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An orbital is a one-electron wavefunction, usually derived by solving the Schrodinger equation. This tag applies to questions about all forms of orbitals; additionally, questions about the construction and properties of molecular orbitals should be tagged with [molecular-orbital-theory].

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Angular Momentum Quantum Number and Orbitals

In our lecture I was told the angular momentum QN is equal to $n - 1$ of the principle QN, which corresponded to the orbital shape. How is this case, for example in Barium the principle QN is 6 with,...
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Why are the radial wavefunction and radial distribution function different?

I'm having trouble understanding the following two graphs, which are the radial wavefunction of the hydrogen 1s orbital and the corresponding radial distribution function: Specifically, why is the ...
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Implementing the projected atomic orbital (PAO) localization in Gaussian

I am currently attempting to learn how to setup the active space for performing CASSCF calculations. The textbook I am using as a reference is: Roos, Björn O. "Multiconfigurational quantum ...
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HOMO / LUMO energies in a qualitative view

I have a question regarding the HOMO and LUMO energies depending on various effects like substituents and electronegativity. It seems to be a somewhat known topic but I cannot really find a clear ...
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Is the notion of orbitals different in theoretical chemistry?

I am just an average chemistry student that is currently exposed to theoretical chemistry. And I am seeing very puzzling things, such as 1p, 2f, 3g orbitals. In my attempt to reconcile this, I was ...
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Are any other orthonormalizations schemes besides Lowdin normally used when solving SCF equations?

When solving equations of the form: $$F(C)C = SC\epsilon$$ (e.g. Hartree-Fock-Roothan or Kohn-Sham-Roothan) where $F$ is the fock matrix, $C$ is the coefficient matrix and $S$ the overlap matrix, ...
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How do I have to interpret the input to the OCC flag in Molpro?

I'm trying to understand the occupied orbital specification in Molpro. They're specified by the OCC flag, while it's stated in the documentation, that OCC, m1, m2, ..., mn; where the ...
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Molpro - Simple explanation of OCC, CORE, FROZEN and CLOSED orbitals

I'm beginning with quantum chemistry and I'm supposed to do some ab initio calculations with Molpro. The problem is, I don't understand the orbital specification very well. Let's say, I have the ...
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Reducible representations - choice of new basis

I was looking at this tutorial about reductions of representations. At first, the basis consists of four orbitals $(s_N, s_1, s_2, s_3)$ and the representations look like this and we want to reduce ...
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54 views

What is the difference between carbon in an excited state and with sp³ hybridization?

What is the difference between the carbon in the excited state, $\ce{[(1s)^2] (2s)^1 (2p)^3}$, and $\pu{sp^3}$ hybridization?
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pi molecular orbitals of benzene

I found the following picture of the $\pi$ molecular orbitals of benzene. Now, I am having problem on understanding $\pi_3$ and $\pi_5 ^*$ In both of these, we can see that, on right and left, bond ...
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If a single electron fills a degenerate energy level, does it fill all degenerate orbitals at once?

For example, if a single electron fills the 2p orbitals. Since all orbitals are degenerate, there is no reason why there would be any preference for px, py, pz. Is the electron hence in a ...
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The molecular orbitals of lithium hydride

So my understanding of molecular orbitals is as follows: the molecular orbitals of $\ce{LiH}$ can be thought of as being formed from the interaction/overlap of two atomic orbitals, one from lithium ...
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1answer
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What are the magnetic quantum numbers for specific d orbitals? [closed]

I mean I know they’re $\ce{d_{-2}}$, $\ce{d_{-1}}$, $\ce{d_{0}}$, $\ce{d_{1}}$, $\ce{d_{2}}$ but how do these numbers relate to each one of $\ce{d}$ orbitals $\ce{d_{z_2}}$, $\ce{d_{xz}}$, $\ce{d_{yz}}...
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1answer
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Why do the 4f and 5d orbitals have similar energies?

I've come to know this phenomena when learning about the exceptions to the aufbau principle. But there is no explanation of why 4f and 5d have similar energies (as I've read in some websites).
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117 views

Are the 2s and 2p subshells degenerate in the He+ ion?

I know that the 2s and 2p (as well as 3s, 3p, and 3d) electron subshells are degenerate in the hydrogen atom. I was wondering if they are also degenerate in other one-electron species, such as the $\...
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587 views

How is the structure of triiodide ion (I3-) possible?

I have seen the structure of triiodide ion ($\ce{I3-}$) but I cannot understand why this structure is even possible. I have seen in my textbook that $\ce{I_3^-}$ is formed by combination of $\ce{...
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Why are 4s electrons removed before 3d electrons? [duplicate]

According to Aufbau's Principle energy of 3d orbital is greater than 4s orbital, so which filling 4s if filled beforehand 3d. Whereas while removing electrons 4s electrons are removed first. Why? I ...
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1answer
297 views

Rule to determine the total number of elements in a period [closed]

If each orbital can take maximum of 3 electrons, then total number of elements in 2nd and 4th periods respectively are = ? I am not aware of the rule which helps to determine the total number of ...
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92 views

The CASSCF orbitals

I have two questions about the orbitals that we get after the CASSCF calculations. First, what are the CASSCF orbitals that we get from these calculations? I mean after optimization, in the CASSCF ...
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49 views

Effect of oxidation state on d-orbital splitting

I am trying to understand the effect of oxidation state on d-orbital splitting e.g. in Iron. I understand that splitting itself is caused by the fact that different d-orbitals are positioned ...
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How does the Jahn-Teller distortion result in both elongation and compression?

Recently, I have been reading up on the Jahn-Teller effect and I have read articles and posts on it, such as What is the mathematical basis behind the Jahn-Teller effect?. However, many of these ...
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2answers
329 views

Can a π bond form between the py and d(x2-y2) orbitals along the x-axis?

π bond does not form due to overlap between $\ce{d_{x^2-y^2}}$ and $\ce{p_y}$ along x axis? True or false? Here is a diagram of the orbitals. This pair of orbitials should be distingished from $\...
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Valence shell expansion and sulfur

I've been searching some things regarding the ability of sulfur to accomodate negative charge and reached the conclusion that it's due to its size and its ability to expand its valence shell. I can't ...
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Why Gallium has less atomic radius than Aluminium but Thallium has more atomic radius than Indium? [duplicate]

All four elements mentioned here belong to the 13th group, where they follow the order- Al, Ga, In, Tl. Gallium's atomic size is less than that of Aluminium, because of the poor shielding effect of ...
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Importance of higher order exchange terms?

The MP2 ground state energy of a molecule or solid can be written as $$E^{(2)} = \frac{1}{2}\sum^{\text{occ.}}_{ij}\sum^{\text{virt.}}_{ab} \frac{\langle ij | ab \rangle [\langle ab|ij \rangle - \...
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147 views

What red and blue area represent in a orbital software?

I have a software in my android device named hydrogen atom. It show orbital of hydrogen we have to set the quantum numbers and probability of finding particle. But what the blue and red colour area in ...
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Probabilities of Electrons in Orbitals [duplicate]

I've heard both of the following: An orbital is a region where there's a 90% probability of finding an electron An orbital is a region where an electron spends 90% of its time Are these essentially ...
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88 views

Quantum Mechanical Model of An Atom, Shells, Subshells [duplicate]

I've just been introduced to the quantum Mechanical Model of an Atom, so please bear with me on this one. Are Subshells and shell physical things, like do they really exist, or is it a concept only to ...
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2answers
187 views

What is the difference between the mean radial distance and the most probable radial distance of an orbital?

I was reading JD Lee's Concise Inorganic Chemistry and it has given some values of mean radial distance which is increasing from s to p to d orbital. I had earlier read that the most probable radial ...
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Why does s-p orbital separation increase with increasing atomic number? [duplicate]

More specifically, why does s-p energy separation increase: Across the period Down a group I do know that penetration of electrons increase with lower angular momentum and lower principal quantum ...
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Are there bonds which share single electron?

Are there bonds which share single electron? During chemical bonding, I asked our teacher why there are only 2 electrons shared in a bond. He said that because it's that one orbital can accommodate ...
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Why the ground state of H has no angular momentum?

I read that an atom of hydrogen in thr ground state has no orbital angular momentumand consequently no B-field, is that true? If so, why is that and how did they determine the lack of L and B? Is that ...
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Volume of orbitals

As I was learning about atomic structure, the lecturer made a seemingly dubious claim: The volume of a p orbital is one-third that of the s orbital. Thus, inter-electronic repulsions are ...
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285 views

Why does a neutral atom of beryllium not have any electrons in a p orbital?

Here's what I understand about quantum number and orbitals, please correct me if anything is wrong: Electrons enter into these different types of orbitals because they have a higher/lower amount of ...
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Are all degenerate d-orbitals identical?

This discussion spun off from the comments to another question. The basic idea of that question was that electrons don't have a preferred order of filling in $p$ orbitals, i.e. the first electron will ...
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Can carbon be the central atom of a complex? Can it form a quadruple bond with itself? [closed]

Why does $\ce{[C(NH3)2]}$ not exist as a complex? Here, $\ce{C}$ is carbon and the configuration of $\ce{C}$ in ground state is $\ce{[He] 2s^2 2p^2}$. Can't the two $\ce{NH3}$ molecules pair the two ...
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Question regarding orbitals in tetrafluoroethylene

So the question is as stated: What atomic or hybrid orbitals make up the sigma bond between $\ce{C1}$ and $\ce{C2}$ in tetrafluoroethylene, $\ce{C2F4}$? and that What is the approximate $\ce{F-...
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Why is Cr+ unstable?

We know that half-filled and fully filled orbitals are highly stable. In ground state $\ce{Cr}$ has a $\ce{3d^5\! 4s^1}$ configuration. Therefore, the elctronic configuration of $\ce{Cr+}$ should have ...
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117 views

Which orbital lobes are occupied?

In the p-orbitals, there are 3 dumbbell-shaped lobes, each of which can contain 2 electrons. In the diagrams of the d- and f-orbitals, there are two or more lobes (or orbital shapes) or each value of ...
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“Sea of Electrons” - do the individual electron shells interact with each other?

I've often heard metals as having a "sea of electrons". I was wondering how the actual relationships between the electron shells of individual atoms are... do the electrons orbitals overlap the same ...
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Trend in the infrared stretching of molecular hydrogen to group 8 transitions metals?

While going through old notes, in relation to the Dewar-Chatt-Duncanson model, it states that the stretching frequency for $\ce{N2}$ to the group 8 transition metals ($\nu(\ce{NN})$) proceeds as: \...
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1answer
848 views

Why is the difference between atomic radii of Na and K greater than that of Rb and Cs?

I am aware that this question has already been asked here: Why does the "gap" between atomic radii get smaller down the periodic table?. However, I was wondering if there is a way to ...
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1answer
150 views

How to form 6-31G basis set; specific instructions

I'm new to basis sets. I read that for 3-21G, given the following basis set for carbon (from Basis Set Exchange): ...
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2answers
410 views

What is wrong with the Aufbau principle that results in so many exceptions?

From what I have observed in the periodic table is that many transition elements do not follow the Aufbau principle. And it's not just the elements like $\ce{Cu}$ and $\ce{Cr}$ that differ from ...
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580 views

Is it correct to talk about an empty orbital?

Professor A. J. Kirby mentions: The properties of an orbital are those of an electron contained in it. It is normal practice, illogical though it may sound, to talk of 'vacant orbitals'.The ...
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Do 1s & 2s orbitals overlap of different atoms while forming sigma bond? I

Do 1s & 2s orbitals overlap of different atoms while forming sigma bond? I think they should overlap as there will not be enough energy difference between them.
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How to derive Pauli Exclusion Principle without assuming anti-symmetry?

So, it appears that the statement of the Pauli Exclusion Principle is equivalent to the statement that fermions are anti-symmetric. That is, if you assume that fermions are anti-symmetric, then you ...
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789 views

Where is the probability of finding an electron in 1s orbital maximum? [duplicate]

So the way I understand the question is that it asks us at what r (distance from nucleus) and at what angles is the probability going to be maximum. The way I see probability of finding at a point in ...
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443 views

Group 15 Ionisation Energies

I had a little confusion regarding ionisation energies. I get that in general, the second ionisation energy > first ionisation energy, due to increased effective nuclear charge on the second electron....