This chapter explains the machine learning (ML) calculation of the dielectric properties using the molecular dynamics method. For this purpose, we introduce three important quantum mechanical theories: the Wannier function method, the modern theory of polarization, and the linear response theory. The dielectric properties are calculated by combining molecular dynamics and the linear response theory. The linear response theory ensures that the dielectric function, which is the response property to an external field, can be determined solely from the equilibrium properties of the system. The Wannier functions (WFs) are the localized orbitals in the periodic systems, and the modern theory of polarization states that the dipole moments of the periodic systems are determined from the center of mass of the WFs, called Wannier centers (WCs). It is, therefore, sufficient to construct machine learning models that predict the WCs to calculate the polarization of a system. For this purpose, we develop the chemical bond based ML scheme for dipole moments in molecular systems, where we assign each WC to a corresponding chemical bond and train ML models for each chemical bond species.

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Modern Theory and Machine Learning of Polarization

  • Tomohito Amano

摘要

This chapter explains the machine learning (ML) calculation of the dielectric properties using the molecular dynamics method. For this purpose, we introduce three important quantum mechanical theories: the Wannier function method, the modern theory of polarization, and the linear response theory. The dielectric properties are calculated by combining molecular dynamics and the linear response theory. The linear response theory ensures that the dielectric function, which is the response property to an external field, can be determined solely from the equilibrium properties of the system. The Wannier functions (WFs) are the localized orbitals in the periodic systems, and the modern theory of polarization states that the dipole moments of the periodic systems are determined from the center of mass of the WFs, called Wannier centers (WCs). It is, therefore, sufficient to construct machine learning models that predict the WCs to calculate the polarization of a system. For this purpose, we develop the chemical bond based ML scheme for dipole moments in molecular systems, where we assign each WC to a corresponding chemical bond and train ML models for each chemical bond species.