RTM1 - Maple Help
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QuantumChemistry

 RTM1
 compute the 1-electron reduced transition matrix for a ground-to-excited-state transition

 Calling Sequence RTM1(molecule, method, state, 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) and 'DensityFunctional' state - (optional)  state = integer where the integer specifies the excited state (default = 1) options - (optional) equation(s) of the form option = value where option is any valid option of the chosen method

Description

 • 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.

Examples

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

The 1-RDM of the $\mathrm{uracil}$ molecule can be 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 compute the 1-RTM for the ground-to-first-excited-state transition

 >
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