Van der Waals well

The attraction for two neutral atoms separated by more than four Angstroms is approximately zero. The depth of the potential wells is minimal. For the AMBER force field, hydrogen bonds have well depths of about 0.5 kcal/mol the magnitude of individual van der Waals well depths is usually less. 

Moreover, these systems present van der Waals wells from which the system can be promoted to electronic states correlating to excited metal atoms [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28]. After the excitation, the system evolves towards products in several electronic states, thus involving one or several electronic transitions and providing very valuable information of the electronic correlations. 

The van der Waals well depth e increases monotonically as the polarizability of the ground-state partner increase, whereas the location of the well, rm, remains roughly constant at about 6A. This is expected by analogy with the well-known alkali-noble-gas potentials,116-119 although the rm values are larger than for the alkali case, as shown in Table V. 

Fig. 31 Overall interaction energy between two DNA-coated colloids, (a) Sketch of the interacting surfaces of two spheres of radius R0 separated by d. The maximum length of hybridized strands is 2L. (b) Total interaction energy as a function of d. It is the sum of the attractive I/DNA from the binding of accessible DNA strands, the repulsive I/rep from electrostatics and/or polymer steric effect, and the van der Waals attraction t/vdw. (c) For weak, short-range I/rep, particles which are unbound at high temperatures are irreversibly trapped in the van der Waals well after DNA hybridization at low temperatures, (d) For strong, medium-range I/rep, DNA binding produces a secondary minimum of reversible aggregation. Reproduced with permission from [138]...

All these comparisons between theory and various high precision experimental data show that the ab initio SAPT potential for He-C02 reproduces various physical properties of the complex. This suggests that the potential is accurate not only around the van der Waals well, but also its anisotropy in the attractive and repulsive regions, as well as the volume of the van der Waals well are correct. 

The simplest ab initio method used to study van der Waals molecules is the Hartree-Fock method. To the Hartree-Fock interaction energy one should add the dispersion energy, which ranges from some 20% of the dissociation energy for the water dimer to twice the van der Waals well depth for He2, and is thus not negligible. The combined method may be termed SCF + Disp. 

The effect of size-consistency corrections on the van der Waals well depth is quite pronounced if no dimer SCF precedes the Cl-type calculation, but not negligible otherwise even in (HjOfj (Table II). Considering that (H20)2 is among the more strongly bound van der Waals complexes, the relative influence on weaker complexes will be much more serious. 

There is though, one qualitative difference between the more accurate LSTH surface and the PK(II) surface. The former includes the van der Waals wells in the far entrance and exit valleys. Using pods, we We computed the adiabatic well depths for different H2 vibrational states. In addition we We computed the stability frequencies of the quantised pods. These frequencies are now of course real - the pods are truly stable. The results are summarised for Mu+DD in Table HI. Within... 

Table III. Parameters of van der Waals Wells in the MU+D2 Reaction on the LSTH Potential Energy Surface...

Takayanagi, T. and Sato, S., The bending-corrected-rotating-linear-model calculations of the rate constants for the H -I- H2 reaction and its isotopic variants at low temperatures The effect of van der Waals well, J. Chem. Phys., 92, 2862, 1990. Balakrishnan, N., Forrey, R.C., and Dalgarno, A., Quenching of H2 vibrations in ultracold He and He collisions, Phys. Rev. Lett., 80, 3224, 1998. 

Gray, Rice and Davis and Gray and Rice have further developed the theory sketched above, with emphasis on analytical approximations that reduce the complexity of calculations and that permit the interpretation of variation of fragmentation rate with parameters such as vibrational frequency difference, van der Waals well depth, etc. The theory has been applied to the study of isomerization, where it successfully resolves the problem of "surface recrossing. An estimate of the effect of... 

Electric properties of van der Waals complex when using ab initio calculations should be, if possible, corrected for the BSSE and BSIE similar to the interaction energy. The BSSE could reach up to 10 % for the dipole moments in the range of the van der Waals wells for the case of a medium sized basis set, like aug-cc-pVTZ (see Fig. 3.1, for example). However, for the systems with multireference character the BSSE correction is not used when a size-inconsistent method is employed. 

From these data it was inferred that, in the region of the very shallow van der Waals wells of these rare gas oxides, H-type electrostatic interactions are stronger than E ones. The analysis which led to an estimate of the interactions was based on an elastic approximation, as defined in previous papers [lb,6b] this approximation can only be used for qualitative purposes, but the data did not allow a more quantitative approach. 

In the O-CH4 and E>2 cases, the weak long range interacticm obtained by the present technique is well below the energy barriers for reactive chemical processes [11]. The present cross sections are most sensitive to the van der Waals well region determined by a balance between the tail of the repulsion and the long range... 

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