Nonempirical parameters

Here k = 0.804 is a nonempirical parameter chosen to satisfy the Lieb-Oxford bound in its local form F s) 1.804 for any s. The value of p= Pmb(tt /3) = 0.21951 is determined from the condition that the second-order gradient term for exchange cancel that for correlation (i.e. This choice, rather than p = /tak =... 

In the face of this massive unavailability of experimental data for the vast majority of chemicals, practitioners in drug discovery and hazard assessment have developed the use of nonempirical parameters to estimate molecular properties. By... 

Our long term interest in environmental QSAR (quantitative structure-activity relationships) is to develop general, nonempirical model(s) for predicting environmental distributions and toxicities of organic pollutants based only on Information encoded in their structural formulas. This nonempirical approach was selected because it has two major advantages over empirical approaches. First, the determination of nonempirical parameters is faster and less expensive than measurement of empirical parameters and can be performed almost anywhere office, laboratory, home, field, etc., while measurements commonly require laboratory facilities with specialized equipment and qualified and experienced personnel. The second advantage is the higher... 

The determination of the electronic structure of lanthanide-doped materials and the prediction of the optical properties are not trivial tasks. The standard ligand field models lack predictive power and undergoes parametric uncertainty at low symmetry, while customary computation methods, such as DFT, cannot be used in a routine manner for ligand field on lanthanide accounts. The ligand field density functional theory (LFDFT) algorithm23-30 consists of a customized conduct of nonempirical DFT calculations, extracting reliable parameters that can be used in further numeric experiments, relevant for the prediction in luminescent materials science.31 These series of parameters, which have to be determined in order to analyze the problem of two-open-shell 4f and 5d electrons in lanthanide materials, are as follows. 

In the world of increasingly important nonempirical calculations we may tend to underestimate the usefulness of empirical relationships. They have been useful, however, and the range of their application may well extend as the wealth of new geometrical data is being incorporated in the existing empirical relationships or is used for establishing new ones. Some examples of empirical relationships follow here, in which geometrical parameters, primarily bond distances are utilized (they come both from electron diffraction and microwave spectroscopy). More details and examples of application can be found, of course, in the respective sources. 

Like all cathodes, early electrochemical kinetic studies of LSM focused heavily on steady-state d.c. characteristics, attempting to extract mechanistic information from the Tand F02 dependence of linear and Tafel parameters.As recently as 1997, some workers have continued to support a view that LSM is limited entirely by electrochemical kinetics at the LSM/electrolyte Interface based on this type of analysis. However, as we have seen for other materials (including Pt), the fact that an electrode obeys Butler—Volmer kinetics means little in terms of identifying rate-limiting phenomena or in determining how close the reaction occurs to the TPB. To understand LSM at a nonempirical level, we must examine other techniques and results. 

The calculation of AH° and AS° values from the pK-temperature data in each solvent mixture was performed by the nonempirical method of Clarke and Glew (26) as simplified by Bolton (27). In this method the thermodynamic parameters are considered to be continuous, well-behaved functions of temperature, and their values are expressed as perturbations of their values at some reference temperature 0 by a Taylor s series expansion. The basic equation is ... 

The interaction parameters for the water molecules were taken from nonempirical configuration interaction calculations for water dimers (41) that have been shown to give good agreement between experimental radial distribution functions and simulations at low sorbate densities. The potential terms for the water-ferrierite interaction consisted of repulsion, dispersion, and electrostatic terms. The first two of these terms are the components of the 6-12 Lennard-Jones function, and the electrostatic term accounts for long-range contributions and is evaluated by an Ewald summation. The... 

The ESR spin Hamiltonian parameters have been calculated using 77-HMO and 77-SCF MO coefficients in the molecular orbitals176,462,463 as well as those from nonempirical wavefunctions.364 It may be seen that, in general, calculated values are in good agreement with experimental data (Table XXXI). 

The mPBE functional39 is a modification of the nonempirical PBE functional into which one empirical parameter was reintroduced. Compared to PBE, mPBE leads to significantly worse interaction energy for the water dimer, whereas the interaction energies in the cases of hydrogen fluoride and hydrogen chloride dimers are only slightly improved. 

Mikheikin et al. (11) have formulated an alternative approach where terminal valencies are saturated by monovalent atoms whose quantum-chemical parameters (the shape of AO, electronegativity, etc.) are specially adjusted for the better reproduction of given characteristics of the electron structure of the solid (the stoichiometry of the charge distribution, the band gap, the valence band structure, some experimental properties of the surface groups, etc.). Such atoms were termed pseudo-atoms and the procedure itself was called the method of a cluster with terminal pseudo-atoms (CTP). The corresponding scheme of quantum-chemical calculations was realized within the frames of CNDO/BW (77), MINDO/3 (13), and CNDO/2 (30) as well as within the scope of the nonempirical approach (16). 

Timgsten has been of keen theoretical interest for electron band-structure calculations [1.14-1.25], not only because of its important technical use but also because it exhibits many interesting properties. Density functional theory [1.11], based on the at initio (nonempirical) principle, was used to determine the electronic part of the total energy of the metal and its cohesive energy on a strict quantitative level. It provides information on structural and elastic properties of the metal, such as the lattice parameter, the equilibrium volume, the bulk modulus, and the elastic constants. Investigations have been performed for both the stable (bcc) as well as hypothetical lattice configurations (fee, hep, tetragonal distortion). 

Before mentioning some results obtained by the MINDO technique, it is worthwhile recalling the fundamental difference in philosophy between this method and the similar CNDO and, in particular, INDO methods. In the latter the parametrization was carried on, trying to reproduce for some simple molecules the results of nonempirical SCF calculations. In the former method the choice of parameters aimed to find the best fit with experimental data 132>. 

Electronic structure calculations may be carried out at many levels, differing in cost, accuracy, and reliability. At the simplest level, molecular mechanics (this volume, Chapter 1) may be used to model a wide range of systems at low cost, relying on large sets of adjustable parameters. Next, at the semiempirical level (this volume, Chapter 2), the techniques of quantum mechanics are used, but the computational cost is reduced by extensive use of empirical parameters. Finally, at the most complex level, a rigorous quantum mechanical treatment of electronic structure is provided by nonempirical, wave function-based quantum chemical methods [1] and by density functional theory (DFT) (this volume, Chapter 4). Although not treated here, other less standard techniques such as quantum Monte Carlo (QMC) have also been developed for the electronic structure problem (for these, we refer to the specialist literature, Refs. 5-7). 

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