Quasi-particle energies and band gaps in particular are critical for investigating novel materials. Commonly used density functional approximations (DFAs) systematically underestimate band gaps, and GW approximation is the established method of choice for good accuracy and reliability. However, G 0 W 0 has some undesired dependence on the DFA, while self-consistent GW (scGW) is expensive and not consistent in accuracy improvement. Here a simple and efficient G RS W 0 approach has been developed: a subspace diagonalization of the Hartree−Fock (HF) Hamiltonian with the DFA density matrix provides the new reference Green's function G RS that incorporates the effect of all single excitation contributions to the self-energy, thereby essentially eliminating the starting-point dependence. Calculations for molecules and large band gap solids demonstrate the significant improvement over G 0 W 0 and greatly reduced dependence on the initial DFA. G RS W 0 approach also improve results for other bulks over G 0 W 0 , but to a lesser extent, which could be due to the limitations in current implementation for bulks. The results demonstrate that to achieve good accuracy, it is not necessary to use hybrid DFA, which is expensive for bulks. This work should be greatly significant in making GW a more robust approach.

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. 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 absolute errors <0.2 eV the best results.

To describe static correlation, we develop a new approach to density functional theory (DFT), which uses a generalized auxiliary system that is of a different symmetry, such as particle number or spin, from that of the physical system. The total energy of the physical system consists of two parts: the energy of the auxiliary system, which is determined with a chosen density functional approximation (DFA), and the excitation energy from an approximate linear response theory that restores the symmetry to that of the physical system, thus rigorously leading to a multideterminant description of the physical system. The electron density of the physical system is different from that of the auxiliary system and is uniquely determined from the functional derivative of the total energy with respect to the external potential. Our energy functional is thus an implicit functional of the physical system density, but an explicit functional of the auxiliary system density. We show that the total energy minimum and stationary states, describing the ground and excited states of the physical system, can be obtained by a self-consistent optimization with respect to the explicit variable, the generalized Kohn–Sham noninteracting density matrix. We have developed the generalized optimized effective potential method for the self-consistent optimization. Among options of the auxiliary system and the associated linear response theory, reformulated versions of the particle–particle random phase approximation (pp-RPA) and the spin-flip time-dependent density functional theory (SF-TDDFT) are selected for illustration of principle. Numerical results show that our multireference DFT successfully describes static correlation in bond dissociation and double bond rotation.

A new self-consistent procedure for calculating the total energy with an orbital-dependent density functional approximation (DFA), the generalized optimized effective potential (GOEP), is developed in the present work. The GOEP is a nonlocal Hermitian potential that delivers the sets of occupied and virtual orbitals and minimizes the total energy. The GOEP optimization leads to the same minimum as does the orbital optimization. The GOEP method is promising as an effective optimization approach for orbital-dependent functionals, as demonstrated for the self-consistent calculations of the random phase approximation (RPA) to the correlation functionals in the particle—hole (ph) and particle—particle (pp) channels. The results show that the accuracy in describing the weakly interacting van der Waals systems is significantly improved in the self-consistent calculations. In particular, the important single excitations contribution in non-self-consistent RPA calculations can be captured self-consistently through the GOEP optimization, leading to orbital renormalization, without using the single excitations in the energy functional.

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 G0 W0 and ev GW 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 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/ 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.

Potential crystal structures of BeB2 were explored using ab initio evolutionary simulations. A new phase with a Cmcm space group was uncovered. It was determined that the Cmcm phase is mechanically and dynamically stable and has a lower enthalpy, from ambient pressure up to 13 GPa, than any previously proposed phases, as measured using first-principles calculations. The crystal structure, phonon dispersion, phase transitions, and mechanical and electronic properties of this phase were investigated. It was determined that the Cmcm phase may transform into the phase at pressures higher than 13 GPa. The band structures and density of states reveal that the Cmcm phase is metallic. In addition, the Vickers hardness was calculated using three empirical models. To explain the origin of the hardness, charge density difference maps and a Mulliken population analysis were carried out, which demonstrated that there are strong covalent interactions between B atoms. By analyzing the Crystal Orbital Hamilton Population (COHP) diagrams, it was determined that the total interaction of the Be-B bonds is stronger than that of the B-B bonds, indicating a very complex bonding feature in the new phase. It was predicted that the new Cmcm phase is nearly absent of superconductivity.

A major challenge in density functional theory (DFT) is the development of density functional approximations (DFAs) to overcome errors in existing DFA, leading to more complex functionals. For such functionals,...

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.