# Positive potential energy - HELP needed

Dear LAMMPS users,

I’m using LAMMPS with Dreiding FF to compute potential energy of composite membranes and thereby study their stability.
For potential energy calculation, I compute bonded energies (bond, angle, dihedral) and non-bonded energies (van der Waals, electrostatics and hydrogen bonding). Below are styles I used:

#bonded interactions
bond_style harmonic
angle_style cosine/squared
dihedral_style harmonic
#non-bonded interactions
pair_style hybrid/overlay lj/cut/coul/cut hbond/dreiding/lj

I noticed that computed non-bonded energies can be either positive or negative depending on the atomic distance r, which reflects repulsive or attractive interactions. However, for bonded interactions, the computation formulas would always yield positive values for bonded energies. Thus when calculating potential energy, bonded-energies always play as repulsion parts, which is confusing to my understanding about the role of bonded interactions on the stability of the system.

Could someone please explain that for me? Should I change computed bonded energies to negative values when calculating potential energy?
Thank you.

Kind regards
Tan Vu Bui

The absolute value of the potential energy has no specific physical value. Only energy differences matter.

Axel.

…and on a more conceptual level, the distinction between attractive and repulsive “energy” makes no sense for bonded interactions, anyway.
just consider a harmonic bond potential (i.e. a single spring): your potential energy is 0 at rest and then you have a restoring force, i.e. a potential energy > 0 for all other distances. It doesn’t matter whether you move atoms closer or farther apart, the potential “wants” them to be at the equilibrium position. Whether that means attractive or repulsive is arbitrary with respect to the energy. which is presented by the fact that U = k*(r-r0)**2. Now if you look at the forces instead, you can tell.

so it all comes down to basic calculus and elementary physics.

Axel.

Thank you all for your information.

Can I use PE to compare the stability of two systems (for example two composite membranes)? If possible, which one is more stable, the one that has larger PE or smaller PE?

Thank you.

Kind regards
Tan Vu Bui

as already alluded to, you can only compare two conformations of the same system, provided that all other simulation parameters are the same, but nothing else.

axel.

…and for complex dynamical systems, things are even more difficult, since you need to look at free energy differences and not just (static) potential energy differences, since entropy matters, too. axel.

As I understood, if two systems have the same simulation parameters setups, we could compare their free energies, couldn’t we?
Secondly, a higher free energy implies a less stability/cohesion of the system (as greater energy is needed to bring the system to its rest/equilibrium). Could you please let me know if that statement is correct?
Thank you.

Kind regards
Tan Vu Bui

As I understood, if two systems have the same simulation parameters setups, we could compare their free energies, couldn’t we?

no, you cannot. there is no way to determine absolute free energies, you can only compute free energy differences between two states of a system.

Secondly, a higher free energy implies a less stability/cohesion of the system (as greater energy is needed to bring the system to its rest/equilibrium). Could you please let me know if that statement is correct?

not really. for a dynamical system there is no “rest” at finite temperature. free energy differences consist on an internal energy contribution and an entropy contribution. please re-familiarize yourself with the relevant terms in thermodynamics and also check out how macroscopic thermodynamic properties are related to simulation data through statistical mechanics. this discussion is becoming off-topic for this mailing list.

axel.

Hi,

Please look up more information on thermodynamic free energy (https://en.wikipedia.org/wiki/Thermodynamic_free_energy) and also see this page (https://hypermd.wordpress.com/molecular-simulations/umbrella-sampling-2/free-energy-change/) for a short exercise in calculating free energy change in a potential well.