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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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Stabilizing donor-acceptor interaction between orthogonal orbitals in the SN2 transition state?

For the $\mathrm{S_N2}$ reaction between chloroacetone and iodide, my professor has drawn a donor-acceptor interaction between the iodine lone pair attacking the Cl-substituted carbon and the π ...
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diborane fragment orbitals energy of dihydrogen

I want to ask a question about the fragment orbitals of the $\ce{B2H6}$ system, specifically when I combine the $\ce{B2H4}$ with the $\ce{H2}$ fragments. I am halfway through my inorganic chemistry ...
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How to deal with non-symmorphic space groups for orbital/vibrational analysis?

I am learning about how to apply group theory analysis of MO diagrams and vibrational in the solid state context (not isolated molecules). I think the strategy for calculating representations and ...
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Can the plane of symmetry for a compound be the plane of the paper?

1,4-Dichloro-2,5-dimethylbenzene is symmetric about the plane of paper. I have never seen a plane of symmetry positioned like this. Would it be correct to call it a plane of symmetry?
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What does “orthorhombic” actually mean?

I'm trying to understand what it means for a molecule to have orthorhombic symmetry. According to Di Lauro's "Rotational Structure in Molecular Infrared Spectra," a molecule is orthorhombic if the ...
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Point group of cis- and trans-decalin

What is the point group of of cis- and trans-decalin? I watched a video saying that it is $C_\mathrm{2h}$ for cis-isomer, but my friend says it is $D_\mathrm{2h}.$ I'm so confused.
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Character table and symmetry operations

It's been a while since I've dealt with these, but do character tables include all possible symmetry operations? I am looking at the $D_{\infty h}$ point group table and it lists $C_\infty$, $\...
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Number of stereoisomers of polysubstituted cubane

The molecule given below is a substituted cubane. a) How many stereoisomers exist for this molecule? b) How many pairs of enantiomers are possible? How do I calculate the number of ...
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Conditions for molecular dissymmetry

In my textbook, under the topic "Asymmetric and Dissymmetric Compounds", the following statement is given: A molecule which does not possess plane of symmetry, centre of symmetry, and alternating ...
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How do computational chemistry programs determine the irreducible representation of a molecular orbital?

I was coding a simple RHF code to test my understanding of computational chemistry when I stumbled upon this question. How exactly do computer programs like Gaussian, GAMESS-US etc. know which ...
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Molecular Orbitals (only pi system) of Allyl system using group theory

I have just started reading group theory and their applications in the MO theory. I tried to get the equations of the pi molecular orbitals of allyl system using group theory, but I am stuck at the ...
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Procedure to assign the irreducible representation of a derivative operator

How can we assign an irreducible representation to a derivative operator like $\displaystyle\frac{\mathrm d}{\mathrm dx}$ or the whole gradient operator $\nabla$ in a given point group? Since the ...
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AB5E type molecule

In $\ce{AB5E}$-type molecules, why are the lone pairs in axial bonds? If the lone pair is present in axial bonds it repels four other bonds. On the other hand if the lone pair is in equatorial ...
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Spacial Wavefunction Symmetries and Identical particles

I was reading this and it mentions in the 3-electron section, that for a spacial wave function to be symmetric under fermion swapping, it must be a function of even parity. Similarly for anti-symmetry ...
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Horizontal symmetry plane of cis-dichloroosmiumtetracarbonyl

Consider the molecule $\ce{Os(CO)4Cl2}$ with a drawing given below via Chemtube3d: I thought in this molecule, if I drew a horizontal plane, then a $σ_\mathrm{h}$ would be present i.e. A ‘horizontal’ ...
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Multiplicity letter codes for large amount of states

Well, let's say we have a large amount of states computed (e.g. over 50), all with the same multiplicity. So, our ground state can be $X^2\Sigma^+_g$ and we can continue with $B^2, C^2$ etc. as ...
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Why do most explosives have symmetrical chemical structures?

I was just turning the pages of my chemistry dictionary, when I found the structure of TNT (Trinitrotoluene): ...there after I got interested in its symmetry as an explosive, and started looking for ...
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Point group from mono to bulk MoS2

Many articles say even numbers of layers or bulk crystal MoS2 have D6h point group and odd numbers of layers (including monolayer) MoS2 have D3h point group But whenever looking at the figure of ...
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Sulfuric acid symmetry point group

On the following page: https://cccbdb.nist.gov/pglist.asp It appears that the point symmetry group of sulphuric acid is $C_2$. I know that $C_2$ means that there is an axis of symmetry of order 2 (180 ...
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Relationship between the symmetry number of a molecule as used in rotational spectroscopy and point group

While doing a problem set I noticed that the symmetry number of a molecule turns out (usually) to be half the number of symmetry elements that the point group the molecule belongs to. When I say ...
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Why does the 31P{1H} NMR spectrum of cis-[Mo(CO)2(dppe)2] show two signals?

I've tried searching for literature references that explain this, finding only a single reference which refers to the two signals as originating from phosphine environments cis/trans to carbonyls, ...
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Misunderstanding about the spin part of the Jahn Teller effect

In the paper Stability if Polyatomic Molecules in Degenerate Electronic States II - Spin Degeneracy the author wrote: Thus a twofold degeneracy cannot produce instability for a molecule containing ...
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What is a “symmetrical product” of an irreducible representation with itself?

In their classic paper outlining the Jahn–Teller theorem (Proc. R. Soc. Lond. A 1937, 161 (905), 220–235), the authors wrote "where $[\phi^2]$ denotes the representation of the symmetrical product of $...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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 ...