Questions tagged [orbitals]

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].

Filter by
Sorted by
Tagged with
78
votes
7answers
115k views

Why is the 2s orbital lower in energy than the 2p orbital when the electrons in 2s are usually farther from the nucleus?

My chemistry book explains that even though electrons in the $\mathrm{2p}$ orbital are closer to the nucleus on average, electrons from the $\mathrm{2s}$ orbital spend a very short time very close to ...
72
votes
2answers
28k views

What is Bent's rule?

I'm all bent out of shape trying to figure out what Bent's rule means. I have several formulations of it, and the most common formulation is also the hardest to understand. Atomic s character ...
62
votes
4answers
28k views

Why do elements in columns 6 and 11 assume 'abnormal' electron configurations?

When I look around for why copper and chromium only have one electron in their outermost s orbital and 5/10 in their outermost d orbital, I'm bombarded with the fact that they are more stable with a ...
55
votes
2answers
3k views

Striking examples where Kohn-Sham orbitals clearly have no physical meaning

In Density Functional Theory courses, one is often reminded that Kohn-Sham orbitals are often said to bear no any physical meaning. They only represent a noninteracting reference system which has the ...
39
votes
3answers
106k views

What is the inert pair effect?

I was reading about the p-block elements and found that the inert pair effect is mentioned everywhere in this topic. However, the book does not explain it very well. So, what is the inert pair effect? ...
36
votes
5answers
5k views

How do I visualize an atom?

I have searched and searched, oh how I have searched. I am looking for a 3-dimensional visualization of a whole atom, one that that includes all the orbital geometry. A proper "layered" view of the ...
34
votes
4answers
3k 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 ...
34
votes
1answer
4k views

Natural Bond Orbital analysis: Significance of stabilization energy determined by 2nd order perturbation

PREFACE: I am no expert on this topic. My questions at the bottom may be off base. I have some experience with symmetry-adapted perturbation theory (SAPT) when it comes to analyzing intermolecular ...
33
votes
2answers
236k views

Difference between shells, subshells and orbitals

What are the definitions of these three things and how are they related? I've tried looking online but there is no concrete answer online for this question.
32
votes
1answer
7k views

When is it true that more nodes equals higher energy?

Consider all the MOs of some isolated molecule. (It could be a single atom too; I'll use MO to refer to AOs as well.) Number them in increasing order of the number of nodes (node = surface where the ...
32
votes
1answer
3k views

What would follow in the series sigma, pi and delta bonds?

I realise, that this question is a stretch, but I was wondering, how would a bonding orbital be called if it was formed from two $f_{x(x^2−3y^2)}$ or $f_{y(3x^2−y^2)}$ orbitals. Have there been any ...
32
votes
1answer
856 views

Why does hyperconjugation help for ring cleavage?

The question was to rationalize it the ring cleavage happens concerted or non-concerted. The papers "The Mechanism of the Thermal Decomposition of 1-Pyrazolines and Its Relationship to ...
29
votes
5answers
7k views

How do orbitals coexist with a nucleus?

Many diagrams of orbitals I've seen involve electrons moving through a center point—where the nucleus is. How can this be? Clearly they don't actually pass through the nucleus, so what does happen?
26
votes
3answers
48k views

Why are covalent bonds directional?

It is said that covalent bonds are directional, while ionic bonds are not. Why? Is it because of the orientation/directional properties of the overlapping orbitals?
25
votes
2answers
30k views

Why do atoms “want” to have a full outer shell?

Okay, so I know that this is about filling the orbitals of the atom, and I understand that. What I don't understand is why? For example, an Oxygen atom has 8 protons and 8 electrons spinning around it....
24
votes
10answers
8k views

Simple Explanation of orbitals

Imagine I was your little brother, how would you explain an orbital to him? (assuming he knows what atoms electrons and neutrons are, and the rest of the basics till that point.) I have been reading ...
24
votes
1answer
2k views

Canonical MOs vs. Localized MOs: Do both represent reality in the same way?

In my understanding localized molecular orbitals (LMOs) are equivalent to "standard" molecular orbitals, often called canonical orbitals (CMOs—by the way, why are they called canonical?). We can ...
23
votes
4answers
64k views

Reason for the stronger acidic property of phenol than alcohol

In phenol, pulling the $\mathrm{p}_z$ electrons from the oxygen atom into the ring causes the hydrogen atom to be more partially positive than it is in aliphatic alcohols. This means it is much more ...
23
votes
3answers
2k views

Symmetry lost in orbitals?

I've always thought that orbitals lead to a loss of symmetry, and have never been able to give myself a satisfactory answer to this. I'll explain via an example: Let's take an $\ce{N^3+}$ atom. It's ...
22
votes
2answers
1k views

Why do n AOs only form n MOs? [duplicate]

The textbooks I have read introduce LCAO by considering the H2 molecule. In this example, there are only two possible combinations of the two 1s orbitals (in phase and out of phase). When there are ...
22
votes
1answer
5k views

Why are atoms with eight electrons in the outer shell extremely stable?

Atoms that have eight electrons in their outer shell are extremely stable. It can't be because both the $s$ and the $p$ orbitals are full, because then an atom with 13 or 18 valence electrons would be ...
21
votes
5answers
11k views

Physical intuition behind negative values for wave function?

So a positive and a positive wave function create a bonding orbital where the probability of finding an electron is summed while a positive and a negative create an anti-bonding orbital with a lower ...
21
votes
2answers
5k views

Shape of the P1/2 Orbital

I always thought that p-orbitals had a dumbbell shape as pictured below. (image source) However, I was reading an article (see Table 1, item 2) that says, "...the spherical $\mathrm{p_{1/2}}$ ...
21
votes
3answers
30k views

What is the origin of the differences between the MO schemes of O₂ and N₂?

Here are the MO schemes of $\ce{N2}$ (left) and $\ce{O2}$ (right). Why is the $\sigma$-MO formed by the $p$ AOs energetically above the $\pi$-MO for $\ce{N2}$ but not for $\ce{O2}$? Can it be ...
20
votes
3answers
95k views

Angular and radial nodes

Nodes are the points in space around a nucleus where the probability of finding an electron is zero. However, I heard that there are two kinds of nodes, radial nodes and angular nodes. What are they ...
19
votes
1answer
18k views

What is Drago's rule? Does it really exist?

My textbooks states the Drago's rule in inorganic chemistry as follows: The more electronegative atom prefers the orbital having more p character, and lone-pairs or less electronegative elements ...
18
votes
5answers
9k views

Evidence of orbitals?

How do we know that there are different types of orbitals? For example, what evidence is there for the existence of $\mathrm{p}$ orbitals instead of there being multiple $\mathrm{s}$ orbitals (for ...
18
votes
3answers
9k views

When are two orbitals orthogonal?

When are two orbitals considered to be orthogonal? It will be helpful if you can provide an example molecule (or molecular orbitals in a molecule) since I can't really think of a scenario where ...
18
votes
2answers
1k 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 ...
18
votes
2answers
1k views

How to convert from spin orbitals to spatial orbitals in the Hartree-Fock approximation?

I need to calculate some of the more complicated self-energy terms from chapter 7 of Szabo and Ostlund's "Modern Quantum Chemistry", and I'm having trouble converting summations from spin orbitals to ...
17
votes
3answers
949 views

Have there been no advances in the determination of effective nuclear charges since Clementi and Raimondi in the 60s?

Effective nuclear charge is a very important concept in chemistry, and is the basis for the qualitative explanation of many observed chemical and physical properties, including several periodic trends....
17
votes
3answers
5k views

Why is one lobe of an sp3 hybridized orbital smaller than its other half?

A hybrid sp3 orbital is drawn with one lobe smaller than its other half, the latter which is of equal size when drawing the p orbital. Why is it so?
17
votes
1answer
366 views

Observability of Orbitals and Orbital Energies

This question comes from some thoughts I had after reading this question. First of all, is an orbital an observable? I know the answer to this question is no because there is no "single-orbital ...
16
votes
4answers
388 views

Hierarchy of electronic wavefunctions

The previous question contained too much unnecessary information and was edited. I am wondering about the "hierarchy" of wavefunctions. If one can combine atomic orbitals (AO) into molecular orbitals ...
16
votes
3answers
2k views

Computing two-electron integrals with an STO-3G basis set

I am trying to implement a restricted Hartree-Fock calculation using an STO-3G basis set, for fun. I managed to perform this calculation where only $\mathrm{1s}$ orbitals are present ($\ce{H2}$ and $\...
16
votes
3answers
704 views

Disproportionation of Au(II)

$\ce{Cu(II)}$ and $\ce{Ag(II)}$ complexes are known to exist while $\ce{Au(II)}$ is unstable and disproportionates to $\ce{Au(I)}$ and $\ce{Au(III)}$. My guess as to possible reasons to this effect ...
15
votes
1answer
16k 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 ...
15
votes
1answer
2k views

Why do the d orbitals have these notations?

Why do the d orbitals have the following notations: $xy, yz, xz, z^2$ and $ x^2-y^2$? What do they represent in their wave-functions?
15
votes
2answers
14k views

How to rationalise with MO theory that CO is a two-electron donor through carbon?

A question I am looking at is as follows: $\ce{CO}$ is isoelectronic with $\ce{N2}$. Sketch MO diagrams for $\ce{CO}$ and $\ce{N2}$. Point out key differences between the diagrams and use the ...
15
votes
1answer
269 views

Photoionisation microscopy of hydrogen - where are the p orbitals?

In this Physics Review Letters article, which was published in 2013, but I found recently, the authors report photoionisation microscopy images of hydrogen atoms in various electronic states. A. S....
14
votes
1answer
643 views

Shape of a wavefunction

I am trying to plotting the angular parts of a wavefunction ($Y_{(m,l)}(\theta, \phi)$) with Wolfram Mathematica. this is the table of spherical harmonics. I think the shape of these function should ...
14
votes
1answer
1k views

Are the canonical orbitals of Hartree-Fock also the natural orbitals?

My question stems from the comments on my answer to After a unitary transformation, is Koopmans' theorem still valid?. There was some confusion relating to differing terminology referring to different,...
14
votes
1answer
23k views

Difference between radial, planar, angular and spherical nodes

What is the difference between them? I think radial nodes and spherical nodes are the same, and angular and planar nodes are the same. Reference Finally, how many spherical nodes are there in ...
14
votes
1answer
2k views

Why only two atoms share an electron and not three?

In a covalent bond between two atoms, an electron from one of the either atom is shared by overlapping of their orbitals. So, Why can't three atoms share an electron and overlap their orbitals?
13
votes
2answers
16k views

The effect of hyperconjugation on the stability of alkenes with MO theory

Hyperconjugation stabilizes carbocations and that makes sense because electrons are given to the empty p orbital. But how does it stabilize alkenes? Can molecular orbital theory be used to explain it?...
13
votes
3answers
6k views

Correlation between Coulomb's law and VSEPR theory

I've always been told in chemistry lessons that lone pairs repel more due to a greater charge density than bonding pairs. And that makes sense when steric effects are involved when bond orbitals ...
13
votes
1answer
4k views

Splitting of $d$ orbitals when ligands approach central metal ion

In my high school chemistry book, it is written that when ligands approach the central metal ion (transition metal ion) to form dative bonds, the $3d$ orbitals split into two: two which are in higher ...
13
votes
2answers
1k views

What is the purpose of calculating other orbitals than HOMO and LUMO?

In this video of benzene orbitals, a lot of different orbitals are presented. Even orbitals that, I assume, could never be occupied. What is the purpose of calculating all these orbitals? Isn't all ...
13
votes
1answer
818 views

Photoisomerization of Azobenzene

Rotation around the double bond of azobenzene is restricted because it would distort the P orbital overlap between the nitrogen atoms. However, in the $n \rightarrow \pi^*$ excited state ($S_1$), the ...
13
votes
2answers
9k views

Resonance stability: ester vs. thioester

My problem set solution cites: "Although sulfur is less electronegative than oxygen, overlap is a more important consideration. Sulfur is a member of the third period. As a consequence, a ...

1
2 3 4 5
10