A tight-binding study of logic gate circuits for adding numbers inside a molecule

The possibilities for the design of larger diode logic circuits such as a one-bit half-adder inside a molecule are investigated, based on a recent extension of the elastic scattering quantum chemistry technique. Since any diode logic circuit for an adder needs OR-gates and AND-gates as basic components and the properties of OR-gates have already been discussed in the ballistic and tunnelling electron transport regime, we focus on the more complicated AND-gates in the present work. For this case the output current, calculated from the transmission coefficients by using the Landauer-Büttiker formula, shows four different logical levels instead of two. The origin of this level variety is analysed in detail. The concept of programmable gate logic arrays is also addressed, where for intra-molecular circuits distinct deviations from earlier macroscopic or mesoscopic implementations of this scheme are found.