Force stretching

There are forces other than bond stretching forces acting within a typical polyatomic molecule. They include bending forces and interatomic repulsions. Each force adds a dimension to the space. Although the concept of a surface in a many-dimensional space is rather abstract, its application is simple. Each dimension has a potential energy equation that can be solved easily and rapidly by computer. The sum of potential energies from all sources within the molecule is the potential energy of the molecule relative to some arbitrary reference point. A... 

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. 

The functional form for bond stretching in AMBER is quadratic only and is identical to that shown in equation (11) on page 175. The bond stretching force constants are in units of kcal/mol per A and are in the file pointed to by the QuadraticStretch entry for the parameter set in the Registry or the chem.ini file, usually called =>istr.txt(dbf). 

The default parameters for bond stretching are an equilibrium bond length and a stretching force constant. The functional form is just that of the MM-t force field including a correction for cubic stretches. The default force constant depends only on the bond... 

Elastomers. Elastomers is a generic name for polymers that exhibit rubberlike elasticity. Elastomers are soft yet sufficiently elastic that they can be stretched several hundred percent under tension. When the stretching force is removed, they retract rapidly and recover their original dimensions. 

Most extmded latex fibers are double covered with hard yams in order to overcome deficiencies of the bare threads such as abrasiveness, color, low power, and lack of dyeabiUty. During covering, the elastic thread is wrapped under stretch which prevents its return to original length when the stretch force is removed thus the fiber operates farther on the stress—strain curve to take advantage of its higher elastic power. Covered mbber fibers are commonly found in narrow fabrics, braids, surgical hosiery, and strip lace. 

Among the basic mechanical properties of fibers are their deformability and tenacity. When an axial stretching force is applied to the fiber, the principal quantitative indices of deformability are the axial elastic modulus (E)... 

If the stretching force F is applied to a system of these molecules the distribution function is given by51)... 

Fig. 33 Relationship between the logarithm of the bond stretching force constant/r of an S-S bond and the logarithm of its length rss [198]...

The effect shown in Fig. 9 is a result of the bond-bond interaction which is a characteristic feature for chains and rings of two-valent chalcogen atoms. It can also be recognized from the relatively large bond interaction force constants fir of such compounds. The stretching force constants /r(SS) of polysulfur compounds depend on the SS bond distances as shown in Fig. 10. The data used in this figure include several excited electronic states of the S2 molecule as well as the disulfide anion and a number of sulfur homocycles [77]. 

Fig. 10 Linear relationship between the logarithms of the SS bond length d and the stretching force constantof this bond in various sulfur compounds...

Fig. 19 Variation of the intermolecular stretching force constant ka with nucleophilicity Nb for several series of halogen-bonded complexes B- XY, where B is one of a series of Lewis bases and XY is Cl2, Br2, BrCl, C1F or IC1. N% were assigned by use of Eq. 4 with the choice of ICi = 10.0, hence the perfect straight line for the B- -IC1 series. The lines for the other series are those obtained by least-squares fits to the ka values using the Mb determined from the B- IC1 series. Points for E P- -IC1, E N- -C1F and EEN- BrCl are anomalous and were excluded from the fits (see text for discussion)... 

Evidence for a significant contribution from the ionic form [BX] + - -Y in a gas-phase complex B- XY was first deduced from the spectroscopic constants of H3N- -ClF, as obtained by analysis of its rotational spectrum [63]. In particular, the value ka = 34.3 N m 1 of the intermolecular stretching force constant (obtained from the centrifugal distortion constant Dj in the man-... 

Sefcik J, Demiralp E, Cagin T, Goddard WA (2002) Dynamic charge equilibration-morse stretch force field application to energetics of pure silica zeolites. J Comput Chem 23(16) 1507-1514... 

The relationships between bond length, stretching force constant, and bond dissociation energy are made clear by the potential energy curve for a diatomic molecule, the plot of the change in the internal energy AU of the molecule A2 as the internuclear separation is increased until the molecule dissociates into two A atoms ... 

For polyatomic molecules, the stretching force constant for a particular bond cannot in general be obtained in an unambiguous manner because any given vibrational mode generally involves movements of more than two of the atoms, which prevent the expression of the observed frequency in terms of the force constant for just one bond. The vibrational modes of a polyatomic molecule can be analyzed by a method known a normal coordinate analysis to... 

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