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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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 ...
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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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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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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 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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