Dispersion nonbonded interactions

Fig. 7.5 Illustration of how dispersion forces affect gauche (G) conformations. Compared to structures with gauche forms devoid of dispersion forces (i.e., HF-optimized), structures with gauche forms subject to dispersion forces (MP2 optimized) contract in such a way that the 1. ..5 nonbonded interactions in an attractive part of the van der Waals potential are shortened. Thus, in GG-pentane (shown above), MP2-optimized torsional angles are contracted by several degrees compared to the HF-optimized geometry, causing a reduction in the 1...5 nonbonded distances by several tenths of an A. For additional details and the numerical values see R. F. Frey, M. Cao, S. Q. Newton, and L. Schafer, J. Mol. Struct. 285 (1993) 99.

The nonbonded interactions commonly consist of a sum of two-body repulsion and dispersion energy terms between atoms that are often of the Lennard-Jones form in addition to the energy from the interactions between fixed partial atomic or ionic charges (Coulomb interaction)... 

Nonbonding interactions play a major role in determining the three-dimensional structure of a molecule. Such interactions are composed of repulsive and attractive contributions, such as van der Waals repulsion, London dispersion forces, coulombic interactions, and delocalizations of electrons due to the through-space interactions between atomic orbitals. 

The extent to which this kind of calculation is able to predict the effect of the solvent on conformational properties of carbohydrates has been thoroughly tested on 2-substituted oxane derivatives, D-glucopyranose, and methyl a- and y -D-glucopyranoside. In the model applied, the cavity term in Eq. 7 is based on an expression taken from the Scaled Particle Theory, and the electrostatic term is calculated according to the reaction held theory. The dispersion term takes into account both attractive and repulsive nonbonding interactions by using a combination of Lx)ndon dispersion energy and Bom-type repulsion. ... 

Lennard-Jones potential As two atoms approach one another there is the attraction due to London dispersion forces and eventually a van der Waals repulsion as the interatomic distance r gets smaller than the equilibrium distance. A well-known potential energy function to describe this behavior is the Lennard-Jones (6-12) potential (LJ). The LJ (6-12) potential represents the attractive part as r-6-dependent whereas the repulsive part is represented by an r n term. Another often used nonbonded interaction potential is the Buckingham potential which uses a similar distance dependence for the attractive part as the LJ (6-12) potential but where the repulsive part is represented by an exponential function. 

Usually it is assumed that nonbonded interactions have the same form as interactions between rare gas atoms, i.e., a long range R attraction due to induced dipole-induced dipole interaction (also called dispersion interaction), and a short-range repulsion that results from the overlap of electron clouds. 

Here r, e, and (T,y are the internuclear distance, the dispersion well depth, and the Lennard—Jones diameter, respectively. The 12th power term describes the repulsive interaction, whereas the 6th power term represents the attractive term. Nonbonded interactions are calculated between atoms that are three or more atoms apart. 

Nonbonded interaction energies are the most difficult contribution to evaluate, and may be attractive or repulsive. When two uncharged spherical atoms approach each other, the interaction between them is very small at large distances, becomes increasingly attractive as the separation approaches the sum of their van der Waals radii, then becomes strongly repulsive as the atoms approach each other with a separation less than the sum of their van der Waals radii. This behavior is represented graphically by the familiar Morse potential diagram in Fig. 3.2. The attractive interaction results from a mutual polarization of the electrons of each atom by the other. Such attractive forces are called London forces or dispersion forces, and are normally weak interactions. London forces vary inversely with the sixth power of... 

The nonbond interactions are summed over all partial atomic charges in pairs (separated by three or more bonds) taken as point monopoles in the Coulombic term. The dipole-induced dipole (London dispersion) interaction between polarizable atoms is contained in the last term, with the atomic overlap repulsion being included here (for algebraic convenience) as the 9th or 12th power. (CFF uses the 9th power, whereas the traditional Lennard-Jones choice is the 12th.)... 

A few highly parametrized functionals that do not include explicit allowance for dispersion do fairly well for nonbonded interactions. An example is the M06-2X functional. 

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