All Optical Full Adder Based on Intramolecular Electronic Energy Transfer in the Rhodamine-Azulene Bichromophoric System Olga Kuznetz, ‡ Husein Salman, ‡ Yoav Eichen, ‡ F. Remacle, §,† R. D. Levine, ⊥ and Shammai Speiser* ,‡ Schulich Faculty of Chemistry, Technion - Israel Institute of Technology, Haifa 32000, Israel, Department of Chemistry, B6c, UniVersity of Liege, B4000 Liege, Belgium, and Fritz Haber Research Center, Hebrew UniVersity, Jerusalem 91904, Israel ReceiVed: May 27, 2008; ReVised Manuscript ReceiVed: July 21, 2008 Charge and electronic energy transfer (ET and EET) are well-studied examples whereby different molecules can signal their state from one (the donor, D) to the other (the acceptor, A). The electronic energy transfer from the donor (Rh) to the acceptor (Az) is used to build an all-optical full adder on a newly synthesized bichromophoric molecule Rh-Az. The results are supported and interpreted by a full kinetic simulation. It is found that the optimal design for the implementation of the full adder relies in an essential way on the intramolecular transfer of information from the donor to the acceptor moiety. However, it is not the case that the donor and the acceptor each act as a half adder. Introduction A full adder adds two binary numbers and also takes into consideration a carry from a previous addition. There are three inputs. Since each input is binary, there are eight distinct input triplets. These generate four output doublets consisting of the values of the two outputs, the sum, and the new carry digit. (The explicit input-output correspondence is shown in a truth table shown below; Table 1.) In an all-optical case, the 3 inputs, at the frequency ω i , as well as the sum out and carry out outputs are optical signals. Several implementations of logic circuits, including full adders, have already been reported at the molecular level. 1-7 In conventional computer circuits, a full adder is typically realized by the concatenation of two half adders. 1 While a donor-acceptor could be a candidate for such an implementation of a full adder, we show in this paper, using the support of a kinetic model, that for the particular molecular system under study, a more optimal way is to map directly the photophysics onto a full addition without an intermediate decomposition into two concatenated half adders. The scheme proposed uses in an essential way the transfer of information from the donor to the acceptor molecule. This was the idea in our original work, 2 and it has since been applied also in the implementation of a full adder on the 2-phenylethyl-N,N- dimethylamine (PENNA) molecule. 3 In both examples, the inputs are provided optically. However, in our previous work, 3 some of the outputs were read by detecting fragments, which means that the molecule self-destructs at the end of the computation. In the scheme discussed here, we can devise a completely optical readout, that is, we are able to realize an all-optical full adder. Moreover, as we demonstrated below, the optical readout can be performed separately for the two outputs of the full adder, the sum out, and the carry out, which are encoded into the laser-induced fluorescence, LIF, yields of two different excited states of the bichromophoric complex. The threshold levels for the optical readout rely on the photoquenching (PQ) effect. 4 This effect is manifested in chromophores that possess several optically active excited electronic states, so that it is possible to excite the lowest excited state, S 1 , with one photon and higher excited states, S n , n > 1, with more than one photon, typically two. In this case, a decrease of the fluorescence quantum yield of the S 1 state is observed with increasing exciting light intensity. This comes about because as the intensity increases, the transient population in the S 1 excited level decreases due to excitation to higher S n states. Thus, this absorbed photon does not contribute to the fluorescence yield for S 1 , causing the decrease in the S 1 relative fluorescence quantum yield. Kinetic analysis, under steady-state conditions and for optically thin sample, assuming ultrafast radiationless decay of the S n (gn) states back to S 1 , yields a “Stern-Volmer” type photoquenching relation (for n ) 2) given by 4,5 φ 0 /φ ) 1 + τ 10 σ 12 I p (1) In eq 1, φ is the intensity-dependent relative fluorescence quantum yield, φ 0 is the relative quantum yield in the absence laser pumping, τ 10 is the fluorescence lifetime in the absence laser pumping, σ 12 is the absorption cross section for the S 1 f S 2 transition (cm 2 /molecule), and I p is the laser pump intensity (photon/cm 2 · s). Note that to determine the values of the molecular parameters in eq 1, only measurement of the relative * To whom correspondence should be addressed. Telephone: + 972 4 8293735. Fax: +972 4 8295703. E-mail: speiser@technion.ac.il. ‡ Technion - Israel Institute of Technology. § University of Liege. † Also the Director of Research at FNRS, Belgium. ⊥ Hebrew University. TABLE 1: Truth Table for a Full Adder ω 1 ω 2 carry in ≡ ω 3 sum out carry out 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 J. Phys. Chem. C 2008, 112, 15880–15885 15880 10.1021/jp804658b CCC: $40.75  2008 American Chemical Society Published on Web 09/12/2008