Does the radical GPRI strongly depend on the population scheme? A comparative study to predict radical attack on unsaturated molecules with the radical general-purpose reactivity indicator.

The reactivity of 22 unsaturated molecules undergoing attack by a methyl radical (⋅CH3) have been elucidated using the condensed radical general-purpose reactivity indicator (condensed radical GPRI) appropriate for relatively nucleophilic or electrophilic molecules. Using the appropriate radical GPRI equation for electrophilic attack or nucleophilic radical attack, seven different population schemes were used to assign the most reactive atoms in each of the 22 molecules. The results show that the condensed radical GPRI is sensitive to the population scheme chosen, but less sensitive than the radical Fukui function. Therefore, the reliability of these methods depends on the population scheme. Our investigation indicates that the condensed radical GPRI is most accurate in predicting the dominant products of the methyl radical addition reactions on a variety of unsaturated molecules when the Hirshfeld, Merz-Singh-Kollman, or Voronoi deformation density population schemes are used. Furthermore, for all populations schemes in the majority of instances where the radical Fukui function failed the radical GPRI was able to identify the most reactive atom under certain reactivity conditions.

Bioaccumulative chemicals are either too hard or too soft: Conceptual density functional theory as a screening tool for emerging pollutants.

Conceptual density functional theory (CDFT) descriptors were computed to predict the environmental fate of approximately 6,000 widely used industrial chemicals. CDFT descriptors aligned with a molecule's possible bioaccumulation mechanism, i.e., soft chemicals are lipophilic, whereas hard chemicals may bioaccumulate by other mechanisms such as protein binding. The results have provided us with a new "rule of thumb" to guide risk assessment of chemical hazards: suspected persistent organic pollutants are either too hard (η > 0.40 hartree) or too soft (α > 200 Å3). This offers a novel approach to environmental risk assessment using two fundamental properties of a molecule.

Warning! The negative divergence of the stress-tensor does not always yield the Ehrenfest force.

It has been assumed that the negative divergence of all stress tensors in common use yields the same force. This work finds that this is untrue, and, in fact, can vary wildly. We demonstrate this for the hydrogen atom, the one-particle isotropic harmonic oscillator, and a particle in an infinite spherical well where the exact density, pair-density, and the first order reduced density matrix are known for ground and excited states without any approximation. The Ehrenfest stress-tensor is introduced as any stress-tensor whose negative divergence will yield the corresponding Ehrenfest force for the same system when the exact wave-function is utilized. Stress-tensors within the literature are examined to show those that are Ehrenfest stress-tensors. Those that differ are demonstrated by how they differ within an exact formulation. The proof that the negative divergence of an Ehrenfest stress-tensor yields the Ehrenfest force is summarized.

An information-theoretic approach to basis-set fitting of electron densities and other non-negative functions.

The numerical ill-conditioning associated with approximating an electron density with a convex sum of Gaussian or Slater-type functions is overcome by using the (extended) Kullback-Leibler divergence to measure the deviation between the target and approximate density. The optimized densities are non-negative and normalized, and they are accurate enough to be used in applications related to molecular similarity, the topology of the electron density, and numerical molecular integration. This robust, efficient, and general approach can be used to fit any non-negative normalized functions (e.g., the kinetic energy density and molecular electron density) to a convex sum of non-negative basis functions. We present a fixed-point iteration method for optimizing the Kullback-Leibler divergence and compare it to conventional gradient-based optimization methods. These algorithms are released through the free and open-source BFit package, which also includes a L2-norm squared optimization routine applicable to any square-integrable scalar function.

Predicting the Mass Spectra of Environmental Pollutants Using Computational Chemistry: A Case Study and Critical Evaluation.

Organic pollutants can be identified by comparing their electron ionization (EI) mass spectra with those in libraries or obtained from authentic standards. Nevertheless, libraries are incomplete; standards may be unavailable or too costly, or their synthesis may be too time-consuming. This study evaluates the performance of quantum chemical electron ionization mass spectrometry (QCEIMS) vis-à-vis competitive fragmentation modeling (CFM) for suspect screening and unknown identification. EI mass spectra of 35 compounds, including halogenated organics, organophosphorus flame retardants (OPFRs), and disinfection byproducts were computed. Computational results were compared with EI mass spectra compiled in the NIST Library as well as collision-induced dissociation (CID) mass spectra obtained from radical cations M•+ generated by charge-exchange atmospheric pressure chemical ionization (APCI). The results indicate that QCEIMS performs equivalently or better than CFM. Average match factors between computed and experimental (NIST) EI mass spectra were 656 vs 503 for the halogenated organics, and on average, QCEIMS predicted 55% of the products generated by CID vs 17% predicted by CFM. QCEIMS predicted 37% of the OPFR CID products whereas CFM predicted 29%. QCEIMS performed comparably to a commercial combinatorial fragmentation method for suspect screening of a dust sample, identifying 19/20 targets. Examples of unknown pollutants, whose reference spectra were unavailable at the time of discovery, are also presented. The computational results suggest that QCEIMS can help guide the analyst in obtaining authentic standards and raise the possibility that, with advances in computing, an unknown may eventually be confirmed in hours as opposed to the days or months required to obtain authentic standards.

Molecular QTAIM Topology Is Sensitive to Relativistic Corrections.

The topology of the molecular electron density of benzene dithiol gold cluster complex Au4 -S-C6 H4 -S'-Au'4 changed when relativistic corrections were made and the structure was close to a minimum of the Born-Oppenheimer energy surface. Specifically, new bond paths between hydrogen atoms on the benzene ring and gold atoms appeared, indicating that there is a favorable interaction between these atoms at the relativistic level. This is consistent with the observation that gold becomes a better electron acceptor when relativistic corrections are applied. In addition to relativistic effects, here, we establish the sensitivity of molecular topology to basis sets and convergence thresholds for geometry optimization.

The general setting for the zero-flux condition: The lagrangian and zero-flux conditions that give the heisenberg equation of motion.

Generalizing our recent work on relativistic generalizations of the quantum theory of atoms in molecules, we present the general setting under which the principle of stationary action for a region leads to open quantum subsystems. The approach presented here is general and works for any Hamiltonian, and when a reasonable Lagrangian is selected, it often leads to the integral of the Laplacian of the electron density on the region vanishing as a necessary condition for the zero-flux surface. Alternatively, with this method, one can design a Lagrangian that leads to a surface of interest (though this Lagrangian may not be, and indeed probably will not be, "reasonable"). For any reasonable Lagrangian for the electronic wave function and any two-component method (related by integration by parts to the Hamiltonian) considered, the Bader definition of an atom is recaptured. © 2018 Wiley Periodicals, Inc.

A reference-free stockholder partitioning method based on the force on electrons.

We argue that when one divides a molecular property into atom-in-a-molecule contributions, one should perform the division based on the property density of the quantity being partitioned. This is opposition to the normal approach, where the electron density is given a privileged role in defining the properties of atoms-in-a-molecule. Because partitioning each molecular property based on its own property density is inconvenient, we design a reference-free approach that does not (directly) refer atomic property densities. Specifically, we propose a stockholder partitioning method based on relative influence of a molecule's atomic nuclei on the electrons at a given point in space. The resulting method does not depend on an "arbitrary" choice of reference atoms and it has some favorable properties, including the fact that all of the electron density at an atomic nucleus is assigned to that nucleus and the fact all the atoms in a molecule decay at a uniform asymptotic rate. Unfortunately, the resulting model is not easily applied to spatially degenerate ground states. Furthermore, the practical realizations of this strategy that we tried here gave disappointing numerical results. © 2017 Wiley Periodicals, Inc.

Relativistic (SR-ZORA) quantum theory of atoms in molecules properties.

The Quantum Theory of Atoms in Molecules (QTAIM) is used to elucidate the effects of relativity on chemical systems. To do this, molecules are studied using density-functional theory at both the nonrelativistic level and using the scalar relativistic zeroth-order regular approximation. Relativistic effects on the QTAIM properties and topology of the electron density can be significant for chemical systems with heavy atoms. It is important, therefore, to use the appropriate relativistic treatment of QTAIM (Anderson and Ayers, J. Phys. Chem. 2009, 115, 13001) when treating systems with heavy atoms. © 2016 Wiley Periodicals, Inc.

Using the general-purpose reactivity indicator: challenging examples.

We elucidate the regioselectivity of nucleophilic attack on substituted benzenesulfonates, quinolines, and pyridines using a general-purpose reactivity indicator (GPRI) for electrophiles. We observe that the GPRI is most accurate when the incoming nucleophile resembles a point charge. We further observe that the GPRI often chooses reactive "dead ends" as the most reactive sites as well as sterically hindered reactive sites. This means that care must be taken to remove sites that are inherently unreactive. Generally, among sites where reactions actually occur, the GPRI identifies the sites in the molecule that lead to the kinetically favored product(s). Furthermore, the GPRI can discern which sites react with hard reagents and which sites react with soft reagents. Because it is currently impossible to use the mathematical framework of conceptual DFT to identify sterically inaccessible sites and reactive dead ends, the GPRI is primarily useful as an interpretative, not a predictive, tool.

Holospinal epidural abscess of the spinal axis: two illustrative cases with review of treatment strategies and surgical techniques.

Despite the increasing prevalence of spinal infections, the subcategory of holospinal epidural abscesses (HEAs) is extremely infrequent and requires unique management. Panspinal imaging (preferably MRI), modern aggressive antibiotic therapy, and prompt surgical intervention remain the standard of care for all spinal axis infections including HEAs; however, the surgical decision making on timing and extent of the procedure still remain ill defined for HEAs. Decompression including skip laminectomies or laminoplasties is described, with varied clinical outcomes. In this review the authors present the illustrative cases of 2 patients with HEAs who were treated using skip laminectomies and epidural catheter irrigation techniques. The discussion highlights different management strategies including the role of conservative (nonsurgical) management in these lesions, especially with an already identified pathogen and the absence of mass effect on MRI or significant neurological defects. Among fewer than 25 case reports of HEA published in the past 25 years, the most important aspect in deciding a role for surgery is the neurological examination. Nearly 20% were treated successfully with medical therapy alone if neurologically intact. None of the reported cases had an associated cranial infection with HEA, because the dural adhesion around the foramen magnum prevented rostral spread of infection. Traditionally a posterior approach to the epidural space with irrigation is performed, unless an extensive focal ventral collection is causing cord compression. Surgical intervention for HEA should be an adjuvant treatment strategy for all acutely deteriorating patients, whereas aspiration of other infected sites like a psoas abscess can determine an infective pathogen, and appropriate antibiotic treatment may avoid surgical intervention in the neurologically intact patient.

Surgical versus nonsurgical treatment of subaxial cervical pedicle fractures.

BACKGROUND: Pedicle fractures in the cervical spine are common. They may occur in isolation or in combination with other concomitant fractures. Multiple classification systems have been introduced to provide a clinical framework when approaching these types of fractures; however, these systems do not provide guidelines for optimal treatment. Data regarding decision making are limited. Conservative treatment with orthoses may result in subluxation and instability requiring further treatment. Surgery may not be required in all instances because many of these injuries may heal without surgical intervention. METHODS: All cases of cervical fractures treated at a single institution over a 5-year period were retrospectively reviewed. Cases with pedicle fractures were further evaluated, and 40 cases managed either with or without surgery were identified. Data on presenting history, neurologic examination, imaging findings, comorbidity, method of treatment, complication rate, and length of hospital stay were collected. Fractures were classified based on computed tomography scans. Data on associated injuries were also collected. Fusion rate and fracture displacement were assessed by plain radiographs and computed tomography scans at follow-up. Follow-up time points included 2, 6, and 12 weeks and 6 months after injury. Primary outcome was fracture healing regardless of modality in the absence of progressive deformity (i.e., listhesis, kyphosis) and need for further surgery. RESULTS: Conservative therapy was administered to 26 patients, and 14 patients underwent surgery. There were no statistically significant differences between the 2 groups in terms of total levels injured (P = 0.9) or injury severity score (P = 0.5). Patients who presented with intact neurologic status were more likely to be treated conservatively (88% vs. 29%; P = 0.0004), whereas patients presenting with spinal cord injuries were more likely to undergo surgical fixation (35% vs. 0%; P = 0.0004). Length of hospital stay trended toward being significantly greater in patients who underwent surgery (10.6 days vs. 5.5 days; P = 0.07). According to our classification system, the most common fracture type was single line horizontal fracture occurring in 68% (27 of 40 cases). Vertical split pedicle fracture occurred in 28% (11 of 40 cases), and double line horizontal fracture occurred in 5% (2 of 40 cases). Posttreatment progressive listhesis was significantly higher in patients who were treated conservatively (31% vs. 0%; P = 0.03), especially when associated with comminuted lateral mass or subluxation or both. CONCLUSIONS: This study describes and classifies unique cervical pedicle fractures and associated injuries. Our findings suggest that surgical treatment results in definitive stability for these injuries compared with conservative therapy, particularly for pedicle fractures associated with comminuted lateral mass or initially displaced fractures. However, nondisplaced vertical split pedicle fractures and isolated single line horizontal fractures may be treated nonsurgically without occurrence of further instability. A larger prospective study is required to confirm these findings.

Kinetic and electron-electron energies for convex sums of ground state densities with degeneracies and fractional electron number.

Properties of exact density functionals provide useful constraints for the development of new approximate functionals. This paper focuses on convex sums of ground-level densities. It is observed that the electronic kinetic energy of a convex sum of degenerate ground-level densities is equal to the convex sum of the kinetic energies of the individual degenerate densities. (The same type of relationship holds also for the electron-electron repulsion energy.) This extends a known property of the Levy-Valone Ensemble Constrained-Search and the Lieb Legendre-Transform refomulations of the Hohenberg-Kohn functional to the individual components of the functional. Moreover, we observe that the kinetic and electron-repulsion results also apply to densities with fractional electron number (even if there are no degeneracies), and we close with an analogous point-wise property involving the external potential. Examples where different degenerate states have different kinetic energy and electron-nuclear attraction energy are given; consequently, individual components of the ground state electronic energy can change abruptly when the molecular geometry changes. These discontinuities are predicted to be ubiquitous at conical intersections, complicating the development of universally applicable density-functional approximations.

In pursuit of negative Fukui functions: molecules with very small band gaps.

A justification for the likely presence of negative Fukui functions in molecules with small band gaps is given, and a computational study performed to check whether molecules with small band gaps have negative Fukui functions to a chemically significant extent is reported. While regions with negative Fukui functions were observed, significantly negative values for the atom-condensed Fukui functions were not observed.

The Ehrenfest force topology: a physically intuitive approach for analyzing chemical interactions.

Modified ANO-RCC basis sets are used to determine twelve molecular graphs of the Ehrenfest force for H2, CH4, CH2O, CH3NO, C2H2, C2H4, C3H3NO, N4H4, H2O, (H2O)2, (H2O)4 and (H2O)6. The molecular graphs include all types of topological critical points and a mix of bonding types is chosen to include sigma-, π- and hydrogen-bonding. We then compare a wide range of point properties: charge density, trace of the Hessian, eigenvalues, ellipticity, stiffness, total local energy and the eigenvectors are calculated at the bond critical points (BCPs) and compared for the Ehrenfest, QTAIM and stress tensor schemes. QTAIM is found to be the only partitioning scheme that can differentiate between shared- and closed-shell chemical bond types. Only the results from the Ehrenfest force partitioning, however, are demonstrated to be physically intuitive. This is demonstrated for the water molecule, the water-dimer and the water clusters (H2O)4 and (H2O)6. In particular, both the stiffness and the trace of the Hessians of the appropriate quantities of the sigma-bond BCPs for the water clusters are found to depend on the quantum topology dimension of the molecular graph. The behavior of all the stress tensor point properties is found to be erratic. This is explained by the ambiguity in the theoretical definition of the stress tensor. As a complementary approach the Ehrenfest force provides a new indicator of the mixed chemical character of the hydrogen-bond BCP, which arises from the collinear donor sigma-bond donating a degree of covalent character to the hydrogen-bond. This indicator takes the form of the relative orientation of the shallowest direction of the Ehrenfest potential of the hydrogen-bond BCPs and the corresponding direction for the collinear sigma-bond BCP.

In pursuit of negative Fukui functions: examples where the highest occupied molecular orbital fails to dominate the chemical reactivity.

In our quest to explore molecules with chemically significant regions where the Fukui function is negative, we explored reactions where the frontier orbital that indicates the sites for electrophilic attack is not the highest occupied molecular orbital. The highest occupied molecular orbital (HOMO) controls the location of the regions where the Fukui function is negative, supporting the postulate that negative values of the Fukui function are associated with orbital relaxation effects and nodal surfaces of the frontier orbitals. Significant negative values for the condensed Fukui function, however, were not observed.

The misapplication of the term spinal cord injury without radiographic abnormality (SCIWORA) in adults.

BACKGROUND: Spinal cord injury without radiographic abnormality (SCIWORA) is generally considered a disease of children; however, it is commonly used when referring to adults who have spinal cord injury without computed tomography evidence of trauma (SCIWOCTET). The purpose of this study was to describe characteristics of patients with both adult and pediatric cervical SCIWOCTET admitted to hospitals in our region. METHODS: A retrospective review of all patients admitted to our two ACS-verified trauma centers with cervical spinal cord injury from January 2005 to December 2009 was performed. All patients with vertebral or ligamentous injury identified on computed tomographic (CT) scan of the cervical spine were excluded. Data gathered on the remaining patients included demographics, injury mechanism, Injury Severity Score, neurologic level and severity of spinal cord injury, magnetic resonance imaging results, and mortality rates. RESULTS: During the 5-year period of this study, 11,644 adult patients and 3,458 pediatric trauma patients were admitted. Of these, 313 patients were thought to have cervical spinal cord injury based on International Classification of Diseases, Ninth Revision (ICD-9) codes, 279 (89.1%) were excluded due to injury noted on CT cervical spine, and 9 were excluded as they were found to not truly have cervical spinal cord injury after review of the medical record. The remaining 25 patients were identified as having cervical SCIWOCTET. Twenty-three patients (92%) were male. The patient ages ranged from 10 to 83 years with a median age of 56 years. The mean Injury Severity Score was 22.6. Sixty-eight percent had a mechanism of fall. Degenerative changes were found on the CT scan of the cervical spine in 96% of all patients and in all 24 adult patients. There was only one pediatric patient with SCIWORA, a 10-year-old boy who had a normal CT scan of the cervical spine but had a persistent neurologic deficit. CONCLUSION: SCIWOCTET is mainly a disease of adults, and its subset SCIWORA, a disease of children, is much less common. Adults with this disease have CT scans showing canal stenosis and significant degenerative changes in the cervical spine; thus, it is not accurate to state that they have SCIWORA. The characteristics of this patient population are important as SCIWOCTET is the concern when clearing the cervical spines of trauma patients with a CT scan of the cervical spine negative for injury. LEVEL OF EVIDENCE: Epidemiologic study, level III.

Longitudinal performance of a surgically implanted neuroprosthesis for lower-extremity exercise, standing, and transfers after spinal cord injury.

OBJECTIVE: To investigate the longitudinal performance of a surgically implanted neuroprosthesis for lower-extremity exercise, standing, and transfers after spinal cord injury. DESIGN: Case series. SETTING: Research or outpatient physical therapy departments of 4 academic hospitals. PARTICIPANTS: Subjects (N=15) with thoracic or low cervical level spinal cord injuries who had received the 8-channel neuroprosthesis for exercise and standing. INTERVENTION: After completing rehabilitation with the device, the subjects were discharged to unrestricted home use of the system. A series of assessments were performed before discharge and at a follow-up appointment approximately 1 year later. MAIN OUTCOME MEASURES: Neuroprosthesis usage, maximum standing time, body weight support, knee strength, knee fatigue index, electrode stability, and component survivability. RESULTS: Levels of maximum standing time, body weight support, knee strength, and knee fatigue index were not statistically different from discharge to follow-up (P>.05). Additionally, neuroprosthesis usage was consistent with subjects choosing to use the system on approximately half of the days during each monitoring period. Although the number of hours using the neuroprosthesis remained constant, subjects shifted their usage to more functional standing versus more maintenance exercise, suggesting that the subjects incorporated the neuroprosthesis into their lives. Safety and reliability of the system were demonstrated by electrode stability and a high component survivability rate (>90%). CONCLUSIONS: This group of 15 subjects is the largest cohort of implanted lower-extremity neuroprosthetic exercise and standing system users. The safety and efficiency data from this group, and acceptance of the neuroprosthesis as demonstrated by continued usage, indicate that future efforts toward commercialization of a similar device may be warranted.

Quantum theory of atoms in molecules: results for the SR-ZORA Hamiltonian.

The quantum theory of atoms in molecules (QTAIM) is generalized to include relativistic effects using the popular scalar-relativistic zeroth-order regular approximation (SR-ZORA). It is usually assumed that the definition of the atom as a volume bounded by a zero-flux surface of the electron density is closely linked to the form of the kinetic energy, so it is somewhat surprising that the atoms corresponding to the relativistic kinetic-energy operator in the SR-ZORA Hamiltonian are also bounded by zero-flux surfaces. The SR-ZORA Hamiltonian should be sufficient for qualitative descriptions of molecular electronic structure across the periodic table, which suggests that QTAIM-based analysis can be useful for molecules and solids containing heavy atoms.

Computed tomography alone may clear the cervical spine in obtunded blunt trauma patients: a prospective evaluation of a revised protocol.

BACKGROUND: Cervical spine (CS) clearance in obtunded blunt trauma patients (OBTPs) remains controversial. When computed tomography (CT) of the CS is negative for injury, debate continues over the role of magnetic resonance imaging (MRI). Use of MRI in OBTPs is costly, time-consuming, and potentially dangerous. Our study evaluated the safety of a protocol to discontinue the cervical collar in OBTPs based on CT scan alone. METHODS: A prospective study was performed from October 2006 to September 2008 at a regional Level I trauma center on OBTPs with gross movement of all extremities. After a CT of the CS was read as negative for injury, the CS was cleared and the collar was removed. Patients were then followed prospectively for related complications. RESULTS: One hundred ninety-seven patients had their collars removed and CS cleared at a mean of 3.3 days. There were 144 males (73%), and the average age was 47.1 years. Sixty-two percent of patients were reexamined by a physician when no longer obtunded and found to have no CS signs or symptoms. Five patients (2.5%), when no longer obtunded, had persistent pain for which MRI CS was negative for injury. Coroner reports and autopsies were reviewed for missed spinal cord injuries in the 13% who died before reexamination. One of these patients had an autopsy report of an isolated CS ligamentous injury, deemed to be stable by our attending neurosurgeon. We followed up an additional 12% by phone or chart review, with no report of new onset neurologic deficit. The remaining 11% were lost to follow-up, but no patient contacted our hospital to report deterioration in function. One patient (0.5%) developed a minor CS decubitus ulceration. CONCLUSION: Removal of CS precautions in OBTPs with gross movement of all extremities is safe and efficacious if CT CS is negative for injury. Supplemental MRI CS is not needed in this patient population.