Assessment of DLPNO-MP2 Approximations in Double-Hybrid DFT

The unfavorable scaling (N5) of the conventional second-order Møller–Plesset theory (MP2) typically prevents the application of double-hybrid (DH) density functionals to large systems with more than 100 atoms. A prominent approach to reduce the computational demand of electron correlation methods is the domain-based local pair natural orbital (DLPNO) approximation that is successfully used in the framework of DLPNO-CCSD(T). Its extension to MP2 [Pinski P.; Riplinger, C.; Valeev, E. F.; Neese, F. J. Chem. Phys.2015, 143, 034108.] paved the way for DLPNO-based DH (DLPNO-DH) methods. In this work, we assess the accuracy of the DLPNO-DH approximation compared to conventional DHs on a large number of 7925 data points for thermochemistry and 239 data points for structural features, including main-group and transition-metal systems. It is shown that DLPNO-DH-DFT can be applied successfully to perform energy calculations and geometry optimizations for large molecules at a drastically reduced computational cost. Furthermore, PNO space extrapolation is shown to be applicable, similar to its DLPNO-CCSD(T) counterpart, to reduce the remaining error.

Table S1: All truncation thresholds for the different accuracy settings of RKS DLPNO-DHs.Thresholds that occur only once in a row apply to the whole row.
Threshold loosePNO normalPNO tightPNO verytightPNO Table S2: All truncation thresholds for the different accuracy settings of UKS DLPNO-DHs.
Thresholds that occur only once in a row apply to the whole row.

S-3
The WTMAD-2 C values were calculated according to The WTMAD-2 subset C values for the subsets were calculated according to: The corresponding MAD C , N i and |∆E| i values are given in Table S3 and S4

Figure S1 :
FigureS1: Computation wall-times in h for energy and gradient evaluation with conventional and DLPNO-B2PLYP/def2-TZVP(-f) (with normalPNO thresholds) for selected molecules in the range of 56 to 126 atoms (shown in Figure7of the manuscript) with respect to the number of basis functions.
i |∆E| i loose normal tight vtight l → n n → t t →

Table S6 :
Statistical error measures for the TMCONF16 in kcal•mol −1 .

Table S7 :
Statistical error measures for the TMBH in kcal•mol −1 .
loose normal tight verytight l → n n → t t → vt

Table S8 :
Statistical error measures for the ROST61 in kcal•mol −1 .

Table S9 :
Statistical error measures for the TMIP in kcal•mol −1 .

Table S10 :
Statistical error measures for the MOBH35 in kcal•mol −1 .

Table S11 :
Statistical error measures for the WCCR10 in kcal•mol −1 .

Table S12 :
Statistical error measures for the IONPI19 in kcal•mol −1 .
loose normal tight verytight l → n n → t t →

Table S13 :
Statistical error measures for the X40x10 in kcal•mol −1 .

Table S14 :
Statistical error measures for the CHAL336 in kcal•mol −1 .

Table S15 :
Statistical error measures for the LP14 in kcal•mol −1 .

Table S16 :
Statistical error measures for the HB300SPX in kcal•mol −1 .

Table S17 :
Statistical error measures for the L7 in kcal•mol −1 .

Table S18 :
Statistical error measures for the ACONFL in kcal•mol −1 .

Table S19 :
Statistical error measures for the S30L in kcal•mol −1 .

Table S20 :
Statistical error measures for the HS13L in kcal•mol −1 .

Table S21 :
Statistical error measures for the revBH9 in kcal•mol −1 .

Table S23 :
Statistical error measures for the R160x6 in kcal•mol −1 .

Table S24 :
Statistical error measures for the CCse21 bond lengths in pm.

Table S26 :
Statistical error measures for the HMGB11 bond lengths in pm.

Table S27 :
Statistical error measures for the TMC32 bond lengths in pm.

Table S28 :
Statistical error measures for the ROT34 rotational constants in MHz.

Table S29 :
Statistical error measures for the LMGB bond lengths in pm.

Table S30 :
Statistical error measures for the LB12 bond lengths in pm.