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Triplet-triplet energy-transfer coupling: Theory and calculation
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Image of FIG. 1.
FIG. 1.

A schematic picture of TT energy transfer as two simultaneous electron transfers between the donor and acceptor .

Image of FIG. 2.
FIG. 2.

Face-to-face arrangements of (A) two ethylenes, and (B) an ethylene and a methaniminium cation. denotes the intermolecular distance.

Image of FIG. 3.
FIG. 3.

Distance and basis set dependence of TT coupling, calculated from the DC scheme for the two-ethylene system. Bases sets used are as follows: 3-21G (filled squares), (open squares), DZP (filled circles), and (open circles).

Image of FIG. 4.
FIG. 4.

Distance and basis set dependence of TT coupling. Shown are half of the CIS energy gaps between the two lowest triplet states for the two-ethylene system. Basis sets used are as follows: 3-21G (filled squares), (open squares), DZP (filled circles), (open circles), and aug-cc-pVTZ (open triangles).

Image of FIG. 5.
FIG. 5.

Potential-energy curves of the two lowest triplet states for the ethylene-methaniminium cation system [as in Fig. 2(B)]. The reaction coordinate is as described in Eq. (25). Calculations were performed at level, with an intermolecular distance fixed at 4.5 Å. The inset is a magnified plot of the region near the curve crossing, with grids representing 0.01 (abscissa) and 0.002 hartrees (ordinate).

Image of FIG. 6.
FIG. 6.

TT energy-transfer coupling for the asymmetric ethylene-methaniminium ion system, face to face stacked, as shown in Fig. 2(B). The coupling calculated by HF-CIS (open symbols with dashed lines) and DC (closed symbols and solid lines) with (squares), DZP (circles), and (triangles) basis sets. DC results were obtained at the transition-state geometry, i.e., where the minimum CIS energy gap was found.

Image of FIG. 7.
FIG. 7.

Stacked pairs of hexatrienes in three different arrangements. (A) A maximum contact is allowed. Panels (B) and (C) show two configurations where the close-contact area exists only in the terminal bonds. Pairs of all-trans butadienes and octatetraenes in similar arrangements were also studied.

Image of FIG. 8.
FIG. 8.

Dependence of molecular size and intermolecular contacts for TT couplings. (A) Couplings are for a pair of butadienes (triangles), hexatrienes (inverse triangles), and octatetraenes (squares) at a number of intermolecular distances. The open symbols are for the results from a fully stacked configuration [Fig. 7(A)] and the closed symbols represent the results from the flipped configuration [Fig. 7(B)]. Data for a pair of ethylenes (open circles) were also included for comparison. (B) For a pair of hexatrienes, we show the coupling of fully stacked (open squares), partially stacked as in Fig. 7(B) (filled squares), and as in Fig. 7(C) (open diamonds) configurations. All the results are from calculations.

Image of FIG. 9.
FIG. 9.

Effects of orientations in TT couplings. Couplings are for a pair of side-by-side ethylenes intermolecular distances obtained by (circles) and (triangles). For comparison, the results for face-to-face ethylenes are included (crosses).


Generic image for table
Table I.

TT energy transfer coupling (in meV) for a pair of ethylenes [Fig. 2(A)] calculated by direct coupling (DC) or configuration-interaction singles (CIS).


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Triplet-triplet energy-transfer coupling: Theory and calculation