ADDF 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, ADDF 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, ADDF 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 ADDF on F(Q) are re-optimized to actual TSs afterword.
An example of input for an automated exploration of the S2 PES is:
# ADDF/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, and xxx_DC_list.log files of this calculation, EQs, TSs, and DCs on the model function AMF are obtained. These structures are just approximate structures, and therefore need to be reoptimized without ModelF(Smooth).
Note: the initial structure in the above input is optimized local minimum on the model function AMF.