From 0ffd9ac4ad322aa709942b6d269f365f31c3ca95 Mon Sep 17 00:00:00 2001 From: sjplimp Date: Fri, 22 Oct 2010 22:22:44 +0000 Subject: [PATCH] git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@5111 f3b2605a-c512-4ea7-a41b-209d697bcdaa --- doc/Section_howto.html | 84 +++++++++++++++++++++++++++++++++++++++++- doc/Section_howto.txt | 81 +++++++++++++++++++++++++++++++++++++++- 2 files changed, 163 insertions(+), 2 deletions(-) diff --git a/doc/Section_howto.html b/doc/Section_howto.html index 9615a86166..6fc10741c4 100644 --- a/doc/Section_howto.html +++ b/doc/Section_howto.html @@ -31,7 +31,8 @@ certain kinds of LAMMPS simulations. 4.15 Output from LAMMPS (thermo, dumps, computes, fixes, variables)
4.16 Thermostatting, barostatting and computing temperature
4.17 Walls
-4.18 Elastic constants
+4.18 Elastic constants
+4.19 Computing free energies from thermodyanmic integration

The example input scripts included in the LAMMPS distribution and highlighted in this section also show how to @@ -1609,6 +1610,72 @@ converge and requires careful post-processing (Shinoda)

+

4.19 Computing free energies from thermodynamic integration +

+

Thermodynamic integration is a widely used method to compute free +energies from atomistic simulations. LAMMPS can be used to run +thermodynamic integration calculations using the methods discussed in +this section and the fix adapt command. Currently, +it is capable of the transformations essential for computing melting +points using the pseudo-supercritical path method developed by Eike +and Maginn. +

+

See the examples/TI directory for more information and sample files +that compute a melting point using the techniques described in this +section. That directory has its own README file. See also the paper +by Jayaraman for an example of using this implementation +of thermodynamic integration in LAMMPS to compute melting points of +alkali nitrate salts, using the steps outlined here. +

+

In this method, three intermediate "pseudo-supercritical" states are +accessed in the transformation between the liquid and solid +phases. These pseudo-states are a weak liquid, a dense weak liquid, +and an ordered weak phase. The transformation between the liquid and +solid states can also be driven uisng the fix adapt +command. +

+

For the transformation from the liquid to the weak phase, the +intermolecular interactions need to be weakened. Appropriate scale +factors, computed by variables you define, and applied to pair styles +by fix adapt, can be used to do this, as in the +example scripts. The compute ti command can +accumulate the value of dU/dlambda. See Jayaraman and +Maginn for more information about calculating a +free energy from dU/dlambda. +

+

IMPORTANT NOTE: The pair styles that fix adapt can scale on-the-fly +are listed on the fix adapt doc page. interaction scaling +is desired. If a pair style is not on that list, it is generally +quite easy to add an extract() method to the pair style, to enable fix +adapt to rescale it. +

+

Step 2 is the transformation of the simulation box density from the +liquid phase to that of the equilibrated crystal. The parameters for +box1 and box2 should be obtained from equilibrated NPT simulations of +the liquid and crystal phases and used in a fix +deform command to change the box size and/or shape. +It also advisable to use fix adapt on the pair styles +to prevent overlaps which may occur during the box transformation. +

+

In step 3, the dense, weak system is transformed to an ordered state, +which has the same ordering as in the equilibrated crystal. Ordering +is achieved by introducing an attractive potential between atoms and +lattice sites. These lattice sites can be calculated as the mean +positions of the atoms in an equilibrium simulation of the +crystal. The pair/gauss command can be used to +introduce an attractive Gaussian potential between the atoms and their +corresponding lattice sites. The prefactor of the Gaussian pair +potential can be scaled by fix adapt to turn on the +attractions. Again, the quantity dU/dlambda can be tracked via the +compute ti command. +

+

Step 4 is the transformation of the ordered state to the final +crystal. In this step, the intermolecular interactions are scaled +back to full strength, while the Gaussian tethers are removed, all via +fix adapt. +

+
+
@@ -1644,4 +1711,19 @@ Phys, 79, 926 (1983).

(Shinoda) Shinoda, Shiga, and Mikami, Phys Rev B, 69, 134103 (2004).

+ + +

(Eike and Maginn) Eike and Maginn, J Chem Phys, 124, +164503 (2006). +

+ + +

(Jayaraman and Maginn) Jayaraman and Maginn, Journal of Chemical Physics, +127, 214504 (2007). +

+ + +

(Jayaraman) Jayaraman, Thompson, von Lilienfeld and Maginn, Industrial +and Engineering Chemistry Research, 49, 559-571 (2010). +

diff --git a/doc/Section_howto.txt b/doc/Section_howto.txt index 335dc255b3..22ab363dce 100644 --- a/doc/Section_howto.txt +++ b/doc/Section_howto.txt @@ -28,7 +28,8 @@ certain kinds of LAMMPS simulations. 4.15 "Output from LAMMPS (thermo, dumps, computes, fixes, variables)"_#4_15 4.16 "Thermostatting, barostatting and computing temperature"_#4_16 4.17 "Walls"_#4_17 -4.18 "Elastic constants"_#4_18 :all(b) +4.18 "Elastic constants"_#4_18 +4.19 "Computing free energies from thermodyanmic integration"_#4_19 :all(b) The example input scripts included in the LAMMPS distribution and highlighted in "this section"_Section_example.html also show how to @@ -1595,6 +1596,72 @@ tensor. Another approach is to sample the triclinic cell fluctuations that occur in an NPT simulation. This method can also be slow to converge and requires careful post-processing "(Shinoda)"_#Shinoda +:line + +4.19 Computing free energies from thermodynamic integration :link(4_19),h4 + +Thermodynamic integration is a widely used method to compute free +energies from atomistic simulations. LAMMPS can be used to run +thermodynamic integration calculations using the methods discussed in +this section and the "fix adapt"_fix_adapt.html command. Currently, +it is capable of the transformations essential for computing melting +points using the pseudo-supercritical path method developed by "Eike +and Maginn"_#Eike_Maginn. + +See the examples/TI directory for more information and sample files +that compute a melting point using the techniques described in this +section. That directory has its own README file. See also the paper +by "Jayaraman"_#Jayaraman for an example of using this implementation +of thermodynamic integration in LAMMPS to compute melting points of +alkali nitrate salts, using the steps outlined here. + +In this method, three intermediate "pseudo-supercritical" states are +accessed in the transformation between the liquid and solid +phases. These pseudo-states are a weak liquid, a dense weak liquid, +and an ordered weak phase. The transformation between the liquid and +solid states can also be driven uisng the "fix adapt"_fix_adapt.html +command. + +For the transformation from the liquid to the weak phase, the +intermolecular interactions need to be weakened. Appropriate scale +factors, computed by variables you define, and applied to pair styles +by "fix adapt"_fix_adapt.html, can be used to do this, as in the +example scripts. The "compute ti"_compute_ti.html command can +accumulate the value of dU/d{lambda}. See "Jayaraman and +Maginn"_#Jayaraman_Maginn for more information about calculating a +free energy from dU/d{lambda}. + +IMPORTANT NOTE: The pair styles that fix adapt can scale on-the-fly +are listed on the "fix adapt"_fix_adapt doc page. interaction scaling +is desired. If a pair style is not on that list, it is generally +quite easy to add an extract() method to the pair style, to enable fix +adapt to rescale it. + +Step 2 is the transformation of the simulation box density from the +liquid phase to that of the equilibrated crystal. The parameters for +box1 and box2 should be obtained from equilibrated NPT simulations of +the liquid and crystal phases and used in a "fix +deform"_fix_deform.html command to change the box size and/or shape. +It also advisable to use "fix adapt"_fix_adapt.html on the pair styles +to prevent overlaps which may occur during the box transformation. + +In step 3, the dense, weak system is transformed to an ordered state, +which has the same ordering as in the equilibrated crystal. Ordering +is achieved by introducing an attractive potential between atoms and +lattice sites. These lattice sites can be calculated as the mean +positions of the atoms in an equilibrium simulation of the +crystal. The "pair/gauss"_pair_gauss.html command can be used to +introduce an attractive Gaussian potential between the atoms and their +corresponding lattice sites. The prefactor of the Gaussian pair +potential can be scaled by "fix adapt"_fix_adapt.html to turn on the +attractions. Again, the quantity dU/d{lambda} can be tracked via the +"compute ti"_compute_ti.html command. + +Step 4 is the transformation of the ordered state to the final +crystal. In this step, the intermolecular interactions are scaled +back to full strength, while the Gaussian tethers are removed, all via +"fix adapt"_fix_adapt.html. + :line :line @@ -1623,3 +1690,15 @@ Phys, 79, 926 (1983). :link(Shinoda) [(Shinoda)] Shinoda, Shiga, and Mikami, Phys Rev B, 69, 134103 (2004). + +:link(Eike_Maginn) +[(Eike and Maginn)] Eike and Maginn, J Chem Phys, 124, +164503 (2006). + +:link(Jayaraman_Maginn) +[(Jayaraman and Maginn)] Jayaraman and Maginn, Journal of Chemical Physics, +127, 214504 (2007). + +:link(Jayaraman) +[(Jayaraman)] Jayaraman, Thompson, von Lilienfeld and Maginn, Industrial +and Engineering Chemistry Research, 49, 559-571 (2010).