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Questions tagged [symmetry]

The description of the symmetry present in molecules. Molecular symmetry is useful for explaining or predicting of a molecule's chemical properties.

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Symmetry labels of D4h [on hold]

Derive the symmetry labels for the $D_\mathrm{4h}$ point group, the $z$ axis should be the $C_4$ axis. For the degenerate orbitals, you only need to look at ONE symmetry element. Also remember $C_2'$ ...
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1answer
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C5v E1 SALC production using Full Projection

I have another SALC question. @Andrew and @user5713492 did a phenomenal job clarifying my previous confusion with Methane T2 SALC production, so I attempted to apply this to a new point group, and ...
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1answer
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How do I interpret characters that are not 1 or -1 in a point group table?

When the character in a point group table is listed as 1 or -1, I understand how an object/orbital etc. transforms to give either itself or the negative of itself. When the character in a point ...
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3answers
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Methane T2 SALCs

So I have a question on the form of the $T_2$ SALCs of methane. Below I show the $T_d$ character table and the accompanying reducible representation for the sigma framework (using, in the case of ...
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What happens when a symmetry element is added or removed from a point group? [closed]

What new point group is formed if symmetry element i is added to C3 point group?
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Theory of symmetry breaking in water?

As we all know $\ce{H2O}$ is bent ($C_\mathrm{2v}$) in its ground state equilibrium structure, rather than linear ($D_\mathrm{\infty h}$), which can be readily understood e.g. from the MO diagram of ...
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How to derive a state symmetry in D2h point group from its wavefunction?

Let's have an atomic carbon with the following electron configuration: $$ 1s^2 2s^2 2p^2 $$ One of it's levels is ${}^1S_0$, which is corresponding with the following state: $$ \begin{align} \left| ...
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Vibronic coupling: How do I determine the new point group after vibration?

So I was recently discussing the transitions in Egyptian Blue ($\ce{CaCu[Si4O10]}$) with some of my students, who had to prepare this compound. What I like in particular in this case is how, at least ...
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Infrared Spectroscopy of N2O [closed]

Would you be able to identify the stretch and bend in the spectrum? I can not find much information about the $\ce{N2O}$.It's solved, does anyone know the symmetry of these vibrations?
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What is symmetry of p- and d-orbitals in ${D_{3h}}$?

To identify IR and Raman active, symmetry of p- and d-orbitals are used. If we start since making ${D_{3h}}$ character table, how to match between symmetry of p- and d-orbitals and Mulliken symbol? ...
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1answer
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Cs Point Group's “Horizontal” Reflection Plane

Why is it that $C_s$ character tables always list a $\sigma_h$ operation despite the definition of $C_s$ not necessitating the reflection plane be horizontal? In fact, how can the reflection plane ...
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1answer
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Why does benzene have 3 π–π* transitions in the UV range, but ethene, butadiene, and hexatriene each have only 1?

Are the π and π* orbitals of benzene much closer together in energy which allows for multiple transitions? Why is this not the case for hexatriene if they both contain the same number of pi bonds?
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Are there any descent symmetry tables for character tables of linear structures?

I know about tables containing information about descending in symmetry, i.e. from larger point groups to their sub-groups. We can see such tables in this answer, or in this PDF. My question is - ...
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1answer
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Molecular orbitals symmetry - states notation

I'm reading some papers and I'm repeatedly seeing the following notation of system states: Could you, please, explain to me the meaning of it? E.g. the state $B^2 \Sigma_u^+$ - I'm aware, that $\...
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1answer
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Use of axis of symmetry

Does an axis of symmetry determine chiralty? Is axis of symmetry considered a true symmetry? From the above two links, I read that a compound having axis /alternating axis of symmetry is NOT ...
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Reading Stereographs

On an old paper, I found an interesting representation of some symmetry operations: stereographs. Online I found a set of symmetry operations and related stereographs (see: http://newton.ex.ac.uk/...
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1answer
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Why is CO2 not in the C∞v point group?

It seems to me that CO2, since it can be linearly rotated around the z-axis without change of shape, ought to be in the C∞v point group. However, in all the character tables I can find, it's listed ...
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Mirror planes of symmetry in bicyclo[2.2.2]octane?

One of the questions in my book has answer given as one mirror plane of symmetry perpendicular to the 3-fold rotation axis, but I think it has 3 more, each parallel to the 3-fold rotation axis as I ...
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1answer
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How to explain the excited states in the dinitrogen cation?

The $\ce{N2^+}$ molecule has the molecular orbitals $$\ce{\sigma(1s)^2\; \sigma^*(1s)^2\; \sigma(2s)^2\; \sigma^*(2s)^2\; \pi(2p_x)^2 \; \pi(2p_y)^2 \; \sigma(2p_z)^1,}$$ which can be seen on the ...
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1answer
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How do I have to interpret the input to the OCC flag in Molpro?

I'm trying to understand the occupied orbital specification in Molpro. They're specified by the OCC flag, while it's stated in the documentation, that OCC, m1, m2, ..., mn; where the ...
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1answer
58 views

POI is a bent molecule similar to water. How are the two molecules different it terms of bond angles and what causes this?

phosphorus oxyiodide ($\ce{POI}$) has the VSPER AXE formula of $\ce{AX2E}$ while water, $\ce{H2O}$ has the AXE code of $\ce{AX2E2}$. According to my work sheet $\ce{POI}$ should have a $120^\circ$ ...
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N2 symmetry representation in higher symmetry groups (D3h…)

I'd like to describe the symmetry of the ground state of $N_2$ in the higher symmetry groups like $D_{3h}$ and $D_{\infty h}$. In this answer the topic is covered very good, but only for $D_{2h}$ ...
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What is the diagram of the roto-inversion of $\bar 6$?

Using the standard way of representation: Here we have a rotation followed by an inversion (technically called 'rotational inversion'). So as to represent it, what I have done is: 1) Both rotation ...
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1answer
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Reducible representation of planar molecule N2H2 with bond lengths as a basis

I'm studying about molecular symmetry and its representations. Today I got a little confused about the planar $\ce{N2H2}$ molecule. It looks like this The basis in the example was chosen as $\Delta ...
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1answer
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Molecular electronic state symmetry

I am trying to work out the ground state symmetry of electronic states. The paper states the GS symmetry is $^6A_1$ for the right hand side electron configuration and $^4B_1$ for the LHS in the D$_{2\...
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Is there a physical explanation why benzene's pi molecular orbitals in a Frost circle are degenerate but pyridine's are not?

From here, the Frost Circles for both benzene and pyridine: The $\pi$-MOs formed by 6 $\pi$-AOs of an aromatic ring are: Listed with respect to the ordering in the above image, these MOs in benzene'...
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What is a quick and easy way to find an alternative axis of symmetry?

According to a question in my book (1​R,3​R)-1,3-dichloro-2,2-bis[(S)-chloro(2H1)methyl](1,3-2H2)propane has an S4 alternative axis symmetry. I tried trial-and-error method using an axis that passes ...
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Why does the bending vibration of H2O span the A1 (rather than B1) irreducible representation?

Defining the $H_20$ molecule as being in the xz plane with the z axis being the principal axis. Why does water have a bending vibration from the $A_1$ irrep and not $B_1$? Since $B_1$ contains the $...
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1answer
442 views

How to systematically find the reducible representation of a molecule? (eg: XeF4)

I am attempting to use the reduction formula to find the irreducible representation of $\ce{XeF4}$ to determine its IR stretching vibrations. I know the point group of $\ce{XeF4}$ is $D_{4h}$ and have ...
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Breaking degeneracy in phosphorus pentachloride

Recently, in a class discussion, the following point was brought up: Although the axial and equatorial bond lengths in $\ce {PCl5}$ are inequivalent, when we consider the time-averaged $\ce {P-Cl}$...
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Applying a symmetry operation to a function

I had a hard time understanding what it means to apply a symmetry operator to a function, so i wondered if there is a formal way to define this ? As far as i understand it, applying a symmetry ...
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Whats the symmetric, anti-symmetric and non-symmetric part of the direct product of irreducible representations?

I am trying to understand how to see if a vibrational mode is Jahn-Teller active or not. According to the group theoretical description of the Jahn-Teller effect one needs to check if the symmetric ...
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1answer
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Total spin number 0 together with $B_2$ state - confusion

I'm trying to understand molecular symmetry and I got confused reading the Molpro documentation. There is an example of a system with $B_2$ symmetry written like this: $$ wf,10,3,0, $$ which means, ...
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How to pass a Plane of symmetry?

While passing a plane of symmetry through any compound inorganic or organic should it contain a minimum number of atoms or can it be passed without containing any atoms ?
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1answer
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ligand pi system irreducible representation for trigonal bipyramidal transition metal complex

I am considering a D$_{3h}$ trigonal bipyramidal transition metal complex MX$_5$. I have found that the irreducible representation for the ligand s and $\sigma$ systems is 2A$_1'$+A$_2''$+E$'$. I ...
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Determining overtones bands of degenerate modes

I have a question of a more mathematical nature on the mathSE (Symmetric Direct Product Distributive?) that received a good answer, but I think an answer more oriented to chemists would be a useful ...
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1answer
841 views

How are these molecules chiral and achiral?

I always thought that a molecule couldn't be chiral if it had a plane of symmetry. Doesn't the chiral molecule here have symmetry diagonally across the OHs? The achiral one doesn't look symmetrical ...
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Why are there no dihedral mirror planes in the D3h point group?

Consider the molecule $\ce{BH3}$, which belongs to the $D_\mathrm{3h}$ point group. Why are the three mirror planes in this point group labelled as $\sigma_\mathrm v$ instead of $\sigma_\mathrm d$? ...
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For two compounds that are symmetrical, why does the more compact one have a higher melting point?

In this post, I refer to two molecules B (Di-tert-butyl ether) and C (Dibutyl ether). Wikipedia: Di-tert-butyl ether (B) b.p. 107.2 C m.p. - 61 C ...
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D3d point group matrices

I am trying to construct all the matrices for the point group D3d operations. I find that the matrices of E, i, S6, inverse of S6, C3, and inverse of C3 are easy, but I do not know how to construct ...
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Can a molecule be neither gerade nor ungerade?

Or can any molecular orbit always be written a linear combination of gerade and ungerade basis states?
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Rotovibrational selection rules for symmetric tops

The selection rules for symmetric top molecules are $\Delta J = 0, \pm1$ and $\Delta K = 0$ for $K \neq 0$ (parallel transition) $\Delta J = \pm1$ and $\Delta K = 0$ for $K = 0$ (parallel ...
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XeF4 - why are there only 2 dihedral mirror planes?

I started studying molecular symmetry and I became somehow confused about dihedral mirror planes. I found a definition, which says, that it is a vertical mirror plane, which bisects two $C_2$ axes. ...
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Mulliken Symbols in group theory

How does one assign subscripts 1 and 2 in the B representations for the D4 symmetry group. There are two classes of C2 axis perpendicular to the principle C4 axis. I referred to F. Albert Cotton's '...
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What system of nomenclature can I use to indicate the positions of specific kinds of atoms of a surface reconstruction?

I was reading a journal based on SiC reconstructions, and they seem to mention that every dangling bond in the $(1\times 1)$ unreconstructed Si face or the $(0001)$ direction bonds up with a Si adatom ...
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309 views

Where is the mirror plane in 1-bromo-1-chloroethene?

I am studying point groups in inorganic chemistry and having a very difficult time understanding some of these concepts. In my book, Inorganic Chemistry: Fifth Edition by Miessler, Fischer, & ...
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Is there a possible distortion of XeF6 from Oh point group to reduced symmetry?

Below the molecular orbital diagram for $\ce{XeF6}$ (from What is the molecular structure of xenon hexafluoride?) I am trying to figure out if a distortion from $O_h$ can take place and to which (...
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1answer
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How do I show that a transition is magnetic dipole allowed with group theory/symmetry?

I am taking an introductory course in symmetry and bonding and have so far learnt about SALCs and various point groups etc... one of my problems asks me to show a $\mathrm{^{2}T_{2g}\rightarrow\ ^{2}...
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2answers
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What constraints are imposed on a wavefunction by the symmetry of the system?

As a follow-up to my answer here, I'd like to ask what exactly does it mean for a wavefunction to "respect the symmetry" of the system. The original context is: immediately after ionisation of $\ce{...
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How is group theory (and matrices) used in symmetry operations? [closed]

I am a high school IB student. For my 2-year math course, there is an internal assessment called "exploration" which should be max. 12 pages long. The goal of this assignment is for students to ...