## FANDOM

32.652 Seiten

 Typus KomplettPlagiat Bearbeiter Klgn Gesichtet
Untersuchte Arbeit:
Seite: 43, Zeilen: 1 ff. (entire page)
Quelle: Accelrys Inc. - Forcefield-Based Simulations 1998
Seite(n): 39, 40, Zeilen: 39: 23 ff., 40: 1 ff.
[The rules associated with this expression depend on the central bond order, ring size of the angles, hybridization of the atoms, and two atomic parameters for the central] atom, which is fit. The functional form of the out-of-plane energy is the same as in CFF91, where the coordinate (Φ) is an average of the three possible angles associated with the out-of-plane center. The single parameter that is associated with the central atom is a fit quantity.

The charges are determined by minimizing the electrostatic energy with respect to the charges under the constraint that the sum of the charges is equal to the net charge on the molecule. This is equivalent to equalization of electronegativities.

The derivation of the rule begins with the following equation for the electrostatic energy:

$E=\sum_{i}\left ( E_i^0 + \chi _i q_i + \frac{1}{2}\eta _i q_i^2\right )+\sum_{i>j} B \frac{q_i q_j}{R_{ij}}$ (2.8)

where χ is the electronegativity and η the hardness. The first term is just a Taylor series expansion of the energy of each atom as a function of charge, and the second is the Coulomb interaction law between charges. The Coulomb law term introduces a geometry dependence that ESFF for the time being ignores, by considering only topological neighbors at effectively idealized geometries.

Minimizing the energy with respect to the charges leads to the following expression for the charge on atom i:

$q_i=\frac{\lambda - \chi_i - \Delta \chi_i }{\eta_i}$ (2.9)

where λ is the Lagrange multiplier for the constraint on the total charge, which physically is the equalized electronegativity of all the atoms. The Δχ term contains the geometry-independent remnant of the full Coulomb summation.

Equations (2.8) and (2.9) give a totally delocalized picture of the charges in a relatively severe approximation. To obtain reasonable charges as judged by, for example, crystal packing calculations, some modifications to the above picture have been made.

[page 39]

The rules associated with this expression depend on the central bond order, ring size of the angles, hybridization of the atoms, and two atomic parameters for the central atom which is fit.

The functional form of the out-of-plane energy is the same as in CFF91, where the coordinate (Φ) is an average of the three possible angles associated with the out-of-plane center. The single parameter that is associated with the central atom is a fit quantity.

The charges are determined by minimizing the electrostatic energy with respect to the charges under the constraint that the sum of the charges is equal to the net charge on the molecule. This is equivalent to equalization of electronegativities.

The derivation of the rule begins with the following equation for the electrostatic energy:

[page 40]

$E=\sum_{i}\left ( E_i^0 + \chi _i q_i + \frac{1}{2}\eta _i q_i^2\right )+\sum_{i>j} B \frac{q_i q_j}{R_{ij}}$ Eq. 12

where χ is the electronegativity and η the hardness. The first term is just a Taylor series expansion of the energy of each atom as a function of charge, and the second is the Coulomb interaction law between charges. The Coulomb law term introduces a geometry dependence that ESFF for the time being ignores, by considering only topological neighbors at effectively idealized geometries.

Minimizing the energy with respect to the charges leads to the following expression for the charge on atom i:

$q_i=\frac{\lambda - \chi_i - \Delta \chi_i }{\eta_i}$ Eq. 13

where λ is the Lagrange multiplier for the constraint on the total charge, which physically is the equalized electronegativity of all the atoms. The ∆χ term contains the geometry-independent remnant of the full Coulomb summation.

Eqns. 12 and 13 give a totally delocalized picture of the charges in a relatively severe approximation. To obtain reasonable charges as judged by, for example, crystal packing calculations, some modifications to the above picture have been made.

 Anmerkungen The source is not given. Sichter (Klgn), SleepyHollow02