Overcoming Systematic Errors for Hydrocarbon Reaction Energies

Supporting Information for:

System-DependentDensity-Based Empirical Dispersion Correction

Overcoming Systematic Errors for Hydrocarbon Reaction Energies

Stephan N. Steinmann1, Matthew D. Wodrich1,2 and Clémence Corminboeuf1*

1Laboratory for Computational Molecular Design, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland

2Current address: School of Chemistry and Biochemistry, University of Geneva, Switzerland

* Corresponding author:

To be published inTheoretical Chemistry Accounts

This supporting information was prepared on September 22, 2010 andcontains15 pages.

Contents:

Table S1: Electronic energy of the bond-separation equation for cyclohexane.

Figure S1:Electronic energy of the bond-separation equation for cyclohexane.

TableS2: Experimental BSE values, thermal corrections (B3LYP/6-311+G*) and CCSD(T)/CBS reference values for chains, rings and cages.

Table S3: Mean absolute deviations over chains, rings, cages, IDHC and all together for all methods tested compared to experimental reference values.

Table S4: Mean absolute deviations over chains, rings, cages, IDHC and all together for all methods tested compared to CCSD(T)/CBS reference values.

Figure S2:Performance for standard functionals compared to CCSD(T)/CBS reference values.

Figure S3:Performance for “modern” functionals compared to CCSD(T)/CBS reference values

Figure S4:Performance for dispersion corrected functionals compared to CCSD(T)/CBS reference values.

Figure S5:Correlations of “standard” and “modern” functionals between the methane interaction energy and the mean absolute deviations for the four test sets using CCSD(T)/CBS reference values.

Figure S6:Correlations of “standard” semi-local and hybrid density functionals between the methane interaction energy and the mean absolute deviations for the four test sets using CCSD(T)/CBS reference values.

Geometries used

Table S5: All reaction electronic reaction energies.

For one particular case, cyclohexane, we tested composite methodsdesigned to match experiment closely. Interestingly, methods like G3 or CBS-QB3 agree better with experiment than with CCSD(T)/CBS (see Table S1 and Figure S1). Apparently, the empirically designed schemes (composite methods and dDXDM) try to account for some, as for now unidentified, effects absent in CCSD(T)/CBS. Note, that the difference is unlikely to be the use of a single (the lowest lying) conformer, since CCSD(T)/CBS already underestimates the BSE.

Table S1 Electronic energy of the bond-separation equation for cyclohexane, derived from experiment by subtracting B3LYP/6-311G* thermal corrections, three different CCSD(T)/CBS estimates (MP2/(aug-cc-pVTZ, aug-cc-pVQZ)+ΔCCSD(T)/aug-cc-pVDZ; MP2/(aug-cc-pVTZ, aug-cc-pVQZ)+ΔCCSD(T)/aug-cc-pVTZ; CCSD-F12b/(VDZ-F12,VTZ-F12)[1]+Δ(T)/aug-cc-pVTZ) and eight composite methods for which E=E(0K)-ZPE).

Figure S1. Electronic energy of the bond-separation equation for cyclohexane, derived from experiment by subtracting B3LYP/6-311G* thermal corrections are compared to three different CCSD(T)/CBS estimates (MP2/(aug-cc-pVTZ, aug-cc-pVQZ)+ΔCCSD(T)/aug-cc-pVDZ; MP2/(aug-cc-pVTZ, aug-cc-pVQZ)+ΔCCSD(T)/aug-cc-pVTZ; CCSD-F12b/(VDZ-F12,VTZ-F12)[1]+Δ(T)/aug-cc-pVTZ) and eight composite methods for which E=E(0K)-ZPE).

Estimated CCSD(T)/CBS values were obtained by extrapolating df-MP2/aug-cc-pVTZ, df-MP2/aug-cc-pVQZ values and adding ΔCCSD(T)/aug-cc-pVDZ (i.e., CCSD(T)-MP2). All these computations were performed with Molpro 2009.1.[2]

Table S2. Experimental BSE values, thermal corrections (B3LYP/6-311+G*) and CCSD(T)/CBS reference values for chains, rings and cages.

Table S3. Mean absolute deviations (MADs) over chains, rings, cages, IDHC and all together for all methods tested. Basis set: cc-pVTZ, geometries and thermal corrections: B3LYP/6-311+G*; experimental reference values.

Table S4. Mean absolute deviations (MADs) over chains, rings, cages, IDHC and all together for all methods tested. Basis set: cc-pVTZ, geometries B3LYP/6-311+G*; CCSD(T)/CBS reference values without thermal corrections.

Figure S2. Performance for standard functionals: Mean absolute deviations for bond separation energies over hydrocarbon chains, rings and cages and for reaction energies of the test set “intramolecular dispersion interactions” (IDHC) using the cc-pVTZ basis set and CCSD(T)/CBS reference values.

Figure S3 Performance for “modern” functionals: Mean absolute deviations for bond separation energies over hydrocarbon chains, rings and cages and for reaction energies of the test set “intramolecular dispersion interactions” (IDHC) using the cc-pVTZ basis set and CCSD(T)/CBS reference values.

Figure S4. Performance for dispersion corrected functionals: Mean absolute deviations for bond separation energies over hydrocarbon chains, rings and cages and for reaction energies of the test set “intramolecular dispersion interactions” (IDHC) using the cc-pVTZ basis set and CCSD(T)/CBS reference values.

Figure S5. Correlations of “standard” and “modern” functionals between the methane interaction energy (a at equilibrium distance and b at 2.4 Å) and the mean absolute deviations for, bond separation energies over hydrocarbon chains, rings and cages and for reaction energies of the test set “intramolecular dispersion interactions” (IDHC) using CCSD(T)/CBS reference values.

Figure S6. Correlations of “standard” semi-local and hybrid density functionals between the methane interaction energy and the mean absolute deviations for, bond separation energies over hydrocarbon chains, rings and cages and for reaction energies of the test set “intramolecular dispersion interactions” (IDHC) using CCSD(T)/CBS reference values.

Geometry for R14 (B3LYP/6-311+G*; all the others are taken from ref [3]):

C -0.06057 0.77306 0.68794

C 0.06058 -0.77306 0.68794

C -0.76142 -1.41360 -0.44792

C 1.53949 -1.20840 0.68039

C 0.76142 1.41360 -0.44791

C -1.53950 1.20841 0.68039

C -2.23162 -0.97262 -0.40837

C 2.35884 -0.55625 -0.44367

C 2.23162 0.97262 -0.40837

C -2.35884 0.55625 -0.44367

H 0.38145 1.12826 1.62958

H -0.38145 -1.12826 1.62958

H -0.33638 -1.15155 -1.42338

H -0.69372 -2.50475 -0.36863

H 1.60322 -2.30058 0.61183

H 1.98852 -0.93276 1.64340

H 0.69373 2.50475 -0.36862

H 0.33638 1.15156 -1.42338

H -1.60322 2.30058 0.61182

H -1.98852 0.93276 1.64340

H -2.78311 -1.41991 -1.24218

H -2.69692 -1.35164 0.51131

H 2.02068 -0.92710 -1.41872

H 3.40979 -0.85093 -0.35344

H 2.69693 1.35164 0.51130

H 2.78310 1.41991 -1.24219

H -3.40978 0.85093 -0.35344

H -2.02068 0.92709 -1.41872

Table S5. Electronic reaction energies for all methods considered using the cc-pVTZ basis set.

a CCSD(T)/CBS for chains (H), rings (R) and cages (C), see above and from ref. [4] for the reactions of the IDHC test set.

Table S5. continued

Table S5. continued

Table S5. continued

1. Hill JG, Peterson KA, Knizia G, Werner H-J (2009) J Chem Phys 131 (19):194105

2. Werner H-J, Knowles PJ, Lindh R, Manby FR, Schütz M, Celani P, Korona T, Mitrushenkov A, Rauhut G, Adler TB, Amos RD, Bernhardsson A, Berning A, Cooper DL, Deegan MJO, Dobbyn AJ, Eckert F, Goll E, Hampel C, Hetzer G, Hrenar T, Knizia G, Köppl C, Liu Y, Lloyd AW, Mata RA, May AJ, McNicholas SJ, Meyer W, Mura ME, Nicklass A, Palmieri P, Pflüger K, Pitzer R, Reiher M, Schumann U, Stoll H, Stone AJ, Tarroni R, Thorsteinsson T, Wang M, Wolf A (2009) Molpro, version 2009.1, a package of ab initio programs.

3. Steinmann SN, Corminboeuf C (2010) J Chem Theory Comput 6 (7):1990-2001

4. Schwabe T, Grimme S (2007) Phys Chem Chem Phys 9 (26):3397-3406

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