Localized Orbital Scaling Correction Research Articles

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 method consistently improves the band gap compared to the parent density functional approximation.

Describing Chemical Reactivity with Frontier Molecular Orbitalets.

Locality in physical space is critical in understanding chemical reactivity in the analysis of various phenomena and processes in chemistry, biology, and materials science, as exemplified in the concepts of reactive functional groups and active sites. Frontier molecular orbitals (FMOs) pinpoint the locality of chemical bonds that are chemically reactive because of the associated orbital energies and thus have achieved great success in describing chemical reactivity, mainly for small systems. For large systems, however, the delocalization nature of canonical molecular orbitals makes it difficult for FMOs to highlight the locality of the chemical reactivity. To obtain localized molecular orbitals that also reflect the frontier nature of the chemical processes, we develop the concept of frontier molecular orbitalets (FMOLs) for describing the reactivity of large systems. The concept of orbitalets was developed recently in the localized orbital scaling correction method, which aims for eliminating the delocalization error in common density functional approximations. Orbitalets are localized in both physical and energy spaces and thus contain both orbital locality and energy information. The FMOLs are thus the orbitalets with energies highest among occupied orbitalets and lowest among unoccupied ones. The applications of FMOLs to hexadeca-1,3,5,7,9,11,13,15-octaene in its equilibrium geometry, inter- and intra-molecular charge-transfer systems, and two transition states of a bifurcating reaction demonstrate that FMOLs can connect quantum mechanical treatments of chemical systems and chemical reactivities by locating the reactive region of large chemical systems. Therefore, FMOLs extend the role of FMOs for small systems and describe the chemical reactivity of large systems with energy and locality insight, with potentially broad applications.

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 to or better than GW Green's function approach and with much less computational cost. The QP energies from LOSC, instead of commonly used G0W0 and evGW, are directly used in BSE. We show that the BSE/LOSC approach greatly outperforms the commonly used BSE/G0W0 approach for predicting excitations with different characters. For the calculations of Truhlar-Gagliardi test set containing valence, charge transfer, and Rydberg excitations, BSE/LOSC with the Tamm-Dancoff approximation provides a comparable accuracy to time-dependent density functional theory (TDDFT) and BSE/evGW. For the calculations of Stein CT test set and Rydberg excitations of atoms, BSE/LOSC considerably outperforms both BSE/G0W0 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.

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). On the basis of 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 lightweight 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.

Describing polymer polarizability with localized orbital scaling correction in density functional theory.

Polarizability reflects the response of the molecular charge distribution to an applied external electric field and thus closely relates to the molecular electron density. For the calculation of polarizability within density functional theory (DFT), it is well known that conventional density functional approximations (DFAs) greatly overestimate the results for polymers with long chains and the π-conjugated system. This is a manifestation of the delocalization error of the commonly used DFAs-they normally produce too delocalized electron density and underestimate the total energy for systems with fractional charge character, which occurs for long molecules in a longitudinal electric field. Thus, to achieve an accurate description of polarizabilities for polymeric molecular systems from DFT, applying DFAs with minimal delocalization error is very important. In this work, we use the recently developed localized orbital scaling correction (LOSC) to the conventional DFAs, which has been shown to largely eliminate the delocalization error, to calculate and study the polarizabilities of three classic polymers, polyyne, polyacetylene, and hydrogen chain. The results from this work demonstrate that applying LOSC to conventional DFAs with self-consistent field calculations can largely improve the description of polarizability from DFT calculations and the improved quality of electron density in LOSC leads to the improved results of polarizability of the polymers. However, the improvement is not complete and adjustment of the parameters in the LOSC method can further improve the accuracy to reach the level similar to the MP2 method. This work also points to the direction for the further development of LOSC in self-consistent calculations.

Self-Consistent Calculation of the Localized Orbital Scaling Correction for Correct Electron Densities and Energy-Level Alignments 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). However, the application of LOSC to DFAs was mainly through a post self-consistent field (SCF) manner, and few results from applying LOSC to DFAs in an SCF manner have been reported. The reason is that the originally proposed SCF approach to 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 for studying problems for correct electron densities and energy-level alignments in large systems.

Revisiting the Hole Size in Double Helical DNA with Localized Orbital Scaling Corrections.

The extent of electronic wave function delocalization for the charge carrier (electron or hole) in double helical DNA plays an important role in determining the DNA charge transfer mechanism and kinetics. The size of the charge carrier's wave function delocalization is regulated by the solvation induced localization and the quantum delocalization among the π stacked base pairs at any instant of time. Using a newly developed localized orbital scaling correction (LOSC) density functional theory method, we accurately characterized the quantum delocalization of the hole wave function in double helical B-DNA. This approach can be used to diagnose the extent of delocalization in fluctuating DNA structures. Our studies indicate that the hole state tends to delocalize among 4 guanine-cytosine (GC) base pairs and among 3 adenine-thymine (AT) base pairs when these adjacent bases fluctuate into degeneracy. The relatively small delocalization in AT base pairs is caused by the weaker π-π interaction. This extent of delocalization has significant implications for assessing the role of coherent, incoherent, or flickering coherent carrier transport in DNA.

Preserving Symmetry and Degeneracy in the Localized Orbital Scaling Correction Approach.

Symmetry is a fundamental concept that plays a critical role in many chemical and physical phenomena and processes, which highlights the importance of theoretical methods to correctly handle symmetry. The recently developed localized orbital scaling correction (LOSC1) shows great improvement on the description of band gaps, photoemission spectra, and dissociation limits of cationic species. However, issues remain with LOSC1 in dealing with the symmetry and degeneracy of electronic states, which are also relevant to other methods using localization. In this work, we utilize a new method that deals with the physical-space and the energy-space localization on an equal footing. The resulting localized orbitals, i.e., orbitalets, are able to maintain more symmetry and the desired state degeneracy, which is important in calculating the electronic structure of both molecules and periodic bulk systems. Furthermore, the curvature matrix is redefined to improve potential energy curves for systems with stretched bonds, while retaining the correct dissociation limits. This new approach, termed LOSC2, includes only two fitting parameters. It maintains accuracy similar to that of LOSC1 over many properties, while overcoming LOSC1's deficiencies in symmetry and degeneracy. Our tests have shown that LOSC2 orbitalets possess the full- or subgroup of molecular symmetry if allowed, which preserves the state degeneracy. Tests on differently sized planar annulenes, odd-numbered allenes, and triphenylene again verify that LOSC2 is able to maintain the state degeneracy, while LOSC1 cannot. All the tests demonstrate the advantage of LOSC2 in the calculation of molecular systems and its potential for application to periodic bulk systems.

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 the 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 dependent 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 ΔSCF, G0W0 with Bethe-Salpeter equations, particle-particle random phase approximation, and even high-level wavefunction methods like CC2. Our analysis shows that the correct 1/R trend for CT excitation can be captured from LOSC-DFA calculations, stressing that the application of DFAs with the minimal delocalization error is essential within this methodology. This work provides an efficient way to calculate CT excitation energies from ground state DFT.

Describing strong correlation with fractional-spin correction in density functional theory

An effective fractional-spin correction is developed to describe static/strong correlation in density functional theory. Combined with the fractional-charge correction from recently developed localized orbital scaling correction (LOSC), a functional, the fractional-spin LOSC (FSLOSC), is proposed. FSLOSC, a correction to commonly used functional approximations, introduces the explicit derivative discontinuity and largely restores the flat-plane behavior of electronic energy at fractional charges and fractional spins. In addition to improving results from conventional functionals for the prediction of ionization potentials, electron affinities, quasiparticle spectra, and reaction barrier heights, FSLOSC properly describes the dissociation of ionic species, single bonds, and multiple bonds without breaking space or spin symmetry and corrects the spurious fractional-charge dissociation of heteroatom molecules of conventional functionals. Thus, FSLOSC demonstrates success in reducing delocalization error and including strong correlation, within low-cost density functional approximation.

Localized orbital scaling correction for systematic elimination of delocalization error in density functional approximations

AbstractThe 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.