# Geometry optimization: nuclear coordinates vs lattice parameters

I would like to know whether, at least in principle, minimization of energy with respect to nuclear coordinates leads to the same result as minimization of cell energy with respect to lattice parameters. Is one way computationally more advantageous than the other? Thanks in advance, also I'm sorry if the question might not be accurately formulated.

Minimizing energy with respect to nuclear coordinates and with respect to lattice parameters are two very different things.

Minimizing energy with respect to nuclear coordinates can be used for periodic and isolated systems.

In the case of a periodic system, this will lead to knowing how the atoms and/or molecules are arranged inside a given crystallographic cell. In this instance, the crystal symmetry is a constraint on your system. If your system is an isolated molecule, there are no constraints, and you will have the conformer with the lowest energy.

Minimizing the lattice parameters (in general, together with the nuclear coordinates) is done when you are starting from a bad structure, or you need to know if the system can have another crystallographic phase. If you have crystallographic evidence that there are no other phases, then you can use the experimental lattice parameters as constants, and there is no need to optimize them.

Is one way computationally more advantageous than the other? There is no such thing as an advantage. All of this will depend on what you are studying and your needs.

• Thank you very much. Let's say I want to find the equilibrium structure of solid material for which there are no experimental structural data. What will I need to do to find its equilibrium structure at room temperature? Am i going to have to request both kind of optimization? May 22, 2023 at 15:32
• If you don't have any experimental structure, you need to predict the crystal structure first. This is a very difficult task. Take a look at this site: https://uspex-team.org/en/uspex/overview.
– Camps
May 22, 2023 at 16:08
• Thank you again, I'll take a look at it. Since you seem to know very much about this topic, I have one more questions. If this is a difficult task to accomplish then what kind of optimizations are routinely done? May 22, 2023 at 16:48
• The difficult task is to predict the crystal structure (lattice parameters and atoms positions) of a material starting only with the type of atoms it is made on, not the optimization of nucleus/lattice parameters.
– Camps
May 22, 2023 at 20:24