# density functional theory

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1. #### Quantum Mechanics II

Fundamentals of Physics, II (PHYS 201) Lecture begins with a detailed review of the double slit experiment with electrons. The fate of an electron traversing the double slit is determined by a wave putting an end to Newtonian mechanics. The momentum and position of an electron cannot both be totally known simultaneously. The wave function is used to describe a probability density function for an electron. Heuristic arguments are given for...more

2. #### Seeing Bonds by Electron Difference Density

Professor McBride uses a hexagonal "benzene" pattern and Franklin's X-ray pattern of DNA, to continue his discussion of X-ray crystallography by explaining how a diffraction pattern in "reciprocal space" relates to the distribution of electrons in molecules and to the repetition of molecules in a crystal lattice. He then uses electron difference density mapping to reveal bonds, and unshared electron pairs, and their shape, and to show that...more

4. #### The Perfect Gas Law

The Perfect Gas Law relates temperature, pressure, and density of gases in the atmosphere. It can be used to demonstrate why warm air rises, cool air sinks, and helium balloons float in the air. Buoyancy forces act in fluids (both water and air) when fluid is displaced by a parcel of a fluid with a different density. A combination of buoyancy force and the relationship given in the Ideal Gas Law govern the motion of parcels of gas in the a...more

5. #### Triple Integrals Part 2

Using a triple integral to find the mass of a volume of variable density.

6. #### Vertical Structure of the atmosphere; Residence Time

Pressure and density decrease exponentially with altitude in the atmosphere. This leads to buoyancy effects in the atmosphere when parcels of air are heated or cooled, or raised or lowered in the atmosphere. Temperature varies in a more complicated way with altitude in the atmosphere, with several inversions which occur at the boundaries of the various layers of the atmosphere. Solar radiation interacts differently with the gases that comp...more