Density Functional Theory for Microwave Spectroscopy of

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Density Functional Theory for Microwave Spectroscopy of Non-Covalent Complexes: A Benchmark Study Peter Kraus, and Irmgard Frank J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b03345 • Publication Date (Web): 11 May 2018 Downloaded from http://pubs.acs.org on May 15, 2018

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The Journal of Physical Chemistry

Density Functional Theory for Microwave Spectroscopy of Non-Covalent Complexes: A Benchmark Study P. Kraus∗ and I. Frank Institut f¨ ur Physikalische Chemie und Elektrochemie, Leibniz Universität Hannover, Callinstraße 3A, 30167 Hannover, Germany E-mail: [email protected]

Abstract In this work, we compare the results obtained with 89 computational methods for predicting non-covalent bond lengths in weakly bound complexes. Evaluations for the performance in non-covalent interaction energies and covalent bond lengths obtained from five other datasets are included. The overall best performing density functional is the ωB97M-V method, achieving balanced results across all three categories. For non-covalent geometries the best methods include B97M-V, B3LYP-D3(BJ) and DSDPBEPBE-D3(BJ). The effects of systematic improvement of the density functional approximation and of dispersion corrections are also discussed.

1

1

Introduction

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For non-covalently bound complexes, a large portion of recent efforts in research, develop-

3

ment, and benchmarking of computational methods focuses on obtaining accurate interaction

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energies. 1–4 A great amount of progress has been achieved in this field over the recent years.

5

At the highest levels of wavefunction theory (WFT), it has been shown that interaction ener-

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gies computed with coupled cluster calculations including singles, doubles, and pertubative 1

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triples used with a basis set extrapolated to the complete basis set limit (CCSD(T)/CBS) are

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in excellent agreement with calculations also including core-core and core-valence correlation,

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relativistic effects and quadruple excitations. 3 On the other hand, the advent of easy-to-use

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empirical dispersion corrections, 5 now including three-body interactions and effects of local

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chemical environment, 6 dynamic polarisabilities of atoms, 7 or non-local correlation, 8 allows

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density functional theory (DFT) methods to achieve a comparatively good performance in

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the description of interaction energies, provided large enough basis sets are applied, 4 even

14

when comparatively dated density functionals are used. Additionally, with double-hybrid

15

density functional methods, which include a part of MP2 correlation in addition to the part

16

of Hartree-Fock (HF) exchange used in single-hybrid DFT methods, accuracy comparable to

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CCSD(T)-based benchmarks is possible. 9,10

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However, accurate description of energies is only one aspect that makes a computa-

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tional method generally applicable. For certain structure-sensitive applications, including

20

microwave spectroscopy, an accurate prediction of geometries is equally, if not more im-

21

portant. The data acquisition in such experiments generally starts with a computation of

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a predicted structure, to obtain a first guess of the rotational constants. If the predicted

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rotational constants differ significantly (> 10 MHz) from the true values, the potential to

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waste valuable instrument time is high, especially if a broadband instrument is unavailable.

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In addition to the data collection issues, accurate structural predictions and ab initio based

26

spectra can decrease the difficulty in interpretation of experimental data. Furthermore, there

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is currently little guidance for an unbiased choice of computational methods, as accuracy for

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non-covalent structures does not immediately follow from an accurate prediction of energies.

29

Therefore, in the current work, we attempt to answer the question: Which affordable com-

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putational method is currently the best for predicting geometries of non-covalently bound

31

complexes? To help us answer this question, we have used the recently developed dataset

32

of semi-experimental non-covalent bond lengths in dimers and trimers (NCDT16) 11 and 89

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computational methods, including the HF, MP2, CCSD and CCSD(T) wavefunction-based

2


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methods. On the density functional front, 16 generalised density gradient approximation

35

(GGA) methods, 11 meta-GGA functionals depending also on the kinetic energy density, 28

36

hybrid GGA functionals incorporating HF-exchange, 20 hybrid meta-GGA functionals and

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8 double-hybrid functionals also incorporating MP2 correlation are compared. Additionally,

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two composite methods are included: an “affordable” PBEh-3c method intended to predict

39

good geometries 12 and a “near gold-standard” MP2/CBS + δCCSD(T)/3-ζ extrapolated-

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basis method (shortened to MP2 + δ(T) in the following). The NCDT16 dataset comprises

41

45 non-covalent bond lengths between the heavy atoms of 16 dimers and trimers, obtained

42

using experimental rotational constants corrected for non-equilibrium effects at the double-

43

hybrid level of DFT. While angles are not included in the database, angular information is

44

included by considering more than one bond length for all non-symmetric complexes. 11 The

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current dataset is somewhat skewed towards dispersion interactions, with 9 out of 16 com-

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plexes having interaction energies below 4 kJ/mol. However, three complexes with dominant

47

π–π interactions and four H–bonded systems ensure that the interaction energy ranges of

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5–10 kJ/mol and > 15 kJ/mol, respectively, are also considered. Interaction energies for

49

clusters in the NCDT16 dataset, obtained with the best-performing methods, are presented

50

at the semi-experimental (reSE ) geometries and compared to Eint results at the optimized ge-

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ometries. To make our analysis more robust, we have carried out further calculations on five

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other previously published benchmark datasets: a set of semi-experimental bond lengths

53

in small covalently bound compounds (CCse22), 13 its ab initio bond length counterpart

54

(CS20), 14 two datasets of highly-accurate ab initio interaction energies at the prescribed ge-

55

ometries (NCCE31 14 and A24 3 ), and a database of 21 equilibrium CCSD(T)/CBS structures

56

(A21G) 3 to serve as a counterpart to our NCDT16 set.

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Table 1: An overview of the computational methods used in this work, grouped according to their classification (“Jacob’s ladder”): GGAs (F (∇ρ[r])), meta-GGAs (F (∇ρ[r], τ [r])), single hybrids, single meta-GGA hybrids, double hybrids, and coupled cluster methods. GGA BLYP BLYP-D2 BLYP-D3(BJ) BLYP-D3m(BJ) PBE PBE-D2 PBE-D3(BJ) PBE-D3m(BJ) HCTH/120 HCTH/120-D3(BJ) VV10 B97-D2 B97-D3(BJ) B97-D3m(BJ) N12 N12-D3(BJ)

meta-GGA M06-L M06-L-D3 M11-L M11-L-D3(BJ) MN12-L MN12-L-D3(BJ) MN15-L MN15-L-D3 TPSS TPSS-D3(BJ) B97M-V

XHF + GGA HF B3LYP B3LYP-D2 B3LYP-D3 B3LYP-D3(BJ) B3LYP-D3m(BJ) B3PW91 B3PW91-D3(BJ) ωPBE ωPBE-D3(BJ) ωPBE-D3m(BJ) PBE0 PBE0-D2 PBE0-D3 PBE0-D3(BJ) PBE0-D3m(BJ) ωPBE0 LC-VV10 B97 ωB97X ωB97X-D ωB97X-V BHandH BHandHLYP HSE06 HSE06-D3(BJ) SOGGA11-X SOGGA11-X-D3(BJ) PBEh-3c

XHF + meta-GGA M05 M05-D3 M05-2X M05-2X-D3 M06 M06-D3 M06-2X M06-2X-D3 M06-HF M06-HF-D3 M08-HX M08-HX-D3 M08-SO M11 M11-D3(BJ) MN15 MN15-D3(BJ) TPSSH TPSSH-D3(BJ) ωB97M-V

XHF + CMP2 + GGA MP2 B2PLYP B2PLYP-D3(BJ) B2PLYP-D3m(BJ) PBE0-2 DSD-BLYP-D3(BJ) DSD-PBEP86-D3(BJ) DSD-PBEPBE-D3(BJ)

CC CCSD CCSD(T) MP2 + δ(T)

57

2

58

All ab initio calculations were performed using a development version (ver. > 1.2a1.dev781)

59

of the electronic structure code ψ 4 , 15 coupled to the DFT exchange-correlation library

60

Libxc v. 3.0.0. 16 Our modifications to the ψ 4 codebase consisted of adding numerous density

61

functionals which are a part of Libxc v. 3.0.0; they are now included in the development

62

version. The use of such open-source programs is in our view critical for reproducibility and

63

auditing of computational data. As a result, the driver routines used in the current work are

64

available in the Supporting information code archive.

65

Computational methods

All electronic structure calculations were carried out with the density-fitted variants of 4


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66

WFT (including MP2, CCSD or CCSD(T)) and DFT methods. An “ultra fine” (99, 590)

67

integration grid was used; for cases where SCF convergence was difficult, an even larger

68

(250, 974) grid was applied with a density damping of 20%. The convergence thresholds in ge-

69

ometry optimisations were tightened to ∆E < 1µEh, Fmax < 60 µEh/a0 , FRM S < 40 µEh/a0 ,

70

∆Rmax < 1 ma0 and ∆RRM S < 1 ma0 . In some complexes, such as for the Ne–OCS dimer,

71

results vary significantly when the default (looser) convergence thresholds are used. For

72

all methods with the exception of coupled cluster and composite calculations, the def2-

73

TZVPD basis set was used 17,18 due to its availability for heavier elements. For the CCSD and

74

CCSD(T) calculations, the may-cc-pVTZ basis set was used 19 to reduce computational cost.

75

The PBEh-3c composite method has been applied with its modified double-ζ basis set. 12

76

Finally, the extrapolated composite method denoted “MP2 + δ(T)” comprises a frozen-core

77

density-fitted MP2 calculation extrapolated towards the basis set limit 20 by using triple- and

78

quadruple-ζ correlation-consistent basis sets (ie. MP2/aug-cc-pV[TQ]Z), 21,22 with further

79

correlation effects (“δ(T)”) approximated from the difference between frozen-core density-

80

fitted CCSD(T) and MP2 energies at the may-cc-pVTZ level. The use of quadruple-ζ basis

81

in the MP2 extrapolation is critical, as the extrapolation from double- and triple-ζ basis

82

sets (ie. MP2/aug-cc-pV[DT]Z) performs considerably worse than the MP2/def2-TZVPD

83

method. An overview of the computational methods used in the current work is shown in

84

Table 1. For full references of all listed methods, see the Supporting information.

85

3

86

The mean absolute errors (MAEs) of selected non-covalent bond lengths (|∆reSE |) averaged

87

88

Results and discussion

over the 16 complexes comprising the NCDT16 dataset (|∆reSE |) are shown in Figure 1 √ along with their associated standard errors (σ(|∆reSE |)/ 16). The best performer is the

89

meta-GGA functional B97M-V, 23 with |∆reSE | = 48 m˚ A. This corresponds to an accuracy

90

better than several double hybrid functionals and even the considerably more expensive

5



0

25

50

75

100

100

150

200

HSE06-D3(BJ)

M05-2X ωPBE-D3m(BJ) B3LYP-D3 MP2 PBE-D3m(BJ) MN15-D3(BJ) B3LYP-D3m(BJ)

50

75

100

0

50

300

400

B97-D2

M06 B97 BHandHLYP M06-D3 B3PW91-D3(BJ) N12-D3(BJ) ωPBE0 ωPBE SOGGA11-X-D3(BJ) MN12-L MN12-L-D3(BJ) BHandH TPSSH TPSS M11-L-D3(BJ)

443 461 788 936 1302 1400 1495 1694

M11-L SOGGA11-X HF N12 B3LYP B3PW91 BLYP

B3LYP-D2 M06-HF-D3 PBEh-3c M08-HX-D3 HSE06 B97-D2

MN15 ωB97X PBE-D3(BJ) HSE06-D3(BJ)

200

PBE PBE0 ωB97X-D HCTH/120

VV10 M05 CCSD M05-D3 PBE0-D2 B2PLYP M08-SO M06-L-D3 MN12-SX PBE-D2 M06-HF BLYP-D2 MN15-L MN15-L-D3 M06-L TPSS-D3(BJ) MN12-SX-D3(BJ)

M05-2X-D3 PBE0-D3(BJ) DSD-BLYP-D3(BJ)

100

M08-HX B97-D3(BJ) B97-D3m(BJ)

M11 HCTH/120-D3(BJ) TPSSH-D3(BJ) BLYP-D3(BJ) M11-D3(BJ)

PBE0-D3 M06-2X M06-2X-D3 DSD-PBEP86-D3(BJ) PBE0-D3m(BJ) BLYP-D3m(BJ)

0

B97M-V

ωPBE-D3(BJ)

ωB97M-V ωB97X-V B3LYP-D3(BJ) MP2 + δ(T) CCSD(T) B2PLYP-D3m(BJ)

25

50

B97M-V

B97M-V DSD-PBEPBE-D3(BJ) PBE0-2 LC-VV10 B2PLYP-D3(BJ)

0

0

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100 |∆reSE |

150 ˚] / [mA

200

0

100

200

300

Figure 1: The MAE of various computational methods in selected non-covalent bond lengths averaged over the 16 complexes in the NCDT16 dataset. The colour denotes the class of the method (dark gray: GGA, light gray: meta-GGA, blue: global hybrid, light blue: rangeseparated hybrid, purple: meta-GGA hybrid, pink: range-separated meta-GGA hybrid, orange: double hybrid, yellow: coupled cluster). √ Accuracy decreases from left to right. Error SE bar shows one standard error (σ(|∆re |)/ 16). 91

CCSD(T) method. The only other method with a MAE below 50 m˚ A is the double-hybrid

92

DSD-PBEPBE-D3(BJ). 24 Other methods achieving lower MAE than CCSD(T), as well as

93

the extrapolated MP2 + δ(T) composite method, include the dispersion corrected global

94

hybrid B3LYP-D3(BJ), 25–27 two range-separated functionals ωB97X-V 28 and ωB97M-V 29

95

related to the best performing meta-GGA, the original double-hybrid with dispersion cor-

96

rection B2PLYP-D3(BJ), 9,27 and the range-separated functional with non-local correlation

97

LC-VV10. 8 Somewhat surprisingly, the dispersionless double hybrid PBE0-2 10 also performs 6


400

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0

A) Ne–complexes 20 40 60

80

B) dispersion dominated 0 8 16 24 32

0

C) π–π interactions 11 22 33 44

0

D) H–bonded 11 22 33

B3LYP-D3(BJ)

B97M-V

BLYP-D3(BJ)

MN12-SX

DSD-PBEPBE-D3(BJ)

ωB97X-V

B3PW91-D3(BJ)

MN12-L

PBE0-D3

BLYP-D3m(BJ)

B97-D3(BJ)

MP2 + δ(T)

BLYP-D3m(BJ)

M05-2X

N12-D3(BJ)

MN12-SX-D3(BJ)

CCSD(T)

B3LYP-D3(BJ)

LC-VV10

MN12-L-D3(BJ)

PBE0-D3m(BJ)

PBE0-D2

B3LYP-D3(BJ)

MN15-D3(BJ)

PBE-D3(BJ)

ωB97M-V

B2PLYP-D3(BJ)

M08-SO

PBE0-2

B2PLYP-D3m(BJ)

ωPBE-D3(BJ)

MN15

B97M-V

B2PLYP-D3(BJ)

ωB97X-V

M06-D3

B3LYP-D3m(BJ)

DSD-PBEPBE-D3(BJ)

TPSSH-D3(BJ)

ωB97X-V

0

20

40

60

80

0

8

16

24

32

0

11

|∆reSE | / [m˚ A]

22

33

44

0

11

22

33

Figure 2: The MAE of the ten best computational methods in subsets of the NCDT16 dataset: A) dispersion dominated complexes including Ne, B) other dispersion dominated complexes, C) complexes with significant π–π interactions and D) H–bonded complexes. Colours as in Fig. 1. 98

very well.

99

A more detailed look into the top performers in the four categories of complexes compris-

100

ing the NCDT16 dataset is shown in Fig. 2. Detailed results for all methods are listed in the

101

Supporting information. The ranking of the methods varies significantly, with only B3LYP-

102

D3(BJ) 25–27 achieving a “top 10” result in three out of the four categories – its performance

103

for the H–bonded dataset is average. The lowest MAE for the five Ne–containing complexes

104

is significantly higher than in the other three categories, with meta-GGA’s performing com-

105

parably poorly: the best meta-GGA hybrid M06-2X-D3 30,31 is only rank 17. On the other

106

hand, for H–bonded complexes, the more recent meta-GGA’s of Truhlar and co-workers 32,33

107

top the field – the overall MAE of the range-separated meta-GGA MN12-SX, 34 which is

108

the top method in this category, is hampered only by the large MAE for the Ne–Ne–N2 O

109

trimer. On the other hand, the highest ranked double hybrid for the H–bonded complexes

110

is the PBE0-2 functional 10 at number 13. The other two classifications show more mixed

111

results. The excellent performance of dispersion-corrected GGA’s for π–π bonded systems is

112

somewhat surprising, especially in the case of the 4th best N12-D3(BJ) 35,36 functional which

113

has a 10× larger overall |∆reSE | at ∼ 270 m˚ A. Also notable are the rather average results 7


44

44


0

50

100

150

200

Ne–C2 H4 Ne–OCS

Ne–Ne–N2 O Ne–Ar–N2 O

Ne–complexes

Ne–Ar–HCl Ar–C2 H4 Ar–OCS Kr–OCS Ar–Ar–N2 O

dispersion

CS2 –OCS HCCH–HCCH CH2 ClF–HCCH

π–π

HF–H2 CO HCl–H2 CO HCN–H2 CO HF–HF-NH3

0

50

100 |∆reSE | / [m˚ A]

150

H–bonded

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 24

200

Figure 3: The absolute deviations of the non-covalent bond lengths calculated with B97M-V (gray) and MP2 + δ(T) (red) compared to the semi-experimental uncertainties (error bars).

114

of MP2 + δ(T) for π–π interactions, at rank 30.

115

The absolute deviations of the calculated bond lengths from the semi-experimental

116

equilibrium values (|∆reSE |) are shown for the top density functional B97M-V and the

117

MP2 + δ(T) methods in Figure 3. The reported uncertainties in the semi-experimental bond

118

lengths 11 are also included. For Ne–containing complexes, both methods struggle with the

119

Ne–OCS complex and with the position of Ne in the Ne–Ar–N2 O and Ne–Ar–HCl trimers. In

120

other dispersion dominated complexes, the rather poor performance of the composite method

121

for the Kr–OCS dimer could be due to the frozen core approximation or neglection of rela-

122

tivistic effects in the basis sets used. The results of the two methods for π–π interactions is

8


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0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 B97M-V DSD-PBEPBE-D3(BJ) PBE0-2 LC-VV10 B2PLYP-D3(BJ) ωB97M-V ωB97X-V B3LYP-D3(BJ) CCSD(T) PBE0-D3 BLYP-D3m(BJ) M05-2X MN15-D3(BJ) BLYP-D3(BJ) M08-SO MN12-SX B97-D3(BJ) MN12-L B3PW91-D3(BJ) N12-D3(BJ)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 |∆Eint | / [kJ/mol]

Figure 4: MAE values of counterpoise-corrected interaction energies obtained with the listed methods with respect to the MP2 + δ(T) data at reSE geometries (blue) and at optimized geometries (orange). 123

comparable, with the large deviation in one of the CS2 –OCS parameters due to a different

124

angle between the two monomers. In H–bonded complexes, the composite method gener-

125

ally performs better than B97M-V, with the latter method significantly overpredicting the

126

H2 C=O–HCN angle compared to both MP2 + δ(T) and the semi-experimental uncertainty.

127

3.1

128

Counterpoise-corrected interaction energies of the 16 weakly-bound clusters have been cal-

129

culated at the semi-experimental geometries, as well as at the optimised geometries, with

130

the ten best-performing methods. The full results are listed in the Supporting information

131

files. The MAE values with respect to the MP2 + δ(T) results are shown in Fig. 4. The

132

average difference between Eint values at reSE and at the MP2 + δ(T)–optimized geometries

133

is just below 1.1 kJ/mol, with the highest difference (10.8 kJ/mol or 43%) obtained for the

134

HF–H2 CO complex. This increase in interaction energies and associated errors should be

135

considered when further components of binding energies are required, as zero point vibra-

136

tional corrections have to be obtained at the minima.

Interaction energies of the NCDT16 dataset

9



137

The MN15-D3(BJ) functional performs rather well for both sets of interaction energies

138

and it is the best out of the 20 methods studied. Among the best methods for non-covalent

139

geometries (top part of Fig. 4), the error in the interaction energies at the minima increases

140

compared to the error at the reSE structures, mainly due to a further overprediction of the

141

interaction energies in H–bonded complexes. Methods without empirical or non-local disper-

142

sion terms generally underpredict the interactions for dispersion-dominated complexes, even

143

when MP2 correlation is included (cf. PBE0-2). The only exception among the functionals

144

shown is M05-2X, which on average overpredicts Eint of Ne–containing complexes by about

145

0.5 kJ/mol. The large absolute error in CCSD(T) data compared to the MP2 + δ(T) results

146

is a systematic underprediction of the interaction energies due to the smaller basis set used,

147

possibly further exacerbated by the application of counterpoise corrections. 37

148

3.2

149

The performance of the methods listed in Table 1 for the accuracy of non-covalent bond

150

lengths has been correlated with the performance observed for five other benchmark datasets,

151

with the overall results shown in Table 2. The six datasets can be split into three pairs:

152

non-covalent semi-experimental and theoretical equilibrium bond lengths (NCDT16 11 and

153

A21G, 3 respectively), counterpoise-corrected interaction energies (A24 3 and NCCE31 14 ),

154

and covalent semi-experimental and theoretical equilibrium bond lengths (CCse22 13 and

155

CS20, 14 respectively). Despite using different basis sets, our results calculated for the five

156

datasets are generally comparable to literature data, obtaining qualitative agreement with

157

the A21G data of Mardirossian and Head-Gordon, 28 an agreement within 0.64 kJ/mol with

158

the results of Peverati and Truhlar 14 and Roch 38 for the A24 and NCCE31 datasets, or

159

within 1 m˚ A for the CS20 results of Peverati and Truhlar. 14

Correlations with other datasets

160

The average errors of the methods for the two datasets of non-covalent bond lengths are

161

strongly correlated, with ρNCDT16, A21G = 0.94. The MAEs obtained for the A21G dataset

162

are much lower than for the NCDT16 dataset, as in the A21G benchmark the whole bond 10


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Table 2: Pearson’s correlation coefficient between studied benchmark datasets.

NCDT16 A21G A24 NCCE31 CCse22

A21G 0.94

A24 0.84 0.87

NCCE31 0.56 0.62 0.74

CCse22 0.21 0.21 0.31 0.54

CS20 0.24 0.19 0.38 0.48 0.81

163

matrix is assessed. The only bond length present in both datasets – the r(C–C) of the

164

T-shaped HCCH–HCCH dimer – differs by 70 m˚ A, with CCSD(T)/CBS underpredicting

165

A from our CCSD(T) and the reSE . This difference is consistent with the |∆reSE | ∼ 65 m˚

166

MP2 + δ(T) results.

167

The correlation between the two datasets of counterpoise-corrected interaction ener-

168

gies is also strong (ρA24, NCCE31 = 0.74).

Similarly to the NCDT16 data above, our

169

counterpoise-corrected CCSD(T)/may-cc-pVTZ calculation consistently overpredicts the ref-

170

erence CP-CCSD(T)/CBS binding energies with |∆Eint | = 1.5 kJ/mol. As our extrapolated

171

MP2 + δ(T) results have a much lower |∆Eint | = 0.1 kJ/mol, the difference is attributed

172

to the basis set incompleteness error. The correlation between the covalent bond length

173

datasets (ρCCse22, CS20 = 0.81) is weaker than for the non-covalent bond datasets.

174

The SOGGA11-X 39 method has been previously highlighted as an excellent functional

175

for covalent bond lengths. 40 However, for non-covalent bond lenghts, its performance is poor

176

(|∆reSE | > 750 m˚ A, 300 m˚ A with D3(BJ)) even when compared to non-dispersion corrected

177

single hybrids, such as PBE0 (|∆reSE | = 182 m˚ A). The lack of transferability between er-

178

rors in covalent and non-covalent bonds is also confirmed by the low correlation coefficient

179

ρNCDT16,CCse22 = 0.21. On the other hand, the comparably high correlation coefficient be-

180

tween interaction energies and non-covalent bonds (ρNCDT16,A24 = 0.84) shows that accurate

181

description of energetics generally corresponds to accurate geometries – the notable excep-

182

tions with poorly predicted geometries despite |∆Eint | < 1 kJ/mol are ωB97X-D, 41 B97-

183

D3, 6,42 TPSS-D3(BJ) 27,43 and M08-HX(-D3). 44,45 Curiously, the two half-and-half hybrid 11



2.0

|∆Eint | / [kJ/mol]

1.5

0

15

150

200 (A)

PBE-D3m(BJ) PBE0-2

M06-L-D3 VV10 M05

7

PBEh-3c B97-D2

MP2 MN15-D3(BJ) M06-2X-D3 5 HSE06-D3(BJ) M08-HX-D3 LC-VV10 1 M08-SO 4 B97M-V TPSS-D3(BJ) 6 TPSSH-D3(BJ) 2 ωB97M-V 3 ωPBE-D3m(BJ) ωB97X-V M05-2X-D3 MP2+δ(T)

(B)

(A): PBE0-D3 BLYP-D3m(BJ) (B): M06-2X-D3 PBE-D3m(BJ) (C): M05-2X-D3 MN15-L (D): MN15-D3(BJ) (E): TPSSH-D3(BJ) VV10 B97-D2 (F): ωB97M-V MN12-SX (G): ωPBE-D3m(BJ) (H): DSD-PBEPBE-D3(BJ) TPSS-D3(BJ) M08-SO (I): MP2 + δ(T)

10

LC-VV10 B3LYP-D3(BJ)

PBEh-3c

M11

M06-HF HCTH/120-D3(BJ) B97M-V C G MP2 M05 B ωB97X-V D E M06-L-D3 PBE0-2 A CCSD H F HSE06-D3(BJ) I ωB97X B2PLYP-D3(BJ) DSD-PBEP86-D3(BJ) CCSD(T) DSD-BLYP-D3(BJ)

5 0

100

B2PLYP-D3(BJ) DSD-BLYP-D3(BJ) M06-HF DSD-PBEP86-D3(BJ) DSD-PBEPBE-D3(BJ) MN15-L BLYP-D3m(BJ) CCSD(T) B3LYP-D3(BJ) M11 ωB97X HCTH/120-D3(BJ)

PBE0-D3

0.5 0.0 20

50

(1): (2): (3): (4): (5): (6): (7):

1.0

SE | / [m˚ |∆rcov A]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 24

0

50

100 |∆reSE |

M08-HX-D3

150

200

/ [m˚ A]

Figure 5: Correlation diagrams for performance in prediction of non-covalent bonds (|∆reSE |, NCDT16 dataset): (A) correlation with MAE of counterpoise-corrected interaction energies SE |, CCse22). The dashed (|∆Eint |, A24); (B) correlation with MAE of covalent bonds (|∆rcov line shows average performance of the dataset. For clarity, only selected methods are shown. Colours as in Figure 1. 184

functionals 25 (BHandH with 50% Slater exchange and BHandHLYP with 50% B88 exchange)

185

perform much better than both three-parameter functionals (B3PW91 25 and B3LYP 25,26 ).

186

This is due to the poor description of dispersion in the three-parameter functionals in all rare

187

gas complexes (see Supporting information for details). However, with dispersion corrections,

188

the B3LYP-D3(BJ) method 25–27 is one of the top methods.

189

The latter two correlations are shown in graphical form in Figure 5. Only methods with

190

|∆reSE | < 200 m˚ A in the NCDT16 dataset are listed, and only the best-performing dispersion

191

correction is shown for each functional, if it is better than the parent functional. While the

12


Page 13 of 24

192

B97M-V 23 functional is the best studied method for non-covalent bond lengths, the related

193

range-separated ωB97M-V 29 offers a more balanced performance for accurate interaction

194

energies (Figure 5 (A), |∆Eint | = 0.3 kJ/mol) and covalent bond lengths (Figure 5 (B),

195

SE | = 4 m˚ |∆rcov A). The most balanced double hybrid functional remains DSD-PBEPBE-

196

D3(BJ), 24 as its somewhat large |∆Eint | of 0.5 kJ/mol in the A24 dataset is offset by its

197

remarkably good performance for the NCCE31 dataset. For non-meta-GGA single hybrid

198

functionals, good overall functionals are the range-separated ωB97X-V 28 and global hybrid

199

B3LYP-D3(BJ). 25–27 With the exception of B97M-V, the meta-GGA functionals achieve

200

worse results than dispersion-corrected GGA functionals. The most balanced GGA func-

201

SE | = 9 m˚ A, as the tional is HCTH/120-D3(BJ) 27,46 with |∆Eint | = 1.3 kJ/mol and |∆rcov

202

dispersion-corrected forms of PBE and BLYP have comparably large deviation in covalent

203

SE | > 16 m˚ A). bond lengths (|∆rcov

204

3.3

Climbing the Jacob’s ladder

|∆reSE | / [m˚ A]

200 150

(A)

100 50 GGA

GSH

RSH DH

DSD

1.5 GGA

GSH

RSH DH

DSD

|∆Eint | / [kJ/mol]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.0 0.5 (B)

0.0

Figure 6: Performance of related functionals in non-covalent interactions: (A) bond lengths, (B) interaction energies. Colour denotes functional family (green: BLYP, red: PBE, blue: B97, cyan: meta-B97) and dispersion corrections (yellow: empirical, black: VV10). Vertical lines delineate GGA’s from global single hybrids, range-separated hybrids, double hybrids and spin-component scaled double hybrids.

13



205

The large amount of collected data allows us to investigate the effects of systematic

206

improvement of DFT methods by climbing the so-called “Jacob’s ladder”. The resulting av-

207

erage errors in non-covalent bond lengths and interaction energies are shown in Figure 6. In

208

the BLYP-based series (BLYP-D3(BJ), B3LYP-D3(BJ), B2PLYP-D3(BJ) and DSD-BLYP-

209

D3(BJ); green), a significant improvement in prediction of the structure is achieved by in-

210

clusion of HF exchange, while the inclusion of MP2 correlation shows mixed results. In

211

the PBE-based series (PBE-D3(BJ), PBE0-D3(BJ), ωPBE-D3(BJ), LC-VV10, PBE0-2 and

212

DSD-PBEPBE-D3(BJ); red), inclusion of HF-exchange leads to a better prediction of inter-

213

action energies in addition to the structural parameters, especially in the range-separated

214

form and with inclusion of the VV10 non-local correlation. The dispersionless PBE0-2 dou-

215

ble hybrid functional performs well for structures, but interaction energies are not improved

216

from the related single hybrids, as a consequence of the lack of dispersion corrections. In

217

the B97-based data (blue), the results are mixed. Without dispersion corrections, the range-

218

separated hybrid ωB97X performs quite poorly for interaction energies - worse than the

219

original B97-D2 form. The empirical dispersion correction included in ωB97X-D improves

220

the agreement in interaction energies, but significantly degrades the structural performance;

221

inclusion of the VV10 non-local correlation in ωB97X-V remedies this problem.

222

3.4

223

It is widely accepted 47 that correctly scaled dispersion corrections can greatly improve the

224

agreement in non-covalent interaction energies. For non-covalent bond lengths, near-MP2

225

quality can be achieved with dispersion corrected GGAs. 27 This statement is further con-

226

firmed by our overall results (cf. Figure 1) and is especially pronounced for π–π interactions

227

(cf. Figure 2). For the “worst case” of BLYP and B3LYP functionals, which do not describe

228

dispersion interactions well, the inclusion of D2 correction 5 already reduces |∆reSE | at least

229

by a factor of 7. However, the D3 and D3(BJ) corrections 6,27 perform much better, with

230

further reduction in MAE’s by a factor of 2. The the revised version (D3m(BJ)) 48 shows no

Role of dispersion corrections

14


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231

systematic improvement compared to the original Becke-Johnson-damped version (D3(BJ)).

232

However, the most accurate method for improving non-covalent bond lengths is the non-local

233

correlation in VV10, 8 with 4 out of 5 methods including this component performing better

234

than CCSD(T). In light of this, the recently developed spin-component scaled double hybrids

235

with non-local correlation in place of the empirical dispersion term (ie. DSD-PBEPBE-NL)

236

are likely to achieve good results, 49 however the availability of such methods is limited. On

237

the other hand, the non-local correlation approach has a higher computational cost than

238

empirical dispersion corrections, especially as the implementation of analytical gradients

239

for these functionals is not widespread. It would be interesting to compare the current re-

240

sults to methods including with the recently-developed D4 correction, 7 unfortunately their

241

availability is also currently limited.

242

The importance of developing density functionals with systematic consideration of dis-

243

persion corrections can also be highlighted. The dispersion-corrected spin-component-scaled

244

double hybrids of Kozuch and Martin 24,50 as well as the recent functionals of Mardirossian

245

and Head-Gordon 23,28,29 were systematically parametrised with dispersion corrections, and

246

as a result show good performance for dispersion dominated complexes. However, some dis-

247

persionless functionals trained on datasets including non-covalent interactions, such as the

248

functionals from the Truhlar group, 30,33,34,51 are excellent for H–bonded systems even with-

249

out empirical dispersion terms. While applying such further corrections to these functionals

250

is possible, 36,45 it does not lead to a systematic improvement of non-covalent geometries.

251

4

252

In the current work, we have benchmarked 89 ab initio methods using the NCDT16 dataset 11

253

to establish their performance for prediction of non-covalent bond lengths, and five other

254

reference datasets to analyse correlations with accuracy for interaction energies and cova-

255

lent bonds. The best overall method is the ωB97M-V range-separated meta-GGA hybrid

Conclusions

15



256

functional of Mardirossian and Head-Gordon, 29 thanks to its balanced performance for non-

257

covalent structures, interaction energies and covalent bond lengths. The best results in non-

258

covalent structures were achieved by the related meta-GGA B97M-V. 23 Other recommended

259

methods include the single hybrid B3LYP-D3(BJ) 25–27 with excellent results for complexes

260

with binding energies below 10 kJ/mol and its widespread availability, and the double hy-

261

brid DSD-PBEPBE-D3(BJ) 24 which is considerably more accurate in interaction energies.

262

For π–π interactions, the B97-D3 method 6,42 performs rather well, while for H–bonded com-

263

plexes the newer Minnesota functionals from the MN12 family 32,34 and MN15-D3(BJ) 33,45

264

are excellent performers.

265

The results also highlight that the ranking of a method for covalent bonds is not neces-

266

sarily transferable to non-covalent bonds, while a low average error in interaction energies

267

generally correlates with the quality of prediction of non-covalent bond lengths. Additionally,

268

at the highest level of theory used in the current work (MP2/CBS + δCCSD(T)/3-ζ), the

269

differences in interaction energies between the semi-experimental and optimized geometries

270

can be as large as 40% (HF–H2 CO complex). The MAE between the two sets of structures of

271

62 m˚ A confirms the importance of validation of computational methods against experimental

272

observables.

273

Furthermore, systematic improvements of the density functional approximations by

274

range-separation, MP2 correlation and empirical dispersion generally improve the agree-

275

ment with reference interaction energies. However, the most consistent functionals for non-

276

covalent bond lengths contain the non-local correlation from the VV10 8 functional, and are

277

systematically parametrised with the dispersion terms taken into account.

278

Acknowledgements

279

PK would like to thank Dr. S. Lehtola for his help with Libxc, Dr. D.G.A. Smith and

280

Dr. L.A. Burns for their help with ψ 4 , and Dr. D.A. Obenchain for his support and helpful

16


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281

comments. This work was partially carried out on the Leibniz Universität Hannover compute

282

cluster, which is funded by the Leibniz Universität Hannover, the Lower Saxony Ministry of

283

Science and Culture (MWK) and the German Research Association (DFG).

284

Supporting information

285

A spreadsheet with the MAE values for all six datasets and all complexes in the NCDT16

286

dataset, a document containing detailed references for all functionals, an archive of Python

287

driver routines for performing the benchmarks, an archive of optimized structures with se-

288

lected methods.

289

References

290

(1) Zhao, Y.; Truhlar, D. G. Benchmark databases for nonbonded interactions and their

291

use to test density functional theory. J. Chem. Theory Comput. 2005, 1, 415–432.

292

(2) Hohenstein, E. G.; Sherrill, C. D. Wavefunction methods for noncovalent interactions.

293

Wiley Interdiscip. Rev. Comput. Mol. Sci. 2012, 2, 304–326.

294

ˇ aˇc, J.; Hobza, P. Describing noncovalent interactions beyond the common approx(3) Rez´

295

imations: How accurate is the “gold standard,” CCSD(T) at the complete basis set

296

limit? J. Chem. Theory Comput. 2013, 9, 2151–2155.

297

298

299

300

301

ˇ aˇc, J.; Hobza, P. Benchmark calculations of interaction energies in noncovalent (4) Rez´ complexes and their applications. Chem. Rev. 2016, 116, 5038–5071. (5) Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 2006, 27, 1787–1799. (6) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio

17



302

parametrization of density functional dispersion correction (DFT-D) for the 94 elements

303

H-Pu. J. Chem. Phys. 2010, 132, 154104.

304

305

306

307

308

309

310

311

(7) Caldeweyher, E.; Bannwarth, C.; Grimme, S. Extension of the D3 dispersion coefficient model. J. Chem. Phys. 2017, 147, 034112. (8) Vydrov, O. A.; Van Voorhis, T. Nonlocal van der Waals density functional: The simpler the better. J. Chem. Phys. 2010, 133, 244103. (9) Grimme, S. Semiempirical hybrid density functional with perturbative second-order correlation. J. Chem. Phys. 2006, 124, 034108. (10) Chai, J. D.; Mao, S. P. Seeking for reliable double-hybrid density functionals without fitting parameters: The PBE0-2 functional. Chem. Phys. Lett. 2012, 538, 121–125.

312

(11) Kraus, P.; Obenchain, D. A. D.; Frank, I. Benchmark-quality semiexperimental struc-

313

tural parameters of van der Waals complexes. J. Phys. Chem. A 2018, 122, 1077–1087.

314

(12) Grimme, S.; Brandenburg, J. G.; Bannwarth, C.; Hansen, A. Consistent structures and

315

interactions by density functional theory with small atomic orbital basis sets. J. Chem.

316

Phys. 2015, 143, 054107.

317

(13) Piccardo, M.; Penocchio, E.; Puzzarini, C.; Biczysko, M.; Barone, V. Semi-experimental

318

equilibrium structure determinations by employing B3LYP/SNSD anharmonic force

319

fields: Validation and application to semirigid organic molecules. J. Phys. Chem. A

320

2015, 119, 2058–2082.

321

(14) Peverati, R.; Truhlar, D. G. Quest for a universal density functional: the accuracy

322

of density functionals across a broad spectrum of databases in chemistry and physics.

323

Philos. Trans. A. Math. Phys. Eng. Sci. 2014, 372, 20120476.

324

(15) Parrish, R. M. et al. Psi4 1.1: An open-source electronic structure program emphasizing

18


Page 18 of 24

Page 19 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


325

automation, advanced libraries, and interoperability. J. Chem. Theory Comput. 2017,

326

13, 3185–3197.

327

(16) Lehtola, S.; Steigemann, C.; Oliveira, M. J.; Marques, M. A. Recent developments in

328

LIBXC – A comprehensive library of functionals for density functional theory. Soft-

329

wareX 2018, 7, 1–5.

330

331

(17) Rappoport, D.; Furche, F. Property-optimized Gaussian basis sets for molecular response calculations. J. Chem. Phys. 2010, 133, 134105.

332

(18) Hellweg, A.; Rappoport, D. Development of new auxiliary basis functions of the Karl-

333

sruhe segmented contracted basis sets including diffuse basis functions (def2-SVPD,

334

def2-TZVPPD, and def2-QVPPD) for RI-MP2 and RI-CC calculations. Phys. Chem.

335

Chem. Phys. 2015, 17, 1010–1017.

336

(19) Papajak, E.; Zheng, J.; Xu, X.; Leverentz, H. R.; Truhlar, D. G. Perspectives on basis

337

sets beautiful: Seasonal plantings of diffuse basis functions. J. Chem. Theory Comput.

338

2011, 7, 3027–3034.

339

(20) Halkier, A.; Helgaker, T.; Jørgensen, P.; Klopper, W.; Olsen, J. Basis-set convergence

340

of the energy in molecular Hartree–Fock calculations. Chem. Phys. Lett. 1999, 302,

341

437–446.

342

(21) Kendall, R. A.; Dunning, T. H.; Harrison, R. J. Electron affinities of the first-row

343

atoms revisited. Systematic basis sets and wave functions. J. Chem. Phys. 1992, 96,

344

6796–6806.

345

(22) Woon, D. E.; Dunning, T. H. Gaussian basis sets for use in correlated molecular cal-

346

culations. X. The atoms aluminum through argon revisited. J. Chem. Phys. 1993, 98,

347

1358–1371.

19



348

(23) Mardirossian, N.; Head-Gordon, M. Mapping the genome of meta-generalized gradient

349

approximation density functionals: The search for B97M-V. J. Chem. Phys. 2015, 142,

350

074111.

351

(24) Kozuch, S.; Martin, J. M. L. Spin-component-scaled double hybrids: An extensive

352

search for the best fifth-rung functionals blending DFT and perturbation theory. J.

353

Comput. Chem. 2013, 34, 2327–2344.

354

355

(25) Becke, A. D. A new mixing of Hartree–Fock and local density-functional theories. J. Chem. Phys. 1993, 98, 1372–1377.

356

(26) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. Ab initio calculation

357

of vibrational absorption and circular dichroism spectra using density functional force

358

fields. J. Phys. Chem. 1994, 98, 11624–11627.

359

360

(27) Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the damping function in dispersion corrected density functional theory. J. Comput. Chem. 2011, 32, 1456–1465.

361

(28) Mardirossian, N.; Head-Gordon, M. ωB97X-V: A 10-parameter, range-separated hy-

362

brid, generalized gradient approximation density functional with nonlocal correlation,

363

designed by a survival-of-the-fittest strategy. Phys. Chem. Chem. Phys. 2014, 16, 9904.

364

(29) Mardirossian, N.; Head-Gordon, M. ωB97M-V: A combinatorially optimized, range-

365

separated hybrid, meta-GGA density functional with VV10 nonlocal correlation. J.

366

Chem. Phys. 2016, 144, 0–23.

367

(30) Zhao, Y.; Truhlar, D. G. The M06 suite of density functionals for main group ther-

368

mochemistry, thermochemical kinetics, noncovalent interactions, excited states, and

369

transition elements: Two new functionals and systematic testing of four M06-class

370

functionals and 12 other function. Theor. Chem. Acc. 2008, 120, 215–241.

20


Page 20 of 24

Page 21 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


371

(31) Goerigk, L.; Grimme, S. A thorough benchmark of density functional methods for gen-

372

eral main group thermochemistry, kinetics, and noncovalent interactions. Phys. Chem.

373

Chem. Phys. 2011, 13, 6670–6688.

374

(32) Peverati, R.; Truhlar, D. G. An improved and broadly accurate local approximation

375

to the exchangecorrelation density functional: The MN12-L functional for electronic

376

structure calculations in chemistry and physics. Phys. Chem. Chem. Phys. 2012, 14,

377

13171–13174.

378

(33) Yu, H. S.; He, X.; Li, S. L.; Truhlar, D. G. MN15: A Kohn–Sham global-hybrid

379

exchange-correlation density functional with broad accuracy for multi-reference and

380

single-reference systems and noncovalent interactions. Chem. Sci. 2016, 7, 5032–5051.

381

(34) Peverati, R.; Truhlar, D. G. Screened-exchange density functionals with broad accuracy

382

for chemistry and solid-state physics. Phys. Chem. Chem. Phys. 2012, 14, 16187–16191.

383

(35) Peverati, R.; Truhlar, D. G. Exchange-correlation functional with good accuracy for

384

both structural and energetic properties while depending only on the density and its

385

gradient. J. Chem. Theory Comput. 2012, 8, 2310–2319.

386

387

388

389

(36) Goerigk, L. Treating London-dispersion effects with the latest Minnesota density functionals: Problems and possible solutions. J. Phys. Chem. Lett. 2015, 6, 3891–3896. (37) Mentel, M.; Baerends, E. J. Can the counterpoise correction for basis set superposition effect be justified? J. Chem. Theory Comput. 2014, 10, 252–267.

390

(38) Roch, L. M.; Baldridge, K. K. Dispersion-corrected spin-component-scaled double-

391

hybrid density functional theory: Implementation and performance for non-covalent

392

interactions. J. Chem. Theory Comput. 2017, 13, 2650–2666.

393

(39) Peverati, R.; Truhlar, D. G. Communication: A global hybrid generalized gradient

394

approximation to the exchange-correlation functional that satisfies the second-order 21



395

density-gradient constraint and has broad applicability in chemistry. J. Chem. Phys.

396

2011, 135, 191102.

397

´ Savarese, M.; Su, N. Q.; Pérez-Jiménez, A. ´ J.; Xu, X.; Sancho(40) Brémond, E.;

398

Garc´ıa, J. C.; Adamo, C. Benchmarking density functionals on structural parameters of

399

small-/medium-sized organic molecules. J. Chem. Theory Comput. 2016, 12, 459–465.

400

(41) Chai, J.-D.; Head-Gordon, M. Long-range corrected hybrid density functionals with

401

damped atomatom dispersion corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615–

402

6620.

403

404

(42) Becke, A. D. Density-functional thermochemistry. V. Systematic optimization of exchange-correlation functionals. J. Chem. Phys. 1997, 107, 8554–8560.

405

(43) Tao, J.; Perdew, J. P.; Staroverov, V. N.; Scuseria, G. E. Climbing the density functional

406

ladder: Non-Empirical meta-generalized gradient approximation designed for molecules

407

and solids. Phys. Rev. Lett. 2003, 91, 146401.

408

(44) Zhao, Y.; Truhlar, D. G. Exploring the limit of accuracy of the global hybrid meta den-

409

sity functional for main-group thermochemistry, kinetics, and noncovalent interactions.

410

J. Chem. Theory Comput. 2008, 4, 1849–1868.

411

(45) Goerigk, L.; Hansen, A.; Bauer, C. A.; Ehrlich, S.; Najibi, A.; Grimme, S. A look

412

at the density functional theory zoo with the advanced GMTKN55 database for gen-

413

eral main group thermochemistry, kinetics and noncovalent interactions. Phys. Chem.

414

Chem. Phys. 2017, 19, 32184–32215.

415

416

417

(46) Boese, A. D.; Doltsinis, N. L.; Handy, N. C.; Sprik, M. New generalized gradient approximation functionals. J. Chem. Phys. 2000, 112, 1670–1678. (47) Kruse, H.; Goerigk, L.; Grimme, S. Why the standard B3LYP/6-31G* model chemistry

22


Page 22 of 24

Page 23 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


418

should not be used in DFT calculations of molecular thermochemistry: Understanding

419

and correcting the problem. J. Org. Chem. 2012, 77, 10824–10834.

420

(48) Smith, D. G. A.; Burns, L. A.; Patkowski, K.; Sherrill, C. D. Revised damping parame-

421

ters for the D3 dispersion correction to density functional theory. J. Phys. Chem. Lett.

422

2016, 7, 2197–2203.

423

(49) Kesharwani, M. K.; Karton, A.; Martin, J. M. Benchmark ab initio conformational

424

energies for the proteinogenic amino acids through explicitly correlated methods. As-

425

sessment of density functional methods. J. Chem. Theory Comput. 2016, 12, 444–454.

426

(50) Kozuch, S.; Martin, J. M. L. DSD-PBEP86: in search of the best double-hybrid DFT

427

with spin-component scaled MP2 and dispersion corrections. Phys. Chem. Chem. Phys.

428

2011, 13, 20104–20107.

429

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(51) Peverati, R.; Truhlar, D. G. Improving the accuracy of hybrid meta-GGA density functionals by range separation. J. Phys. Chem. Lett. 2011, 2, 2810–2817.

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Density Functional Theory for Microwave Spectroscopy of

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