arXiv subjects

Moritz Humer

Publications and source records attributed to Moritz Humer.

4 recordsLinked to original sources

arXiv2026

Auxiliary field quantum Monte Carlo at the basis set limit: application to lattice constants

We present a plane-wave (PW) implementation of the auxiliary-field quantum Monte Carlo (AFQMC) method within the projector augmented-wave (PAW) formalism in the Vienna ab initio Simulation Package (VASP). By employing an exact inversion of the PAW overlap operator, our approach maintains cubic scaling while naturally operating at the complete basis set limit defined by the PW cutoff. We benchmark this framework by calculating the equilibrium lattice constants and bulk moduli of C, BN, BP, and Si. Our analysis demonstrates that AFQMC systematically corrects the lack of long-range screening in MP2 and the missing higher-order exchange in RPA. We identify RPA as the optimal reference method due to the rapid convergence of the remaining short-range correlations with respect to supercell size. The resulting lattice constants exhibit a mean absolute relative error of 0.14 % relative to experiment, establishing the method as a rigorous benchmark tool for structural properties in condensed matter systems.

physics.comp-ph↗

arXiv2024

Towards Large-Scale AFQMC Calculations: Large Time Step Auxiliary-Field Quantum Monte Carlo

We report modifications of the ph-AFQMC algorithm that allow the use of large time steps and reliable time step extrapolation. Our modified algorithm eliminates size-consistency errors present in the standard algorithm when large time steps are employed. We investigate various methods to approximate the exponential of the one-body operator within the AFQMC framework, distinctly demonstrating the superiority of Krylov methods over the conventional Taylor expansion. We assess various propagators within AFQMC and demonstrate that the Split-2 propagator is the optimal method, exhibiting the smallest time-step errors. For the HEAT set molecules, the time-step extrapolated energies deviate on average by only 0.19 kcal/mol from the accurate small time-step energies. For small water clusters, we obtain accurate complete basis-set binding energies using time-step extrapolation with a mean absolute error of 0.07 kcal/mol compared to CCSD(T). Using large time-step ph-AFQMC for the N$_2$ dimer, we show that accurate bond lengths can be obtained while reducing CPU time by an order of magnitude.

physics.chem-ph↗

arXiv2023

Phaseless auxiliary field quantum Monte Carlo with projector-augmented wave method for solids

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 comparing to a well-established quantum-chemistry approach, the coupled-cluster ansatz including singles, doubles and perturbative triple particle-hole excitation operators.

physics.chem-ph↗

arXiv2022

Approaching the basis-set limit of the dRPA correlation energy with explicitly correlated and Projector Augmented-wave methods

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.

physics.chem-ph↗