Free parameters

Gear s method, 118 Gibbs (free) energy of activation (see Activation parameters Free energy) Guggenheim method, 26-27... 

In this section we aim to introduce some of the main theoretical ideas which underlie the strategies for modelling liquid crystal molecules. It is clear that there are a very wide range of methods available and we will not attempt to be comprehensive. Instead, we will begin with a brief overview of traditional semi-empirical approaches and then progress to concentrate on treating fully predictive parameter-free calculations of molecular electronic structure and properties in some depth. 

Scheffler M, Dabrowski J. 1988. Parameter-free calculations of total energies, interatomic forces and vibrational entropies of defects in semiconductors. Phil Mag A 58 107-121. 

Keywords Spatial-energy parameter, free radicals, structural interactions, photosynthesis. 

Parameter-Free Treatment of Star Polymer Melts.218... 

Fig. 8. Predictions of parameter-free theory for G"(co) and data for a star polybutadiene from [33]. Small shifts in the two prefactors bring the experiments and theory into quantitative agreement over five decades in timescale. Dilution exponent a=4/3 and Mg=1850...

Fig.9. Predictions of parameter-free theory for G (co) with 0(1) corrections to Gq and Tg as for Fig. 8 and data for a range of 3- and 4-arm star polyisoprenes from [5]. Arm molecular weights in 10 g mol are 11.4,17, 36.7,44,47.5, 95 and 105. The entanglement molecular weight has been taken as 5000 g mol" ...

By means of the parameter-free, one-sided X-test, the protection in days after cessation of the vitamin A supply was statistically evaluated (Van der Waerden and Nievergelt, 1956). These results question whether an increase in amount and retention time of Aronal forte toothpaste results in an elongation of epithelial protection. With the short supply of vitamin A for 1 minute, no dose-dependent improvement was detected. However, with a retention time of 3 minutes, the higher dose correlated positively with the duration of vitamin A protection. The differences between the higher and lower dose were statistically significant (p < 0.025). 

This ab-initio Gutzwiller approach is able to handle correctly the correlation aspects without loosing the ab-initio adjustable parameters free aspect of the more familiar DFT-LDA, and that way, corrects the deficiency of this method. It gives similar results to the methods that account for many-body effects like the LDA+DMFT of Ref. [10] from the ab-initio levels or that can have an orbital dependent potential like in the LDA+ 7 calculation of Ref. [36], which is impossible to DFT-LDA approach. On another hand, we stress again that our approach is clearly variational, and is able to provide an approximate ground state in contrast with those of Refs. [10] and [36]. 

Although based on a simplified parametric description of the electronic structure of the molecule and of the leads, the framework discussed in this section has the advantage of leading directly to the computation of measurable quantities (the I-V curves). Thus, it is possible to relate the experimental observations to the quantum-mechanical properties of the systems under investigation, e.g., the electronic energy-level structure of the molecule and the relation of such levels to the energy of the leads. A timely improvement in this direction will come from the implementation of manageable methods, which combine a parameter-free atomistic description of the electronic... 

In Fenske and Hall s parameter-free SCF calculations (80-84), the He1t 1-electron operator is substituted by a model 1-electron operator that has a kinetic energy and potential energy term for each atomic center in the complex. This approach assumes that the electron density may be assigned to appropriate centers. The partitioning of electron density is done through Mulliken population analyses (163) until self-consistency is obtained. The Hamiltonian elements are evaluated numerically, and the energies of the MO s depend only on the choice of basis functions and the intemuclear distance. 

Two groups have studied the bonding in pentadienyl-metal-tricar-bonyl complexes (119, 238) and are agreed that effective overlap between the pentadienyl nonbonding orbital and an orbital of suitable symmetry on the metal (Fig. 17) makes a major contribution to the stability of these complexes. However, the two types of molecular orbital calculation [one an extended Hiickel (119) and the other a parameter-free approximate Hartree-Fock calculation (255)] disagree about the precise ordering of energy levels in this type of complex. 

An alternative approach is to derive scale factors from the structure of the differential equations, seeking parameter-free equations. Starting from Eq. 4.102, the following... 

As in previous analyses, nondimensionalizing the equations leads to results that have general applicability. Here, however, it is not a simple task to identify a length scale and a velocity scale based on an inspection of the geometry and the boundary velocities. In fact, it was an insightful contribution of Hiemenz to identify the length and velocity scales that are required to develop a parameter-free system of nondimensional equations. They are... 

As with semi-infinite stagnation flow, there are no natural physically observable length and velocity scales that form the basis for nondimensionalization. Rather, mathematically derived length and velocity scales lead to a nondimensional system of equations that are parameter free. These scales are... 

Table I Phase transitions, Flory interaction parameters (/), free energies (AG) and differences of Hildebrand solubility parameters (A<5) depending on the molecular structure (fluorination of the alkyl chain) [25]...

Fig. 14 shows the amplitudes of the two components and of the whole concentration signal as a function of xp. Both modes could be resolved for all exposure times, and the insert of Fig. 14 shows, as an example, the rate distribution for xp = 0.2 s as obtained from a CONTIN analysis. The solid lines are the parameter-free predictions according to Eq. (32). 

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