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QuantumChemistry

 ExcitonPopulationsPlot
 plot the exciton populations

 Calling Sequence ExcitonPopulationsPlot(molecule, method = name/procedure, options) ExcitonPopulationsPlot(molecule, data, options) ExcitonPopulationsPlot(populations)
 Parameters

 molecule - list of lists; each list has 4 elements, the string of an atom's symbol and the atom's x, y, and z coordinates method - method = name/procedure where name/procedure is a method that can return a correlated 2-RDM such as data - table; table returned by one of the electronic structure methods listed under method containing a 2-RDM populations - Vector; Vector of exciton populations returned by ExcitonPopulations options - (optional) equation(s) of the form option = value where option is one of the following plot options: axes, symbol, symbolsize, color, axesfont, labels, labeldirections, or labelfont.  When one of the first two calling sequences is used, the options of ExcitonPopulations are also valid: excitontype, nexcitons, excitonmatrix, showtable, or returnvecs.  When the first calling sequence is used, any option of the method can also be supplied such as basis, charge, spin, symmetry, active, ect.

Description

 • The ExcitonPopulationsPlot command plots the occupations (populations) of a molecule's exciton states.
 • Excitons are quasi-particles that consist of an electron and a hole (the absence of an electron).  The exciton populations and states are computed from the eigenvalues and eigenvectors of the particle-hole matrix (G matrix) or its modified form (Gt matrix).  The exciton population can become large on the order of the total number of excitons (electron-hole pairs).  The phenomenon of having a large number of excitons in the same exciton state is known as exciton condensation.  Recently, exciton condensates have been experimentally realized in graphene double layers and van der Waals heterostructures.  Refer to the References for further details.
 • The opions axes, symbol, symbolsize, color, axesfont, labels, labeldirections, or labelfont are described at plot/options.
 • The options excitontype, nexcitons, excitonmatrix, showtable, and returnvecs are described at ExcitonPopulations.
 • Note that if the exciton populations have already been computed by ExcitonPopulations, then the third calling sequence is the most efficient.

References

 1 S. Safaei and D. A. Mazziotti, Phys. Rev. B 98, 045122 (2018). "Quantum signature of exciton condensation"
 2 Anna O. Schouten, LeeAnn M. Sager, and David A. Mazziotti, J. Phys. Chem. Lett. 12 9906 (2021). "Exciton Condensation in Molecular-Scale van der Waals Stacks"
 3 X. Liu  and J. I. A. Li, K. Watanabe, T. Taniguchi, J. Hone, B. I. Halperin, P. Kim, and C. R. Dean, Science 375, 6577 (2022). "Crossover between strongly coupled and weakly coupled exciton superfluids"

Examples

 > $\mathrm{with}\left(\mathrm{QuantumChemistry}\right):$

Consider the benzene molecule

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 ${\mathrm{benzene}}{≔}\left[\left[{"C"}{,}{-1.21310000}{,}{-0.68840000}{,}{0}\right]{,}\left[{"C"}{,}{-1.20280000}{,}{0.70640000}{,}{0.00010000}\right]{,}\left[{"C"}{,}{-0.01030000}{,}{-1.39480000}{,}{0}\right]{,}\left[{"C"}{,}{0.01040000}{,}{1.39480000}{,}{-0.00010000}\right]{,}\left[{"C"}{,}{1.20280000}{,}{-0.70630000}{,}{0}\right]{,}\left[{"C"}{,}{1.21310000}{,}{0.68840000}{,}{0}\right]{,}\left[{"H"}{,}{-2.15770000}{,}{-1.22440000}{,}{0}\right]{,}\left[{"H"}{,}{-2.13930000}{,}{1.25640000}{,}{0.00010000}\right]{,}\left[{"H"}{,}{-0.01840000}{,}{-2.48090000}{,}{-0.00010000}\right]{,}\left[{"H"}{,}{0.01840000}{,}{2.48080000}{,}{0}\right]{,}\left[{"H"}{,}{2.13940000}{,}{-1.25630000}{,}{0.00010000}\right]{,}\left[{"H"}{,}{2.15770000}{,}{1.22450000}{,}{0}\right]\right]$ (1)

We perform a variational 2-RDM calculation with a 6-electrons-in-6-orbitals [6,6] active space

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After the calculation we use the new command ExcitonPopulations to compute the exciton populations, the number of excitons in a given exciton (particle-hole) state

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The populations can be plotted with the command ExcitonPopulationsPlot

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