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[lammps-users] Total energy calculation
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[lammps-users] Total energy calculation


From: Gideon Simpson <gideon.simpson@...24...>
Date: Thu, 7 Dec 2017 08:29:19 -0800

I’ve been playing with a very simple problem, a Lennard-Jones 7 cluster in 2D, and I noticed something I do not understand about the energy that is computed.  In particular, I do not understand how it’s counting bonds.  

I set up the cluster with the commands:

boundary p p p
units lj
atom_style atomic
atom_modify map array sort 0 0.0
dimension 2

region box block 0 20 0 20 0 10 units box
create_box 1 box

create_atoms 1 single 10 10 0
create_atoms 1 single 11 10 0
create_atoms 1 single 10.5 10.866025403784 0
create_atoms 1 single 9.5 10.866025403784 0
create_atoms 1 single 9 10 0
create_atoms 1 single 9.5 9.1339745962156 0
create_atoms 1 single 10.5 9.1339745962156 0

mass 1 1.0
pair_style lj/cut 2.5
pair_coeff 1 1 1.0 1.0
pair_modify shift yes
neighbor 0.3 bin
neigh_modify delay 0 every 1 check yes
fix 99 all enforce2d
run 0
thermo 1
min_style cg
minimize 1.e-14 1.e-14 1000 1000

And if I look at the output, I see:

Step Temp E_pair E_mol TotEng Press 
       0            0 -0.099697525            0 -0.099697525   0.35246486 
       1            0   -1.7219978            0   -1.7219978  0.021817974 
       2            0   -1.7276334            0   -1.7276334 -0.015209308 
       3            0   -1.7415426            0   -1.7415426 0.0020181014 
       4            0    -1.741734            0    -1.741734 0.00045648444 
       5            0   -1.7417403            0   -1.7417403 -0.00028734981 
       6            0   -1.7417442            0   -1.7417442 -7.997489e-05 
       7            0   -1.7417445            0   -1.7417445 -6.8336763e-06 
       8            0   -1.7417445            0   -1.7417445 -5.1660289e-08 
       9            0   -1.7417445            0   -1.7417445 -2.9622362e-12 
      10            0   -1.7417445            0   -1.7417445 -1.1339129e-12 


The thing that I want to highlight here is that the E_pair and TotEng are the same value, of about -1.74.  Now, if I think about my cluster of 7 atoms, and assume that near equilibrium for this, all the pair distances are close to the equilibrium value of 2^(1/6).  In this case, the energy of nearest neighbor pair bonds is about -1.  Each of the atoms on the exterior of the heptameter has 3 nearest neighbors, and the atom in the center has 6, so the total energy would be about -24, which is quite a bit different than the TotEng value.  

To put it another way, I would have assumed that 

TotEng = sum_{i<j} phi(r_{ij})

But that seems not to be the case.

-gideon