# Questions tagged [group-theory]

The systematic discussion of molecular symmetry is known as group theory. Group theory is a systematic way of describing the symmetry of molecules using concepts/rules borrowed from mathematics. This tag should be applied to any question which involves the theory or application of point groups, symmetry elements, or character tables.

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### Literature towards: how molecular symmetry simplifies/accelerates quantum chemistry calculations?

I am looking for some literature regarding the topic how molecular or crystal symmetry (point groups, space groups, e.g. $C_{2v}$ symmetry of $H_2O$ molecule) simplifies/fastens the quantum chemistry ...
1 vote
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### Intersection of symmetry elements in space groups

How can I estabilish a priori if two symmetry elements can intersect or not in a space groups? If I understand correctly, when the group is symmorphic I don't have problems: derive the general ...
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### Space group P4nc

I'm trying to understand space group diagrams and I have basics of symmorphic and non-symmorphic space groups and matrix calculation. I don't know how to interpret the c in third place. How can I ...
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### Identifying Type of Symmetry Operations

From the given set of symmetry operations for a space group, say, P-3m1 or Cmma, how can one identify the type of all symmetry operations. For example, how to distinguish the axis of rotation symmetry ...
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### How do we determine the local symmetry of anatase TiO2?

In this physical review B paper, the authors mentioned that the local symmetry of anatase TiO2 is D2d point group. Also, in this applied physics letters paper, the authors mentioned that the symmetry ...
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Today I had the first lesson about UV-Vis spectrum. From the picture, the transition from HOMO to LUMOs of 1,3-butadiene depends on whether the structure is s-trans or s-cis. My question is: Why the ...
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### Point group of trimethyl borate $\ce{B(OCH_3)3}$

What's the point group of trimethyl borate $\ce{B(OCH_3)3}$. The answer that my teacher gave is $D_{3h}$ but I'm struggling to see the n perpendicular $C_2$ axes and the horizontal plane of reflection....
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### Electronic configuration and symmetry labels of 3d$^7$ ions

In 3d$^7$ ions, e.g. Co$^{2+}$, the ground state is $^4$F, and it contains different levels due to the crystal field, such as $^4T_{1g}$, $^4T_{2g}$ and $^4A_{2g}$. Can anyone tell me what exactly ...
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### Mulliken Labels: How do I tell apart E, doubly degenerate, symmetry apart from T, triply degenerate, symmetry for a molecular orbital?

With A and B, it's pretty simple. If you rotate the molecule about its principle axis to where the orbitals line up, and the signs change, it's Mulliken label has a B. otherwise, it's A. I heard E ...
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### When relaxing the strong field interaction, the (t2g)^2 configuration splits into 4 states. What is the symbolic configuration of the Eg state?

When relaxing the infinitely strong field, the electrons start to feel one another's presence. They will, therefore, give rise to sets of states such as T1g, T2g... for the (t2g)^2 initial ...
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### Bonding and symmetry

So I have been looking at different ways of symmetry and bonding The so called counting method is something that I don't get For each operation in the group: ...
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### Reduction of direct product representation

When we do the reduction of the reducible representation generated from the total wavefunction expressed as product of MOs of appropriate symmetry, we can find the direct sum of more than one ...
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### Group theory and exact Eigenfunctions of Hamiltonian

I think I've understand why the real Eigenfunctions of Hamiltonian belong to a given irreducible representation and I've read that also MOs have to transform as irreducible representation due to the ...
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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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### 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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### Why not just use the x,y,z as basis functions instead of linear/quadratic functions of these unit vectors?

I am going through Applications of Group Theory to the Physics of Solids by M. S. Dresselhaus. In chapter 4 he states This is with respect to the P(3) group. I understand basis functions must ...
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### Why are 2D block matrices considered irreducible?

I am currently reading Applications of Group Theory by M.S. Dresselhaus On page 18 irreducible representations are defined and an example is given as follows: The author claims that these ...
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### Electronic states of VO vanadium oxide in $C_{2v}$ point group

The electron configuration of $V^{2+}$: ... 3$d^{3}$ with 3 d electrons in 3 d orbitals. In $C_{\infty v}$, $d_{xz}$ and $d_{yz}$ have $\Pi$ IRREP; $d_{z}^{2}$ has $\Sigma^{+}$ IRREP; $d_{x^{2}-y^{2}}$...
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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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### 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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### Why are Methyl vibr. modes called r modes and methylene vibr. modes called d modes

I am coming from a chemical background and currently work in the field of vibrational spectroscopy. When I talk to fellow physicists or chemists I always encounter the same question. "Why are 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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### Help determining normalisation constant in SALC of methane

We have been told that a symmetry adapted combination of four hydrogen orbitals is used to create localised hydrogen orbitals for methane. These orthonormal combinations are denoted ψa1, ψt’2, ψt’’2 ...
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### What does the order of a class mean in a character table?

I am not from a chemistry background. I am trying to see how the symmetry operations affect the stiffness tensor which led me in the path of understanding character tables. I am looking at the ...
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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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### Finding Equivalent representation of a molecule/crystal

Is there a website or online calculator to determine the reducible representation of a crystal/molecule using wyckoff positions without having to analyse the number of unmoved atoms/bonds for ...
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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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