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Basis‐Set Quality and Basis‐Set Bias in Molecular Property Calculations
Author(s) -
Rappoport Dmitrij
Publication year - 2011
Publication title -
chemphyschem
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.016
H-Index - 140
eISSN - 1439-7641
pISSN - 1439-4235
DOI - 10.1002/cphc.201100502
Subject(s) - basis set , sto ng basis sets , basis (linear algebra) , ground state , gaussian , rydberg formula , chemistry , mathematics , physics , computational chemistry , atomic physics , linear combination of atomic orbitals , geometry , quantum mechanics , density functional theory , ionization , ion
Quality measures for Gaussian basis sets are proposed that are based on principal angles between the basis set and reference molecular orbitals. The principal angles are obtained from the cosine–sine (CS) decomposition of orthogonal matrices and yield detailed information about basis‐set convergence with respect to different regions of space. Principal angles for occupied orbitals show excellent correlation with basis‐set errors in ground‐state energies. Furthermore, ground‐state bias in finite basis sets can be estimated from the relation between principal angles for occupied and Rydberg orbitals. Ground‐state bias is observed in basis sets including extensive diffuse augmentation and affects the quality of computed molecular response properties. Principal angles and ground‐state bias are investigated for the H–Ne atoms and a series of diatomics using numerical Hartree–Fock calculations as a reference. Convergence of ground‐state energies and static polarizabilities is studied for the hierarchies of correlation‐consistent and Karlsruhe segmented def2 basis sets including different levels of diffuse augmentation.