For harmonic force field calculations it is usual to express the force field in terms of internal co-ordinates Ri defined through a linear transformation from cartesian displacement co-ordinates 8xm (a = x, y, or z) in the molecule-fixed axis system.24 The molecule-fixed axes are located using the Eckart conditions.24 The equations are written in the form [Pg.124]

A general harmonic force field for trans- or C/S-N2H2 contains ten independent potential constants. In terms of internal coordinates, there are two stretching constants, ff, and fr, with R = r(NN) and r=r(NH), two angle deformation constants, f and f, with a= in-plane deformation and y = out-of-plane torsion, and six interaction constants, frr. Ra. a> [Pg.49]

The diagonal and off-diagonal force constants of the internal harmonic force field [Pg.119]

Starting from a set of harmonic force constants calculated in terms of internal coordinates, one can determine in this way the normal coordinates of the different vibrations (phonons) of an infinite chain as a function of (the columns of matrices L , ) as well as the corresponding phonon dispersion curves One should note that, in order to [Pg.298]

You need to specify two parameters the et uilibrium value ofthe internal coordinate and the force constant for the harmonic poten tial, T h e equilibrium restraint value deperi ds on the reason you choosea restraint. If, for example, you would like a particular bond length to remain constant during a simulation, then the equ ilibritirn restrain t value would probably be Lh e initial len gth of the bond. If you wan t to force an internal coordinate to a new value, the equilibrium internal coordinate is the new value. [Pg.105]

The symbols immediately following the summation symbols in Eq. (2), (3), and (4) represent harmonic force constants. The subscripts denote the internal coordinates they refer to. The notation of the internal coordinates (general symbol p) is as follows [Pg.166]

For his calculations, Burton chose the simplest possible material—a cluster of atoms interacting with nearest-neighbor harmonic forces and with the atoms packed onto lattice positions of a close-packed cubic material. He then calculated the partition functions in Eq. (43) and ultimately the cluster concentrations and nucleation rates. The major problem in this calculation was the internal partition function Zmt> which was calculated by diagonalizing the 3i X 3i dynamical matrices of i atom clusters to obtain normal mode vibrational frequencies and ultimately harmonic oscillator partition functions. This calculation was very expensive and could not be done for i larger than about 100. [Pg.219]

A simplified version of the vibrationally-adiabatic approximation is to neglect the curvilinear effects, i.e., the internal centrifugal forces,which means to choose in the usual way the reaction path as curve L representing the reaction coordinate. Then,using a harmonic approximation for the vibration, we obtain the classical potential energy (117 11) in the simple form [Pg.82]

To enable an atomic interpretation of the AFM experiments, we have developed a molecular dynamics technique to simulate these experiments [49], Prom such force simulations rupture models at atomic resolution were derived and checked by comparisons of the computed rupture forces with the experimental ones. In order to facilitate such checks, the simulations have been set up to resemble the AFM experiment in as many details as possible (Fig. 4, bottom) the protein-ligand complex was simulated in atomic detail starting from the crystal structure, water solvent was included within the simulation system to account for solvation effects, the protein was held in place by keeping its center of mass fixed (so that internal motions were not hindered), the cantilever was simulated by use of a harmonic spring potential and, finally, the simulated cantilever was connected to the particular atom of the ligand, to which in the AFM experiment the linker molecule was connected. [Pg.86]

Wynen, E. 2005. Effects of Non-Harmonization on Production and Trade of Organic Products. Report for the International Task Force on Harmonization of Organic Standards and Certification. IFOAM/FAO/UNCTAD, Bonn. [Pg.244]

Vibrational Spectra Many of the papers quoted below deal with the determination of vibrational spectra. The method of choice is B3-LYP density functional theory. In most cases, MP2 vibrational spectra are less accurate. In order to allow for a comparison between computed frequencies within the harmonic approximation and anharmonic experimental fundamentals, calculated frequencies should be scaled by an empirical factor. This procedure accounts for systematic errors and improves the results considerably. The easiest procedure is to scale all frequencies by the same factor, e.g., 0.963 for B3-LYP/6-31G computed frequencies [95JPC3093]. A more sophisticated but still pragmatic approach is the SQM method [83JA7073], in which the underlying force constants (in internal coordinates) are scaled by different scaling factors. [Pg.6]

© 2019 chempedia.info