To be published in Theor. Chem. Acc. (Mark S. Gordon Festschrift Issue)

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1 S-1 Supporting Information for: The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06 Functionals and Twelve Other Functionals Yan Zhao and Donald G. Truhlar To be published in Theor. Chem. Acc. (Mark S. Gordon Festschrift Issue) This supporting information was prepared on Dec. 7, 2006 and consists of a total of 29 pages. Contents: page Table S1. MGAE109/05 database: zero-point-exclusive atomization energies S-2 Table S2. IP13/3 and EA13/3 databases S-4 Table S3. PA8 database S-5 Table S4. HTBH38/04 database S-6 Table S5. NHTBH38/04 databases S-7 Table S6. Noncovalent interaction databases S-9 Table S7. Interaction energies and sources of geometries in the S22 database S-10 Table S8. TMAE9/05 and MLBE21/05 databases S-11 Table S9. π system databases S-12 Table S10. Spin-orbit contribution to bond energies in Table S8. S-13 Table S11. Cartesian Coordinates for the HC7 database S-14 Table S12. Cartesian coordinates for the DC10 database S-20 Figure S1. Cumulenes and poly-ynes S-24 Figure S2. Conjugated polyenes and protonated polyenes S-25 Figure S3. Conjugated Schiff bases and protonated conjugated Schiff bases S-26 Figure S4. Hydrogen bonded complexes in the S22 database S-27 Figure S5. Dispersion-dominated complexes in the S22 database S-28 Figure S6. Mixed complexes in the S22 database. S-29

2 S-2 Table S1: MGAE109/05 database of zero-point-exclusive atomization energies (kcal/mol) Molecule D e Molecule D e Molecule D e CH ( 2 П) S H 2 CCH CH 2 ( 3 B 1 ) Cl HCOOCH CH 2 ( 1 A 1 ) SiO HCOOH CH 3 ( 2 A" 2 ) SC NF CH SO PF NH ClO SH NH ClF SiCl NH Si 2 H SiF OH CH 3 Cl C 2 H OH CH 3 SH C 4 H 6 d FH HOCl C 4 H 6 e SiH 2 ( 1 A 1 ) SO HCOCOH SiH 2 ( 3 B 1 ) AlCl CH 3 CHO SiH AlF C 2 H 4 O SiH BCl C 2 H 5 O PH BF H 3 COCH PH C 2 Cl H 3 CCH 2 OH SH C 2 F C 3 H 4 f ClH C 3 H 4 a C 3 H g HCCH C 4 H 4 O H 3 CCOOH H 2 CCH C 4 H 4 S H 3 CCOCH H 3 CCH C 4 H 5 N C 3 H CN C 4 H 6 b H 3 CCHCH HCN C 4 H 6 c C 3 H CO C 5 H 5 N C 2 H 5 OCH HCO CCH C 4 H 10 h H 2 CO CCl C 4 H 10 i H 3 COH CF 3 CN C 4 H 8 j

3 S-3 N CF C 4 H 8 k H 2 NNH CH 2 OH C 5 H 8 l NO CH 3 CN C 6 H O CH 3 NH CH 3 CO HOOH CH 3 NO (CH 3 ) 2 CH F CHCl (CH 3 ) 3 C CO CHF H 2 CCO Si ClF P H a propyne b trans-1,3-butadiene c 2-butyne d bicylobutane e cyclobutene f allene g cyclopropene h isobutane i antiperiplanar butane j cyclobutane k isobutene l spiropentane

4 S-4 Table S2: Zero-point-exclusive ionization potentials (IP13/3) and electron affinities (EA13/3) databases (kcal/mol) IP EA C S SH Cl Cl OH O O P PH PH S Si

5 S-5 Table S3. Zero-point-exclusive proton affinities (PA8) database (kcal/mol) Molecule proton affinities NH H 2 O C 2 H SiH PH H 2 S HCl H

6 S-6 Table S4: HTBH38/04 database (kcal/mol) Reaction best estimate A + BC AB + C V f V r 1. H + HCl H 2 + Cl OH + H 2 H + H 2 O CH 3 + H 2 H + CH OH + CH 4 CH 3 + H 2 O H + H 2 H 2 + H OH + NH 3 H 2 O + NH HCl + CH 3 Cl + CH OH + C 2 H 6 H 2 O + C 2 H F + H 2 HF + H O + CH 4 OH + CH H + PH 3 PH 2 + H H + HO H 2 +O H + H 2 S H 2 + HS O + HCl OH + Cl NH 2 + CH 3 CH 4 + NH NH 2 + C 2 H 5 C 2 H 6 + NH C 2 H 6 + NH 2 NH 3 + C 2 H NH 2 + CH 4 CH 3 + NH s-trans cis-c 5 H 8 s-trans cis-c 5 H

7 S-7 Table S5: NHTBH38/04 databases Reactions Best Estimate (kcal/mol) Heavy-atom transfer reactions H + N 2 O OH + N 2 V f V r H + FH HF + H V f V r H + ClH HCl + H V f V r H + FCH 3 HF + CH 3 V f V r H + F 2 HF + F V f 2.27 V r V CH 3 + FCl CH 3 F + Cl f 7.43 V r Nucleophilic substitution reactions F - + CH 3 F FCH 3 + F - V f 0.34 V r 0.34 F - CH 3 F FCH 3 F - V f V r Cl - + CH 3 Cl ClCH 3 + Cl - V f 3.10 V r 3.10 Cl - CH 3 Cl ClCH 3 Cl - V f V r F - + CH 3 Cl FCH 3 + Cl - V f V r F - CH 3 Cl FCH 3 Cl - V f 2.89 V r OH - + CH 3 F HOCH 3 + F - V f 2.78 V r OH - CH 3 F HOCH 3 F - V f V r Unimolecular and association reactions H + N 2 HN 2 V f V r 10.72

8 S-8 H + CO HCO H + C 2 H 4 CH 3 CH 2 CH 3 + C 2 H 4 CH 3 CH 2 CH 2 HCN HNC V f 3.17 V r V f 1.72 V r V f 6.85 V r V f V r 33.11

9 S-9 Table S6: Noncovalent interaction databases (kcal/mol) HB6/04 CT7/04 DI6/04 WI7/05 PPS5/05 Complex D e Complex D e Complex D e Complex D e Complex D e (NH 3 ) C 2 H 4 F (H 2 S) HeNe 0.04 (C 2 H 2 ) (HF) NH 3 F (HCl) HeAr 0.06 (C 2 H 4 ) (H 2 O) C 2 H 2 ClF 3.81 HCl H 2 S 3.35 Ne Sandwich (C 6 H 6 ) NH 3 H 2 O 6.41 HCN ClF 4.86 CH 3 Cl HCl 3.55 NeAr 0.13 T-Shaped (C 6 H 6 ) (HCONH 2 ) NH 3 Cl HCN CH 3 SH 3.59 CH 4 Ne 0.22 Parallel-Displaced (C 6 H 6 ) (HCOOH) H 2 O ClF 5.36 CH 3 SH HCl 4.16 C 6 H 6 Ne 0.47 NH 3 ClF (CH 4 ) Average

10 S-10 Table S7: Interaction energies (kcal/mol) and sources of geometries in the S22 database a Complex (symmetry) Best Estimate b Geometries b Hydrogen bonded complexes (NH 3 ) 2 (C 2h ) 3.17 CCSD(T)/QZ (H 2 O) 2 (C s ) 5.02 CCSD(T)/QZ Formic acid dimer (C 2h ) CCSD(T)/TZ Formamide dimer (C 2h ) CCSD(T)/TZ Uracil dimer (C 2h ) MP2/TZ-CP 2-pyridoxine 2-aminopyridine (C 1 ) MP2/TZ-CP Adenine thymine WC (C 1 ) MP2/TZ-CP Dispersion-dominated complexes (CH 4 ) 2 (D 3d ) 0.53 CCSD(T)/TZ (C 2 H 4 ) 2 (D 2d ) 1.51 CCSD(T)/QZ Benzene CH 4 (C 3 ) 1.50 MP2/TZ-CP Benzene dimer (C 2h ) 2.73 MP2/TZ-CP Pyrazine dimer (C s ) 4.42 MP2/TZ-CP Uracil dimer (C 2 ) MP2/TZ-CP Indole benzene (C 1 ) 5.22 MP2/TZ-CP Adenine thymine stack (C 1 ) MP2/TZ-CP Mixed complexes Ethene ethyne (C 2v ) 1.53 CCSD(T)/QZ Benzene H 2 O (C s ) 3.28 MP2/TZ-CP Benzene NH 3 (C s ) 2.35 MP2/TZ-CP Benzene HCN (C s ) 4.46 MP2/TZ-CP Benzene dimer (C 2v ) 2.74 MP2/TZ-CP Indole benzene T-shaped (C 1 ) 5.73 MP2/TZ-CP Phenol dimer (C 1 ) 7.05 MP2/TZ-CP a The best estimate are taken from a paper by Jurecka et al. b P. Jurecka, J. Sponer, J. Cerny, and P. Hobza, Phys. Chem. Chem. Phys. 8, 1985 (2006).

11 S-11 Table S8: TMAE9/05 and MLBE21/05 databases (kcal/mol) TMAE9/05 MLBE21/05 Molecule D e Molecule D e Ag AgH Cr BeO Cu CoH CuAg CoO Mo CoOH Ni CrCH V CuH 2 O Zr FeH ZrV Fe(CO) a Ag FeO FeS LiCl LiO MgO MnCH NiCH Ni(CO) a RhC VCO VO VS a average of breaking five or four carbonyl bonds to metal. All other values in this table are breaking one metal-metal or metal-ligand bond.

12 S-12 Table S9: π system databases (kcal/mol) a π PA-P5 PA-SB5 E2-E P SB E4-E P SB E6-E P SB P SB P SB a See Figure S1, S2, and S3 for the structures of the molecules in these databases.

13 S-13 Table S10: Spin-orbit contributions (kcal/mol) to bond energies in Table S8. a TMAE9/05 MLBE21/05 Molecule ΔE SO Molecule ΔE SO Ag 2 0 AgH 0 Cr 2 0 BeO b Cu 2 0 CoH b CuAg 0 CoO b Mo 2 0 CoOH c Ni b + CrCH 3 0 V b CuH 2 O + 0 Zr b FeH b ZrV b Fe(CO) d Ag 2 0 FeO b FeS -1.2 b LiCl b LiO 0.14 b MgO b + MnCH 3 0 NiCH 2 + Ni(CO) 4 RhC c d b VCO + 0 VO b VS b a The values in this table are added to the nonrelativistic DFT results before they are compared to the experimental values in the TMAE9/05 and MLBE12/05 databases. b ΔE SO = E SO (A) + E SO (B) E SO (AB), where E SO (A) and E SO (B) are the spin-orbit energies of atoms A and B and E SO (AB) is the spin orbit energy of the diatomic molecules AB. In the case of CoO +, A is charged, i.e., A = Co +. c ΔE SO = E SO (L) + E SO (M + ) E SO (ML + ), where L denotes ligand.. d ΔE SO ne SO (L) + E SO (M) E SO (ML n ), where n is the number of ligands, E SO (L) is the spin orbit energy of the ligand, E SO (M) is the spin orbit energy of the metal atom/ion, and E SO (ML n ) is the spin orbit energy of the metal ligand complex.

14 S-14 Table S11: Cartesian coordinates for the HC7 database (MP2/6-311+G(d,p)) (CH) 12 Structure 1 C C H C C H C H H C H C C C H C C C H H H H H H (CH) 12 Structure 22 C C C C C C C C C H C H H H H H C

15 S-15 C H H H H H H (CH) 12 Structure 31 C C C C C C C H H H H H H H C C C C C H H H H H Adamantane C C C C C C C C C C H

16 S-16 H H H H H H H H H H H H H H H bicycle[2.2.2]octane C C C C C C C C H H H H H H H H H H H H H H Ethyne C C H H

17 S-17 Ethylene C C H H H H Ethane C C H H H H H H Methane C H H H H Hexane C C C C C C H H H H H H H H H H H H H H

18 S-18 2,2,3,3-Tetramethylbutane C C C C C C C C H H H H H H H H H H H H H H H H H H n-octane C C C C C C C C H H H H H H H H

19 S-19 H H H H H H H H H H

20 S-20 Table S12: Cartesian coordinates for the DC10 database (MP2/6-311+G(d,p)) C 6 Cl 6 C C C C C C Cl Cl Cl Cl Cl Cl C 6 F 6 C C C C C C F F F F F F C 6 H 6 C C C C C C H H H H H H

21 S-21 Cl 2 Cl Cl HCl Cl H HCN C N H HCN-BF 3 B F F F N C H BF 3 B F F F O 3 O O O P 4 P P P P PF 5 P F F F F F

22 S-22 P 4 O 10 P O P O P O O P O O O O O O SF6 S F F F F F F (CH 3 O) 4 Si Si O O O O C C C C H H H H H H H H H H H

23 S-23 H Urotopin (C 6 N 4 H 12 ) N C N C N C C C C N H H H H H H H H H H H H

24 S-24 1: allene (C 3 H 4 ) 2: propyne (C 3 H 4 ) 3: penta-1,2,3,4-tetraene (C 5 H 4 ) 4: penta-1,3-diyne (C 5 H 4 ) 5: hepta-1,2,3,4,5,6-hexaaene (C 7 H 4 ) 6: hepta-1,3,5-triyne (C 7 H 4 ) Figure S1. Structures of cumulenes and poly-ynes

25 S-25 P-2 P-2P P-4 P-4P P-6 P-6P P-8 P-8P P-10 P-10P Figure S2. Structures of conjugated polyenes and protonated polyenes

26 S-26 HN SB-2 H 2 N SB-2P HN SB-4 H 2 N SB-4P HN H 2 N SB-6 SB-6P HN H 2 N SB-8 SB-8P HN H 2 N SB-10 SB-10P Figure S3. Structures of conjugated Schiff bases and protonated conjugated Schiff bases

27 S-27 A TWC 2-pyridoxine 2-aminopyridine Hydrogen bonded uracil dimer (NH 3 ) 2 (H 2 O) 2 (HCONH 2 ) 2 (HCOOH) 2 Figure S4. Structures of hydrogen bonded complexes in the S22 database

28 S-28 Stacked A T Stacked uracil dimer Pyrazine dimer Stacked indole-benzene (CH 4 ) 2 Benzene CH 4 PD-Benzene dimer (C 2 H 4 ) 2 Figure S5. Structures of dispersion-dominated complexes in the S22 database

29 S-29 T-shaped indole benzene T-shaped benzene dimer Phenol dimer Benzene H2O Benzene NH 3 Benzene HCN Ethene ethyne Figure S6. Structures of mixed complexes in the S22 database.

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