Strain-free parameter

The calculation demonstrates that the concept of a strain-free bond has a clear electronic basis. It is important to note that in molecular mechanics the concepts of force constant and strain-free parameter are intimately linked. The calculated C-C pair, ke, do = (4.88 Ncm-1,1.51 A), are very close to the best empirically optimized values of the most extended force fields. Although special strategies will be required to calculate specific ke, do pairs, the problem may be considered solved in general and the empirical estimates used with confidence. As a rule of thumb it is noted that, to first approximation,... 

Once in-plane d and out-of-plane rfx lattice parameters can be measured, one can determine the stress- and strain-free parameter using the biaxial modulus M, and the ratio of out-of-plane to in-plane strains r since we have... 

Like many other chemical concepts the concept of strain is only semi-quantitative and lacks precise definition. Molecules are considered strained if they contain internal coordinates (interatomic distances (bond lengths, distances between non-bonded atoms), bond angles, torsion angles) which deviate from values regarded as normal and strain-free . For instance, the normal bond angle at the tetra-coordinated carbon atom is close to the tetrahedral value of 109.47°. In the course of force field calculations these normal values are defined more satisfactorily, though in a somewhat different way, as force field parameters. 

The 6th, 7th, and 8th terms of expression (9) are sometimes neglected or is related to (24,25). The potential constants of UBFF s, including the reference parameters, often deviate markedly from the corresponding VFF-constants. Especially the reference bond lengths b may assume values which hardly agree with intuitive ideas about strain-free bond lengths. 

Most of the force fields described in the literature and of interest for us involve potential constants derived more or less by trial-and-error techniques. Starting values for the constants were taken from various sources vibrational spectra, structural data of strain-free compounds (for reference parameters), microwave spectra (32) (rotational barriers), thermodynamic measurements (rotational barriers (33), nonbonded interactions (1)). As a consequence of the incomplete adjustment of force field parameters by trial-and-error methods, a multitude of force fields has emerged whose virtues and shortcomings are difficult to assess, and which depend on the demands of the various authors. In view of this, we shall not discuss numerical values of potential constants derived by trial-and-error methods but rather describe in some detail a least-squares procedure for the systematic optimisation of potential constants which has been developed by Lifson and Warshel some time ago (7 7). Other authors (34, 35) have used least-squares techniques for the optimisation of the parameters of nonbonded interactions from crystal data. Overend and Scherer had previously applied procedures of this kind for determining optimal force constants from vibrational spectroscopic data (36). 

For a given set of flow parameters, the strained flame speed is taken as the fluid velocity at the minimum in the profile just upstream of the flame. Law and collaborators developed an analysis that uses a series of variously strained flames to predict strain-free laminar burning velocities [238,438,448]. As the strain rate is decreased, the strained flame speed decreases and the flame itself moves farther from the symmetry plane. There is an approximately linear relationship between the strained flame speed and the strain rate. Thus, after measuring the velocity profiles (e.g., by laser-dopler velocimetry) for a number of different strain rates, the strain-free burning velocity can be determined by extrapolating the burning velocity to zero strain. 

From the previous data, one can conclude that the bandedge structure of a-GaN, including the effect of heteroepitaxial strain, is well understood. The remaining difficulty is in finding the correct crystal field parameter A , for strain free GaN. Clearly, this point will be solved soon, with inproving sample quality. Similarly, the optical constants of a-GaN, measured by a variety of techniques, are in overall... 

The fact that the computed Co-N distance for D3o63-[Co(sar)]3+ is smaller than that preferred by the metal-free ligand indicates that the Co-N bonds are elongated in this compound (the fact that the computed and observed values for Co-N are larger than the strain-free distance r0, used in our force field (1.905 A) is irrelevant since force field parameters are not necessarily physically meaningful, see Sections 3.5, 9.2 and 10.2). 

The strain properties of these materials have been investigated by high resolution XRD. Studies involving samples that span a wide range of concentrations show fully strained (tensile and compressively strained), as well as relaxed Si-Ge-Sn films are obtained on strain-free Ge-Sn buffer layers. These results show that strain engineering can be achieved in Si-Ge-Sn heterostructures and multilayers by tuning the lattice parameter of the Ge-Sn buffer layer. 

The strain susceptibilities of these operators are again given by eq. (36). As a new free parameter one has the ratio /g p. This ratio is varied to obtain the... 

If a structure is well modeled by the parameters in the force field, molecular mechanics provides a means to calculate its AH that is said to rival experiment for accuracy. Molecular mechanics can also be used to calculate a value for the strain energy of a structure. The strain energy of a molecule is not the same as the steric energy obtained from a molecular mechanics calculation, however, and the term strain is less precise than one might expect. "Qualitatively, organic chemists usually recognize a strained molecule when they see one," ° but strain is a parameter that can only be determined by reference to a model structure that is defined to be strain free. 

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