A detailed analysis of the theoretical x-ray absorption near-edge structures (XANES) for the boron and nitrogen K edge in hexagonal boron nitride (h-BN) employing density-functional theory calculations is presented. The supercell core-hole method and the Bethe-Salpeter equation are used for the description of electron-hole interactions. The calculations are carried out with two different codes, the VASP and the WIEN2K codes, employing the projector augmented-wave and the full-potential linear augmented-plane-wave methods, respectively. We find close agreement between spectra obtained from the two codes and between calculations using the supercell core-hole method and the Bethe-Salpeter approach. All our calculations, as well as previous calculations using the ground-state structure, yield a single 2p σ * peak in the boron K-edge spectrum and hence fail to describe the experimental double-peak structure. We find that the inclusion of electron-phonon interactions is crucial to obtain the experimentally observed double-peak structure. We include these effects fully parameter free and ab initio using a one-shot sampling method and obtain excellent agreement with experiment.

We report a scalable Fortran implementation of the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) and demonstrate its excellent performance and beneficial scaling with respect to system size. Furthermore, we investigate modifications of the phaseless approximation that can help to reduce the overcorrelation problems common to the ph-AFQMC. We apply the method to the 26 molecules in the HEAT set, the benzene molecule, and water clusters. We observe a mean absolute deviation of the total energy of 1.15 kcal/mol for the molecules in the HEAT set, close to chemical accuracy. For the benzene molecule, the modified algorithm despite using a single-Slater-determinant trial wavefunction yields the same accuracy as the original phaseless scheme with 400 Slater determinants. Despite these improvements, we find systematic errors for the CN, CO 2 , and O 2 molecules that need to be addressed with more accurate trial wavefunctions. For water clusters, we find that the ph-AFQMC yields excellent binding energies that differ from CCSD(T) by typically less than 0.5 kcal/mol.

We implement the phaseless auxiliary field quantum Monte Carlo method using the plane-wave based projector augmented wave method and explore the accuracy and the feasibility of applying our implementation to solids. We use a singular value decomposition to compress the two-body Hamiltonian and, thus, reduce the computational cost. Consistent correlation energies from the primitive-cell sampling and the corresponding supercell calculations numerically verify our implementation. We calculate the equation of state for diamond and the correlation energies for a range of prototypical solid materials. A down-sampling technique along with natural orbitals accelerates the convergence with respect to the number of orbitals and crystal momentum points. We illustrate the competitiveness of our implementation in accuracy and computational cost for dense crystal momentum point meshes compared to a well-established quantum-chemistry approach, the coupled-cluster ansatz including singles, doubles, and perturbative triple particle–hole excitation operators.

The direct random-phase approximation (dRPA) is used to calculate and compare atomization energies for the HEAT set and 10 selected molecules of the G2-1 set using both plane waves and Gaussian-type orbitals. We describe detailed procedures to obtain highly accurate and well converged results for the projector augmented-wave (PAW) method as implemented in the Vienna Ab-initio Simulation Package (VASP) as well as the explicitly correlated dRPA-F12 method as implemented in the TURBOMOLE package. The two approaches agree within chemical accuracy (1 kcal/mol) for the atomization energies of all considered molecules, both for the exact exchange as well as for the dRPA. The root mean-square deviation is 0.41 kcal/mol for the exact exchange (evaluated using density functional theory orbitals) and 0.33 kcal/mol for exact exchange plus the random-phase approximation.