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Re: [lammps-users] Total energy calculation
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# Re: [lammps-users] Total energy calculation

 From: Stefan Paquay Date: Thu, 7 Dec 2017 11:39:59 -0500

Ah, I just realized where you got 24 from: You were counting each bond twice. The center atom has 6 bonds and each outer has 3, but if you correct for the factor 2 (which goes automatically if you sum over only i<j) you get 12 too.

On Thu, Dec 7, 2017 at 11:36 AM, Stefan Paquay wrote:
With units lj the thermo_output is normalized, so TotEng is the average total energy. Since there is twelve bonds, that amounts to -1 * 12 / 7.0 which is about -1.714285. The additional energy is probably from the second-nearest neighbor interactions.

On Thu, Dec 7, 2017 at 11:29 AM, Gideon Simpson wrote:
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

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