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7.9 Restricted Open-Shell and ΔSCF Methods

7.9.6 Non-equilibrium Solvation for ROKS and ΔSCF Methods

(April 13, 2024)

Both ΔSCF calculations (e.g., based on MOM) and ROKS calculations can be performed with continuum solvation effects modeled by a polarizable continuum model (PCM). (The solvation model itself is described in Section 11.2.3.) As for the ground state, the self-consistent PCM treatment along the SCF procedure provides equilibrium solvation of the calculated excited state (set SOLVENT_METHOD = PCM and include the $pcm block). During equilibrium solvation, both slow (nuclear) and fast (electronic) solvent degrees of freedom are relaxed (governed by Dielectric in the $solvent block), as is appropriate for long-lived states. However, fast vertical excitation or emission occurs on a shorter timescale, requiring the relaxation of only the fast electronic solvent polarization (governed by Dielectric_Infi, see Section 11.2.3.3). In Q-Chem, such nonequilibrium solvation effects can be included to first order with a perturbative state-specific (ptSS) correction. 1368 You Z.-Q. et al.
J. Chem. Phys.
(2015), 143, pp. 204104.
Link
, 842 Mewes J.-M. et al.
J. Phys. Chem. A
(2015), 119, pp. 5446.
Link

To begin with, a nonequilibrium ΔSCF or ROKS calculation requires equilibrium solvation of the initial state (ground state for absorption and excited state for emission). By activating RF_ptSS_Save= true in the $pcm block, the equilibrated reaction field is then stored on disk. Setting RF_ptSS_Read = true in an arbitrary later job for the final state reads the reaction field again. This automatically triggers a frozen reaction-field (fRF) SCF with the stored reaction field of the initial state. The resulting SCF energy corresponds to a zeroth order calculation of the final state in the reaction field of the initial state. To obtain the first-order nonequilibrium result, the fast solvent polarization is relaxed for the final state by adding a perturbative ptSS correction, which is printed after the converged fRF-SCF calculation.

RF_ptSS_Save
       Save the current reaction field to disk.
INPUT SECTION: $pcm
TYPE:
       BOOLEAN
DEFAULT:
       FALSE
OPTIONS:
       TRUE Save the reaction field in the current job. FALSE Do not save the reaction field in the current job.
RECOMMENDATION:
       The reaction field is saved for the reference state, which is for ΔSCF or ROKS just the SCF result, but for TDDFT + II-SS-PCM the chosen reference state (see Section 7.3.4.2). Activating RF_ptSS_SAVE for several subsequent jobs overwrites the reaction field.

RF_ptSS_Read
       Read the reaction field from disk and perform a fRF-SCF + ptSS-PCM calculation with it.
INPUT SECTION: $pcm
TYPE:
       BOOLEAN
DEFAULT:
       FALSE
OPTIONS:
       TRUE Read the reaction field in the current job. FALSE Do not read the reaction field in the current job.
RECOMMENDATION:
       The SCF result corresponds to zeroth order solvation of the final state. For first-order nonequilibrium solvation add the ptSS correction printed after the fRF-SCF.

Example 7.41  Vertical emission energy of formaldehyde in acetonitrile with ROKS + PCM and a nonequilibrium ptSS-PCM correction.

$rem
   jobtype             sp
   method              PBE0
   basis               def2-SVP
   scf_convergence     8
point_group_symmetry False
   solvent_method      pcm
$end
$pcm
   theory              iefpcm
   rf_ptss_save        true            ! Save the final ground state reaction field
$end
$solvent
   Dielectric          35.688000       ! Acetonitrile
   Dielectric_Infi     1.806874
$end
$molecule
   0 1
   H      -0.940372    0.000000    1.268098
   H       0.940372    0.000000    1.268098
   C       0.000000    0.000000    0.682557
   O       0.000000    0.000000   -0.518752
$end

@@@

$rem
   method              PBE0
   jobtype             sp
   basis               def2-SVP
   scf_guess           read
   roks                true
   unrestricted        false
   scf_convergence     8
point_group_symmetry False
   solvent_method      pcm
$end
$pcm
   theory              iefpcm
   rf_ptss_read        true            ! Read the prior reaction field and start fRF-SCF
$end
$solvent
   Dielectric          35.688000       ! Acetonitrile
   Dielectric_Infi     1.806874
$end
$molecule
   0 1
   read
$end