Illustration of fragmentation pattern employed in MTA, taking hexamer (hex-01) as a prototypical case.
optimized geometries of three predominant structures of benzene dimers. Important and interactions in these clusters are depicted along with distances (in angstrom) between H-atom and ring center for interaction and between two ring centers for interaction. These dimers are used as building blocks for higher clusters with three or more benzene units. Total energy of the structures (in hartree) along with complexation energies (CE in kcal/mol) for each structure is mentioned.
(a) Numbering key for fragments used to study the effect of BSSE by MTA. Optimized geometry of tet-09 at level of theory chosen to study the effect. (b) MTA-optimized geometry of a hexamer (hex-10) chosen to study the effect of missing two- and three-body correction terms for improvement of MTA-energy estimates. The numbering key for fragments used is also indicated.
optimized geometries of selected structures of , to 8. Important and interactions in these clusters are depicted along with distances (in angstrom) between H-atom and ring center for interaction and between two ring centers for interaction at (bold) and (italics) level. Total energy (in hartrees) of each cluster at is also indicated in italics. In case of heptamers and octamers distances in bold are those obtained at MP2/STO-3G level. tri-05 is optimized at level of theory.
(i) MESP isosurface at −0.015 a.u. for pen-18 at level plotted using METASTUDIO (Ref. 43). The white dot depicting the deepest minimum is the most suitable site for the next incoming benzene monomer. (ii) Different ways of adding a benzene (red line) to 5 benzenes (black lines) of pen-18 (A) perfect T-shaped interaction, [(B) and (C)] parallel shifted interactions, and (D) the most stable trimer formation as highlighted by a circle.
(i) MESP isosurface at −0.015 a.u. for hex-10 evaluated at level, plotted using METASTUDIO (Ref. 43). The deepest minimum, , and other local minima depicted by white dots indicate the most suitable sites for addition of the next benzene moiety. (ii) Different possible ways of adding new benzene (shown by red line) to hex-18 (black lines): (A) a perfect T-shaped interaction, [(B) and (C)] parallel shifted interactions, and [(D) and (E)] most stable trimer formation as highlighted by circles.
Actual total energies ( in a.u.) with corresponding complexation energies (CE in kcal/mol) at , MP2/STO-3G levels of theory, and MTA-based estimates of energy ( in a.u.) with corresponding complexation energies ( in kcal/mol) at level of theory for selected important benzene clusters . Optimization of dimers and trimers are done only at level of theory. See Figs. 2 and 4 for optimized geometries and text for details.
Actual total energies, MTA-based single point energies, and MTA-based optimized energies (, , and in a.u.) with corresponding complexation energies (CE, and in kcal/mol) at the level of theory for benzene tetramers shown below.
MTA-optimized energies, actual single point energy from calculation on MTA-optimized geometries (, in a.u.), and their corresponding complexation energies (, in kcal/mol) at for benzene tetramers . BSSE-corrected complexation energy is indicated as .
Comparison of CE and complexation energy per interaction for optimized clusters at and level (MTA-optimized) to assess cooperativity. denotes the number of interactions present in the type of cluster. PD indicates parallel displaced clusters. See Fig. 2 and 4 for optimized structures and text for details.
Missing two- and three-body correction to the MTA-based energy estimate for hex-10 [cf. Figs. 3(b) and 4 for structure]. and denote MTA-energy before and after missing two- and three-body contributions are added. All the energies are in a.u. See text for details.
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