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1 Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is the Owner Societies 2017 S-1 ELECTRONIC SUPPLEMENTARY INFORMATION January 22, 2017 Reaction of SO 2 with OH in the Atmosphere a,b Bo Long Junwei Lucas Bao, b and Donald G. Truhlar b * a College of Material Science and Engineering, Guizhou Minzu University, Guiyang, , China b Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota , USA These authors contributed equally. *truhlar@umn.edu Basis set abbreviations Basis set Reference Abbrev. cc-pvdz-f12 1 DZF cc-pvtz-f12 1 TZF aug-cc-pv(t+d)z 2 atz maug-cc-pv(t+d)z 3 matz G(2df,2p) 4 STZ modified G3Large semidiffuse 5 MG3S 1 Peterson, K. A.; Adler, T. B.; Werner, H.-J. Systematically convergent basis sets for explicitly correlated wavefunctions: The atoms H, He, B--Ne, and Al--Ar. J. Chem. Phys. 2008, 128, Dunning, T. H. Jr.; Peterson, K. A.; Wilson, A. K. Gaussian basis sets for use in correlated molecular calculations. X. The atoms aluminum through argon revisited. J. Chem. Phys. 2001, 114, Papajak, E.; Leverentz, H. R.; Zheng, J.; Truhlar, D. G. Efficient Diffuse Basis Sets: cc-pvxz+ and maug-cc-pvxz. J. Chem. Theory. Comput. 2009, 5, Frisch, M. J.; Pople, J. A.; Binkley, J. S. Self-consistent molecular orbital methods 25. Supplementary functions for Gaussian basis sets. J. Chem. Phys. 1984, 80, Lynch, B. J.; Zhao, Y.; Truhlar, D. G. The Effectiveness of Diffuse Basis Functions for Calculating Relative Energies by Density Functional Theory. J. Phys. Chem. A 2003, 107,

2 S-2 Table S1. The optimized bond lengths (in Å) of the transition structure for the OH + SO 2 reaction by spin-orbit-free theoretical methods with mean unsigned error (MUE) and maximum absolute derivation (MAD) Method HO1 SO1 SO2 SO3 MUE MAD CCSD(T)-F12a/TZF CCSD(T)-F12a/DZF M06/MG3S M06/STZ PW6B95/STZ MPW1B95/STZ BMK/STZ mpw1pw91/stz SOGGA11-X/STZ wb97xd/stz CCSD(T)/aTZ MPW3LYP/STZ BB1K/STZ TPSSIKCIS/STZ MPW1K/STZ B97-1/STZ B98/STZ MN12-L/STZ M11-L/STZ B1LYP/STZ B3LYP/STZ M05/STZ M05-2X/STZ MN12-SX/STZ M11/STZ B97-3/STZ B97-2/STZ M06-2X/STZ CCSD/aTZ M08-SO/STZ M08-HX/maTZ M08-HX/aTZ BHandHLYP/STZ M08-HX/STZ M08-HX/MG3S MP2(Full)/aTZ BHandH/STZ MP2(Full)/STZ M06-L/STZ O3LYP/STZ τ-hcthhyb/stz TPSSh/STZ BLYP/STZ

3 S-3 Table S2. The optimized bond angles (in degrees) of the transition structure for the OH + SO 2 reaction by spin-orbit-free theoretical methods Method Bend Bend Bend Torsion Torsion HO1S O1SO2 O1SO3 HO1SO2 HO1SO3 MUE MAD CCSD(T)-F12a/TZF CCSD(T)-F12a/DZF M08-HX/MG3S M08-HX/maTZ M08-HX/STZ M08-HX/aTZ BHandHLYP/STZ CCSD(T)/aTZ CCSD/aTZ MP2(Full)/STZ MP2(Full)/aTZ M06-2X/STZ M08-SO/STZ MPW1K/STZ M11-L/STZ O3LYP/STZ MN12-SX/STZ M05-2X/STZ B97-3/STZ M11/STZ BB1K/STZ SOGGA11-X/STZ BMK/STZ TPSSh/STZ B1LYP/STZ M05/STZ wb97xd/stz MN12-L/STZ M06/STZ M06/MG3S mpw1pw91/stz MPW1B95/STZ PW6B95/STZ B97-2/STZ B3LYP/STZ B98/STZ MPW3LYP/STZ B97-1/STZ TPSSIKCIS/STZ BHandH/STZ M06-L/STZ BLYP/STZ τ-hcthhyb/stz

4 S-4 Table S3. The enthalpies of activation ( ΔH,º 0, 0 K) and reaction ( Δ H, 0 K) of the OH + 0 SO 2 reaction by spin-orbit-free theoretical methods (in kcal/mol) Method a,b ΔH,º 0 ΔH 0 MUE b Scale factor c MW3.2//C d W3X-L//C d M08-HX/MG3S e W3X//C d CCSD(T)-F12a/TZF d W3X-L//QCISD/STZ d W2X//C d CCSD(T)-F12a/DZF d CCSD(T)-F12b/VQZ-F12//C d CCSD(T)-F12b/VQZ-F12//CCSD(T)-F12a/DZF d M08-HX/maTZ e M08-HX/aTZ e M06-2X/maTZ e M06-2X/aTZ e CCSD(T)/aTZ d M06/MG3S e a //C denotes at the geometry calculated by CCSD(T)-F12a/TZF. b Mean unsigned error averaged over the two previous columns, rrelative to the first row. c Unitless factor by which vibrational frequencies were scaled. d The scale factor is calculated in the present work. e The scale factor is obtained from reference 6. 6 Alecu, I. M.; Zheng, J.; Zhao, Y.; Truhlar, D. G. Computational Thermochemistry: Scale Factor Databases and Scale Factors for Vibrational Frequencies Obtained from Electronic Model Chemistries, J. Chem. Theory Comput. 2010, 6,

5 S-5 Table S4. The barrier height (ΔE, 0 K) and reaction energy (ΔE, 0 K) of the OH + SO 2 reaction by spin-orbit-free theoretical methods (in kcal/mol) Method a V ΔV MUE b MW3.2//C W3X-L//C M08-HX/MG3S W3X//C CCSD(T)-F12a/TZF W2X//C W3X-L//QCISD/STZ M08-HX/maTZ CCSD(T)-F12a/DZF M08-HX/aTZ CCSD(T)-F12b/VQZ-F12//C CCSD(T)-F12b/VQZ-F12//CCSD(T)-F12a/DZF M06-2X/MG3S M06-2X/maTZ M06/STZ M06-2X/aTZ CCSD(T)/aTZ M06/MG3S MP2(full)/aTZ CCSD(T)-F12a/TZF b Mean unsigned error averaged over the two previous columns

6 S-6 Table S5. The rate constant of the OH + SO 2 reaction at the different temperatures and pressures. (a) bath gas: N 2 T/K P/bar k (cm 3 molecule 1 s 1 ) T/K P/bar k (cm 3 molecule 1 s 1 ) T/K P/bar k (cm 3 molecule 1 s 1 ) T/K P/bar k (cm 3 molecule 1 s 1 ) T/K P/bar k (cm 3 molecule 1 s 1 ) T/K P/bar k (cm 3 molecule 1 s 1 )

7 (b) bath gas: He T/K P/bar k (cm 3 molecule 1 s 1 ) T/K P/bar k (cm 3 molecule 1 s 1 ) T/K P/bar k (cm 3 molecule 1 s 1 ) T/K P/bar k (cm 3 molecule 1 s 1 ) T/K P/bar k (cm 3 molecule 1 s 1 ) T/K P/bar k (cm 3 molecule 1 s 1 ) S-7

8 (c) bath gas: Ar T/K P/bar k (cm 3 molecule 1 s 1 ) T/K P/bar k (cm 3 molecule 1 s 1 ) T/K P/bar k (cm 3 molecule 1 s 1 ) T/K P/bar k (cm 3 molecule 1 s 1 ) T/K P/bar k (cm 3 molecule 1 s 1 ) T/K P/bar k (cm 3 molecule 1 s 1 ) S-8

9 Table S6. Computed p 1/2 (in the unit of bar) for SO 2 + OH reaction with N 2 as bath gas at various temperatures. T/K p 1/2 /bar S-9

10 Table S7. Computed k(t, p) (in the unit of cm 3 molecule -1 s -1 ) for SO 2 + OH reaction with N 2 as S-10 bath gas, and the fitted k(t, p) at various pressures (bar) and at 190 K, 298 K and 450 K. T/K p/bar B/bar -1 d / bar 2 F a Fitted Computed k(t, p) k(t, p) Error% E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E a The ratio of fitted k(t, p) to fitted k (T).

11 S-11 Table S8. The Cartesian coordinates (Å) of the optimized geometries by different theoretical methods. Species Methods Cartesian Coordindates OH CCSD(T)-F12a/TZF O H CCSD(T)-F12a/DZF O H CCSD(T)/aTZ O H M08-HX/MG3S O H QCISD/STZ O H M08-HX/maTZ O H M08-HX/aTZ O H M06-2X/MG3S O H M06-2X/maTZ O H M06-2X/aTZ O H SO 2 CCSD(T)-F12a/TZF S O O CCSD(T)-F12a/DZF S O O CCSD(T)/aTZ S O O M08-HX/MG3S S O O QCISD/STZ S O O M08-HX/maTZ S O O M08-HX/aTZ S O O M06-2X/MG3S S O O M06-2X/maTZ S

12 S-12 O O M06-2X/aTZ S O O HOSO 2 CCSD(T)-F12a/TZF S O O O H CCSD(T)-F12a/DZF S O O O H CCSD(T)/aTZ S O O O H M08-HX/MG3S S O O O H QCISD/STZ S O O O H M08-HX/maTZ S O O O H M08-HX/aTZ S O O O H M06-2X/MG3S S O O O H M06-2X/maTZ S O O

13 S-13 O H M06-2X/aTZ S O O O H TS1 CCSD(T)-F12a/TZF S O O O H CCSD(T)-F12a/DZF S O O O H CCSD(T)/aTZ S O O O H M08-HX/MG3S S O O O H QCISD/STZ S O O O H M08-HX/maTZ S O O O H M08-HX/aTZ S O O O H M06-2X/MG3S S O O O H M06-2X/maTZ S

14 O O O H M06-2X/aTZ S O O O H S-14

15 S-15 Table S9. Absolute energies in hartrees. Methods Species OH SO 2 TS1 HOSO 2 MW3.2//CCSD(T)-F12a/TZF W3X-L//CCSD(T)-F12a/TZF M08-HX/MG3S W3X//CCSD(T)-F12a/TZF CCSD(T)-F12a/TZF W3X-L//QCISD/STZ W2X//CCSD(T)-F12a/TZF CCSD(T)-F12a/DZF CCSD(T)-F12b/VQZ-F12//CCSD(T)-F12a/TZF CCSD(T)-F12b/VQZ-F12//CCSD(T)-F12a/DZF M08-HX/maTZ M08-HX/aTZ M06-2X/maTZ M06-2X/aTZ CCSD(T)/aTZ M06-2X/MG3S

16 S-16 Table S10. Parameters used to fit k(t,p). a k (T ) k 0 (T ) p 1/2 A a n a E a T l l T T a Units are given in text.

17 S V G a /kcal/mol s/angstrom Figure S1. Vibrationally adiabatic potential energy along the minimum energy path for the OH + SO 2 reaction.

18 S log 10 k mbar 10 5 mbar 10 4 mbar 10 3 mbar 10 2 mbar 10 1 mbar 1.3 mbar T/1000 Figure S2. The rate constant of the OH + SO 2 reaction at the different temperatures and pressures (bath gas: Ar).

19 S log 10 k mbar 10 5 mbar 10 4 mbar 10 3 mbar 10 2 mbar 10 1 mbar 1.3 mbar T/1000 Figure S3. The rate constant of the OH + SO2 reaction at the different temperatures and pressures (bath gas: He).

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