Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 SUPPORTING INFORMATION Dependence of pKa on Solute Cavity for Diprotic and Triprotic Acids Tae Bum Lee and Michael L. McKee* Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849 [email protected] S1 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 Table S1. Point Group, DFT Method, Cavity Model, Total Energies (hartrees), Zero-point Energies (kcal/mol) with number of Imaginary Frequencies in Parentheses, Thermal Corrections (kcal/mol), Entropies (cal/mol·K), and Free energy of Solvation (kcal/mol) CO32HCO3H2CO3 CO32HCO3H2CO3 CO32HCO3H2CO3 CO32HCO3H2CO3 CO32HCO3H2CO3 CO32HCO3H2CO3 CO32HCO3H2CO3 CO32HCO3H2CO3 CO32HCO3H2CO3 CO32HCO3H2CO3 CO32HCO3H2CO3 CO32HCO3H2CO3 CO32HCO3- PGa DFT Cavity Model SCF Energy ZPEb (NIF) TCc Sd Solvation Free Energye D3h Cs C2v D3h Cs C2v D3h Cs C2v D3h Cs C2v D3h Cs C2v D3h Cs C2v D3h Cs C2v D3h Cs C2v D3h Cs C2v D3h Cs C2v D3h Cs C2v D3h Cs C2v D3h Cs B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling -263.79277 -264.57336 -265.12195 -263.79277 -264.57336 -265.12195 -263.79277 -264.57336 -265.12195 -263.79277 -264.57336 -265.12195 -263.79277 -264.57336 -265.12195 -263.52597 -264.30257 -264.84861 -263.52597 -264.30257 -264.84861 -263.52597 -264.30257 -264.84861 -263.52597 -264.30257 -264.84861 -263.52597 -264.30257 -264.84861 -263.82022 -264.59765 -265.14436 -263.82022 -264.59765 -265.14436 -263.82022 -264.59765 8.20(0) 16.28(0) 24.77(0) 8.20(0) 16.28(0) 24.77(0) 8.20(0) 16.28(0) 24.77(0) 8.20(0) 16.28(0) 24.77(0) 8.20(0) 16.28(0) 24.77(0) 7.77(0) 15.67(0) 24.01(0) 7.77(0) 15.67(0) 24.01(0) 7.77(0) 15.67(0) 24.01(0) 7.77(0) 15.67(0) 24.01(0) 7.77(0) 15.67(0) 24.01(0) 7.75(0) 15.62(0) 23.96(0) 7.75(0) 15.62(0) 23.96(0) 7.75(0) 15.62(0) 2.62 2.82 2.92 2.62 2.82 2.92 2.62 2.82 2.92 2.62 2.82 2.92 2.62 2.82 2.92 2.66 2.86 2.96 2.66 2.86 2.96 2.66 2.86 2.96 2.66 2.86 2.96 2.66 2.86 2.96 2.66 2.87 2.96 2.66 2.87 2.96 2.66 2.87 59.07 63.70 62.91 59.07 63.70 62.91 59.07 63.70 62.91 59.07 63.70 62.91 59.07 63.70 62.91 59.32 63.98 63.15 59.32 63.98 63.15 59.32 63.98 63.15 59.32 63.98 63.15 59.32 63.98 63.15 59.32 64.01 63.16 59.32 64.01 63.16 59.32 64.01 -264.00 -244.44 -63.63 -3.83 -255.08 -70.20 -12.01 -262.91 -73.01 -13.02 -246.01 -64.99 -255.86 -68.48 -8.53 -6.21 -241.50 -62.59 -3.43 -251.73 -68.79 -11.66 -258.57 -70.86 -12.42 -242.96 -63.91 -252.26 -66.85 -7.94 -5.45 -242.42 -62.89 -3.47 -252.79 -69.12 -11.69 -259.87 S2 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 H2CO3 CO32HCO3H2CO3 CO32HCO3H2CO3 CO32HCO3H2CO3 CO32HCO3H2CO3 CO32HCO3H2CO3 CO32HCO3H2CO3 CO32HCO3H2CO3 SO32HSO3H2SO3 SO32HSO3H2SO3 SO32HSO3H2SO3 SO32HSO3H2SO3 SO32HSO3H2SO3 SO32HSO3H2SO3 SO32HSO3H2SO3 SO32HSO3H2SO3 SO32- C2v D3h Cs C2v D3h Cs C2v D3h Cs C2v D3h Cs C2v D3h Cs C2v D3h Cs C2v D3h Cs C2v C3V C1 Cs C3V C1 Cs C3V C1 Cs C3V C1 Cs C3V C1 Cs C3V C1 Cs C3V C1 Cs C3V C1 Cs C3V BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE Pauling Klamt Klamt Klamt Klamt Klamt Klamt UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klmat SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt -265.14436 -263.82022 -264.59765 -265.14436 -263.82022 -264.59765 -265.14436 -263.76479 -264.54603 -265.09311 -263.76479 -264.54603 -265.09311 -263.76479 -264.54603 -265.09311 -263.76479 -264.54603 -265.09311 -263.76479 -264.54603 -265.09311 -623.89243 -624.64482 -625.17435 -623.89243 -624.64482 -625.17435 -623.89243 -624.64482 -625.17435 -623.89243 -624.64482 -625.17435 -623.89243 -624.64482 -625.17435 -623.49623 -624.24488 -624.77117 -623.49623 -624.24488 -624.77117 -623.49623 -624.24488 -624.77117 -623.49624 S3 23.96(0) 7.75(0) 15.62(0) 23.96(0) 7.75(0) 15.62(0) 23.96(0) 8.63(0) 16.78(0) 25.25(0) 8.63(0) 16.78(0) 25.25(0) 8.63(0) 16.78(0) 25.25(0) 8.63(0) 16.78(0) 25.25(0) 8.63(0) 16.78(0) 25.25(0) 5.80(0) 12.81(0) 20.07(0) 5.80(0) 12.81(0) 20.07(0) 5.80(0) 12.81(0) 20.07(0) 5.80(0) 12.81(0) 20.07(0) 5.80(0) 12.81(0) 20.07(0) 5.48(0) 12.28(0) 19.30(0) 5.48(0) 12.28(0) 19.30(0) 5.48(0) 12.29(0) 19.30(0) 5.48(0) 2.96 2.66 2.87 2.96 2.66 2.87 2.96 2.59 2.78 2.89 2.59 2.78 2.89 2.59 2.78 2.89 2.59 2.78 2.89 2.59 2.78 2.89 2.95 3.46 3.72 2.95 3.46 3.72 2.95 3.46 3.72 2.95 3.46 3.72 2.95 3.46 3.72 3.02 3.53 3.82 3.02 3.53 3.82 3.02 3.53 3.82 3.02 63.16 59.32 64.01 63.16 59.32 64.01 63.16 58.91 63.46 62.72 58.91 63.46 62.72 58.91 63.46 62.72 58.91 63.46 62.72 58.91 63.46 62.72 63.78 69.17 70.97 63.78 69.15 70.97 63.78 69.17 70.97 63.78 69.16 70.97 63.78 69.16 70.97 64.21 69.63 71.77 64.21 69.65 71.77 64.21 69.63 71.77 64.21 -71.36 -12.54 -243.91 -64.22 -253.45 -67.29 -8.03 -5.49 -248.54 -65.15 -4.33 -259.86 -71.75 -12.61 -269.03 -75.38 -14.07 -250.18 -66.61 -261.00 -70.45 -9.09 -231.27 -59.68 -4.27 -224.11 -56.26 -3.80 -246.74 -68.20 -12.91 -232.65 -60.74 -6.18 -238.03 -65.49 -9.83 -228.12 -58.50 -3.67 -221.46 -55.37 -3.24 -242.13 -65.77 -11.57 -229.40 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 HSO3H2SO3 SO32HSO3H2SO3 SO32HSO3H2SO3 SO32HSO3H2SO3 SO32HSO3H2SO3 SO32HSO3H2SO3 SO32HSO3H2SO3 SO32HSO3H2SO3 SO32HSO3H2SO3 SO32HSO3H2SO3 SO32HSO3H2SO3 SO32HSO3H2SO3 SO42HSO4H2SO4 SO42HSO4H2SO4 SO42HSO4H2SO4 SO42HSO4H2SO4 C1 Cs C3V C1 Cs C3V C1 Cs C3V C1 Cs C3V C1 Cs C3V C1 Cs C3V C1 Cs C3V C1 Cs C3V C1 Cs C3V C1 Cs C3V C1 Cs C3V C1 Cs Td Cs C2 Td Cs C2 Td Cs C2 Td Cs C2 PBE PBE PBE PBE PBE BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klmat Klamt Klmat SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt -624.24488 -624.77117 -623.49624 -624.24488 -624.77117 -623.95859 -624.70848 -625.23572 -623.95859 -624.70848 -625.23572 -623.95859 -624.70848 -625.23572 -623.95859 -624.70848 -625.23572 -623.95859 -624.70848 -625.23572 -623.84443 -624.59720 -625.12652 -623.84443 -624.59719 -625.12652 -623.84443 -624.59719 -625.12652 -623.84443 -624.59719 -625.12652 -623.84443 -624.59719 -625.12652 -699.18733 -699.91122 -700.41831 -699.18733 -699.91122 -700.41831 -699.18733 -699.91122 -700.41831 -699.18733 -699.91122 -700.41832 S4 12.29(0) 19.30(0) 5.48(0) 12.29(0) 19.30(0) 5.45(0) 12.23(0) 19.24(0) 5.45(0) 12.25(0) 19.24(0) 5.45(0) 12.23(0) 19.24(0) 5.45(0) 12.23(0) 19.24(0) 5.45(0) 12.23(0) 19.24(0) 6.17(0) 13.34(0) 20.61(0) 6.17(0) 13.35(0) 20.61(0) 6.17(0) 13.31(0) 20.61(0) 6.17(0) 13.29(0) 20.61(0) 6.17(0) 13.29(0) 20.61(0) 9.25(0) 16.52(0) 24.17(0) 9.25(0) 16.52(0) 24.17(0) 9.25(0) 16.52(0) 24.17(0) 9.25(0) 16.52(0) 24.17(0) 3.53 3.82 3.02 3.53 3.82 3.03 3.54 3.83 3.03 3.53 3.83 3.03 3.55 3.83 3.03 3.55 3.83 3.03 3.55 3.83 2.89 3.34 3.63 2.89 3.33 3.63 2.89 3.35 3.63 2.89 3.37 3.63 2.89 3.37 3.63 3.18 3.78 3.89 3.18 3.78 3.89 3.18 3.78 3.89 3.18 3.78 3.89 69.63 71.77 64.21 69.63 71.77 64.24 69.72 71.84 64.24 69.62 71.84 64.24 69.76 71.84 64.24 69.77 71.84 64.24 69.77 71.84 63.43 68.34 70.27 63.43 68.28 70.27 63.43 68.46 70.27 63.43 68.65 70.27 63.43 68.65 70.27 63.72 73.59 71.40 63.72 73.59 71.40 63.72 73.59 71.40 63.72 73.59 71.41 -59.52 -5.48 -234.21 -63.78 -9.02 -229.12 -58.84 -3.72 -222.26 -55.54 -3.24 -243.53 -66.37 -11.71 -230.44 -59.82 -5.52 -235.37 -63.22 -9.10 -235.74 -61.76 -4.99 -227.79 -57.67 -4.23 -253.21 -71.15 -13.75 -237.30 -62.96 -6.91 -242.98 -67.58 -10.55 -225.59 -59.49 -5.93 -233.95 -66.76 -15.76 -241.52 -68.38 -16.09 -227.73 -61.28 -8.93 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 SO42HSO4H2SO4 SO42HSO4H2SO4 SO42HSO4H2SO4 SO42HSO4H2SO4 SO42HSO4H2SO4 SO42HSO4H2SO4 SO42HSO4H2SO4 SO42HSO4H2SO4 SO42HSO4H2SO4 SO42HSO4H2SO4 SO42HSO4H2SO4 SO42HSO4H2SO4 SO42HSO4H2SO4 SO42HSO4H2SO4 SO42HSO4H2SO4 SO42HSO4- Td Cs C2 Td C1 C1 Td C1 C1 Td C1 C1 Td C1 C1 Td C1 C1 Td C1 C1 Td C1 C1 Td C1 C1 Td C1 C1 Td C1 C1 Td Cs C2 Td Cs C2 Td Cs C2 Td Cs C2 Td Cs B3LYP B3LYP B3LYP PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD -699.18733 -699.91122 -700.41832 -698.71636 -699.43954 -699.94622 -698.71636 -699.43954 -699.94622 -698.71636 -699.43954 -699.94622 -698.71636 -699.43954 -699.94622 -698.71636 -699.43954 -699.94622 -699.25677 -699.98084 -700.48822 -699.25677 -699.98084 -700.48822 -699.25677 -699.98084 -700.48822 -699.25677 -699.98084 -700.48822 -699.25677 -699.98084 -700.48822 -699.14473 -699.86492 -700.36830 -699.14473 -699.86492 -700.36830 -699.14473 -699.86492 -700.36830 -699.14473 -699.86492 -700.36830 -699.14473 -699.86492 S5 9.25(0) 16.52(0) 24.17(0) 8.80(0) 15.76(0) 23.28(0) 8.80(0) 15.76(0) 23.28(0) 8.80(0) 15.76(0) 23.28(0) 8.79(0) 15.76(0) 23.28(0) 8.79(0) 15.76(0) 23.28(0) 8.77(0) 15.72(0) 23.23(0) 8.77(0) 15.72(0) 23.23(0) 8.77(0) 15.72(0) 23.23(0) 8.76(0) 15.72(0) 23.23(0) 8.76(0) 15.72(0) 23.23(0) 9.74(0) 17.06(0) 24.71(0) 9.74(0) 17.07(0) 24.71(0) 9.74(0) 17.07(0) 24.71(0) 9.74(0) 17.07(0) 24.70(0) 9.74(0) 17.07(0) 3.18 3.78 3.89 3.27 3.95 4.00 3.27 3.95 4.00 3.27 3.95 4.00 3.27 3.95 4.00 3.27 3.95 4.00 3.27 3.95 4.00 3.27 3.95 4.00 3.27 3.95 4.00 3.27 3.95 4.00 3.27 3.95 4.00 3.11 3.71 3.83 3.11 3.70 3.83 3.11 3.70 3.83 3.11 3.70 3.83 3.11 3.70 63.72 73.59 71.41 64.23 77.85 72.06 64.23 77.85 72.06 64.23 77.85 72.06 64.24 77.78 72.06 64.24 77.78 72.06 64.25 77.40 72.09 64.25 77.40 72.09 64.25 77.40 72.09 64.25 77.39 72.09 64.25 77.39 72.09 63.33 73.59 71.02 63.33 73.25 71.02 63.33 73.25 71.02 63.33 73.25 71.02 63.33 73.25 -234.08 -65.92 -12.76 -223.72 -58.03 -5.11 -231.80 -65.44 -14.78 -238.49 -66.61 -14.94 -225.75 -59.74 -8.01 -231.56 -64.31 -11.63 -224.50 -58.30 -5.15 -232.67 -65.69 -14.81 -239.65 -67.11 -15.06 -226.55 -60.07 -8.05 -232.51 -64.66 -11.70 -228.41 -61.04 -6.91 -237.07 -68.51 -16.92 -245.88 -70.95 -17.70 -230.67 -62.95 -10.00 -237.17 -67.63 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 H2SO4 C2O42HC2O4H2C2O4 C2O42HC2O4H2C2O4 C2O42HC2O4H2C2O4 C2O42HC2O4H2C2O4 C2O42HC2O4H2C2O4 C2O42HC2O4H2C2O4 C2O42HC2O4H2C2O4 C2O42HC2O4H2C2O4 C2O42HC2O4H2C2O4 C2O42HC2O4H2C2O4 C2O42HC2O4H2C2O4 C2O42HC2O4H2C2O4 C2O42HC2O4H2C2O4 C2O42- C2 D2d Cs C2h D2d Cs C2h D2d Cs C2h D2d Cs C2h D2d Cs C2h D2d Cs C2h D2d Cs C2h D2d Cs C2h D2d Cs C2h D2d Cs C2h D2d Cs C2h D2d Cs C2h D2d Cs C2h D2d M052X B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt - Cs C2h D2d Cs C2h BVP86 BVP86 BVP86 BVP86 BVP86 Klamt Klamt SMD SMD SMD HC2O4 H2C2O4 C2O42HC2O4H2C2O4 -700.36830 -377.24423 -377.95099 -378.48315 -377.24423 -377.95099 -378.48315 -377.24423 -377.95099 -378.48315 -377.24423 -377.95099 -378.48315 -377.24423 -377.95099 -378.48315 -376.86088 -377.56577 -378.09449 -376.86088 -377.56577 -378.09449 -376.86088 -377.56577 -378.09449 -376.86088 -377.56577 -378.09449 -376.86088 -377.56577 -378.09449 -377.28170 -377.98765 -378.51710 -377.28170 -377.98765 -378.51710 -377.28170 -377.98765 -378.51710 24.70(0) 14.40(0) 22.14(0) 30.58(0) 14.40(0) 22.14(0) 30.58(0) 14.40(0) 22.14(0) 30.58(0) 14.40(0) 22.14(0) 30.58(0) 14.40(0) 22.14(0) 30.58(0) 13.77(0) 21.26(0) 29.57(0) 13.77(0) 21.26(0) 29.57(0) 13.77(0) 21.26(0) 29.57(0) 13.77(0) 21.26(0) 29.57(0) 13.77(0) 21.26(0) 29.57(0) 13.74(0) 21.21(0) 29.49(0) 13.74(0) 21.21(0) 29.49(0) 13.74(0) 21.21(0) 29.49(0) 3.83 3.81 4.07 4.11 3.81 4.07 4.11 3.81 4.07 4.11 3.81 4.07 4.11 3.81 4.07 4.11 3.88 4.14 4.18 3.88 4.14 4.18 3.88 4.14 4.18 3.88 4.14 4.18 3.88 4.14 4.18 3.88 4.14 4.19 3.88 4.14 4.19 3.88 4.14 4.19 71.02 71.46 76.16 76.95 71.46 76.16 76.95 71.46 76.16 76.95 71.46 76.16 76.95 71.46 76.16 76.95 71.92 76.57 77.43 71.92 76.57 77.37 71.92 76.57 77.43 71.92 76.56 77.44 71.92 76.56 77.44 71.87 76.56 78.50 71.87 76.56 78.50 71.87 76.56 78.50 -13.80 -213.35 -58.86 -5.58 -222.80 -66.67 -13.98 -228.01 -69.93 -19.35 -214.92 -60.52 -7.51 -221.86 -64.28 -11.00 -211.00 -57.59 -4.73 -219.99 -65.12 -13.79 -224.24 -67.02 -17.15 -212.45 -59.21 -7.11 -218.99 -62.41 -10.03 -211.94 -57.92 -4.79 -221.08 -65.48 -13.82 -225.61 -67.60 -17.34 -377.28170 -377.98765 -378.51710 -377.28170 -377.98765 -378.51710 13.74(0) 21.21(0) 29.49(0) 13.74(0) 21.21(0) 29.49(0) 3.88 4.14 4.19 3.88 4.14 4.19 71.88 76.56 78.50 71.88 76.56 78.50 -213.43 -59.37 -7.18 -220.20 -62.83 -10.26 S6 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 C2O42HC2O4H2C2O4 C2O42HC2O4H2C2O4 C2O42HC2O4H2C2O4 C2O42HC2O4H2C2O4 C2O42HC2O4H2C2O4 C3H2O42HC3H2O4H2C3H2O4 C3H2O42HC3H2O4H2C3H2O4 C3H2O42HC3H2O4H2C3H2O4 C3H2O42HC3H2O4H2C3H2O4 C3H2O42HC3H2O4H2C3H2O4 C3H2O42HC3H2O4H2C3H2O4 C3H2O42HC3H2O4H2C3H2O4 C3H2O42HC3H2O4H2C3H2O4 C3H2O42HC3H2O4H2C3H2O4 C3H2O42HC3H2O4H2C3H2O4 C3H2O42HC3H2O4- D2d Cs C2h D2d Cs C2h D2d Cs C2h D2d Cs C2h D2d Cs C2h Cs C1 C1 Cs C1 C1 Cs C1 C1 Cs C1 C1 Cs C1 C1 Cs C1 C1 Cs C1 C1 Cs C1 C1 Cs C1 C1 Cs C1 C1 Cs C1 M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE BVP86 BVP86 UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF -377.20607 -377.91051 -378.44201 -377.20607 -377.91051 -378.44201 -377.20607 -377.91051 -378.44201 -377.20607 -377.91051 -378.44201 -377.20607 -377.91051 -378.44201 -416.58947 -417.30938 -417.82894 -416.58947 -417.30938 -417.82894 -416.58947 -417.30938 -417.82894 -416.58947 -417.30938 -417.82894 -416.58947 -417.30938 -417.82894 -416.14727 -416.86818 -417.38260 -416.14727 -416.86818 -417.38260 -416.14727 -416.86818 -417.38260 -416.14727 -416.86818 -417.38259 -416.14727 -416.86818 -417.38259 -416.62523 -417.34714 S7 14.97(0) 22.78(0) 31.24(0) 14.97(0) 22.78(0) 31.24(0) 14.97(0) 22.78(0) 31.24(0) 14.97(0) 22.78(0) 31.24(0) 14.97(0) 22.78(0) 31.24(0) 31.72(0) 39.14(0) 48.53(0) 31.72(0) 39.14(0) 48.53(0) 31.72(0) 39.14(0) 48.53(0) 31.72(0) 39.14(0) 48.52(0) 31.72(0) 39.14(0) 48.52(0) 30.59(0) 37.11(0) 47.00(0) 30.59(0) 37.11(0) 47.00(0) 30.59(0) 37.11(0) 47.00(0) 30.59(0) 37.11(0) 46.99(0) 30.59(0) 37.11(0) 46.99(0) 30.54(0) 37.03(0) 3.78 4.05 4.06 3.78 4.05 4.06 3.78 4.05 4.06 3.78 4.05 4.06 3.78 4.05 4.06 4.70 4.52 4.79 4.70 4.52 4.79 4.70 4.52 4.79 4.70 4.52 4.79 4.70 4.52 4.79 4.77 4.64 4.82 4.77 4.64 4.82 4.77 4.64 4.82 4.77 4.64 4.82 4.77 4.64 4.82 4.78 4.66 71.35 76.38 75.55 71.35 76.38 75.55 71.35 76.38 75.55 71.35 76.38 75.55 71.35 76.38 75.55 85.68 81.77 84.09 85.68 81.77 84.09 85.68 81.77 84.09 85.68 81.77 84.09 85.68 81.77 84.09 84.77 82.21 83.18 84.77 82.21 83.18 84.77 82.21 83.18 84.77 82.21 83.20 84.77 82.21 83.20 85.11 82.27 -216.45 -60.57 -6.04 -226.33 -68.60 -14.99 -232.72 -72.34 -20.54 -218.09 -62.34 -8.49 -225.79 -66.25 -11.99 -200.81 -51.76 -6.01 -212.69 -57.38 -14.34 -217.24 -63.02 -19.40 -202.87 -53.73 -8.68 -211.68 -56.74 -12.36 -198.33 -50.61 -5.09 -209.80 -56.20 -14.29 -213.25 -59.88 -17.05 -200.30 -52.27 -7.73 -208.63 -54.76 -11.22 -199.18 -50.92 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 H2C3H2O4 C3H2O42HC3H2O4H2C3H2O4 C3H2O42HC3H2O4H2C3H2O4 C3H2O42HC3H2O4H2C3H2O4 C3H2O42HC3H2O4H2C3H2O4 C3H2O42HC3H2O4H2C3H2O4 C3H2O42HC3H2O4H2C3H2O4 C3H2O42HC3H2O4H2C3H2O4 C3H2O42HC3H2O4H2C3H2O4 C3H2O42HC3H2O4H2C3H2O4 HPO32H2PO3H3PO3 HPO32H2PO3H3PO3 HPO32H2PO3H3PO3 HPO32H2PO3H3PO3 HPO32H2PO3H3PO3 HPO32H2PO3H3PO3 HPO32- C1 Cs C1 C1 Cs C1 C1 Cs C1 C1 Cs C1 C1 Cs C1 C1 Cs C1 C1 Cs C1 C1 Cs C1 C1 Cs C1 C1 C3v C1 C1 C3v C1 C1 C3v C1 C1 C3v C1 C1 C3v C1 C1 C3v C1 C1 C3v BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP PBE PBE PBE PBE UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS -417.86235 -416.62523 -417.34714 -417.86235 -416.62523 -417.34714 -417.86235 -416.62523 -417.34714 -417.86235 -416.62523 -417.34714 -417.86235 -416.54713 -417.26899 -417.78425 -416.54713 -417.26899 -417.78425 -416.54713 -417.26899 -417.78425 -416.54713 -417.26899 -417.78426 -416.54713 -417.26899 -417.78426 -567.76830 -568.51148 -569.04709 -567.76830 -568.51148 -569.04710 -567.76830 -568.51148 -569.04709 -567.76830 -568.51148 -569.04709 -567.76830 -568.51148 -569.04709 -567.36540 -568.10375 -568.63581 -567.36540 S8 46.94(0) 30.54(0) 37.03(0) 46.94(0) 30.54(0) 37.03(0) 46.94(0) 30.54(0) 37.03(0) 46.94(0) 30.54(0) 37.03(0) 46.94(0) 32.67(0) 39.91(0) 49.41(0) 32.67(0) 39.91(0) 49.41(0) 32.67(0) 39.91(0) 49.41(0) 32.67(0) 39.91(0) 49.39(0) 32.67(0) 39.91(0) 49.39(0) 11.76(0) 19.69(0) 26.88(0) 11.76(0) 19.69(0) 26.87(0) 11.76(0) 19.69(0) 26.88(0) 11.76(0) 19.69(0) 26.88(0) 11.76(0) 19.69(0) 26.88(0) 11.08(0) 18.87(0) 25.95(0) 11.08(0) 4.82 4.78 4.66 4.82 4.78 4.66 4.82 4.78 4.66 4.82 4.78 4.66 4.82 4.63 4.41 4.77 4.63 4.41 4.77 4.63 4.41 4.77 4.63 4.41 4.77 4.63 4.41 4.77 2.97 3.33 3.86 2.97 3.33 3.87 2.97 3.33 3.86 2.97 3.33 3.86 2.97 3.33 3.86 3.05 3.41 3.92 3.05 83.28 85.11 82.27 83.28 85.11 82.27 83.28 85.04 82.27 83.30 85.04 82.27 83.30 84.23 80.71 84.68 84.23 80.71 84.68 84.23 80.71 84.68 84.23 80.71 84.28 84.23 80.71 84.28 64.05 68.34 72.13 64.05 68.34 72.24 64.05 68.34 72.13 64.05 68.34 72.13 64.05 68.34 72.13 64.51 68.80 72.51 64.51 -5.17 -210.80 -56.45 -14.30 -214.53 -60.48 -17.27 -201.18 -52.60 -7.82 -209.72 -55.24 -11.35 -204.43 -53.05 -6.40 -216.97 -58.63 -15.49 -222.75 -64.33 -20.47 -206.64 -54.94 -9.14 -216.43 -58.24 -13.21 -229.09 -62.26 -6.97 -229.25 -63.34 -9.63 -246.09 -72.91 -17.87 -230.67 -63.90 -9.37 -237.27 -66.37 -11.36 -225.81 -60.66 -5.94 -226.02 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 H2PO3H3PO3 HPO32H2PO3H3PO3 HPO32H2PO3H3PO3 HPO32H2PO3H3PO3 HPO32H2PO3H3PO3 HPO32H2PO3H3PO3 HPO32H2PO3H3PO3 HPO32H2PO3H3PO3 HPO32H2PO3H3PO3 HPO32H2PO3H3PO3 HPO32H2PO3H3PO3 HPO32H2PO3H3PO3 HPO32H2PO3H3PO3 HPO32H2PO3H3PO3 C2H2O2S2HC2H2O2SH2C2H2O2S C2H2O2S2HC2H2O2SH2C2H2O2S C1 C1 C3v C1 C1 C3v C1 C1 C3v C1 C1 C3v C1 C1 C3v C1 C1 C3v C1 C1 C3v C1 C1 C3v C1 C1 C3v C1 C1 C3v C1 C1 C3v C1 C1 C3v C1 C1 C3v C1 C1 Cs Cs Cs Cs Cs Cs PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS -568.10375 -568.63580 -567.36540 -568.10375 -568.63581 -567.36540 -568.10375 -568.63581 -567.36540 -568.10375 -568.63581 -567.81452 -568.55388 -569.08690 -567.81452 -568.55388 -569.08690 -567.81452 -568.55388 -569.08690 -567.81452 -568.55388 -569.08690 -567.81452 -568.55388 -569.08690 -567.72507 -568.46950 -569.00509 -567.72507 -568.46951 -569.00509 -567.72507 -568.46951 -569.00509 -567.72507 -568.46950 -569.00509 -567.72507 -568.46950 -569.00509 -626.14461 -626.85928 -627.40046 -626.14461 -626.85928 -627.40046 S9 18.87(0) 25.95(0) 11.08(0) 18.87(0) 25.95(0) 11.08(0) 18.87(0) 25.95(0) 11.08(0) 18.87(0) 25.95(0) 11.10(0) 18.87(0) 25.97(0) 11.10(0) 18.87(0) 25.95(0) 11.10(0) 18.87(0) 25.97(0) 11.10(0) 18.87(0) 25.97(0) 11.10(0) 18.87(0) 25.97(0) 12.25(0) 20.24(0) 27.35(0) 12.25(0) 20.27(0) 27.40(0) 12.25(0) 20.27(0) 27.35(0) 12.25(0) 20.24(0) 27.35(0) 12.25(0) 20.24(0) 27.35(0) 24.49(0) 30.23(0) 38.47(0) 24.49(0) 30.23(0) 38.47(0) 3.41 3.92 3.05 3.41 3.92 3.05 3.41 3.92 3.05 3.41 3.92 3.05 3.40 3.91 3.05 3.40 3.92 3.05 3.40 3.91 3.05 3.40 3.91 3.05 3.40 3.91 2.92 3.27 3.85 2.92 3.27 3.80 2.92 3.27 3.85 2.92 3.27 3.85 2.92 3.27 3.85 3.78 3.96 4.30 3.78 3.96 4.30 68.80 72.56 64.51 68.80 72.51 64.51 68.80 72.51 64.51 68.80 72.51 64.48 68.79 72.35 64.48 68.78 72.49 64.48 68.78 72.35 64.48 68.79 72.35 64.48 68.79 72.35 63.78 67.97 72.31 63.78 67.98 71.72 63.78 67.98 72.31 63.78 67.97 72.31 63.78 67.97 72.31 75.05 75.09 77.84 75.05 75.09 77.84 -62.02 -9.30 -241.07 -70.17 -16.12 -227.25 -62.20 -8.75 -233.02 -64.21 -10.03 -226.85 -61.05 -6.05 -227.02 -62.32 -9.35 -242.53 -70.84 -16.34 -228.33 -62.61 -8.86 -234.28 -64.78 -10.19 -233.34 -64.22 -7.55 -233.19 -64.98 -10.34 -252.39 -76.18 -19.21 -235.05 -65.99 -10.49 -242.65 -69.05 -12.49 -205.74 -55.55 -3.15 -213.93 -60.97 -9.47 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 C2H2O2S2HC2H2O2SH2C2H2O2S C2H2O2S2HC2H2O2SH2C2H2O2S C2H2O2S2HC2H2O2SH2C2H2O2S C2H2O2S2HC2H2O2SH2C2H2O2S C2H2O2S2HC2H2O2SH2C2H2O2S C2H2O2S2HC2H2O2SH2C2H2O2S C2H2O2S2HC2H2O2SH2C2H2O2S C2H2O2S2HC2H2O2SH2C2H2O2S C2H2O2S2HC2H2O2SH2C2H2O2S C2H2O2S2HC2H2O2SH2C2H2O2S C2H2O2S2HC2H2O2SH2C2H2O2S C2H2O2S2HC2H2O2SH2C2H2O2S C2H2O2S2HC2H2O2SH2C2H2O2S C2H2O2S2HC2H2O2SH2C2H2O2S C2H2O2S2HC2H2O2SH2C2H2O2S C2H2O2S2HC2H2O2S- Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs C1 Cs Cs C1 Cs Cs B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 M052X M052X M052X M052X M052X M052X M052X M052X Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling -626.14461 -626.85928 -627.40046 -626.14461 -626.85928 -627.40046 -626.14461 -626.85928 -627.40046 -625.70638 -626.41382 -626.95678 -625.70638 -626.41382 -626.95678 -625.70638 -626.41382 -626.95678 -625.70638 -626.41382 -626.95678 -625.70638 -626.41382 -626.95678 -626.19650 -626.90427 -627.44808 -626.19650 -626.90427 -627.44808 -626.19650 -626.90427 -627.44808 -626.19650 -626.90427 -627.44808 -626.19650 -626.90427 -627.44808 -626.09557 -626.80919 -627.35164 -626.09557 -626.80919 -627.35164 -626.09557 -626.80919 S10 24.49(0) 30.23(0) 38.47(0) 24.49(0) 30.23(0) 38.47(0) 24.49(0) 30.23(0) 38.47(0) 23.62(0) 29.15(0) 37.32(0) 23.62(0) 29.15(0) 37.32(0) 23.62(0) 29.15(0) 37.32(0) 23.62(0) 29.15(0) 37.32(0) 23.62(0) 29.15(0) 37.32(0) 23.59(0) 29.11(0) 37.27(0) 23.59(0) 29.11(0) 37.27(0) 23.59(0) 29.11(0) 37.27(0) 23.59(0) 29.11(0) 37.27(0) 23.59(0) 29.11(0) 37.27(0) 25.26(0) 31.28(0) 39.34(0) 25.26(0) 31.28(0) 39.34(0) 25.26(0) 31.28(0) 3.78 3.96 4.30 3.78 3.96 4.30 3.78 3.96 4.30 3.85 4.18 4.35 3.85 4.18 4.35 3.85 4.18 4.35 3.85 4.18 4.35 3.85 4.18 4.35 3.85 4.18 4.35 3.85 4.18 4.35 3.85 4.18 4.35 3.85 4.18 4.35 3.85 4.18 4.35 3.72 3.86 4.28 3.72 3.86 4.28 3.72 3.86 75.05 75.09 77.84 75.05 75.09 77.84 75.05 75.09 77.84 75.73 76.67 78.08 75.73 76.67 78.08 75.73 76.67 78.08 75.73 76.67 78.08 75.73 76.67 78.08 75.80 76.69 78.14 75.80 76.69 78.14 75.80 76.69 78.14 75.80 76.69 78.14 75.80 76.69 78.14 74.63 74.57 78.36 74.63 74.57 78.36 74.63 74.57 -215.98 -63.85 -12.17 -204.30 -56.25 -5.34 -205.52 -59.95 -7.89 -203.75 -58.00 -1.70 -211.80 -63.72 -9.73 -213.27 -66.18 -11.09 -202.24 -59.18 -4.80 -203.30 -62.36 -7.46 -204.39 -58.36 -1.73 -212.50 -64.09 -9.70 -214.11 -66.74 -11.18 -202.89 -59.53 -4.82 -203.99 -62.81 -7.49 -209.73 -57.56 -2.64 -218.27 -62.93 -9.10 -221.11 -66.32 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 H2C2H2O2S C2H2O2S2HC2H2O2SH2C2H2O2S C2H2O2S2HC2H2O2SH2C2H2O2S f C4H2O42f HC4H2O4f H2C4H2O4 f C4H2O42f HC4H2O4f H2C4H2O4 f C4H2O42f HC4H2O4f H2C4H2O4 f C4H2O42f HC4H2O4f H2C4H2O4 f C4H2O42f HC4H2O4f H2C4H2O4 f C4H2O42f HC4H2O4f H2C4H2O4 f C4H2O42f HC4H2O4f H2C4H2O4 f C4H2O42f HC4H2O4f H2C4H2O4 f C4H2O42f HC4H2O4f H2C4H2O4 f C4H2O42f HC4H2O4f H2C4H2O4 f C4H2O42f HC4H2O4f H2C4H2O4 f C4H2O42f HC4H2O4f H2C4H2O4 f C4H2O42f HC4H2O4f H2C4H2O4 f C4H2O42- C1 Cs Cs C1 Cs Cs C1 C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 M052X M052X M052X M052X M052X M052X M052X B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt -627.35164 -626.09557 -626.80919 -627.35164 -626.09557 -626.80919 -627.35164 -454.69350 -455.40920 -455.92464 -454.69350 -455.40920 -455.92464 -454.69350 -455.40920 -455.92464 -454.69350 -455.40920 -455.92464 -454.69350 -455.40920 -455.92464 -454.20573 -454.92030 -455.43110 -454.20573 -454.92030 -455.43110 -454.20573 -454.92030 -455.43110 -454.20573 -454.92030 -455.43110 -454.20573 -454.92030 -455.43110 -454.73231 -455.44797 -455.95959 -454.73231 -455.44797 -455.95959 -454.73231 -455.44797 -455.95959 -454.73231 S11 39.34(0) 25.26(0) 31.28(0) 39.34(0) 25.26(0) 31.28(0) 39.34(0) 34.84(0) 42.50(0) 52.22(0) 34.84(0) 42.50(0) 52.22(0) 34.84(0) 42.50(0) 52.22(0) 34.84(0) 42.50(0) 52.22(0) 34.84(0) 42.50(0) 52.22(0) 33.55(0) 40.45(0) 50.46(0) 33.55(0) 40.45(0) 50.46(0) 33.55(0) 40.45(0) 50.46(0) 33.55(0) 40.45(0) 50.46(0) 33.55(0) 40.45(0) 50.46(0) 33.51(0) 40.36(0) 50.39(0) 33.51(0) 40.36(0) 50.39(0) 33.51(0) 40.36(0) 50.39(0) 33.51(0) 4.28 3.72 3.86 4.28 3.72 3.86 4.28 5.22 4.88 5.12 5.22 4.88 5.12 5.22 4.88 5.12 5.22 4.88 5.12 5.22 4.88 5.12 5.34 5.01 5.22 5.34 5.01 5.22 5.34 5.01 5.22 5.34 5.01 5.22 5.34 5.01 5.22 5.34 5.02 5.22 5.34 5.02 5.22 5.34 5.02 5.22 5.34 78.36 74.63 74.57 78.36 74.63 74.57 78.36 89.23 83.71 85.67 89.23 83.71 85.67 89.23 83.71 85.67 89.23 83.71 85.67 89.23 83.71 85.67 90.10 84.41 86.46 90.10 84.41 86.46 90.10 84.41 86.46 90.10 84.41 86.46 90.10 84.41 86.46 90.12 84.40 86.40 90.12 84.40 86.40 90.12 84.40 86.40 90.12 -11.25 -208.25 -58.38 -4.50 -209.89 -62.14 -8.57 -193.67 -49.92 -5.21 -204.54 -53.98 -12.01 -209.21 -60.55 -18.96 -195.72 -51.23 -7.34 -204.31 -54.30 -11.10 -191.26 -48.50 -4.36 -201.67 -52.73 -11.67 -205.18 -57.49 -16.79 -193.17 -49.81 -6.54 -201.28 -52.48 -10.22 -191.95 -48.83 -3.25 -202.48 -53.01 -11.71 -206.32 -58.16 -17.00 -193.88 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 f HC4H2O4H2C4H2O4 f C4H2O42f HC4H2O4f H2C4H2O4 f C4H2O42f HC4H2O4f H2C4H2O4 f C4H2O42f HC4H2O4f H2C4H2O4 f C4H2O42f HC4H2O4f H2C4H2O4 f C4H2O42f HC4H2O4f H2C4H2O4 f C4H2O42f HC4H2O4f H2C4H2O4 C4H5NO42HC4H5NO4H2C4H5NO4 C4H5NO42HC4H5NO4H2C4H5NO4 C4H5NO42HC4H5NO4H2C4H5NO4 C4H5NO42HC4H5NO4H2C4H5NO4 C4H5NO42HC4H5NO4H2C4H5NO4 C4H5NO42HC4H5NO4H2C4H5NO4 C4H5NO42HC4H5NO4H2C4H5NO4 C4H5NO42HC4H5NO4H2C4H5NO4 C4H5NO42HC4H5NO4H2C4H5NO4 f Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs BVP86 BVP86 BVP86 BVP86 BVP86 M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt -455.44797 -455.95959 -454.73231 -455.44797 -455.95959 -454.64572 -455.36428 -455.87459 -454.64572 -455.36428 -455.87459 -454.64572 -455.36428 -455.87459 -454.64572 -455.36428 -455.87459 -454.64572 -455.36428 -455.87459 -511.31958 -511.99740 -512.51258 -511.31958 -511.99740 -512.51258 -511.31958 -511.99740 -512.51258 -511.31958 -511.99740 -512.51258 -511.31958 -511.99740 -512.51258 -510.75819 -511.43550 -511.94703 -510.75819 -511.43550 -511.94703 -510.75819 -511.43550 -511.94703 -510.75819 -511.43550 -511.94703 S12 40.36(0) 50.39(0) 33.51(0) 40.36(0) 50.39(0) 35.86(0) 42.95(0) 53.06(0) 35.86(0) 42.95(0) 53.06(0) 35.86(0) 42.95(0) 53.06(0) 35.86(0) 42.95(0) 53.06(0) 35.86(0) 42.95(0) 53.06(0) 60.04(0) 67.95(0) 77.46(0) 60.04(0) 67.95(0) 77.46(0) 60.04(0) 67.95(0) 77.46(0) 60.04(0) 67.95(0) 77.46(0) 60.04(0) 67.95(0) 77.46(0) 57.98(0) 64.51(0) 75.03(0) 57.98(0) 64.51(0) 75.03(0) 57.98(0) 64.51(0) 75.03(0) 57.98(0) 64.51(0) 75.03(0) 5.02 5.22 5.34 5.02 5.22 5.17 4.85 5.11 5.17 4.85 5.11 5.17 4.85 5.11 5.17 4.85 5.11 5.17 4.85 5.11 6.19 5.99 6.36 6.19 5.99 6.36 6.19 5.99 6.36 6.19 5.99 6.36 6.19 5.99 6.36 6.30 6.27 6.44 6.30 6.27 6.44 6.30 6.27 6.44 6.30 6.27 6.44 84.40 86.40 90.12 84.40 86.40 88.47 83.43 85.80 88.47 83.43 85.80 88.47 83.43 85.80 88.47 83.43 85.80 88.47 83.43 85.80 96.24 93.33 96.68 96.24 93.33 96.68 96.24 93.33 96.68 96.24 93.33 96.68 96.24 93.33 96.68 96.90 97.00 97.16 96.90 97.00 97.16 96.90 97.00 97.16 96.90 97.00 97.16 -50.14 -6.61 -202.23 -52.97 -10.36 -197.63 -51.63 -5.80 -208.90 -55.09 -12.81 -214.97 -62.34 -19.99 -199.75 -52.42 -7.99 -209.36 -55.61 -11.75 -177.96 -50.09 -9.66 -193.69 -62.19 -24.53 -194.77 -62.26 -23.87 -180.79 -52.52 -13.65 -191.89 -60.06 -19.63 -175.66 -48.74 -6.32 -190.95 -61.25 -23.85 -190.35 -58.89 -21.44 -179.34 -51.12 -11.68 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 C4H5NO42HC4H5NO4H2C4H5NO4 C4H5NO42HC4H5NO4H2C4H5NO4 C4H5NO42HC4H5NO4H2C4H5NO4 C4H5NO42HC4H5NO4H2C4H5NO4 C4H5NO42HC4H5NO4H2C4H5NO4 C4H5NO42HC4H5NO4H2C4H5NO4 C4H5NO42HC4H5NO4H2C4H5NO4 C4H5NO42HC4H5NO4H2C4H5NO4 C4H5NO42HC4H5NO4H2C4H5NO4 C4H5NO42HC4H5NO4H2C4H5NO4 C4H5NO42HC4H5NO4H2C4H5NO4 C5H7NO42HC5H7NO4H2C5H7NO4 C5H7NO42HC5H7NO4H2C5H7NO4 C5H7NO42HC5H7NO4H2C5H7NO4 C5H7NO42HC5H7NO4H2C5H7NO4 C5H7NO42HC5H7NO4- Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 PBE PBE PBE BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD -510.75819 -511.43550 -511.94703 -511.36030 -512.03865 -512.55110 -511.36030 -512.03865 -512.55110 -511.36030 -512.03865 -512.55110 -511.36030 -512.03865 -512.55110 -511.36030 -512.03865 -512.55110 -511.26718 -511.26096 -512.45762 -511.26718 -511.26096 -512.45762 -511.26718 -511.26096 -512.45762 -511.26718 -511.26096 -512.45762 -511.26718 -511.26096 -512.45762 57.98(0) 64.51(0) 75.03(0) 57.89(0) 64.48(0) 74.95(0) 57.89(0) 64.48(0) 74.95(0) 57.89(0) 64.48(0) 74.95(0) 57.89(0) 64.48(0) 74.95(0) 57.89(0) 64.48(0) 74.95(0) 61.72(0) 86.50(0) 79.16(0) 61.72(0) 86.50(0) 79.16(0) 61.72(0) 86.50(0) 79.16(0) 61.72(0) 86.50(0) 79.16(0) 61.72(0) 69.72(0) 79.16(0) 6.30 6.27 6.44 6.31 6.26 6.45 6.31 6.26 6.45 6.31 6.26 6.45 6.31 6.26 6.45 6.31 6.26 6.45 6.09 6.76 6.28 6.09 6.76 6.28 6.09 6.76 6.28 6.09 6.76 6.28 6.09 6.76 6.28 96.90 97.00 97.16 97.01 96.94 97.22 97.01 96.94 97.22 97.01 96.94 97.22 97.01 96.94 97.22 97.01 96.94 97.22 95.49 98.96 96.17 95.49 98.96 96.17 95.49 98.96 96.17 95.49 98.96 96.17 95.49 98.96 96.17 -550.63401 -551.31529 -551.83209 -550.63401 -551.31529 -551.83209 -550.63401 -551.31529 -551.83209 -550.63401 -551.31529 -551.83209 -550.63401 -551.31529 77.22(0) 84.72(0) 94.70(0) 77.22(0) 84.72(0) 94.70(0) 77.22(0) 84.72(0) 94.70(0) 77.22(0) 84.72(0) 94.70(0) 77.22(0) 84.72(0) 6.95 6.90 7.15 6.95 6.90 7.15 6.95 6.90 7.15 6.95 6.90 7.15 6.95 6.90 101.50 99.42 101.51 101.48 99.42 101.51 101.48 99.42 101.51 101.48 99.43 101.51 101.48 99.43 S13 -188.50 -57.81 -18.11 -176.49 -49.14 -6.43 -191.87 -61.09 -23.73 -191.50 -59.58 -21.65 -179.49 -51.51 -9.56 -189.57 -58.32 -18.23 -182.76 -50.68 -10.77 -198.27 -62.13 -26.22 -200.65 -60.68 -25.11 -184.65 -53.57 -13.85 -196.70 -60.80 -21.02 -174.92 -48.63 -6.66 -190.50 -59.89 -20.16 -190.62 -58.97 -19.08 -177.61 -51.65 -10.69 -189.73 -58.62 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 H2C5H7NO4 C5H7NO42HC5H7NO4H2C5H7NO4 C5H7NO42HC5H7NO4H2C5H7NO4 C5H7NO42HC5H7NO4H2C5H7NO4 C5H7NO42HC5H7NO4H2C5H7NO4 C5H7NO42HC5H7NO4H2C5H7NO4 C5H7NO42HC5H7NO4H2C5H7NO4 C5H7NO42HC5H7NO4H2C5H7NO4 C5H7NO42HC5H7NO4H2C5H7NO4 C5H7NO42HC5H7NO4H2C5H7NO4 C5H7NO42HC5H7NO4H2C5H7NO4 C5H7NO42HC5H7NO4H2C5H7NO4 C5H7NO42HC5H7NO4H2C5H7NO4 C5H7NO42HC5H7NO4H2C5H7NO4 C5H7NO42HC5H7NO4H2C5H7NO4 C5H7NO42HC5H7NO4H2C5H7NO4 Fe(CO)42- Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Cs C1 Cs Td B3LYP PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X B3LYP SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF -551.83209 -550.01612 -550.69556 -551.20871 -550.01612 -550.69556 -551.20871 -550.01612 -550.69556 -551.20871 -550.01612 -550.69556 -551.20871 -550.01612 -550.69556 -551.20871 -550.67512 -551.35567 -551.86969 -550.67512 -551.35567 -551.86969 -550.67512 -551.35567 -551.86969 -550.67512 -551.35567 -551.86969 -550.67512 -551.35567 -551.86969 -550.57799 -551.22543 -551.77530 -550.57799 -551.22543 -551.77530 -550.57799 -551.22543 -551.77530 -550.57799 -551.22543 -551.77530 -550.57799 -551.22543 -551.77530 -1717.31851 S14 94.70(0) 74.64(0) 81.20(0) 91.72(0) 74.64(0) 81.20(0) 91.72(0) 74.64(0) 81.20(0) 91.72(0) 74.64(0) 81.20(0) 91.72(0) 74.64(0) 81.20(0) 91.72(0) 74.55(0) 81.10(0) 91.64(0) 74.55(0) 81.10(0) 91.64(0) 74.55(0) 81.10(0) 91.64(0) 74.55(0) 81.10(0) 91.64(0) 74.55(0) 81.10(0) 91.64(0) 79.45(0) 87.64(0) 96.85(0) 79.45(0) 87.64(0) 96.85(0) 79.45(0) 87.64(0) 96.85(0) 79.45(0) 87.64(0) 96.85(0) 79.45(0) 87.64(0) 96.85(0) 19.60(0) 7.15 7.07 7.11 7.26 7.07 7.11 7.26 7.07 7.11 7.26 7.07 7.11 7.26 7.07 7.11 7.26 7.07 7.13 7.27 7.07 7.13 7.27 7.07 7.13 7.27 7.07 7.13 7.27 7.07 7.13 7.27 6.76 6.99 7.00 6.76 6.99 7.00 6.76 6.99 7.00 6.76 6.99 7.00 6.76 6.99 7.00 6.54 101.51 102.10 100.75 102.13 102.10 100.75 102.13 102.10 100.75 102.13 102.10 100.75 102.13 102.10 100.75 102.13 102.10 100.93 102.22 102.10 100.93 102.22 102.10 100.93 102.22 102.10 100.93 102.22 102.10 100.93 102.22 99.69 101.18 100.27 99.69 101.18 100.27 99.69 101.18 100.27 99.69 101.18 100.27 99.69 101.18 100.27 95.44 -18.26 -171.95 -47.17 -3.82 -187.42 -58.46 -19.48 -186.03 -55.63 -16.61 -174.51 -49.87 -7.07 -185.82 -56.34 -16.63 -172.71 -47.53 -3.72 -188.17 -58.65 -19.35 -187.48 -56.29 -16.85 -175.34 -50.25 -7.14 -186.98 -56.86 -16.72 -179.41 -61.92 -7.67 -196.07 -78.94 -21.81 -197.50 -77.08 -20.32 -182.33 -65.47 -10.87 -195.59 -76.12 -19.48 -171.07 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 HFe(CO)4H2Fe(CO)4 Fe(CO)42HFe(CO)4H2Fe(CO)4 Fe(CO)42HFe(CO)4H2Fe(CO)4 Fe(CO)42HFe(CO)4H2Fe(CO)4 Fe(CO)42HFe(CO)4H2Fe(CO)4 Fe(CO)42HFe(CO)4H2Fe(CO)4 Fe(CO)42HFe(CO)4H2Fe(CO)4 Fe(CO)42HFe(CO)4H2Fe(CO)4 Fe(CO)42HFe(CO)4H2Fe(CO)4 Fe(CO)42HFe(CO)4H2Fe(CO)4 Fe(CO)42HFe(CO)4H2Fe(CO)4 Fe(CO)42HFe(CO)4H2Fe(CO)4 Fe(CO)42HFe(CO)4H2Fe(CO)4 Fe(CO)42HFe(CO)4H2Fe(CO)4 Fe(CO)42HFe(CO)4H2Fe(CO)4 Fe(CO)42HFe(CO)4H2Fe(CO)4 C3v C2v Td C3v C2v Td C3v C2v Td C3v C2v Td C3v C2v Td C3v C2v Td C3v C2v Td C3v C2v Td C3v C2v Td C3v C2v Td C3v C2v Td C3v C2v Td C3v C2v Td C3v C2v Td C3v C2v Td C3v C2v B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt -1718.02018 -1718.53458 -1717.31851 -1718.02018 -1718.53458 -1717.31851 -1718.02018 -1718.53458 -1717.31851 -1718.02018 -1718.53458 -1716.65700 -1717.34756 -1717.85016 -1716.65700 -1717.34756 -1717.85016 -1716.65700 -1717.34756 -1717.85016 -1716.65700 -1717.34756 -1717.85016 -1717.62208 -1718.31416 -1718.81793 -1717.62208 -1718.31416 -1718.81793 -1717.62208 -1718.31416 -1718.81793 -1717.62208 -1718.31416 -1718.81793 -1717.03509 -1717.74905 -1718.27641 -1717.03509 -1717.74905 -1718.27641 -1717.03509 -1717.74905 -1718.27641 -1717.03509 -1717.74905 -1718.27641 S15 25.12(0) 30.96(0) 19.60(0) 25.12(0) 30.96(0) 19.60(0) 25.12(0) 30.96(0) 19.60(0) 25.12(0) 30.96(0) 18.99(0) 24.50(0) 30.17(0) 18.99(0) 24.50(0) 30.17(0) 18.99(0) 24.50(0) 30.17(0) 18.99(0) 24.50(0) 30.17(0) 19.00(0) 24.50(0) 30.21(0) 19.00(0) 24.50(0) 30.21(0) 19.00(0) 24.50(0) 30.21(0) 19.00(0) 24.50(0) 30.21(0) 20.11(0) 25.27(0) 30.97(0) 20.11(0) 25.27(0) 30.97(0) 20.11(0) 25.27(0) 30.97(0) 20.11(0) 25.27(0) 30.97(0) 6.71 6.85 6.54 6.71 6.85 6.54 6.71 6.85 6.54 6.71 6.85 6.66 6.82 6.94 6.66 6.82 6.94 6.66 6.82 6.94 6.66 6.82 6.94 6.65 6.80 6.92 6.65 6.80 6.92 6.65 6.80 6.92 6.65 6.80 6.92 6.46 6.74 6.98 6.46 6.74 6.98 6.46 6.74 6.98 6.46 6.74 6.98 97.67 98.33 95.44 97.67 98.33 95.44 97.67 98.33 95.44 97.67 98.33 96.88 98.73 99.21 96.88 98.73 99.21 96.88 98.73 99.21 96.88 98.73 99.21 96.67 98.53 99.06 96.67 98.53 99.06 96.67 98.53 99.06 96.67 98.53 99.06 95.10 97.93 99.20 95.10 97.93 99.20 95.10 97.93 99.20 95.10 97.93 99.20 -33.92 8.18 -173.68 -36.87 5.88 -176.58 -37.99 -2.19 -170.42 -34.46 7.93 -170.59 -33.48 8.66 -173.40 -36.64 6.49 -175.97 -37.12 0.01 -170.25 -34.03 8.26 -170.67 -33.64 8.65 -173.68 -36.78 6.49 -177.02 -37.38 -0.07 -169.38 -34.17 8.26 -174.87 -34.90 7.47 -177.37 -37.73 5.53 -182.12 -39.26 -2.45 -174.24 -35.40 7.31 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 Fe(CO)42HFe(CO)4H2Fe(CO)4 Fe(CO)42HFe(CO)4H2Fe(CO)4 Fe(CO)42HFe(CO)4H2Fe(CO)4 Fe(CO)42HFe(CO)4H2Fe(CO)4 g C4H2O42g HC4H2O4g H2C4H2O4 g C4H2O42g HC4H2O4g H2C4H2O4 g C4H2O42g HC4H2O4g H2C4H2O4 g C4H2O42g HC4H2O4g H2C4H2O4 g C4H2O42g HC4H2O4g H2C4H2O4 g C4H2O42g HC4H2O4g H2C4H2O4 g C4H2O42g HC4H2O4g H2C4H2O4 g C4H2O42g HC4H2O4g H2C4H2O4 g C4H2O42g HC4H2O4g H2C4H2O4 g C4H2O42g HC4H2O4g H2C4H2O4 g C4H2O42g HC4H2O4g H2C4H2O4 g C4H2O42g HC4H2O4- Td C3v C2v Td C3v C2v Td C3v C2v Td C3v C2v C2h C1 C2h C2h C1 C2h C2h C1 C2h C2h C1 C2h C2h C1 C2h C2h C1 C2h C2h C1 C2h C2h C1 C2h C2h C1 C2h C2h C1 C2h C2h C1 C2h C2h C1 M05 M05 M05 M05 M05 M05 M05 M05 M05 M05 M05 M05 B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE BVP86 BVP86 BVP86 BVP86 BVP86 UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS -1717.04526 -1717.74609 -1718.25634 -1717.04526 -1717.74609 -1718.25634 -1717.04526 -1717.74609 -1718.25634 -1717.04526 -1717.74609 -1718.25634 -454.71679 -455.38647 -455.92879 -454.71679 -455.38647 -455.92879 -454.71679 -455.38647 -455.92879 -454.71679 -455.38647 -455.92879 -454.71679 -455.38647 -455.92879 -454.22689 -454.89753 -455.43332 -454.22689 -454.89753 -455.43332 -454.22689 -454.89753 -455.43332 -454.22689 -454.89753 -455.43332 -454.22689 -454.89753 -455.43332 -454.75367 -455.42518 -455.96185 -454.75367 -455.42518 S16 19.63(0) 24.85(0) 30.44(0) 19.63(0) 24.85(0) 30.44(0) 19.63(0) 24.85(0) 30.44(0) 19.63(0) 24.85(0) 30.44(0) 35.18(0) 43.09(0) 51.76(0) 35.18(0) 43.09(0) 51.76(0) 35.18(0) 43.09(0) 51.76(0) 35.18(0) 43.09(0) 51.76(0) 35.18(0) 43.09(0) 51.76(0) 33.87(0) 41.54(0) 50.11(0) 33.87(0) 41.54(0) 50.11(0) 33.87(0) 41.54(0) 50.11(0) 33.87(0) 41.54(0) 50.11(0) 33.87(0) 41.54(0) 50.11(0) 33.83(0) 41.49(0) 50.04(0) 33.83(0) 41.49(0) 6.62 6.89 7.04 6.62 6.89 7.04 6.62 6.89 7.04 6.62 6.89 7.04 5.20 5.42 5.44 5.20 5.42 5.44 5.20 5.42 5.44 5.20 5.42 5.44 5.20 5.42 5.44 5.34 5.57 5.53 5.34 5.57 5.53 5.34 5.57 5.53 5.34 5.57 5.53 5.34 5.57 5.53 5.33 5.57 5.53 5.33 5.57 97.35 99.52 99.92 97.35 99.52 99.92 97.35 99.52 99.92 97.35 99.52 99.92 86.48 89.58 86.98 86.48 89.58 86.98 86.48 89.58 86.98 86.48 89.58 86.98 86.48 89.58 86.98 87.93 91.36 87.51 87.93 91.36 87.51 87.93 91.36 87.51 87.93 91.36 87.51 87.93 91.36 87.51 87.88 91.30 87.54 87.88 91.30 -171.44 -34.04 8.16 -174.33 -36.98 5.83 -178.02 -38.30 -1.59 -171.17 -34.56 7.86 -186.21 -55.40 -2.79 -196.75 -65.19 -12.52 -201.58 -68.64 -17.05 -187.92 -57.79 -5.67 -196.16 -63.32 -10.21 -184.00 -52.70 -1.30 -194.01 -62.27 -12.45 -197.77 -63.99 -14.76 -185.65 -55.00 -3.68 -193.43 -60.12 -9.27 -184.79 -53.04 -1.37 -194.92 -62.66 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 g H2C4H2O4 C4H2O42g HC4H2O4g H2C4H2O4 g C4H2O42g HC4H2O4g H2C4H2O4 g C4H2O42g HC4H2O4g H2C4H2O4 g C4H2O42g HC4H2O4g H2C4H2O4 g C4H2O42g HC4H2O4g H2C4H2O4 g C4H2O42g HC4H2O4g H2C4H2O4 g C4H2O42g HC4H2O4g H2C4H2O4 g C4H2O42g HC4H2O4g H2C4H2O4 C4H4O42HC4H4O4H2C4H4O4 C4H4O42HC4H4O4H2C4H4O4 C4H4O42HC4H4O4H2C4H4O4 C4H4O42HC4H4O4H2C4H4O4 C4H4O42HC4H4O4H2C4H4O4 C4H4O42HC4H4O4H2C4H4O4 C4H4O42HC4H4O4H2C4H4O4 C4H4O42g C2h C2h C1 C2h C2h C1 C2h C2h C1 C2h C2h C1 C2h C2h C1 C2h C2h C1 C2h C2h C1 C2h C2h C1 C2h C2 C1 C1 C2 C1 C1 C2 C1 C1 C2 C1 C1 C2 C1 C1 C2 C1 C1 C2 C1 C1 C2 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP PBE PBE PBE PBE PBE PBE PBE UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling -455.96185 -454.75367 -455.42518 -455.96185 -454.75367 -455.42518 -455.96185 -454.75367 -455.42518 -455.96185 -454.67230 -455.33862 -455.87984 -454.67230 -455.33862 -455.87984 -454.67230 -455.33862 -455.87984 -454.67230 -455.33862 -455.87984 -454.67230 -455.33862 -455.87984 -455.94110 -456.63686 -457.15912 -455.94110 -456.63686 -457.15912 -455.94110 -456.63686 -457.15912 -455.94110 -456.63686 -457.15912 -455.94110 -456.63686 -457.15912 -455.44070 -456.13699 -456.65369 -455.44070 -456.13699 -456.65369 -455.44070 S17 50.04(0) 33.83(0) 41.49(0) 50.04(0) 33.83(0) 41.49(0) 50.04(0) 33.83(0) 41.49(0) 50.04(0) 36.24(0) 44.32(0) 52.86(0) 36.24(0) 44.32(0) 52.86(0) 36.24(0) 44.32(0) 52.86(0) 36.24(0) 44.32(0) 52.86(0) 36.24(0) 44.32(0) 52.86(0) 49.48(0) 56.95(0) 66.75(0) 49.48(0) 56.95(0) 66.75(0) 49.48(0) 56.95(0) 66.75(0) 49.48(0) 56.95(0) 66.75(0) 49.48(0) 56.95(0) 66.75(0) 47.84(0) 54.59(0) 64.67(0) 47.84(0) 54.59(0) 64.67(0) 47.84(0) 5.53 5.33 5.57 5.53 5.33 5.57 5.53 5.33 5.57 5.53 5.10 5.30 5.37 5.10 5.30 5.37 5.10 5.30 5.37 5.10 5.30 5.37 5.10 5.30 5.37 5.56 5.19 5.50 5.56 5.19 5.50 5.56 5.19 5.50 5.56 5.19 5.50 5.56 5.19 5.50 5.65 5.31 5.58 5.65 5.31 5.58 5.65 87.54 87.88 91.30 87.54 87.88 91.30 87.54 87.88 91.30 87.54 85.30 88.29 86.45 85.30 88.29 86.45 85.30 88.29 86.45 85.30 88.29 86.45 85.30 88.29 86.45 91.14 86.04 88.54 91.14 86.04 88.54 91.14 86.04 88.54 91.14 86.04 88.54 91.14 86.04 88.54 91.25 86.61 89.11 91.21 86.61 89.11 91.25 -12.47 -198.98 -64.66 -14.96 -186.46 -55.36 -4.87 -194.49 -60.65 -9.41 -188.87 -58.11 -3.12 -199.78 -67.99 -13.62 -206.04 -72.80 -17.98 -190.65 -60.41 -6.16 -199.76 -66.51 -10.96 -185.66 -51.01 -5.23 -198.61 -57.18 -14.16 -201.91 -61.43 -17.34 -188.31 -53.19 -7.98 -197.92 -57.47 -13.44 -183.35 -49.39 -4.46 -195.77 -55.80 -14.28 -197.95 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 HC4H4O4H2C4H4O4 C4H4O42HC4H4O4H2C4H4O4 C4H4O42HC4H4O4H2C4H4O4 C4H4O42HC4H4O4H2C4H4O4 C4H4O42HC4H4O4H2C4H4O4 C4H4O42HC4H4O4H2C4H4O4 C4H4O42HC4H4O4H2C4H4O4 C4H4O42HC4H4O4H2C4H4O4 C4H4O42HC4H4O4H2C4H4O4 C4H4O42HC4H4O4H2C4H4O4 C4H4O42HC4H4O4H2C4H4O4 C4H4O42HC4H4O4H2C4H4O4 C4H4O42HC4H4O4H2C4H4O4 a C1 C1 C2 C1 C1 C2 C1 C1 C2 C1 C1 C2 C1 C1 C2 C1 C1 C2 C1 C1 C2 C1 C1 C2 C1 C1 C2 C1 C1 C2 C1 C1 C2 C1 C1 C2 C1 C1 PBE PBE PBE PBE PBE PBE PBE PBE BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD UFF UFF UFF UAKS UAKS UAKS Pauling Pauling Pauling Klamt Klamt Klamt SMD SMD SMD -456.13699 -456.65369 -455.44070 -456.13699 -456.65369 -455.44070 -456.13699 -456.65369 -455.97579 -456.67304 -457.19050 -455.97579 -456.67304 -457.19050 -455.97579 -456.67304 -457.19050 -455.97579 -456.67304 -457.19050 -455.97579 -456.67304 -457.19050 -455.89443 -456.59208 -457.11074 -455.89443 -456.59208 -457.11074 -455.89443 -456.59208 -457.11074 -455.89443 -456.59208 -457.11074 -455.89443 -456.59208 -457.11074 b 54.59(0) 64.67(0) 47.84(0) 54.59(0) 64.67(0) 47.84(0) 54.59(0) 64.67(0) 47.79(0) 54.53(0) 64.62(0) 47.79(0) 54.53(0) 64.62(0) 47.79(0) 54.53(0) 64.62(0) 47.79(0) 54.53(0) 64.62(0) 47.79(0) 54.53(0) 64.62(0) 50.74(0) 58.13(0) 68.05(0) 50.74(0) 58.13(0) 68.05(0) 50.74(0) 58.13(0) 68.05(0) 50.74(0) 58.13(0) 68.05(0) 50.74(0) 58.13(0) 68.05(0) 5.31 5.58 5.65 5.31 5.58 5.65 5.31 5.58 5.66 5.32 5.58 5.66 5.32 5.58 5.66 5.32 5.58 5.66 5.32 5.58 5.66 5.32 5.58 5.50 5.08 5.45 5.50 5.08 5.45 5.50 5.08 5.45 5.50 5.08 5.45 5.50 5.08 5.45 86.61 89.11 91.25 86.61 89.11 91.25 86.61 89.11 91.29 86.64 89.10 91.29 86.64 89.10 91.29 86.64 89.10 91.29 86.64 89.10 91.29 86.64 89.10 90.83 85.26 88.25 90.83 85.26 88.25 90.83 85.26 88.25 90.83 85.26 88.25 90.83 85.26 88.25 -58.33 -15.50 -186.04 -51.51 -7.80 -194.89 -55.36 -12.47 -184.16 -49.72 -4.60 -196.73 -56.08 -14.33 -199.21 -59.01 -13.05 -186.90 -51.87 -7.92 -196.01 -55.88 -12.63 -188.96 -52.48 -5.53 -202.46 -58.69 -15.12 -207.14 -63.54 -17.52 -191.77 -54.71 -8.96 -202.39 -59.22 -14.25 Point group. Zero-point energies and number of imaginary frequencies. d e Thermal corrections to 298K. Entropies. Free energy of solvation is the sum of energy difference between gaseous and aqueous state and total nonelectrostatic contribution. A correction factor of 1.89 kcal/mol should be added to the calculated values to account for the change of state from 1 mol/atm (24.47 L at 298 K in gas phase) to 1 mol/L (aqueous phase). f g Maleic acid (D). Fumaric acid (N). c S18 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 Table S2. Point Group, DFT Method, Cavity Model, Total Energies (hartrees), Zero-point Energies (kcal/mol) with number of Imaginary Frequencies in Parentheses, Thermal Corrections (kcal/mol), Entropies (cal/mol·K), and Free energy of Solvation (kcal/mol) f PO43g HPO42HPO42H2PO4H3PO4 f PO43g HPO42HPO42H2PO4H3PO4 f PO43g HPO42HPO42H2PO4H3PO4 f PO43g HPO42HPO42H2PO4H3PO4 f PO43g HPO42HPO42H2PO4H3PO4 f PO43g HPO42HPO42H2PO4H3PO4 f PO43g HPO42HPO42H2PO4H3PO4 f PO43g HPO42HPO42H2PO4- PGa DFT Cavity Model SCF Energy ZPEb (NIF) TCc Sd Solvation Free Energye Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE UFF UFF UFF UFF UFF UAKS UAKS UAKS UAKS UAKS Pauling Pauling Pauling Pauling Pauling Klamt Klamt Klamt Klamt Klamt SMD SMD SMD SMD SMD UFF UFF UFF UFF UFF UAKS UAKS UAKS UAKS UAKS Pauling Pauling Pauling Pauling -642.04528 -643.02988 -643.07253 -643.80998 -644.34250 -642.04528 -643.02988 -643.07253 -643.80998 -644.34250 -642.04528 -643.02988 -643.07253 -643.80998 -644.34250 -642.04528 -643.02988 -643.07252 -643.80998 -644.34250 -642.04528 -643.02988 -643.07252 -643.80998 -644.34250 -641.56233 -642.54807 -642.59608 -643.32928 -643.85834 -641.56233 -642.54807 -642.59608 -643.32928 -643.85834 -641.56233 -642.54807 -642.59608 -643.32928 8.58(0) 15.80(0) 15.48(0) 23.16(0) 30.29(0) 8.58(0) 15.80(0) 15.48(0) 23.16(0) 30.29(0) 8.58(0) 15.80(0) 15.48(0) 23.16(0) 30.29(0) 8.58(0) 15.80(0) 15.48(0) 23.16(0) 30.28(0) 8.58(0) 15.80(0) 15.48(0) 23.16(0) 30.28(0) 8.18(0) 15.18(0) 14.81(0) 22.29(0) 29.34(0) 8.18(0) 15.18(0) 14.81(0) 22.29(0) 29.34(0) 8.18(0) 15.18(0) 14.81(0) 22.29(0) 3.30 3.75 3.83 4.13 4.53 3.30 3.75 3.83 4.13 4.53 3.30 3.75 3.83 4.13 4.53 3.30 3.75 3.83 4.12 4.53 3.30 3.75 3.83 4.12 4.53 3.38 3.81 3.92 4.23 4.62 3.38 3.81 3.92 4.23 4.62 3.38 3.81 3.92 4.23 64.56 72.13 72.72 74.57 77.15 64.56 72.13 72.72 74.57 77.15 64.56 72.13 72.72 74.57 77.15 64.56 72.14 72.73 74.55 77.18 64.56 72.14 72.73 74.55 77.18 65.07 72.52 73.24 75.25 77.76 65.07 72.52 73.24 75.25 77.76 65.07 72.52 73.24 75.25 -526.28 -234.69 -226.04 -62.83 -8.37 -528.89 -232.24 -225.06 -64.07 -12.65 -567.94 -258.16 -244.82 -75.30 -21.27 -529.03 -236.97 -228.09 -65.33 -12.01 -549.64 -246.90 -235.61 -68.51 -15.09 -525.44 -233.07 -222.93 -61.39 -7.71 -528.01 -230.60 -222.15 -62.72 -12.29 -565.84 -255.25 -240.10 -72.43 S19 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 H3PO4 f PO43g HPO42HPO42H2PO4H3PO4 f PO43g HPO42HPO42H2PO4H3PO4 f PO43g HPO42HPO42H2PO4H3PO4 f PO43g HPO42HPO42H2PO4H3PO4 f PO43g HPO42HPO42H2PO4H3PO4 f PO43g HPO42HPO42H2PO4H3PO4 f PO43g HPO42HPO42H2PO4H3PO4 f PO43g HPO42HPO42H2PO4H3PO4 f PO43g HPO42HPO42- C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 M052X M052X M052X M052X M052X M052X M052X M052X Pauling Klamt Klamt Klamt Klamt Klamt SMD SMD SMD SMD SMD UFF UFF UFF UFF UFF UAKS UAKS UAKS UAKS UAKS Pauling Pauling Pauling Pauling Pauling Klamt Klamt Klamt Klamt Klamt SMD SMD SMD SMD SMD UFF UFF UFF UFF UFF UAKS UAKS UAKS -643.85834 -641.56234 -642.54807 -642.59608 -643.32928 -643.85834 -641.56234 -642.54807 -642.59608 -643.32928 -643.85834 -642.09631 -643.08032 -643.12402 -643.85816 -644.38812 -642.09631 -643.08032 -643.12402 -643.85816 -644.38812 -642.09631 -643.08032 -643.12402 -643.85816 -644.38812 -642.09631 -643.08032 -643.12402 -643.85816 -644.38812 -642.09631 -643.08032 -643.12402 -643.85816 -644.38812 -642.02662 -643.00157 -643.03359 -643.77085 -644.30171 -642.02662 -643.00157 -643.03359 29.34(0) 8.18(0) 15.18(0) 14.81(0) 22.29(0) 29.34(0) 8.18(0) 15.18(0) 14.81(0) 22.29(0) 29.34(0) 8.17(0) 15.14(0) 14.79(0) 22.27(0) 29.31(0) 8.17(0) 15.14(0) 14.79(0) 22.27(0) 29.31(0) 8.17(0) 15.14(0) 14.79(0) 22.27(0) 29.31(0) 8.17(0) 15.14(0) 14.79(0) 22.27(0) 29.31(0) 8.17(0) 15.14(0) 14.79(0) 22.27(0) 29.31(0) 8.91(0) 16.20(0) 15.93(0) 23.67(0) 30.67(0) 8.91(0) 16.20(0) 15.93(0) 4.62 3.38 3.81 3.92 4.23 4.62 3.38 3.81 3.92 4.23 4.62 3.38 3.82 3.92 4.23 4.62 3.38 3.82 3.92 4.23 4.62 3.38 3.82 3.92 4.23 4.62 3.38 3.82 3.92 4.23 4.62 3.38 3.82 3.92 4.23 4.62 3.24 3.71 3.78 4.05 4.51 3.24 3.71 3.78 77.76 65.07 72.52 73.24 75.21 77.76 65.07 72.52 73.24 75.21 77.76 65.07 72.57 73.24 75.20 77.73 65.07 72.57 73.24 75.20 77.73 65.07 72.57 73.24 75.20 77.73 65.07 72.56 73.24 75.24 77.72 65.07 72.56 73.24 75.24 77.72 64.22 71.94 72.53 74.07 77.15 64.22 71.94 72.53 -19.62 -528.09 -235.19 -224.78 -63.51 -11.24 -548.08 -244.57 -231.58 -66.16 -13.73 -525.21 -233.13 -223.90 -61.81 -7.82 -527.80 -230.66 -223.02 -63.03 -12.35 -565.59 -255.40 -241.43 -73.10 -19.85 -527.87 -235.27 -225.80 -63.76 -11.37 -547.91 -244.71 -232.78 -66.76 -13.90 -527.03 -236.24 -229.86 -64.64 -9.39 -529.68 -233.77 -228.56 H2PO4H3PO4 C1 C1 M052X M052X UAKS UAKS -643.77085 -644.30171 23.67(0) 30.67(0) 4.05 4.51 74.07 77.15 -65.59 -13.55 S20 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 f PO43HPO42HPO42H2PO4H3PO4 f PO43g HPO42HPO42H2PO4H3PO4 f PO43g HPO42HPO42H2PO4H3PO4 f AsO43g HAsO42HAsO42H2AsO4H3AsO4 f AsO43g HAsO42HAsO42H2AsO4H3AsO4 f AsO43g HAsO42HAsO42H2AsO4H3AsO4 f AsO43g HAsO42HAsO42H2AsO4H3AsO4 f AsO43g HAsO42HAsO42H2AsO4H3AsO4 f AsO43g HAsO42HAsO42H2AsO4H3AsO4 f AsO43g HAsO42g Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE Pauling Pauling Pauling Pauling Pauling Klamt Klamt Klamt Klamt Klamt SMD SMD SMD SMD SMD UFF UFF UFF UFF UFF UAKS UAKS UAKS UAKS UAKS Pauling Pauling Pauling Pauling Pauling Klamt Klamt Klamt Klamt Klamt UFF UFF UFF UFF UFF UAKS UAKS UAKS UAKS UAKS Pauling Pauling -642.02662 -643.00157 -643.03359 -643.77085 -644.30171 -642.02662 -643.00157 -643.03359 -643.77085 -644.30171 -642.02662 -643.00157 -643.03359 -643.77085 -644.30171 -2536.54836 -2537.55828 -2537.51531 -2538.28696 -2538.81779 -2536.54836 -2537.55828 -2537.51531 -2538.28696 -2538.81779 -2536.54836 -2537.55828 -2537.51531 -2538.28696 -2538.81779 -2536.54836 -2537.55828 -2537.51531 -2538.28696 -2538.81779 -2535.87351 -2536.88970 -2536.84167 -2537.61438 -2538.14256 -2535.87351 -2536.88970 -2536.84167 -2537.61438 -2538.14256 -2535.87351 -2536.88970 S21 8.91(0) 16.20(0) 15.93(0) 23.67(0) 30.67(0) 8.91(0) 16.20(0) 15.93(0) 23.68(0) 30.67(0) 8.91(0) 16.20(0) 15.93(0) 23.68(0) 30.67(0) 6.72(0) 13.64(0) 13.93(0) 21.03(0) 27.72(0) 6.72(0) 13.64(0) 13.93(0) 21.03(0) 27.72(0) 6.72(0) 13.64(0) 13.93(0) 21.03(0) 27.72(0) 6.72(0) 13.64(0) 13.93(0) 21.03(0) 27.72(0) 6.37(0) 13.07(0) 13.39(0) 20.27(0) 27.06(0) 6.37(0) 13.07(0) 13.39(0) 20.27(0) 27.06(0) 6.37(0) 13.07(0) 3.24 3.71 3.78 4.05 4.51 3.24 3.71 3.78 4.05 4.51 3.24 3.71 3.78 4.05 4.51 3.74 4.25 4.15 4.62 5.36 3.74 4.25 4.15 4.62 5.36 3.74 4.25 4.15 4.62 5.36 3.74 4.25 4.15 4.62 5.36 3.84 4.36 4.23 4.72 5.34 3.84 4.36 4.23 4.72 5.34 3.84 4.36 64.22 71.94 72.53 74.07 77.15 64.23 71.94 72.54 74.06 77.14 64.23 71.94 72.54 74.06 77.14 68.69 76.76 76.06 79.11 86.19 68.69 76.76 76.06 79.11 86.19 68.69 76.76 76.06 79.11 86.19 68.70 76.76 76.06 79.12 86.16 69.35 77.48 76.64 79.87 85.04 69.35 77.48 76.64 79.87 85.04 69.35 77.48 -569.56 -260.66 -250.55 -78.07 -22.37 -530.12 -238.67 -232.05 -67.00 -13.16 -550.95 -249.00 -240.44 -70.78 -16.36 -505.10 -222.90 -214.36 -56.83 -5.43 -516.40 -229.90 -222.14 -65.11 -15.66 -543.20 -244.90 -232.08 -68.86 -17.70 -506.90 -224.90 -216.23 -58.82 -8.51 -504.20 -221.20 -211.49 -54.94 -4.27 -514.20 -227.60 -218.81 -63.24 -14.98 -540.70 -241.70 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 HAsO42H2AsO4H3AsO4 f AsO43g HAsO42HAsO42H2AsO4H3AsO4 f AsO43g HAsO42HAsO42H2AsO4H3AsO4 f AsO43g HAsO42HAsO42H2AsO4H3AsO4 f AsO43g HAsO42HAsO42H2AsO4H3AsO4 f AsO43g HAsO42HAsO42H2AsO4H3AsO4 f AsO43g HAsO42HAsO42H2AsO4H3AsO4 f AsO43g HAsO42HAsO42H2AsO4H3AsO4 f AsO43g HAsO42HAsO42H2AsO4H3AsO4 f AsO43g HAsO42HAsO42- C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 PBE PBE PBE PBE PBE PBE PBE PBE BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X Pauling Pauling Pauling Klamt Klamt Klamt Klamt Klamt UFF UFF UFF UFF UFF UAKS UAKS UAKS UAKS UAKS Pauling Pauling Pauling Pauling Pauling Klamt Klamt Klamt Klamt Klamt UFF UFF UFF UFF UFF UAKS UAKS UAKS UAKS UAKS Pauling Pauling Pauling Pauling Pauling Klamt Klamt Klamt -2536.84167 -2537.61438 -2538.14256 -2535.87355 -2536.88970 -2536.84167 -2537.61438 -2538.14256 -2536.83066 -2537.84094 -2537.79724 -2538.56651 -2539.09445 -2536.83066 -2537.84094 -2537.79724 -2538.56651 -2539.09445 -2536.83066 -2537.84094 -2537.79724 -2538.56651 -2539.09445 -2536.83066 -2537.84094 -2537.79724 -2538.56651 -2539.09445 -2536.44668 -2537.43643 -2537.40369 -2538.16531 -2538.69550 -2536.44668 -2537.43643 -2537.40369 -2538.16531 -2538.69550 -2536.44668 -2537.43643 -2537.40369 -2538.16531 -2538.69550 -2536.44668 -2537.43643 -2537.40369 S22 13.39(0) 20.27(0) 27.06(0) 6.37(0) 13.07(0) 13.39(0) 20.28(0) 27.06(0) 6.33(0) 13.04(0) 13.35(0) 20.23(0) 26.84(0) 6.33(0) 13.04(0) 13.35(0) 20.23(0) 26.84(0) 6.33(0) 13.04(0) 13.35(0) 20.23(0) 26.84(0) 6.33(0) 13.04(0) 13.34(0) 20.23(0) 26.84(0) 7.24(0) 14.34(0) 14.53(0) 21.77(0) 28.20(0) 7.24(0) 14.34(0) 14.53(0) 21.77(0) 28.20(0) 7.24(0) 14.34(0) 14.53(0) 21.77(0) 28.20(0) 7.24(0) 14.35(0) 14.53(0) 4.23 4.72 5.34 3.85 4.36 4.23 4.72 5.34 3.86 4.36 4.24 4.73 5.43 3.86 4.36 4.24 4.73 5.44 3.86 4.36 4.24 4.73 5.44 3.86 4.36 4.24 4.73 5.43 3.61 4.09 4.03 4.45 5.33 3.61 4.09 4.03 4.45 5.33 3.61 4.09 4.03 4.45 5.33 3.61 4.09 4.03 76.64 79.87 85.04 69.38 77.47 76.64 79.85 85.04 69.43 77.51 76.71 79.92 88.35 69.43 77.51 76.71 79.92 88.49 69.43 77.51 76.71 79.92 88.50 69.43 77.51 76.72 79.91 88.36 67.90 75.68 75.32 77.95 86.92 67.90 75.68 75.32 77.95 86.92 67.90 75.68 75.32 77.95 86.92 67.90 75.68 75.32 -227.06 -65.50 -15.74 -505.80 -223.00 -213.19 -56.82 -7.23 -504.0 -221.2 -212.09 -55.31 -4.19 -514.30 -227.70 -219.74 -63.58 -15.07 -540.60 -241.80 -228.36 -66.15 -15.75 -505.50 -223.00 -214.11 -57.20 -7.30 -506.60 -225.20 -219.01 -59.04 -6.31 -518.90 -233.00 -227.13 -67.80 -16.96 -546.30 -248.70 -238.91 -72.55 -19.02 -508.50 -227.30 -221.04 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 H2AsO4H3AsO4 f VO43g HVO42HVO42H2VO4H3VO4 f VO43g HVO42HVO42H2VO4H3VO4 f VO43g HVO42HVO42H2VO4H3VO4 f VO43g HVO42HVO42H2VO4H3VO4 f VO43g HVO42HVO42H2VO4H3VO4 f VO43g HVO42HVO42H2VO4H3VO4 f VO43g HVO42HVO42H2VO4H3VO4 f VO43g HVO42HVO42H2VO4H3VO4 f VO43g HVO42HVO42H2VO4H3VO4 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 M052X M052X B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE BVP86 BVP86 BVP86 BVP86 BVP86 Klamt Klamt UFF UFF UFF UFF UFF UAKS UAKS UAKS UAKS UAKS Pauling Pauling Pauling Pauling Pauling Klamt Klamt Klamt Klamt Klamt UFF UFF UFF UFF UFF UAKS UAKS UAKS UAKS UAKS Pauling Pauling Pauling Pauling Pauling Klamt Klamt Klamt Klamt Klamt UFF UFF UFF UFF UFF -2538.16531 -2538.69551 -1244.81570 -1245.76232 -1245.78414 -1246.52079 -1247.05254 -1244.81570 -1245.76232 -1245.78414 -1246.52079 -1247.05254 -1244.81570 -1245.76232 -1245.78414 -1246.52079 -1247.05254 -1244.81570 -1245.76232 -1245.78414 -1246.52079 -1247.05254 -1244.32023 -1245.25895 -1245.28270 -1246.01480 -1246.54449 -1244.32023 -1245.25895 -1245.28270 -1246.01480 -1246.54449 -1244.32023 -1245.25895 -1245.28270 -1246.01480 -1246.54449 -1244.32023 -1245.25895 -1245.28270 -1246.01480 -1246.54449 -1245.02310 -1245.96247 -1245.98462 -1246.71741 -1247.24778 S23 21.76(0) 28.24(0) 6.26(0) 13.33(0) 13.26(0) 20.27(0) 27.39(0) 6.26(0) 13.33(0) 13.26(0) 20.27(0) 27.39(0) 6.26(0) 13.33(0) 13.26(0) 20.27(0) 27.39(0) 6.26(0) 13.33(0) 13.26(0) 20.27(0) 27.39(0) 5.81(0) 12.86(0) 12.77(0) 19.76(0) 26.59(0)/ 5.81(0) 12.86(0) 12.77(0) 19.76(0) 26.59(0) 5.81(0) 12.86(0) 12.77(0) 19.76(0) 26.59(0) 5.81(0) 12.86(0) 12.77(0) 19.76(0) 26.59(0) 5.87(0) 12.86(0) 12.78(0) 19.80(0) 26.24(0) 4.45 5.29 3.95 4.46 4.45 4.82 5.01 3.95 4.46 4.45 4.82 5.01 3.95 4.46 4.45 4.82 5.01 3.95 4.46 4.45 4.82 5.01 4.11 4.52 4.52 4.83 5.11 4.11 4.52 4.52 4.83 5.11 4.11 4.52 4.52 4.83 5.11 4.11 4.52 4.52 4.83 5.11 4.08 4.52 4.52 4.80 5.23 77.96 85.91 69.55 78.03 77.81 79.91 80.63 69.55 78.03 77.81 79.91 80.63 69.55 78.03 77.81 79.91 80.63 69.55 78.03 77.81 79.91 80.63 70.59 78.41 78.31 79.96 81.32 70.59 78.41 78.31 79.96 81.32 70.59 78.41 78.31 79.96 81.32 70.59 78.41 78.31 79.96 81.32 70.45 78.41 78.26 79.72 82.18 -61.16 -9.59 -485.45 -216.19 -211.93 -54.48 -1.83 -507.32 -226.81 -222.09 -62.68 -11.45 -519.70 -236.85 -230.53 -67.90 -17.67 -489.34 -218.90 -214.44 -56.62 -4.42 -480.70 -214.29 -209.28 -52.94 -1.18 -501.74 -224.79 -219.68 -61.89 -11.34 -512.62 -233.25 -226.29 -65.45 -16.03 -484.44 -216.83 -211.94 -55.53 -3.54 -482.32 -215.04 -210.27 -53.33 -1.08 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 f VO43HVO42HVO42H2VO4H3VO4 f VO43g HVO42HVO42H2VO4H3VO4 f VO43g HVO42HVO42H2VO4H3VO4 f VO43g HVO42HVO42H2VO4H3VO4 f VO43g HVO42HVO42H2VO4H3VO4 f VO43g HVO42HVO42H2VO4H3VO4 f VO43g HVO42HVO42H2VO4H3VO4 f C5H2NO33g HC5H2NO32HC5H2NO32H2C5H2NO3H3C5H2NO3 f C5H2NO33g HC5H2NO32HC5H2NO32H2C5H2NO3H3C5H2NO3 f C5H2NO33g HC5H2NO32g Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 Td C1 C1 C1 C1 C2v C2v C2v Cs Cs C2v C2v C2v Cs Cs C2v C2v BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP UAKS UAKS UAKS UAKS UAKS Pauling Pauling Pauling Pauling Pauling Klamt Klamt Klamt Klamt Klamt UFF UFF UFF UFF UFF UAKS UAKS UAKS UAKS UAKS Pauling Pauling Pauling Pauling Pauling Klamt Klamt Klamt Klamt Klamt UFF UFF UFF UFF UFF UAKS UAKS UAKS UAKS UAKS Pauling Pauling -1245.02310 -1245.96247 -1245.98462 -1246.71741 -1247.24778 -1245.02310 -1245.96247 -1245.98462 -1246.71741 -1247.24778 -1245.02310 -1245.96247 -1245.98462 -1246.71741 -1247.24778 -1244.65486 -1245.60439 -1245.62233 -1246.36080 -1246.89071 -1244.65486 -1245.60439 -1245.62233 -1246.36080 -1246.89071 -1244.65486 -1245.60439 -1245.62233 -1246.36080 -1246.89071 -1244.65486 -1245.60439 -1245.62233 -1246.36080 -1246.89071 5.87(0) 12.86(0) 12.78(0) 19.80(0) 26.24(0) 5.87(0) 12.86(0) 12.78(0) 19.80(0) 26.24(0) 5.87(0) 12.86(0) 12.78(0) 19.80(0) 26.24(0) 6.80(0) 13.86(0) 13.75(0) 20.95(0) 27.86(0) 6.80(0) 13.86(0) 13.75(0) 20.95(0) 27.86(0) 6.80(0) 13.86(0) 13.75(0) 20.95(0) 27.86(0) 6.80(0) 13.86(0) 13.75(0) 20.95(0) 27.86(0) 4.08 4.52 4.52 4.80 5.23 4.08 4.52 4.52 4.80 5.23 4.08 4.52 4.52 4.80 5.23 3.79 4.32 4.34 4.64 4.97 3.79 4.32 4.34 4.64 4.97 3.79 4.32 4.34 4.64 4.97 3.79 4.32 4.34 4.64 4.97 70.45 78.41 78.26 79.72 82.18 70.45 78.41 78.26 79.72 82.18 70.45 78.41 78.26 79.72 82.18 68.44 76.99 77.07 78.57 80.27 68.44 76.99 77.07 78.57 80.27 68.44 76.99 77.07 78.57 80.27 68.44 76.99 77.07 78.57 80.27 -471.99272 -472.91285 -472.94381 -473.63940 -474.16500 -471.99272 -472.91285 -472.94381 -473.63940 -474.16500 -471.99272 -472.91285 38.50(0) 47.37(0) 47.26(0) 55.62(0) 63.98(0) 38.50(0) 47.37(0) 47.26(0) 55.62(0) 63.98(0) 38.50(0) 47.37(0) 4.74 4.93 4.93 5.14 5.29 4.74 4.93 4.93 5.14 5.29 4.74 4.93 80.34 81.53 81.51 83.88 84.60 80.34 81.53 81.51 83.88 84.60 80.34 81.53 S24 -503.57 -225.64 -220.72 -62.36 -11.34 -227.69 -514.65 -234.12 -66.18 -16.07 -486.08 -217.60 -212.96 -55.43 -3.80 -493.27 -219.36 -216.02 -55.70 -2.37 -510.97 -230.39 -226.78 -64.14 -12.11 -524.67 -241.51 -236.51 -70.22 -18.64 -497.18 -222.10 -218.61 -58.11 -5.07 -436.11 -192.40 -187.39 -52.40 -7.35 -452.28 -202.11 -197.45 -62.84 -20.66 -465.51 -210.31 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 HC5H2NO32H2C5H2NO3H3C5H2NO3 f C5H2NO33g HC5H2NO32HC5H2NO32H2C5H2NO3H3C5H2NO3 f C5H2NO33g HC5H2NO32HC5H2NO32H2C5H2NO3H3C5H2NO3 f C5H2NO33g HC5H2NO32HC5H2NO32H2C5H2NO3H3C5H2NO3 f C5H2NO33g HC5H2NO32HC5H2NO32H2C5H2NO3H3C5H2NO3 f C5H2NO33g HC5H2NO32HC5H2NO32H2C5H2NO3H3C5H2NO3 f C5H2NO33g HC5H2NO32HC5H2NO32H2C5H2NO3H3C5H2NO3 f C5H2NO33g HC5H2NO32HC5H2NO32H2C5H2NO3H3C5H2NO3 f C5H2NO33g HC5H2NO32HC5H2NO32H2C5H2NO3H3C5H2NO3 f C5H2NO33g HC5H2NO32HC5H2NO32H2C5H2NO3- C2v Cs Cs C2v C2v C2v Cs Cs C2v C2v C2v Cs Cs C2v C2v C2v Cs Cs C2v C2v C2v Cs Cs C2v C2v C2v Cs Cs C2v C2v C2v Cs Cs C2v C2v C2v Cs Cs C2v C2v C2v Cs Cs C2v C2v C2v Cs B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 Pauling Pauling Pauling Klamt Klamt Klamt Klamt Klamt SMD SMD SMD SMD SMD UFF UFF UFF UFF UFF UAKS UAKS UAKS UAKS UAKS Pauling Pauling Pauling Pauling Pauling Klamt Klamt Klamt Klamt Klamt SMD SMD SMD SMD SMD UFF UFF UFF UFF UFF UAKS UAKS UAKS UAKS -472.94381 -473.63940 -474.16500 -471.99272 -472.91285 -472.94381 -473.63940 -474.16500 -471.99272 -472.91285 -472.94381 -473.63940 -474.16500 -471.47103 -472.38868 -472.42341 -473.11534 -473.63781 -471.47103 -472.38868 -472.42341 -473.11534 -473.63781 -471.47103 -472.38868 -472.42341 -473.11534 -473.63781 -471.47103 -472.38868 -472.42341 -473.11534 -473.63781 -471.47103 -472.38868 -472.42341 -473.11534 -473.63781 -472.03715 -472.95347 -472.98480 -473.67764 -474.20095 -472.03715 -472.95347 -472.98480 -473.67764 S25 47.26(0) 55.62(0) 63.98(0) 38.50(0) 47.37(0) 47.26(0) 55.62(0) 63.98(0) 38.50(0) 47.37(0) 47.26(0) 55.62(0) 63.98(0) 37.21(0) 45.87(0) 45.76(0) 53.92(0) 62.11(0) 37.21(0) 45.87(0) 45.76(0) 53.92(0) 62.11(0) 37.21(0) 45.87(0) 45.76(0) 53.92(0) 62.11(0) 37.21(0) 45.87(0) 45.76(0) 53.92(0) 62.11(0) 37.21(0) 45.87(0) 45.76(0) 53.92(0) 62.11(0) 37.11(0) 45.76(0) 45.67(0) 53.83(0) 62.00(0) 37.11(0) 45.76(0) 45.67(0) 53.83(0) 4.93 5.14 5.29 4.74 4.93 4.93 5.14 5.29 4.74 4.93 4.93 5.14 5.29 4.88 5.08 5.09 5.29 5.44 4.89 5.08 5.09 5.29 5.44 4.88 5.08 5.09 5.29 5.44 4.89 5.08 5.09 5.29 5.44 4.89 5.08 5.09 5.29 5.44 4.89 5.09 5.09 5.29 5.44 4.89 5.09 5.09 5.29 81.51 83.88 84.60 80.34 81.53 81.51 83.88 84.60 80.34 81.53 81.51 83.88 84.60 81.24 82.56 82.53 84.83 85.49 81.24 82.56 82.53 84.83 85.49 81.24 82.56 82.53 84.83 85.49 81.24 82.56 82.53 84.83 85.49 81.24 82.56 82.53 84.83 85.49 81.28 82.61 82.53 84.84 85.53 81.28 82.61 82.53 84.84 -202.95 -63.96 -20.62 -437.44 -194.71 -189.10 -55.17 -11.40 -455.62 -204.61 -198.31 -60.92 -17.27 -434.31 -191.42 -185.30 -51.25 -6.60 -451.03 -201.36 -195.65 -62.14 -20.56 -463.45 -208.51 -199.73 -61.88 -19.12 -435.93 -193.45 -187.61 -53.97 -10.62 -453.84 -203.27 -195.82 -59.58 -16.52 -434.46 -191.43 -186.12 -51.60 -6.71 -450.93 -201.47 -196.37 -62.43 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 H3C5H2NO3 f C5H2NO33g HC5H2NO32HC5H2NO32H2C5H2NO3H3C5H2NO3 f C5H2NO33g HC5H2NO32HC5H2NO32H2C5H2NO3H3C5H2NO3 f C5H2NO33g HC5H2NO32HC5H2NO32H2C5H2NO3H3C5H2NO3 f C5H2NO33g HC5H2NO32HC5H2NO32H2C5H2NO3H3C5H2NO3 f C5H2NO33g HC5H2NO32HC5H2NO32H2C5H2NO3H3C5H2NO3 f C5H2NO33g HC5H2NO32HC5H2NO32H2C5H2NO3H3C5H2NO3 f C5H2NO33g HC5H2NO32HC5H2NO32H2C5H2NO3H3C5H2NO3 f C5H2NO33g HC5H2NO32HC5H2NO32H2C5H2NO3H3C5H2NO3 Q_D2h Q_D3 Q_M2 Q_M3 Q_M4 Q_N2 Cs C2v C2v C2v Cs Cs C2v C2v C2v Cs Cs C2v C2v C2v Cs Cs C2v C2v C2v Cs Cs C2v C2v C2v Cs Cs C2v C2v C2v Cs Cs C2v C2v C2v Cs Cs C2v C2v C2v Cs Cs Cs C1 Cs C2v Cs Cs BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP UAKS Pauling Pauling Pauling Pauling Pauling Klamt Klamt Klamt Klamt Klamt SMD SMD SMD SMD SMD UFF UFF UFF UFF UFF UAKS UAKS UAKS UAKS UAKS Pauling Pauling Pauling Pauling Pauling Klamt Klamt Klamt Klamt Klamt SMD SMD SMD SMD SMD UFF UFF UFF UFF UFF UFF -474.20095 -472.03715 -472.95347 -472.98480 -473.67764 -474.20095 -472.03715 -472.95347 -472.98480 -473.67764 -474.20095 -472.03715 -472.95347 -472.98480 -473.67764 -474.20095 -471.96958 -472.88071 -472.90498 -473.59926 -474.12290 -471.96958 -472.88071 -472.90498 -473.59926 -474.12290 -471.96958 -472.88071 -472.90498 -473.59926 -474.12290 -471.96958 -472.88071 -472.90498 -473.59926 -474.12290 -471.96958 -472.88071 -472.90498 -473.59926 -474.12290 -472.90361 -472.89667 -473.61791 -473.62107 -473.60397 -474.17131 S26 62.00(0) 37.11(0) 45.76(0) 45.67(0) 53.83(0) 62.00(0) 37.11(0) 45.76(0) 45.67(0) 53.83(0) 62.00(0) 37.11(0) 45.76(0) 45.67(0) 53.83(0) 62.00(0) 39.63(0) 48.49(0) 48.40(0) 56.78(0) 65.16(0) 39.63(0) 48.49(0) 48.40(0) 56.78(0) 65.16(0) 39.63(0) 48.49(0) 48.40(0) 56.78(0) 65.16(0) 39.63(0) 48.49(0) 48.40(0) 56.78(0) 65.16(0) 39.63(0) 48.49(0) 48.40(0) 56.78(0) 65.16(0) 46.52(0) 46.35(0) 55.30(0) 55.61(0) 54.99(0) 64.12(0) 5.44 4.89 5.09 5.09 5.29 5.44 4.89 5.09 5.09 5.29 5.44 4.89 5.09 5.09 5.29 5.44 4.66 4.86 4.85 5.06 5.23 4.66 4.86 4.85 5.06 5.23 4.66 4.86 4.85 5.06 5.23 4.66 4.86 4.85 5.06 5.23 4.66 4.86 4.85 5.06 5.23 5.07 5.10 5.26 5.09 5.27 5.19 85.53 81.28 82.61 82.53 84.84 85.53 81.27 82.61 82.53 84.84 85.53 81.27 82.61 82.53 84.84 85.53 79.80 81.07 81.01 83.39 84.24 79.80 81.07 81.01 83.39 84.24 79.80 81.07 81.01 83.39 84.24 79.80 81.07 81.01 83.39 84.24 79.80 81.07 81.01 83.39 84.24 83.54 83.72 84.72 81.99 84.54 83.76 -20.60 -463.18 -208.67 -200.77 -62.50 -19.34 -435.94 -192.84 -187.62 -54.32 -10.72 -453.83 -203.47 -196.87 -60.07 -16.65 -438.44 -194.17 -190.63 -54.03 -8.32 -451.77 -204.41 -200.91 -64.84 -21.93 -468.93 -213.41 -207.74 -66.81 -22.16 -439.97 -195.80 -192.24 -56.90 -12.52 -458.50 -207.00 -202.40 -63.19 -18.53 -196.66 -200.27 -57.33 -52.41 -59.83 -1.74 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 Q_N3 Q_D2 Q_D3 Q_M2 Q_M3 Q_M4 Q_N2 Q_N3 Q_D2 Q_D3 Q_M2 Q_M3 Q_M4 Q_N2 Q_N3 Q_D2 Q_D3 Q_M2 Q_M3 Q_M4 Q_N2 Q_N3 Q_D2 Q_D3 Q_M2 Q_M3 Q_M4 Q_N2 Q_N3 Q_D2 Q_D3 Q_M2 Q_M3 Q_M4 Q_N2 Q_N3 Q_D2 Q_D3 Q_M2 Q_M3 Q_M4 Q_N2 Q_N3 Q_D2 Q_D3 Q_M2 Q_M3 C2v Cs C1 Cs C2v Cs Cs C2v Cs C1 Cs C2v Cs Cs C2v Cs C1 Cs C2v Cs Cs C2v Cs C1 Cs C2v Cs Cs C2v Cs C1 Cs C2v Cs Cs C2v Cs C1 Cs C2v Cs Cs C2v Cs C1 Cs C2v B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE PBE UFF UAKS UAKS UAKS UAKS UAKS UAKS UAKS Pauling Pauling Pauling Pauling Pauling Pauling Pauling Klamt Klamt Klamt Klamt Klamt Klamt Klamt UFF UFF UFF UFF UFF UFF UFF UAKS UAKS UAKS UAKS UAKS UAKS UAKS Pauling Pauling Pauling Pauling Pauling Pauling Pauling Klamt Klamt Klamt Klamt -474.14958 -472.90361 -472.89667 -473.61791 -473.62107 -473.60397 -474.17131 -474.14958 -472.90361 -472.89667 -473.61791 -473.62107 -473.60397 -474.17131 -474.14958 -472.90361 -472.89667 -473.61791 -473.62107 -473.60397 -474.17131 -474.14958 -472.38501 -472.36757 -473.09424 -473.09699 -473.08049 -473.64325 -473.62178 -472.38501 -472.36757 -473.09424 -473.09699 -473.08049 -473.64325 -473.62178 -472.38501 -472.36757 -473.09424 -473.09699 -473.08049 -473.64325 -473.62178 -472.38501 -472.36757 -473.09424 -473.09699 S27 63.73(0) 46.52(0) 46.35(0) 55.30(0) 55.61(0) 54.99(0) 64.12(0) 63.73(0) 46.52(0) 46.35(0) 55.30(0) 55.61(0) 54.99(0) 64.12(0) 63.73(0) 46.52(0) 46.35(0) 55.30(0) 55.61(0) 54.99(0) 64.12(0) 63.73(0) 44.85(0) 44.62(0) 53.57(0) 53.89(0) 53.26(0) 62.30(0) 61.86(0) 44.85(0) 44.62(0) 53.57(0) 53.89(0) 53.26(0) 62.30(0) 61.86(0) 44.85(0) 44.62(0) 53.57(0) 53.89(0) 53.26(0) 62.30(0) 61.86(0) 44.85(0) 44.62(0) 53.57(0) 53.89(0) 5.43 5.07 5.10 5.26 5.09 5.27 5.19 5.43 5.07 5.10 5.26 5.09 5.27 5.19 5.43 5.07 5.10 5.26 5.09 5.27 5.19 5.43 5.29 5.35 5.42 5.22 5.42 5.31 5.58 5.29 5.35 5.42 5.22 5.42 5.31 5.58 5.29 5.35 5.42 5.22 5.42 5.31 5.58 5.29 5.35 5.42 5.22 84.11 83.54 83.72 84.72 81.99 84.54 83.76 84.11 83.54 83.72 84.72 81.99 84.54 83.76 84.11 83.54 83.72 84.72 81.99 84.54 83.76 84.11 84.96 85.37 85.79 82.84 85.48 84.50 85.07 84.96 85.37 85.79 82.84 85.48 84.50 85.07 84.96 85.37 85.79 82.84 85.48 84.50 85.07 84.96 85.37 85.79 82.84 -9.85 -206.48 -210.42 -70.16 -64.09 -70.24 -14.08 -23.93 -212.32 -216.00 -70.25 -62.94 -71.77 -13.06 -23.97 -198.83 -202.24 -60.18 -55.03 -62.56 -5.35 -14.05 -194.00 -198.56 -55.86 -50.85 -58.54 -1.15 -8.79 -204.86 -208.68 -68.68 -62.79 -69.45 -13.75 -23.87 -208.35 -212.95 -67.61 -61.12 -69.48 -11.83 -22.42 -196.02 -200.43 -58.82 -53.72 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 Q_M4 Q_N2 Q_N3 Q_D2 Q_D3 Q_M2 Q_M3 Q_M4 Q_N2 Q_N3 Q_D2 Q_D3 Q_M2 Q_M3 Q_M4 Q_N2 Q_N3 Q_D2 Q_D3 Q_M2 Q_M3 Q_M4 Q_N2 Q_N3 Q_D2 Q_D3 Q_M2 Q_M3 Q_M4 Q_N2 Q_N3 Q_D2 Q_D3 Q_M2 Q_M3 Q_M4 Q_N2 Q_N3 Q_D2 Q_D3 Q_M2 Q_M3 Q_M4 Q_N2 Q_N3 Q_D2 Q_D3 Cs Cs C2v Cs C1 Cs C2v Cs Cs C2v Cs C1 Cs C2v Cs Cs C2v Cs C1 Cs C2v Cs Cs C2v Cs C1 Cs C2v Cs Cs C2v Cs C1 Cs C2v Cs Cs C2v Cs C1 Cs C2v Cs Cs C2v Cs C1 PBE PBE PBE BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 BVP86 M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X Klamt Klamt Klamt UFF UFF UFF UFF UFF UFF UFF UAKS UAKS UAKS UAKS UAKS UAKS UAKS Pauling Pauling Pauling Pauling Pauling Pauling Pauling Klamt Klamt Klamt Klamt Klamt Klamt Klamt UFF UFF UFF UFF UFF UFF UFF UAKS UAKS UAKS UAKS UAKS UAKS UAKS Pauling Pauling -473.08049 -473.64325 -473.62178 -472.94624 -472.92986 -473.65654 -473.65938 -473.64278 -474.20647 -474.18493 -472.94624 -472.92986 -473.65654 -473.65938 -473.64278 -474.20647 -474.18493 -472.94624 -472.92986 -473.65654 -473.65938 -473.64278 -474.20647 -474.18493 -472.94624 -472.92986 -473.65654 -473.65938 -473.64278 -474.20647 -474.18493 -472.86642 -472.85893 -473.57744 -473.58409 -473.56607 -474.13281 -474.10786 -472.86642 -472.85893 -473.57744 -473.58409 -473.56607 -474.13281 -474.10786 -472.86642 -472.85893 S28 53.26(0) 62.30(0) 61.86(0) 44.85(0) 44.28(0) 53.47(0) 53.80(0) 53.16(0) 62.19(0) 61.75(0) 44.85(0) 44.28(0) 53.47(0) 53.80(0) 53.16(0) 62.19(0) 61.75(0) 44.85(0) 44.28(0) 53.47(0) 53.80(0) 53.16(0) 62.19(0) 61.75(0) 44.85(0) 44.28(0) 53.47(0) 53.80(0) 53.16(0) 62.19(0) 61.75(0) 47.78(0) 47.48(0) 56.55(0) 56.91(0) 56.25(0) 65.28(0) 64.85(0) 47.78(0) 47.48(0) 56.55(0) 56.91(0) 56.25(0) 65.28(0) 64.85(0) 47.78(0) 47.48(0) 5.42 5.31 5.58 5.25 5.53 5.43 5.22 5.42 5.32 5.59 5.25 5.53 5.43 5.22 5.42 5.32 5.59 5.25 5.53 5.43 5.22 5.42 5.32 5.59 5.25 5.52 5.43 5.22 5.42 5.32 5.59 4.97 5.09 5.16 5.00 5.18 5.13 5.39 4.97 5.09 5.16 5.00 5.18 5.13 5.39 4.97 5.09 85.48 84.50 85.07 84.65 87.36 85.84 82.84 85.51 84.53 85.13 84.65 87.35 85.84 82.84 85.51 84.53 85.13 84.65 87.35 85.84 82.84 85.51 84.53 85.13 84.65 87.35 85.84 82.84 85.51 84.53 85.13 82.92 83.71 84.08 81.44 84.01 83.39 83.85 82.92 83.71 84.08 81.44 84.01 83.39 83.85 82.92 83.71 -61.24 -4.71 -13.15 -194.92 -199.75 -56.22 -51.37 -58.95 -1.21 -9.09 -205.81 -209.87 -69.09 -63.18 -69.82 -14.06 -23.86 -209.63 -214.52 -68.23 -61.59 -70.12 -11.99 -22.67 -196.98 -201.61 -59.20 -54.06 -61.66 -4.75 -13.22 -200.53 -204.87 -59.39 -53.79 -62.19 -2.58 -10.87 -210.55 -215.21 -72.61 -66.32 -72.88 -15.16 -24.83 -217.74 -222.15 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 Q_M2 Q_M3 Q_M4 Q_N2 Q_N3 Q_D2 Q_D3 Q_M2 Q_M3 Q_M4 Q_N2 Q_N3 a Cs C2v Cs Cs C2v Cs C1 Cs C2v Cs Cs C2v M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X M052X Pauling Pauling Pauling Pauling Pauling Klamt Klamt Klamt Klamt Klamt Klamt Klamt -473.57744 -473.58409 -473.56607 -474.13281 -474.10786 -472.86642 -472.85893 -473.57744 -473.58409 -473.56607 -474.13281 -474.10786 56.55(0) 56.91(0) 56.25(0) 65.28(0) 64.85(0) 47.78(0) 47.48(0) 56.55(0) 56.91(0) 56.25(0) 65.28(0) 64.85(0) 5.16 5.00 5.18 5.13 5.39 4.97 5.09 5.16 5.00 5.18 5.13 5.39 84.08 81.44 84.01 83.39 83.85 82.92 83.71 84.08 81.44 84.01 83.39 83.85 -73.30 -65.67 -74.82 -14.14 -25.33 -202.76 -206.83 -62.57 -56.69 -65.08 -6.35 -15.11 b Point group. Zero-point energies and number of imaginary frequencies. c d e Thermal corrections to 298K. Entropies. Free energy of solvation sum is the energy difference between gaseous and aqueous state and total nonelectrostatic contribution. A correction factor of 1.89 kcal/mol should be added to the calculated values to account for the change of state from 1 mol/atm (24.47 L at 298 K in gas phase) to 1 mol/L (aqueous phase). f g Calculation based on cc-pVTZ basis set. Calculation based on cc-pVTZ h basis set. The series of neutral, monoanion, and dianion isomers based on symbols in Scheme 2. S29 Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 Table S3. Atomic Radii for Cavity Models UFF UAKSa Pauling Klamt SMD Hydrogen 1.443 1.000 1.200 1.300 1.200 Carbon 1.925 1.500 1.500 2.000 1.850 Nitrogen 1.830 1.500 1.500 1.830 1.890 Oxygen 1.750 1.500 1.400 1.720 1.520 Fluorine 1.682 1.500 1.350 1.720 1.730 Phosphorus 2.074 1.980 1.900 1.800 2.100 Sulfur 2.018 1.980 1.850 2.160 2.490 Vanadium 1.572 2.008 1.572 1.900 Arsenic 2.115 2.115 2.000 1.900 Iron 1.456 1.456 1.456 1.900 a In the atom topological model (UATM), the hydrogen atoms are enclosed in the same sphere of the heavy atom they are bound to, and the sphere radii are set according to the atomic number, the charge and the hybridization of the atom, possibly corrected for first neighbor effects. The UAKS valuesb are UATM basis radii optimized for PBE0/6-31G(d). environment modifies the actual radii. J Chem Phys 1997, 107, 3210. S30 b The molecular Barone, V.; Cossi, M.; Tomasi, J. Supplementary Material (ESI) for Physical Chemistry Chemical Physics This journal is (c) The Owner Societies 2011 Table S4. G4MP2 level of theory for free energies (Ggas) of H2Fe(CO)4, H1Fe(CO)4-, and Fe(CO)42- (hartree unit) H2Fe(CO)4 H1Fe(CO)4- Fe(CO)42- -1715.99603 -1715.46509 -1714.74594 -1716.90714 -1716.54064 -1715.97107 -1715.93547 -1715.54683 -1714.97090 -1715.99603 -1715.46509 -1714.74594 CCSD(T)/m6-31G(d)+rel -1723.32529 -1722.79726 -1722.07780 HF/3 -1714.53061 -1713.94246 -1713.17675 HF/4 -1714.56355 -1713.97429 -1713.20742 Extrapolation -1714.57157 -1713.98204 -1713.21490 HF/G3LargeXP -1714.50112 -0.24780 -1713.91264 -0.24780 -1713.14614 -0.24780 ZPE B3LYP/m6-31G(2df,p)b 0.04907 0.04017 0.03194 T.C. B3LYP/m6-31G(2df,p)b 0.01088 0.01066 0.01031 c b -0.04650 -0.04635 -0.04491 -1724.60176 -1724.10380 -1723.39720 Steps Method E(CCSD(T)) CCSD(T)/m6-31G(d)a a •E(MP2) MP2/G3MP2LargeXP a MP2/m6-31G(d) •E(rel) CCSD(T)/m6-31G(d)a a •E(HF) E(HLC) -T•S B3LYP/m6-31G(2df,p) G(G4MP2) a For MP2 and CCSD(T) level of theory, the number of frozen orbital is 13 b In frequency (1s,2s,2p orbitals for Fe and 1s orbital for C and O). calculation process, scale factor 0.9854 is applied for every c thermochemical properties. T=298.15K. S31
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