# 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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### 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 ...
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### 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 ...
15k 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 ...
199 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. ...
2k views

### What is the mathematical basis behind the Jahn-Teller effect?

Both first-order and second-order Jahn-Teller distortions play a very important role in chemistry. It is often said that the Jahn-Teller effect is based on symmetry arguments, and hence nothing can ...
2k views

### Why is the letter J omitted in the spdf… sequence?

Under spherical symmetry, the irreducible representations corresponding to $L = 0, 1, 2, \cdots$ are assigned the letters $\mathrm{S}, \mathrm{P}, \mathrm{D}, \mathrm{F}, \cdots$ after which the ...
696 views

### Irreducible representations and system states connection

Let's say I have the molecule $\ce{N2+}$. Its symmetry point group is clearly $D_{\infty\mathrm h}$. But I'm confused by its irreducible representations. I know there are 8 of them, but as I ...
6k 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 ...
63k 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 ...
5k views

### Using group theory to make molecular orbital diagrams

Because of Orthocresols' meta post I ask this question about application of group theory to molecular orbital theory. In my undergraduate lecturers, we've seen many examples of making qualitative MO ...
847 views

### How do I determine the molecular vibrations of linear molecules?

I know how to do it for just about every other point group, but the $D_{\infty \mathrm h}$ and $C_{\infty \mathrm v}$ character tables aren't as straightforward. In particular, I'm interested in the ...
2k views

### Molecular orbital diagram and irreducible representations for dinitrogen

I'm trying to understand how to draw molecular orbital diagrams, since I'd like to use the molecular orbitals to determine the total state of the molecule (i.e. $A_1$, $B_1$ etc.), so I prefer the ...
755 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 ...
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 ...
390 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 ...
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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### 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 ...
3k views

### How to systematically find the reducible representation of a molecule? (eg: XeF4)

I am attempting to use the reduction formula to find the irreducible representation of $\ce{XeF4}$ to determine its IR stretching vibrations. I know the point group of $\ce{XeF4}$ is $D_{4h}$ and have ...
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 ...