Absterac: In this thesis we investigate the resonating valence bond (RVB) description of aromatic compounds. We start by introducing the Heisenberg Hamiltonian and describe its ground and excited states in the valence bond (VB) basis. Excited states are constructed from the very same basis, by turning one of the singlets into triplet. Such excited states are called triplons. We derive the calculus of such wave functions by calculating the matrix elements of the Hamiltonian and the unit operator between such states. These results are general and are valid for arbitrary planar lattice and arbitrary number of triplons. We use these rules to construct exact ground and excited states of the benzene molecule. We confirm that, as pointed out by Kekule, the short VB configurations in benzene are dominant both in ground and excited states. This is quantified in term of a very small ration of the configurations involving longer singlets/triplets. Next we study the dynamics of one triplon in the benzene molecule employing the Green's function method. In agreement with the qualitative picture of the ground and one-triplon excited states, the transition from short bond configurations to those with longer bonds are not likely to occur. Our analytic results for benzene molecule have been confirmed by numeric methods. In the second part of the thesis, we consider a linear chain of such molecules, the so called polyacene. We implement the rules obtained in the first part on the computer for larger systems to stochastically optimize a wave function constructed from the VB configurations for the ground state of polyacene. The computer code is benchmarked against existing literature for square and honeycomb lattice where we find some residual Neel order. In the case of polyacene, we find that the ground state is a gapped spin liquid, characterized with short range correlations and no long range Neel order. Key words: RVB, VB, Triplon, Benzene molecule, Polyacine.
