This is the additional material for the paper:


Free energies of Hydration from Thermodynamic Integration:
Comparison of Molecular Mechanics Force Fields and Evaluation of Calculation Accuracy

V.Helms and R.C.Wade, J.Comp.Chem. (1997) 18, 449-462.

European Molecular Biology Laboratory, Heidelberg, Germany


The aim of this additional material is to provide access to energy values calculated from computationally expensive molecular dynamics simulations. We hope that they might be useful in other applications, e.g. the development of linear free energy methods.

  • Unscaled ESP charges were determined from an HF/6-31G* calculation + CHELPG, they are named 1.0 x ESP charges. 0.8 x ESP and 0.6 x ESP charges are scaled ESP charges by 0.8 and 0.6.
  • Interaction energies were calculated during 100 ps of MD simulation.
  • Note the approximate linear relationship between interaction energies and hydration free energies that supports the application of a linear free energy approach.

    ACETONE

    electrostatic energies between acetone and solvent during MD equilibration [kJ/mol]
    1.0 x ESP0.8 x ESP0.6 x ESP
    CHARMM-49.8 -29.4 -15.6
    OPLS_SPCE-64.6 -39.1 -16.4
    OPLS_TIP3P-58.4 -34.6 -18.4
    CVFF-65.0 -38.7 -19.1
    GROMOS87-62.0 -34.2 -16.3
    GROMOS_690-56.4 -34.0 -14.8
    GROMOS_POL-55.2 -31.2 -15.1
    Lennard Jones energies between acetone and solvent during MD equilibration [kJ/mol]
    1.0 x ESP0.8 x ESP0.6 x ESP
    CHARMM-48.1 -50.2 -51.6
    OPLS_SPCE-29.1 -33.4 -35.6
    OPLS_TIP3P-28.3 -32.1 -33.9
    CVFF-37.4 -41.1 -43.3
    GROMOS87-40.0 -44.1 -46.9
    GROMOS_690-28.6 -31.4 -34.4
    GROMOS_POL-25.2 -28.9 -31.7
    deltaGhydr (longest simulation for each system) [kJ/mol]
    1.0 x ESP0.8 x ESP0.6 x ESP
    CHARMM-28.4 -18.9 -12.3
    OPLS_SPCE-19.2 -5.5 +2.8
    OPLS_TIP3P-16.5 -8.1 -2.7
    CVFF-28.2 -17.1 -8.3
    GROMOS87-34.0 -24.5 -15.1
    GROMOS_690-17.9 -6.3 +1.0
    GROMOS_POL-13.2 -1.7 +4.4


    DIMETHYL ETHER

    electrostatic energies between dimethyl ether and solvent during MD equilibration [kJ/mol]
    1.0 x ESP0.8 x ESP0.6 x ESP
    CHARMM-23.3 -14.2 -7.8
    OPLS_SPCE-31.0 -17.9 -7.9
    OPLS_TIP3P-28.3 -17.0 -8.2
    CVFF-31.3 -17.7 -9.0
    GROMOS87-24.4 -12.7 -6.3
    GROMOS_690-22.7 -13.7 -6.0
    GROMOS_POL-23.0 -12.8 -5.5
    Lennard Jones energies between dimethyl ether and solvent during MD equilibration [kJ/mol]
    1.0 x ESP0.8 x ESP0.6 x ESP
    CHARMM-41.6 -41.2 -42.3
    OPLS_SPCE-24.0 -26.9 -28.3
    OPLS_TIP3P-23.9 -26.4 -27.3
    CVFF-33.3 -35.7 -36.0
    GROMOS87-37.7 -39.1 -40.2
    GROMOS_690-26.9 -27.1 -29.5
    GROMOS_POL-24.0 -25.6 -26.9
    deltaGhydr (longest simulation for each system) [kJ/mol]
    1.0 x ESP0.8 x ESP0.6 x ESP
    CHARMM-12.2 -7.0 -5.6
    OPLS_SPCE+1.5 +3.4 +5.7
    OPLS_TIP3P-2.0 +2.3 +5.2
    CVFF-11.1 -4.6 -2.9
    GROMOS87-17.4 -13.3 -11.7
    GROMOS_690-3.2 +2.2 +3.5
    GROMOS_POL+1.8 +5.4 +8.5


    PROPANE

    Simulations for OPLS_TIP3P only performed with 1.0 x ESP charges.
    electrostatic energies between propane and solvent during MD equilibration [kJ/mol]
    1.0 x ESP0.8 x ESP0.6 x ESP0 charges
    CHARMM-0.3 -0.2 -0.2
    OPLS_SPCE-0.3 -0.2 -0.1
    OPLS_TIP3P-0.5
    CVFF-0.3 -0.2 -0.1
    GROMOS87 0
    GROMOS_690 0
    GROMOS_POL 0
    Simulations for OPLS_TIP3P only performed with 1.0 x ESP charges.
    Lennard Jones energies between propane and solvent during MD equilibration [kJ/mol]
    1.0 x ESP0.8 x ESP0.6 x ESP0 charges
    CHARMM-46.5 -46.6 -46.4
    OPLS_SPCE-31.4 -30.9 -29.8
    OPLS_TIP3P-30.2
    CVFF-41.8 -42.2 -41.5
    GROMOS87 -47.7
    GROMOS_690 -32.9
    GROMOS_POL -29.8
    Simulations for OPLS_TIP3P only performed with 1.0 x ESP charges.
    deltaGhydr (longest simulation for each system) [kJ/mol]
    1.0 x ESP0.8 x ESP0.6 x ESP0 charges
    CHARMM-1.6 -0.9 -1.4
    OPLS_SPCE+12.1 +13.2 +9.1
    OPLS_TIP3P10.2
    CVFF+1.5 +2.2 -0.1
    GROMOS87 -11.7
    GROMOS_690 +7.6
    GROMOS_POL +15.1


    CYCLO-PROPANE


    Simulations only performed with 1.0 x ESP charges or zero charges.
    electrostatic energies between cyclopropane and solvent during MD equilibration [kJ/mol]
    1.0 x ESP0.8 x ESP0.6 x ESP0 charges
    CHARMM-3.2
    OPLS_SPCE-3.1
    OPLS_TIP3P-3.2
    CVFF-2.2
    GROMOS87 0
    GROMOS_690 0
    GROMOS_POL 0
    Simulations only performed with 1.0 x ESP charges or zero charges.
    Lennard Jones energies between cyclopropane and solvent during MD equilibration [kJ/mol]
    1.0 x ESP0.8 x ESP0.6 x ESP0 charges
    CHARMM-40.6
    OPLS_SPCE-27.5
    OPLS_TIP3P-25.9
    CVFF-38.2
    GROMOS87 -45.6
    GROMOS_690 -31.8
    GROMOS_POL -28.8
    Simulations only performed with 1.0 x ESP charges or zero charges.
    deltaGhydr (longest simulation for each system) [kJ/mol]
    1.0 x ESP0.8 x ESP0.6 x ESP0 charges
    CHARMM-3.0
    OPLS_SPCE+11.1
    OPLS_TIP3P+9.7
    CVFF-0.5
    GROMOS87 -11.9
    GROMOS_690 +6.7
    GROMOS_POL +15.6


    CAMPHOR

    electrostatic energies between camphor and solvent during MD equilibration [kJ/mol]
    1.0 x ESP0.8 x ESP0.6 x ESP
    CHARMM-46.5 -28.4 -15.0
    OPLS_SPCE-63.5 -37.9 -17.7
    OPLS_TIP3P-58.3 -33.0 -16.7
    CVFF-62.0 -34.2 -19.1
    GROMOS87-65.6 -36.6 -18.5
    GROMOS_690-62.6 -36.2 -18.5
    GROMOS_POL-60.5 -35.7 -17.4
    Lennard Jones energies between camphor and solvent during MD equilibration [kJ/mol]
    1.0 x ESP0.8 x ESP0.6 x ESP
    CHARMM-99.0 -103.8 -106.0
    OPLS_SPCE-68.9 -71.6 -75.1
    OPLS_TIP3P-65.1 -68.2 -71.5
    CVFF-90.0 -94.7 -95.5
    GROMOS87-105.5 -108.4 -111.3
    GROMOS_690-74.9 -78.0 -81.9
    GROMOS_POL-67.4 -71.7 -75.0
    deltaGhydr (longest simulation for each system) [kJ/mol]
    1.0 x ESP0.8 x ESP0.6 x ESP
    CHARMM-41.6 -27.5 -26.8
    OPLS_SPCE-23.9 -3.7 +1.6
    OPLS_TIP3P-17.7 -14.2 -3.2
    CVFF-44.0 -33.6 -28.0
    GROMOS87-66.2 -52.2 -40.2
    GROMOS_690-29.2 -17.3 -11.3
    GROMOS_POL-22.6 -10.9 -3.3


    STATISTICAL ERRORS

    Hydration free energies were calculated from MCTI calculations where the interactions between the solute molecule and the solvent box were switched off during the simulations. This was done in 21 incremental steps, so-called windows, each of which corresponds to a separate molecular dynamics simulation. The statistical error of a simulation is calculated as the square root of the sum of the squares of the statistical errors of the individual windows. Those were calculated by the ARGOS program from an analysis of the autocorrelation of the free energy gradient. In the plot, each row contains various entries that correspond to different window lengths of one simulation :
    A + B stands for windows of A equilibration steps and B data acquisition steps, A + (B < x < C) stands for windows of A equilibration steps and between B and C data acquisition steps :
    (+) 1000 + 5000, (filled diamond) 1000 + (5000 < x < 30000) , (open square) 6000 + 15000, and (cross) 6000 + (15000 < x < 30000)

    AVERAGE STATISTICAL ERROR PER WINDOW

    This plots shows how the statistical error is distributed on average over the 21 simulation windows. The width of the columns corresponds to the frequency of occurence among the 86 individual simulations. The solid line shows the average value of (1000+5000) step windows, the broken line that of (6000+15000) step windows. Note that while extending the simulation windows the average error decreases, the errors are largest in the last few windows.

    Volkhard Helms

    Rebecca Wade

    15 November 1996

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