A time-dependent density functional study of the singlet-triplet energy gap in charge-separated states of rigid bichromophoric molecules

Time-dependent density functional theory (TD-DFT) has been used to calculate gas-phase singlet-triplet energy gaps, DeltaE(ST), for the charge-separated states of a series of donor-[bridge]-acceptor molecules, in which a dimethoxynaphthalene (DMN) donor and a dicyanovinyl (DCV) acceptor are connected by a rigid hydrocarbon (norbornylogous) bridge, ranging from four bonds to 13 bonds in length. Through the use of five different functionals, B3P86, B3LYP, B3PW91, BPW91, and BLYP, together with the 6-311G(d) basis set, it is found that TD-DFT theory gives a good description of the electron density distribution in the charge-separated (CS) states in that the calculated dipole moments of the CS states are in acceptable agreement with experimental data. The calculated DeltaE(ST) values for all members of the donor-[bridge]-acceptor series are positive (i.e., the singlet CS state lies higher in energy than the triplet CS state), and the distance dependence of DeltaE(ST) follows an exponential decay with increasing number, n, of bridge bonds: DeltaE(ST) = A exp(-beta(ST)n), with beta(ST) approximate to 0.91 per bond. Both the sign and distance dependence of DeltaE(ST) are in good agreement with available solution-phase experimental results. The calculated DeltaE(ST) values for the 12-bond and 13-bond systems are about 40% smaller than the experimental ones. It was found that the TD-DFT method overestimates the stabilities of the CS states, relative to the non-CS states. Hence, it is possible that the good agreement between the gas-phase TD-DFT results and the corresponding solution-phase experimental results for the DMN[n]-DCV series is due to this exaggerated stability of the CS states compensating for the explicit neglect of solvation effects in the calculations. It was found that the magnitude (but not the sign, which remains positive) of DeltaE(ST) is quite sensitive to the direction of pyramidalization about the DCV radical anion moiety and to the number of gauche arrangements of vicinal bridge bonds. This sensitivity, together with the distance dependence of DeltaE(ST), is explained in terms of a through-bond coupling mechanism.