Implement a Python code which determines the minimum of a 2D Morse potential by an optimization procedure. 

• Allow the user to define a 2D Morse potential using the equilibrium distances x0, respectively y0, the asymptotic limits Dx, repectively Dy, and the potential well widths a, respectively b.

• Implement a class which determines the analytical gradient of the 2D Morse potential.

• Implement a class which performs the optimization, starting from user-defined input coordinates (x1, y1). Implement at least one optimization algorithm, see several examples here.

• Optional: implement routines to visualize the potential and the path followed during optimization.

Implement a Python program which can perform different types of spectral analysis.

• Implement a Spectrum class which can read and perform different operations (normalize, calculate area, etc.) on spectra of your choice (e.g. IR, optical, X-ray, etc. absorption or emission spectra, Raman, NMR or anything else). For example, you could use a database like NIST (experimental), SpectraBase (experimental), or MaterialsProject (calculated data), or spectra which you measured/calculated yourself.

• Implement a class which can perform operations with two or more spectra (addition, subtraction, average/weighted average, etc.).

• Implement a class for plotting and visualizing spectra in a Jupyter notebook.

• Optional: Implement a class which can handle a collection of spectra (performed under different conditions) and represent it as a 2D map. 

Implement a Python code which can perform different operations on molecules. 

• Implement an Atom class where atoms are defined by their atomic number or symbol and have different properties like mass, single bond radius, double bond radius, etc.

• Implement a Molecule class as a collection of Atoms and read in the atomic coordinates from an xyz file. Implement routines to allow the user to rotate the molecule, stretch bonds, or rotate dihedral angles.

• Using py3Dmol, write a routine to visualize molecules in a Jupyter notebook. 

• Optional: using RDKit, enable the user to create a molecule based on its SMILES string. See some examples here.

Implement a Python program which determines the pressure, temperature, and balck-body emission spectrum of a star based on the simple model described in problem 4 of problem set 8, Introduction to Astronomy, MIT course. In your program:

• Implement a Star class where a star object is defined by its total mass (M) and radius (R).

• Implement a routine which calculates the pressure and temperature as a function of radius within the star.

• Implement a routine which computes the black-body emission of the star based on its surface temperature.  To obtain the surface temperature, modify the quadratic temperature profile as T(r) = Tc ( 1 - b (r/R)**2 ), where b=0.9991 and Tc is the temperature at the star's center (r=0). The surface temperature is obtained at the radius for which the inward optical depth from the surface is 2/3. In the equation for the optical depth, consider a constant Rosseland mean opacity k = 0.034 m**2/kg.

• Implement a StarCluster class which consists of a collection of stars and implement routines which plot the pressure and temperature at the stars' core as a function of their mass or radius.

• Optional: enable computing the Kelvin-Helmholtz timescale according to the model described in problem 4.

Implement a Python code which generates a solar system based on a simple heliocentric model with circular orbits in 2D.

• Implement a Sun class with mass, radius and luminosity as attributes.

• Implement a Planet class with attributes mass, radius, type, starting position, distance from the sun, orbital velocity, period, etc. 

• Implement a SolarSystem class consisting of one sun and a collection of planets. Allow the user to define the attributes of the sun and the number of planets in the solar system, then generate a set of planets following (some) of the rules described here. Determine the planets' periods of rotation based on Kepler's third law.

• Optional: create a routine which allows to visualize the solar system in a Jupyter notebook. For example, see here or here.