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'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 $A''$.
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Why are certain lattices compatible with only certain point groups and not all point groups?
I will limit this discussion to 2 dimensions for ease of intuition. My understanding of the 17 crystallographic plane groups is that these 17 groups represent all the possible symmetry groups of any ...
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How do I assign functions for cartesian coordinates and rotations to irreducible representations of a character table?
I do not really understand the intuition behind the functions assigned to irreducible representations.
For example, in H₂O, the A₂ representation is given by
...
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Is there a difference between $A_{1g}$ modes and $A_{g}$ modes?
I know that both are totally symmetric and that the '$1$', according to the Mulliken table, refers to symmetry around the $C_2$ axis but I was reading some papers and found that modes were sometimes ...
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Are A1g modes reduced at 180 degrees polarisation in Raman spectra?
I have read that A1g modes are identifiable in Raman spectra by looking at cross-polarised Raman spectra and seeing peaks that strongly reduce in intensity. So essentially, the intensity of A1g modes ...
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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{...
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Factor Group Analysis of Na2SO4 - Site Group Symmetry
I'm still trying to understand how to construct a factor group analysis for a given molecular point group and the resulting solid state group symmetry. For this I searched for some examples and found ...
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Relation between symmetry of a reciprocal vector and lattice planes perpendicular to it
What is the relation the symmetry of a high-symmetry point in the first Brillouin zone and lattice planes perpendicular to it? Are the two symmetries equivalent?
I have this question because I want to ...
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What does it mean that a state belongin to a given irrep transforms like $Rx$, $Ry$ or $Rz$
The present question is related to this other question I did few days ago.
Given a point group and the list of the irreps (see for example here) the meaning of an irrep which transforms like $x$ or $x^...
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When does the angle between the planes in tetrahedral molecule with central atom deviate from 90°?
Consider an atom X bonded to four other atoms A, B, C, D in a tetrahedral fashion with sp³ hybridisation. If A, B, C, D are the same, every bond angle is 109.47°, and the angle between the planes ...
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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 ...
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What is m.2m point group?
I'm using Bilbao Crystallographic Server to find 3D crystallographic point groups of the K points of anatase TiO2.
Since the space group of anatse TiO2 is $I4_1/amd$, on this page, I found the point ...
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Determination of energies in MO diagrams
How do we determine the relative placements of molecular orbitals in their diagrams? I understand that we can use point groups to find symmetry-allowed interactions between orbitals that we write on ...
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is this compound meso? trans-1,4 dimethylcyclohexane [duplicate]
I had a question on a quiz that asked if the compound below was meso or not. I thought that it would be meso because there is a plane of symmetry going through the two methyls, but the answer was that ...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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 ...
user92687
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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 ...
user92687
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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, ...
user98209
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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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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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