ExcitationEnergies computes the excitation energies from a molecule's ground state to its excited states.

The procedure returns the excitation energies as a (n+1)x2 Matrix containing the state indices and energies in columns 1 and 2.

Methods, set by the method keyword, include 'HartreeFock' (default) and 'DensityFunctional'.

The number n of excited states 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.          

The data can be displayed in a fancy table by setting the optional keyword showtable to true (the default is false).

When the HartreeFock method is selected, excitation energies can be computed by 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, excitation energies can be computed by 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.

Because the methods employ Maple remember tables, the procedure only computes the excitation energies if they have not been previously computed by calling the method directly or indirectly through another property.

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

$\mathrm{molecule} ≔ \mathrm{MolecularGeometry}\left(''uracil''\right)\;$

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

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

$\mathrm{energies\_hf} ≔ \mathrm{ExcitationEnergies}\left(\mathrm{molecule}\right)\;$

$\mathrm{energies\_hf} ≔ \mathrm{ExcitationEnergies}\left(\mathrm{molecule}\,\mathrm{showtable}\=\mathrm{true}\right)\:$

$\mathrm{energies\_hf} ≔ \mathrm{ExcitationEnergies}\left(\mathrm{molecule}\,\mathrm{nstates}\=1\, \mathrm{showtable}\=\mathrm{true}\right)\:$