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Exercise 11

Part of the course Computational Chemistry.

Task 11.1: Define

Of the following terms, pick three which you think you understood well and write two sentences defining the term in the most precise language possible. You may use German or English.

  • Density Functional
  • Born-Oppenheimer Approximation
  • Self-Consistent Field
  • Basis set
  • Slater Determinant

Task 11.2: Explain

Pick those two of the following terms that you feel are hardest to explain concisely and do so in at most five sentences each.

  • Electron correlation
  • Density Functional Theory
  • Hartree-Fock
  • Coulomb energy vs exchange energy
  • Normal modes

Task 11.3: Resolve

Pick any of the following statements and try to resolve the contradiction. Every question has an optional hint. Try to do it without researching the answer first.

  1. When improving both the basis set and the method, at some points vibrational frequencies from the Hessian do not improve w.r.t. experiment, even though the calculations get better and better. Why is that? Hint: Morse.
  2. For many molecules, better methods yield worse results. How is this possible? Hint: Expectation value.
  3. When calculating interaction energies of two system parts, we subtract the sum of the fragment energies from the energy of the combined systems. This benefits from error cancellation: is one fragment energy wrong then likely the same error persists in the combined systems. In Hartree-Fock however, interaction energies are almost always overestimated. Why? Hint: Variational.