Search of excited state transition states by AFIR

SC-AFIR is not applicable directly to the adiabatic PES of electronic excited states, because the adiabatic PES is not continuous on a conical intersection (CI) with the lower electronic state. Therefore, SC-AFIR is applied to the following model function F(Q) called avoiding model function (AMF), that consists of a mean energy term for the target (higher) PES E^X(Q) and the lower PES E^Y(Q) and a smoothing function.

The function U(Q) in the smoothing function is given as,

where β is a constant parameter (in default, β = 30 kJ/mol). Typically, β is set to ∼1/10 of the vertical excitation energy in the target system, and search results are not very sensitive to the value of β. U(Q) shifts the F(Q) value upward near a CI region, and smoothens the discontinuous region of the upper PES associated with the CI. Therefore, SC-AFIR can be applied directly to this smooth single-valued function F(Q). Moreover, U(Q) rapidly decreases to zero away from CI regions, and thus F(Q) is very similar to E^X(Q) except for CI regions. In other words, first-order saddle points obtained on Y(Q) are very similar to those on E^X(Q). Thus, approximate TSs obtained by SC-AFIR on F(Q) are re-optimized to actual TSs afterword.

An example of input for an automated exploration of the S₂ PES is:

# SC-AFIR/B3LYP/6-31G* TD(Singlets,Root=2)
 
0 1
C         -0.134297351352         -0.196771288036         -1.115967049885
C         -0.134290391096          1.030735034056         -0.428915490659
C         -0.134296118774          1.015543169300          1.000087540551
N         -0.134281964285         -0.196775119748          1.538537357005
C         -0.134296118729         -1.409091621952          1.000083923402
C         -0.134290390957         -1.424279782560         -0.428919268562
H         -0.134288708911         -0.196774519174         -2.202260434589
H         -0.134290353801          1.990664775698         -0.931232868793
H         -0.134292329603          1.887545404102          1.640483678804
H         -0.134292329349         -2.281090113371          1.640485778988
H         -0.134290354145         -2.384212733314         -0.931230468259
Options
Add Interaction
Gamma=150.0
END
ModelF(Smooth)
Second Input
B3LYP/6-31G* TD(Singlets,Root=1)
0 1
END
FirstOnly
 

The ModelF(Smooth) option is used together with the Second Input … END option. Lines between Second Input and END specify the computation method and [spin charge] of the lower state Y. In the xxx_EQ_list.log, xxx_TS_list.log, xxx_DC_list.log, and xxx_PT_list.log of this calculation, EQs, TSs, DCs, and PTs on the model function AMF are obtained. These structures are just approximate structures, and therefore need to be reoptimized without ModelF(Smooth).

Frequently used options

See Global reaction route mapping by single-component algorithm (SC-AFIR).