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].

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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 ...
72
votes
2answers
29k 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 ...
78
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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 ...
39
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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? ...
22
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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 ...
32
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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 ...
19
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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 ...
11
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2answers
1k views

What exactly is an orbital?

What exactly is an orbital? Atomic or molecular. Is it the function that describes the behaviour of the electron? Is it the Schroedinger's equation solution, e.g., for Hydrogen atom? Is it the ...
8
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1answer
844 views

How does the radial distribution function of Vanadium differ from that of Calcium and how does this affect the ionic electron configurations?

When Vanadium is ionised it loses the 4s electron first, meaning that it's 3+ ion has a different electron configuration to Calcium despite it being isoelectronic. Can it be explained in terms of ...
10
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2answers
7k views

How do Electrons Cross Nodes in Orbitals?

I was wondering in orbitals that have nodes such as the p orbital, how does the electron move from one lobe to the other? I know that people say it is because of the wave/particle nature of electrons ...
9
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2answers
3k views

Why do copper (II) complexes contain so many valence electrons?

Consider tetraaminecopper (II) ion. $\ce{[Cu(NH3)4]^2+}$ or $\ce{[Cu(NH3)4(H2O)2]^2+}$. The copper(II) ion has the electron configuration $\mathrm{[Ar]\ 3d^9}$. How do the 4 electron pairs from the ...
33
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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.
21
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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 ...
20
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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 ...
15
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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 ...
32
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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 ...
25
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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....
15
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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?
13
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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?...
9
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3answers
14k views

What is hyperconjugation?

What is hyperconjugation and how do you know if there is hyperconjugation in a compound? Which orbitals are involved in hyperconjugation?
6
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3answers
2k views

Why do atomic orbitals have their unique shapes?

Is there a scientific explanation to why p orbitals are shaped like two balloons, etc. I think it has got to do with electron repulsions. Wikipedia says they are 'characterised by unique values of ...
55
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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 ...
21
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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
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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 ...
13
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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 ...
6
votes
1answer
15k views

What are the magnetic quantum numbers for the three real p orbitals?

The form of the p orbitals that we are familiar with are the $\mathrm{p}_x$, $\mathrm{p}_y$, and $\mathrm{p}_z$ orbitals: (source: ChemTube 3D) I also know that the p subshells have the quantum ...
16
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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 $\...
7
votes
2answers
8k views

Periodic trend in difference of energy between the s and p orbitals

Why does the difference of energy between the 2s and 2p orbitals of the second period elements increase with increasing atomic number? Does this difference increases by moving down a group, e.g. is ...
3
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4answers
5k views

What are similarities and differences among shells, orbitals, subshells, and energy levels?

I think I know what these terms mean: each row on the periodic table has a new shell of electrons, a subshell is e.g. 1s, 2s, 2p, 3s, 3p, etc., and energy levels are the same as shells, whilst ...
12
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2answers
6k views

Why do octahedral metal ligand complexes have greater splitting than tetrahedral complexes?

Octahedral complexes have greater splitting in the d orbitals. Is it because octahedral complexes have more atoms and thus more interactions?
3
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1answer
3k views

Whats the difference between ionization energy and orbital energy?

If you look at the trend in orbital energies as you go across a period the pattern is clear (orbital energy decreases with increasing effective nuclear charge) and, to my knowledge, it has no ...
9
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1answer
4k views

Do electrons only fill 'spin up' first? Or could it start filling 'down spins' first? [duplicate]

Due to Hund's rule, electrons start filling up the orbitals without pairing up. When this is happening, do the electrons all fill up the 'up' spin? Could they fill in the 'down' spin? Why do they ...
5
votes
2answers
514 views

Is the 5d orbital involved in triiodide ion?

Is the $5\mathrm{d}$ orbital involved in the triiodide ion, $\ce{I3-}$? There are $5$ electron pairs around the central iodine. (Almost) all of the hypervalent compounds involve the most ...
4
votes
0answers
183 views

Howcome orbitals become 'core-like' when electrons are removed?

It seems to me that f-orbitals for lanthanide metals are treated as 'core-like' when a certain number of electrons have been removed. Or, as Radiochemistry puts it, The 4f binding energy is so ...
3
votes
1answer
357 views

How can the size of atom be the cause of octet expansion?

Lately, I was reading The Lewis Theory of Covalent Bonding by Peter Atkins in Appendix 4 of 'Elements of Physical Chemistry'. There he was talking about expansion of octet . As he wrote: Many ...
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 ...
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 ...
10
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3answers
3k views

LCAO (Linear Combination of Atomic Orbitals) and Phases

So when combining atomic orbitals to form molecular orbitals, you can either add the wave functions or subtract them. But at the same time, orbitals can exist in opposite phases (say one lobe of the p ...
9
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2answers
5k views

What are overlap integrals?

I came across something called overlap integrals. I could understand that it is something about the overlapping of orbitals. What is it actually?
15
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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 ...
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 ...
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 ...
10
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1answer
6k views

The “rules” for LCAOs in Molecular Orbital Theory

In our course on physical chemistry, which involves MOT, we have been taught that in the LCAO approach, the wave function for a molecule … say hydrogen ion ($\ce{H2+}$), can be approximated by a ...
8
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2answers
1k views

In an octahedral complex, what happens to the electrons donated by the ligand?

I am trying to understand how complexes are coloured. After some reading, I found out this was due to the d-d splitting induced by the coordinate bonds of ligands to the central metal ion. The ...
4
votes
1answer
10k views

Correlating the decrease in orbital radius and penetrating power with the increase in l value

I have read that s-orbitals have a stronger penetration effect as compared to p-orbitals and p-orbitals have a stronger penetration effect as compared to d-orbitals, etc. Therefore, the electrons in ...
34
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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 ...
18
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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 ...
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 ...
10
votes
1answer
11k views

Predicting sigma bond overlap strengths of s-s, p-p, s-p, sp-sp etc

How can we qualitatively predict $\sigma-$bond strengths of overlap between: $\ce{s-s}$ $\ce{s-p}$ $\ce{p-p}$ $\ce{sp-s}$ $\ce{sp-p}$ $\ce{sp-sp}$ etc.? My school-book says $\ce{s-s}$ overlap bond ...
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 ...