RTM1 computes the 1-electron reduced transition matrix (1-RTM) for a transition from the ground state to an excited state.

The procedure returns a two-dimensional n_o x n_v or n_a x n_a Array.  If the method is 'HartreeFock' or 'DensityFunctional', then the Array has dimensions n_o x n_v where n_o is the number of occupied orbitals and n_v is the number of virtual (unoccupied) orbitals.

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

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 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, the excited states are 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, excited states are 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 1-RTM if it has not been previously computed by calling the method directly or indirectly through another property.

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

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

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

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

$\mathrm{rtm1} ≔ \mathrm{RTM1}\left(\mathrm{molecule}\,\mathrm{state}\=1\right)\;$