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 *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, 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 *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 ADDF on *F*(**Q**) are re-optimized to *actual* TSs afterword.

An example of input for an automated exploration of the S_{2} PES is:

` # ADDF/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 ModelF(Smooth) Second Input B3LYP/6-31G* TD(Singlets,Root=1) 0 1 END FirstOnly `

The ** ModelF(Smooth)** option is used together with the

**Note**: the initial structure in the above input is optimized local minimum on the model function AMF.

See Global reaction route mapping by ADDF.

Updated At:Aug. 4, 2020, 2:02 p.m.