# Energy

Hi all
I have a small question on energy variation through displacing atoms.
When I displace atoms on x “or” y-direction with a specific value (i.e. 0.01 A) the potential energy variation is different with when I displace atoms on two directions (x and y-direction) with half of this value (i.e. 0.005 A). Is there any reason for this event?

variable a1 atom 0.005y
variable a2 atom 0.005
x
displace_atoms all move v_a1 v_a2 0 units box

====> E = -15.717594

variable a1 atom 0.01*y
displace_atoms all move v_a1 0 0 units box

====> E = -15.71712

variable a2 atom 0.01*x
displace_atoms all move 0 v_a2 0 units box
====> E = -15.71712

and this is my input file:

echo both

# ---------- Initialize Simulation ---------------------

units metal
dimension 3
atom_style atomic
boundary p p p
atom_modify map array
timestep 1e-3

# ---------- Simulation Box -----------------------------

lattice fcc 4.07
region box block 0.0 1.0 0.0 1.0 0.0 1.0
create_box 1 box
create_atoms 1 region box
mass 1 196.97

# ---------- Define Interatomic Potential --------------

#pair_style meam
#pair_coeff * * library.meam Au NULL Au
pair_style eam
pair_coeff * * Au_u3.eam

Hi all
I have a small question on energy variation through displacing atoms.
When I displace atoms on x "or" y-direction with a specific value (i.e.
0.01 A) the potential energy variation is different with when I displace
atoms on two directions (x and y-direction) with half of this value (i.e.
0.005 A). Is there any reason for this event?

​the reason is simple vector algebra: ​sqrt(0.005**2+0.005**2) != 0.01

​axel.​

I don’t understand Axel. If all atoms are displaced in any direction, there shouldn’t be any change in energy? Distance between any set of atoms remain unchanged…

Anders

I don't understand Axel. If all atoms are displaced in any direction,
there shouldn't be any change in energy? Distance between any set of atoms
remain unchanged...

​in the example given, atoms are displaced by factor*position, i.e. the
system is stretched. what you say applies to displacement by a constant
(assuming no external interactions), i. e. the system is moved.

axel.

Thank you for your help.That’s right.

Only there is one extra question:
Why when I change displacement from ux = 0.01x , uy = 0.01y to ux = -0.01x, uy = 0.01y or ux = -0.01x, uy = -0.01y, there isnot any change in potential energy?

Indeed, the negative or positive sign of displacement does not affect the energy?

Thank you for your help.That's right.

​well this only applies to small displacements.​

Only there is one extra question:
Why when I change displacement from ux = 0.01x , uy = 0.01y to ux =
-0.01x, uy = 0.01y or ux = -0.01x, uy = -0.01y, there isnot any change in
potential energy?
Indeed, the negative or positive sign of displacement does not affect the
energy?

​that depends on your lattice. for small enough displacements, you may
assume linear response. remember, that you are stretching/compressing your
system, and the corresponding pairwise potentials are not harmonic.

axel.

Thanks
But I change EAM potential to different ones like meam, reax and “lj/charmm/coul/long, as harmonic pairwise potential”, and this independancy to the positive and negative sign of displacement has remained.
Additionally, my lattice is fcc with only 4 atoms (Lx = Ly = Lz = 4.07A) and displacements are nearly small (0.01x or 0.01y).