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 EX(Q) and the lower PES EY(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 EX(Q) except for CI regions. In other words, first-order saddle points obtained on Y(Q) are very similar to those on EX(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)
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
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).