We present a detailed investigation of the acene series using high-level wave function theory. Our ab initio density matrix renormalization group algorithm has enabled us to carry out complete active space calculations on the acenes from napthalene to dodecacene correlating the full -valence space. While we find that the ground state is a singlet for all chain lengths, examination of several measures of radical character, including the natural orbitals, effective number of unpaired electrons, and various correlation functions, suggests that the longer acene ground states are polyradical in nature.

The Density Matrix Renormalisation Group (DMRG) is an electronic structure method that has recently been applied to ab-initio quantum chemistry. Even at this early stage, it has enabled the solution of many problems that would previously have been intractable with any other method, in particular, multireference problems with very large active spaces. Historically, the DMRG was not originally formulated from a wavefunction perspective, but rather in a Renormalisation Group (RG) language. However, it is now realised that a wavefunction view of the DMRG provides a more convenient, and in some cases more powerful, paradigm. Here we provide an expository introduction to the DMRG ansatz in the context of quantum chemistry.

To overcome the limitations of the traditional state-averaging approaches in excited state calculations, where one solves and represents all states between the ground state and excited state of interest, we have investigated a number of new excited state algorithms. Building on the work of van der Vorst and Sleijpen ͓SIAM J. Matrix Anal. Appl. 17, 401 ͑1996͔͒, we have implemented harmonic Davidson and state-averaged harmonic Davidson algorithms within the context of the density matrix renormalization group ͑DMRG͒. We have assessed their accuracy and stability of convergence in complete-active-space DMRG calculations on the low-lying excited states in the acenes ranging from naphthalene to pentacene. We find that both algorithms offer increased accuracy over the traditional state-averaged Davidson approach, and, in particular, the state-averaged harmonic Davidson algorithm offers an optimal combination of accuracy and stability in convergence.

We propose an analytic response theory for the density matrix renormalisation group whereby response properties correspond to analytic derivatives of density matrix renormalisation group observables with respect to the applied perturbations.Both static and frequency-dependent response theories are formulated and implemented. We evaluate our pilot implementation by calculating static and frequencydependent polarisabilities of short oligo-di-acetylenes. The analytic response theory is competitive with dynamical density matrix renormalisation group methods and yields significantly improved accuracies when using a small number of density matrix renormalisation group states. Strengths and weaknesses of the analytic approach are discussed.

We describe the results of a theoretical study of transport through gated metallic graphene nanoribbons using a nonequilibrium Green function method. Although analogies with quantum field theory predict perfect transmission of chiral fermions through gated regions in one dimension, we find perfect reflection of chiral fermions in armchair ribbons for specific configurations of the gate. This effect should be measurable in narrow graphene constrictions gated by a charged carbon nanotube.

We describe the results of a theoretical study of transport through gated metallic graphene nanoribbons using a non-equilibrium Green function method. Although analogies with quantum field theory predict perfect transmission of chiral fermions through gated regions in one dimension, we find perfect reflection of chiral fermions in armchair ribbons for specific configurations of the gate. This effect should be measurable in narrow graphene constrictions gated by a charged carbon nanotube.

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