Cubic constant

However, if isotopomers are considered in which the point group symmetry is lowered by substitution it is necessary to calculate additional cubic constants. Isotopomers III and V in the present work are of this type, so the full cubic force field was evaluated. 

The results of this study are somewhat atypical in the sense that the inferred re and tq structures of Sis are nearly the same. This is a somewhat fortuitous circumstance, which cannot be attributed entirely to the fact that Sis appears to be only weakly anharmonic (see cubic constants in Table I), since it has a relatively low-frequency bending mode that is potentially problematic. Nonetheless, it can be stated with some certainty that the structure obtained in the present research is accurate to within 0.002A and 0.2 . Hence, this structure can be used as a reference for benchmarking quantum chemical methods intended for high accuracy calculations on silicon clusters, as well as for comparison with structures of other silicon-containing molecules. 

Although symmetry reduces the number of independent force constants, they still grow rapidly with the order of anharmonicity. For example, for a CH3X molecule of C.. symmetry there are 12 independent quadratic constants, 38 cubic constants, and 102 quartic constants. 

It is clear that a strong Fermi resonance of the type described above may in principle be analysed directly to give an observed value of the single anharmonic constant rrs, in Section 5 (p. 143) we give examples of such analyses, and their use in anharmonic calculations. In the absence of Fermi resonance, information on the cubic constants like rrK comes mainly from the vibrational dependence of the rotational constants a , which determine linear combinations of the cubic constants 4>m as described earlier. 

N02,239,247,248,256 and C102256 should be regarded as tentative since they are based on various model potentials (as indicated in the footnotes) and on much less extensive sets of data. Table 3 lists the values of the cubic constants in the valence-force coordinate space (fyt) and in the dimensionless normal coordinate space (kg/s") as obtained for... 

Equation [3] looks complicated at first sight, but is just Eq, [2] to which a cubic term has been added. The cubic constant has the value - 2.00 times the quadratic constant. The factor of 143.88 converts the units to kcal/mol. Judicious. selection of the force constant parameter for this cubic expression allowed for accurate treatments of bond length deformations in a wide variety of molecules. 

The cubic constant varies with the physico-chemical properties (temperatme, gas pressure) as the rate at a given fractional extent, or the reactivity. 

Figure C2.16.3. A plot of tire energy gap and lattice constant for tire most common III-V compound semiconductors. All tire materials shown have cubic (zincblende) stmcture. Elemental semiconductors. Si and Ge, are included for comparison. The lines connecting binary semiconductors indicate possible ternary compounds witli direct gaps. Dashed lines near GaP represent indirect gap regions. The line from InP to a point marked represents tire quaternary compound InGaAsP, lattice matched to InP.

For tliis model tire parameter set p consists of tire rate constants and tire constant pool chemical concentrations l A, 1 (Most chemical rate laws are constmcted phenomenologically and often have cubic or otlier nonlinearities and irreversible steps. Such rate laws are reductions of tire full underlying reaction mechanism.)... 

Hach molecular mechanics method has its own functional form MM+. AMBER, OPL.S, and BIO+. The functional form describes the an alytic form of each of th e term s in th e poteri tial. For exam pie, MM+h as both a quadratic and a cubic stretch term in th e poten tial whereas AMBER, OPES, and BIO+ have only c nadratic stretch term s, I h e functional form is referred to here as the force field. For exam pie, th e fun ction al form of a qu adratic stretch with force constant K, and equilibrium distance i q is ... 

The default parameters for bond stretching are an ec iiilibriiim bond length an d a stretch in g force eon starit. fb e fun etion al form isjiist that of the. M.M+ force field including a correction for cubic stretches. The default force constant depends only on the bond... 

A cubic lattice is superimposed onto the solute(s) and the surrounding solvent. Values of the electrostatic potential, charge density, dielectric constant and ionic strength are assigned to each grid point. The atomic charges do not usually coincide with a grid point and so the... 

A larger value for the stretch force constant Kj. leads to a greater tendency for the bond to remain at its equilibrium distance rg Higher powers of r - rg, giving cubic, quartic, or higher terms are also common. A Morse function might also be employed. 

A larger value for the bending force constant K0 leads to a greater tendency for the angle to remain at its equilibrium value 0g. There may be cubic, quartic, etc. terms as with the corresponding bond stretch term in addition to the quadratic term shown here. 

The cubic stretch term is a factor CS times the quadratic stretch term. This constant CS can be set to an arbitrary value by an entry in the Registry or the chem. ini file. The default value for MM2 and MMh- is CS=-2.0. 

The gas permeability constant is the amount of gas expressed in cubic centimeters passed in 1 s through a 1-cm area of film when the pressure across a film thickness of 1 cm is 1 cmHg and the temperature is 25°C. All tabulated values are multiplied by 10 and are in units of seconds" (centimeters of Hg) k Other temperatures are indicated by exponents and are expressed in degrees Celsius. 

The authors of this research selected units which could be written with maximum simplification to report their results. We must replace the factors which have canceled out. Assuming that the cgs system of units was used throughout, we note that possible units for H are grams per square centimeter and possible unts for C2 are grams per cubic centimeter, which yield the required units for n/c2 Note that these units of H must be multiplied by the gravitational constant to give H in dynes per square centimeter ... 

Scratch Te.st. The scratch microhardness test is a refinement of the Mohs test. The corner of a cubic diamond is drawn across the surface of a metaHographicaHy poHshed sample under a constant load, usuaHy 29.4 N (3 kgf). The width of the resultant Vee groove scratch varies inversely with the hardness of the material displaced where H = scratch hardness number and A = groove width in micrometers. 

Epitaxial crystal growth methods such as molecular beam epitaxy (MBE) and metalorganic chemical vapor deposition (MOCVD) have advanced to the point that active regions of essentially arbitrary thicknesses can be prepared (see Thin films, film deposition techniques). Most semiconductors used for lasers are cubic crystals where the lattice constant, the dimension of the cube, is equal to two atomic plane distances. When the thickness of this layer is reduced to dimensions on the order of 0.01 )J.m, between 20 and 30 atomic plane distances, quantum mechanics is needed for an accurate description of the confined carrier energies (11). Such layers are called quantum wells and the lasers containing such layers in their active regions are known as quantum well lasers (12). 

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