# Tag Info

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Quick Summary: There's no way around performing a convergence test. However, it is possible to obtain convergence much faster than the Phonopy approach by using nondiagonal supercells [1]. The basic quantity you build when performing a phonon calculation is the matrix of force constants, given by: $$D_{i\alpha,i^{\prime}\alpha^{\prime}}(\mathbf{R}_p,\... 20 Phonons are a measure of the curvature of the potential energy surface about a stationary point. In particular, the matrix of force constants is calculated as:$$ D_{i\alpha,i^{\prime}\alpha^{\prime}}(\mathbf{R}_p,\mathbf{R}_{p^{\prime}})=\frac{\partial^2 E}{\partial u_{p\alpha i}\partial u_{p^{\prime}\alpha^{\prime}i^{\prime}}}, $$where E is the ... 17 Short answer: Modern implementations of these two methods lead to similar accuracies. Longer answer: The calculation of phonons requires the calculation of the Hessian of the potential energy surface V(\mathbf{R}), also known as the matrix of force constants:$$ \frac{\partial^2 V(\mathbf{R})}{\partial \mathbf{R}_i\partial\mathbf{R}_j}=-\frac{\partial \...

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Ideally, a convergence test would be the best way to decide the required size of the supercell, but it can get expensive. When phonopy (or any similar calculation technique) finds displacements in the cell based on symmetry, the idea is to see how the displacement of certain ions affects the forces on every ion within the cell. We must then take care that ...

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Considering this in terms of a 2x2x2 supercell matrix is the wrong way to think about this, as choice depends on the cell length and bonding type. Given that rigorous convergence testing is near-impossible (see ProfM's answer), what saves the method is the rapid fall-off with distance of the force constant matrix $\Phi$. This "nearsigtedness" ...

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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 ...

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[Disclaimer - I am one of the co-authors of the 2D database on Materials Cloud (What you call "2D structures and layered materials", publishing the data of this work: N. Mounet et al., Nature Nanotech. 13, 246–252 (2018) so I will mostly refer to it below] In general, these studies "extract" a layer from a bulk 3D material, and then often ...

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Disclaimer: I have never used Phonopy. The advantage of using DFPT is that in principle it can be used to calculate a perturbation of finite wave vector $\mathbf{q}$ using the primitive cell. This should be contrasted with finite differences, which can only be used to calculate perturbations at the $\Gamma$ point. If you want to access a non-$\Gamma$ wave ...

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You can minimize the free energy F(a,c) as a function of (a,c), which is simply high school math. An example is provided in the section III (A) of the Supplementary Material of Phys. Rev. B 100, 161101(R) (2019): https://journals.aps.org/prb/supplemental/10.1103/PhysRevB.100.161101/supplemental.pdf

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I have never used Phonopy, so we will have to wait for an actual user for a full answer. However, I can make some general statements about phonon calculations that could plausibly explain your error. The starting point of any phonon calculation is the construction of the matrix of force constants: $$D_{\alpha i;\alpha'i'}(\mathbf{R}_p,\mathbf{R}_{p'})=\frac{... 5 ProfM's answer gets the core idea perfectly right: Symmetry really is your best friend here. However, symmetry analysis is often quite involved, especially for larger unit cells. I recently discovered the hiPhive package, which uses statistical fits (forces from random displacements fit to a force-constant potential), combined with with symmetry analysis (... 5 You can (should) use symmetry to reduce the number of displacements needed to construct the matrix of force constants. A nice pratical description of how to do this can be found in the description of the PHON package by Dario Alfè. In short: if you have the force constants for displacing a given atom, and when you apply the symmetry operations of the crystal ... 5 There are two major techniques used to model phonon interactions - The frozen phonon method and density functional perturbation theory (DFPT). Phonopy is used to carry out calculations in the frozen phonon scheme. ProfM does a fantastic job delineating the differences between the two methods here. The first step in such a finite displacement scheme is to ... 5 There are two possible things tripping you up here: Phonons are collective oscillations: they involve the motion of all the atoms together. Therefore it only makes sense to talk about the phonons of the whole system, not any individual atom. The density of states only makes sense as you take N\to \infty. For finite N, there is a finite/discrete number ... 4 In a calculation of the phonon density of states, \mathbf{q}-points feature in two ways: Explicitly calculated \mathbf{q}-points. These are the \mathbf{q}-points for which you explicitly calculate the dynamical matrix, and are typically referred to as forming the "coarse \mathbf{q}-point grid". If you are using finite differences to ... 4 Background. The phonon density of states g is given by:$$ \tag{1} g(\omega)=\sum_{\nu}\int\frac{d\mathbf{q}}{(2\pi)^3}\delta(\omega-\omega_{\mathbf{q}\nu})\approx\frac{1}{N_{\mathbf{q}}}\sum_{\nu}\sum_{\mathbf{q}}\Delta(\omega-\omega_{\mathbf{q}\nu}),  where $\omega$ is the energy and $\omega_{\mathbf{q}\nu}$ the energy of a phonon of wave vector \$\...

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This error (input forces are not enough to calculate force constants) may arise when you are trying to plot the band structure or the density of state plots for some systems. Sometimes setting a higher symmetry tolerance for a structure may cause this type of error. A lower symmetry setting can solve the issue. The following command can be used in phonopy ...

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It is always better to write your own code to get elastic constants. For example , In case of cubic system, we need three types of distorsion to unit cell. Now elastic constant is simply slope of second order fit of energies at different value of distorsion (see different publications) normalized with Volume minima (volume corresponds to minimum energy) . ...

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As known [1], the eigenvalues of the dynamical Hessian matrix represent the phonon frequencies, whereas the eigenvectors represent the particular atomic displacement patterns contributing to the vibrations. Therefore you might be interested in analyzing the eigenvectors and building the atomic visualizations based on them. In many cases (especially in the ...

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Your interpretation of the results. I agree with you that if you find no imaginary frequencies in the cubic phase it means it is at a local minimum of the potential energy landscape, and that if you do find imaginary frequencies for the tetragonal phase, then that one is at a saddle point. I also agree that a phase exhibiting imaginary frequencies may be ...

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