ExcitonDensityPlot - Maple Help

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QuantumChemistry

 ExcitonDensityPlot
 plot the relative hole and particle densities of an exciton state

 Calling Sequence ExcitonDensityPlot(molecule, method = name/procedure, options) ExcitonDensityPlot(molecule, data, options) ExcitonDensityPlot(molecule, data, vecs, options)
 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 vecs - Matrix; Matrix of the exciton states (eigenvectors) from ExcitonPopulations with returnvecs = true options - (optional) equation(s) of the form option = value where option is one of excitonindex, aoindex, setparticle, densitycutoff, or colors (see section Options for details).  Options of DensityPlot3D can also be employed.  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 ExcitonDensityPlot command plot the relative hole and particle densities of an exciton state.  Specifically, for a selected exciton state the command plots the hole density relative to a given atomic-orbital (AO) density of the particle.
 • 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 keyword excitonindex is an integer that selects the exciton state (Default is 1).
 • The keyword aoindex is an integer that sets the atomic orbital (AO) for the particle density.  Note that the integer follows the order of AOs in t[ao_labels] where t is the table returned by the electronic structure method (Default is 1).
 • The roles of the particle and hole densities can be exchanged by setting the keyword setparticle to false.
 • The keyword densitycutoff is a list of two floats that determine the density cutoff of the particle and hole density plots, respectively.  The default list is [0.005,0.005].
 • The keyword colors is a list of 4 colors which may be strings or any color object accepted by Maple (see ColorTools package).  The first two colors set the colors of the positive and negative phases of the particle's density, and the last two colors set the colors of the positive and negative phases of the holes's density.  The default list is ["red","red","green","green"].
 Options
 • excitonindex = posint -- an integer that selects the exciton state.  Default is 1.
 • aoindex = integer -- an integer that sets the atomic orbital (AO) for the particle density.  Note that the integer follows the order of AOs in t[ao_labels] where t is the table returned by the electronic structure method.  Default is 1.
 • setparticle = truefalse -- if true, the particle density is fixed by aoindex, but if false, the hole density is fixed.   Default is true.
 • densitycutoff = list of two floats -- a list of two floats that determine the density cutoff of the particle and hole density plots, respectively.  The default list is [0.005,0.005].
 • colors = list of four strings/objects -- a list of 4 colors which may be strings or any color object accepted by Maple (see ColorTools package).  The first two colors set the colors of the positive and negative phases of the particle's density, and the last two colors set the colors of the positive and negative phases of the holes's density.  The default list is ["red","red","green","green"].
 • The keyword viewpoint generates a molecular fly-through animation.  It can be set to one of the following strings "flythrough", "flythrough2", "flythrough3", "flythrough4", "circleleft", and "circleright".  It can also be set to a custom fly-through animation as described on the help page for viewpoint.

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

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The particle and hole relationship of the first exciton state can be visualized with the command ExcitonDensityPlot.  We set the particle density to the 5th atomic orbital (which is a carbon 2pz orbital) and use Nautical Red for the particle density and Nautical Light Blue for the hole density.

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By adding the viewpoint option, we can generate a fly-through animation

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