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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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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162 views

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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215 views

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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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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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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Do we consider the spatial orientation of a molecular orbital while assigning plane of symmetry?

I am following the video lectures by Neeraj Saini sir and in this video$^{\dagger}$ he said that $\ce{CO2}$ has infinite planes of symmetry. But I think that if we take into account the orientation of ...
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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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C₂ axis of symmetry in 1,3-dichloroallene

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 rutile structure have primitive unit cell instead of body centered?

In the literature (Wikipedia), I read that $\ce{MgH2}$ have a structure of rutile. Then, I looked at its space group which is $P4_2/mnm$. From this notation, I understood that it possesses a (...
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What is the precise meaning of “in-phase” (and “out-of-phase”) in this context?

I am currently studying the textbook Infrared and Raman Spectroscopy, 2nd edition, by Peter Larkin. In a section entitled Symmetry: Infrared and Raman Active Vibrations, the author says the following: ...
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Origin in a crystal

I am trying to understand the International Tables for Crystallography. How can I identify the origin in the image on the left? Without knowing the origin, I cannot identify the position of the ...
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Determining symmetry correction by looking at rotational quantum states

I'm trying to understand the relationship between symmetry correction and rotational quantum states, particularly in the case of dipoles with identical atoms. For an angular momentum quantum number $...
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Do SALC-AOs really belong to their symmetry species?

I'm working through a molecular symmetry textbook and something keeps nagging at me. If I derive the SALC-AOs for NH3 (using the projection operator method), I'll get A1: $ \frac{1}{\sqrt{3}}(\...
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XRD: Can stacking faults cause pseudo-centring?

Consider a cP lattice with a = 10 Å and an octahedron residing on each of the unit cell's vertices as shown below: The maximum symmetry will be Pm-3 m. Now, let's consider there are stacking defects ...
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Why is the transition (0,0,0) -> (1,0,1) observed in a gas phase IR spectrum of CO2?

Let ($v_1$,$v_2$,$v_3$) denote the vibrational state of $CO_2$. Why is the transition $(0,0,0)\rightarrow (1,0,1)$ observed when the trasition $(0,0,0)\rightarrow(1,0,0)$ (asymmetric stretch) is not ...
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Determine and draw planes and axes of symmetry of a molecule using software (VESTA or Mercury)

I designed the $\text{MoS}_2$ molecule (bilayer), with polytype 2H in the VESTA. My goal is to draw the plans and axes of symmetry of the bilayer set. According to the information in the literature, ...
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How to define axes if all rotation axes pass through the same number of atoms?

I was wondering how one can define the axes for a molecule with several equal axes of rotation, all of which pass through the same atom. I know that the $z$-axis is usually defined as the principal ...
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Symmetries and degeneracies of the s,p, and d orbitals

Consider the molecular AB_8 (complex with central atom A and 8 B ligands (coordination number 8), for which I determined the point group D_4d) and determine the symmetries and degeneracies of the s, p,...
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Are centre of symmetry(COS) and alternate axis of symmetry(AAOS) dependent on each other?

COS=Centre of symmetery AAOS=Alternate axis of symmetry Lets suppose a molecule has a COS. Does it need to have AAOS? What about the converse? If a molecule has AAOS does it necessarily have a COS? ...
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Finding Symmetry number of a molecule [closed]

An isotopic variant of the molecule SF$_6$ is S$^{19}$F$_4^{18}$F$_2$, with the two $^{18}$F nuclei oriented axially, so that the $^{18}$F-S-$^{18}$F angle is 180°and the four $^{19}$F nuclei form a ...
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Why sigma bond has C2 symmetry not C∞?

I have seen some books indicated sigma bond has C2 symmetry. I understand pi and delta bond change their signs about C2 and C4 rotation about bond axis, but I don't understand why sigma bond has C2 ...
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Are there optically active molecules in which all atoms lie in the same plane?

I've learnt that when a molecule is non-superposable on its mirror image, it exists as a pair of enantiomers and is optically active. Absence of plane of symmetry is given to be one of the properties ...
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What is the symmetry of dxy orbital?

Considering the sign of orbital and assuming the $z$-axis as a principal axis, for me, it looks like that it has two perpendicular $C_2$ axes that penetrate the lobes, so I think it is $C_\mathrm{2v}$....
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On the meaning of distinguishability, and wavefunctions for 3 electron atoms

In a 2-electron atom at lowest energy, the $(1s)^2$ is occupied and the electronic wave-function must satisfy anti-symmetry requirements in the particle coordinates, as the spatial wave function is ...
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Symmetry of an FO

I want to ask a question about the symmetry of an FO for $\ce{[CuL2]^-}$ where L is a $1e^-$ donor sigma bonding ligand (e.g. Me). For the ligand orbitals, I produced the following orbitals shown ...
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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 ...
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Why does dipole must lie parallel to a rotation symmetry axis?

While studying group theory, I've got confused by the following statement: For a molecule to have a permanent dipole moment, it must have an asymmetric charge distribution. The point group of the ...
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Link between centrosymmetry, dipole moment and chirality

What is the relationship between the three concepts in the title? I know all centrosymmetric molecules are achiral, but not all achiral molecules are centrosymmetric. Thus, there are no molecules ...
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Optical activity of cis coordination compounds

I came across a statement saying, "Consider a Octahedral coordination compound of type [MA2X2]. Then, if the compound is in a cis form, it shows optical activity as there is no plane of ...
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no positive $+$ or $-$ or negative label for $\pi$ orbitals

I want to ask a question about the symmetry for $\pi$ orbitals. We were learning today about the deduction of an MO diagram for a typical $\ce{M-M}$ system with $\ce{D_{\infty h}}$ and I was ...
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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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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 stereoisomers? ...
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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 ...