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QuantumChemistry

 TransitionOrbitalPlot
 plot a pair of natural transition orbitals of a ground-to-excited-state transition

 Calling Sequence TransitionOrbitalPlot(molecule, method, state, orbitalindex, options)

Parameters

 molecule - list of lists; each list has 4 elements, the string of an atom's symbol and atom's x, y, and z coordinates method - (optional)  method = name/procedure where name is one of 'HartreeFock' (default), 'DensityFunctional' state - (optional)  state = integer where the integer specifies the excited state (default = 1) orbitalindex - (optional)  orbitalindex = integer where the integer specifies the orbital (default = 1) options - (optional) equation(s) of the form option = value where option is any valid option of the chosen method

Description

 • TransitionOrbitalPlot plots a pair of natural transition orbitals of a ground-to-excited-state transition.
 • The index of the excited state can be set with the optional keyword state, i.e. state = 1 (default) sets the first excited state where the excited states are ordered from lowest to highest in energy.
 • The index of the orbital pair can be set with the optional keyword state, i.e. orbitalindex = 1 (default) sets the orbital pair associated with the largest singular value.  The orbital pair consists of a natural transition orbital of the ground state and a natural transition orbital of the excited state.
 • The 3D plot shows the electron densities of the ground-state natural transition orbital (left) and the excited-state natural transition orbital (right), both of which are associated with the same singular value.  The natural transition orbitals reveal the most significant orbitals (those with the largest singular values) that are involved in the transition from the electronic ground state to the electronic excited state.
 • Methods, set by the method keyword, include 'HartreeFock' (default) and 'DensityFunctional'.
 • The number n of excited states in the calculation is determined by the optional keyword nstates.  If nstates = n, then n singlet and n triplet states are computed.  If nstates=[n,m], then n singlet and m triplet states are computed.  By default, nstates = 6.
 • When the HartreeFock method is selected, transition orbitals can be computed from either the time-dependent Hartree-Fock (TDHF) or the configuration interaction singles (CIS) method.  By default TDHF is performed.  TDHF and CIS can be directly selected by setting the optional keyword excited_states to the string "TDHF" or "CIS".
 • When the DensityFunctional method is selected, transition orbitals can be computed from either the time-dependent density functional theory (TDDFT) or the Tamm-Dancoff approximation (TDA) method.  By default TDDFT is performed.  TDDFT and TDA can be directly selected by setting the optional keyword excited_states to the string "TDDFT" or "TDA".
 • The result depends upon the chosen molecule, method, and basis set among other options such as charge, spin, and symmetry.  The ground-state molecule must be in a singlet state, that is spin = 0.
 • The command only works with methods that return excitation energies.
 • The command accepts options keywords of not only the method but also DensityPlot3D.
 • Because the methods employ Maple remember tables, the procedure only computes the transition orbitals if they have not been previously computed by calling the method directly or indirectly through another property.

Examples

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

Let us plot the natural transition orbitals of the $\mathrm{uracil}$ molecule computed with the Hartree-Fock (TDHF) method

First, we define the molecule's geometry with the MolecularGeometry command

 >
 ${\mathrm{molecule}}{≔}\left[\left[{"O"}{,}{2.32640000}{,}{0.96510000}{,}{0.00010000}\right]{,}\left[{"O"}{,}{-2.29720000}{,}{1.02320000}{,}{0.00050000}\right]{,}\left[{"N"}{,}{0.01800000}{,}{1.01990000}{,}{-0.00020000}\right]{,}\left[{"N"}{,}{1.16370000}{,}{-1.02210000}{,}{0.00010000}\right]{,}\left[{"C"}{,}{1.25240000}{,}{0.36290000}{,}{0}\right]{,}\left[{"C"}{,}{-1.23150000}{,}{0.41410000}{,}{-0.00040000}\right]{,}\left[{"C"}{,}{-0.02680000}{,}{-1.69550000}{,}{0.00020000}\right]{,}\left[{"C"}{,}{-1.20490000}{,}{-1.06760000}{,}{-0.00020000}\right]{,}\left[{"H"}{,}{0.03820000}{,}{2.03570000}{,}{-0.00010000}\right]{,}\left[{"H"}{,}{2.01870000}{,}{-1.57020000}{,}{0.00040000}\right]{,}\left[{"H"}{,}{-2.14430000}{,}{-1.60630000}{,}{-0.00020000}\right]{,}\left[{"H"}{,}{0.04690000}{,}{-2.77610000}{,}{0.00040000}\right]\right]$ (1)

Second, we plot uracil with the PlotMolecule command

 > $\mathrm{PlotMolecule}\left(\mathrm{molecule}\right);$

Finally, we plot the pair of transition orbitals associated with the first singular value of the ground-to-first-excited-state transition

 > $\mathrm{TransitionOrbitalPlot}\left(\mathrm{molecule},\mathrm{state}=1,\mathrm{orbitalindex}=1\right);$

By left clicking on the plot, styles can be customized, and the plot can be exported to a range of image files including PNG and EPS.

Similarly, we plot the pair of transition orbitals associated with the second singular value of the transition

 > $\mathrm{TransitionOrbitalPlot}\left(\mathrm{molecule},\mathrm{state}=1,\mathrm{orbitalindex}=2\right);$

 >