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Plotting Atomic Orbitals (AOs) with Mathematica

Plotting Molecular Orbitals (MOs) with Mathematica

Manipulate CUBE format volume data ﬁles

Crystal ﬁeld Hamiltonian and atomic shell splitting

PNMRShift: A software tool for NMR shifts of paramagnetic molecules

KK-GUI: Software with graphical interface to perform Kramers-Kronig
transformations

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(explore on GitHub)

You can use this notebook to visualize the orbitals (wavefunctions) of hydrogen-like
atoms. The plot interface is shown above, along with visualizations of a 3p_{x}
hydrogen orbital. For non-zero values of the magnetic quantum number m, the usual
real ’sine’ and ’cosine’ linear combinations are created for -/+m.

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(explore on GitHub)

Rather: Plotting isosurfaces of molecular orbitals... Please follow the link to GitHub
shown above, then follow the links that mention orbital plotting, to see detailed
descriptions and download options. The notebooks use volume data in the popular
cube format.

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(explore on GitHub)

A Mathematica notebook for plotting graphical representations of NMR shielding
tensors; easily adaptable for other types of rank-2 tensors (EFG, Optical Rotation,
…).

Description and some examples

Download the Mathematica (v. 12 and higher) notebook (60 kByte)

Here is the notebook for older Mathematica versions (up to v. 11) (52 kByte)

Download an XYZ molecular coordinate ﬁle read by the notebook (16 kByte)

If you use this plotting tool for your research, please cite the recommended references
given at the top in the notebook.

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See the repository on on GitHub. manipulatecube is a Fortran tool used by me and my group to work with volume data ﬁles in the ’Gaussian cube’ format. You can use manipulatecube to multiply the volume data by a factor and integrate the cube, take linear combinations of two data sets (same grid, same molecule), add or multiply two cube ﬁles (same grid, same molecule), or use manipulatecube to bring a data set for an orthogonal but unsorted (not in the order x, y, z) grid, or a grid with negative steps (going from positive to negative coordinate values), into a more standard grid format. [Not all of the available visualization software packages can handle grids with negative steps or grids with vectors that aren’t in the order of x, y, z direction].

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(explore on GitHub)

A Mathematica notebook for the symbolic calculation of a crystal ﬁeld Hamiltonian and
the spin-orbit coupling Hamiltonian in a basis of atomic orbitals for a given angular
momentum $\ell $,
along with other calculations.

Description and some examples

Downloads the Mathematica notebook (792 kBytes)

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(explore on GitHub)

Here you can download the source code along with Linux and Windows (32 bit)
binaries of a program that reads calculated magnetic resonance tensors (Ramsey
shielding, EPR Zeeman and hyperﬁne coupling), and optionally zero-ﬁeld splitting,
and assembles chemical shift tensors for a given temperature and pseudo-spin. For
details see Reference [224]

Download PNMRShift (4.2 MByte. GPL)

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(explore on GitHub)

This software is useful if you have absorptive or dispersive spectral data and want to
perform a Kramers-Kronig (KK) transformation to obtain the dispersive /
absorptive counterpart. Works under Linux and Windows and comes in two
versions that are both included in the package. Both versions are written
in Python and use the Python interface with Tcl/Tk and Matplotlib for
the GUI and the resulting plots. One version includes numerical routines
in Fortran that need to be compiled. The second version is Python-only
and does not require a compiler, but its KK transformations are slower. It
is possible to perform ‘anchored’ KK transformations known as multiply
subtractive KK (MSKK) or chained doubly-subtractive KK (CDKK); these
methods are described in Reference [92]. KK-GUI was developed in 2017 by
Mr. Herbert Ludowieg, then an undergraduate research assistant in my group,
based on prior developments by Mark Rudolph, Patrick Dawson, and Mikhail
Krykunov.

Download KK-GUI (458 KByte. GPL)

Below is a screen shot of the interface. We loaded optical rotatory dispersion data
(red curve) into the software and let it generate the corresponding circular dichroism
spectrum (blue curve).

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Note: Our spec-gen Python script provides much of the functionality of the old CD spectra toolkit, which is therefore no longer maintained.

Here you can download a package containing some Unix shell scripts and the
Fortran source code for two programs. Compiled binaries for a 32 bit Linux system
are included. The Fortran source code should compile with any f90 compiler. Please
email me if it doesn’t.

Download gzipped tar archive (781 kByte)

Together the scripts and programs process the output of a time-dependent DFT CD
spectrum calculation and generate a nice simulated spectrum. The CD spectrum can
be calculated with ADF or with Turbomole. The parsers are easily adapted for
other programs. Please see the included README ﬁle for instructions. You
need gnuplot to generate the spectra. Here is an example from Reference
[17]:

Simulated CD spectrum of [Co(en)3](3+)

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© 2013 – 2024 J. Autschbach. Some of the material that can be downloaded on this web page and the associated GitHub repository is in parts or wholly based on the results of research funded by grants from the National Science Foundation [NSF, grants CHE 0447321, 0952253, 1265833, 1560881, 1855470], the US Department of Energy (Basic Energy Sciences, Heavy Element Chemistry program, grant DE-SC0001136), and educational projects supported by these grants. Any opinions, ﬁndings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reﬂect the views of these funding agencies.