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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32
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1answer
7k views

When is it true that more nodes equals higher energy?

Consider all the MOs of some isolated molecule. (It could be a single atom too; I'll use MO to refer to AOs as well.) Number them in increasing order of the number of nodes (node = surface where the ...
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Theoretical basis behind orbital correlation diagram for pericyclic reactions

When discussing pericyclic reactions, the Woodward-Hoffman rules allow one to predict whether a reaction will be thermally/photochemically allowed. This has been discussed in many questions on chem.SE,...
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What is the mathematical basis behind the Jahn-Teller effect?

Both first-order and second-order Jahn-Teller distortions play a very important role in chemistry. It is often said that the Jahn-Teller effect is based on symmetry arguments, and hence nothing can ...
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Molecular chirality and optical rotation

Why does having molecular chirality result in optical rotation? The dissymetry or chirality of molecules translates to the rotation of plane polarized light, the magnitude and direction depending on ...
19
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1answer
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What are t2g and eg in CFT?

In the crystal field theory (CFT), when the splitting of the d-orbital occurs, it gets divided into two parts. The upper part with higher energy is the $\mathrm{t_{2g}}$ and the lower part with lower ...
19
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733 views

Symmetrize nearly symmetric molecule

In the overall good paper of Beruski et. al.,[1] an algorithm of how to symmetrize an "almost symmetric" molecule by symmetrizing the distance matrix is given for the example of Methane. The ...
19
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Jahn-Teller Distortions in Square Planar Complexes?

A Jahn-Teller distortion is predicted whenever a non-linear symmetric molecule has degenerate orbitals and has unequal electron occupation in those degenerate orbitals. Of course, this most often is ...
17
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1answer
421 views

Are chiral quasicrystals possible?

Quasicrystals are materials that have long-range atomic order but lack the translational symmetry of conventional crystals. All quasicrystalline tilings and packings I have read about thus far, whilst ...
15
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How can I find the symmetry labels of atomic orbitals in a molecule?

What are the symmetry labels for the p and d orbitals of platinum in $\ce{[PtCl4]^2-}$? I understand how to find the point group of a molecule, but am not sure how to use the character table to find ...
15
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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{...
15
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1answer
191 views

Are there any non-Jahn-Teller type distortions?

My question is essentially, if ANY gradual type of deviation from a higher possible symmetric arrangement of the nuclei in a molecule is covered by the Jahn-Teller model. More specifically I have in ...
13
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Rule of mutual exclusion: is the converse true?

There is a "famous" rule in spectroscopy,1 that goes this way: If a compound is centrosymmetric, then its normal vibrational modes cannot be simultaneously IR and Raman active. and this is simple ...
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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 ...
13
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347 views

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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How does one recognized Td/Oh symmetry in molecules?

The identification of point groups of a molecule is usually done following a strict scheme, either manually or algorithmically. In all textbooks I could find, however, the first step of the scheme is ...
10
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2answers
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Does trans-decalin really have a plane of symmetry?

My teacher told me that trans-decalin (see below) is achiral due to the presence of both, a centre of symmetry and a plane of symmetry. But I could not spot the plane of symmetry untill now. Can ...
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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'...
10
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1answer
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Derivation of the Orgel diagram for octahedral d2 complexes

The Orgel diagram for a typical octahedral $\mathrm{d^2}$ complex is shown below: (source: Kettle, Physical Inorganic Chemistry, p 146) I understand that the right-hand half of the graph shows how ...
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In a molecular dynamics context, is the methyl rotation in propene a symmetric or asymmetric internal rotor?

In a prior question, I asked about the (a)symmetry of the potential energy surface of the methyl rotation of propene. In that context, the kinetic energy of the nuclear motions is of course assumed ...
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1answer
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Symmetry representations

I'm Having a real struggle trying to understand symmetry representations matrices and character tables. Is there anyone who would be kind enough to help me out here? I understand it is probably a ...
9
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812 views

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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How do I find the ground state term symbol for transition metal complexes?

I have a problem where I'm trying to match metal complexes with the proper ground state term symbol. I've tried doing a Google search and looking for a process, but haven't had any luck. I decided ...
9
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297 views

Does the methyl rotation in propene have a symmetric or asymmetric potential energy surface?

Depending on how one imagines the methyl rotation of propene to occur, it seems like it could exhibit either a symmetric or an asymmetric potential energy surface. If the $\ce{H2C=CH\! -}$ portion ...
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Why is 2-methyl-2,3-pentadiene achiral (allene)?

2-Methyl-2,3-pentadiene is achiral. Why? Centre of symmetry Plane of symmetry C2 axis of symmetry Centre and Plane of symmetry. I've drawn the structure: So far I've dealt ...
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351 views

Are all cubic point groups encountered?

My symmetry lecture notes state that there are seven high-symmetry 3D point groups, which have more than one rotation axis of order greater than 2: $T$, $T_d$, $T_h$, $O$, $O_h$, $I$, $I_h$. I ...
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How to get the reducible representations of the B-B and the B-Cl bond of B2Cl4

I just can't seem to get the correct answer to this symmetry question in my book. "Introduction to molecular symmetry J.S.Ogden." I am trying to find the reducible representations of both the $\ce{B-...
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Determination of +/- reflections in sigma molecular term symbols

This page, which depicts the molecular term symbols for the $\ce{O2}$ and $\ce{O2-}$ (Edit: Mistaken on $\ce{O2-}$) molecules, perhaps best summarizes the full scope of my questions. In general, I don'...
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Nomenclature: equivalent atoms by single locant

Sometimes the IUPAC name is too verbose despite the structure's high symmetry. If we could use only the first locant of the ("topologically symmetrically") equivalent set of locants, and designate all ...
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Does symmetry lower the energy of molecules?

Why does nature "prefer" symmetry? Why is symmetry energy-lowering? I keep hearing statements along the lines of this tossed around by chemists. Here are some examples: https://physics.stackexchange....
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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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Identifying the C3, C4, S4, and S6 symmetry operations in the Oh point group

The Oh character table has ten symmetry classes. I am trying to identify them, but my stumbling block is in identifying the order of each class. I will use this diagram as a reference, from Sydney ...
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295 views

Why does (2z²-x²-y², x²-y²) have -1 trace in the character table of Td for C3 rotation?

I'm trying to understand the irreducible rep for $(2z^2-x^2-y^2, x^2-y^2)$ in the $T_\mathrm{d}$ point group. Specifically, for $C_3$ rotations, a trace of $-1$ is listed in the character table for ...
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1answer
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How do I determine the crystal field splitting for an arbitrary point group?

How can I figure out the degeneracy of the d orbitals for a site that has a given point group? Specifically I'm interested in $D_{3d}$ and $D_{3h}$, but it would be good to know how to do it in the ...
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1answer
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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 (...
7
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1answer
791 views

Are these two space groups in a group–subgroup relationship?

Given two crystal space groups, how can one determine if they are in a group-subgroup relationship? The specific case at hand is P 21/m 2/m 2/a (aka P m m a, #51) and P m m 2 (#25), but knowing how to ...
7
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In what way trans alkenes are more symmetric than cis alkenes?

While providing the reason for the higher melting point of trans molecules, everyone says that trans molecules are more symmetric than cis molecules. An example can be found over here, where the OP ...
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What is the rotational symmetry number used to calculate the rotational entropy from an ORCA frequency calculation?

The quantum chemistry software ORCA gives the following warning on frequency calculations: ...
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Enantiotopic hydrogens in cyclopropanone

Are the hydrogens that on the same carbon and those that are cis enantiotopic? And are they isogamous or anisogamous? And will they anisochronous in a chiral environment NMR? Isochronous - hydrogens ...
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Does an axis of symmetry determine chiralty?

What I've understood about chirality and elements of symmetry: A molecule that is not superposable on its mirror image is said to be chiral. Plane of symmetry: An imaginary plane cutting a compound ...
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226 views

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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Why can anthracene, but not phenanthrene, take part in Diels–Alder reactions?

Both anthracene and phenanthrene seem to be structurally similar, with three aromatic rings. The middle rings in particular seem to be similarly activated towards cycloadditions.
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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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1answer
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How does B2Cl4 have two perpendicular c2' axes?

I have been looking at the symmetry of $\ce{B2Cl4}$ and was cannot understand how it has two perpendicular $C_2'$ axes? I understand it has a $C_2(z)$, $S_4(z)$ and two dihedral planes bisecting ...
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Is a 2-D periodic structure isomorphic with the surface of a torus, a sphere, neither or both?

When I was reading through the ADF-BAND tutorials, one of the toy systems presented was a 1-D periodic structure involving 3 collinear hydrogen atoms. The tutorial pointed out that, topologically ...
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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 ...
6
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121 views

Accessible statement on the intuition and usefulness of group theory to chemistry

I am writing a lesson plan for high school students who are studying group theory, and I am having difficulty in relating the subject matter to the real world. I have quite a few examples using the ...
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What is the point group of hexachloridotitanate(III)?

I found the answer to this question to be $D_\mathrm{3h}$ but I am not convinced. Can someone explain me with a diagram if possible and explain why it doesn't belong to the octahedral point group $O_\...
6
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3answers
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Why does symmetry have to be maintained in molecular orbitals?

Using the example of $\ce{XeF4}$: What is the physical explanation enforcing the symmetry of the $\ce{1b_{1g}}$ orbital on the fluorine atoms? Why isn't the symmetry of a nonbonding orbital arbitrary?...
6
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1answer
316 views

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 ...
6
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Symmetry and SALC: choosing coordinate basis

When we construct symmetry adapted linear combinations of orbitals (aka SOs) to build an MO diagram, we choose the z axis as the axis of highest symmetry and all other axis to make symmetry operations ...