, we also integrated LibSC with two popular and open-source quantum chemistry packages, the Psi4 package and the PySCF package, which provides immediate access for general users to perform calculations with SC methods.

physics.chem-ph↗

arXiv2021

The Exact Second Order Corrections and Accurate Quasiparticle Energy Calculations in Density Functional Theory

We develop a second order correction to commonly used density functional approximations (DFA) to eliminate the systematic delocalization error. The method, based on the previously developed global scaling correction (GSC), is an exact quadratic correction to the DFA for the fractional charge behavior and uses the analytical second derivatives of the total energy with respect to fractional occupation numbers of the canonical molecular orbitals. For small and medium-size molecules, this correction leads to ground-state orbital energies that are highly accurate approximation to the corresponding quasiparticle energies. It provides excellent predictions of ionization potentials, electron affinities, photoemission spectrum and photoexcitation energies beyond previous approximate second order approaches, thus showing potential for broad applications in computational spectroscopy.

physics.chem-ph↗

arXiv2021

Renormalized Singles Green's Function in the T-Matrix Approximation for Accurate Quasiparticle Energy Calculation

We combine the renormalized singles (RS) Green's function with the T-Matrix approximation for the single-particle Green's function to compute quasiparticle energies for valence and core states of molecular systems. The $G_{\text{RS}}T_0$ method uses the RS Green's function that incorporates singles contributions as the initial Green's function. The $G_{\text{RS}}T_{\text{RS}}$ method further calculates the generalized effective interaction with the RS Green's function by using RS eigenvalues in the T-Matrix calculation through the particle-particle random phase approximation. The $G_{\text{RS}}T_{\text{RS}}$ method provides significant improvements over the one-shot T-Matrix method $G_0T_0$ as demonstrated in calculations for GW100 and CORE65 test sets. It also systematically eliminates the dependence of $G_{0}T_{0}$ on the choice of density functional approximations (DFAs). For valence states, the $G_{\text{RS}}T_{\text{RS}}$ method provides an excellent accuracy, which is better than $G_0T_0$ with Hartree-Fock (HF) or other DFAs. For core states, the $G_{\text{RS}}T_{\text{RS}}$ method correctly identifies desired peaks in the spectral function and significantly outperforms $G_0T_0$ on core level binding energies (CLBEs) and relative CLBEs, with any commonly used DFAs.

physics.chem-ph↗

arXiv2020

Self-consistent calculation of localized orbital scaling correction for correct electron densities and energy level alignment in density functional theory

The recently developed localized orbital scaling correction (LOSC) method shows the ability to systematically and size-consistently reduce the delocalization error existing in conventional density functional approximations (DFAs). Applying LOSC to conventional DFAs (LOSC-DFAs) gives much improvement for the description of related properties, including band gaps, total energies and photoemission spectra. However, concern and issue remain: the application of LOSC to DFAs is mainly through a post self-consistent field (SCF) manner, and few results from applying LOSC to DFAs with a SCF manner have been reported. The reason is the originally proposed SCF approach for SCF-LOSC calculation uses an approximate Hamiltonian and encounters convergence problems easily in practice. In this work, we develop a new SCF approach with a correct Hamiltonian and achieve reliable SCF-LOSC calculations. We demonstrate the capability of the new SCF approach for SCF-LOSC to correctly describe the electron densities, total energies and energy level alignment for the molecular dissociation process, while conventional DFAs or LOSC-DFAs with post-SCF calculations show large errors. This work demonstrates that the new SCF approach for SCF-LOSC would be a promising method to study problems for correct electron densities and energy level alignment in large systems.

physics.chem-ph↗

arXiv2019

Charge Transfer Excitation Energies From Ground State Density Functional Theory Calculations

Calculating charge transfer (CT) excitation energies with high accuracy and low computational cost is a challenging task. Kohn-Sham density functional theory (KS-DFT), due to its efficiency and accuracy, has achieved great success in describing ground state problems. To extend to excited state problems, our group recently demonstrated an approach with good numerical results to calculate low-lying and Rydberg excitation energies of an $N$-electron system from a ground state KS or generalized KS calculations of an $(N-1)$-electron system via its orbital energies. In present work, we explore further the same methodology to describe CT excitations. Numerical results from this work show that performance of conventional density functional approximations (DFAs) is not as good for CT excitations as for other excitations, due to the delocalization error. Applying localized orbital scaling correction (LOSC) to conventional DFAs, a recently developed method in our group to effectively reduce the delocalization error, can improve the results. Overall, the performance of this methodology is better than time dependant DFT (TDDFT) with conventional DFAs. In addition, it shows that results from LOSC-DFAs in this method reach similar accuracy to other methods, such as $Δ$SCF, $G_0W_0$ with Bethe-Salpeter equations, particle-particle random phase approximation, and even high-level wavefunction method like CC2. Our analysis show that the correct $1/R$ trend for CT excitation can be captured from LOSC-DFA calculations, stressing that the application of DFAs with minimal delocalization error is essential within this methodology. This work provides an efficient way to calculate CT excitation energies from ground state DFT.

physics.chem-ph↗

arXiv2018

Approximating Quasiparticle and Excitation Energies from Ground State Generalized Kohn-Sham Calculations

Quasiparticle energies and fundamental band gaps in particular are critical properties of molecules and materials. It was rigorously established that the generalized Kohn-Sham HOMO and LUMO orbital energies are the chemical potentials of electron removal and addition and thus good approximations to band edges and fundamental gaps from a density functional approximation (DFA) with minimal delocalization error. For other quasiparticle energies, their connection to the generalized Kohn-Sham orbital energies has not been established but remains highly interesting. We provide the comparison of experimental quasiparticle energies for many finite systems with calculations from the GW Green's function and localized orbitals scaling correction (LOSC), a recently developed correction to semilocal DFAs, which has minimal delocalization error. Extensive results with over forty systems clearly show that LOSC orbital energies achieve slightly better accuracy than the GW calculations with little dependence on the semilocal DFA, supporting the use of LOSC DFA orbital energies to predict quasiparticle energies. This also leads to the calculations of excitation energies of the $N$-electron systems from the ground state DFA calculations of the $\left(N-1\right)$-electron systems. Results show good performance with accuracy similar to TDDFT and the delta SCF approach for valence excitations with commonly used DFAs with or without LOSC. For Rydberg states, good accuracy was obtained only with the use of LOSC DFA. This work highlights the pathway to quasiparticle and excitation energies from ground density functional calculations.

physics.chem-ph↗

arXiv2017

Localized Orbital Scaling Correction for Systematic Elimination of Delocalization Error in Density Functional Approximations

The delocalization error of popular density functional approximations (DFAs) leads to diversified problems in present-day density functional theory calculations. For achieving a universal elimination of delocalization error, we develop a localized orbital scaling correction (LOSC) framework, which unifies our previously proposed global and local scaling approaches. The LOSC framework accurately characterizes the distributions of global and local fractional electrons, and is thus capable of correcting system energy, energy derivative and electron density in a self-consistent and size-consistent manner. The LOSC-DFAs lead to systematically improved results, including the dissociation of cationic species, the band gaps of molecules and polymer chains, the energy and density changes upon electron addition and removal, and photoemission spectra.

physics.chem-ph↗

arXiv2017

Understanding Band Gaps of Solids in Generalized Kohn-Sham Theory

The fundamental energy gap of a periodic solid distinguishes insulators from metals and characterizes low-energy single-electron excitations. But the gap in the band-structure of the exact multiplicative Kohn-Sham (KS) potential substantially underestimates the fundamental gap, a major limitation of KS density functional theory. Here we give a simple proof of a new theorem: In generalized KS theory (GKS), the band gap of an extended system equals the fundamental gap for the approximate functional if the GKS potential operator is continuous and the density change is delocalized when an electron or hole is added. Our theorem explains how GKS band gaps from meta-generalized gradient approximations (meta-GGAs) and hybrid functionals can be more realistic than those from GGAs or even from the exact KS potential. The theorem also follows from earlier work. The band edges in the GKS one-electron spectrum are also related to measurable energies. A linear chain of hydrogen molecules, solid aluminum arsenide, and solid argon provide numerical illustrations.

cond-mat.mtrl-sci↗