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UMRSF-TDDFT: An Unrestricted Reference

MRSF-TDDFT builds its states from a restricted open-shell (ROHF/ROKS) triplet reference. UMRSF-TDDFT uses an unrestricted (UHF/UKS) triplet reference instead, in which α and β electrons have different spatial orbitals. The two are compared here for formaldehyde at the same geometry and level.

Formaldehyde

Formaldehyde at the PBE0/6-31G* geometry

Copy and run

formaldehyde-umrsf.oqp
umrsf(nstate=3)/bhhlyp/6-31g*
geom="""
C      0.000000     0.000000    -0.526342
O      0.000000     0.000000     0.676110
H      0.000000     0.937620    -1.119884
H      0.000000    -0.937620    -1.119884
"""

Download formaldehyde-umrsf.oqp

openqp formaldehyde-umrsf.oqp

The only difference from the MRSF input of the SOC example is the route name umrsf. OpenQP selects the UHF triplet reference automatically, as the log reports:

   PyOQP Reference:                   triplet UHF (internal working reference)

The run takes about 3 seconds.

What you get

 State      Energy       Excitation   Excitation(eV)  <S^2>  ...  Oscillator
    S0   -114.4196483022    -2.903524     0.000000      0.002  ...      0.0000
   REF   -114.3129457579     0.000000     2.903524        (triplet ROHF/UHF internal working reference)
    S1   -114.2666186519     1.260625     4.164149      0.008  ...      0.0000
    S2   -114.1003391297     5.785321     8.688845      0.023  ...      0.0049
Quantity MRSF-TDDFT (ROHF reference) UMRSF-TDDFT (UHF reference)
Triplet reference energy −114.3083030 hartree −114.3129458 hartree
S0 −114.4212164 hartree −114.4196483 hartree
S0 → S1 (n→π*) 4.087 eV 4.164 eV
⟨S²⟩ of S1 — 0.008

The MRSF values are from the Python analysis example at the same geometry.

Reading the result

  • The UHF reference is lower (by 4.6 millihartree) because its α and β orbitals can relax independently; an ROHF reference forces them to share spatial orbitals.
  • The excited states stay close. S0→S1 differs by 0.08 eV between the two references, and the UMRSF states remain essentially spin-pure (⟨S²⟩ ≤ 0.023).
  • UMRSF-TDDFT has analytic gradients and the same geometry drivers as MRSF (grad, opt, meci, mecp), so either reference can be used for the workflows on the other pages. Report which one was used, because energies at the 0.1 eV level depend on the choice.

Try next

  • Optimize S1 with umrsf(nstate=3)/bhhlyp/6-31g* opt(S1) and compare with the MRSF S1 optimization.
  • Repeat for a molecule whose triplet reference has strong spin polarization, such as a twisted or stretched double bond, and compare the two references carefully.

See also: MRSF-TDDFT, tdhf keywords.

Scientific references

MRSF-TDDFT; OpenQP.