Aurora E. Clark

Density and wave function analysis of actinide complexes: what can fuzzy atom, atoms-in-molecules, Mulliken, Lowdin, and natural population analysis tell us?

Recent advances in computational methods have made it possible to calculate the wave functions for a wide variety of simple actinide complexes. Equally important is the ability to analyze the information contained therein and produce a chemically meaningful understanding of the electronic structure. Yet the performance of the most common wave function analyses for the calculation of atomic charge and bond order has not been thoroughly investigated for actinide systems. This is particularly relevant because the calculation of charge and bond order even in transition metal complexes is known to be fraught with difficulty. Here we use Mulliken, Lowdin, natural population analysis, atoms-in-molecules (AIM), and fuzzy atom techniques to determine the charges and bond orders of UO(2)(2+), PuO(2)(2+), UO(2), UO(2)Cl(4)(2-), UO(2)(CO)(5)(2+), UO(2)(CO)(4)(2+), UO(2)(CN)(5)(3-), UO(2)(CN)(4)(2-), UO(2)(OH)(5)(3-), and UO(2)(OH)(4)(2-). This series exhibits a clear experimental and computational trend in bond lengths and vibrational frequencies. The results indicate that Mulliken and Lowdin populations and bond orders are unreliable for the actinyls. Natural population analysis performs well after modification of the partitioning of atomic orbitals to include the 6d in the valence space. The AIM topological partitioning is insensitive to the electron donating ability of the equatorial ligands and the relative atomic volume of the formally U(VI) center is counterintuitively larger than that of O(2-) in the UO(2)(2+) core. Lastly, the calibrated fuzzy atom method yields reasonable bond orders for the actinyls at significantly reduced computational cost relative to the AIM analysis.

Local spin II

Equations are discussed for computing, from ah initio wavefunctions, average values of quantities like SA. SB which appear in the Heisenberg model Hamiltonian of magnetism. These equations are based on projection operators onto local regions of space. They result in local spin operators SA which obey the definition of angular momentum operators and commute with each other. These averages are evaluated for UHF and CI wavefunctions for a few examples of closed and open shell molecules. The calculations are compared with the assumptions made in the Noodleman method for evaluating the parameters in the Heisenberg Hamiltonian and with various definitions of bond order.

Trends in Aqueous Hydration Across the 4f Period Assessed by Reliable Computational Methods

The geometric and electronic structures, as well as the thermodynamic properties of trivalent lanthanide hydrates {Ln(H(2)O)(8,9)(3+) and Ln(H(2)O)(8,9)(H(2)O)(12,14)(3+), Ln = La-Lu} have been examined using unrestricted density functional theory (UDFT), unrestricted Möller-Plesset perturbation theory (UMP2), and multiconfigurational self-consistent field methods (MCSCF). While Ln-hydrates with 2-5 unpaired f-electrons have some multiconfigurational character, the correlation energy lies within 5-7 kcal/mol across the period and for varying coordination numbers. As such DFT yields structural parameters and thermodynamic data quite close to experimental values. Both UDFT and UMP2 predict free energies of water addition to the Ln(H(2)O)(8)(3+) species to become less favorable across the period; however, it is a non-linear function of the surface charge density of the ion. UDFT further predicts that the symmetry of the metal-water bond lengths is sensitive to the specific f-electron configuration, presumably because of repulsive interactions between filled f-orbitals and water lone-pairs. Within the Ln(H(2)O)(8,9)(H(2)O)(12,14)(3+) clusters, interactions between solvation shells overrides this orbital effect, increasing the accuracy of the geometric parameters and calculated vibrational frequencies. Calculated atomic charges indicate that the water ligands each donate 0.1 to 0.2 electrons to the Ln(III) metals, with increasing electron donation across the period. Significant polarization and charge transfer between solvation shells is also observed. The relationship between empirical effective charges and calculated atomic charges is discussed with suggestions for reconciling the trends across the period.

Thermodynamic and Structural Features of Aqueous Ce(III)

With a single f-electron, Ce(III) is the simplest test case for benchmarking the thermodynamic and structural properties of hydrated Ln(III) against varying density functionals and reaction field models, in addition to determining the importance of multiconfigurational character in their wave functions. Here, the electronic structure of Ce(H2O)x(H 2O)y(3+) (x = 8, 9; y = 0, 12-14) has been examined using DFT and CASSCF calculations. The latter confirmed that the wave function of octa- and nona-aqua Ce(III) is well-described by a single configuration. Benchmarking was performed for density functionals, reaction field cavity types, and solvation reactions against the experimental free energy of hydration, DeltaG(hyd)(Ce(3+)). The UA0, UAKS, Pauling, and UFF polarized continuum model cavities displayed different performance, depending on whether one or two hydration shells were examined, and as a function of the size of the metal basis set. These results were essentially independent of the density functional employed. Using these benchmarks, the free energy for water exchange between CN = 8 and CN = 9, for which no experimental data are available, was estimated to be approximately -4 kcal/mol.

Density Functional and Basis Set Dependence of Hydrated Ln(III) Properties

Benchmark studies of Ln(H2O)1,8-9(3+) (Ln = La, Lu) have been performed to assess the calculated properties obtained with local density approximation, generalized gradient approximation (GGA), meta-GGA, and hybrid functionals, when used with small- and large-core relativistic effective core potentials and their associated bases. Basis set dependence and the importance of specific functions to adequately describe the Ln atomic orbitals have been determined. The lanthanide contraction has been found to be an insufficient metric for characterizing the quality of a method/basis set combination due to cancellation of the errors. The electrostatic description obtained by natural population analysis has been examined, and an alternative partitioning of the valence space, which includes the 6s6p5d4f natural atomic orbitals, has been proposed.

Analysis of wave functions for open-shell molecules

During the past decade we have looked at several ways to track the distribution of unpaired electrons during chemical reactions and in different spin states. These methods were inspired by our previous work on singlet di-radicals where the spin density is zero yet there are clearly singly occupied orbitals. More recently we have been concerned with analysis of wave functions for single molecule magnets. This review discusses the mathematical framework by which open-shell systems can be described, in addition to methods that extract the effectively unpaired electron density, the spin state of atoms in a molecule, and other useful properties from a molecular wave function. Some of the difficulties associated with using broken spin Slater determinants to evaluate the exchange coupling parameters in the Heisenberg Hamiltonian are also mentioned.

Hydration properties of aqueous Pb(II) ion.

Using density functional theory and polarized continuum models, we have determined the most probable coordination number and structure of the first hydration shell of aqueous Pb(II). The geometries and hydration free energies of Pb(H2O)(1-9)(2+) were examined and benchmarked against experimental values. The free energies of hydration of Pb(H2O)(6-8)(2+) were found to match the experimental value within 10 kcal/mol. Moreover, based upon our thermochemical results for single water addition, primary hydration numbers of 6, 7, and 8 are all thermally accessible at STP. Use of a small-core 60 electron effective core potential (ECP) with the aug-cc-pvdz-PP basis on Pb resulted in structures that are significantly less hemidirected than predicted when using the large-core 78 electron ECP and the lanl2DZ basis on the metal. Our results imply that the hemi- to holo-directed transition in Pb(II)-water complexes is driven by coordination number and not hybridization of the 6s lone-pair orbital or enhanced covalent bonding in the Pb-OH2 bond. In addition to basis set effects, the influence of different solvation models on hydration reactions has further been examined so as to determine the relative accuracy of the calculated hydration thermochemistry.

ChemNetworks: a complex network analysis tool for chemical systems.

Many intermolecular chemical interactions persist across length and timescales and can be considered to form a “network” or “graph.” Obvious examples include the hydrogen bond networks formed by polar solvents such as water or alcohols. In fact, there are many similarities between intermolecular chemical networks like those formed by hydrogen bonding and the complex and distributed networks found in computer science. Contemporary network analyses are able to dissect the complex local and global changes that occur within the network over multiple time and length scales. This work discusses the ChemNetworks software, whose purpose is to process Cartesian coordinates of chemical systems into a network/graph formalism and apply topological network analyses that include network neighborhood, the determination of geodesic paths, the degree census, direct structural searches, and the distribution of defect states of network. These properties can help to understand the network patterns and organization that may influence physical properties and chemical reactivity. The focus of ChemNetworks is to quantitatively describe intermolecular chemical networks of entire systems at both the local and global levels and as a function of time. The code is highly general, capable of converting a wide variety of systems into a chemical network formalism, including complex solutions, liquid interfaces, or even self‐assemblies.

MoleculaRnetworks: An integrated graph theoretic and data mining tool to explore solvent organization in molecular simulation

This work discusses scripts for processing molecular simulations data written using the software package R: A Language and Environment for Statistical Computing. These scripts, named moleculaRnetworks, are intended for the geometric and solvent network analysis of aqueous solutes and can be extended to other H‐bonded solvents. New algorithms, several of which are based on graph theory, that interrogate the solvent environment about a solute are presented and described. This includes a novel method for identifying the geometric shape adopted by the solvent in the immediate vicinity of the solute and an exploratory approach for describing H‐bonding, both based on the PageRank algorithm of Google search fame. The moleculaRnetworks codes include a preprocessor, which distills simulation trajectories into physicochemical data arrays, and an interactive analysis script that enables statistical, trend, and correlation analysis, and other data mining. The goal of these scripts is to increase access to the wealth of structural and dynamical information that can be obtained from molecular simulations.

ForceFit: A Code to Fit Classical Force Fields to Quantum Mechanical Potential Energy Surfaces

The ForceFit program package has been developed for fitting classical force field parameters based upon a force matching algorithm to quantum mechanical gradients of configurations that span the potential energy surface of the system. The program, which runs under UNIX and is written in C++, is an easy‐to‐use, nonproprietary platform that enables gradient fitting of a wide variety of functional force field forms to quantum mechanical information obtained from an array of common electronic structure codes. All aspects of the fitting process are run from a graphical user interface, from the parsing of quantum mechanical data, assembling of a potential energy surface database, setting the force field, and variables to be optimized, choosing a molecular mechanics code for comparison to the reference data, and finally, the initiation of a least squares minimization algorithm. Furthermore, the code is based on a modular templated code design that enables the facile addition of new functionality to the program.