Publication

Mixed Wannier-Bloch functions for electrons and phonons in periodic systems

Alfredo Pasquarello
2006
Journal Articles

Abstract

We introduce mixed Wannier-Bloch functions for studying electronic and vibrational spectra of periodic systems. These functions carry both spatial localization and limited spectral broadening, thereby combining the advantages of descriptions based on energy eigenstates (Bloch states) and position eigenstates (Wannier states). For the analysis of vibrational modes, a lattice position operator is introduced, analogous to the electronic Berry-phase position operator. Application to vitreous SiO2 demonstrates that mixed Wannier-Bloch functions constitute a powerful tool for tracking fingerprints of short- and medium-range structural order in electronic and vibrational spectra.

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https://infoscience.epfl.ch/entities/publication/b5bfca10-76a2-4fd4-864a-10fb18263cb7

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Alfredo Pasquarello
2006
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/b5bfca10-76a2-4fd4-864a-10fb18263cb7

About this result

Related concepts (32)

Quantum state

In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a quantum mechanical prediction for the system represented by the state. Knowledge of the quantum state together with the quantum mechanical rules for the system's evolution in time exhausts all that can be known about a quantum system. Quantum states may be defined in different ways for different kinds of systems or problems.

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Rotational–vibrational spectroscopy is a branch of molecular spectroscopy concerned with infrared and Raman spectra of molecules in the gas phase. Transitions involving changes in both vibrational and rotational states can be abbreviated as rovibrational (or ro-vibrational) transitions. When such transitions emit or absorb photons (electromagnetic radiation), the frequency is proportional to the difference in energy levels and can be detected by certain kinds of spectroscopy.

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A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 1013 Hz to approximately 1014 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm−1 and wavelengths of approximately 30 to 3 μm. For a diatomic molecule A−B, the vibrational frequency in s−1 is given by , where k is the force constant in dyne/cm or erg/cm2 and μ is the reduced mass given by .

Related publications (8)

Mixed Wannier-Bloch functions for electrons and phonons in periodic systems

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