8
You can use the "compare" command in the Jmol program, either online or as free-standing program. A tutorial on how to use the program for this purpose is here, http://proteopedia.org/wiki/index.php/Superposition_with_jmol. It outputs the root mean square of the pairwise differences (RMSD) as well as the superposed coordinates.
6
For the more recent structures, you can view the density (based on measured diffraction data and the model, so-called 2Fo-Fc density) directly in the protein data bank, e.g. http://www.rcsb.org/3d-view/6QU9?preset=electronDensityMaps:
For a theoretical model or a model without deposited diffraction data, you would first have to generate structure factors, ...
6
You can do a structural comparison with VMD, using the RMSD trajectory tool. The RMSDTT is a default plugin for VMD (it comes with it, no need to do any fancy installation, so should help students access it).
6
The implementations of MNDO, AM1, and PM3 along with PM6 and PM7 in MOPAC include Sr and Ba, but not Ra. MOPAC is free for academic use, but modern versions of it are not open source. Most of these models have an open-source implementation in SPARROW (GitHub). An entirely different class of semiempirical models (GFNx) is available in the open-source XTB code ...
5
Various custom software exists to create nanotubes.
The following appears suitable:
http://www.jcrystal.com/products/wincnt/
A Wolfram Demonstrations application may also be of some use:
https://demonstrations.wolfram.com/NanotubeBuilder/
Furthermore, you may have further considerations like how to generate molecular mechanics parameters. For example, ...
4
There's a "pair-fitting" function in pymol that will align molecules given some user-defined reference atoms, and output an RMSD across those points of comparison. You can get pymol educational version for free, so students would be able to install it themselves.
4
To study surface reactions I recommend the growing string method (GSM) for surfaces. Here is a nice quote from the paper which developed it (Ref. 1)
GSM’s efficacy was confirmed by comparison with CI-NEB on
an extensive set of reactions characteristic of modern surface chemistry studies. In these cases, GSM reduces the computational cost (in terms of ...
4
What you've described is the field of electronic structure theory. To obtain the electronic density from the cartesian coordinates of the atoms requires immense amount of computation (assuming you have a protein in your pdb file). If you have a small molecule, you could use any number of common electronic structure packages. ORCA is open-source (assuming ...
3
Solution
$S^2\alpha = \left(S_x^2 + S_y^2 +S_z^2 \right)\alpha= S_x(S_x(\alpha)) + S_y(S_y(\alpha)) +S_z(S_z(\alpha)) $
from the ''rules", where for instance $S_x$ operating on $\alpha$ gives $\frac{1}{2}\hbar\beta$, we make the three replacements to get
$=S_x(\frac{1}{2}\hbar\beta) +S_y(\frac{1}{2}i\hbar\beta) +S_z(\frac{1}{2}\hbar\alpha) $
Now take ...
3
One possible way:
As you say
$${\bf{S}^2} = S_x^2+S_y^2+S_z^2$$
Thus
\begin{align}
{\bf{S}^2} &= \left( \frac{\hbar}{2}\right)^2
\left[\begin{pmatrix}
0 & 1 \\
1 & 0 \\
\end{pmatrix}\begin{pmatrix}
0 & 1 \\
1 & 0 \\
\end{pmatrix}
+
\begin{pmatrix}
0 & -i \\
i & 0 \\
\end{pmatrix}
\begin{pmatrix}
0 & -i \\
i & 0 \\...
3
I would say Chimera, no question. It has a good GUI with a lot of tools, including ensemble comparison. I find it both much easier and much prettier than VMD which has been recommended here.
3
There's a free software quantum chemistry package called Psi4. If you're a GNU/Linux user, under Ubuntu or any Debian-based distro, you can install it with a simple terminal command.
sudo apt-get install psi4
They have a well documented site, including a section dedicated to education with simple projects and friendly message boards. As of today, they list ...
3
You can reorder the Z-matrix with a free program like Molden. For example open the molecule in Molden and press the ZMat editor. From there you should see a button that says reorder Z-matrix. Click the atoms one by one, making sure to select the HCH atoms sequentially so they have an explicit angle. Dummy atoms are another good option.
3
SDD is a basis set description, which uses Stuttgart/Dresden ECPs. They are readily available for download at the BSE, but also via Univ. Köln. And they are pretty easy to pick out. See the Pseudo keyword for what is Gaussian 16 is using currently, which should be the same for 09. At least in the BSE there hasn't been an update to the S/D ECPs since their ...
2
Anton and its successor Anton2 are highly specialized pieces of machinery. In fact, the computer, the chip, and the only code that can run on the chip are all called Anton. There's a reason why the only Anton computer outside of D.E. Shaw is located in the Pittsburgh Supercomputing Center (Anton now deprecated there, replaced by Anton2): this highly ...
1
Semiempirical quantum chemistry models do carry out proper Hartree-Fock calculations, including both Hartree (electron-electron electrostatics) and Fock exchange contributions to the total electronic energy. As noted in the question, the tensor of 4-center Coulomb integrals is heavily sparsified, approximated, and parameterized to simplify and accelerate ...
1
Let us begin with the following principle: the CC ansatz always returns an appropriate electronic wavefunction (meaning a combination of Slater determinants). Still, at least in a non-relativistic approach, the Hamiltonian does commute with the Spin operator
\begin{equation}
S^{2}=S_{+}S_{-}-S_{z}+S_{z}^{2}
\end{equation}
(I'm using atomic units here)
and ...
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