Multireference Correlation in Long Molecules with the Quadratic Scaling Density Matrix Renormalization Group

We have devised and implemented a local ab initio Density Matrix Renormalization Group (DMRG) algorithm to describe multireference nondynamic correlations in large systems. For long molecules that are extended in one of their spatial dimensions, this method allows us to obtain an exact characterisation of correlation, in the given basis, with a cost that scales only quadratically with the size of the system. The reduced scaling is achieved solely through integral screening and without the construction of correlation domains. We demonstrate the scaling, convergence, and robustness of the algorithm in polyenes and hydrogen chains. We converge to exact correlation energies (with 1-10 microhartree precision) in all cases and correlate up to 100 electrons in 100 active orbitals. We further use our algorithm to obtain exact energies for the metal-insulator transition in hydrogen chains and compare and contrast our results with those from conventional quantum chemical methods.Comment: 14 pages, 12 figures, tciLaTeX, aip-BibTeX styl

Ab Initio Density Matrix Renormalization Group Methodology And Computational Transition Metal Chemistry

This thesis is concerned with two topics from the field of computational electronic structure theory. In the first part we will describe our contributions to the ab initio density matrix renormalization group (DMRG) methodology in quantum chemistry, in particular our quadratically scaling local algorithm. We will present applications aimed towards new insights into the physics of conjugated π-electron systems as found, e.g., in organic electronic materials. The second part of this thesis covers our computational study of 3d-M(smif)2 complexes synthesized and characterized in the Wolczanski Group. These compounds exhibit unusual electronic structure phenomena which we address from a theoretical perspective

Orbital Optimization in the Density Matrix Renormalization Group, with applications to polyenes and \beta-carotene

In previous work we have shown that the Density Matrix Renormalization Group (DMRG) enables near-exact calculations in active spaces much larger than are possible with traditional Complete Active Space algorithms. Here, we implement orbital optimisation with the Density Matrix Renormalization Group to further allow the self-consistent improvement of the active orbitals, as is done in the Complete Active Space Self-Consistent Field (CASSCF) method. We use our resulting DMRGCASSCF method to study the low-lying excited states of the all-trans polyenes up to C24H26 as well as \beta-carotene, correlating with near-exact accuracy the optimised complete \pi-valence space with up to 24 active electrons and orbitals, and analyse our results in the light of the recent discovery from Resonance Raman experiments of new optically dark states in the spectrum.Comment: 16 pages, 8 figure

Targeted Excited State Algorithms

To overcome the limitations of the traditional state-averaging approaches in excited state calculations, where one solves for 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 (1996)), we have implemented Harmonic Davidson and State-Averaged Harmonic Davidson algorithms within the context of the Density Matrix Renormalization Group (DMRG). 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

Analytic response theory for the density matrix renormalization group

We propose an analytic response theory for the density matrix renormalization group whereby response properties correspond to analytic derivatives of density matrix renormalization 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 frequency dependent polarizabilities of short oligo-di-acetylenes. The analytic response theory is competitive with dynamical density matrix renormalization group methods and yields significantly improved accuracies when using a small number of density matrix renormalization group states. Strengths and weaknesses of the analytic approach are discussed.Comment: 19 pages, 3 figure

An Introduction to the Density Matrix Renormalization Group Ansatz in Quantum Chemistry

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.Comment: 17 pages, 3 figure

The radical character of the acenes: A density matrix renormalization group study

We present a detailed investigation of the acene series using high-level wavefunction 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 pi-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.Comment: 10 pages, 8 figures, supplementary material, to be published in J. Chem. Phys. 127, 200