Johannes Hachmann

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

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 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.

Orbital optimization in the density matrix renormalization group, with applications to polyenes and β-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 optimization with the DMRG 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 DMRG-CASSCF 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 optimized complete pi-valence space with up to 24 active electrons and orbitals, and analyze our results in the light of the recent discovery from resonance Raman experiments of new optically dark states in the spectrum.

Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group

We have devised a local ab initio density matrix renormalization group algorithm to describe multireference correlations in large systems. For long molecules that are extended in one of their spatial dimensions, we can obtain an exact characterization 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 (in the sense of full configuration interaction, with 1-10 microE(h) 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.

Lead candidates for high-performance organic photovoltaics from high-throughput quantum chemistry - the Harvard Clean Energy Project

The virtual high-throughput screening framework of the Harvard Clean Energy Project allows for the computational assessment of candidate structures for organic electronic materials – in particular photovoltaics – at an unprecedented scale. We report the most promising compounds that have emerged after studying 2.3 million molecular motifs by means of 150 million density functional theory calculations. Our top candidates are analyzed with respect to their structural makeup in order to identify important building blocks and extract design rules for efficient materials. An online database of the results is made available to the community.

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.

Targeted excited state algorithms

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 (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 oligodiacetylenes. 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.

The Harvard organic photovoltaic dataset

The Harvard Organic Photovoltaic Dataset (HOPV15) presented in this work is a collation of experimental photovoltaic data from the literature, and corresponding quantum-chemical calculations performed over a range of conformers, each with quantum chemical results using a variety of density functionals and basis sets. It is anticipated that this dataset will be of use in both relating electronic structure calculations to experimental observations through the generation of calibration schemes, as well as for the creation of new semi-empirical methods and the benchmarking of current and future model chemistries for organic electronic applications.

A theoretical study of the 3d-M(smif)2 complexes: structure, magnetism, and oxidation states.

We carry out a theoretical investigation of the recently reported M(smif)(2) series1,2 and find a number of interesting phenomena. These include complex potential energy surfaces with near-degenerate stationary points, low-lying states, non-trivial electron configurations, as well as non-innocent ligand behavior. The M(smif)(2) exhibit a delicate balance between geometry and electronic structure, which has implications not only for their reactivity but also for controlling their properties through ligand design. We address methodological issues and show how conceptual quantities such as oxidation states and electronic configurations can be extracted through a simple analysis of the electron and spin densities-without a complicated examination of the underlying orbitals.

Combining First-Principles and Data Modeling for the Accurate Prediction of the Refractive Index of Organic Polymers

Organic materials with a high index of refraction (RI) are attracting considerable interest due to their potential application in optic and optoelectronic devices. However, most of these applications require an RI value of 1.7 or larger, while typical carbon-based polymers only exhibit values in the range of 1.3-1.5. This paper introduces an efficient computational protocol for the accurate prediction of RI values in polymers to facilitate in silico studies that can guide the discovery and design of next-generation high-RI materials. Our protocol is based on the Lorentz-Lorenz equation and is parametrized by the polarizability and number density values of a given candidate compound. In the proposed scheme, we compute the former using first-principles electronic structure theory and the latter using an approximation based on van der Waals volumes. The critical parameter in the number density approximation is the packing fraction of the bulk polymer, for which we have devised a machine learning model. We demonstrate the performance of the proposed RI protocol by testing its predictions against the experimentally known RI values of 112 optical polymers. Our approach to combine first-principles and data modeling emerges as both a successful and a highly economical path to determining the RI values for a wide range of organic polymers.