NEW DEVELOPMENTS IN LOCAL CONFIGURATION INTERACTION THEORY

Many chemical phenomena, from the freezing point of water to the strength of a chemical bond, are determined by the distribution of electrons which make up matter. We can model and predict chemical phenomena by using quantum mechanics to determine the electrons' distribution (wavefunction). Multireference configuration interaction (MRCI) provides a flexible wavefunction for capturing crucial electron correlation effects. Unfortunately, MRCI's computational cost grows rapidly, O(N^6 ), limiting its application to small molecules. Over the last three decades, researchers have exploited the spatial locality of electron correlation to reduce the costs of correlated quantum chemistry methods like MRCI. The local electron correlation approximation removes insignificant long range correlations thereby reducing MRCI's cost. By so doing, local MRCI methods can be applied to much large molecules than canonical MRCI. In this thesis, previous efforts by Carter and co-workers applying the local correlation approximation to MRCI are expanded upon: both computational speedups and improved accuracy are considered. The state-of-the art local MRCI algorithm scales as O(N^3 ) which, while cheaper than conventional MRCI, scales rapidly with system size. Converting the previously serial local MRCI code to parallel code allows exploitation of multicore architectures common in modern CPUs. Replacing the Cholesky-decomposed two-electron integrals with cheaper density-fitted two-electron integrals reduces local MRCI's cost. These two advances don't effect the O(N^3 ) scaling, but rather reduce the scaling prefactor, thereby allowing simulation of larger molecules. MRCI's accuracy is hampered by the well-known size extensivity error, which grows with molecular size. We introduce previously proposed MRCI size- extensivity corrections to the O(N^3 ) local MRCI. Both a priori and a posteriori size extensivity corrections can be applied. However, a priori corrections can cause numerical instabilities in both canonical and local MRCI. We show that these instabilities are avoided crossings with spurious low energy states. This analysis suggests two different approaches to maintain a stable size extensivity correction. Finally, we improve the accuracy of local MRCI by optimizing the parameters controlling the local electron correlation. The combination of these developments provides a faster, more accurate method for modeling larger scale chemical phenomena than previously possible

Size-extensivity-corrected multireference configuration interaction schemes to accurately predict bond dissociation energies of oxygenated hydrocarbons

Oxygenated hydrocarbons play important roles in combustion science as renewable fuels and additives, but many details about their combustion chemistry remain poorly understood. Although many methods exist for computing accurate electronic energies of molecules at equilibrium geometries, a consistent description of entire combustion reaction potential energy surfaces (PESs) requires multireference correlated wavefunction theories. Here we use bond dissociation energies (BDEs) as a foundational metric to benchmark methods based on multireference configuration interaction (MRCI) for several classes of oxygenated compounds (alcohols, aldehydes, carboxylic acids, and methyl esters). We compare results from multireference singles and doubles configuration interaction to those utilizing a posteriori and a priori size-extensivity corrections, benchmarked against experiment and coupled cluster theory. We demonstrate that size-extensivity corrections are necessary for chemically accurate BDE predictions even in relatively small molecules and furnish examples of unphysical BDE predictions resulting from using too-small orbital active spaces. We also outline the specific challenges in using MRCI methods for carbonyl-containing compounds. The resulting complete basis set extrapolated, size-extensivity-corrected MRCI scheme produces BDEs generally accurate to within 1 kcal/mol, laying the foundation for this scheme's use on larger molecules and for more complex regions of combustion PESs

Local Electron Correlation Treatment in Extended Multireference Calculations: Effect of Acceptor–Donor Substituents on the Biradical Character of the Polycyclic Aromatic Hydrocarbon Heptazethrene

The implementation of a local correlation (LC) treatment of multireference (MR) configuration interaction approaches within the COLUMBUS program system is reported. The LC treatment is based on the weak pairs approximation of Sæbø and Pulay (Ann. Rev. Phys. Chem. 1993, 44, 213) and a geometrical analysis of Walter et al. (Chem. Phys. Lett. 2001, 346, 177). The removal of simultaneous single excitations out of the weak pairs is based on the reference doubly occupied space only, leading to a straightforward program implementation and a conceptual simplicity in terms of well-defined localized orbitals. Reductions of up to an order of magnitude in the configuration space expansion and in computer time for the Davidson diagonalization step are found. The selection of the active and the virtual orbital spaces is not affected by this procedure. This treatment is successfully applied to the singlet biradical heptazethrene and its different acceptor–donor substituents: 4,12-dicyanoheptazethrene, 4,12-diaminoheptazethrene, and 4-amino-12-cyanoheptazethrene. Simultaneous insertion of pairs of donor and acceptor groups increases the biradical character; for push–pull substitution, this effect is significantly smaller. In addition, results obtained from spin-corrected unrestricted density functional theory calculations are supported by our MR calculations

Density Fitting and Cholesky Decomposition of the Two-Electron Integrals in Local Multireference Configuration Interaction Theory

To treat large molecules with accurate ab initio quantum chemistry, reduced scaling correlated wave function methods are now commonly employed. Optimization of these wave functions in practice requires some approximation of the two-electron integrals. Both Cholesky decomposition (CD) and density fitting (DF) are widely used approaches to approximate these integrals. Here, we compare CD and DF for use in local multireference singles and doubles configuration interaction (LMRSDCI). DF-LMRSDCI provides less accurate total energies than CD-LMRSDCI, but both methods are accurate for energy differences. However, DF-LMRSDCI is significantly less computationally expensive than CD-LMRSDCI on the molecules tested, suggesting that DF-LMRSDCI is an efficient, often sufficiently accurate alternative to our previously reported CD-LMRSDCI method

Multireference Approaches for Excited States of Molecules

International audienceObtaining an understanding of the properties of electronically excited states is a challenging task that becomes increasingly important for numerous applications in Chemistry, Molecular Physics, Molecular Biology, and Materials Science. A substantial impact is exerted by the fascinating progress in time-resolved spectroscopy, which leads to a strongly growing demand for theoretical methods to describe the characteristic features of excited states accurately. Whereas for electronic ground state problems of stable molecules the quantum chemical methodology is now so well developed that informed non-experts can use it efficiently, the situation is entirely different concerning the investigation of excited states. This review is devoted to a specific class of approaches, usually denoted as multireference (MR) methods, the generality of which is needed for solving many spectroscopic or photodynamical problems. However, the understanding and proper application of these MR methods is often found to be difficult due to their complexity and their computational cost. The purpose of this review is to provide an overview of the most important facts about the different theoretical approaches available and to present by means of a collection of characteristic examples useful information, which can guide the reader in performing their own applications

Ab Initio Reaction Kinetics of Hydrogen Abstraction from Methyl Formate by Hydrogen, Methyl, Oxygen, Hydroxyl, and Hydroperoxy Radicals

Combustion of renewable biofuels, including energydense biodiesel, is expected to contribute significantly toward meeting future energy demands in the transportation sector. Elucidating detailed reaction mechanisms will be crucial to understanding biodiesel combustion, and hydrogen abstraction reactions are expected to dominate biodiesel combustion during ignition. In this work, we investigate hydrogen abstraction by the radicals H·, CH 3·, O·, HO 2·, and OH· from methyl formate, the simplest surrogate for complex biodiesels. We evaluate the H abstraction barrier heights and reaction enthalpies, using multireference correlated wave function methods including size-extensivity corrections and extrapolation to the complete basis set limit. The barrier heights predicted for abstraction by H·, CH 3·, and O· are in excellent agreement with derived experimental values, with errors ≤1 kcal/mol. We also predict the reaction energetics for forming reactant complexes, transition states, and product complexes for reactions involving HO 2· and OH·. High-pressure-limit rate constants are computed using transition state theory within the separable-hindered-rotor approximation for torsions and the harmonic oscillator approximation for other vibrational modes. The predicted rate constants differ significantly from those appearing in the latest combustion kinetics models of these reactions. © 2012 American Chemical Society