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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What does it mean by non-bonding p pi orbital?

In a paper by Peng et. al.,[1] I read about the valence band maximum of $\ce{TiO2}$ consists of non-bonding O pπ orbitals ... the valence band maximum (VBM) consists of non-bonding O pπ states What ...
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How do we find the SALCs?

I am trying to understand exactly what IRREPs are and, in order to know more about it, I started reading the chem.libretext course on molecular symmetry which up to this point seemed fairly ...
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Why are there only 14 types of Bravais lattices and not 28 when there are 7 types of unit cells and each can have four variations?

As the title suggests, I can't understand why certain kinds of variations (like Face-centred or Body-centred) are restricted to certain types of unit cells. An orthorhombic unit cell has Primitive, ...
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Of 2-bromobutan-2-ol and trans-1,2-dimethylcyclobutane which is chiral as well as dissymmetric?

In an examination I was asked to determine the molecules which are chiral as well as dissymmetric. There were four options, and among them, two were achiral, as they had an improper axis of symmetry. ...
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Planes of symmetry of a molecule

Are we limited to use only xy, yz and zx planes to check for planes of symmetry of a molecule? Because I see a plane of symmetry in the following molecule through the two shown H atoms or OH groups. ...
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Solution of the Roothaan Equations of H2 by Symmetry Arguments

FWIW my background is in physics and maths, but I am just starting a chemistry PhD (the last time I took a chemistry class was high school). I have only some background in representation theory, and ...
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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 ...
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Analysis of metal carbonyl bonding in Fe(CO)5 using molecular orbitals

I am really struggling with this question we have been set in class: Metal-carbonyl bonding: Conceptionally, one can build up $\ce{[Fe(CO)5]}$ from the $\ce{Fe(CO)4}$ fragment plus free $\ce{CO}$ in ...
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Why does an improper rotation axis preclude chirality?

Can anybody prove that any molecule with an axis of improper rotation is nonchiral? I still do not understand why this is so, any proper mathematical proof or visualisation of a generalised molecule ...
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d orbital irreducible representations in metal in ML4 model [closed]

In ML4 (Metal—4 ligands)model which has a square planar shape and D4h point group, what is the irreducible representation for the 5 kinds of d orbitals in the central metal?
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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 ...
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High symmetry points and x-coordinates

Is it possible to work out the x-coordinates related to high symmetry points? The software I'm using doesn't provide me with that, so I was wondering if there is a way to manually figure it out, as I ...
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Symmetry representations for acetonitrile (CH3CN)

Can anybody share the symmetry labels for acetonitrile ($\ce{CH3CN}$), please? I mean to assign the symmetry labels to orbitals of acetonitrile
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Is there a geometrically intuitive explanation of the equivalence of the numbers of irreducible representations and symmetry classes?

In group theory, as used in chemistry, we’re familiar with the idea that the number of irreducible representations of a symmetry group equals the number of classes of symmetry operations, e.g. three ...
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Is there any mathematical or logical proof that carbon with 4 different groups would be chiral?

In chemistry; chirality is generally defined in 2 ways. Lord Kelvin's definition: "I call any geometrical figure, or group of points, chiral, and say it has chirality, if its image in a plane ...
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How many stereoisomers are present in octahedral complexes of type MA3B2C?

Does $\ce{MA3B2C}$ type have optical isomerism or just geometric isomerism? I was told that it has three isomers, two cis and one trans. Are the two cis isomers optically active?
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D-orbitals of point group C2v

I'm trying to construct an MO diagram for cisplatin, which has C2v symmetry. However, there is no Mulliken label for the d(x^2-y^2) orbital in the character table. Does this orbital not form molecular ...
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Does 1,3-dichloroallene possess a C2 symmetry axis?

Is there an $C_2$ axis of symmetry in $\ce{Cl-CH=C=CH-Cl}$? A $C_2$ axis of symmetry means that I should be able to rotate the molecule about an axis by $180^\circ$. But I would need a composition ...
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Why does hydrogenation of this compound not result in a diastereomeric mixture? [duplicate]

In a question, this compound was given and it was asked: "Hydrogenation of the above compound in the presence of poisoned Palladium catalyst gives?" When I was answering it, I thought that ...
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Why is the base-centered orthorhombic crystal lattice a unique crystal system?

I'm having difficulty understanding why the base-centered orthorhombic crystal system is a unique crystal system. When I draw two base-centered orthorhombic unit cells next to each other there appears ...
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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 ...
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electronic transition for polyenic molecules

I am having troubles with polyenes states symmetry. I found an exercise on the pentadien, where they ask us to analyze the symmetry of the singlet excited states corresponding to: State S1: π+ →π+ ...
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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. ...
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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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Mathematical definition of a symmetry operator

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, applying a symmetry operation ...
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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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687 views

Example of an achiral molecule without a plane of symmetry or inversion center?

Some websites, such as this textbook, mention how generally a plane of symmetry or inversion center in a molecule is enough to consider it achiral. Nonetheless, this source clarifies but if these ...
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are the exact and kohn-sham electron densities totally symmetric?

For any molecule with open or closed shells considering the electronic state to be the ground state: Is the exact electron density totally symmetric? is the Kohn-Sham electron density totally ...
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A question about rotational symmetry of organic molecules and in particular, the cyclic Isomers of C3H4X2

I was thinking about an organic chemistry problem a few days ago but reached a dead end. There were 2 parts to this question. The first was thinking about the isomers of 'C3H4X2' [where X could be ...
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Optical activity of tartaric acid

The meso-form of tartaric acid is optically inactive due to the plane of symmetry. But how are these forms able to show optical activity when the σ-bonds can freely rotate, which can change the ...
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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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Is there a better coordinate framework and symmetry operator for constructing molecular orbitals of molecules with higher-order geometry?

The following excerpt is taken from [1] (with a few rewording, emphasizes are mine). In an attempt to construct molecular orbital (MO) of any molecule, one needs to determine the symmetries of ...
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Tetrahedral complex and vibronic coupling or different rule for d-d transition?

I'm currently preparing a few slides for an upcoming talk in our group. I would like to mention some of the very basics regarding crystal field and ligand field theory as well, though this will not be ...
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Conventional unit cell for a hexagonal crystal system

The figure shows a unit cell of a hexagonal crystal system. Drawn in bold, is the unit cell. The lightly shaded one is a unit cell as well and has a six fold symmetry along an axis, hence is more ...
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Software for determining symmetry elements and point group of drawn molecules

The title represents my overall question. I would like to have a software that able to draw molecules (especially coordination complexes) and determine the symmetry elements and point group of the ...
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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 $D_\mathrm{\infty h}$ point group table and it lists $C_\infty$, $\...
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How many peaks would there be in H1 NMR of ethene?

Since the bonds can't rotate, would there be 2 peaks? Likewise, how many peaks would there be in trans-but-2-ene and cis-but-2-ene?
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Symmetry Operation on Product of Functions

In regards to direct product representations, I'm trying to find a proof for: $R(X_iY_j)=R(X_i)R(Y_j)$ Where $R$ is a symmetry operation of a group and $X_i$ and $Y_j$ are members of different basis ...
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Manually changing symmetry

I have two crystal structures, one in R3m and one in Cm symmetry. Both structures also differ in stoichiometric ratios, $ABC_4$ and $A_2B_2C_8$, respectively. Both structures look nigh on identical, ...
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Point group specific definition

Does the term only refer to molecules that have the same symmetry elements or exactly the same symmetry operations. Online I see that its the same symmetry operation however my professor's slides show ...
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Is plane of symmetry a necessary and sufficient condition for optical inactivity in coordination compounds? [closed]

In organic chemistry, we have to check for all three types of symmetry in a compound to check its chirality, ie, plane, alternate axis and centre of symmetry. But in coordination compounds, do we need ...
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Do we need to check for all kinds of symmetry in a compound to declare it achiral?

I know that a compound is achiral if it contains any one of the following kind of symmetry. 1.Plane of symmetry 2.Centre of symmetry 3.Normal axis of symmetry 4.Alternate axis of symmetry It is ...
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What is cn axis of symmetry [closed]

While reading about axis of symmentry and I'm not able to comprehend what does C infinite or rather n signify in a molecule I know axis of symmetry is the axis along which rotation of molecule ...
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How to identify whether a molecule is planar [closed]

While solving for plane of symmetry of molecules I came across 1,3-dichlorocyclobutane (1) and I realized it does not have any plane of symmetry because we don't know whether hydrogen and chlorine are ...
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Stereo-isomerism in 7-methylbicyclo[2.2.1]hept-2-ene

The above are two compounds. The objective is to find if the compounds are identical/enantiomers/diastereomers I can see a plane of symmetry if we keep the $\ce{H-C-CH3}$ in the plane. So, ...
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Why should the scalar product of the components along two axes remain unchanged after transformation?

A couple of proofs from Chapter 2 of "Space Groups for Solid State Scientists" are giving me a hard time (see attached image). So what I understand is: "r" was the original ...
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$Q_3$ is symmetric with respect to the $\sigma_v$ operation?

I am currently studying the textbook Infrared and Raman Spectroscopy: Principles and Spectral Interpretation, second edition, by Peter J. Larkin. Section 8. Symmetry: Infrared and Raman Active ...
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How to find a symmetry group of a system if all the symmetry transformations do not obey closure and don't form a group?

For instance, consider a system with $p_x$ and $p_z$ orbitals at the vertices of a square (on xy-plane). A square by itself would have $D_4$ symmetry. However, because of the $p_x$ orbital; the $90^\...
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What is the link between the classical and quantum definition of the symmetry number?

From what I understand, the symmetry number for a molecule can be defined in 2 ways: 1. The quantum mechanical symmetry number corrects for overcounting the number of possible rotational states of a ...
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Why do most character tables include an $(x^2 + y^2)$ term?

Why do most character tables (e.g. $C_{3h}$ but not $C_{2h}$) include an $(x^2 + y^2)$ term? Is it an abbreviated form for $d_{z^2}$, applying only where $3d$ (and higher) orbitals might be involved, ...

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