# Questions tagged [symmetry]

Questions relating to symmetries and symmetry groups encountered in materials modeling.

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### Calculating degrees of freedom with fixed symmetry

I stumbled upon a problem recently: I want to compute the number of degrees of freedom for a crystal/molecule if its symmetry is fixed. I think what needs to be done is to compute the number of normal ...
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### Are there non-antisymmetric solutions to the electronic Hamiltonian?

In electronic structure theory, one seeks solutions of the molecular electronic Hamiltonian $$H_e(\vec{R}) = T_n(\vec{r}) + V_{ne}(\vec{r};\vec{R}) + V_{ee}(\vec{r}) + const,$$ where $\vec{r}$ are ...
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### Can conventional unit cell have higher symmetry than primitive cell for the same crystal?

This question arises from the last sentence of the first paragraph (see here) of the section "Formalism". If primitive cell can have lower symmetry, why don't the DFT results using these two ...
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### In which irreducible representations shall I put the electrons in an F atom in PySCF?

Iām looking to complete ROHF energy calculations in PySCF for the F atom. I need to update the irrep_nelec dictionary for F. I know that the one for the O atom is: ...
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### How can we identify the symmetry of the molecule from its IC table?

We are given the IC table for benzene in CHARMM format, which can be written as follows: ...
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### What is the correct way to set up occupation for single atom in CFOUR software?

I am doing some calculations on single oxygen atom (O) using CFOUR. According to a previous answer to this question and according to how CFOUR treats non-Abelian groups, I am considering the (O) atom ...
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### For one atom, what is the correct point group?

I have a concern related to the follwoing question When orbitals are labeled based on their irreps in D2h, how are the orbitals ordered for an N atom? In which the following Answer clearly states that ...
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### When orbitals are labeled based on their irreps in D2h, how are the orbitals ordered for an N atom?

I am performing calculations on a Nitrogen atom using CFOUR. A nitrogen atom has a point group of Dinfh, but ā CFOUR uses a lower symmetry of D2h instead. So, looking at the available Irreducible ...
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### How to Obtain the Zak Phase in Symmetric one-dimensional (1D) Systems?

In a symmetric 1D system, the intrinsic topological orders are characterized by the total Zak phase ($\gamma$) summed over all occupied states$$\tag{1}\gamma=\sum_{n}^{}\gamma_n$$where $n$ is the band ...
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### Is there a difference between space_group and ibrav in terms of Quantum espresso performance?

I am trying to understand the use of space_group in Quantum Espresso. I note that the keyword can be used with and without ibrav....
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### Why does the C6z operator have 6 eigenvectors in this paper?

In this paper, I couldn't understand this line in the 3rd section (i.e. III. SYMMETRY ARGUMENTS): In the absence of SOC, the eigenvalues of $C_{6z}$ rotation operator are $e^{i2\pi n/6}$ where $n = 0$...
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### Symmetries and band structure

I am currently trying to understand the relation between the symmetries of a crystal and its band structure. However, I am having a hard time figuring out how symmetries protect degeneracies in the ...
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### Non-Equivalent T-Sites from a cif file

I am trying to find symmetrically inequivalent T-atoms in a crystal structure (zeolite). Does anyone happen to know any package that can help with that? I see that pymatgen does have options for ...
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### Can a tool āSet space groupā be useful?

In my program Chemcraft, a popular tool is the āSet point groupā utility: it symmetrizes the molecule according to a specified point group, and then the symmetry of the molecule is correctly ...
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### About high-symmetry points in the first Brillouin zone of space group R-3m

I want to figure out the high-symmetry points in the first Brillouin zone of space group R-3m (166). For example, there are points K and M just like the bandstructure in this paper. But I can't figure ...
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### UseSym Keyword in ORCA fails to find appropriate number of SALCs

I am trying to run some geometry optimizations in ORCA 5.0.4 and I am using the UseSym keyword to ensure that my molecules retain Cs Symmetry during optimization. ...
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### Inconsistencies in a famous point group table

The original resource "Tables for Group Theory" By Peter Atkins, Mark Child and Courtenay Phillips (1970). I have been using this 2008 version, in which Pg. 37 has the following table: Some ...
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### Why are some point groups for single atoms listed as Oh in the CCCBDB?

Does anyone know why the CCCBDB database lists the tin cation and antimony atom as having the Oh point group (please see the screenshot below from CCCBDB when I look at "All molecules sorted by ...
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### How to transform a perturbed surface structure to a reference surface structure?

Say I have a bulk FCC Pt structure obtained from Materials Project with a lattice constant a = 3.94 Ć. I first did DFT to relax the bulk structure, and the optimized lattice constant becomes for ...
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### Help setting the input geometry into standard orientation for a single point g09 calculation

I am trying to run a single point g09 calculation for a pentagonal planar molecule with D5h symmetry using the B3LYP/LANL2DZ level or theory. I would like the calculation to use symmetry, however the ...
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### Graphene Band Structure with SIESTA [closed]

I am struggling with getting a correct band structure for even pristine graphene using SIESTA. The issue is almost certainly the K point path. My graphene sheet (128C atoms) isn't the traditional ...
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### LO-TO Splitting and Group Theory

I am curious whether or not there is a connection between the group theoretical assignment of phonon modes and LO-TO splitting. For example, is it true that the frequency of a gerade mode will depend ...
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### How to determine dimensionality of a structure with pymatgen?

Is there a neat way to figure out if a crystal structure in pymatgen is 2D or 3D? If we have a molecule we can feed its coordinates to (say) the ConvexHull method in scipy. Is there way to do the same ...
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### Electronic structure of s-indacene

Structure shown in (a) is the regular $s$-indacene molecule, and (b) is a structure that i generated such that the central six-member ring remains similar to benzene. It is well-known in literature ...
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### Computing the rotational entropy in RRHO approximation

I am implementing the computation of Gibbs energies by their molecular parameters (structure, frequencies) in my program Chemcraft (the main task is the possibility to cut small frequencies which ...
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### Database (or table) of functions obeying symmetry properties of space groups

I'm looking for a table or database containing mathematical functions that belong to crystallographic space groups by having the same symmetry elements. Imagine a 2D square planar lattice. It has a 4-...
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### How to determine high-symmetry points in case of PBE0 using Quantum ESPRESSO? [closed]

Normally when we use PBE-GGA as an approximation we can determine the high symmetry points in x coordinate from the output file of bands.x calculation . But in the ...
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### Which crystal structure I have to choose for DFT calculations? [closed]

I want to study the properties of NiO as a hole transporting material adapted for perovskite solar cells using Quantum ESPRESSO. From Materials Project website, I saw that NiO can exist in different ...
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### Difference and meaning of isopointal and isoconfigurational structures [closed]

These are the meanings I`ve found, but I do not completely understand them. Isopointal: Two structures that have the same space-group type or belong to a pair of enantiomorphic space groups. And that ...
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### How do I know which is the asymmetric unit of a unit cell?

I need the number of independent atoms in the asymmetric unit I have to introduce them in this form: ...
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### Primitive Translation Vectors from Lattice Vectors (with varying Space Groups) [closed]

I am looking at some raw POSCAR data of some Primitive Cells, and I wonder how I can get a simplified directional representation of the lattice vectors. I have two examples: Example 1: ...
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### Change in space group upon application of stress during geometry relaxation in VASP

I am trying to duplicate the results of this study using VASP. Where they have observed that the structure of $\ce{Cs_2SnI_6}$ switches from Fm-3m to I2/m upon application of pressure more than 3.3 ...
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### When we can justify the response to be hold in terms of symmetry?

In this paper, the authors argue the following response relation $$j_a=\sigma_{abc}E_bE_c \tag{1}$$ can occur in systems with $\mathcal{P}\mathcal{T}$-symmetry with $\mathcal{T}$ the time-reversal ...
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### How to transform the conventional cell to primitive cell, by hand?

I am following this tutorial to transform a conventional cell to a primitive cell, but I am not sure how to determine the primitive copy of some atom in the conventional cell. For example, in the ...
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### About the mechanism of opening of the band gap in topological insulator with the inclusion of SOC [closed]

When we work on the topological insulator (protected by time reversal symmetry ), it is often said that the SOC is the main ingredient because it is a way to open a gap when the band inversion present....
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### Error termination while performing NTO analysis in G09?

I'm trying to perform an NTO analysis (Natural transition orbitals) for my system. I first used TDDFT to calculate the excited states and then generated my chk file and copied it under the name of ...
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### How can I distinguish between n, pi, pi* orbitals when looking for excited states?

I recently asked about how to distinguish between transition types. I got an answer there about determining the character or type of the orbitals. My problem now is that I'm not sure how to determine ...
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### What is the best cell shape to calculate the energy of a free atom with a periodic DFT code (VASP)?

I want to study the adsorption energies of many different atoms to some surfaces. For that, I need to calculate the energies of free atoms (adsorbates) in a vacuum. I understand that I am supposed to ...
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### How to find magnetic materials in terms of magnetic point groups?

Are there any methods to find materials in terms of the assigned magnetic point group? For example, I know the magnetic point groups $6'mm'$ and $6'22'$, and I want to find the corresponding ...
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### Examples of anti-symmetric rank-3/4 tensors?

The anti-symmetric rank-3 and rank-4 tensors hold the following properties: \begin{align} \sigma_{mnk} &=-\sigma_{nmk} \\ \sigma_{mnkp} &=-\sigma_{nmkp} \end{align} Note I'm using ...
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### How to quantify the lattice distortion from XRD?

In real crystals, the atoms may not always sit at their ideal lattice sites. How to quantify this lattice distortion? Based on my understanding from X-ray diffraction books, the Radial Distribution ...
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### Why do we need to use fake k-points when doing HSE band structure in VASP?

I want to know why we need fake k-points in HSE band structure calculation? I mean why we can't take a simple high symmetric path like we do in PBE calculation?
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### How to extract the crystal symmetry from VASPs POSCAR/CONTCAR file?

VASPs POSCAR/CONTCAR file does not contain any direct information about the cell symmetry. If I run for example a calculation on simple TiN in space group 225, this symmetry is (should be) preserved. ...
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