Van der Waals minimum

The van der Waals distance, Rq, and softness parameters, depend on both atom types. These parameters are in all force fields written in terms of parameters for the individual atom types. There are several ways of combining atomic parameters to diatomic parameters, some of them being quite complicated. A commonly used method is to take the van der Waals minimum distance as the sum of two van der Waals radii, and the interaction parameter as the geometrical mean of atomic softness constants. 

For the strong interactions dealt with in the last section, interatomic potentials are determined by overlap-dependent terms which have an inverse exponential variation with internuclear distance (R). At large separations the interactions are independent of overlap and may be represented by inverse powers ofR. There will be between these two an intermediate region, which encompasses the van der Waals minimum for non-bonded interactions, and we will take this to be contained in our definition of a weak-interaction. 

W. Meyer, P. C. Hariharan, and W. Kutzelnigg. Refined ab initio calculation of the potential energy surface of the H2-He interaction with special emphasis to the region of the van der Waals minimum. J. Chem. Phys., 73 1880, 1980. 

The potential-energy curves of the noble-gas diatomic molecules are rather unusual.65,84,85 The ground state of the He2 molecule is purely repulsive save for a weak van der Waals minimum (well depth 1 meV), which might not support a bound state. The next four excited states correlate asymptotically with He(2 S) and He(23S), respectively. As can be seen from Fig. 11, these states have deep chemical wells at about 1 A and intermediate maxima at 2 to 3 A. 

A. He/H2 and Ha.—It is convenient to consider first these species. Tsapline and Kutzelnigg375 have applied the IEPA-PNO method, previously described, to the ground state of the He/Ha system. The van der Waals minimum was computed, using a gaussian lobe basis set with carefully optimized exponents. The collinear arrangement with a depth of 21 K was found for the van der Waals minimum, with a saddle point of 14 K for the Czv geometry. The computed surface was compared with experiment and with the R 6 term. The anisotropy of the potential is larger than that predicted asymptotically. 

C. A4 Molecules.—There are two cases of interest here stable species such as P4 and interactions between homonuclear diatomic molecules. H4 is the simplest of the species, and it has been the subject of a great deal of theoretical study because of its relevance to the H2 + D2 - -2HD exchange reaction. Early work has been carefully discussed by Schaefer,1 and Bender and Schaefer have carried out more extensive calculations since then on the linear form.604 It is predicted that two H2 molecules may approach to within 1.6 bohr with an energy only 181 kJ above that of the separated molecules. A van der Waals attraction of 22 K is predicted at a separation of the centre of mass of H2-H2 of 7.1 bohr. The results of other studies have failed to find a transition state lying less than 458 kJ above H2 + D2. The calculations of Bender et al. used a DZ basis plus 2p-functions, larger than that used in earlier work by Wilson and Goddard, and by Rubinstein and Shavitt (see ref. 1). Full Cl with 2172 configurations was carried out, and the van der Waals minimum predicted was not found by the earlier workers. 

Recently, this problem was treated by a rigorous quantum chemistry calculation by Bakalov et al. [28], First, the authors calculated ab initio the interatomic interaction V(R,r, ) between an atomcule pHe- and a He atom based on the Born-Oppenheimer approximation. Since the rotational frequency of the p (of order of 1015 s-1) is much higher than the collision frequency (of order of 1012 s-1), the angular dependence is smeared out, and typically, the Van der Waals minimum occurs around R 5.5 a.u., and the repulsive barrier starts around R 5 a.u. The potential V(R) depends on (n,l), and thus, a small difference AV(R) occurs between an initial state and a final state. It is this difference that causes pressure shifts and broadening in the resonance line. 

The other kind of systems largely studied, consists of polymethylmethacrylate (PMMA) or silica spherical particles, suspended in organic solvents [23,24]. In these solvents Q 0 and uy(r) 0. The particles are coated by a layer of polymer adsorbed on their surface. This layer of polymer, usually of the order of 10-50 A, provides an entropic bumper that keeps the particles far from the van der Waals minimum, and therefore, from aggregating. Thus, for practical purposes uw(r) can be ignored. In this case the systems are said to be sterically stabilized and they are properly considered as suspensions of colloidal particles with hard-sphere interaction [the pair potential is of the form given by Eq. (5)]. 

Equation (1-92) is very important since in the region of the Van der Waals minimum the charge-overlap contribution to the dispersion energy is always substantial. Additionally, the powerful computational techniques, developed in the 1980 s to obtain accurate polarization propagators118 can be utilized via Eq. (1-92) in the calculations of the dispersion energies at finite distances. 

The idea of correlating momentary multipoles stands behind the customary modeling of dispersion interaction in the form of a multipole expansion, including dipole-dipole (D-D), dipole-quadrupole (D-Q), quadrupole-quadrupole (Q-Q), and so on, terms. We owe the earliest variational treatments of this problem not only to Slater and Kirkwood [34], but also to Pauling and Beach [35], However, when the distance R decreases and reaches the Van der Waals minimum separation, the assumption that electrons of A and B never cross their trajectories in space becomes too crude. The calculation of the intermonomer electron... 

C). The exchange repulsion contour of H2O derived from the He-H20 complex at R(He-0)=3.5 A, defined by two polar coordinates (Energy, 0), and drawn in the same plane as the Laplacian. The contour is the image of the water molecule shape, detected by a rare-gas atom [31]. The regions of lone electron pairs are indicated with arrows, but no apparent sign of their presence is observed. The lone pairs electron concentrations are not diffuse enough to show up in the van der Waals minimum region. 

Recently, mainly based on the very accurate ab initio results of Partridge and Schwenke [66] complemented with other data [68,69] and on a careful description of the long range interactions between the different dissociation channels [70], Brandao and Rio presented another double-valued PES for this system [43]. This BR PES displays a small van der Waals minimum and a small saddle point under the dissociation limit for the C2v approach of the O ( D) atom to the H2 molecule and a very small barrier (< 0.4 kJmoP ) to collinear addition ( 27+ surface) in agreement with the findings of Walch and Harding [68]. 

Van der Waals minimum. This intermolecular additivity problem is more extensively discussed by Margenau and Kestner by Murrell and by Claverie The third additivity question which is sometimes asked, regards the possibility of representing an intermolecular interaction potential as a sum of (isotropic) atom-atom potentials (8) (or bond-bond potentials). Not much is known about this question, since most of the atom-atom potentials used in practice are purely empirical. We consider this question in section 4 for C2 4 C2 4 Nj... 

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