GradQuantumSpring2014

Quantum Mechanics II

Course Info

• Course Number: CHM 6938-009
• Meeting Times: Tuesdays and Thursdays, 12:30 - 01:45PM
  • No meetings on Mar. 11 or 13 due to USF Spring Break (Mar. 10-15)
  • Midterm: Thursday, February 20, 12:30-13:45 (regular class time)
  • Final: Thursday, May 1, 10:00-12:00 (following USF finals schedule)
• Credit Hours: 3
• CRN: 11305

Advanced Reference Material

• Primary Literature to be Discussed in Class
• Everything from GradQuantumFall2013
• D.R. Yarkony, ed., Modern Electronic Structure Theory, (World Scientific, Singapore, 1995).

The instructor may be reached anytime by phone 4-4298 or email (username: davidrogers on usf.edu).

Course Overview & Objectives

Having mastered the foundations of Quantum Mechanics, this course explores advanced and emerging topics through critical reading of the primary literature. By the end of the course, you will be able to evaluate, propose and carry out critical tests of ideas and methods directly from the literature.

Grading & Due Dates

Your work will be graded based on homework assignments (20%), participation in class discussion (20%), and two exams (30% each).

• Homework 3 - DFT Due Thurs., Apr. 10

Planned Topics

Phase I

Topics:

• Thermochemistry, chemical reactions and kinetics
• Scripting for Managing El. Structure Calcs
  • Working with atomistic data
  • Running large parallel electronic structure calculations
  • The role of basis functions and convergence
• Basic statistics of Boson and Fermion energy distributions - (stat) statistics on top of (QM) statistics.

References:

• Thermochemistry in Gaussian
• Materials Project
  • Hybrid density functional calculations of redox potentials and formation energies of transition metal compounds
• On the quantum theory of radiation
  • Rereading Einstein on Radiation

Phase II

Topics:

• Excited States, Rayleigh-Schrodinger Perturbation (compare to MP2)
• Polarizablility and other Dispersion Forces
• Coupled-Cluster Expansions
• Perturbation Theory Decomposition of Intermolecular Energies

References:

• Bes, Chapter 8.1-8.3
• File:Multipoles.pdf Multipole Electrostatic Interactions
• Temperature and Pressure Dependence of the AMOEBA Water Model
• Intermolecular Forces in Van der Waals Dimers
• Polarization damping in halide–water dimers
• Perturbation Theory Approach to Intermolecular Potential Energy Surfaces of van der Waals Complexes (sections 1-3 and 7)

Phase III

Topics:

• Foundations of Density Functional Theory
  • Statistics of an electron gas. The Kohn-Sham decomposition and the resulting alphabet soup of density functionals.
• Shortcomings of DFT (reproducing electron number discontinuities)
• Solvent Effects and Approximations
  • QM/MM methods applicable to the condensed phase

References:

• 1998 Nobel Prize Lecture
• Inhomogeneous Electron Gas
• Issues and challenges in orbital-free density functional calculations
• MSCALE: A General Utility for Multiscale Modeling
• [http://pubs.acs.org/doi/full/10.1021/ct300493y

Improving Generalized Born Models by Exploiting Connections to Polarizable Continuum Models. II. Corrections for Salt Effects]

Phase IV

Topics:

• Path Integral Formulations
  • Derivation of classical mechanics, Heisenberg and Schrodinger.
  • Elementary path integrals
• Quantum and Classical Fluctuation-Dissipation Theorems
• Optional material: Quaternion representation of rotations and the Dirac equation.

References:

• Reforming the Mathematical Language of Physics
  • Consistency in the formulation of the Dirac, Pauli, and Schrödinger theories
• Spectroscopic and Dielectric Properties of Liquid Water: A Molecular Dynamics Simulation Study