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QuantumChemistry

 OscillatorStrengths
 compute oscillator strengths of ground-to-excited-state transitions

 Calling Sequence OscillatorStrengths(molecule, method, 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), 'DensityFunctional' nstates - (optional)  nstates = integer/list where the integer specifies the number of excited states computed showtable - (optional)  showtable = true or false (default) displays a fancy table when set to true options - (optional) equation(s) of the form option = value where option is any valid option of the chosen method

Description

 • OscillatorStrengths computes the oscillator strengths in the length gauge of ground-to-excited-state transitions.
 • The procedure returns the oscillator strengths as a (n+1)x2 Matrix containing the state indices and oscillator strengths.
 • 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, oscillator strengths 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, oscillator strengths 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 oscillator strengths if they have not been previously computed by calling the method directly or indirectly through another property.

Examples

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

The oscillator strengths 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 oscillator strengths

 >

By double clicking the output matrix above, the result can be viewed in a Matrix Browser with options to export the data.

The oscillator strengths can also be displayed in a fancy table by setting the optional keyword showtable to true

 >

 State Oscillator $1$ $0.09549895$ $2$ $1.11703648$ $3$ $0.00124086$ $4$ $0.19791056$ $5$ $0.00044464$ $6$ $5.27818615{10}^{-6}$ $7$ $3.18802655{10}^{-6}$ $8$ $0.44300524$ $9$ $0.03274886$ $10$ $0.09522948$ $11$ $0.31692231$ $12$ $0.01142447$

The number of states computed can be controlled with the keyword nstates; i.e., nstates=1 computes 1 singlet and 1 triplet state

 >

 State Oscillator $1$ $0.09562993$ $2$ $0.00044473$

 >