Supplementary Material for “Benchmarking density-functional-theory calculations of rotational g tensors and magnetizabilities using accurate coupled-cluster calculations”

calculations of rotational g tensors and magnetizabilities using accurate coupled-cluster calculations”

Ola B. Lutnæs, Andrew M. Teale, Trygve Helgaker Centre for Theoretical and Computational Chemistry,

Department of Chemistry, University of Oslo, P.O.B. 1033 Blindern, N-0315 Oslo, Norway

David J. Tozer

Department of Chemistry, Durham University, South Road, Durham, DH1 3LE,UK

Kenneth Ruud

Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø,

N-9037 Tromsø, Norway, J¨ urgen Gauss,

Institut f¨ ur Physikalische Chemie, Universit¨ at Mainz, D-55099 Mainz, Germany

September 11, 2009

1

1 The optimized CCSD(T)/cc-pVTZ geometries used in the present study (a.u.) . . . . 5

2 Rotational g tensors: DFT/aug-cc-pCVQZ values. . . . . 6

3 Rotational g tensors: DFT-OEP/aug-cc-pCVQZ values. . . . 7

4 Magnetizabilities: DFT/aug-cc-pCVQZ values. All quantities in SI units (10 ⁻³⁰ JT ⁻² ). . . . . 8

5 Magnetizabilities: DFT-OEP/aug-cc-pCVQZ values. All quantities in SI units (10 ⁻³⁰ JT ⁻² ). . . . 9

6 Rotational g tensors: a comparison of WY(CC) and coupled-cluster results. ^a . . . . 10

7 Magnetizabilities: a comparison of WY(CC) and coupled-cluster results. ^a All quantities in SI units (10 ⁻³⁰ JT ⁻² ). . . . 11

8 Rotational g tensors calculated by wave function methods with the cc-pVDZ basis set. . . . 12

9 Rotational g tensors calculated by density functional methods with the cc-pVDZ basis set. . . . 13

10 Rotational g tensors calculated by wave function methods with the cc-pVTZ basis set . . . . 14

11 Rotational g tensors calculated by density functional methods with the cc-pVTZ basis set. . . . 15

12 Rotational g tensors calculated by wave function methods with the cc-pVQZ basis set. . . . 16

13 Rotational g tensors calculated by density functional methods with the cc-pVQZ basis set. . . . 17

14 Rotational g tensors calculated by wave function methods with the cc-pCVDZ basis set. . . . 18

15 Rotational g tensors calculated by density functional methods with the cc-pCVDZ basis set. . . . 19

16 Rotational g tensors calculated by wave function methods with the cc-pCVTZ basis set. . . . 20

17 Rotational g tensors calculated by density functional methods with the cc-pCVTZ basis set. . . . 21

18 Rotational g tensors calculated by wave function methods with the cc-pCVQZ basis set. . . . 22

19 Rotational g tensors calculated by density functional methods with the cc-pCVQZ basis set. . . . 23

20 Rotational g tensors calculated by wave function methods with the aug-cc-pVDZ basis set. . . . . 24

21 Rotational g tensors calculated by density functional methods with the aug-cc-pVDZ basis set. . . . . 25

22 Rotational g tensors calculated by wave function methods with the aug-cc-pVTZ basis set. . . . . 26

23 Rotational g tensors calculated by density functional methods with the aug-cc-pVTZ basis set. . . . . 27

24 Rotational g tensors calculated by wave function methods with the aug-cc-pVQZ basis set. . . . . 28

25 Rotational g tensors calculated by density functional methods with the aug-cc-pVQZ basis set . . . . . 29

26 Rotational g tensors calculated by wave function methods with the aug-cc-pCVDZ basis set. . . . 30

27 Rotational g tensors calculated by density functional methods with the aug-cc-pCVDZ basis set. . . . 31

28 Rotational g tensors calculated by wave function methods with the aug-cc-pCVTZ basis set. . . . 32

29 Rotational g tensors calculated by density functional methods with the aug-cc-pCVTZ basis set. . . . 33

30 Rotational g tensors calculated by wave function methods with the aug-cc-pCVQZ basis set. . . . 34

31 Rotational g tensors calculated by density functional methods with the aug-cc-pCVQZ basis set. . . . 35

32 Magnetizabilities Calculated using wave function methods with the cc-pVDZ basis set. All quantities in SI units (10 ⁻³⁰ JT ⁻² ) . . . . 36

33 Magnetizabilities Calculated using wave function methods with the cc-pVTZ basis set. All quantities in SI units (10 ⁻³⁰ JT ⁻² ) . . . . 37

34 Magnetizabilities Calculated using wave function methods with the cc-pVQZ basis set. All quantities in SI units (10 ⁻³⁰ JT ⁻² ) . . . . 38

35 Magnetizabilities Calculated using wave function methods with the cc-pCVDZ basis set. All quantities in SI units (10 ⁻³⁰ JT ⁻² ) . . . . 39

36 Magnetizabilities Calculated using wave function methods with the cc-pCVTZ basis set. All quantities in SI units (10 ⁻³⁰ JT ⁻² ) . . . . 40

37 Magnetizabilities Calculated using wave function methods with the cc-pCVQZ basis set. All quantities in SI units (10 ⁻³⁰ JT ⁻² ) . . . . 41

38 Magnetizabilities Calculated using wave function methods with the aug-cc-pVDZ basis set. All quan- tities in SI units (10 ⁻³⁰ JT ⁻² ) . . . . 42

39 Magnetizabilities Calculated using wave function methods with the aug-cc-pVTZ basis set. All quan- tities in SI units (10 ⁻³⁰ JT ⁻² ) . . . . 43

40 Magnetizabilities Calculated using wave function methods with the aug-cc-pVQZ basis set. All quan- tities in SI units (10 ⁻³⁰ JT ⁻² ) . . . . 44

41 Magnetizabilities Calculated using wave function methods with the aug-cc-pCVDZ basis set. All quan-

tities in SI units (10 ⁻³⁰ JT ⁻² ) . . . . 45

tities in SI units (10 ⁻³⁰ JT ⁻² ) . . . . 46 43 Magnetizabilities Calculated using wave function methods with the aug-cc-pCVQZ basis set. All quan-

tities in SI units (10 ⁻³⁰ JT ⁻² ) . . . . 47 44 Magnetizabilities Calculated using DFT methods with the cc-pVDZ basis set. All quantities in SI units

(10 ⁻³⁰ JT ⁻² ) . . . . 48 45 Magnetizabilities Calculated using DFT methods with the cc-pVTZ basis set. All quantities in SI units

(10 ⁻³⁰ JT ⁻² ) . . . . 49 46 Magnetizabilities Calculated using DFT methods with the cc-pVQZ basis set. All quantities in SI units

(10 ⁻³⁰ JT ⁻² ) . . . . 50 47 Magnetizabilities Calculated using DFT methods with the cc-pCVDZ basis set. All quantities in SI

units (10 ⁻³⁰ JT ⁻² ) . . . . 51 48 Magnetizabilities Calculated using DFT methods with the cc-pCVTZ basis set. All quantities in SI

units (10 ⁻³⁰ JT ⁻² ) . . . . 52 49 Magnetizabilities Calculated using DFT methods with the cc-pCVQZ basis set. All quantities in SI

units (10 ⁻³⁰ JT ⁻² ) . . . . 53 50 Magnetizabilities Calculated using DFT methods with the aug-cc-pVDZ basis set. All quantities in SI

units (10 ⁻³⁰ JT ⁻² ) . . . . 54 51 Magnetizabilities Calculated using DFT methods with the aug-cc-pVTZ basis set. All quantities in SI

units (10 ⁻³⁰ JT ⁻² ) . . . . 55 52 Magnetizabilities Calculated using DFT methods with the aug-cc-pVQZ basis set. All quantities in SI

units (10 ⁻³⁰ JT ⁻² ) . . . . 56 53 Magnetizabilities Calculated using DFT methods with the aug-cc-pCVDZ basis set. All quantities in

SI units (10 ⁻³⁰ JT ⁻² ) . . . . 57 54 Magnetizabilities Calculated using DFT methods with the aug-cc-pCVTZ basis set. All quantities in

SI units (10 ⁻³⁰ JT ⁻² ) . . . . 58 55 Magnetizabilities Calculated using DFT methods with the aug-cc-pCVQZ basis set. All quantities in

SI units (10 ⁻³⁰ JT ⁻² ) . . . . 59

• All calculations were performed using molecular geometries optimized at the all-electron CCSD(T) / cc-pVTZ level (obtainable from the authors on request).

• Spherical-harmonic basis functions were used throughout.

• In the coupled-cluster property calculations all electrons were correlated.

• In the tables, Benchmark refers to all-electron CCSD(T) / aug-cc-pCV[TQ]Z results. See main text for details of extrapolation techniques.

• Empirical equilibrium values for the rotational g tensors were obtained by subtracting B3LYP / aug-cc-pCVTZ ZPVCs from experimental results.

• References to the experimental data used for the rotational g tensors can be found in the main text.

Table 1: The optimized CCSD(T)/cc-pVTZ geometries used in the present study (a.u.)

HF

H 0.000000 0.000000 1.644119 F 0.000000 0.000000 -0.087217

CO

C 0.000000 0.000000 1.212532 O 0.000000 0.000000 -0.927517

N

N 0.000000 0.000000 1.039909 N 0.000000 0.000000 -1.039909

H

O

O 0.000000 0.000000 -0.136392 H 0.000000 1.423659 0.981343 H 0.000000 -1.423659 0.981343

HCN

H 0.000000 0.000000 3.065393 C 0.000000 0.000000 1.059657 N 0.000000 0.000000 -1.126448

HOF

O -1.418692 0.109003 0.000000 H -1.731365 -1.689574 0.000000 F 1.289927 0.003159 0.000000

O

O 0.000000 0.000000 0.836474 O 0.000000 2.047812 -0.418237 O 0.000000 -2.047812 -0.418237

NH

N 0.140247 -0.000044 0.000000 H -0.596990 1.763051 0.000000 H -0.597203 -0.881503 1.526834 H -0.597203 -0.881503 -1.526834

CH

O

O 0.000000 0.000000 -1.141647 C 0.000000 0.000000 1.138301 H 0.000000 1.762395 2.235653 H 0.000000 -1.762395 2.235653

CH

C 0.000000 0.000000 0.000000 H 0.000000 1.675468 1.184736 H 0.000000 -1.675468 1.184736 H 1.675468 0.000000 -1.184734 H -1.675468 0.000000 -1.184734

C

H

C 0.000000 1.259465 0.000000 C 0.000000 -1.259465 0.000000 H 1.740064 2.321626 0.000000 H -1.740064 2.321626 0.000000 H 1.740064 -2.321626 0.000000 H -1.740064 -2.321626 0.000000

AlF

Al 0.000000 0.000000 -1.308405 F 0.000000 0.000000 1.856777

CH

F

C -1.415757 0.000027 0.000000 F 1.188948 0.000010 0.000000 H -2.089940 -1.939604 0.000000 H -2.089922 0.969848 1.679773 H -2.089922 0.969848 -1.679773

C

H

C 0.000000 0.000000 1.665529 C 0.000000 1.224758 -0.906882 C 0.000000 -1.224758 -0.906882 H 0.000000 2.975838 -1.918779 H 0.000000 -2.975838 -1.918779 H 1.719445 0.000000 2.777316 H -1.719445 0.000000 2.777316

FCCH

C 0.000000 0.000000 2.592052 C 0.000000 0.000000 0.326613 H 0.000000 0.000000 4.585734 F 0.000000 0.000000 -2.088915

FCN

F 0.000000 0.000000 2.064937 C 0.000000 0.000000 -0.328104 N 0.000000 0.000000 -2.519310

H

S

S 0.000000 0.000000 -0.110773 H 0.000000 1.822447 1.640654 H 0.000000 -1.822447 1.640654

HCP

H 0.000000 0.000000 4.026662 C 0.000000 0.000000 2.011473 P 0.000000 0.000000 -0.916741

HFCO

O -2.087492 0.692863 0.000000 C -0.377439 -0.739889 0.000000 F 2.038239 0.001906 0.000000 H -0.466335 -2.791172 0.000000

H

C

O

C 0.000000 0.000000 -2.442179 C 0.000000 0.000000 0.038704 O 0.000000 0.000000 2.238037 H 0.000000 1.772139 -3.428402 H 0.000000 -1.772139 -3.428402

LiF

Li 0.000000 0.000000 -2.173222 F 0.000000 0.000000 0.803950

LiH

H 0.000000 0.000000 2.637010 Li 0.000000 0.000000 -0.378734

N

O

N 0.000000 0.000000 -2.268420 N 0.000000 0.000000 -0.134930 O 0.000000 0.000000 2.104236

OCS

O 0.000000 0.000000 3.183208 C 0.000000 0.000000 0.993454 S 0.000000 0.000000 -1.971392

OF

O 0.000000 0.000000 1.162482 F 0.000000 2.082491 -0.489006 F 0.000000 -2.082491 -0.489006

H

C

O

O 0.000000 0.000000 1.518240 C 0.000000 1.382495 -0.796276 C 0.000000 -1.382495 -0.796276 H 1.731975 2.379466 -1.212540 H -1.731975 2.379466 -1.212540 H 1.731975 -2.379466 -1.212540 H -1.731975 -2.379466 -1.212540

PN

N 0.000000 0.000000 -1.951610 P 0.000000 0.000000 0.889157

SO

S 0.000000 0.000000 -0.703245

O 0.000000 2.355745 0.692198

O 0.000000 -2.355745 0.692198

Table 2: Rotational g tensors: DFT/aug-cc-pCVQZ values.

Molecule LDA BLYP PBE KT2 B3LYP B97-2 B97-3 PBE0 CAM

HF 0.7520 0.7298 0.7333 0.7241 0.7401 0.7391 0.7409 0.7439 0.7478 CO −0.2876 −0.2825 −0.2868 −0.2703 −0.2826 −0.2841 −0.2875 −0.2866 −0.2801

15

N

−0.2787 −0.2740 −0.2787 −0.2606 −0.2735 −0.2764 −0.2773 −0.2778 −0.2703 H

O 0.6727 0.6429 0.6498 0.6354 0.6564 0.6568 0.6596 0.6636 0.6675 0.7335 0.7050 0.7120 0.7059 0.7149 0.7155 0.7180 0.7216 0.7221 0.6613 0.6294 0.6370 0.6295 0.6413 0.6421 0.6444 0.6489 0.6504 HC

N −0.1085 −0.1052 −0.1081 −0.0940 −0.0990 −0.0994 −0.0990 −0.1002 −0.0951 HOF 0.6839 0.6544 0.6606 0.6507 0.6693 0.6692 0.6722 0.6762 0.6803

−0.1272 −0.1297 −0.1269 −0.1185 −0.1200 −0.1151 −0.1143 −0.1151 −0.1182

−0.0727 −0.0766 −0.0737 −0.0685 −0.0676 −0.0632 −0.0623 −0.0630 −0.0656 O

−3.4348 −3.3005 −3.3322 −2.9551 −3.6721 −3.6711 −3.8352 −3.8066 −3.8103

−0.2434 −0.2424 −0.2413 −0.2303 −0.2635 −0.2613 −0.2705 −0.2679 −0.2708

−0.0801 −0.0820 −0.0801 −0.0788 −0.0780 −0.0749 −0.0749 −0.0753 −0.0774 NH

0.5891 0.5470 0.5606 0.5513 0.5603 0.5641 0.5664 0.5731 0.5711 0.5258 0.4839 0.4973 0.4890 0.4943 0.4975 0.4990 0.5065 0.5038 CH

O −3.4608 −3.1655 −3.2347 −2.9514 −3.0880 −3.0183 −3.0564 −3.1169 −3.1224

−0.2416 −0.2383 −0.2399 −0.2280 −0.2341 −0.2318 −0.2339 −0.2348 −0.2317

−0.1119 −0.1167 −0.1115 −0.1067 −0.1009 −0.0915 −0.0892 −0.0927 −0.0966 CH

0.3566 0.3011 0.3223 0.3111 0.3087 0.3152 0.3149 0.3270 0.3192 C

H

−0.4958 −0.4665 −0.4714 −0.4404 −0.4358 −0.4263 −0.4245 −0.4317 −0.4258

−0.1318 −0.1277 −0.1294 −0.1185 −0.1249 −0.1237 −0.1250 −0.1258 −0.1251 0.0506 0.0399 0.0460 0.0441 0.0472 0.0527 0.0535 0.0543 0.0511 AlF −0.0800 −0.0805 −0.0812 −0.0784 −0.0805 −0.0818 −0.0817 −0.0814 −0.0806 CH

F 0.2873 0.2337 0.2522 0.2436 0.2516 0.2581 0.2603 0.2694 0.2662

−0.0698 −0.0743 −0.0707 −0.0693 −0.0676 −0.0625 −0.0619 −0.0629 −0.0665 C

H

−0.0971 −0.1010 −0.0997 −0.0920 −0.0977 −0.0960 −0.0960 −0.0961 −0.0957

−0.1624 −0.1682 −0.1620 −0.1646 −0.1611 −0.1527 −0.1518 −0.1538 −0.1581 0.0553 0.0478 0.0515 0.0492 0.0529 0.0558 0.0566 0.0572 0.0567 FCCH −0.0101 −0.0116 −0.0102 −0.0078 −0.0093 −0.0074 −0.0072 −0.0075 −0.0086 FC

N −0.0525 −0.0528 −0.0519 −0.0487 −0.0516 −0.0500 −0.0502 −0.0504 −0.0515 H

S 0.4205 0.3637 0.3913 0.3877 0.3753 0.3901 0.3858 0.4004 0.3874 0.2298 0.1372 0.1808 0.1761 0.1469 0.1699 0.1607 0.1853 0.1575 0.2637 0.1968 0.2276 0.2247 0.2041 0.2196 0.2137 0.2311 0.2130 HCP −0.0545 −0.0514 −0.0526 −0.0439 −0.0475 −0.0466 −0.0464 −0.0476 −0.0465 HFCO −0.4876 −0.4751 −0.4796 −0.4478 −0.4625 −0.4566 −0.4615 −0.4636 −0.4582

−0.0825 −0.0824 −0.0819 −0.0790 −0.0811 −0.0797 −0.0803 −0.0804 −0.0809

−0.0388 −0.0407 −0.0394 −0.0386 −0.0389 −0.0374 −0.0373 −0.0374 −0.0385 H

C

O −0.3096 −0.4039 −0.3593 −0.3684 −0.4074 −0.3818 −0.3991 −0.3695 −0.4112

−0.0369 −0.0398 −0.0377 −0.0361 −0.0377 −0.0350 −0.0350 −0.0353 −0.0371

−0.0248 −0.0287 −0.0268 −0.0254 −0.0273 −0.0254 −0.0259 −0.0253 −0.0266 LiF 0.0541 0.0510 0.0535 0.0616 0.0585 0.0626 0.0644 0.0619 0.0603 LiH −0.6557 −0.6345 −0.6367 −0.5879 −0.6593 −0.6567 −0.6727 −0.6621 −0.6728 N

O −0.0825 −0.0845 −0.0828 −0.0805 −0.0826 −0.0800 −0.0800 −0.0806 −0.0824 OCS −0.0301 −0.0314 −0.0303 −0.0292 −0.0303 −0.0288 −0.0290 −0.0290 −0.0299 OF

−0.2553 −0.2518 −0.2495 −0.2280 −0.2179 −0.2098 −0.2049 −0.2079 −0.2098

−0.0656 −0.0659 −0.0648 −0.0605 −0.0603 −0.0581 −0.0575 −0.0579 −0.0591

−0.0758 −0.0770 −0.0755 −0.0725 −0.0735 −0.0711 −0.0709 −0.0711 −0.0721 H

C

O −0.1052 −0.1110 −0.1052 −0.1028 −0.1007 −0.0933 −0.0922 −0.0931 −0.0982 0.0173 0.0072 0.0124 0.0120 0.0165 0.0212 0.0222 0.0229 0.0209 0.0347 0.0284 0.0320 0.0336 0.0320 0.0345 0.0346 0.0358 0.0332 PN −0.2554 −0.2506 −0.2548 −0.2393 −0.2485 −0.2496 −0.2515 −0.2521 −0.2440 SO

−0.6547 −0.6495 −0.6579 −0.6356 −0.6591 −0.6686 −0.6692 −0.6703 −0.6525

−0.1235 −0.1241 −0.1235 −0.1212 −0.1234 −0.1222 −0.1226 −0.1226 −0.1224

−0.0893 −0.0901 −0.0888 −0.0873 −0.0894 −0.0876 −0.0881 −0.0881 −0.0895

a

CAM-B3LYP functional

Table 3: Rotational g tensors: DFT-OEP/aug-cc-pCVQZ values.

Molecule O-B3LYP O-B97-2 O-B97-3 O-PBE0 O-CAM

HF 0.7402 0.7391 0.7415 0.7440 0.7473

CO −0.2735 −0.2751 −0.2752 −0.2753 −0.2697

15

N

−0.2632 −0.2660 −0.2633 −0.2649 −0.2597

H

O 0.6551 0.6554 0.6588 0.6620 0.6649

0.7146 0.7152 0.7181 0.7214 0.7216 0.6401 0.6409 0.6434 0.6475 0.6486 HC

N −0.0953 −0.0958 −0.0940 −0.0955 −0.0914

HOF 0.6677 0.6675 0.6701 0.6743 0.6770

−0.1209 −0.1162 −0.1151 −0.1164 −0.1205

−0.0696 −0.0653 −0.0648 −0.0655 −0.0689 O

−2.9298 −2.9062 −2.8193 −2.8580 −2.8219

−0.2253 −0.2218 −0.2183 −0.2192 −0.2209

−0.0780 −0.0750 −0.0753 −0.0758 −0.0779

NH

0.5573 0.5616 0.5645 0.5698 0.5675

0.4928 0.4960 0.4977 0.5049 0.5024 CH

O −2.9699 −2.8858 −2.8953 −2.9597 −2.9492

−0.2254 −0.2226 −0.2226 −0.2242 −0.2220

−0.1044 −0.0911 −0.0908 −0.0944 −0.1015

CH

0.3073 0.3137 0.3131 0.3253 0.3174

C

H

−0.4512 −0.4424 −0.4453 −0.4507 −0.4536

−0.1210 −0.1198 −0.1197 −0.1210 −0.1194 0.0450 0.0501 0.0507 0.0512 0.0462 AlF −0.0802 −0.0816 −0.0813 −0.0811 −0.0801 CH

F 0.2510 0.2570 0.2555 0.2681 0.2605

−0.0686 −0.0637 −0.0638 −0.0642 −0.0690 C

H

−0.0933 −0.0917 −0.0902 −0.0907 −0.0901

−0.1630 −0.1543 −0.1540 −0.1554 −0.1623 0.0505 0.0532 0.0533 0.0540 0.0521 FCCH −0.0095 −0.0077 −0.0076 −0.0079 −0.0093 FC

N −0.0512 −0.0495 −0.0495 −0.0499 −0.0511

H

S 0.3719 0.3870 0.3813 0.3965 0.3811

0.1477 0.1711 0.1624 0.1863 0.1607 0.2015 0.2171 0.2106 0.2280 0.2110 HCP −0.0456 −0.0449 −0.0440 −0.0454 −0.0433 HFCO −0.4447 −0.4395 −0.4389 −0.4420 −0.4354

−0.0796 −0.0782 −0.0784 −0.0786 −0.0792

−0.0392 −0.0377 −0.0376 −0.0377 −0.0387 H

C

O −0.3730 −0.3486 −0.3510 −0.3286 −0.3482

−0.0372 −0.0346 −0.0347 −0.0348 −0.0369

−0.0261 −0.0243 −0.0244 −0.0240 −0.0254

LiF 0.0590 0.0630 0.0648 0.0623 0.0605

LiH −0.6568 −0.6557 −0.6716 −0.6611 −0.6707 N

O −0.0811 −0.0785 −0.0784 −0.0790 −0.0808 OCS −0.0299 −0.0284 −0.0285 −0.0285 −0.0295 OF

−0.2271 −0.2196 −0.2167 −0.2192 −0.2241

−0.0613 −0.0593 −0.0588 −0.0592 −0.0608

−0.0721 −0.0699 −0.0694 −0.0697 −0.0713 H

C

O −0.1039 −0.0965 −0.0963 −0.0970 −0.1036 0.0135 0.0182 0.0182 0.0192 0.0161 0.0302 0.0326 0.0323 0.0335 0.0309 PN −0.2348 −0.2356 −0.2330 −0.2349 −0.2266 SO

−0.6195 −0.6279 −0.6169 −0.6213 −0.6035

−0.1203 −0.1191 −0.1186 −0.1189 −0.1188

−0.1203 −0.1191 −0.1186 −0.1189 −0.1188

−0.0892 −0.0875 −0.0879 −0.0879 −0.0891

a

O-CAM-B3LYP method

Table 4: Magnetizabilities: DFT/aug-cc-pCVQZ values. All quantities in SI units (10 ⁻³⁰ JT ⁻² ).

Molecule LDA BLYP PBE KT2 B3LYP B97-2 B97-3 PBE0 CAM ^a

HF −181.1 −181.0 −180.1 −176.8 −178.5 −175.9 −176.2 −177.1 −179.0 CO −206.6 −209.1 −205.6 −209.1 −206.8 −202.5 −201.2 −202.9 −208.5 N ₂ −201.0 −203.6 −199.7 −204.9 −202.1 −197.1 −197.1 −198.1 −204.2 H ₂ O −241.0 −239.5 −238.5 −235.1 −236.9 −233.6 −234.0 −235.3 −237.6 HCN −265.1 −268.7 −264.4 −270.6 −269.6 −265.0 −265.4 −266.0 −272.0 HOF −228.9 −226.6 −227.4 −227.5 −231.1 −230.7 −232.1 −232.8 −233.4 O ₃ 195.4 180.3 183.7 138.8 238.8 239.7 264.4 258.0 258.5 NH 3 −298.2 −293.4 −293.1 −289.7 −291.5 −288.0 −288.4 −290.5 −292.7 CH ₂ O −95.8 −109.3 −104.9 −118.0 −114.9 −116.6 −115.4 −112.8 −115.4 CH ₄ −329.5 −318.2 −320.4 −316.1 −317.4 −314.7 −314.7 −318.5 −320.1 C 2 H 4 −331.1 −333.4 −330.8 −335.2 −336.9 −334.3 −334.5 −335.3 −339.3 AlF −396.0 −399.4 −397.1 −392.6 −397.0 −393.6 −392.8 −394.5 −397.1 CH ₃ F −315.4 −309.6 −311.3 −307.4 −312.5 −312.2 −313.4 −314.4 −314.6 C 3 H 4 −464.4 −458.4 −459.5 −457.4 −463.1 −462.6 −464.1 −465.1 −468.1 FCCH −438.6 −438.5 −437.6 −440.2 −440.2 −438.3 −439.2 −439.9 −441.8 FCN −365.3 −366.4 −365.0 −367.6 −367.6 −365.4 −366.0 −366.6 −369.5 H 2 S −466.1 −457.2 −458.8 −455.9 −455.6 −452.1 −452.6 −456.4 −456.9 HCP −477.5 −485.6 −479.2 −487.9 −487.8 −481.9 −483.0 −482.7 −488.5 HFCO −296.9 −299.4 −296.9 −299.0 −300.7 −298.1 −298.0 −298.7 −302.9 H 2 C 2 O −427.7 −420.7 −421.9 −422.2 −422.4 −421.2 −421.0 −423.7 −424.9 LiF −196.4 −196.4 −196.2 −196.2 −194.9 −193.5 −194.6 −194.2 −195.7 LiH −135.9 −136.6 −135.2 −137.1 −131.2 −129.5 −127.0 −129.1 −129.2 N 2 O −334.5 −332.2 −332.0 −330.6 −334.0 −332.7 −334.2 −334.3 −336.1 OCS −576.7 −576.2 −574.8 −575.7 −579.9 −577.3 −578.8 −579.7 −583.5 OF ₂ −220.1 −220.5 −221.4 −226.2 −233.9 −235.0 −237.9 −238.1 −239.6 H 4 C 2 O −529.8 −520.4 −523.9 −521.3 −527.0 −527.3 −529.0 −531.5 −531.3 PN −284.2 −292.1 −283.9 −296.6 −292.2 −285.0 −284.0 −284.6 −297.0 SO ₂ −294.6 −298.0 −293.3 −296.6 −295.9 −289.0 −290.6 −291.0 −300.2

a CAM-B3LYP functional

Table 5: Magnetizabilities: DFT-OEP/aug-cc-pCVQZ values. All quantities in SI units (10 ⁻³⁰ JT ⁻² ).

Molecule O-B3LYP O-B97-2 O-B97-3 O-PBE0 O-CAM

HF −178.5 −175.9 −176.2 −177.1 −179.0 CO −210.5 −206.2 −206.2 −207.6 −212.6 N

−206.4 −201.4 −203.0 −203.5 −208.7 H

O −236.8 −233.5 −233.9 −235.2 −237.4 HCN −271.6 −266.9 −268.1 −268.6 −274.1 HOF −229.8 −229.2 −230.1 −231.1 −230.8

O

123.9 121.4 108.3 112.1 107.0

NH

−291.1 −287.7 −288.1 −290.0 −292.3 CH

O −121.0 −124.4 −124.5 −121.7 −123.6 CH

−317.0 −314.3 −314.3 −318.1 −319.6 C

H

−336.0 −333.3 −333.5 −334.3 −336.9 AlF −397.1 −393.7 −393.1 −394.7 −397.4 CH

F −310.7 −310.3 −311.1 −312.3 −311.8 C

H

−461.6 −461.1 −462.2 −463.4 −463.9 FCCH −439.6 −437.6 −438.3 −438.9 −440.2 FCN −368.7 −366.6 −367.3 −367.9 −370.5 H

S −455.3 −451.8 −452.1 −456.0 −456.5 HCP −489.9 −483.8 −485.6 −485.3 −492.0 HFCO −304.0 −301.3 −302.1 −302.8 −307.1 H

C

O −425.7 −424.4 −425.3 −427.6 −429.2 LiF −195.1 −193.7 −194.6 −194.4 −195.7 LiH −131.4 −129.6 −127.0 −129.2 −129.4 N

O −336.9 −335.5 −337.2 −337.4 −339.3 OCS −581.5 −579.0 −581.0 −581.6 −585.0 OF

−232.7 −233.4 −236.2 −236.3 −236.0 H

C

O −522.5 −522.5 −522.9 −525.8 −524.2 PN −305.9 −299.1 −302.4 −301.9 −314.7 SO

−307.3 −300.4 −305.4 −305.2 −314.5

a

O-CAM-B3LYP method

Table 6: Rotational g tensors: a comparison of WY(CC) and coupled-cluster results. ^a Molecule WY(CCSD) WY(CCSD(T)) CCSD CCSD(T)

HF 0.7511 0.7504 0.7535 0.7527

CO −0.2717 −0.2789 −0.2669 −0.2678

15 N ₂ −0.2654 −0.2720 −0.2576 −0.2591

H 2 O 0.6678 0.6666 0.6725 0.6707

0.7273 0.7279 0.7281 0.7284

0.6515 0.6517 0.6550 0.6547

HC ¹⁵ N −0.0949 −0.1008 −0.0846 −0.0882

NH ₃ 0.5709 0.5719 0.5755 0.5757

0.5032 0.5046 0.5084 0.5093

CH 2 O −2.8110 −2.9294 −2.8013 −2.8659

−0.2162 −0.2232 −0.2175 −0.2197

−0.0979 −0.1035 −0.0856 −0.0924

CH 4 0.3135 0.3163 0.3209 0.3231

C 2 H 4 −0.4381 −0.4465 −0.3561 −0.3688

−0.1190 −0.1233 −0.1110 −0.1123

0.0481 0.0472 0.0561 0.0538

CH 3 F 0.2602 0.2600 0.2731 0.2711

−0.0634 −0.0652 −0.0586 −0.0606 FC ¹⁵ N −0.0497 −0.0503 −0.0483 −0.0487

H 2 S 0.3864 0.3918 0.3945 0.3974

0.1690 0.1786 0.1778 0.1861

0.2149 0.2227 0.2234 0.2300

HCP −0.0442 −0.0484 −0.0359 −0.0385 N ₂ O −0.0794 −0.0794 −0.0775 −0.0780 PN −0.2350 −0.2482 −0.2253 −0.2285

a all-electron/aug-cc-pCVQZ values

Table 7: Magnetizabilities: a comparison of WY(CC) and coupled-cluster results. ^a All quantities in SI units (10 ⁻³⁰ JT ⁻² ).

Molecule WY(CCSD) WY(CCSD(T)) CCSD CCSD(T) HF −175.9 −176.7 −176.0 −176.7 CO −208.6 −206.4 −210.1 −210.4 N ₂ −202.6 −200.4 −206.0 −206.0 H 2 O −234.3 −235.4 −234.5 −235.5 HCN −268.2 −265.9 −273.8 −272.7 NH ₃ −288.9 −290.1 −289.6 −290.8 CH ₂ O −127.4 −119.9 −132.1 −127.8 CH 4 −314.8 −316.0 −316.5 −317.5 C2H ₄ −334.4 −332.6 −347.7 −346.1 CH ₃ F −310.9 −310.9 −317.1 −316.3 FCN −368.7 −367.3 −371.7 −370.9 H ₂ S −453.3 −455.1 −454.7 −456.3 HCP −487.3 −482.7 −497.1 −494.4 N 2 O −337.1 −337.5 −340.8 −339.8 PN −302.7 −289.8 −312.5 −309.7

a all-electron/aug-cc-pCVQZ values

Table 8: Rotational g tensors calculated by wave function methods with the cc-pVDZ basis set.

Molecule RHF CCSD CCSD(T) Benchmark emp. eq. exp.

HF 0.7407 0.7203 0.7181 0.7542 0.7543 0.7416

CO -0.2820 -0.2617 -0.2627 -0.2681 -0.2676 -0.2689 15N₂ -0.2820 -0.2657 -0.2677 -0.2591 -0.2577 -0.2593

H₂O 0.6641 0.6441 0.6411 0.6717 0.686 0.657

0.6964 0.6702 0.6669 0.7303 0.733 0.718

0.6297 0.6029 0.6003 0.6563 0.654 0.645

HC¹⁵N -0.0763 -0.0803 -0.0830 -0.0882 -0.0872 -0.0904

HOF 0.6885 0.6586 0.6544 0.6853 0.672 0.642

-0.0851 -0.0930 -0.0959 -0.1107 -0.108 -0.119 -0.0395 -0.0519 -0.0547 -0.0596 -0.060 -0.061 O₃ -6.6439 -3.2418 -2.9322 -2.8980 -3.1333 -2.9877 -0.4204 -0.2456 -0.2205 -0.2247 -0.2360 -0.2295 -0.0653 -0.0702 -0.0714 -0.0741 -0.0777 -0.0760

NH3 0.5572 0.5349 0.5320 0.5770 0.5795 0.5654

0.4823 0.4676 0.4659 0.5107 0.5086 0.5024

CH2O -2.7714 -2.8097 -2.8455 -2.8641 -2.8939 -2.9017 -0.2165 -0.2050 -0.2062 -0.2194 -0.2222 -0.2243 -0.0651 -0.0916 -0.0969 -0.0910 -0.0945 -0.0994

CH₄ 0.3032 0.3039 0.3033 0.3236 0.3217 0.3133

C₂H₄ -0.3257 -0.3444 -0.3550 -0.3679 N/A N/A

-0.1149 -0.1091 -0.1102 -0.1118 N/A N/A

0.0603 0.0501 0.0479 0.0550 N/A N/A

AlF -0.0824 -0.0770 -0.0763 -0.0794 -0.0808 -0.0805

CH₃F 0.2521 0.2283 0.2240 0.2724 0.277 0.265

-0.0514 -0.0572 -0.0586 -0.0601 -0.060 -0.062 C₃H₄ -0.0949 -0.0787 -0.0794 -0.0802 -0.0828 -0.0897 -0.1383 -0.1340 -0.1365 -0.1424 -0.1447 -0.1492

0.0646 0.0604 0.0590 0.0595 0.0586 0.0536

FCCH 0.0014 -0.0010 -0.0015 -0.0062 -0.0066 -0.0077 FC¹⁵N -0.0440 -0.0429 -0.0429 -0.0487 -0.0499 -0.0504

H2S 0.4116 0.3956 0.3929 0.3978 0.378 0.355

0.2053 0.2095 0.2078 0.1883 0.216 0.195

0.2267 0.2287 0.2275 0.2321 0.208 0.209

HCP -0.0297 -0.0331 -0.0353 -0.0382 -0.0389 -0.0430 HFCO -0.4141 -0.4190 -0.4207 -0.4268 -0.4270 -0.4227 -0.0737 -0.0711 -0.0710 -0.0770 -0.0703 -0.0771 -0.0341 -0.0350 -0.0354 -0.0367 -0.0366 -0.0371 H₂C₂O -0.3822 -0.4275 -0.4265 -0.4300 -0.4394 -0.4182 -0.0255 -0.0257 -0.0260 -0.0345 -0.0352 -0.0356 -0.0220 -0.0214 -0.0214 -0.0243 -0.0233 -0.0238

LiF 0.0889 0.0868 0.0861 0.0678 0.0733 0.0737

LiH -0.6190 -0.5611 -0.5610 -0.6649 -0.6646 -0.6584 N₂O -0.0723 -0.0694 -0.0696 -0.0778 -0.0780 -0.0789 OCS -0.0247 -0.0228 -0.0229 -0.0279 -0.0282 -0.0288 OF₂ -0.1317 -0.1678 -0.1763 -0.1972 -0.202 -0.213 -0.0449 -0.0489 -0.0506 -0.0550 -0.057 -0.058 -0.0610 -0.0631 -0.0656 -0.0671 -0.067 -0.068 H4C2O -0.0750 -0.0837 -0.0862 -0.0905 -0.0905 -0.0946

0.0341 0.0192 0.0162 0.0267 0.0256 0.0189

0.0406 0.0371 0.0362 0.0369 0.0333 0.0318

PN -0.2472 -0.2171 -0.2190 -0.2285 N/A N/A

SO₂ -0.7805 -0.6608 -0.6535 -0.5988 -0.5929 -0.6043 -0.1199 -0.1111 -0.1112 -0.1165 -0.1156 -0.1163 -0.0757 -0.0728 -0.0726 -0.0873 -0.0888 -0.0887 Errors Relative to Benchmark Set over all Molecules

ME -0.0703 -0.0068 -0.0029

MAE 0.0919 0.0229 0.0159

MaxE 3.7459 0.3438 0.1039

MRE 2.2 7.0 6.9

MARE 16.8 9.9 9.0

SD 0.5115 0.0537 0.0257

Errors Relative to Benchmark Set over Molecules Excluding O₃ ME 0.0026 -0.0001 -0.0025

MAE 0.0198 0.0171 0.0160

MaxE 0.1817 0.1038 0.1039

MRE 6.3 7.8 7.2

MARE 13.4 9.9 9.4

SD 0.0350 0.0271 0.0260

Errors Relative to emp. eq. over all Molecules

ME -0.0704 -0.0019 0.0027 0.0061

MAE 0.0953 0.0206 0.0215 0.0092

MaxE 3.5106 0.1085 0.2011 0.2353

MRE 3.0 7.5 7.4 0.4

MARE 17.7 10.4 9.7 2.7

SD 0.4986 0.0332 0.0400 0.0341

Errors Relative to emp. eq. over Molecules Excluding O₃

ME 0.0035 0.0004 -0.0019 0.0012

MAE 0.0225 0.0193 0.0181 0.0045

MaxE 0.1876 0.1035 0.1037 0.0298

MRE 6.9 8.0 7.4 0.0

MARE 14.5 10.7 9.9 2.5

SD 0.0393 0.0303 0.0286 0.0084

Errors Relative to exp. over all Molecules

ME -0.0684 0.0001 0.0046 0.0081

MAE 0.0979 0.0232 0.0176 0.0095

MaxE 3.6562 0.2541 0.0975 0.0897

MRE 1.8 7.1 7.1 0.1

MARE 19.6 11.4 10.4 5.0

SD 0.5198 0.0456 0.0259 0.0160

Errors Relative to exp. over Molecules Excluding O₃

ME 0.0088 0.0057 0.0034 0.0065

MAE 0.0221 0.0188 0.0173 0.0080

MaxE 0.1762 0.0973 0.0975 0.0433

MRE 6.0 7.7 7.3 -0.1

MARE 16.2 11.7 10.8 5.1

SD 0.0382 0.0278 0.0256 0.0112

Table 9: Rotational g tensors calculated by density functional methods with the cc-pVDZ basis set.

Molecule LDA BLYP PBE KT2 O-B3LYP O-B97-2 O-B97-3 O-PBE0 O-CAM B3LYP B97-2 B97-3 PBE0 CAM

-B3LYP -B3LYP

HF 0.7034 0.6760 0.6831 0.6759 0.6946 0.6999 0.7003 0.7033 0.7034 0.6951 0.6994 0.7020 0.7038 0.7036

CO -0.2908 -0.2862 -0.2902 -0.2734 -0.2820 -0.2846 -0.2830 -0.2838 -0.2792 -0.2854 -0.2859 -0.2889 -0.2888 -0.2832 15N2 -0.2946 -0.2901 -0.2947 -0.2764 -0.2792 -0.2804 -0.2769 -0.2790 -0.2745 -0.2884 -0.2904 -0.2903 -0.2921 -0.2858 H₂O 0.6334 0.5993 0.6091 0.5953 0.6221 0.6283 0.6313 0.6342 0.6339 0.6195 0.6233 0.6280 0.6304 0.6318 0.6540 0.6213 0.6346 0.6303 0.6357 0.6460 0.6474 0.6505 0.6415 0.6438 0.6532 0.6572 0.6586 0.6523 0.5975 0.5638 0.5752 0.5704 0.5856 0.5933 0.5942 0.5983 0.5935 0.5840 0.5902 0.5936 0.5967 0.5933 HC¹⁵N -0.1051 -0.1028 -0.1059 -0.0928 -0.0936 -0.0951 -0.0924 -0.0941 -0.0890 -0.0970 -0.0978 -0.0962 -0.0984 -0.0934

HOF 0.6445 0.6121 0.6209 0.6127 0.6318 0.6363 0.6391 0.6425 0.6435 0.6356 0.6394 0.6440 0.6462 0.6479

-0.1081 -0.1084 -0.1076 -0.1015 -0.1058 -0.1041 -0.1031 -0.1031 -0.1050 -0.1025 -0.1010 -0.1003 -0.1002 -0.1005 -0.0652 -0.0684 -0.0662 -0.0621 -0.0623 -0.0596 -0.0591 -0.0592 -0.0608 -0.0605 -0.0577 -0.0568 -0.0570 -0.0581 O₃ -3.7464 -3.5717 -3.6079 -3.1741 -3.0936 -3.0928 -2.9871 -3.0274 -2.9720 -3.9924 -3.9729 -4.1735 -4.1470 -4.1825 -0.2468 -0.2441 -0.2439 -0.2315 -0.2235 -0.2223 -0.2186 -0.2194 -0.2177 -0.2687 -0.2673 -0.2779 -0.2749 -0.2779 -0.0761 -0.0763 -0.0755 -0.0749 -0.0748 -0.0739 -0.0739 -0.0738 -0.0743 -0.0735 -0.0720 -0.0721 -0.0721 -0.0727 NH₃ 0.5388 0.4977 0.5139 0.5053 0.5097 0.5190 0.5213 0.5264 0.5187 0.5172 0.5255 0.5299 0.5339 0.5289 0.4833 0.4401 0.4551 0.4489 0.4648 0.4731 0.4749 0.4812 0.4742 0.4554 0.4607 0.4643 0.4702 0.4664 CH₂O -3.5083 -3.2151 -3.2777 -2.9949 -3.1165 -3.0513 -3.0477 -3.1001 -3.0943 -3.1498 -3.0647 -3.1098 -3.1721 -3.1945 -0.2287 -0.2264 -0.2280 -0.2169 -0.2177 -0.2167 -0.2149 -0.2165 -0.2135 -0.2238 -0.2220 -0.2237 -0.2247 -0.2219 -0.1127 -0.1162 -0.1102 -0.1055 -0.1094 -0.1001 -0.0993 -0.1016 -0.1079 -0.1006 -0.0906 -0.0885 -0.0919 -0.0961 CH₄ 0.3438 0.2871 0.3095 0.3021 0.2976 0.3081 0.3098 0.3193 0.3076 0.2986 0.3060 0.3095 0.3186 0.3102 C2H4 -0.4928 -0.4670 -0.4700 -0.4424 -0.4868 -0.4765 -0.4816 -0.4851 -0.4903 -0.4349 -0.4237 -0.4209 -0.4287 -0.4242 -0.1297 -0.1261 -0.1278 -0.1172 -0.1234 -0.1221 -0.1220 -0.1231 -0.1217 -0.1239 -0.1227 -0.1235 -0.1248 -0.1245 0.0467 0.0346 0.0420 0.0408 0.0335 0.0415 0.0409 0.0419 0.0338 0.0435 0.0501 0.0519 0.0518 0.0479 AlF -0.0745 -0.0746 -0.0756 -0.0736 -0.0747 -0.0764 -0.0767 -0.0759 -0.0749 -0.0757 -0.0774 -0.0779 -0.0770 -0.0757 CH₃F 0.2347 0.1786 0.2018 0.2001 0.1972 0.2116 0.2134 0.2209 0.2080 0.2096 0.2221 0.2274 0.2335 0.2263 -0.0672 -0.0715 -0.0677 -0.0661 -0.0650 -0.0602 -0.0601 -0.0606 -0.0651 -0.0645 -0.0595 -0.0586 -0.0597 -0.0629 C₃H₄ -0.0991 -0.1035 -0.1017 -0.0937 -0.0976 -0.0947 -0.0937 -0.0939 -0.0945 -0.0997 -0.0974 -0.0966 -0.0976 -0.0977 -0.1526 -0.1569 -0.1513 -0.1537 -0.1597 -0.1524 -0.1536 -0.1536 -0.1604 -0.1507 -0.1435 -0.1436 -0.1443 -0.1479 0.0554 0.0478 0.0516 0.0495 0.0502 0.0529 0.0535 0.0539 0.0513 0.0533 0.0562 0.0573 0.0577 0.0573 FCCH -0.0040 -0.0048 -0.0040 -0.0018 -0.0032 -0.0025 -0.0025 -0.0024 -0.0030 -0.0032 -0.0022 -0.0021 -0.0021 -0.0025 FC¹⁵N -0.0450 -0.0447 -0.0446 -0.0422 -0.0441 -0.0441 -0.0441 -0.0440 -0.0439 -0.0447 -0.0444 -0.0447 -0.0446 -0.0447 H₂S 0.4286 0.3752 0.4004 0.3980 0.3949 0.4112 0.4070 0.4194 0.4050 0.3902 0.4043 0.4032 0.4141 0.4041 0.2614 0.1814 0.2160 0.2134 0.2075 0.2282 0.2215 0.2411 0.2220 0.1961 0.2130 0.2092 0.2276 0.2105 0.2760 0.2148 0.2419 0.2413 0.2368 0.2542 0.2482 0.2628 0.2476 0.2257 0.2399 0.2369 0.2505 0.2366 HCP -0.0536 -0.0511 -0.0520 -0.0435 -0.0453 -0.0450 -0.0437 -0.0451 -0.0428 -0.0468 -0.0457 -0.0453 -0.0466 -0.0458 HFCO -0.4864 -0.4789 -0.4808 -0.4490 -0.4556 -0.4491 -0.4461 -0.4502 -0.4458 -0.4652 -0.4564 -0.4592 -0.4634 -0.4614 -0.0750 -0.0746 -0.0747 -0.0724 -0.0733 -0.0733 -0.0732 -0.0732 -0.0727 -0.0746 -0.0743 -0.0749 -0.0747 -0.0744 -0.0363 -0.0377 -0.0369 -0.0362 -0.0373 -0.0360 -0.0362 -0.0361 -0.0370 -0.0363 -0.0353 -0.0351 -0.0353 -0.0357 H₂C₂O -0.3237 -0.4165 -0.3713 -0.3707 -0.3555 -0.3323 -0.3214 -0.3080 -0.3258 -0.4127 -0.3857 -0.3949 -0.3726 -0.4132 -0.0271 -0.0286 -0.0275 -0.0262 -0.0274 -0.0263 -0.0266 -0.0263 -0.0271 -0.0275 -0.0265 -0.0267 -0.0264 -0.0271 -0.0201 -0.0238 -0.0223 -0.0209 -0.0209 -0.0195 -0.0196 -0.0190 -0.0201 -0.0228 -0.0217 -0.0220 -0.0214 -0.0222 LiF 0.0745 0.0726 0.0732 0.0800 0.0779 0.0805 0.0827 0.0806 0.0810 0.0789 0.0806 0.0826 0.0807 0.0811 LiH -0.5798 -0.5591 -0.5641 -0.5205 -0.5773 -0.5851 -0.6009 -0.5871 -0.5893 -0.5819 -0.5853 -0.6014 -0.5884 -0.5914 N₂O -0.0724 -0.0731 -0.0726 -0.0710 -0.0712 -0.0704 -0.0706 -0.0703 -0.0706 -0.0727 -0.0720 -0.0723 -0.0722 -0.0724 OCS -0.0246 -0.0252 -0.0248 -0.0240 -0.0243 -0.0238 -0.0241 -0.0238 -0.0239 -0.0248 -0.0244 -0.0247 -0.0244 -0.0244 OF₂ -0.2339 -0.2253 -0.2269 -0.2083 -0.2180 -0.2168 -0.2126 -0.2136 -0.2155 -0.1958 -0.1936 -0.1883 -0.1901 -0.1872 -0.0601 -0.0593 -0.0592 -0.0557 -0.0580 -0.0575 -0.0569 -0.0569 -0.0576 -0.0550 -0.0544 -0.0538 -0.0539 -0.0537 -0.0742 -0.0743 -0.0737 -0.0711 -0.0699 -0.0690 -0.0683 -0.0684 -0.0688 -0.0715 -0.0705 -0.0703 -0.0703 -0.0701 H₄C₂O -0.1013 -0.1060 -0.1003 -0.0983 -0.1019 -0.0964 -0.0958 -0.0965 -0.1021 -0.0957 -0.0889 -0.0875 -0.0886 -0.0924 0.0076 -0.0031 0.0033 0.0039 0.0017 0.0083 0.0085 0.0089 0.0031 0.0087 0.0150 0.0171 0.0167 0.0140 0.0336 0.0283 0.0315 0.0329 0.0301 0.0322 0.0323 0.0331 0.0311 0.0324 0.0347 0.0352 0.0360 0.0340 PN -0.2550 -0.2503 -0.2548 -0.2393 -0.2360 -0.2373 -0.2340 -0.2358 -0.2270 -0.2499 -0.2510 -0.2529 -0.2539 -0.2469 SO2 -0.7439 -0.7391 -0.7436 -0.7134 -0.7039 -0.7069 -0.6931 -0.6992 -0.6850 -0.7543 -0.7571 -0.7589 -0.7621 -0.7529 -0.1183 -0.1189 -0.1187 -0.1169 -0.1158 -0.1156 -0.1149 -0.1151 -0.1143 -0.1195 -0.1192 -0.1195 -0.1194 -0.1187 -0.0729 -0.0733 -0.0731 -0.0724 -0.0742 -0.0737 -0.0744 -0.0740 -0.0745 -0.0737 -0.0733 -0.0739 -0.0736 -0.0737 Errors Relative to Benchmark Set over all Molecules

ME -0.0389 -0.0418 -0.0385 -0.0207 -0.0226 -0.0173 -0.0146 -0.0146 -0.0158 -0.0416 -0.0357 -0.0402 -0.0393 -0.0422

MAE 0.0543 0.0479 0.0478 0.0326 0.0320 0.0296 0.0264 0.0291 0.0278 0.0480 0.0448 0.0484 0.0502 0.0499

MaxE 0.8484 0.6737 0.7099 0.2761 0.2524 0.1948 0.1836 0.2360 0.2302 1.0944 1.0749 1.2755 1.2490 1.2844

MRE -2.3 1.6 0.3 4.9 3.6 3.3 3.8 3.0 3.9 1.6 1.8 1.2 0.6 1.1

MARE 14.7 15.2 14.1 12.8 13.0 11.9 11.4 11.9 12.4 11.9 11.0 10.8 11.4 11.1

SD 0.1471 0.1058 0.1143 0.0561 0.0539 0.0494 0.0429 0.0505 0.0468 0.1543 0.1502 0.1772 0.1759 0.1804

Errors Relative to Benchmark Set over Molecules Excluding O₃

ME -0.0241 -0.0306 -0.0264 -0.0163 -0.0201 -0.0145 -0.0138 -0.0131 -0.0155 -0.0217 -0.0159 -0.0166 -0.0162 -0.0184

MAE 0.0404 0.0371 0.0363 0.0289 0.0300 0.0274 0.0261 0.0282 0.0279 0.0285 0.0254 0.0252 0.0276 0.0266

MaxE 0.6442 0.3509 0.4136 0.1444 0.2524 0.1872 0.1836 0.2360 0.2302 0.2857 0.2006 0.2457 0.3079 0.3303

MRE -1.6 2.4 1.0 5.5 4.0 3.6 4.0 3.2 4.1 2.8 3.0 2.6 1.9 2.4

MARE 14.7 15.4 14.3 13.2 13.6 12.4 11.9 12.5 13.0 11.4 10.5 10.1 10.7 10.4

SD 0.0978 0.0609 0.0681 0.0447 0.0495 0.0439 0.0428 0.0492 0.0473 0.0512 0.0434 0.0463 0.0544 0.0550

Errors Relative to emp. eq. over all Molecules

ME -0.0324 -0.0359 -0.0323 -0.0141 -0.0151 -0.0097 -0.0068 -0.0067 -0.0080 -0.0366 -0.0306 -0.0355 -0.0343 -0.0375

MAE 0.0500 0.0431 0.0433 0.0282 0.0285 0.0261 0.0268 0.0280 0.0287 0.0449 0.0419 0.0461 0.0475 0.0473

MaxE 0.6144 0.4384 0.4746 0.1441 0.2227 0.1575 0.1538 0.2062 0.2004 0.8591 0.8396 1.0402 1.0137 1.0491

MRE -1.0 2.6 1.5 5.9 4.6 4.4 4.9 4.1 4.8 2.6 2.9 2.4 1.8 2.1

MARE 13.6 14.2 13.1 12.1 12.0 11.0 10.6 11.1 11.5 11.4 10.9 10.9 11.3 10.7

SD 0.1264 0.0825 0.0915 0.0445 0.0472 0.0422 0.0457 0.0489 0.0502 0.1286 0.1243 0.1518 0.1508 0.1553

Errors Relative to emp. eq. over Molecules Excluding O3

ME -0.0212 -0.0287 -0.0241 -0.0143 -0.0172 -0.0116 -0.0108 -0.0098 -0.0124 -0.0200 -0.0141 -0.0148 -0.0142 -0.0168

MAE 0.0399 0.0363 0.0357 0.0290 0.0291 0.0265 0.0250 0.0271 0.0267 0.0287 0.0259 0.0259 0.0280 0.0270

MaxE 0.6144 0.3212 0.3839 0.1441 0.2227 0.1575 0.1538 0.2062 0.2004 0.2559 0.1708 0.2159 0.2782 0.3006

MRE -0.6 3.1 2.0 6.2 4.7 4.5 4.8 4.1 4.7 3.5 3.8 3.5 2.8 3.2

MARE 13.9 14.6 13.4 12.7 12.6 11.5 10.9 11.5 11.9 11.1 10.6 10.4 10.8 10.1

SD 0.0976 0.0602 0.0675 0.0456 0.0477 0.0427 0.0411 0.0474 0.0450 0.0509 0.0437 0.0462 0.0542 0.0546

Errors Relative to exp. over all Molecules

ME -0.0304 -0.0339 -0.0303 -0.0122 -0.0131 -0.0078 -0.0049 -0.0048 -0.0060 -0.0346 -0.0286 -0.0335 -0.0323 -0.0356

MAE 0.0498 0.0414 0.0425 0.0277 0.0257 0.0238 0.0204 0.0234 0.0222 0.0440 0.0425 0.0466 0.0485 0.0477

MaxE 0.7587 0.5840 0.6202 0.1864 0.2148 0.1496 0.1460 0.1984 0.1926 1.0047 0.9852 1.1858 1.1593 1.1948

MRE -0.7 3.4 2.0 6.2 5.0 4.6 5.0 4.2 5.1 2.8 2.8 2.2 1.6 2.0

MARE 12.7 12.6 11.8 11.2 10.6 10.0 9.5 10.2 10.3 10.1 10.7 10.6 11.3 10.3

SD 0.1404 0.0967 0.1058 0.0469 0.0447 0.0401 0.0359 0.0430 0.0402 0.1476 0.1436 0.1717 0.1703 0.1749

Errors Relative to exp. over Molecules Excluding O₃

ME -0.0159 -0.0234 -0.0188 -0.0090 -0.0119 -0.0062 -0.0055 -0.0045 -0.0070 -0.0147 -0.0088 -0.0095 -0.0088 -0.0115

MAE 0.0365 0.0313 0.0318 0.0254 0.0250 0.0228 0.0214 0.0238 0.0230 0.0245 0.0233 0.0232 0.0259 0.0243

MaxE 0.6066 0.3134 0.3760 0.1379 0.2148 0.1496 0.1460 0.1984 0.1926 0.2481 0.1630 0.2081 0.2704 0.2928

MRE -0.1 4.2 2.7 6.7 5.3 4.8 5.2 4.4 5.3 4.0 4.0 3.5 2.8 3.4

MARE 12.8 12.9 12.0 11.7 11.1 10.4 9.9 10.7 10.8 9.6 10.2 9.9 10.6 9.5

SD 0.0960 0.0569 0.0647 0.0409 0.0439 0.0387 0.0370 0.0440 0.0413 0.0481 0.0406 0.0436 0.0518 0.0525

Table 10: Rotational g tensors calculated by wave function methods with the cc-pVTZ basis set

Molecule RHF CCSD CCSD(T) Benchmark emp. eq. exp.

HF 0.7568 0.7427 0.7409 0.7542 0.7543 0.7416

CO -0.2811 -0.2654 -0.2664 -0.2681 -0.2676 -0.2689 15N₂ -0.2730 -0.2619 -0.2637 -0.2591 -0.2577 -0.2593

H₂O 0.6779 0.6654 0.6631 0.6717 0.686 0.657

0.7163 0.6992 0.6967 0.7303 0.733 0.718

0.6568 0.6368 0.6352 0.6563 0.654 0.645

HC¹⁵N -0.0768 -0.0819 -0.0853 -0.0882 -0.0872 -0.0904

HOF 0.6991 0.6783 0.6748 0.6853 0.672 0.642

-0.0890 -0.0973 -0.1010 -0.1107 -0.108 -0.119 -0.0406 -0.0520 -0.0554 -0.0596 -0.060 -0.061 O₃ -6.0041 -3.1747 -2.9077 -2.8980 -3.1333 -2.9877 -0.3945 -0.2446 -0.2214 -0.2247 -0.2360 -0.2295 -0.0654 -0.0705 -0.0720 -0.0741 -0.0777 -0.0760

NH3 0.5765 0.5648 0.5635 0.5770 0.5795 0.5654

0.5029 0.4996 0.4997 0.5107 0.5086 0.5024

CH2O -2.7183 -2.7876 -2.8447 -2.8641 -2.8939 -2.9017 -0.2196 -0.2121 -0.2137 -0.2194 -0.2222 -0.2243 -0.0663 -0.0872 -0.0936 -0.0910 -0.0945 -0.0994

CH₄ 0.3045 0.3215 0.3230 0.3236 0.3217 0.3133

C₂H₄ -0.3293 -0.3431 -0.3556 -0.3679 N/A N/A

-0.1144 -0.1091 -0.1105 -0.1118 N/A N/A

0.0611 0.0527 0.0505 0.0550 N/A N/A

AlF -0.0817 -0.0771 -0.0764 -0.0794 -0.0808 -0.0805

CH₃F 0.2610 0.2592 0.2557 0.2724 0.277 0.265

-0.0540 -0.0578 -0.0596 -0.0601 -0.060 -0.062 C₃H₄ -0.0941 -0.0769 -0.0774 -0.0802 -0.0828 -0.0897 -0.1444 -0.1376 -0.1404 -0.1424 -0.1447 -0.1492

0.0637 0.0606 0.0592 0.0595 0.0586 0.0536

FCCH -0.0015 -0.0029 -0.0036 -0.0062 -0.0066 -0.0077 FC¹⁵N -0.0465 -0.0462 -0.0464 -0.0487 -0.0499 -0.0504

H2S 0.3969 0.4008 0.4015 0.3978 0.378 0.355

0.1628 0.1964 0.2011 0.1883 0.216 0.195

0.2081 0.2291 0.2332 0.2321 0.208 0.209

HCP -0.0310 -0.0344 -0.0370 -0.0382 -0.0389 -0.0430 HFCO -0.4121 -0.4173 -0.4209 -0.4268 -0.4270 -0.4227 -0.0753 -0.0743 -0.0744 -0.0770 -0.0703 -0.0771 -0.0347 -0.0352 -0.0358 -0.0367 -0.0366 -0.0371 H₂C₂O -0.3883 -0.4146 -0.4125 -0.4300 -0.4394 -0.4182 -0.0303 -0.0298 -0.0303 -0.0345 -0.0352 -0.0356 -0.0240 -0.0231 -0.0232 -0.0243 -0.0233 -0.0238

LiF 0.0778 0.0749 0.0741 0.0678 0.0733 0.0737

LiH -0.6787 -0.6415 -0.6409 -0.6649 -0.6646 -0.6584 N₂O -0.0752 -0.0732 -0.0735 -0.0778 -0.0780 -0.0789 OCS -0.0271 -0.0258 -0.0259 -0.0279 -0.0282 -0.0288 OF₂ -0.1350 -0.1717 -0.1826 -0.1972 -0.202 -0.213 -0.0458 -0.0502 -0.0524 -0.0550 -0.057 -0.058 -0.0601 -0.0627 -0.0654 -0.0671 -0.067 -0.068 H4C2O -0.0788 -0.0851 -0.0883 -0.0905 -0.0905 -0.0946

0.0351 0.0242 0.0211 0.0267 0.0256 0.0189

0.0394 0.0370 0.0362 0.0369 0.0333 0.0318

PN -0.2433 -0.2249 -0.2273 -0.2285 N/A N/A

SO₂ -0.7091 -0.6230 -0.6194 -0.5988 -0.5929 -0.6043 -0.1177 -0.1125 -0.1128 -0.1165 -0.1156 -0.1163 -0.0823 -0.0803 -0.0800 -0.0873 -0.0888 -0.0887 Errors Relative to Benchmark Set over all Molecules

ME -0.0567 -0.0025 0.0004

MAE 0.0755 0.0140 0.0069

MaxE 3.1061 0.2767 0.0336

MRE 1.2 4.2 3.6

MARE 13.0 5.8 4.6

SD 0.4245 0.0408 0.0100

Errors Relative to Benchmark Set over Molecules Excluding O₃

ME 0.0041 0.0031 0.0005

MAE 0.0155 0.0089 0.0071

MaxE 0.1459 0.0765 0.0336

MRE 4.6 4.8 3.7

MARE 10.0 5.7 4.7

SD 0.0301 0.0148 0.0102

Errors Relative to emp. eq. over all Molecules

ME -0.0556 0.0028 0.0063 0.0061

MAE 0.0775 0.0121 0.0140 0.0092

MaxE 2.8708 0.1063 0.2256 0.2353

MRE 1.9 4.6 4.0 0.4

MARE 13.8 6.7 5.7 2.7

SD 0.4084 0.0205 0.0347 0.0341

Errors Relative to emp. eq. over Molecules Excluding O₃

ME 0.0050 0.0039 0.0015 0.0012

MAE 0.0177 0.0117 0.0097 0.0045

MaxE 0.1756 0.1063 0.0492 0.0298

MRE 5.1 4.8 3.8 0.0

MARE 11.0 6.8 5.6 2.5

SD 0.0356 0.0200 0.0146 0.0084

Errors Relative to exp. over all Molecules

ME -0.0537 0.0048 0.0082 0.0081

MAE 0.0818 0.0152 0.0108 0.0095

MaxE 3.0164 0.1870 0.0800 0.0897

MRE 0.9 4.1 3.7 0.1

MARE 15.9 8.5 6.8 5.0

SD 0.4297 0.0337 0.0167 0.0160

Errors Relative to exp. over Molecules Excluding O₃

ME 0.0103 0.0093 0.0068 0.0065

MAE 0.0191 0.0117 0.0096 0.0080

MaxE 0.1834 0.1141 0.0570 0.0433

MRE 4.3 4.5 3.7 -0.1

MARE 12.9 8.6 7.0 5.1

SD 0.0356 0.0196 0.0135 0.0112

Table 11: Rotational g tensors calculated by density functional methods with the cc-pVTZ basis set.

Molecule LDA BLYP PBE KT2 O-B3LYP O-B97-2 O-B97-3 O-PBE0 O-CAM B3LYP B97-2 B97-3 PBE0 CAM

-B3LYP -B3LYP

HF 0.7380 0.7133 0.7181 0.7093 0.7222 0.7235 0.7242 0.7276 0.7305 0.7268 0.7275 0.7303 0.7323 0.7349

CO -0.2874 -0.2825 -0.2870 -0.2700 -0.2748 -0.2776 -0.2770 -0.2771 -0.2717 -0.2824 -0.2840 -0.2869 -0.2865 -0.2800 15N2 -0.2846 -0.2802 -0.2845 -0.2662 -0.2691 -0.2716 -0.2691 -0.2706 -0.2659 -0.2788 -0.2809 -0.2812 -0.2824 -0.2757 H₂O 0.6630 0.6318 0.6399 0.6257 0.6423 0.6447 0.6459 0.6509 0.6525 0.6468 0.6483 0.6521 0.6553 0.6581 0.6973 0.6658 0.6755 0.6705 0.6726 0.6774 0.6793 0.6825 0.6803 0.6825 0.6872 0.6901 0.6929 0.6908 0.6439 0.6113 0.6204 0.6120 0.6210 0.6242 0.6250 0.6301 0.6296 0.6265 0.6294 0.6316 0.6360 0.6357 HC¹⁵N -0.1068 -0.1035 -0.1065 -0.0919 -0.0941 -0.0955 -0.0937 -0.0949 -0.0902 -0.0977 -0.0983 -0.0976 -0.0990 -0.0939

HOF 0.6739 0.6429 0.6501 0.6401 0.6539 0.6556 0.6567 0.6619 0.6647 0.6609 0.6620 0.6660 0.6690 0.6726

-0.1145 -0.1154 -0.1133 -0.1065 -0.1124 -0.1097 -0.1096 -0.1092 -0.1117 -0.1086 -0.1053 -0.1052 -0.1050 -0.1069 -0.0665 -0.0698 -0.0672 -0.0628 -0.0658 -0.0622 -0.0627 -0.0621 -0.0644 -0.0619 -0.0583 -0.0579 -0.0579 -0.0598 O₃ -3.5512 -3.4038 -3.4339 -3.0301 -3.0121 -3.0081 -2.9288 -2.9635 -2.9144 -3.7801 -3.7661 -3.9371 -3.9134 -3.9289 -0.2432 -0.2413 -0.2404 -0.2289 -0.2242 -0.2222 -0.2194 -0.2202 -0.2193 -0.2631 -0.2612 -0.2707 -0.2679 -0.2707 -0.0780 -0.0789 -0.0772 -0.0764 -0.0771 -0.0745 -0.0752 -0.0750 -0.0767 -0.0754 -0.0726 -0.0732 -0.0730 -0.0748 NH₃ 0.5782 0.5381 0.5520 0.5423 0.5459 0.5514 0.5520 0.5593 0.5544 0.5527 0.5576 0.5610 0.5663 0.5640 0.5180 0.4751 0.4895 0.4813 0.4880 0.4936 0.4875 0.5014 0.4940 0.4869 0.4913 0.4927 0.5003 0.4971 CH₂O -3.4579 -3.1627 -3.2312 -2.9437 -3.0269 -2.9732 -2.9644 -3.0280 -3.0093 -3.0935 -3.0238 -3.0498 -3.1230 -3.1319 -0.2343 -0.2308 -0.2328 -0.2211 -0.2191 -0.2185 -0.2171 -0.2186 -0.2152 -0.2280 -0.2266 -0.2284 -0.2293 -0.2257 -0.1117 -0.1165 -0.1109 -0.1064 -0.1061 -0.0957 -0.0955 -0.0978 -0.1042 -0.1010 -0.0911 -0.0894 -0.0925 -0.0969 CH₄ 0.3567 0.3011 0.3224 0.3132 0.3077 0.3145 0.3127 0.3257 0.3171 0.3091 0.3156 0.3150 0.3275 0.3198 C2H4 -0.4928 -0.4636 -0.4686 -0.4345 -0.4531 -0.4464 -0.4479 -0.4541 -0.4546 -0.4330 -0.4237 -0.4205 -0.4290 -0.4228 -0.1315 -0.1276 -0.1292 -0.1175 -0.1206 -0.1196 -0.1194 -0.1206 -0.1190 -0.1249 -0.1236 -0.1245 -0.1257 -0.1252 0.0510 0.0400 0.0463 0.0437 0.0435 0.0495 0.0492 0.0504 0.0446 0.0474 0.0529 0.0538 0.0545 0.0512 AlF -0.0764 -0.0765 -0.0773 -0.0747 -0.0768 -0.0784 -0.0781 -0.0780 -0.0768 -0.0769 -0.0784 -0.0782 -0.0780 -0.0769 CH₃F 0.2683 0.2128 0.2329 0.2280 0.2256 0.2363 0.2341 0.2454 0.2382 0.2359 0.2449 0.2468 0.2559 0.2512 -0.0690 -0.0737 -0.0699 -0.0684 -0.0699 -0.0641 -0.0649 -0.0651 -0.0699 -0.0669 -0.0616 -0.0613 -0.0620 -0.0657 C₃H₄ -0.0970 -0.1011 -0.0996 -0.0907 -0.0937 -0.0919 -0.0906 -0.0909 -0.0908 -0.0977 -0.0959 -0.0956 -0.0960 -0.0958 -0.1580 -0.1627 -0.1570 -0.1600 -0.1599 -0.1521 -0.1526 -0.1536 -0.1597 -0.1565 -0.1485 -0.1486 -0.1497 -0.1539 0.0564 0.0490 0.0526 0.0501 0.0511 0.0540 0.0538 0.0547 0.0524 0.0540 0.0567 0.0575 0.0582 0.0577 FCCH -0.0077 -0.0087 -0.0075 -0.0049 -0.0069 -0.0053 -0.0056 -0.0055 -0.0067 -0.0068 -0.0052 -0.0054 -0.0054 -0.0062 FC¹⁵N -0.0500 -0.0498 -0.0491 -0.0462 -0.0486 -0.0474 -0.0478 -0.0477 -0.0485 -0.0492 -0.0479 -0.0485 -0.0483 -0.0491 H₂S 0.4293 0.3749 0.4010 0.3975 0.3843 0.3989 0.3941 0.4087 0.3953 0.3870 0.4007 0.3978 0.4111 0.4000 0.2517 0.1666 0.2059 0.2004 0.1788 0.1992 0.1911 0.2148 0.1942 0.1766 0.1960 0.1883 0.2114 0.1890 0.2759 0.2110 0.2407 0.2376 0.2189 0.2349 0.2275 0.2457 0.2298 0.2192 0.2341 0.2288 0.2456 0.2293 HCP -0.0544 -0.0514 -0.0525 -0.0433 -0.0458 -0.0454 -0.0446 -0.0457 -0.0436 -0.0474 -0.0466 -0.0461 -0.0474 -0.0464 HFCO -0.4834 -0.4721 -0.4767 -0.4426 -0.4439 -0.4402 -0.4369 -0.4415 -0.4343 -0.4598 -0.4546 -0.4568 -0.4610 -0.4554 -0.0794 -0.0788 -0.0786 -0.0758 -0.0763 -0.0755 -0.0757 -0.0757 -0.0758 -0.0782 -0.0771 -0.0780 -0.0778 -0.0780 -0.0380 -0.0396 -0.0384 -0.0376 -0.0383 -0.0368 -0.0370 -0.0370 -0.0381 -0.0380 -0.0365 -0.0365 -0.0365 -0.0374 H₂C₂O -0.3024 -0.3968 -0.3524 -0.3568 -0.3408 -0.3135 -0.3178 -0.2935 -0.3296 -0.3978 -0.3732 -0.3870 -0.3599 -0.3991 -0.0329 -0.0349 -0.0332 -0.0316 -0.0328 -0.0308 -0.0314 -0.0310 -0.0329 -0.0334 -0.0313 -0.0318 -0.0315 -0.0329 -0.0229 -0.0266 -0.0248 -0.0235 -0.0240 -0.0224 -0.0229 -0.0221 -0.0235 -0.0254 -0.0237 -0.0245 -0.0236 -0.0247 LiF 0.0616 0.0595 0.0615 0.0695 0.0674 0.0708 0.0736 0.0700 0.0689 0.0658 0.0692 0.0719 0.0686 0.0679 LiH -0.6318 -0.6136 -0.6172 -0.5669 -0.6359 -0.6426 -0.6548 -0.6412 -0.6531 -0.6392 -0.6404 -0.6528 -0.6441 -0.6511 N₂O -0.0779 -0.0788 -0.0776 -0.0757 -0.0765 -0.0745 -0.0750 -0.0749 -0.0761 -0.0778 -0.0759 -0.0764 -0.0764 -0.0775 OCS -0.0283 -0.0292 -0.0282 -0.0273 -0.0278 -0.0266 -0.0271 -0.0267 -0.0275 -0.0284 -0.0272 -0.0277 -0.0273 -0.0280 OF₂ -0.2374 -0.2312 -0.2301 -0.2111 -0.2181 -0.2141 -0.2113 -0.2120 -0.2149 -0.2017 -0.1963 -0.1924 -0.1937 -0.1937 -0.0623 -0.0619 -0.0611 -0.0572 -0.0596 -0.0582 -0.0580 -0.0580 -0.0591 -0.0572 -0.0556 -0.0553 -0.0553 -0.0560 -0.0743 -0.0747 -0.0734 -0.0706 -0.0708 -0.0690 -0.0687 -0.0687 -0.0699 -0.0716 -0.0696 -0.0697 -0.0696 -0.0703 H₄C₂O -0.1037 -0.1093 -0.1033 -0.1009 -0.1047 -0.0964 -0.0975 -0.0972 -0.1045 -0.0991 -0.0915 -0.0909 -0.0914 -0.0964 0.0145 0.0040 0.0096 0.0090 0.0098 0.0154 0.0150 0.0163 0.0123 0.0141 0.0193 0.0204 0.0210 0.0187 0.0346 0.0287 0.0322 0.0336 0.0304 0.0329 0.0325 0.0338 0.0310 0.0325 0.0351 0.0352 0.0363 0.0339 PN -0.2546 -0.2496 -0.2541 -0.2384 -0.2348 -0.2366 -0.2340 -0.2359 -0.2271 -0.2485 -0.2500 -0.2517 -0.2526 -0.2447 SO2 -0.6912 -0.6857 -0.6936 -0.6665 -0.6548 -0.6623 -0.6501 -0.6552 -0.6380 -0.6959 -0.7044 -0.7027 -0.7066 -0.6901 -0.1203 -0.1204 -0.1201 -0.1179 -0.1167 -0.1161 -0.1156 -0.1158 -0.1152 -0.1202 -0.1195 -0.1200 -0.1198 -0.1192 -0.0817 -0.0820 -0.0812 -0.0800 -0.0815 -0.0801 -0.0807 -0.0805 -0.0816 -0.0820 -0.0807 -0.0814 -0.0811 -0.0821 Errors Relative to Benchmark Set over all Molecules

ME -0.0296 -0.0328 -0.0297 -0.0125 -0.0156 -0.0109 -0.0096 -0.0089 -0.0099 -0.0328 -0.0276 -0.0318 -0.0306 -0.0327

MAE 0.0426 0.0363 0.0357 0.0205 0.0205 0.0177 0.0155 0.0179 0.0153 0.0354 0.0321 0.0350 0.0369 0.0351

MaxE 0.6531 0.5058 0.5358 0.1321 0.1628 0.1165 0.1123 0.1639 0.1452 0.8821 0.8680 1.0391 1.0154 1.0309

MRE -6.4 -2.6 -3.5 1.7 0.2 0.9 1.0 0.2 0.3 -1.9 -1.0 -1.6 -2.3 -2.3

MARE 11.7 13.4 11.0 8.4 8.5 6.9 6.6 6.9 7.1 8.3 6.6 6.4 6.8 6.2

SD 0.1223 0.0796 0.0891 0.0330 0.0337 0.0314 0.0267 0.0350 0.0288 0.1230 0.1202 0.1431 0.1426 0.1439

Errors Relative to Benchmark Set over Molecules Excluding O₃

ME -0.0180 -0.0244 -0.0205 -0.0105 -0.0143 -0.0095 -0.0096 -0.0082 -0.0103 -0.0167 -0.0115 -0.0124 -0.0116 -0.0135

MAE 0.0319 0.0281 0.0270 0.0190 0.0194 0.0166 0.0157 0.0176 0.0158 0.0194 0.0162 0.0157 0.0183 0.0160

MaxE 0.5938 0.2986 0.3671 0.0980 0.1628 0.1165 0.1123 0.1639 0.1452 0.2294 0.1597 0.1857 0.2589 0.2678

MRE -6.1 -2.1 -3.1 2.0 0.4 1.0 1.1 0.2 0.3 -1.0 -0.2 -0.6 -1.4 -1.3

MARE 11.7 13.6 11.1 8.7 8.8 7.2 6.9 7.2 7.4 7.9 6.0 5.6 6.2 5.5

SD 0.0891 0.0463 0.0565 0.0293 0.0316 0.0290 0.0272 0.0351 0.0295 0.0362 0.0302 0.0317 0.0421 0.0402

Errors Relative to emp. eq. over all Molecules

ME -0.0223 -0.0264 -0.0229 -0.0055 -0.0085 -0.0037 -0.0022 -0.0013 -0.0026 -0.0272 -0.0219 -0.0264 -0.0249 -0.0274

MAE 0.0378 0.0307 0.0311 0.0204 0.0205 0.0184 0.0190 0.0197 0.0194 0.0313 0.0292 0.0324 0.0337 0.0325

MaxE 0.5640 0.2705 0.3374 0.1032 0.1330 0.1259 0.2046 0.1699 0.2189 0.6468 0.6327 0.8038 0.7801 0.7956

MRE -5.2 -1.8 -2.4 2.4 1.0 1.8 2.0 1.2 1.0 -1.0 0.0 -0.6 -1.3 -1.4

MARE 10.7 12.3 10.3 8.3 8.2 7.0 6.6 6.8 7.0 7.8 7.1 6.9 7.1 6.5

SD 0.1028 0.0557 0.0667 0.0331 0.0348 0.0335 0.0396 0.0411 0.0418 0.0956 0.0928 0.1162 0.1161 0.1171

Errors Relative to emp. eq. over Molecules Excluding O3

ME -0.0147 -0.0222 -0.0179 -0.0082 -0.0119 -0.0070 -0.0072 -0.0054 -0.0078 -0.0147 -0.0094 -0.0103 -0.0093 -0.0116

MAE 0.0312 0.0268 0.0266 0.0193 0.0189 0.0165 0.0155 0.0169 0.0157 0.0190 0.0169 0.0165 0.0185 0.0168

MaxE 0.5640 0.2688 0.3374 0.0978 0.1330 0.1259 0.1217 0.1460 0.1154 0.1996 0.1300 0.1559 0.2292 0.2380

MRE -5.2 -1.6 -2.4 2.4 0.8 1.7 1.8 0.9 0.7 -0.5 0.5 0.1 -0.7 -0.7

MARE 11.0 12.9 10.7 8.7 8.6 7.1 6.7 6.9 7.1 7.5 6.7 6.4 6.6 6.0

SD 0.0882 0.0444 0.0549 0.0299 0.0300 0.0285 0.0266 0.0338 0.0275 0.0349 0.0298 0.0309 0.0411 0.0389

Errors Relative to exp. over all Molecules

ME -0.0204 -0.0245 -0.0209 -0.0036 -0.0066 -0.0018 -0.0003 0.0006 -0.0006 -0.0253 -0.0200 -0.0245 -0.0230 -0.0255

MAE 0.0396 0.0286 0.0303 0.0148 0.0141 0.0125 0.0122 0.0142 0.0128 0.0309 0.0296 0.0330 0.0354 0.0332

MaxE 0.5635 0.4161 0.4462 0.0916 0.1252 0.1047 0.1004 0.1263 0.1076 0.7924 0.7784 0.9494 0.9257 0.9412

MRE -5.0 -1.0 -2.0 2.7 1.4 2.0 2.1 1.2 1.3 -0.8 0.0 -0.7 -1.4 -1.4

MARE 9.3 9.6 8.2 6.7 6.0 5.3 4.8 5.6 5.0 6.1 6.4 6.5 7.3 5.6

SD 0.1153 0.0695 0.0800 0.0249 0.0252 0.0236 0.0231 0.0297 0.0256 0.1152 0.1127 0.1365 0.1359 0.1372

Errors Relative to exp. over Molecules Excluding O₃

ME -0.0093 -0.0168 -0.0125 -0.0029 -0.0066 -0.0016 -0.0018 -0.0001 -0.0024 -0.0093 -0.0041 -0.0050 -0.0040 -0.0062

MAE 0.0298 0.0213 0.0225 0.0149 0.0144 0.0127 0.0115 0.0144 0.0118 0.0153 0.0141 0.0140 0.0171 0.0144

MaxE 0.5562 0.2610 0.3295 0.0916 0.1252 0.1047 0.1004 0.1263 0.1076 0.1918 0.1221 0.1481 0.2213 0.2302

MRE -4.7 -0.6 -1.6 2.9 1.5 2.0 2.1 1.2 1.2 0.0 0.7 0.3 -0.6 -0.5

MARE 9.3 9.7 8.2 7.1 6.3 5.5 5.0 5.8 5.2 5.6 5.8 5.8 6.6 4.9

SD 0.0873 0.0417 0.0529 0.0251 0.0258 0.0242 0.0221 0.0304 0.0240 0.0328 0.0273 0.0290 0.0396 0.0378

Table 12: Rotational g tensors calculated by wave function methods with the cc-pVQZ basis set.

Molecule RHF CCSD CCSD(T) Benchmark emp. eq. exp.

HF 0.7615 0.7501 0.7488 0.7542 0.7543 0.7416

CO -0.2815 -0.2665 -0.2675 -0.2681 -0.2676 -0.2689 15N₂ -0.2714 -0.2595 -0.2612 -0.2591 -0.2577 -0.2593

H₂O 0.6823 0.6707 0.6688 0.6717 0.686 0.657

0.7246 0.7129 0.7113 0.7303 0.733 0.718

0.6613 0.6494 0.6485 0.6563 0.654 0.645

HC¹⁵N -0.0772 -0.0843 -0.0879 -0.0882 -0.0872 -0.0904

HOF 0.7018 0.6843 0.6814 0.6853 0.672 0.642

-0.0922 -0.1017 -0.1058 -0.1107 -0.108 -0.119 -0.0423 -0.0538 -0.0574 -0.0596 -0.060 -0.061 O₃ -5.8932 -3.1590 -2.9013 -2.8980 -3.1333 -2.9877 -0.3919 -0.2460 -0.2232 -0.2247 -0.2360 -0.2295 -0.0662 -0.0715 -0.0732 -0.0741 -0.0777 -0.0760

NH3 0.5791 0.5734 0.5731 0.5770 0.5795 0.5654

0.5056 0.5056 0.5062 0.5107 0.5086 0.5024

CH2O -2.7061 -2.7964 -2.8588 -2.8641 -2.8939 -2.9017 -0.2214 -0.2152 -0.2171 -0.2194 -0.2222 -0.2243 -0.0667 -0.0862 -0.0929 -0.0910 -0.0945 -0.0994

CH₄ 0.3034 0.3194 0.3215 0.3236 0.3217 0.3133

C₂H₄ -0.3321 -0.3532 -0.3660 -0.3679 N/A N/A

-0.1145 -0.1110 -0.1123 -0.1118 N/A N/A

0.0611 0.0557 0.0534 0.0550 N/A N/A

AlF -0.0833 -0.0784 -0.0776 -0.0794 -0.0808 -0.0805

CH₃F 0.2641 0.2644 0.2617 0.2724 0.277 0.265

-0.0548 -0.0586 -0.0605 -0.0601 -0.060 -0.062 C₃H₄ -0.0941 -0.0800 -0.0804 -0.0802 -0.0828 -0.0897 -0.1468 -0.1390 -0.1419 -0.1424 -0.1447 -0.1492

0.0631 0.0610 0.0595 0.0595 0.0586 0.0536

FCCH -0.0025 -0.0048 -0.0055 -0.0062 -0.0066 -0.0077 FC¹⁵N -0.0474 -0.0477 -0.0480 -0.0487 -0.0499 -0.0504

H2S 0.3889 0.3973 0.3995 0.3978 0.378 0.355

0.1446 0.1871 0.1942 0.1883 0.216 0.195

0.1996 0.2269 0.2328 0.2321 0.208 0.209

HCP -0.0312 -0.0355 -0.0381 -0.0382 -0.0389 -0.0430 HFCO -0.4132 -0.4217 -0.4258 -0.4268 -0.4270 -0.4227 -0.0763 -0.0758 -0.0760 -0.0770 -0.0703 -0.0771 -0.0353 -0.0360 -0.0365 -0.0367 -0.0366 -0.0371 H₂C₂O -0.3979 -0.4266 -0.4239 -0.4300 -0.4394 -0.4182 -0.0322 -0.0325 -0.0330 -0.0345 -0.0352 -0.0356 -0.0248 -0.0238 -0.0239 -0.0243 -0.0233 -0.0238

LiF 0.0750 0.0702 0.0691 0.0678 0.0733 0.0737

LiH -0.6908 -0.6670 -0.6663 -0.6649 -0.6646 -0.6584 N₂O -0.0771 -0.0756 -0.0760 -0.0778 -0.0780 -0.0789 OCS -0.0280 -0.0271 -0.0273 -0.0279 -0.0282 -0.0288 OF₂ -0.1388 -0.1775 -0.1895 -0.1972 -0.202 -0.213 -0.0466 -0.0515 -0.0539 -0.0550 -0.057 -0.058 -0.0606 -0.0634 -0.0663 -0.0671 -0.067 -0.068 H4C2O -0.0804 -0.0876 -0.0910 -0.0905 -0.0905 -0.0946

0.0356 0.0274 0.0244 0.0267 0.0256 0.0189

0.0385 0.0369 0.0362 0.0369 0.0333 0.0318

PN -0.2416 -0.2248 -0.2279 -0.2285 N/A N/A

SO₂ -0.6932 -0.6113 -0.6082 -0.5988 -0.5929 -0.6043 -0.1190 -0.1144 -0.1148 -0.1165 -0.1156 -0.1163 -0.0853 -0.0839 -0.0838 -0.0873 -0.0888 -0.0887 Errors Relative to Benchmark Set over all Molecules

ME -0.0552 -0.0031 -0.0004

MAE 0.0735 0.0100 0.0027

MaxE 2.9952 0.2610 0.0190

MRE 0.4 2.1 1.2

MARE 12.2 3.2 1.7

SD 0.4094 0.0374 0.0043

Errors Relative to Benchmark Set over Molecules Excluding O₃ ME 0.0034 0.0022 -0.0004

MAE 0.0157 0.0051 0.0028

MaxE 0.1580 0.0677 0.0190

MRE 3.7 2.5 1.3

MARE 9.2 3.0 1.8

SD 0.0305 0.0109 0.0044

Errors Relative to emp. eq. over all Molecules

ME -0.0540 0.0023 0.0056 0.0061

MAE 0.0749 0.0089 0.0108 0.0092

MaxE 2.7599 0.0975 0.2320 0.2353

MRE 1.1 2.5 1.7 0.4

MARE 13.0 4.8 3.5 2.7

SD 0.3927 0.0170 0.0342 0.0341

Errors Relative to emp. eq. over Molecules Excluding O₃

ME 0.0043 0.0031 0.0007 0.0012

MAE 0.0174 0.0085 0.0062 0.0045

MaxE 0.1877 0.0975 0.0351 0.0298

MRE 4.1 2.6 1.4 0.0

MARE 10.2 4.8 3.3 2.5

SD 0.0362 0.0169 0.0102 0.0084

Errors Relative to exp. over all Molecules

ME -0.0521 0.0043 0.0076 0.0081

MAE 0.0797 0.0134 0.0091 0.0095

MaxE 2.9055 0.1713 0.0864 0.0897

MRE 0.2 2.0 1.4 0.1

MARE 15.1 7.1 5.3 5.0

SD 0.4140 0.0309 0.0159 0.0160

Errors Relative to exp. over Molecules Excluding O₃

ME 0.0097 0.0084 0.0060 0.0065

MAE 0.0193 0.0102 0.0077 0.0080

MaxE 0.1956 0.1053 0.0445 0.0433

MRE 3.5 2.3 1.3 -0.1

MARE 12.2 7.2 5.4 5.1

SD 0.0366 0.0180 0.0114 0.0112

Table 13: Rotational g tensors calculated by density functional methods with the cc-pVQZ basis set.

Molecule LDA BLYP PBE KT2 O-B3LYP O-B97-2 O-B97-3 O-PBE0 O-CAM B3LYP B97-2 B97-3 PBE0 CAM

-B3LYP -B3LYP

HF 0.7473 0.7241 0.7282 0.7193 0.7389 0.7388 0.7414 0.7435 0.7446 0.7359 0.7356 0.7371 0.7404 0.7440

CO -0.2878 -0.2825 -0.2869 -0.2703 -0.2733 -0.2752 -0.2755 -0.2751 -0.2701 -0.2826 -0.2841 -0.2878 -0.2867 -0.2801 15N₂ -0.2820 -0.2776 -0.2822 -0.2635 -0.2663 -0.2690 -0.2663 -0.2679 -0.2628 -0.2764 -0.2790 -0.2796 -0.2805 -0.2733 H₂O 0.6713 0.6411 0.6485 0.6336 0.6531 0.6546 0.6555 0.6607 0.6630 0.6547 0.6555 0.6572 0.6623 0.6659 0.7121 0.6811 0.6896 0.6856 0.6934 0.6964 0.7005 0.7020 0.7017 0.6962 0.6993 0.7020 0.7052 0.7045 0.6535 0.6208 0.6291 0.6224 0.6346 0.6371 0.6397 0.6431 0.6430 0.6347 0.6366 0.6382 0.6432 0.6440 HC¹⁵N -0.1078 -0.1045 -0.1073 -0.0935 -0.0940 -0.0950 -0.0936 -0.0944 -0.0907 -0.0985 -0.0989 -0.0990 -0.0997 -0.0946

HOF 0.6812 0.6513 0.6578 0.6479 0.6668 0.6676 0.6697 0.6739 0.6769 0.6675 0.6678 0.6703 0.6748 0.6791

-0.1198 -0.1213 -0.1189 -0.1119 -0.1163 -0.1127 -0.1129 -0.1126 -0.1156 -0.1137 -0.1096 -0.1095 -0.1095 -0.1120 -0.0689 -0.0724 -0.0696 -0.0652 -0.0681 -0.0643 -0.0648 -0.0644 -0.0669 -0.0643 -0.0602 -0.0598 -0.0600 -0.0623 O3 -3.4879 -3.3508 -3.3814 -2.9888 -2.9500 -2.9355 -2.8553 -2.8929 -2.8488 -3.7205 -3.7126 -3.8801 -3.8533 -3.8614 -0.2430 -0.2416 -0.2406 -0.2295 -0.2234 -0.2206 -0.2179 -0.2189 -0.2184 -0.2630 -0.2609 -0.2704 -0.2676 -0.2703 -0.0789 -0.0804 -0.0786 -0.0777 -0.0775 -0.0746 -0.0752 -0.0751 -0.0772 -0.0767 -0.0737 -0.0740 -0.0742 -0.0761

NH₃ 0.5870 0.5463 0.5597 0.5495 0.5552 0.5591 0.5608 0.5674 0.5651 0.5596 0.5637 0.5650 0.5723 0.5707

0.5230 0.4805 0.4944 0.4860 0.4915 0.4960 0.4976 0.5042 0.5005 0.4915 0.4954 0.4964 0.5043 0.5014 CH₂O -3.4549 -3.1595 -3.2287 -2.9459 -2.9591 -2.8973 -2.8898 -2.9562 -2.9419 -3.0865 -3.0176 -3.0540 -3.1161 -3.1226 -0.2381 -0.2345 -0.2363 -0.2249 -0.2226 -0.2212 -0.2205 -0.2217 -0.2190 -0.2312 -0.2293 -0.2318 -0.2322 -0.2288 -0.1122 -0.1172 -0.1119 -0.1070 -0.1071 -0.0979 -0.0964 -0.0995 -0.1050 -0.1015 -0.0919 -0.0893 -0.0932 -0.0973

CH₄ 0.3566 0.3011 0.3224 0.3111 0.3078 0.3150 0.3145 0.3259 0.3178 0.3087 0.3153 0.3151 0.3271 0.3193

C₂H₄ -0.4947 -0.4654 -0.4705 -0.4394 -0.4538 -0.4475 -0.4473 -0.4545 -0.4558 -0.4347 -0.4254 -0.4228 -0.4308 -0.4247 -0.1319 -0.1279 -0.1296 -0.1186 -0.1216 -0.1210 -0.1205 -0.1218 -0.1200 -0.1250 -0.1238 -0.1250 -0.1260 -0.1253 0.0506 0.0397 0.0459 0.0441 0.0438 0.0497 0.0493 0.0505 0.0451 0.0471 0.0526 0.0534 0.0542 0.0509 AlF -0.0782 -0.0783 -0.0793 -0.0767 -0.0783 -0.0799 -0.0796 -0.0794 -0.0782 -0.0787 -0.0804 -0.0803 -0.0800 -0.0787 CH3F 0.2756 0.2203 0.2399 0.2333 0.2383 0.2473 0.2489 0.2565 0.2515 0.2419 0.2501 0.2529 0.2613 0.2570 -0.0698 -0.0746 -0.0709 -0.0693 -0.0696 -0.0644 -0.0643 -0.0653 -0.0694 -0.0677 -0.0625 -0.0617 -0.0629 -0.0666 C3H4 -0.0972 -0.1012 -0.0997 -0.0922 -0.0939 -0.0925 -0.0909 -0.0913 -0.0909 -0.0978 -0.0960 -0.0962 -0.0962 -0.0959 -0.1604 -0.1656 -0.1597 -0.1626 -0.1626 -0.1550 -0.1539 -0.1560 -0.1619 -0.1591 -0.1509 -0.1500 -0.1520 -0.1563 0.0558 0.0484 0.0521 0.0497 0.0512 0.0543 0.0544 0.0550 0.0527 0.0534 0.0562 0.0569 0.0576 0.0571 FCCH -0.0090 -0.0103 -0.0090 -0.0068 -0.0085 -0.0068 -0.0070 -0.0070 -0.0083 -0.0082 -0.0064 -0.0065 -0.0066 -0.0076 FC¹⁵N -0.0515 -0.0515 -0.0506 -0.0477 -0.0502 -0.0488 -0.0490 -0.0491 -0.0501 -0.0506 -0.0491 -0.0495 -0.0495 -0.0505 H₂S 0.4265 0.3712 0.3982 0.3943 0.3787 0.3932 0.3876 0.4035 0.3897 0.3827 0.3971 0.3925 0.4074 0.3951 0.2437 0.1553 0.1971 0.1914 0.1635 0.1854 0.1751 0.2013 0.1787 0.1645 0.1863 0.1762 0.2014 0.1759 0.2720 0.2062 0.2366 0.2335 0.2109 0.2264 0.2192 0.2375 0.2212 0.2137 0.2292 0.2230 0.2406 0.2232 HCP -0.0545 -0.0514 -0.0526 -0.0439 -0.0452 -0.0446 -0.0436 -0.0449 -0.0428 -0.0474 -0.0466 -0.0465 -0.0475 -0.0464 HFCO -0.4861 -0.4739 -0.4785 -0.4466 -0.4435 -0.4390 -0.4371 -0.4408 -0.4346 -0.4615 -0.4559 -0.4605 -0.4626 -0.4571 -0.0811 -0.0807 -0.0803 -0.0776 -0.0785 -0.0773 -0.0777 -0.0776 -0.0780 -0.0798 -0.0785 -0.0794 -0.0793 -0.0796 -0.0386 -0.0404 -0.0391 -0.0384 -0.0389 -0.0373 -0.0375 -0.0374 -0.0386 -0.0386 -0.0371 -0.0371 -0.0372 -0.0382 H₂C₂O -0.3062 -0.4005 -0.3559 -0.3648 -0.3715 -0.3462 -0.3543 -0.3265 -0.3447 -0.4031 -0.3776 -0.3937 -0.3652 -0.4059 -0.0351 -0.0374 -0.0355 -0.0342 -0.0359 -0.0336 -0.0339 -0.0338 -0.0357 -0.0357 -0.0333 -0.0335 -0.0336 -0.0352 -0.0240 -0.0278 -0.0259 -0.0247 -0.0255 -0.0237 -0.0240 -0.0234 -0.0247 -0.0264 -0.0247 -0.0253 -0.0246 -0.0258

LiF 0.0576 0.0550 0.0573 0.0645 0.0625 0.0663 0.0679 0.0655 0.0639 0.0618 0.0656 0.0673 0.0649 0.0636

LiH -0.6494 -0.6287 -0.6308 -0.5813 -0.6518 -0.6565 -0.6708 -0.6584 -0.6662 -0.6536 -0.6514 -0.6677 -0.6565 -0.6668 N2O -0.0803 -0.0817 -0.0802 -0.0783 -0.0794 -0.0771 -0.0773 -0.0775 -0.0791 -0.0803 -0.0780 -0.0783 -0.0786 -0.0800 OCS -0.0294 -0.0305 -0.0294 -0.0284 -0.0293 -0.0279 -0.0282 -0.0280 -0.0289 -0.0295 -0.0281 -0.0285 -0.0283 -0.0291 OF2 -0.2442 -0.2392 -0.2375 -0.2182 -0.2197 -0.2140 -0.2124 -0.2129 -0.2161 -0.2085 -0.2018 -0.1978 -0.1996 -0.2005 -0.0639 -0.0639 -0.0629 -0.0590 -0.0605 -0.0587 -0.0587 -0.0586 -0.0599 -0.0588 -0.0568 -0.0565 -0.0567 -0.0576 -0.0749 -0.0756 -0.0742 -0.0716 -0.0714 -0.0693 -0.0691 -0.0691 -0.0705 -0.0724 -0.0701 -0.0702 -0.0702 -0.0711 H₄C₂O -0.1055 -0.1116 -0.1056 -0.1031 -0.1062 -0.0986 -0.0982 -0.0992 -0.1057 -0.1011 -0.0935 -0.0921 -0.0933 -0.0984 0.0157 0.0053 0.0107 0.0105 0.0115 0.0165 0.0166 0.0175 0.0141 0.0151 0.0202 0.0213 0.0219 0.0198 0.0342 0.0279 0.0314 0.0332 0.0294 0.0318 0.0315 0.0327 0.0302 0.0317 0.0343 0.0345 0.0356 0.0331 PN -0.2546 -0.2495 -0.2538 -0.2385 -0.2328 -0.2337 -0.2310 -0.2331 -0.2249 -0.2480 -0.2493 -0.2518 -0.2518 -0.2439 SO₂ -0.6743 -0.6686 -0.6770 -0.6532 -0.6388 -0.6467 -0.6358 -0.6402 -0.6235 -0.6785 -0.6879 -0.6888 -0.6898 -0.6722 -0.1221 -0.1223 -0.1218 -0.1198 -0.1187 -0.1177 -0.1173 -0.1175 -0.1173 -0.1219 -0.1209 -0.1215 -0.1213 -0.1209 -0.0853 -0.0858 -0.0847 -0.0835 -0.0848 -0.0831 -0.0837 -0.0835 -0.0849 -0.0855 -0.0839 -0.0846 -0.0844 -0.0857 Errors Relative to Benchmark Set over all Molecules

ME -0.0284 -0.0319 -0.0287 -0.0122 -0.0132 -0.0082 -0.0066 -0.0062 -0.0070 -0.0318 -0.0267 -0.0314 -0.0295 -0.0316

MAE 0.0404 0.0344 0.0333 0.0182 0.0160 0.0120 0.0114 0.0119 0.0125 0.0333 0.0293 0.0330 0.0337 0.0326

MaxE 0.5908 0.4528 0.4834 0.0908 0.0949 0.0838 0.0794 0.1036 0.0879 0.8225 0.8146 0.9821 0.9553 0.9634

MRE -7.9085 -4.2675 -5.0679 -0.1946 -1.3301 -0.4231 -0.2106 -1.1946 -1.1750 -3.2775 -2.1793 -2.6659 -3.5751 -3.6378 MARE 12.3023 14.7685 11.8757 7.8313 9.0197 5.7499 5.6220 5.7323 7.3291 9.3532 5.9090 6.0607 6.1754 7.0321

SD 0.1157 0.0725 0.0825 0.0272 0.0214 0.0193 0.0185 0.0237 0.0220 0.1144 0.1125 0.1352 0.1341 0.1343

Errors Relative to Benchmark Set over Molecules Excluding O₃

ME -0.0180 -0.0245 -0.0205 -0.0110 -0.0129 -0.0080 -0.0079 -0.0068 -0.0085 -0.0168 -0.0116 -0.0131 -0.0117 -0.0136

MAE 0.0308 0.0271 0.0254 0.0173 0.0158 0.0119 0.0111 0.0124 0.0121 0.0184 0.0144 0.0148 0.0161 0.0147

MaxE 0.5908 0.2954 0.3646 0.0836 0.0949 0.0838 0.0794 0.1036 0.0879 0.2224 0.1534 0.1899 0.2520 0.2585

MRE -7.6859 -3.8979 -4.7820 -0.0075 -1.2934 -0.4455 -0.2811 -1.2922 -1.2507 -2.5097 -1.4507 -1.7609 -2.7633 -2.7479 MARE 12.3382 15.0167 11.9902 8.0934 9.4125 6.0139 5.8338 5.9877 7.5902 8.9429 5.3800 5.3522 5.5166 6.3419

SD 0.0881 0.0441 0.0548 0.0256 0.0212 0.0193 0.0176 0.0243 0.0211 0.0336 0.0272 0.0304 0.0396 0.0376

Errors Relative to emp. eq. over all Molecules

ME -0.0210 -0.0254 -0.0218 -0.0051 -0.0059 -0.0007 0.0010 0.0015 0.0006 -0.0261 -0.0208 -0.0259 -0.0238 -0.0262

MAE 0.0355 0.0286 0.0287 0.0196 0.0174 0.0153 0.0158 0.0165 0.0169 0.0287 0.0261 0.0298 0.0305 0.0295

MaxE 0.5610 0.2657 0.3348 0.1445 0.1833 0.1978 0.2780 0.2404 0.2845 0.5872 0.5792 0.7468 0.7200 0.7281

MRE -6.8463 -3.5361 -4.1268 0.4879 -0.6290 0.4627 0.6430 -0.2929 -0.5199 -2.5085 -1.2502 -1.7141 -2.6035 -2.8683 MARE 11.2974 13.6445 11.1679 7.8598 8.4725 5.9613 5.6815 5.7893 7.1979 8.5113 6.1127 6.1591 6.1795 6.6351

SD 0.0971 0.0493 0.0608 0.0330 0.0332 0.0344 0.0436 0.0410 0.0450 0.0867 0.0846 0.1079 0.1072 0.1072

Errors Relative to emp. eq. over Molecules Excluding O₃

ME -0.0146 -0.0222 -0.0178 -0.0086 -0.0104 -0.0054 -0.0053 -0.0040 -0.0058 -0.0147 -0.0094 -0.0110 -0.0094 -0.0117

MAE 0.0300 0.0256 0.0252 0.0177 0.0143 0.0116 0.0105 0.0121 0.0115 0.0174 0.0148 0.0150 0.0164 0.0151

MaxE 0.5610 0.2657 0.3348 0.0834 0.0680 0.0932 0.0851 0.1130 0.0947 0.1927 0.1237 0.1601 0.2223 0.2287

MRE -6.9445 -3.4897 -4.1564 0.3624 -0.9115 0.1339 0.2647 -0.6999 -0.9190 -2.0528 -0.8213 -1.1063 -2.0929 -2.2904 MARE 11.6798 14.2432 11.6471 8.2041 8.7709 5.9834 5.6248 5.7706 7.2914 8.3871 5.7764 5.6345 5.7043 6.2126

SD 0.0870 0.0419 0.0529 0.0256 0.0192 0.0194 0.0176 0.0226 0.0190 0.0319 0.0264 0.0292 0.0383 0.0360

Errors Relative to exp. over all Molecules

ME -0.0191 -0.0234 -0.0199 -0.0032 -0.0039 0.0012 0.0029 0.0034 0.0025 -0.0242 -0.0189 -0.0240 -0.0218 -0.0243

MAE 0.0382 0.0265 0.0276 0.0121 0.0103 0.0087 0.0098 0.0110 0.0109 0.0279 0.0265 0.0306 0.0323 0.0307

MaxE 0.5532 0.3631 0.3937 0.0772 0.0574 0.0720 0.1324 0.0948 0.1389 0.7328 0.7249 0.8924 0.8656 0.8737

MRE -6.5260 -2.6868 -3.5805 0.8591 -0.1544 0.6336 0.8201 -0.1661 -0.1829 -2.2009 -1.2558 -1.7571 -2.6784 -2.7980

MARE 9.5645 10.5957 8.2456 5.7016 5.3866 3.6961 3.4368 3.8579 4.2829 5.7255 5.3213 5.7467 6.1297 4.9564

SD 0.1088 0.0623 0.0733 0.0204 0.0160 0.0168 0.0231 0.0233 0.0250 0.1064 0.1047 0.1283 0.1271 0.1274

Errors Relative to exp. over Molecules Excluding O₃

ME -0.0093 -0.0168 -0.0125 -0.0033 -0.0051 0.0000 0.0000 0.0014 -0.0005 -0.0094 -0.0040 -0.0057 -0.0040 -0.0064

MAE 0.0297 0.0202 0.0207 0.0128 0.0099 0.0080 0.0074 0.0094 0.0083 0.0134 0.0120 0.0127 0.0151 0.0132

MaxE 0.5532 0.2578 0.3270 0.0772 0.0574 0.0720 0.0639 0.0917 0.0735 0.1848 0.1159 0.1523 0.2144 0.2209

MRE -6.3783 -2.3646 -3.3542 0.9620 -0.2049 0.5145 0.6489 -0.3677 -0.3635 -1.4886 -0.5929 -0.9096 -1.9317 -1.9724

MARE 9.6107 10.7784 8.3171 6.0173 5.6046 3.7724 3.4327 3.9131 4.3220 5.2382 4.7894 5.0430 5.5002 4.2686

SD 0.0864 0.0396 0.0512 0.0210 0.0152 0.0155 0.0139 0.0198 0.0159 0.0303 0.0244 0.0279 0.0372 0.0354