Generation of a new molecule using LCAP gradients for GDMC optimization. Here, only two sites are considered. At each site, there are four possible fragments (, , , and for site , and , , , and for site ). A gray box indicates that the fragment is present in the current molecule. Based on the LCAP gradients calculated for molecule , all of the fragments at each site are reordered and the next molecule is generated. If has been visited before, one site is randomly chosen to undergo mutation. In this example, site is chosen and fragment is mutated to fragment (the next highest ranking fragment) and is generated. This procedure is repeated until the maximum number of iterations is reached or no more new molecules can be generated.
Framework for case I. Either a CH or can be placed at each site. 64 possible structures exist without considering symmetry equivalent structures.
Optimization profile for case I . The axis indexes the calculated molecules during the optimization; the axis represents the absolute value of , where empty circles denote negative molecular values and solid circles denote positive values. The initial molecule is structure (a). Three degenerate molecules with structure (b) and the largest value were obtained. During the optimization, the LCAP gradients guided the generation of new molecules and resulted in a greater likelihood of generating a new molecule with a higher property value. The MC random moves in the initial stage assisted in jumping out of local optima ().
Framework for case II. At sites 1 and 2, either H, , , or was placed. Either CH or N was placed at sites 3–6. Sites 1 and 2 are located on the axis. 256 possible structures exist without considering symmetry equivalent structures.
Optimization profiles for case II with three different temperature parameters. The largest molecule (b) was found in all optimizations. When is increased from , the other chemically identical molecule (b) was also found, suggesting that the optimization results do not depend critically on the temperature parameter.
Framework for case III. At site , one of three acceptor groups (, CN, or COH) was placed. At site , one of three donor groups [, or ] was placed. At sites 1–10, either CH or N was placed. 9216 possible molecules exist without considering symmetry equivalent structures.
(a) Initial molecule in case III. (b) Molecule with the largest value after four GDMC optimizations were carried out using three different temperature parameters. (c) Molecule with a normal porphyrin ring and the strongest donor and acceptor groups in case III.
Three optimization profiles for case III with three temperatures ranging from . values are always positive due to the donor--acceptor framework. The rugged surface trapped three optimizations when and . At , GDMC jumped out of the local optimum and yielded molecule (b), as shown in Fig. 7.
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