Many-Electron Problem in an Atomic Lattice Reduced Exactly to Two-Particle <em>Pseudo-Electron</em> Excitations: Key to Alternative First-Principles Methods
Prediction of properties of solids (semiconductors) is based almost entirely on the first-principles methods. The first principles theories are far from being perfect and new schemes are developing. In this study, we do not follow the traditional one-particle-in-effective-field concept. Instead, all...
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| Main Author: | |
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| Format: | Book Chapter |
| Language: | English |
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IntechOpen
2022
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| Online Access: | https://www.intechopen.com/chapters/81253 |
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| Summary: | Prediction of properties of solids (semiconductors) is based almost entirely on the first-principles methods. The first principles theories are far from being perfect and new schemes are developing. In this study, we do not follow the traditional one-particle-in-effective-field concept. Instead, all Coulomb interactions between particles are treated in their original form, i.e., particle-particle discrete interactions. Two-particles Coulomb excitations theory in a crystal lattice is proposed, along with a method for calculations of physical measurables. Most important, the relevant particles are not electrons but pseudo-electrons with both the Coulomb interaction mode and the effective mass different from those of electrons. The unitary transformation represents the many-body system as an ensemble of two-pseudo-electron excitations without neglection of the terms in a Hamiltonian. The many-particle wave function, being derived in a non-trivial two-particle form, ensures a full description of exchange-correlation and screening effects, for both ground and excited states. As an example, the energy of a many-electron system and the quasiparticle energies are expressed in an elegant integral closed-form and compared with the Density Functional Theory. The proposed scheme possibly opens a new route toward the numerical evaluation of properties of many-particle systems. |
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| ISBN: | 978-1-80355-681-9 |
| DOI: | 10.5772/intechopen.103045 |