Forces in molecules

The Hellmann-Feynman theorem demonstrates the central role of p, the electron density distribution, in understanding forces in molecules and therefore chemical bonding. The main appeal and usefulness of this important theorem is that it shows that the effective force acting on a nucleus in a molecule can be calculated by simple electrostatics once p is known. The theorem can be stated as follows ... 

SCHEME 9.2 Contact forces in molecules with strong, permanent dipoles... 

The dispersion forces in molecules with large atoms are quite significant and are often actually more important than dipole-dipole forces. 

The various methods to calculate the vibrational frequencies and force constants from ab-initio data on diatomic molecules is represented in Sections 5 A to K. It is seen that the various approximations yield results which fluctuate from molecule to molecule, although the order of magnitude is mostly correct. It is clear, however, that it is not at the present moment possible to calculate co and ke of molecules to such a d ee of accuracy that the factors which contribute to the intemudear forces in molecules can be pinpointed and compared. This is perhaps the reason why semi-empirical models continue to be exploited, e.g. the simple bond-charge model (electrostatic) model for P.E.-curves of homonudear diatomic molecules of Parr and Borckmann (114) based upon the Fues potential from which the famous Birge-Mecke relation is derived ... 

There is thus considerable activity in this field, and it will no doubt continue to be improved in the future as the understanding of the binding forces in molecules becomes better. 

W. R. Busing, Acta Crystallogr., Sect. A, 28, S252 (1972). A Computer Program to Aid in the Understanding of Interatomic Forces in Molecules and Crystals. 

Dziewonski AM, Gilbert JF (1971) Solidity of the itmer core of the earth inferred from normal mode observations. Nature 234 465-466 Feynman RP (1939) Forces in molecules. Phys Rev 56 340-343... 

The fundamental nature of the electrostatic potential, recognized by Feymnan [119] in his classic paper Forces in Molecules, is reflected in its versatility, which we have tried to demonstrate in this chapter. V(r) provides a powerful means of elucidating and predicting the properties and behavior of molecular systems and, more importantly, is a physical observable. 

Hund, R 1935. Description of the binding forces in molecules and crystal lattices on quantum theory. In International Conference on Physics. Paper and discussions. Volume II. The solid state of matter, 36-45. London Physical Society. 

Felker,P. M.,Zewail,A. H. (1984). Direct observation of nonchaotic multilevel vibrational energy flow in isolated polyatomic molecules. Phys. Rev. Lett. 53, 501-504. Feynman, R. P. (1939). Forces in molecules. Phys. Rev. 56,340-343. 

Feynman R. R, Forces In molecules, Phys. Rev., 56, 340-343 (1939). Payne M. C., Teter M. R, Allan D. C., Arias T. A., and Joannopoulos J. D., Iterative minimization techniques for ab initio total-energy calculations molecular dynamics and conjugate gradients. Rev. Mod. Phys., 64,1045-1097 (1992). 

The fact that forces in molecules are computational observables is extremely useful in the context of force field development. This is because, as indicated above, the atomic charges that appear in the empirical force fields are not observables. One can therefore use ab initio calculations of intermolecular forces, which are readily available, and determine the accuracy of the parameters of the electrostatic interaction that appear in the empirical force fields (e.g., equation 2). 

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