2019/01/01 by Pierre-François Loos, Pierre‐François Loos, Anthony Scemama +1
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Atom (system on chip) #Atomic orbital #Basis (linear algebra) #Basis function #Basis set #Complete active space #Cusp (singularity) #Electron #Gaussian #Geometry #Mathematics #Molecular orbital #Molecule #Monte Carlo method #Physics #Quantum Monte Carlo #Quantum mechanics #Quantum, superfluid, helium dynamics #STO-nG basis sets #Slater determinant #Spectroscopy and Quantum Chemical Studies #Statistical physics #Statistics #Wave function #cond-mat.str-el #physics.chem-ph #physics.comp-ph
paper · pdf · doi:10.1016/bs.aiq.2019.03.003
published as Adv. Quantum Chem. 79, 113 (2019) · 23 pages, 5 figures
openalex publication_date 2019/01/01 · arxiv created 2019/03/12 · arxiv updated 2020/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We describe a method for imposing the correct electron-nucleus (e-n) cusp in molecular orbitals expanded as a linear combination of (cuspless) Gaussian basis functions. Enforcing the e-n cusp in trial wave functions is an important asset in quantum Monte Carlo calculations as it significantly reduces the variance of the local energy during the Monte Carlo sampling. In the method presented here, the Gaussian basis set is augmented with a small number of Slater basis functions. Note that, unlike other e-n cusp correction schemes, the presence of the Slater function is not limited to the vicinity of the nuclei. Both the coefficients of these cuspless Gaussian and cusp-correcting Slater basis functions may be self-consistently optimized by diagonalization of an orbital-dependent effective Fock operator. Illustrative examples are reported for atoms (\ceH, \ceHe and \ceNe) as well as for a small molecular system (\ceBeH2). For the simple case of the \ceHe atom, we observe that, with respect to the cuspless version, the variance is reduced by one order of magnitude by applying our cusp-corrected scheme.