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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3
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2answers
349 views

Deriving the irreps of the d-orbitals under C3 and S6 operations in octahedral symmetry

Contextual background: I am trying to reproduce the symmetries in the graph on this page (MO diagram for $\ce{ML6}$ complex). I have reproduced the metal s and p orbital representations as well as the ...
6
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2answers
9k views

Identifying the C3, C4, S4, and S6 symmetry operations in the Oh point group

The Oh character table has ten symmetry classes. I am trying to identify them, but my stumbling block is in identifying the order of each class. I will use this diagram as a reference, from Sydney ...
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0answers
51 views

Imposing particle number subspace on second quantized Hamiltonians

Here is my question: Second-quantized Hamiltonians act on any state, regardless of how many electrons the state has. They are also block diagonal on different particle-number subspaces, as they ...
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2answers
1k views

Examples of molecules with D4 and C9 point groups

Trying to come up with examples of (hypothetical) molecules/shapes that have $D_4$ and $C_{9h}$ point groups. For $D_4$, I thought a cyclobutane structure, but with 4 substituents coming off of the ...
6
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1answer
2k views

Understanding group theory easily and quickly [closed]

Please can you explain me the group theory especially the reducible and irreducible representation and class and subclass and how to tell they are in the same group or not. I know it is a tedious task ...
5
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1answer
4k views

Molecular term symbols for excited state oxygen

What are the possible term symbols for excited state oxygen with configuration $(1\pi_u)^3$,$(1\pi^*_g)^3$ (all other occupied orbitals are closed shell)? Based on the possible values of S and $\...
2
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1answer
193 views

What does a molecules color have to do with its bond/orbital energies?

For example, elemental iodine is deep violet. Its sigma bond or perhaps the lone pairs are capable of absorbing all visible light frequencies except violet which is why we see it as that color. ...
13
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1answer
1k views

What are point groups and the benefits of using them?

I have heard vague information about point groups and symmetry before but I am unsure how they actually help me predicting physical properties of molecules. How do I assign point groups and what good ...
7
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3answers
260 views

Why does (2z²-x²-y², x²-y²) have -1 trace in the character table of Td for C3 rotation?

I'm trying to understand the irreducible rep for $(2z^2-x^2-y^2, x^2-y^2)$ in the $T_\mathrm{d}$ point group. Specifically, for $C_3$ rotations, a trace of $-1$ is listed in the character table for ...
2
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1answer
453 views

Point Groups and MO Theory

I am a little confused about how point groups give information about MO of polyatomic molecules. Is it true that all molecules of a given point group such as, $\mathrm{C_{2v}}$, will have the same MO ...
5
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1answer
650 views

Non-bonded orbitals in water

General Chemistry perspective: Looking at the molecular orbitals of water, we can see that the oxygen is $sp^3$ hybridized. Oxygen forms two sigma bonds with hydrogens, and there are two lone pair ...
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1answer
2k views

How are point group character tables typeset correctly?

I want to know how to typeset character tables of point groups correctly. Consider the following two extremes using the $C_{\text{2v}}$ (or is it $\text{C}_{\text{2v}}$?) point group as an example. ...
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0answers
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Decomposition of axial vector and vector representions of C4v group

Let $R$ be the orthogonal matrix corresponding to an operation in $O(3)$. If R is a proper rotation, then both vectors $\vec{V}$ and axial vectors $\vec{A}$ are transformed in the same way $$ \vec{V} ...
3
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1answer
477 views

Theoretical Calculation of Lattice Parameter from Space Group

If I am given a compound which belongs to, say the cubic $\text{Ia}\bar 3\text{d}$ space group, is there a known way to calculate the lattice parameter of the compound? In general, can lattice ...
7
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1answer
5k views

How to get the reducible representations of the B-B and the B-Cl bond of B2Cl4

I just can't seem to get the correct answer to this symmetry question in my book. "Introduction to molecular symmetry J.S.Ogden." I am trying to find the reducible representations of both the $\ce{B-...
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1answer
2k views

Symmetry representations

I'm Having a real struggle trying to understand symmetry representations matrices and character tables. Is there anyone who would be kind enough to help me out here? I understand it is probably a ...
5
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0answers
116 views

Finding the irreducible representation which an orbital transforms under [duplicate]

I have some major confusion on irreducible representations. An example of a problem I have is Based on the character table for the point group of each of the follwing molecules, which irreducible ...
15
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1answer
59k views

What are t2g and eg in CFT?

In the Crystal Field Theory, when the splitting of the d-orbital occurs, it gets divided into two parts... The upper part with higher Energy is the $t_{2g}$ and the lower part with lower Energy is ...
6
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2answers
116 views

Accessible statement on the intuition and usefulness of group theory to chemistry

I am writing a lesson plan for high school students who are studying group theory, and I am having difficulty in relating the subject matter to the real world. I have quite a few examples using the ...
2
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1answer
290 views

What is the product of two irreducible representations on the character table?

Let's say the direct product of $\ce{A1}$ and $\ce{B1}$ on $\ce{C}_{2v}$ character table, what is the direct product of the two for water molecule? or for any other instance in general, what does the ...
12
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1answer
13k views

How can I find the symmetry labels of atomic orbitals in a molecule?

What are the symmetry labels for the p and d orbitals of platinum in $\ce{[PtCl4]^2-}$? I understand how to find the point group of a molecule, but am not sure how to use the character table to find ...
5
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0answers
384 views

Determining the lowest rank non-vanishing multipole moment [closed]

I have been told that the multipole moments of rank 0,1,2,3,...n have respectively 1,3,5,7,...2n+1 components which transform like the spherical harmonics of rank 0,1,2,3,...n. How do I use the ...
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2answers
724 views

Group Theory and Chemistry for Undergraduate Thesis

I am advising a student on her senior math thesis. She would like to involve chemistry somehow (her other major). I know no chemistry. I have read in several places that representation theory ...
7
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1answer
4k views

How do I determine the crystal field splitting for an arbitrary point group?

How can I figure out the degeneracy of the d orbitals for a site that has a given point group? Specifically I'm interested in $D_{3d}$ and $D_{3h}$, but it would be good to know how to do it in the ...
5
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1answer
3k views

MO-Scheme of SCN- and its bonding properties when used as a ligand

I tried to figure out the MO-scheme of the tetragonal-bipyramidal complex trans-$\ce{[Co(en)2(NCS)2]SCN}$ in which the isothiocyanate ligands are bound to the $\ce{Co^3+}$-Ion in $\eta^{1}$-mode (en = ...
7
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1answer
743 views

Are these two space groups in a group–subgroup relationship?

Given two crystal space groups, how can one determine if they are in a group-subgroup relationship? The specific case at hand is P 21/m 2/m 2/a (aka P m m a, #51) and P m m 2 (#25), but knowing how to ...
10
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2answers
5k views

How does one recognized Td/Oh symmetry in molecules?

The identification of point groups of a molecule is usually done following a strict scheme, either manually or algorithmically. In all textbooks I could find, however, the first step of the scheme is ...