15

This is a difficult question without a straight-forward answer. In general you have to perform a test to decide whether the harmonic approximation is sufficient or whether you need to include higher order anharmonic terms in the potential expansion. Due to the computational cost of including anharmonic terms, very often systems are assumed to be harmonic ...


15

Background theory. In the harmonic approximation, the potential energy surface (PES) is expanded about an equilibrium point to second order, to obtain the Hamiltonian: $$ \hat{H}=\sum_{p,\alpha}-\frac{1}{2m_{\alpha}}\nabla_{p\alpha}^2+\frac{1}{2}\sum_{p,\alpha,i}\sum_{p^{\prime},\alpha^{\prime},i^{\prime}}D_{i\alpha;i^{\prime}\alpha^{\prime}}(\mathbf{R}_p,\...


12

The answer of @ProfM is already very complete, but I wanted to tackle your question from a more practical point of view. The presence of imaginary frequencies indicate that there are atomic positions which are more energetically favorable at the ground state. So, the concept of "following" a mode means condensing it onto the reference structure, ...


12

TLDR: When you calculate phonons, you can describe electrons at different levels of theory, typically semilocal DFT, but also hybrids or dynamical mean-field theory. Phonons do include zero-point motion, as they are essentially a set of uncoupled quantum harmonic oscillators. Enthalpy can be calculated without reference to phonons, simply adding a PV term to ...


9

I would not recommend applying external hydrostatic pressure by changing the lattice parameter by hand. This is because fixing the lattice parameters by hand may lead to the incorrect structure. For example, the system may have a pressure-induced structural phase transition that may change it from cubic to tetragonal, and by fixing the lattice parameters by ...


8

Lattice statics refer more to the minimum energy lattice structure such as spacegroup, lattice constant, bond distances, or any other property you can derive from a geometric standpoint on that optimized structure. I don't think I would consider the actual optimization to be lattice statics, more of a way to get to the lattice statics. Lattice dynamics such ...


7

Please read the pw.x documentation on the Bravais lattice index (ibrav). The cell vectors for the primitive cell corresponding to the cubic face-centered Bravais lattice (ibrav=2) are v1 = (a/2)(-1,0,1), v2 = (a/2)(0,1,1), v3 = (a/2)(-1,1,0) The cell volume is $V=|v_1 \times v_2 \cdot v_3| = (a/2)^32=328.85\ \mathrm{a.u.}^3$


5

ProfM's answer gets the core idea perfectly right: Symmetry really is your best friend here. However, symmetry analysis is often quite involved, especially for larger unit cells. I recently discovered the hiPhive package, which uses statistical fits (forces from random displacements fit to a force-constant potential), combined with with symmetry analysis (...


5

You can (should) use symmetry to reduce the number of displacements needed to construct the matrix of force constants. A nice pratical description of how to do this can be found in the description of the PHON package by Dario Alfè. In short: if you have the force constants for displacing a given atom, and when you apply the symmetry operations of the crystal ...


5

In your case, the crystallographic axes look to be equivalent, so just use 'relax' to start with. This will fix the lattice constants (equivalent to applying pressure) but will move the atoms around - make sure you modify the lattice parameter to reflect the 5% strain, 10% strain etc. Then, perform your SCF calculation. If your crystallographic axes are ...


5

The starting point of most calculations is the Born-Oppenheimer approximation, which separates the electronic and nuclear degrees of freedom. The electronic structure problem is then solved using a variety of methods (DFT, wave function methods, etc), and the nuclear problem is typically solved using the (quasi)harmonic approximation in solids. To observe a ...


5

There are two possible things tripping you up here: Phonons are collective oscillations: they involve the motion of all the atoms together. Therefore it only makes sense to talk about the phonons of the whole system, not any individual atom. The density of states only makes sense as you take $N\to \infty$. For finite $N$, there is a finite/discrete number ...


4

Got a bit too long for a comment, so I'll leave it as a semi-complete answer for now. In case the paper is inaccessible to other readers, much of the same information is in the gulp5.2 manual. In regards to the question, it does seem to elaborate a little in the sentences following your quote. From earlier in the document: Here the Coulomb interaction, and ...


4

A "pure harmonic system" does not allow opportunity for evolution. It is the equivalent of a fixed point. In initial consideration, its stability seems appealing, as it appears to be a goal (or “the goal”) of an imperfect system. However, it only embodies that moniker once, and change is the only real constant. Pure harmonics are fragile, brittle, ...


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