Stochastic Density Functional Theory at Finite Temperatures

Abstract

Simulations in the warm dense matter regime using finite temperature Kohn-Sham density functional theory (FT-KS-DFT), while frequently used, are computationally expensive due to the partial occupation of a very large number of high-energy KS eigenstates which are obtained from subspace diagonalization. We have developed a stochastic method for applying FT-KS-DFT, that overcomes the bottleneck of calculating the occupied KS orbitals by directly obtaining the density from the KS Hamiltonian. The proposed algorithm, scales as $O\left(N{T}^{-1}\right)$ and is compared with the high-temperature limit scaling $O\left(N^3{T}^3\right)$ of the deterministic approach, where $N$ is the system size (number of electrons, volume etc.) and $T$ is the temperature. The method has been implemented in a plane-waves code within the local density approximation (LDA); we demonstrate its efficiency, statistical errors and bias in the estimation of the free energy per electron for a diamond structure silicon. The bias is small compared to the fluctuations, and is independent of system size. In addition to calculating the free energy itself, one can also use the method to calculate its derivatives and obtain the equations of state.

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• Electronic structure via potential functional approximations
• Finite temperature Green's function approach for excited state and thermodynamic properties of cool to warm dense matter

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• A Model of Electron Transport in Dense Plasmas Spanning Temperature Regimes
• Requirements for very high temperature Kohn-Sham density functional simulations and how to bypass them
• Accelerating Equilibration in First-Principles Molecular Dynamics with Orbital-Free Density Functional Theory
• Multiple Scattering Theory for Dense Plasmas
• From Density Response to Energy Functionals and Back: An ab initio perspective on Matter Under Extreme Conditions
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• First-principles derivation and properties of density-functional average-atom models
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• Efficient Langevin dynamics for "noisy" forces
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• Linear scalability of density functional theory calculations without imposing electron localization
• Electrical Conductivity of Warm Dense Hydrogen from Ohm's Law and Time-Dependent Density Functional Theory
• Stochastic Algorithms for Self-consistent Calculations of Electronic Structures
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• atoMEC: An open-source average-atom Python code
• Unlocking the Power of Orbital-Free Density Functional Theory to Explore the Electronic Structure Under Extreme Conditions