Structures of MESX and MECI can be explored automatically by the SC-AFIR method. In one algorithm termed GP/AFIR, the gradient projection (GP) method, which has been used as a MESX / MECI optimization method, is combined with the SC-AFIR method. The GP method uses a composed gradient **g**^{GP},

where **v**^{DGV} corresponds to the difference gradient vector between the two PESs. The matrix **P** is so called projection matrix, and **P** for MESX optimization is defined as follows.

On the other hand, **P** for MECI optimization is defined as,

where **v**′ is an arbitrary vector not parallel to **v**^{DGV} on the branching plane (BP), and the derivative coupling vector or a vector obtained by the BP updating (BPU) method is used. In GRRM17, **v**′ is obtained by BPU as a unit vector perpendicular to **v**^{DGV}. In the combined GP/AFIR method, the composed gradient **g**^{GP/AFIR} is,

where *J*(**Q**) is the artificial force term in the AFIR function. This equation can be obtained just by substituting the AFIR function for *E*^{X} and *E*^{Y} into *E*^{X} and *E*^{Y} in the expression of gGP, respectively. In the SC-AFIR search, the GP/AFIR path is calculated by inducing structural deformations using gGP/AFIR. A GP/AFIR path leads to an approximate MESX / MECI structure within the seam of crossing / conical intersection hyperspace, where different structures can be obtained depending on a fragment pair in the force term, as in the same way in the SC-AFIR search on a single PES. Therefore, the SC-AFIR algorithm using gGP/AFIR generates various approximate MESX / MECI structures automatically. These approximate structures are further optimized to actual MESX / MECI automatically during the search. Thus, many actual MESX / MECI structures are obtained and appear in xxx_EQ_list.log.

An example of input for an automated exploration of S_{0}/T_{1} MESX structures with the GP/AFIR approach is:

` # SC-AFIR/UB3LYP/6-31+G** 0 1 C -0.450261277786 0.001229457926 -0.553082461345 O 0.054687651811 -0.003728650367 0.666230115529 H 0.197675109173 0.761833114909 -1.107795147264 H 0.197898516798 -0.759333922472 -1.108541506919 Options Add Interaction Gamma=150.0 END OptX(Seam) Second Input UB3LYP/6-31+G** 0 3 END MaxStepSize=0.1 Stable=Opt `

The ** OptX(Seam)** option is used together with the

In the other algorithm, SC-AFIR is applied to the following model function *F*(**Q**) called **seam model function (SMF)**, which consists of a mean energy term for the two target PESs, *E*^{X}(**Q**) and *E*^{Y}(**Q**), and a penalty function for their energy gap,

where **Q** is the atomic coordinates {*Q _{i}*} and

An example of input for an automated exploration of S_{0}/T_{1} MESX structures with the SMF approach is:

` # SC-AFIR/UB3LYP/6-31+G** 0 1 C -0.450261277786 0.001229457926 -0.553082461345 O 0.054687651811 -0.003728650367 0.666230115529 H 0.197675109173 0.761833114909 -1.107795147264 H 0.197898516798 -0.759333922472 -1.108541506919 Options Add Interaction Gamma=150.0 END ModelF Second Input UB3LYP/6-31+G** 0 3 END MaxStepSize=0.1 Stable=Opt `

The ** ModelF** option is used together with the

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

Updated At:Aug. 4, 2020, 2:01 p.m.