13

This sounds like you were exploring work at least related to the work by the Lilienfeld group equally hosting a dedicated site here about data sets already used in their earlier and ongoing exploration of chemical space, programs used to work with the data, and publications. To go considerably higher in molecule count than QM9, you could either go for GDB-...


9

The ISOL24 database (http://www.thch.uni-bonn.de/tc.old/downloads/GMTKN/GMTKN55/ISOL24.html) contains molecules with up to 81 atoms! The other answer says that there's a database called "OE" with molecules that have up to 174 atoms, but it is "not yet publicly available".


7

The $2n^2$ rule is nothing but a mathematical consequence of the mathematical description of electrons around an atom – what chemists call quantum theory and is currently the most accepted description of atomic matter by a mile. Thus, until quantum theory is significantly amended, the fifth shell does, in theory, have the capacity to hold $2\times 5^2=50$ ...


6

Since I was reviewing this in some detail recently, I will try to supplement Prof. Hutchison's already good answer with some more detail as to why one would choose to work with normal coordinates, rather than the already quite simple Cartesian coordinates. The short answer is that, under the assumption of small displacements, normal coordinates decouple the ...


5

If we consider N atoms in a non-linear molecule, then each atom can move independently on the X, Y, and Z axes. That's $3D \times N = 3N$ degrees of freedom. But if I move the whole molecule 3 Å along the x-axis, that doesn't constitute a vibration - it's just a translation. So we have to remove 3 degrees of freedom for translations. Similarly, if I ...


5

There is not much to explain because the concept is wrong. There is no sulphur compounds in which the 3d orbitals (remember: they have an energy level similar to 4s) are involved in bonding in any noteworthy way, shape or form. From what I believe I may remember about the outdated concept, ‘one d orbital’ refers to cases like $\ce{SO3^2-}$ with sulphur in ...


3

Let me start by saying that this is a very difficult question to answer because it's not very hard to come up with pathological cases which I will address at the end. Also, as you point out, it is somewhat non-trivial to calculate $r_0$ from theory and also somewhat non-trivial to determine $r_e$ from experiment. That being said, I think I have a good first ...


3

This image is from Atomic Spectra and Atomic Structure by Gerhard Herzberg, ‎John William Tranter Spinks - 1944. It does not really have boxes (just boxes of a table), but spin +1/2 and spin -1/2 are shown as arrows. Of course, I am not claiming this is the first usage, just that in 1944 it existed.


3

This answer owes a big debt to @orthocresol, who got me back on track after my over-simplified answer to the OP’s question. In the long obsolete Bohr theory of the hydrogen atom, the total energy of the $n$-th energy level, $E_n$, is $-2.179\times10^{-18}/n^2\ \mathrm J$, which is approximately $-2.18\times10^{-18}/n^2\ \mathrm J$. This is depicted in the ...


3

Firstly, regarding the extra question: Atkins' Molecular Quantum Mechanics (5th ed.) uses "term" for $^2\!S$, and "level" for $^2\!S_{1/2}$. Back to the main question. It's been a long time since I did term symbols, so I am happy to be corrected, but if I am not wrong, your $^4\!P$, $^4\!D$, and $^2\!S$ terms are not allowed because of the Pauli exclusion ...


2

Beyond other answers, I'd suggest the original PubChemQC project, which offers ~3 million molecules from PubChem optimized using DFT (B3LYP/6-31G*). Molecules include a wide variety of elements as long as the molecular mass is less than 500 Da. (Roughly speaking that should still handle ~38 carbon atoms.) "PubChemQC Project: A Large-Scale First-Principles ...


2

There are excellent answers already, but I wanted to address the following question [...] how would we mathematically define a normal coordinate for the oxygen(s) and hydrogen during a normal mode vibration of water molecule? The first step is to switch from cartesian coordinates to internal coordinates. For water, it would be the two bond lengths $L_1$ ...


1

I believe this website will be of use to you http://molview.org/ It appears to take names, formulas, smiles etc. If the name/formula/smile ID pops up in the search bar, it will draw it for you. Its database seems quite large, I use it for some pretty big drug molecules. It draws 2D and 3D images, and it also does single/double/triple bonds.


1

Thank you, Buck, for all your suggestions. You're right that a good way to check the influence of the volume is to try varying it. I did that by using the maximum and minimum volumes of the fluctuations in one simulation. There was some variation, so the volume does matter! I was lucky enough to hear about "travis," an amazingly simple-to-compile code (...


1

When doing a CI calculation based on Hartree-Fock orbitals, then usually the HF configuration has a very high weight in the CI vector (>90%). The next largest weight is then very small (for example only 1%), and there is a very large number of those very small configurations. Such cases are called weakly or dynamically correlated. Because of the large weight,...


1

To answer this question it is advantageous to treat a molecule as a graph and use the well known adjacency matrix from graph theory. Here is the wikipedia definition: For a simple graph with vertex set $V$, the adjacency matrix is a square $|V| × |V|$ matrix $\mathbb{A}$ such that its element $\mathbb{A}_{ij}$ is one when there is an edge from vertex $i$ ...


1

I will try to add another point to the discussion which is statistics. Quantum mechanics is a non deterministic theory which can only make assumptions about expectation values and probabilities of obtaining a special value. In general your wave functions or vectors correspond to states while the projection of one wave function onto another (aka the scalar ...


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