Conditional Probability Density Functional Theory - IPAM at UCLA

Explore a groundbreaking approach to electronic structure calculations in this 51-minute lecture by Kieron Burke from the University of California, Irvine. Delve into Conditional Probability Density Functional Theory (CPDFT), a novel method developed during the pandemic that addresses long-standing issues in traditional Density Functional Theory (DFT). Learn how CPDFT resolves challenges in ground-state strong correlation and high-temperature warm dense matter simulations. Examine the theory's foundations, including conditional probabilities, Hohenberg-Kohn mapping, and approximate CP-KS potentials. Investigate applications to various systems such as the uniform electron gas, Hooke's atom, and the hydrogen dimer dissociation. Compare CPDFT results with traditional methods and explore its potential for more complex systems. Gain insights into the origins, limitations, and future prospects of this innovative approach to quantum mechanics calculations.

Intro
Outline
Three recent papers from us
A different approach to electronic structure
Usual notation
Conditional probabilities and holes
Hohenberg-Kohn map
Conditional probability potential
Approximate CP-KS potential
Intuitive motivation: quantum
Motivation: classical
Ground-state uniform gas
Problems with high density limit
Hooke's atom
Hydrogen dimer dissociation
Hy energy components
Free energy of uniform gas
Error in free energy
Zero temp uniform gas
XC holes from LBEA
Failure and fix up for high densities
Spin-DFT CP calculation
Pair distribution functions
TF for uniform gas
1D exact calculations
Exact conditions
PBE Comparison at Low Temperature
Uniform Electron Gas Comparison
Nonzero Gradients
Origins and missing references
Summary