Supporting Information: Predicting the Ionic Product of Water

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1 Supporting Information: Predicting the Ionic Product of Water Eva Perlt 1,+, Michael von Domaros 1,+, Barbara Kirchner 1, Ralf Ludwig 2, and Frank Weinhold 3,* 1 Mulliken Center for Theoretical Chemistry, Institute for Physical and Theoretical Chemistry, University of Bonn, Bonn, 53115, Germany 2 Physical and Theoretical Chemistry, Institute for Chemistry, University of Rostock, Rostock, 18059, Germany 3 Department of Chemistry, University of Wisconsin-Madison, Madison, WI 53706, USA * weinhold@chem.wisc.edu + these authors contributed equally to this work Geometry optimizations and frequency analyses were performed using the ORCA quantum chemistry code. The methods employed in this study are Hartree Fock (HF), density functional theory (DFT) as well as second order Møller Plesset perturbation theory (MP2) and the efficient domain based local pair-natural orbital coupled-cluster method with single, double and perturbative triple excitations (DLPNO-CCSD(T)). For DFT calculations the hybrid functionals B3LYP and PBE0 have been used. The applied basis sets are G** for HF, def2-tzvp for DFT calculations and aug-cc-pvtz in the case of MP2 whereas an extrapolation to the complete basis set limit has been performed in the case of DLPNO-CCSD(T). Both density functionals have been used stand-alone, whereas in a second calculation Grimme s D3 dispersion correction and in a third calculation the D3 dispersion correction and a geometrical counterpoise correction have been applied. Finally, the highly efficient composite method PBEh-3c has been employed. In all cases geometry optimizations have been carried out except for the MP2 and DLPNO-CCSD(T) calculations which are single-point energy calculations on B3LYP-D3,gCP-based geometries. Furthermore, to judge the influence of the counterpoise correction using the supramolecular approach (CP) in comparison to a geometrical ansatz (gcp), B3LYP calculations with the G** basis set and counterpoise correction (with and without D3 dispersion correction) have been conducted. The latter, conventional counterpoise correction has been applied to the energies, only, and has not been included in the geometry optimization. All methods, basis sets, employed corrections, and labels used throughout this article are summarized in Table S1. Tight SCF and geometry convergence criteria were applied in all methods and fine numerical quadrature grids (grid5) were used in DFT calculations. Table S1. Methods, basis sets, employed corrections, and labels used throughout this article. label method basis set corrections comments HF HF G** B3LYP DFT (B3LYP functional) def2-tzvp B3LYP-CP DFT (B3LYP functional) G** CP no W 10 B3LYP-D3 DFT (B3LYP functional) def2-tzvp D3 B3LYP-D3,gCP DFT (B3LYP functional) def2-tzvp D3, gcp B3LYP-D3,CP DFT (B3LYP functional) G** D3, CP no W 10 PBE0 DFT (PBE0 functional) def2-tzvp PBE0-D3 DFT (PBE0 functional) def2-tzvp D3 PBE0-D3,gCP DFT (PBE0 functional) def2-tzvp D3, gcp PBEh-3c DFT (PBEh functional) def2-msvp D3, gcp MP2 MP2 aug-cc-pvtz single point on B3LYP-D3,gCP geometry CCSD(T)* DLPNO-CCSD(T) CBS single point on B3LYP-D3,gCP geometry The interaction energies of all clusters have been calculated with respect to infinitely separated, relaxed, neutral monomers as reference species. The optimized cluster energies are summarized in Table S2. 1

2 Table S2. Adiabatic binding energies binde in kj mol 1. A dash ( ) denotes an unstable geometry at the selected level of theory. Missing numbers indicate that CP corrections have not been evaluated for the neutral decamer. HF B3LYP B3LYP B3LYP B3LYP B3LYP PBE0 PBE0 PBE0 PBEh-3c MP2 CCSD(T)* -CP -D3 -D3,gCP -D3,CP -D3 -D3,gCP W W W3c W3u W5c W5p W5ip W W W8c W8cip W8b W8p W8ip W W10ip W10ip W /11

3 Table S3. H 2 O H 3 O + hydrogen bond lengths for all ion pair clusters in Å as obtained at the B3LYP-D3 level of theory. W 5ip W 8cip W 8ip W 10ip W 10ip r H O Table S4. Optimized QCE parameters a mf and b xv for the different methods applied in this study. a mf [J m 3 mol 1 ] HF B3LYP B3LYP-CP B3LYP-D B3LYP-D3,gCP B3LYP-D3,CP PBE PBE0-D PBE0-D3,gCP PBEh-3c MP CCSD(T)* b xv The values of the ionic product pk W at selected temperatures (298 K and 373 K) are listed in Table S5. In addition to the observations discussed in the main article, it is apparent that conventional couterpoise correction of the basis set superposition error (B3LYP-CP, B3LYP-D3,CP) does not yield satisfying results. 3/11

4 Table S5. Negative logarithm of the ionic product of water pk W at ambient temperature (298 K) and close to the boiling point (373 K). 298 K 373 K HF B3LYP B3LYP-CP B3LYP-D B3LYP-D3,gCP B3LYP-D3,CP PBE PBE0-D PBE0-D3,gCP PBEh-3c MP CCSD(T)* Exp. [ref. 42] The coordinates of all clusters applied in this study are given below for B3LYP-D3 geometries. Table S6. Geometry data in xyz format (Å) of all clusters applied in this study. W 1 O H H W 2 O O H H H H W 3c O O H H H H H O H W 3u O O H H H H /11

5 O H H W 5c O O H H H H O H O H O H H H H W 5p O O O O O H H H H H H H H H H W 5ip O O O O O H H H H H H H H H H /11

6 W 6 O O H H H H O H H O H H O H H O H H W 7 O O O O O H H H H H H H H H H H O H O H H W 8c O O O O O O O O H H H /11

7 H H H H H H H H H H H H H W 8cip O O O O O O O O H H H H H H H H H H H H H H H H W 8b O H H O H H O H H O H H O H /11

8 H O H H O H H O H H W 8p O O O H H H H H O O O H H O O H H H H H H H H H W 8ip O O O O O O O O H H H H H H H H H /11

9 H H H H H H H W 9 O O O O O O O H H H H H H H H H H H H H H O H H O H H W 10ip O O O O O H H H H H H H H H H H O /11

10 O O O O H H H H H H H H H W 10ip2 O O O H H H O H O H H H H H H H O O O O H H H H O H H H H H W 10 O O O O O O O O /11

11 O O H H H H H H H H H H H H H H H H H H H H /11

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