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Thermodynamic Potentials01:26

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Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...
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Implementation of the self-consistent phonons method with ab initio potentials (AI-SCP).

Colin Schiltz1, Dmitrij Rappoport1, Vladimir A Mandelshtam1

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The self-consistent phonon method efficiently calculates anharmonic effects in quantum systems. Combining it with ab initio potentials and quasi-Monte Carlo methods speeds up property estimations.

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Area of Science:

  • Quantum Many-Body Physics
  • Computational Materials Science
  • Statistical Mechanics

Background:

  • The self-consistent phonon (SCP) method incorporates anharmonic effects in quantum systems at thermal equilibrium.
  • This method models systems using an effective temperature-dependent harmonic Hamiltonian for property estimation.

Purpose of the Study:

  • To enhance the efficiency of the ab initio self-consistent phonon (AI-SCP) method.
  • To address the computational bottleneck in evaluating Gaussian averages of ab initio potentials and their derivatives.

Main Methods:

  • Combining the self-consistent phonon (SCP) method with ab initio (AI) potential energy evaluations.
  • Utilizing the quasi-Monte Carlo method with low-discrepancy sequences for efficient computation of Gaussian averages.
  • Implementing a two-grid approach for a significant efficiency improvement by averaging potential differences.

Main Results:

  • Achieved efficient computation of Gaussian averages for AI potentials and derivatives.
  • Demonstrated fast convergence with respect to the number of AI energy evaluations (S) using quasi-Monte Carlo.
  • Obtained an order-of-magnitude efficiency improvement with the two-grid approach.

Conclusions:

  • The developed AI-SCP method with quasi-Monte Carlo and the two-grid approach significantly accelerates the calculation of anharmonic properties.
  • This computational framework provides an efficient tool for studying quantum many-body systems at thermal equilibrium.
  • The provided codes and scripts facilitate the application of these advanced computational techniques.