Correlation consistent auxiliary basis sets in density fitting Hartree–Fock: The atoms sodium through argon revisited

Abstract We present a series of auxiliary basis sets, for the elements Na to Ar, for use in density‐fitted Hartree–Fock calculations with the correlation consistent cc‐pV(n + d)Z orbital basis sets. Benchmarking on total molecular energies, reaction energies and the spectroscopic constants of the SO molecule demonstrate that the new sets address the deficiencies of using existing auxiliary sets in combination with these orbital basis sets. We also report auxiliary basis sets for Na and Mg matched to cc‐pVnZ, along with recommendations for pairing auxiliary basis sets to the cc‐pVnZ‐F12 basis sets for Hartree–Fock calculations.

1 Composition of diffuse augmented auxiliary sets Table S1: Composition of the diffuse augmented JKFit basis sets developed in this work [aug-cc-pV(n+d)Z-JKFit] compared to the existing aug-cc-pVnZ-JKFit.For Al-Ar, only the most diffuse f exponent in the new auxiliary basis set differs from the existing sets.
Orbital basis aug-cc-pVnZ-JKFit aug-cc-pV(n+d)Z-JKFit aug-cc-pV(D+d)Z (14s12p10d4f) (14s12p10d5f) aug-cc-pV(T+d)Z (14s12p10d4f2g) (14s12p10d5f3g) aug-cc-pV(Q+d)Z (14s12p10d5f3g2h) (14s12p10d6f4g2h) aug-cc-pV(5+d)Z (14s12p10d5f4g3h2i) (14s12p10d6f5g3h2i) 2 Molecular test set To determine the errors due to density fitting in molecular energies, molecules containing the second-row elements were selected from the test set of Weigend. 1 The BP86/def-SV(P) optimized geometries provided as part of the test set were used in single point calculations.The molecules selected are: Mg 4 , MgCl    S8: Errors due to the density fitting approximation (mE h ) in Hartree-Fock energies for a test set of 41 second-row element containing molecules using the cc-pVQZ-F12 orbital basis set.Also shown is the number of functions in each auxiliary basis set for a single second-row atom (N ABS ). Auxiliary

HF reaction energies
Tables S9 to S15 present the HF and DF-HF reaction energies for reactions 4, 10, 18, 20, 21, 28 and 38 from the reaction energies test set of Friedrich and Hänchen. 2 The DF-HF results are presented for two different choices of auxiliary basis.Chemical equations for these reactions are given in the main text.

4
Figures S1 to S4 present violin plots of ∆DF for various auxiliary basis sets with the cc-pVnZ orbital basis sets, where n = D, T, Q and 5, respectively.
Figure S1: Violin plots of the ∆DF errors (mE h ) in Hartree-Fock energies for a test set of 41 second-row element containing molecules using the cc-pV(D+d)Z orbital basis set.The individual data points with each auxiliary basis set are shown as jitter scatter plots.The def2-QZVPP -g JKFit basis removes the set of g functions from def2-QZVPP-JKFit.

Figure
FigureS5shows violin plots distributions of the ∆DF error as the orbital basis set size is increased.The def2-QZVPP-JKFit auxiliary basis set is used in all cases.

Figures
Figures S6 and S7 are violin plots showing how distributions of the ∆DF errors change as the orbital basis set size is increased.The cc-pVnZ-JKFit auxiliary basis set family, where the cardinal numbers of the orbital and Figure S6: Violin plots of the ∆DF errors (mE h ) in Hartree-Fock energies for a test set of 41 second-row element containing molecules as the orbital basis set is increased.The existing cc-pVnZ-JKFit family of auxiliary basis sets are used, with the cardinal number matching that of the orbital basis set.The individual data points with each orbital basis set are shown as jitter scatter plots.

Table S2 :
Errors due to the density fitting approximation (mE h ) in Hartree-Fock energies for a test set of 41 second-row element containing molecules using the cc-pV(D+d)Z orbital basis set.The cc-pV(D+d)Z+1g-JKFit set includes an additional g exponent compared to cc-pV(D+d)Z-JKFit, while def2-QZVPP−g-JKFit removes the g functions from def2-QZVPP-JKFit.

Table S5 :
Errors due to the density fitting approximation (mE h ) in Hartree-Fock energies for a test set of 41 second-row element containing molecules using the cc-pV(5+d)Z orbital basis set.

Table S6 :
Errors due to the density fitting approximation (mE h ) in Hartree-Fock energies for a test set of 41 second-row element containing molecules using the cc-pVDZ-F12 orbital basis set.Also shown is the number of functions in each auxiliary basis set for a single second-row atom (N ABS ).

Table S7 :
Errors due to the density fitting approximation (mE h ) in Hartree-Fock energies for a test set of 41 second-row element containing molecules using the cc-pVTZ-F12 orbital basis set.Also shown is the number of functions in each auxiliary basis set for a single second-row atom (N ABS ).

Table S9 :
HF and DF-HF reaction energies (kcal mol −1 ) for the seven reactions from the FH test set that contain second-row elements.The cc-pV(D+d)Z orbital basis set is used.Reference data for the spectroscopic constants of the diatomic molecule SO TablesS16 and S17present the conventional (that is, without density-fitting) HF and MP2 spectroscopic constants of the 3 Σ − state of the diatomic molecule SO.

Table S16 :
HF spectroscopic constants of the 3 Σ − state of the diatomic molecule SO.

Table S17 :
MP2 spectroscopic constants of the 3 Σ − state of the diatomic molecule SO.