Supporting Information for: A Density Functional for Spectroscopy: No Long-Range Self-Interaction
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1 S-1 Supporting Information for: A Density Functional for Spectroscopy: No Long-Range Self-Interaction Error, Good Performance for Rydberg and Charge Transfer States, and Better Performance on Average than B3LYP for Ground States Yan Zhao and Donald G. Truhlar To be published in J. Phys. Chem. A This supporting information was revised on Nov. 6, 2006 and consists of a total of 18 pages. Contents: page Geometries and basis sets S-2 Table S1. MGAE109/05 database: zero-point-exclusive atomization energies S-4 Table S2. IP13/3 and EA13/3 databases S-6 Table S3. PA8 database S-7 Table S4. HTBH38/04 database S-8 Table S5. NHTBH38/04 databases S-9 Table S6. Noncovalent interaction databases S-10 Table S7. π system databases S-11 Table S8. Charge transfer excitation energies of the C 2 H 4 C 2 F 4 dimer S-12 Table S9. Cartesian coordinates for all molecules in TDDFT calculations S-13 Figure S1. Cumulenes and poly-ynes S-15 Figure S2. Conjugated polyenes and protonated polyenes S-16 Figure S3. Conjugated Schiff bases and protonated conjugated Schiff bases S-17 Figure S4. Charge transfer excitation energy of C 2 H 4 C 2 F 4 dimer S-18
2 S-2 Geometries and basis sets The TDDFT calculation of the CO, N 2, and HCHO molecules employed the augmented Sadlej pvtz basis set 1,2 and experimental geometries. The 6-31+G(d,p) basis set was employed for the calculations on NH 3 F 2. The geometry for the charge-transfer complex, NH 3 F 2, was optimized at the MC-QCISD/3 level, then the intermolecular distance of two monomer was changed to 6 Å, without reoptimization. The 6-31G* basis set was employed for the C 2 H 4 C 2 F 4 complex, and we used experimental geometries for each monomer with the intermolecular distance being 8 Å. The geometry of tetracene was optimized at the B3LYP/6-31+G(d,p) level, and all TDDFT calculation for tetracene employed the 6-311G(2d,p) basis set. All calculations for the AE6, MGAE109/05, IP13/3, EA13/3, HTBH38/04, and NHTBH38/05 databases are single-point calculations at QCISD/MG3 geometries, where QCISD is quadratic configuration interaction with single and double excitations, 3 and MG3 is the modified 4,5 G3Large 6 basis set. The MG3 basis set, 4 also called G3LargeMP2, 5 is the same as G(3d2f, 2df, 2p) 7,8 for H-Si, but improved 6 for P-Ar. Geometries for the PA8/06 database are at the MP2(full)/6-31G(2df,p) level of theory. Geometries for all molecules in the HB6/04, CT7/04, DI6/04, and WI7/05 noncovalent databases and the (C 2 H 4 ) 2 and (C 2 H 2 ) 2 dimers in the PPS5/05 database are optimized at the MC-QCISD/3 level, where MC-QCISD is the multi-coefficient QCISD method. 9,10 The geometries for the benzene dimers in the PPS5/05 database are taken from Sinnokrot and Sherrill. 11 Geometries for all molecules in the ABDE4/05 database are optimized at the B3LYP/6-31G(d) level, and they are given in the supporting information of a previous paper. 12 The 6-
3 S G(3df,2p) basis set is used for the calculations of ABDEs; and this choice is made for the purpose of comparison with the previous results. References: (1) Sadlej, A. J. Theor. Chim. Acta 1991, 79, 123. (2) Casida, M. E.; Jamorski, C.; Casida, K. C.; Salahub, D. R. J. Chem. Phys. 1998, 108, (3) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J. Chem. Phys. 1987, 87, (4) Fast, P. L.; Sanchez, M. L.; Truhlar, D. G. Chem. Phys. Lett. 1999, 306, 407. (5) Curtiss, L. A.; Redfern, P. C.; Raghavachari, K.; Rassolov, V.; Pople, J. A. J. Chem. Phys. 1999, 110, (6) Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Rassolov, V.; Pople, J. A. J. Chem. Phys. 1998, 109, (7) Frisch, M. J.; Pople, J. A.; Binkley, J. S. J. Chem. Phys. 1984, 80, (8) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory, 1st ed.; Wiley: New York, (9) Fast, P. L.; Truhlar, D. G. J. Phys. Chem. A 2000, 104, (10) Lynch, B. J.; Truhlar, D. G. J. Phys. Chem. A 2003, 107, (11) Sinnokrot, M. O.; Sherrill, C. D. J. Phys. Chem. A 2004, 108, (12) Izgorodina, E. I.; Coote, M. L.; Radom, L. J. Phys. Chem. A 2005, 109, (13) Tawada, Y.; Tsuneda, T.; Yanagisawa, S.; Yanai, T.; Hirao, K. J. Chem. Phys. 2004, 121, 8425.
4 S-4 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
5 S-5 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
6 S-6 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
7 S-7 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
8 S-8 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
9 S-9 Table S5: NHTBH38/04 databases Reactions Best Estimate (kcal/mol) Heavy-atom transfer reactions V f V r H + N 2 O OH + N H + FH HF + H H + ClH HCl + H H + FCH 3 HF + CH H + F 2 HF + F CH3 + FCl CH 3 F + Cl Nucleophilic substitution reactions F- + CH 3 F FCH 3 + F F- CH 3 F FCH 3 F Cl- + CH 3 Cl ClCH 3 + Cl Cl- CH 3 Cl ClCH 3 Cl F- + CH 3 Cl FCH 3 + Cl F- CH 3 Cl FCH 3 Cl OH- + CH 3 F HOCH 3 + F OH- CH 3 F HOCH 3 F Unimolecular and association reactions H + N 2 HN H + CO HCO H + C 2 H 4 CH 3 CH CH 3 + C 2 H 4 CH 3 CH 2 CH HCN HNC
10 S-10 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
11 S-11 Table S7: 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.
12 Table S8: Charge-transfer excitation energies (in ev) of the C 2 H 4 C 2 F 4 dimer along the intermolecular distances R (in Å) R TPSSh B3LYP B98 PBEh BMK M05-2X M06-HF HF SAC-CI S-12
13 S-13 Table 9: Cartesian coordinates for TDDFT calculations CO C O N 2 N N HCHO O C H H NH 3 F 2 6 Å N H H H F F C 2 H 4 C 2 F 4 8 Å C C F F F F C C H H H H
14 S-14 Tetracene C C C C C C C C C C C C C C C C C C H H H H H H H H H H H H
15 S-15 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
16 S-16 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
17 S-17 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
18 S-18 ωct(r) ωct(5.0) (ev) HF M06-HF SAC-CI M05-2X BMK PBEh B98 B3LYP TPSSh Intermolecular distance R (angstron) Figure S4. The charge transfer excitation energy of ethylene-tetrafluoroethylene dimer. For all functionals, the excitation energy at 5.0 Å is set to zero. The SAC-CI results are taken from Tawada et al. 13 The figure shows that only HF and M06-HF calculations show the correct long-range behavior. The curves arrange themselves roughly in the order of their percentage of Hartree-Fock exchange because a functional with a percentage X of Hartree-Fock exchange has a long-range behavior (in atomic units) of X/100R, as compared to the correct long-range behavior of -1/R.
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