An Operational Definition of Relative Hardness

2007 ◽  
Vol 72 (1) ◽  
pp. 51-63 ◽  
Author(s):  
Peter Politzer ◽  
Jane S. Murray ◽  
Monica C. Concha ◽  
Ping Jin
Keyword(s):  
Density Functional ◽  
Chemical Potential ◽  
Closed Shell ◽  
Operational Definition ◽  
Nuclear Potential ◽  
Small Range ◽  
Average Local Ionization Energy ◽  
Relative Hardness ◽  
Definition Of ◽  
Molecular Components

After a brief review of polarizability, charge capacity and hardness, we look at some of the consequences of the requirement, in density functional theory, that the chemical potential and hardness be evaluated with the nuclear potential being held constant. The effects of this can be quite significant, one of them being that some molecules, especially closed-shell, may have zero chemical potentials. We propose that hardness be defined operationally through its inverse relationship to polarizability. Drawing upon correlations found earlier for the latter property, we present a formula for relative hardness in terms of the volume of a molecule and the average local ionization energy on its surface. The formula can also be applied to molecular components, e.g. functional groups, and we show - within the context of this approach - how their contributions combine to yield the hardness of the molecule. This involves a leveling-off effect that explains the relatively small range of hardness values obtained for a group of 33 molecules.

Self-consistent Field Orbital Methods

2020 ◽  
pp. 128-149
Author(s):  
Jochen Autschbach
Keyword(s):  
Density Functional ◽  
Slater Determinant ◽  
Closed Shell ◽  
Open Shell ◽  
Initial Guess ◽  
Hartree Fock ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Definition Of

This chapter discusses the concepts underlying the Hartree-Fock (HF) electronic structure method. First, it is shown how the energy expectation value is calculated for a Slater determinant (SD) wavefunction in the case of orthonormal orbitals. This leads to the definition of the electron repulsion integrals (ERIs). Next, the energy is minimized subject to the orthonormality constraints. This leads to the HF equation for the orbitals. The HF orbital energies are Langrange multipliers representing the constraints. An unknown set of orbitals can be determined from an initial guess via a self-consistent field (SCF) cycle. The HF scheme is discussed for closed-shell versus open shell systems, leading to the distinction between spin restricted and unrestricted HF (RHF, UHF). Kohn-Sham density functional theory (DFT) is introduced and its approximate version is placed in the context of ab-initio versus semi-empirical quantum chemistry methods.

Understanding functional illiteracy from a policy, adult education, and cognition point of view: Towards a joint referent framework

2019 ◽  
Vol 30 (2) ◽  
pp. 109-122
Author(s):  
Aleksandar Bulajić ◽  
Miomir Despotović ◽  
Thomas Lachmann
Keyword(s):  
Adult Education ◽  
Operational Definition ◽  
Literacy Skills ◽  
Point Of View ◽  
Industrialized Countries ◽  
Functional Illiteracy ◽  
Scale Levels ◽  
Components Of Reading ◽  
The One ◽  
Definition Of

Abstract. The article discusses the emergence of a functional literacy construct and the rediscovery of illiteracy in industrialized countries during the second half of the 20th century. It offers a short explanation of how the construct evolved over time. In addition, it explores how functional (il)literacy is conceived differently by research discourses of cognitive and neural studies, on the one hand, and by prescriptive and normative international policy documents and adult education, on the other hand. Furthermore, it analyses how literacy skills surveys such as the Level One Study (leo.) or the PIAAC may help to bridge the gap between cognitive and more practical and educational approaches to literacy, the goal being to place the functional illiteracy (FI) construct within its existing scale levels. It also sheds more light on the way in which FI can be perceived in terms of different cognitive processes and underlying components of reading. By building on the previous work of other authors and previous definitions, the article brings together different views of FI and offers a perspective for a needed operational definition of the concept, which would be an appropriate reference point for future educational, political, and scientific utilization.

“The Unconscious” in Current Psychology

2010 ◽  
Vol 15 (3) ◽  
pp. 193-201 ◽  
Author(s):  
Elisabeth Norman
Keyword(s):  
Cognitive Psychology ◽  
Verbal Report ◽  
Psychological Research ◽  
Operational Definition ◽  
The Unconscious ◽  
Apparent Lack ◽  
Unconscious Processing ◽  
Unconscious Processes ◽  
Intermediate States ◽  
Definition Of

A series of vignette examples taken from psychological research on motivation, emotion, decision making, and attitudes illustrates how the influence of unconscious processes is often measured in a range of different behaviors. However, the selected studies share an apparent lack of explicit operational definition of what is meant by consciousness, and there seems to be substantial disagreement about the properties of conscious versus unconscious processing: Consciousness is sometimes equated with attention, sometimes with verbal report ability, and sometimes operationalized in terms of behavioral dissociations between different performance measures. Moreover, the examples all seem to share a dichotomous view of conscious and unconscious processes as being qualitatively different. It is suggested that cognitive research on consciousness can help resolve the apparent disagreement about how to define and measure unconscious processing, as is illustrated by a selection of operational definitions and empirical findings from modern cognitive psychology. These empirical findings also point to the existence of intermediate states of conscious awareness, not easily classifiable as either purely conscious or purely unconscious. Recent hypotheses from cognitive psychology, supplemented with models from social, developmental, and clinical psychology, are then presented all of which are compatible with the view of consciousness as a graded rather than an all-or-none phenomenon. Such a view of consciousness would open up for explorations of intermediate states of awareness in addition to more purely conscious or purely unconscious states and thereby increase our understanding of the seemingly “unconscious” aspects of mental life.

Hydrostibination of Alkynes: A Radical Mechanism

2020 ◽  
Author(s):  
Josh MacMillan ◽  
Katherine Marczenko ◽  
Erin Johnson ◽  
Saurabh Chitnis
Keyword(s):  
Density Functional ◽  
Activation Barrier ◽  
Closed Shell ◽  
Reaction Rates ◽  
Radical Mechanism ◽  
Neutral Radical ◽  
Kinetic Isotope ◽  
Rate Limiting Step ◽  
Ionic Mechanisms ◽  
Terminal Acetylenes

The addition of Sb-H bonds to alkynes was reported recently as a new hydroelementation reaction that exclusively yields anti-Markovnikov <i>Z</i>-olefins from terminal acetylenes. We examine four possible mechanisms that are consistent with the observed stereochemical and regiochemical outcomes. A comprehensive analysis of solvent, substituent, isotope, additive, and temperature effects on hydrostibination reaction rates definitively refutes three ionic mechanisms involving closed-shell charged intermediates. Instead the data support a fourth pathway featuring neutral radical Sb<sup>II</sup> and Sb<sup>III</sup> intermediates. Density Functional Theory (DFT) calculations are consistent this model, predicting an activation barrier that is within 1 kcal mol<sup>-1</sup> of the experimental value (Eyring analysis) and a rate limiting step that is congruent with experimental kinetic isotope effect. We therefore conclude that hydrostibination of arylacetylenes is initiated by the generation of stibinyl radicals, which then participate in a cycle featuring Sb<sup>II</sup> and Sb<sup>III</sup> intermediates to yield the observed <i>Z</i>-olefins as products. This mechanistic understanding will enable rational evolution of hydrostibination as a methodology for accessing challenging products such as <i>E</i>-olefins.

Structure, Stability and Water Adsorption on Ultra-Thin TiO2 Supported on TiN

2019 ◽  
Author(s):  
Jose Julio Gutierrez Moreno ◽  
Marco Fronzi ◽  
Pierre Lovera ◽  
alan O'Riordan ◽  
Mike J Ford ◽  
...  
Keyword(s):  
Density Functional ◽  
Water Adsorption ◽  
Chemical Potential ◽  
Energy Gap ◽  
Molecular Water ◽  
Structure Stability ◽  
Ambient Conditions ◽  
Rutile Structure ◽  
The Stability ◽  
The One

<p></p><p>Interfacial metal-oxide systems with ultrathin oxide layers are of high interest for their use in catalysis. In this study, we present a density functional theory (DFT) investigation of the structure of ultrathin rutile layers (one and two TiO<sub>2</sub> layers) supported on TiN and the stability of water on these interfacial structures. The rutile layers are stabilized on the TiN surface through the formation of interfacial Ti–O bonds. Charge transfer from the TiN substrate leads to the formation of reduced Ti<sup>3+</sup> cations in TiO<sub>2.</sub> The structure of the one-layer oxide slab is strongly distorted at the interface, while the thicker TiO<sub>2</sub> layer preserves the rutile structure. The energy cost for the formation of a single O vacancy in the one-layer oxide slab is only 0.5 eV with respect to the ideal interface. For the two-layer oxide slab, the introduction of several vacancies in an already non-stoichiometric system becomes progressively more favourable, which indicates the stability of the highly non-stoichiometric interfaces. Isolated water molecules dissociate when adsorbed at the TiO<sub>2</sub> layers. At higher coverages the preference is for molecular water adsorption. Our ab initio thermodynamics calculations show the fully water covered stoichiometric models as the most stable structure at typical ambient conditions. Interfacial models with multiple vacancies are most stable at low (reducing) oxygen chemical potential values. A water monolayer adsorbs dissociatively on the highly distorted 2-layer TiO<sub>1.75</sub>-TiN interface, where the Ti<sup>3+</sup> states lying above the top of the valence band contribute to a significant reduction of the energy gap compared to the stoichiometric TiO<sub>2</sub>-TiN model. Our results provide a guide for the design of novel interfacial systems containing ultrathin TiO<sub>2</sub> with potential application as photocatalytic water splitting devices.</p><p></p>

An Analysis of the Demand for Reporting on Internal Control

2000 ◽  
Vol 14 (3) ◽  
pp. 325-341 ◽  
Author(s):  
Heather M. Hermanson
Keyword(s):  
Decision Making ◽  
Financial Reporting ◽  
Internal Control ◽  
Operational Definition ◽  
Financial Statement ◽  
Individual Investors ◽  
Internal Auditors ◽  
Additional Information ◽  
User Groups ◽  
Definition Of

The purpose of this study is to analyze the demand for reporting on internal control. Nine financial statement user groups were identified and surveyed to determine whether they agree that: (1) management reports on internal control (MRIC) are useful, (2) MRICs influence decisions, and (3) financial reporting is improved by adding MRICs. In addition, the paper examined whether responses varied based on: (1) the definition of internal control used (manipulated as broad, operational definition vs. narrow, financial-reporting definition) and (2) user group. The results indicate that financial statement users agree that internal controls are important. Respondents agreed that voluntary MRICs improved controls and provided additional information for decision making. Respondents also agreed that mandatory MRICs improved controls, but did not agree about their value for decision making. Using a broad definition of controls, respondents strongly agreed that MRICs improved controls and provided a better indicator of a company's long-term viability. Executive respondents were less likely to agree about the value of MRICs than individual investors and internal auditors.

Shape Dynamics and the Linking Theory

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Line Element ◽  
Hamiltonian Formulation ◽  
Operational Definition ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Problem Of Time ◽  
Definition Of ◽  
Matter Fields

This chapter explains in detail the current Hamiltonian formulation of SD, and the concept of Linking Theory of which (GR) and SD are two complementary gauge-fixings. The physical degrees of freedom of SD are identified, the simple way in which it solves the problem of time and the problem of observables in quantum gravity are explained, and the solution to the problem of constructing a spacetime slab from a solution of SD (and the related definition of physical rods and clocks) is described. Furthermore, the canonical way of coupling matter to SD is introduced, together with the operational definition of four-dimensional line element as an effective background for matter fields. The chapter concludes with two ‘structural’ results obtained in the attempt of finding a construction principle for SD: the concept of ‘symmetry doubling’, related to the BRST formulation of the theory, and the idea of ‘conformogeometrodynamics regained’, that is, to derive the theory as the unique one in the extended phase space of GR that realizes the symmetry doubling idea.

scholarly journals The scale of effect depends on operational definition of forest cover—evidence from terrestrial mammals of the Brazilian savanna

2021 ◽  
Author(s):  
Christophe Amiot ◽  
Cyntia Cavalcante Santos ◽  
Damien Arvor ◽  
Beatriz Bellón ◽  
Hervé Fritz ◽  
...  
Keyword(s):  
Forest Cover ◽  
Operational Definition ◽  
Brazilian Savanna ◽  
Terrestrial Mammals ◽  
Scale Of Effect ◽  
Definition Of

Polaronic and Bipolaronic Enhancement of Second Hyperpolarizabilities in Dithienyl Polyenes from Ab Initio Quantum Methods

1999 ◽  
Vol 597 ◽  
Author(s):  
Steven Trohalaki ◽  
Robert J. Zellmer ◽  
Ruth Pachter
Keyword(s):  
Ab Initio ◽  
Density Functional ◽  
Valence Bond ◽  
Closed Shell ◽  
Functional Theory ◽  
Molecular Conformations ◽  
Hartree Fock ◽  
Molecular Charge ◽  
Field Methodology ◽  
Moller Plesset

AbstractSpangler and He [1,2] have shown that dithienyl polyenes form extremely stable bipolaronic dications when oxidatively doped in solution. Previous theoretical studies applied empirical methods to predict bipolaronic enhancement of hyperpolarizabilities for simple polyenes [3,4]. Here, we employ density functional theory to optimize the gas-phase molecular conformations of neutral, cationic, and dicationic forms of a series of dithienyl polyenes, where the number of ethene units, N, is varied from 1–5. Ab initio Hartree-Fock, generalized valence bond, configuration interaction, and Møller-Plesset calculations demonstrate that the dications are farily well described with a closed shell and therefore have little biradicaloid character. Second hyperpolarizabilities, γ, are subsequently calculated using ab initio Hartree-Fock theory and a finite field methodology. As expected, γ increases with the number of ethene units for a given molecular charge. The cations also show the largest increase in γ with N. For a given value of N, the cations display the largest γ values. However, if we treat the dication as a triplet, which might be present in solution, then it displays the largest γ.

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