Understanding Chemical Selectivity through Well Selected Excited States.

In this publication, we propose a new set of reactivity/selectivity descriptors, derived within a Rayleigh-Schrödinger perturbation theory framework, for chemical systems undergoing an electrostatic (point-charge) perturbation. From the electron density polarization at first order, qualitative insight on reactivity is retrieved, while more quantitative information (noteworthy selectivity) can be obtained from either the second-order energy response or the number of shifted electrons under perturbation. Noteworthily, only a small number of excitations contribute significantly to the overall responses to perturbation, suggesting chemical reactivity could be foreseen by a careful scrutiny of the electron density reorganization upon excitation.

Communication: Kohn-Sham theory for excited states of Coulomb systems.

For obtaining individual excited-state energies and densities of Coulomb electronic systems, by means of an energy stationary principle, it was shown previously that there exists a universal functional of the density, F(Coul)[ϱ], for the kinetic plus electron-electron repulsion part of the total energy. Here, we make knowledge of the existence of F(Coul)[ϱ] practical for calculation by identifying Ts (Coul)[ϱ], the non-interacting kinetic energy component of F(Coul)[ϱ], and by showing that Ts (Coul)[ϱ] may be computed exactly by means of orbitals that are obtained through a set of single-particle Kohn-Sham equations. Constraints for obtaining accurate approximations to the remaining unknown component of F(Coul)[ϱ] are presented.

Creating a National Coalition to Address Tractor Overturn Fatalities.

Tractor overturns continue to be the leading cause of death on U.S. farms. While rollover protective structures (ROPS) are effective in preventing these fatalities, they are underutilized due to a number of barriers. Past programs in the U.S. and abroad have targeted this area of agricultural safety; however, a national program is not yet in place for U.S. farmers. This study seeks to build a national partnership to address tractor overturn fatalities by increasing the number of tractors with ROPS. A diverse, multisector steering committee has been organized and is working together using Whole System in a Room methods. This method brings together partners from nine stakeholder groups to identify and commit to a collaborative solution to the issue.

ACKS2: atom-condensed Kohn-Sham DFT approximated to second order.

A new polarizable force field (PFF), namely atom-condensed Kohn-Sham density functional theory approximated to second order (ACKS2), is proposed for the efficient computation of atomic charges and linear response properties of extended molecular systems. It is derived from Kohn-Sham density functional theory (KS-DFT), making use of two novel ingredients in the context of PFFs: (i) constrained atomic populations and (ii) the Legendre transform of the Kohn-Sham kinetic energy. ACKS2 is essentially an extension of the Electronegativity Equalization Method (EEM) [W. J. Mortier, S. K. Ghosh, and S. Shankar, J. Am. Chem. Soc. 108, 4315 (1986)] in which two major EEM shortcomings are fixed: ACKS2 predicts a linear size-dependence of the dipole polarizability in the macroscopic limit and correctly describes the charge distribution when a molecule dissociates. All ACKS2 parameters are defined as atoms-in-molecules expectation values. The implementation of ACKS2 is very similar to that of EEM, with only a small increase in computational cost.

Hirshfeld-E Partitioning: AIM Charges with an Improved Trade-off between Robustness and Accurate Electrostatics.

For the development of ab initio derived force fields, atomic charges must be computed from electronic structure computations, such that (i) they accurately describe the molecular electrostatic potential (ESP) and (ii) they are transferable to the force-field application of interest. The Iterative Hirshfeld (Hirshfeld-I or HI) scheme meets both requirements for organic molecules. For inorganic oxide clusters, however, Hirshfeld-I becomes ambiguous because electron densities of nonexistent isolated anions are needed as input. Herein, we propose a simple Extended Hirshfeld (Hirshfeld-E or HE) scheme to overcome this limitation. The performance of the new HE scheme is compared to four popular atoms-in-molecules schemes, using two tests involving a set of 248 silica clusters. These tests show that the new HE scheme provides an improved trade-off between the ESP accuracy and the transferability of the charges. The new scheme is a generalization of the Hirshfeld-I scheme, and it is expected that its improvements are to a large extent applicable to molecular systems containing elements from the entire periodic table.

The Significance of Parameters in Charge Equilibration Models.

Charge equilibration models such as the electronegativity equalization method (EEM) and the split charge equilibration (SQE) are extensively used in the literature for the efficient computation of accurate atomic charges in molecules. However, there is no consensus on a generic set of optimal parameters, even when one only considers parameters calibrated against atomic charges in organic molecules. In this work, the origin of the disagreement in the parameters is investigated by comparing and analyzing six sets of parameters based on two sets of molecules and three calibration procedures. The resulting statistical analysis clearly indicates that the conventional least-squares cost function based solely on atomic charges is in general ill-conditioned and not capable of fixing all parameters in a charge-equilibration model. Methodological guidelines are formulated to improve the stability of the parameters. Although in this case a simple interpretation of individual parameters is not possible, charge equilibration models remain of great practical use for the computation of atomic charges.

On the applicability of local softness and hardness.

Global hardness and softness and the associated hard/soft acid/base (HSAB) principle have been used to explain many experimental observed reactivity patterns and these concepts can be found in textbooks of general, inorganic, and organic chemistry. In addition, local versions of these reactivity indices and principles have been defined to describe the regioselectivity of systems. In a very recent article (Chem.-Eur. J. 2008, 14, 8652), the present authors have shown that the picture of these well-known descriptors is incomplete and that the understanding of these reactivity indices must be "reinterpreted". In fact, the local softness and hardness contain the same "potential information" and they should be interpreted as the "local abundance" or "concentration" of their corresponding global properties. In this contribution, we analyze the implications of this new point of view for the applicability of these well-known descriptors when comparing two sites in three situations: two sites within one molecule, two sites in two different, but noninteracting molecules, and two sites in two different, but interacting, molecules. The implications on the HSAB principle are highlighted, leading to the discussion of the role of the electrostatic interaction.

Static simulation and analyses of mower's ROPS behavior in a finite element model.

The goal of this research was to numerically predict the maximum lateral force acting on a mower rollover protective structure (ROPS) and the energy absorbed by the ROPS during a lateral continuous roll. A finite element (FE) model of the ROPS was developed using elastic and plastic theories including nonlinear relationships between stresses and strains in the plastic deformation range. Model validation was performed using field measurements of ROPS behavior in a lateral continuous roll on a purpose-designed test slope. Field tests determined the maximum deformation of the ROPS of a 900 kg John Deere F925 mower with a 183 cm (72 in.) mowing deck during an actual lateral roll on a pad and on soil. In the FE model, lateral force was gradually added to the ROPS until the field-measured maximum deformation was achieved. The results from the FE analysis indicated that the top corners of the ROPS enter slightly into the plastic deformation region. Maximum lateral forces acting on the ROPS during the simulated impact with the pad and soil were 19650 N and 22850 N, respectively. The FE model predicted that the energy absorbed by the ROPS (643 J) in the lateral roll test on the pad was less than the static test requirements (1575 J) of Organization for Economic Development (OECD) Code 6. In addition, the energy absorbed by the ROPS (1813 J) in the test on the soil met the static test requirements (1575 J). Both the FE model and the field test results indicated that the deformed ROPS of the F925 mower with deck did not intrude into the occupant clearance zone during the lateral continuous or non-continuous roll.

Nonuniqueness of magnetic fields and energy derivatives in spin-polarized density functional theory.

The effect of the recently uncovered nonuniqueness of the external magnetic field B(r) corresponding to a given pair of density n(r) and spin density n(s)(r) on the derivative of the energy functional of spin-polarized density functional theory, and its implications for the definition of chemical reactivity descriptors, is examined. For ground states, the nonuniqueness of B(r) implies the nondifferentiability of the energy functional E(v,B)[n,n(s)] with respect to n(s)(r). It is shown, on the other hand, that this nonuniqueness allows the existence of the one-sided derivatives of E(v,B)[n,n(s)] with respect to n(s)(r). Although the N-electron ground state can always be obtained from the minimization of E(v,B)[n,n(s)] without any constraint on the spin number N(s)=integraln(s)(r)dr, the Lagrange multiplier mu(s) associated with the fixation of N(s) does not vanish even for ground states. Mu(s) is identified as the left- or right-side derivative of the total energy with respect to N(s), which justifies the interpretation of mu(s) as a (spin) chemical potential. This is relevant not only for the spin-polarized generalization of conceptual density functional theory, the spin chemical potential being one of the elementary reactivity descriptors, but also for the extension of the thermodynamical analogy of density functional theory for the spin-polarized case. For higher-order reactivity indices, B(r)'s nonuniqueness has similar implications as for mu(s), leading to a split of the indices with respect to N(s) into one-sided reactivity descriptors.

Initial Hardness Response and Hardness Profiles in the Study of Woodward-Hoffmann Rules for Electrocyclizations.

The fundamental principles of pericyclic reactions are governed by the Woodward-Hoffmann rules, which state that these reactions can only take place if the symmetries of the reactants' molecular orbitals and the products' molecular orbitals are the same. As such, these rules rely on the nodal structure of either the wave function or the frontier molecular orbitals, so it is unclear how these rules can be recovered in the density functional reactivity theory (or "conceptual DFT"), where the basic quantity is the strictly positive electron density. A third, nonsymmetry based approach to predict the outcome of pericyclic reactions is due to Zimmerman which uses the concept of the aromatic transition states: allowed reactions possess aromatic transition states, while forbidden reactions possess antiaromatic transition states. Based on our recent work on cycloadditions, we investigate the initial response of the chemical hardness, a central DFT based reactivity index, along the reaction profiles of a series of electrocyclizations. For a number of cases, we also compute complete initial reaction coordinate (IRC) paths and hardness profiles. We find that the hardness response is always higher for the allowed modes than for the forbidden modes. This suggests that the initial hardness response along the IRC is the key for casting the Woodward-Hoffmann rules into conceptual DFT.

Evaluation of engineering plastic for rollover protective structure (ROPS) mounting.

Agriculture has one of the highest fatality rates of any industry in America. Tractor rollovers are a significant contributor to the high death rate. Rollover protective structures (ROPS) have helped lower these high fatality rates on full-size tractors. However, a large number of older tractors still do not use ROPS due to the difficulty of designing and creating a mounting structure. To help reduce this difficulty, engineering plastics were evaluated for use in a ROPS mounting structure on older tractors. The use of engineering plastics around axle housings could provide a uniform mounting configuration as well as lower costs for aftermarket ROPS. Various plastics were examined through shear testing, scale model testing, and compressive strength testing. Once a material was chosen based upon strength and cost, full-scale testing of the plastic's strength on axle housings was conducted. Finally, a mounting structure was tested in static ROPS tests, and field upset tests were performed in accordance with SAE Standard J2194. Initial tests revealed that the ROPS mounting structure and axle housing combination had higher torsional strength with less twisting than the axle housing alone. An engineering plastic ROPS mounting structure was easily successful in withstanding the forces applied during the static longitudinal and lateral ROPS tests. Field upset testing revealed that the mounting structure could withstand the impact loads seen during actual upsets without a failure. During both static testing and field upset testing, no permanent twisting of the mounting structure was found. Engineering plastic could therefore be a viable option for a universal ROPS mounting structure for older tractors.

The Gradient Curves Method: An Improved Strategy for the Derivation of Molecular Mechanics Valence Force Fields from ab Initio Data.

A novel force-field development strategy is proposed that tackles the well-known difficulty of parameter correlations arising in a conventional least-squares optimization. In the first step of the new gradient curves method (GCM), continuity criteria are imposed to transform the raw multidimensional ab initio training data to distinct sets of one-dimensional data, each associated with an individual energy term. In the second step, the transformed data suggest suitable analytical expressions, and the parameters in these expressions are fitted to the transformed data; that is, one does not have to postulate a priori analytical expressions for the force-field energy terms. This approach facilitates the derivation of valence terms. Benchmarks have been performed on a set of small molecules. The results show that the new method yields physically acceptable energy terms exactly when a conventional parametrization would suffer from parameter correlations, that is, when an increasing number of redundant internal coordinates is used in the force-field model. The generic treatment of parameter correlations in the proposed method facilitates an intuitive physical interpretation of the individual terms in the force-field expression, which is a prerequisite for the transferability of force-field models.

Soil properties affecting wheat yields following drilling-fluid application.

Oil and gas drilling operations use drilling fluids (mud) to lubricate the drill bit and stem, transport formation cuttings to the surface, and seal off porous geologic formations. Following completion of the well, waste drilling fluid is often applied to cropland. We studied potential changes in soil compaction as indicated by cone penetration resistance, pH, electrical conductivity (EC(e)), sodium adsorption ratio (SAR), extractable soil and total straw and grain trace metal and nutrient concentrations, and winter wheat (Triticum aestivum L. 'TAM 107') grain yield following water-based, bentonitic drilling-fluid application (0-94 Mg ha(-1)) to field test plots. Three methods of application (normal, splash-plate, and spreader-bar) were used to study compaction effects. We measured increasing SAR, EC(e), and pH with drilling-fluid rates, but not to levels detrimental to crop production. Field measurements revealed significantly higher compaction within areas affected by truck travel, but also not enough to affect crop yield. In three of four site years, neither drilling-fluid rate nor application method affected grain yield. Extractions representing plant availability and plant analyses results indicated that drilling fluid did not significantly increase most trace elements or nutrient concentrations. These results support land application of water-based bentonitic drilling fluids as an acceptable practice on well-drained soils using controlled rates.

On the importance of the "density per particle" (shape function) in the density functional theory.

The central role of the shape function sigma(r) from the density functional theory (DFT), the ratio of the electron density rho(r) and the number of electrons N of the system (density per particle), is investigated. Moreover, its relationship with DFT based reactivity indices is established. In the first part, it is shown that an estimate for the chemical hardness can be obtained from the long range behavior of the shape function and its derivative with respect to the number of electrons at a fixed external potential. Next, the energy of the system is minimized with the constraint that the shape function should integrate to unity; the associated Lagrange multiplier is shown to be related to the electronic chemical potential micro of the system. Finally, the importance of the shape function for both molecular structure, reactivity, and similarity is outlined.

Variational principles for describing chemical reactions. Reactivity indices based on the external potential.

In a recent paper [J. Am. Chem. Soc. 2000, 122, 2010], the authors explored variational principles that help one understand chemical reactivity on the basis of the changes in electron density associated with a chemical reaction. Here, similar methods are used to explore the effect changing the external potential has on chemical reactivity. Four new indices are defined: (1) a potential energy surface that results from the second-order truncation of the Taylor series in the external potential about some reference, Upsilon(R(1),R(2),.,R(M)()); (2) the stabilization energy for the equilibrium nuclear geometry (relative to some reference), Xi; (3) the flexibility, or "lability", of the molecule at equilibrium, Lambda; and (4) the proton hardness, Pi, which performs a role in the theory of Brönsted-Lowry acids and bases that is similar to the role of the chemical hardness in the theory of Lewis acids and bases. Applications considered include the orientation of a molecule in an external electric field, molecular association reactions, and reactions between Brönsted-Lowry acids and bases.

Density per particle as a descriptor of Coulombic systems.

It is shown that for finite Coulombic systems the density per particle, final sigma identical with rho/N, determines the value of any observable quantity. The associated variational principle is derived.

The effect of parathyroid hormone on technetium-99m pyrophosphate distribution in rats.

Sprague-Dawley rats were treated with varying quantities of parathyroid hormone for 1--3 days, then sacrificed at periods ranging from 1--6 h after administration of 99mTc-pyrophosphate. Very little increase in bone accumulation of tracer occurred with this treatment. A small, but obvious decrease occurred in the blood levels of 99mTc-pyrophosphate and a smaller and less consistent decrease was affected in the muscle levels of the radiopharmaceutical. The overall result was an improvement in the bone/blood and bone/muscle ratios. It is suggested that the basis of the "supernormal" bone scan of hyperparathyroidism is achieved by this mechanism and that the increased bone uptake of other ions in response to parathyroid hormone is not shared by 99mTc-pyrophosphate.