Force constant units

Asterisk ( ) indicates that matrix data are available references are given in parentheses matrix material is indicated within brackets. b Force constant units are in millidynes per angstrom, and frequency is expressed per centimeter. c Uncorrected for anharmonicity. 

Stretching force constant units are in millidynes per angstrom, and frequency is expressed per centimeter. 

Table 6 Calculated force constant (unite is mdyne/A)...

The units of A are force constant units (mdyne/A) divided by mass units ( ). Since the wavenumber v is v = yJXUlnc), in the present system of units... 

The m matrix is already diagonalized. Take the masses and the force constant to be 1 arbitrary unit for simplicity and concentrate on the force constant matrix. We can diagonalize the k matrix... 

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). 

By analogy with Eq. (3.1), we seek a description for the relationship between stress and strain. The former is the shearing force per unit area, which we symbolize as as in Chap. 2. For shear strain we use the symbol y it is the rate of change of 7 that is involved in the definition of viscosity in Eq. (2.2). As in the analysis of tensile deformation, we write the strain AL/L, but this time AL is in the direction of the force, while L is at right angles to it. These quantities are shown in Fig. 3.6. It is convenient to describe the sample deformation in terms of the angle 6, also shown in Fig. 3.6. For distortion which is independent of time we continue to consider only the equilibrium behavior-stress and strain are proportional with proportionality constant G ... 

For an elastic material the shear stress is related to the shear strain through a constant of proportionality G, railed the shear modulus. The shear strain is dimensionless, and the shear modulus has units of force per unit area. 

Molecules in a gas are in constant motion at speeds on the order of the speed of a rifle bullet at equilibrium there is no net flow of gas and the motion is random. This motion produces collisions of the molecules with the walls of the vessel containing the gas, with a change in momentum of the gas molecule resulting from each collision. This change in momentum produces a force per unit area, or pressure on the wall. Consider those molecules with the component of velocity in the x direction between the value of vx and vx + dvx. The x direction is defined as the direction normal to the wall. The fraction of molecules with the x component of velocity in this range, denoted dN(vx)/N, is given by the density function, f(vx), where... 

Vectors and matrices are given as boldface symbols throughout.) E is the unit matrix G is a matrix which depends, only although not in a simple fashion, on the geometry and the atomic masses of the molecule. F is the matrix of force constants expressed in the 3 N — 6 independent internal coordinates. Its elements are ... 

These results confirm the important role of the force constant of the reacting bonds in the formation of the activation barrier. The activation energies Ee0 for the R + RX reactions can easily be estimated from the empirical formulas [17] (units are given in brackets) ... 

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