TransitionOrbitals computes the natural transition orbitals for a transition from the ground state to an excited state.

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.

Computation is performed through a singular value decomposition of the 1-electron reduced transition matrix (1-RTM).  

The procedure returns a vector of the singular values, a Matrix whose columns contain the natural transition orbitals of the ground state as a vector of expansion coefficients in terms of the atomic orbitals, and a Matrix whose columns contain the natural transition orbitals of the excited state as a vector of expansion coefficients in terms of the atomic orbitals.

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.  

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, 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 natural transition orbitals if they have not been previously computed by calling the method directly or indirectly through another property.

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

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

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

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

$\mathrm{sv}\,\mathrm{orbs\_gr}\,\mathrm{orbs\_ex} ≔ \mathrm{TransitionOrbitals}\left(\mathrm{molecule}\,\mathrm{state}\=1\right)\:$

$\mathrm{sv}\;$

$\mathrm{orbs\_gr}\;$

$\mathrm{orbs\_ex}\;$