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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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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 ...
Silvio Levy's user avatar
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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 $\mathrm{e_g}$ and the lower part with lower ...
NeilRoy's user avatar
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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 ...
orthocresol's user avatar
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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,...
NotEvans.'s user avatar
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21 votes
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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 ...
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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 ...
Geoff Hutchison's user avatar
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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 ...
Rainer's user avatar
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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 ...
Kinformationist's user avatar
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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 ...
Richard Terrett's user avatar
15 votes
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459 views

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{...
orthocresol's user avatar
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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 ...
Raphael J.F. Berger's user avatar
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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 ...
Martin Medro's user avatar
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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 ...
orthocresol's user avatar
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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 ...
Swedish Architect's user avatar
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How are there two C3 rotation axes in ammonia?

If we look at the character table for the $C_\mathrm{3v}$ point group (which $\ce{NH3}$ is an example of), we see that these are the symmetry elements ${E, 2 C_3, 3 \sigma_v}$ present in the molecule. ...
PV.'s user avatar
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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 ...
orthocresol's user avatar
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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 ...
F'x's user avatar
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Using symmetry and group theory arguments to explain iron(II) in a tetrahedral crystal field

I am trying to figure out how to explain $1s \rightarrow 3d$ spectroscopic transitions for $\ce{Fe^{2+}}$ in $T_\mathrm{d}$ symmetry. These transitions make up the pre-edge region in K edge X-ray ...
Silverwilly's user avatar
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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 ...
hBy2Py's user avatar
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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'...
Blaise's user avatar
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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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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 ...
RedPen's user avatar
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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 ...
MattyT's user avatar
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9 votes
2 answers
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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 ...
Keren Naomi's user avatar
9 votes
2 answers
34k views

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 ...
Blaise's user avatar
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9 votes
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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 ...
hBy2Py's user avatar
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8 votes
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354 views

What's the relation between two symmetry groups, if one has all the symmetry of the other and some more?

Question: Consider two molecular symmetry groups, for example $C_s$ and $C_{2v}$. $C_s$ has one inversion plane, and two irreductible representations: the symmetric $A'$, and the antisymmetric $A''$. ...
Neinstein's user avatar
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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 ...
F'x's user avatar
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8 votes
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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-...
RedPen's user avatar
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8 votes
1 answer
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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'...
Blaise's user avatar
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8 votes
0 answers
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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 ...
mykhal's user avatar
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7 votes
3 answers
2k views

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....
Dissenter's user avatar
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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. ...
Eenoku's user avatar
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3 answers
498 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 ...
dualredlaugh's user avatar
7 votes
1 answer
2k views

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 (...
gamma1's user avatar
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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 ...
Max Radin's user avatar
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Point group of harmonic oscillator

The book Molecular Quantum Mechanics by Atkins and Friedman [1] says the point group of a harmonic oscillator is $C_\mathrm{s},$ composed by the identity operator $E$ and a reflection $\sigma_\mathrm{...
AlfredV's user avatar
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1 answer
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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 ...
F'x's user avatar
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7 votes
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Why is prismane explosive but cubane is not?

So I was reading about polyhedral hydrocarbons, because I dig the topic, and I read (admittedly on wikipedia entries... But they cited papers, I swear!) that prismane is explosive due to the massive ...
urquiza's user avatar
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7 votes
2 answers
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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 ...
Keren Naomi's user avatar
7 votes
1 answer
5k views

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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7 votes
1 answer
3k views

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: ...
logical x 2's user avatar
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7 votes
1 answer
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Why does twistronic 'magic angle' graphene have only 180-degree symmetry?

From Graphene superconductors may be less exotic than physicists hoped[1]: Excitement rose earlier this year with the discovery of superconductivity in a similar system[2]: three layers of graphene ...
Kurt Hikes's user avatar
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7 votes
1 answer
286 views

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 ...
Avishai Barnoy's user avatar
7 votes
1 answer
403 views

How do I show that a transition is electric dipole allowed with group theory/symmetry?

This is actually a follow up of this question The follow-up is not because of the electric instead of magnetic dipole (this is trivial). It is because I'm interested in extra info. Suppose I have a ...
Davide Sangalli's user avatar
7 votes
1 answer
416 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 ...
Tyberius's user avatar
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6 votes
2 answers
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Chromium cyanide complexes

I have rarely seen any chromium $(\ce{Cr})$ square planar complexes and I have been told that $\ce{[Cr(CN)4]-}$ is tetrahedral. So, if the statement is actually correct, are there any other known ...
LM2357's user avatar
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6 votes
2 answers
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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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1 answer
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Why are square planar coordination compounds with four different ligands optically inactive?

Why do square planar coordination compounds of type $\ce{[Mabcd]}$ not show optical activity, although they contain 4 different ligands (i.e. chiral central metal atom)?
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