Composite particles in quantum chemistry: From two‐electron bonds to cold atoms

Abstract

We review the problem of forming composite particles from elementary electrons. Simple pairs are treated first, followed by linear combinations including geminal type wave functions. The antisymmetrized product of strongly orthogonal geminals (APSG) theory can also be developed in this language,and the use of APSG as a reference state is discussed. The theory forming composite particles from more than two electrons is less elaborated,although this idea is routinely used in approximate models in the current literature.

Studies in multireference many-electron theories

“…Here, we would only like to outline the fundamental concepts of MC-SCF theory and to introduce the basic notions. Thereafter geminal based methods are presented from the aspect of composite particles [10][11][12][13][14][15][16]. The connections with standard quantum chemical (multiconfigurational) methods are also discussed.…”

Strategies for extending geminal-based wavefunctions: Open shells and beyond

“…(1) explicitly describes the correlations between the electrons that compose the particle, but not between electrons that compose different particles. [12][13][14][15][16] (Each composite particles moves in the mean-field due to the cloud of other composite particles, so correlations between the electrons in different composite particles are treated only in an average sense.) The words "composite particle" and "quasiparticle" are used more-or-less interchangeably in the literature, with quasiparticle terminology more prevalent when one views the particle as a collective excitation, and composite particle terminology more prevalent when one focuses on the explicit composition of the particles.…”

“…[17][18][19][20][21][22][23] There are numerous examples from the literature that demonstrate that, by making suitable choices for the composite particles, one can ensure computational feasibility. [12,16,24,25] We will explore general principles that ensure computational affordability in subsequent sections of this paper. Similarly, one can always obtain the exact wavefunction by making a suitable choice of composite particles.…”

“…the projected Schrödinger equation in (16) effectively targets the state with the symmetry-label of interest,…”

“…and is therefore equivalent to first projecting the wavefunction onto the symmetry sector of interest, and then solving the projected Schrödinger equation for the symmetry-projected wavefunction. This is helpful because the wavefunction-form of 0  might be very complicated, so much so that expression (18) may be computationally inaccessible even though it is easy to evaluate the (entirely equivalent) expression (16). Notice that the energy value corresponding to the symmetry-restored state can be much lower than the expectation value for the energy of the symmetry-broken state because the non-symmetry-projected wavefunction will generally include contributions from symmetry-states with higher energy than the targeted state: ˆm…”