compute the 1-electron reduced transition matrix for a ground-to-excited-state transition
RTM1(molecule, method, state, options)
list of lists; each list has 4 elements, the string of an atom's symbol and atom's x, y, and z coordinates
(optional) method = name/procedure where name is one of 'HartreeFock' (default) and 'DensityFunctional'
(optional) state = integer where the integer specifies the excited state (default = 1)
(optional) equation(s) of the form option = value where option is any valid option of the chosen method
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 no x nv or na x na Array. If the method is 'HartreeFock' or 'DensityFunctional', then the Array has dimensions no x nv where no is the number of occupied orbitals and nv 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.
The 1-RDM of the uracil molecule can be computed with the Hartree-Fock (TDHF) method.
First, we define the molecule's geometry with the MolecularGeometry command
molecule ≔ MolecularGeometryuracil;
Second, we plot uracil with the PlotMolecule command
Finally, we compute the 1-RTM for the ground-to-first-excited-state transition
rtm1 ≔ RTM1molecule,state=1;
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