Nicholas J. Mayhall

Molecules-in-Molecules: An Extrapolated Fragment-Based Approach for Accurate Calculations on Large Molecules and Materials.

We present a new extrapolated fragment-based approach, termed molecules-in-molecules (MIM), for accurate energy calculations on large molecules. In this method, we use a multilevel partitioning approach coupled with electronic structure studies at multiple levels of theory to provide a hierarchical strategy for systematically improving the computed results. In particular, we use a generalized hybrid energy expression, similar in spirit to that in the popular ONIOM methodology, that can be combined easily with any fragmentation procedure. In the current work, we explore a MIM scheme which first partitions a molecule into nonoverlapping fragments and then recombines the interacting fragments to form overlapping subsystems. By including all interactions with a cheaper level of theory, the MIM approach is shown to significantly reduce the errors arising from a single level fragmentation procedure. We report the implementation of energies and gradients and the initial assessment of the MIM method using both biological and materials systems as test cases.

Many-Overlapping-Body (MOB) Expansion: A Generalized Many Body Expansion for Nondisjoint Monomers in Molecular Fragmentation Calculations of Covalent Molecules

A common approach to approximating the full electronic energy of a molecular system is to first divide the system into nonoverlapping (disjoint) fragments and then compute the two-body or three-body fragment-fragment interactions using a many-body expansion. In this paper, we demonstrate that, by using a set of fragments which overlap with each other, a many-body expansion converges much faster than using nonoverlapping fragments. A new hierarchical fragmentation scheme is therefore proposed which generalizes the many-body expansion expressions and describes a simple procedure for generating the set of overlapping monomers. This method is referred to as the many-overlapping-body (MOB) expansion and is evaluated with two example systems: four dendritic isomers of C29H60 and 10 conformational isomers of a polypeptide molecule. In both examples, the MOB methodology significantly improves the two-body corrected energies.

Investigation of Gaussian4 Theory for Transition Metal Thermochemistry

An investigation of the performance of Gaussian-4 (G4) methods for the prediction of 3d transition metal thermochemistry is presented. Using the recently developed G3Large basis sets for atoms Sc-Zn, the G4 and G4(MP2) methods with scalar relativistic effects included are evaluated on a test set of 20 enthalpies of formation of transition metal-containing molecules. The G4(MP2) method is found to perform significantly better than the G4 method. The G4 method fails due to the poor convergence of the Møller-Plesset perturbation theory at fourth-order in one case. The overall error for G4(MP2) of 2.84 kcal/mol is significantly larger than its previously reported performance for molecules containing main-group elements in the G3/05 test set. However, considering the relatively large uncertainties in the experimental enthalpies, the G4(MP2) method performs reasonably well. The performance of other composite methods based on G3 theory [G3(CCSD)//B3LYP and G3(MP2,CCSD)//B3LYP], as well as several density functional methods, are also presented in this paper. The results presented here will assist future development of composite model techniques suitable for use in transition metal-containing systems.

Computational Quantum Chemistry for Multiple-Site Heisenberg Spin Couplings Made Simple: Still Only One Spin-Flip Required.

We provide a simple procedure for using inexpensive ab initio calculations to compute exchange coupling constants, J(AB), for multiradical molecules containing both an arbitrary number of radical sites and an arbitrary number of unpaired electrons. For a system comprised of 2M unpaired electrons, one needs only to compute states having the Ŝ(z) quantum number M - 1. Conveniently, these are precisely the states that are accessed by the family of single spin-flip methods. Building an effective Hamiltonian with these states allows one to extract all of the J(AB) constants in the molecule. Unlike approaches based on density functional theory, this procedure relies on neither spin-contaminated states nor nonunique spin-projection formulas. A key benefit is that it is possible to obtain completely spin-pure exchange coupling constants with inexpensive ab initio calculations. A couple of examples are provided to illustrate the approach, including a 4-nickel cubane complex and a 6-chromium horseshoe complex with 18 entangled electrons.

ONIOM-based QM:QM electronic embedding method using Löwdin atomic charges: Energies and analytic gradients

In this work, we report a new quantum mechanical:quantum mechanical (QM:QM) method which provides explicit electronic polarization of the high-level region by using the Löwdin atomic charges from the low-level region. This provides an embedding potential which naturally evolves with changes in nuclear geometry. However, this coupling of the high-level and low-level regions introduces complications in the energy gradient evaluation. Following previous work, we derive and implement efficient gradients where a single set of self-consistent field response equations is solved. We provide results for the calculation of deprotonation energies of a hydroxylated spherosiloxane cluster (Si(8)O(12)H(7)OH) and the dissociation energy of a water molecule from a [ZnIm(3)(H(2)O)](2+) complex. We find that the Lowdin charge embedding model provides results which are not only an improvement over mechanical embedding (no electronic embedding) but which are also resistant to large overpolarization effects which occur more often with Mulliken charge embedding. Finally, a scaled-Löwdin charge embedding method is also presented which provides a method for fine tuning the extent of electronic polarization.

Molybdenum Oxides versus Molybdenum Sulfides: Geometric and Electronic Structures of Mo3Xy− (X = O, S and y = 6, 9) Clusters

We have conducted a comparative computational investigation of the molecular structure and water adsorption properties of molybdenum oxide and sulfide clusters using density functional theory methods. We have found that while Mo₃O₆⁻ and Mo₃S₆⁻ assume very similar ring-type isomers, Mo₃O₉⁻ and Mo₃S₉⁻ clusters are very different with Mo₃O₉⁻ having a ring-type structure and Mo₃S₉⁻ having a more open, linear-type geometry. The more rigid ∠(Mo-S-Mo) bond angle is the primary geometric property responsible for producing such different lowest energy isomers. By computing molecular complexation energies, it is observed that water is found to adsorb more strongly to Mo₃O₆⁻ than to Mo₃S₆⁻, due to a stronger oxide-water hydrogen bond, although dispersion effects reduce this difference when molybdenum centers contribute to the binding. Investigating the energetics of dissociative water addition to Mo₃X₆⁻ clusters, we find that, while the oxide cluster shows kinetic site-selectivity (bridging position vs terminal position), the sulfide cluster exhibits thermodynamic site-selectivity.

Charge Transfer Across ONIOM QM:QM Boundaries: The Impact of Model System Preparation.

The inability to describe charge redistribution from regions I to II at the high level of theory imposes limitations on the general applicability of the our own N-layered integrated molecular orbital and molecular mechanics (ONIOM) method. In this report, we exploit the most inexpensive components of an ONIOM QM:QM calculation to provide a new method which has the ability to describe such charge-transfer effects with only a nominal increase in computational effort. Central to this method is the model system preparation step, in which an one-electron potential is optimized to shift density into or out of a defined buffer region. In this initial effort, we treat the link atoms on the model subsystem as the electron buffer region and swell or diminish the link-atom nuclear charges to shift electron density into or out of the buffer region. Due to the relatively small computational cost of the model-low calculation, this procedure can be iteratively optimized to produce a charge distribution equal to the real-low calculation. Initial results for a test set of 20 reaction energies and 8 different combinations of high and low levels of theory show improvements of more than 35% over the standard ONIOM QM:QM approach, with improvements of up to 50% for some high and low combinations.

From Model Hamiltonians to ab Initio Hamiltonians and Back Again: Using Single Excitation Quantum Chemistry Methods To Find Multiexciton States in Singlet Fission Materials.

Due to the promise of significantly enhanced photovoltaic efficiencies, significant effort has been directed toward understanding and controlling the singlet fission mechanism. Although accurate quantum chemical calculations would provide a detail-rich view of the singlet fission mechanism, this is complicated by the multiexcitonic nature of one of the key intermediates, the (1)(TT) state. Being described as two simultaneous and singlet-coupled triplet excitations on a pair of nearest neighbor monomers, the (1)(TT) state is inherently a multielectronic excitation. This fact renders most single-reference ab initio quantum chemical methods incapable of providing accurate results. This paper serves two purposes: (1) to demonstrate that the multiexciton states in singlet fission materials can be described using a spin-only Hamiltonian and with each monomer treated as a biradical and (2) to propose a very simple procedure for extracting the values for this Hamiltonian from single-reference calculations. Numerical examples are included for a number of different systems, including dimers, trimers, tetramers, and a cluster comprised of seven chromophores.

Simple Rule To Predict Boundedness of Multiexciton States in Covalently Linked Singlet-Fission Dimers

Because of the potential for increasing solar cell efficiencies, significant effort has been spent understanding the mechanism of singlet fission. We provide a simple connectivity rule to predict whether the through-bond coupling will be stabilizing or destabilizing for the 1(TT) state in covalently linked singlet-fission chromophores. By drawing an analogy between the chemical system and a simple spin-lattice, one is able to determine the ordering of the multiexciton spin state via a generalized usage of Ovchinnikovs rule. This allows one to predict (without any computation) whether the 1(TT) multiexciton state will be bound or unbound with respect to the separated triplets in covalently linked singlet-fission dimers. To test our hypothesis, we have performed ab initio calculations on a systematic series of covalently linked singlet-fission dimers. Numerical examples are given, and the limitations of the proposed theory are explored.

Using higher-order singular value decomposition to define weakly coupled and strongly correlated cluster states: the n-body Tucker approximation

An approximate wave function ansatz is presented which describes low-energy states of a highly clustered molecular system as a linear combination of multiple reduced-rank tensors. Using the Tucker decomposition as a way to obtain local clusters states, the exact solution is solved for in the space spanned by a small number of states on each cluster, with complete correlation occurring between limited numbers of clusters at a time. In this initial study, we report the implementation for a Heisenberg spin Hamiltonian with numerical examples of regular grid spin lattices, and ab initio-derived spin Hamiltonians used to analyze the approximation. From these results, we find that the proposed method works well when the Hamiltonian interactions within a cluster are larger than between a cluster, and when this is not true, the method is not effective.