Molecular Dynamics Simulation of Water

Molecular Dynamics Water Simulator Test (1-3-95)

Results for Water simulations using the SPC and SPC/E models and with temperature and pressure coupling using the Berendsen coupling technique.

Note: (2/2/2008) This old open source C code is a test of a molecular dynamics simulation of water using the Berendsen Water model. Updated the code (Took out some old archaic code) on 2/2/2008,,, And 13 years later it still runs!

Contents

Source Code

  • Water2a.c — open source.c file (Molecular Dynamics simulation software source)

Notes:

  1. The ensemble is not defined for Berendsen coupling technique. (labeled below “NPT” for convenience)
  2. Cv not valid during NPT ensemble, also since not a true NPT ensemble Cp cannot be calculated correctly.
  3. Velocity AutoCorrelation Coef. (uses Oxygen velocity, not center of mass velocity)
  4. Virial and kinetic energy, calculated using atomic interactions, instead of center of mass. (This will cause larger fluctuations in pressure [per Berendsen et al, 1984].)
  5. Pressure fluctuations became unstable when used isothermal compressibility value much above 2.0e-10.
  6. Property definations:
    • KE,PE,E: in Kcal/mole
    • P: pressure in Bar
    • T: temperature in Kelvin
    • V: volume (meters cubed)
    • Hbonds: average # of hydrogen bonds per molecule (EPD < -2.8 kcal/mol)
    • Density: density (gm/cm cubed)
    • Cv: specific heat (constant volume, Joules/mole)
    • D: self-diffusion coef. (10-9 metersq/sec)
    • <XXXrms>: rms values (fluctuations)
    • gOO,gOH: Radial Pair Distribution, positionAngstrom(height)
    • EPD: Interaction Energy (Energy Pair Dist) (kcal/mol)
    • VACF: Velocity AutoCorrelation function (femptoseconds,fs)
    • Runlength: (in picoseconds)
    • time step (dt): 5e-016 sec. (for Prevost runs = 2e-15)
    • Leonard-jones sigma: 3.16556e-010
    • Leonard-jones epslon: 1.07935e-021
    • bondlength H-O: 1e-010
    • bondangle: 109.47
    • virtualbondlen H-H: 1.63298e-010
    • rcut: 8.5e-010
    • tt: coupling coef for temp .1ps
    • pt: coupling coef for press .1ps
    • isothermal compressibility: 2.0e-10 [berendsen 1984] uses 4.9e-10]
    • To Convert Kcal/mole to Kjoule/mole : kcal/mole x 4.1858 = kj/mole

Results

Simulation results from literature:

               Prevost     Prevost      Prevost
Property       SPC(ewald)  SPC(mei4)    TIPS(ewald)   Exp
----------     ----------  ----------   -----------   ---------
Ensemble       NVE         NVE          NVE            -
T target        -           -            -             -
P target        -           -            -             -
RunLength       -           -            -             -
<KE>            -           -            -             -
<PE>           -9.43       -8.99        -8.11         -9.90
<E>             -           -            -             -
<P>             -           -            -             -
<PV/NKT>       1.3         2.0          .75            -
<T>            299         297          293           300
<V>            6.47e-27
<Hbonds>        -           -            -             -
<Density>      1.00        1.00         1.00           -
Cv             77.4        68.5         68.0          75.1
D              4.69        4.70         6.69          2.40
<KErms>         -           -            -             -
<PErms>         -           -            -             -
<Erms>          -           -            -             -
<Prms>          -           -            -             -
<Trms>          -           -            -             -
<Vrms>          -           -            -             -
gOO Zero1       -          2.5           -             -
gOO Max1       2.75(2.8)   2.75(2.66)   2.79(2.46)    2.85(2.3)
gOO Zero2       -          3.2           -             -
gOO Min1        -          3.8 (.94)     -             -
gOO Zero3       -          4.1           -             -
gOO Max2        -          4.5 (1.04)    -             -
gOH Zero1       -          1.7           -             -
gOH Max1       1.75(1.35)  1.80(1.30)   1.80(1.10)    1.97(1.19)
gOH Zero2       -          1.95          -             -
gOH Min1        -          2.3(.22)      -             -
gOH Zero3       -          3.0           -             -
gOH Max2        -          3.3(1.5)      -             -
EPDmin         -2.9        -2.9          -             -
EPDmax         -4.9        -4.9          -             -
VACFmin1       100         100           100           -
VACFmax1       130         130           130           -
VACFzero1      200         200           250           -
VACFmin2       340         340           400           -

Simulation results from simulator:

Property       Water-run1  Water-run2  Water-run3  Water-run4  Water-run5
----------     ----------  ----------  ----------  ----------  ----------
Ensemble       NPT         NPT         NPT         NPT         NPT
T target       300         300         300         300         300
P target       1000        100         10          4           1
RunLength      7           11          12          19.5        12
<KE>           1.78        1.78        1.78        1.78        1.78
<PE>           -9.60       -9.55       -9.54       -9.54       -9.55
<E>            -7.82       -7.77       -7.76       -7.76       -7.77
<P>            972         94          9.9         1.81        1.8
<PV/NKT>       .68         .07         .01         .005        .005
<T>            299.8       299.76      299.64      299.67      299.82
<V>             -           -          6.42e-27    6.42E-27    6.44e-27
<Hbonds>       2.98        3.16        2.95        2.86        3.04
<Density>      1.04        1.01        1.01        1.01        1.00
Cv              NA          NA         NA           NA         NA
D              4.23        3.98        3.31        3.99        4.13
<KErms>        .048        .050        .048        .049        .048
<PErms>        .055        .063        .072        .061        .070
<Erms>         .028        .039        .053        .036        .051
<Prms>         500         491         495         511         462
<Trms>         8.1         8.4         8.1         8.3         8.1
<Vrms>          -           -          7.02e-29    8.09e-29    5.45e-29
gOO Zero1      2.6         2.6         2.6         2.6         2.6
gOO Max1       2.76(2.74)  2.76(2.76)  2.76(2.77)  2.76(2.75)  2.76(2.83)
gOO Zero2      3.52        3.26        3.26        3.30        3.24
gOO Min1       3.72(.95)   3.6(.918)   3.7(.948)   3.56(.934)  3.62(.933)
gOO Zero3      4.84        4.16        4.12        4.22        4.14
gOO Max2       4.84(1.00)  4.44(1.03)  4.48(1.03)  4.62(1.03)  4.50(1.05)
gOH Zero1      1.68        1.68        1.68        1.68        1.68
gOH Max1       1.78(1.35)  1.78(1.38)  1.78(1.37)  1.78(1.37)  1.78(1.40)
gOH Zero2      1.96        1.92        1.92        1.92        1.92
gOH Min1       2.38(.26)   2.36(.24)   2.42(.25)   2.42(.25)   2.42(.24)
gOH Zero3      2.94        2.96        2.96        2.96        2.96
gOH Max2       3.24(1.53)  3.24(1.51)  3.26(1.53)  3.26(1.52)  3.24(1.54)
EPDmin         -2.9        -2.88       -2.82       -2.84       -2.84
EPDmax         -4.86       -4.94       -4.98       -4.92       -4.92
VACFmin1        -           -          92.5        92.5        92.5
VACFmax1        -           -          130.0       130.0       130.0
VACFzero1       -           -          180         177.5       180
VACFmin2        -           -          242.5       340.0       242.5

Simulation results from simulator:

Started from a previous NPT run with these targets

Property       Water-run6  Water-run7  Water-run8  Water-run9  Water-rn10
----------     ----------  ----------  ----------  ----------  ----------
Ensemble       NVE         NVE         NVE         NVE         NPT
T target       300*        300*        300*        300*        300
P target        ?          10*         4*          1*          2770
RunLength      13          25          20          22          22.5
<KE>           1.77        1.84        1.77        1.80        1.78
<PE>           -9.51       -9.42       -9.57       -9.49       -9.64
<E>            -7.74       -7.57       -7.80       -7.69       -7.86
<P>            -101        64.59       112.4       -18.8       2748
<PV/NKT>       -.07        .17         .08         -.014       1.81
<T>            297.11      309.25      297.0       302.94      299.67
<V>            6.47e-27    6.42e-27    6.42e-27    6.44e-27     -
<Hbonds>       3.07        2.90        3.06        2.79        3.04
<Density>      1.00        1.01        1.01        1.00        1.10
Cv             67.7        63.7        70.1        67.4         NA
D              4.07        4.31        3.57        4.48        4.09
<KErms>        .057        .057        .058        .058        .049
<PErms>        .057        .057        .058        .058        .075
<Erms>         .002        .002        .002        .002        .056
<Prms>         775         786         801         873         513
<Trms>         9.6         9.6         9.8         9.8         8.3
<Vrms>          0          0.00        0.0         0.0         -
gOO Zero1      2.6         2.6         2.6         2.6         2.6
gOO Max1       2.76(2.77)  2.76(2.68)  2.76(2.78)  2.76(2.74)  2.76(2.66)
gOO Zero2      3.28        3.34        3.24        3.28        3.66
gOO Min1       3.56(.928)  3.66(.937)  3.68(.927)  3.68(.938)  4.12(.93)
gOO Zero3      4.12        4.36        4.20        4.14        5.5
gOO Max2       4.26(1.02)  4.54(1.02)  4.56(1.03)  4.58(1.03)  6.12(1.03)
gOH Zero1      1.7         1.70        1.68        1.68        1.7
gOH Max1       1.80(1.37)  1.78(1.32)  1.78(1.38)  1.78(1.35)  1.78(1.29)
gOH Zero2      1.92        1.92        1.92        1.92        1.9
gOH Min1       2.38(.25)   2.40(.24)   2.40(.24)   2.40(.25)   2.36(.27)
gOH Zero3      2.96        2.96        2.96        2.96        2.92
gOH Max2       3.26(1.52)  3.26(1.50)  3.26(1.52)  3.26(1.52)  3.24(1.53)
EPDmin         -3.02       -2.9        -2.82       -2.94       -3.02
EPDmax         -4.86       -4.86       -5.04       -4.90       -4.86
VACFmin1       92.5        95.0        92.5        97.5         -
VACFmax1       127.5       130.0       130.0       130.0        -
VACFzero1      185         185         182.5       187.5        -
VACFmin2       377.5       317.5       232.5       312.5        -

Simulation results from simulator:

Property       Water-rn11  Water-rn12  Water-rn13
----------     ----------  ----------  ----------
Ensemble       NPT         NPT         NPT
T target       300         300         300
P target       10          4           1
RunLength      33.5        28.5        33.5
<KE>           1.78        1.78        1.78
<PE>           -10.68      -10.68      -10.68
<E>            -8.90       -8.89       -8.89
<P>            3.74        -0.33       -3.1
<PV/NKT>       .007        .003        .001
<T>            299.83      299.79      299.82
<V>            6.29e-27    6.30e-27    6.31e-27
<Hbonds>       3.31        3.35        3.3
<Density>      1.03        1.03        1.02
Cv              NA          NA          NA
D              2.71        2.92        2.73
<KErms>        .052        .052        .050
<PErms>        .076        .086        .080
<Erms>         .059        .072        .067
<Prms>         511         523         500
<Trms>         8.7         8.77        8.3
<Vrms>         8.06e-29    6.5e-29     8.0e-29
gOO Zero1      2.58        2.58        2.58
gOO Max1       2.74(2.93)  2.74(2.99)  2.74(3.00)
gOO Zero2      3.10        3.10        3.10
gOO Min1       3.36(.872)  3.32(.874)  3.30(.860)
gOO Zero3      4.08        3.98        4.00
gOO Max2       4.32(1.05)  4.50(1.07)  4.38(1.07)
gOH Zero1      1.66        1.66        1.66
gOH Max1       1.76(1.51)  1.76(1.54)  1.76(1.54)
gOH Zero2      1.90        1.90        1.90
gOH Min1       2.38(.198)  2.40(.200)  2.40(.198)
gOH Zero3      2.96        2.96        2.96
gOH Max2       3.24(1.55)  3.24(1.57)  3.22(1.57)
EPDmin         -2.92       -3.06       -2.96
EPDmax         -5.46       -5.48       -5.38
VACFmin1       85.0        85.0        85.0
VACFmax1       122.5       122.5       125.0
VACFzero1      162.5       162.5       165.0
VACFmin2       297.5       292.5       292.5

Simulation results from simulator:

Started from previous a NPT run with these targets

               spc/e       spc/e       spc/e
Property       Water-rn14  Water-rn15  Water-rn16  Water-rn17  Water-rn18
----------     ----------  ----------  ----------  ----------  ----------
Ensemble       NVE         NVE         NVE         NPT         NVE
T target       300*        300*        300*        300         300*
P target       10*         4*          1*          10          10*
RunLength       6          11           6          80          80
<KE>           1.97        1.80        1.79        1.78        1.99
<PE>           -10.31      -10.62      -10.63      -9.53       -9.13
<E>            -8.34       -8.82       -8.84       -7.74       -7.13
<P>            312         142.53      -22.47      10.7        396.7
<PV/NKT>       .20         .10         -.02        .01         .26
<T>            331         302.2       300.6       299.66      334.99
<V>            6.29e-27    6.30e-27    6.31e-27    6.45e-27    6.45e-27
<Hbonds>       3.13        3.46        3.3         3.04        2.81
<Density>      1.03        1.03        1.02        1.00        1.00
Cv             70.3        72.7        71.4        NA          65.4
D              2.81        3.04        2.68        4.42        5.55
<KErms>        .065        .060        .059        .050        .063
<PErms>        .065        .060        .059        .070        .063
<Erms>         .002        .002        .002        .050        .002
<Prms>         1027        884         919         493         865
<Trms>         10.9        10.1        10.0        8.4         10.6
<Vrms>         0            0           0          6.45e-29    0.00
gOO Zero1      2.6         2.58        2.58        2.6         2.6
gOO Max1       2.74(2.71)  2.74(2.97)  2.74(2.95)  2.76(2.80)  2.76(2.52)
gOO Zero2      3.24        3.12        3.14        3.28        3.48
gOO Min1       3.54(.912)  3.44(.883)  3.34(.891)  3.6(.953)   3.86(.950)
gOO Zero3      4.08        4.04        3.90        4.08        6.10
gOO Max2       4.40(1.04)  4.36(1.07)  4.22(1.05)  4.50(1.04)  6.48(1.00)
gOH Zero1      1.68        1.66        1.66        1.68        1.70
gOH Max1       1.76(1.36)  1.76(1.52)  1.76(1.52)  1.78(1.39)  1.80(1.20)
gOH Zero2      1.90        1.90        1.90        1.92        1.90
gOH Min1       2.38(.25)   2.38(.20)   2.36(.20)   2.40(.25)   2.40(.30)
gOH Zero3      2.94        2.96        2.96        2.96        2.96
gOH Max2       3.26(1.51)  3.24(1.56)  3.24(1.55)  3.26(1.54)  3.26(1.47)
EPDmin         -3.02       -3.06       -2.92       -2.88       -3.04
EPDmax         -5.24       -5.56       -5.44       -4.92       -4.72
VACFmin1       90.0        85.0        92.5        92.5        97.5
VACFmax1       130.0       122.5       127.5       130.0       127.5
VACFzero1      172.5       165.0       167.5       182.5       200.0
VACFmin2       297.5       307.5       212.5       320.0       325.0

References:

  • Prevost, et al. – Mol Physics 1990, 71(3): 587-603 (MEI4, F1)
  • Berendsen, et al. – J phys chem, 1987, 91: 6269-6271 (SPC/E)
  • Brooks et al – J chem phys 1985, 83(11): 5897 (MEI4)
  • Berendsen, et al. – J chem phys, 1984, 81(8): 3684 (Temp/Press Bath)
  • Jorgensen, et al. – J phys chem, 1983, 79(2): 926 (TIPS water)
  • Berendsen, et al. – Intermolecular Forces 1981, 331-342 (SPC water)
  • Allen-Tildesley – computer simulation of liquids

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