Structure of Van der Waals Molecules

If we want to predict the stmcture, the stability and the vibrational and rotational spectra of Van der Waals molecules, we have to know the complete intermolecular potential as a function of the intermolecular distancefs) and the molecular orientations. For rare gas dimers and for some rare gas atom-diatomic molecule (e.g. H2, HCl) systems rather detailed information about the potential is available from experiment , from ab initio calculations or both  

The latter systems have only two internal degrees of freedom, however, (in the rigid molecule approximation) and the rare gas dimers have just a single one, of course. Some ab initio studies have been made of molecular Van der Waals (or hydrogen bonded) systems with more internal coordinates , but mostly they concern only specific points or one-dimensional cuts (e.g. distance curves for fixed molecular orientations) of the potential (hyper) surface. One exception is the case of the simplest molecular dimer (112)2, which has been studied in detail, both ab initio and experimentally Another exception form the two Van der Waals molecules, (C H jj and (Njjj, of which the complete potential surfaces have been obtained in our institute 5. iss, 101,136) initio calculations. 

The N2—N2 potential, in particular, has been the subject of much previous (semi-) empirical work . The dimers (N j 58,159) have been investi- 

Fitting of the Ab Initio Results Atom—Atom Potentials 

For all but the very smallest systems, (such as HeH and even there it is very expensive), it is not possible in practice to calculate the full potential surface, with a grid fine enough that it can be directly used for solving the (nuclear) dynamical problem in Van der Waals molecules (or for scattering calculations). Moreover, such a numerical potential would not be convenient for most purposes. Therefore, one usually represents the potential by some analytical form, for instance, a truncated spherical expansion (1) or another type of model potential (cf. sect. 2). The parameters in this model potential can be obtained by fitting the ab initio results for a limited set of intermolecular distances and molecular orientations. Since we have encountered some difficulties in this fitting procedure which we expect to be typical, we shall describe our experience with the ( 2114)2 and (N2)2 cases in some detail. At the same time, we use the opportunity to make a few comments about the convergence of the spherical expansion used for (Njjj and about the validity of the atom-atom model potential applied to both ( 2114)2 and (Njjx. 

HCl) systems rather detailed information about the potential is available from experiment. 22-27,142.143) from ab initio cakulations or both  

For this dimer the interaction potential has been cakulated for 8 different orientations of the two molecules, for 3 distances around R = 4.8 A (9a,j) including (first order) exchange and penetration effects and for 8 distances from R = 6.4 to 10.6 A (12 to 20ao) in the multipole expansion. Second order overlap effects 

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Buckingham A D and Fowler P W 1983 Do electrostatic interactions predict structures of van der Waals molecules J. Chem. Phys. 79 6426... 

Leaving aside this dynamical problem, we can make some further remarks about the equilibrium structure of Van der Waals molecules. Some attempts have been made to predict this structure from the molecular properties, multipole moments, polarizabilities, which are reflected in the long range interactions (electrostatic, dispersion). Other authors have assumed that the equilibrium structure of Van der Waals dimers resembles the structure of nearest neighbour pairs in molecular crystals. The latter approach could possibly be justified by packing considerations (short range repulsion). An example of the first approach is the prediction of a T-shaped (0 = 90°, 0 = < ) = 0°) equilibrium structure for the Nj-dimer, mainly... 

F. A. Baiocchi, W. Reiher, and W. Klemperer, / Chem. Phys., 79, 6428 (1983). Comment on Do Electrostatic Interactions Predict Structures of van der Waals Molecules ... 

Buckingham, A.D. (1982) Closing remarks. Faraday Discuss. Chem. Soc., 73, 421—423. Buckingham, A.D. and Fowler, P.W. (1983) Do electrostatic interactions predict structures of van der Waals molecules ). Chem. Phys., 79, 6426-6428. 

Van der Waals molecules of heavier homonuclear diatomics have also been studied, using similar techniques to the ones mentioned above. However, the numbers of bound states generally are much greater for such systems, and the band structures are richer and therefore harder to resolve. Detailed work has shown that for the more massive diatomics molecular rotation is more or less hindered and the level structures are much more complex than the ones seen in the H2-X systems. Rather uncertain band contour analyses are used in those cases but a few reasonably well resolved band spectra of van der Waals molecules are known [49, 267]. 

Calculations on the gas phase interactions of most pairs (or small clusters) of molecules have been possible using ORIENT for some time. This program is available on request from the author s web site (http //fandango.ch.cam.ac.uk/). The latest version ORIENT3 not only can determine the minimum energy structures of van der Waals clusters, their transition states, and other stationary points, it also can calculate their vibrational modes, and it has the ability to use anisotropic repulsion, dispersion, and induction energy models. 

V. Subramanian, D. Sivanesan, J. Padmanabhan, N. Lakshminarayanan, and T. Ramasami, Atoms in molecules application to electronic structure of van der Waals complexes, Proc. Indian Acad. Sci. (Chem. Set) 111, 369-375 (1999). 

A discussion of Van der Waals molecules is a natural component of a treatise on resonance phenomena, for a variety of reasons. The most obvious of these is simply the fact that transitions involving both compound-state and shape resonance levels figure prominently in the spectra of these species. Indeed, in many cases the metastable nature of the final states of such transitions is a key feature of the manner in which they are observed (1-3). Moreover, observations of structure due to resonances in scattering cross sections can provide detailed information regarding intermolecular potential energy functions ( ). 

The structural behavior of van der Waals molecules has been reviewed.9,443... 

In the molecular sciences, elueidation of the strueture and property of a van der Waals molecule is an important current researeh subject. The van der Waals molecule is unstable at room temperature, and it is quite difficult to get a concentrated system of van der Waals molecules [14,15]. There is another weakly interactive molecular complex compound, called a moleeular clathrate. Usually, molecular clathrates are unstable at ambient eonditions. Supercritical gas molecules such as N2 and NO are said to tend to produce dimers in micropores [16-20], In particular, NO molecules are adsorbed in micropores of activated carbon fiber (ACF) at ambient conditions in the form of dimers that are typical van der Waals molecules. Water molecules form an organized structure in the carbon micropore [21], The formation of NO hydrate and CH4 hydrate in micropores at a subatmospheric pressure has also been suggested [22,23]. Hence micropores accelerate the formation of van der Waals molecules or molecular clathrate hydrates. In the case of micropores that have a deep potential well, many molecules tend to be adsorbed in the deep potential well. Molecules confined in micropores should form the best dense structure according to the micropore geometry. Therefore, we can control the intermoleeular structure with inicropores even at supercritical conditions of the bulk gas. The molecular field of micropores can stabilize van der Waals molecules and molecular clathrates. 

Once a well-characterized beam of van der Waals molecules is produced, experiments such as photodepletion, photodissociation and photoionization can be undertaken, yielding information about the electronic structure and photofiragmentation dynamics of these molecules. Essentially, four methods have been... 

C. M. Lovejoy and D.J. Nesbitt, Chem. Phvs. Lett. 146 582 (1988). Unpublished, see B.J. Howard, High resolution infrared spectroscopy of van der Waals molecules, in "Structure and D3mamics of Weakly Bound Molecular Complexes," A. Weber, ed.. D. Reidel, Dordrecht (1987) and, G.T. Fraser and A.S. Pine, J. Chem. Phvs. 85 2502 (1986). 

Fourier transform techniques have become very powerful, particularly when used with pulsed sources of the sample. They are ubiquitous in studies of van der Waals molecules, in which two or more entities are very weakly bound together in the gas phase, such as HCT Ar, but are also used to determine structures of many other compounds, of which the mixed alkali halide dimer LiNap2 is an example. In a typical experiment, the sample is introduced into the cell in a pulsed supersonic jet expansion, the rotational temperature being reduced to a few Kelvin. A pulse of microwave radiation then aligns the dipole moments of the molecules, so that the sample is polarized on a macroscopic scale. The subsequent decay of this polarization is recorded, and Fourier transformation of the free induction decay yields the spectrum [9]. 

Often only the bottom of the intermolecular potential surface is characterized but this information gives the geometry or structure of the van der Waals molecule. We will next consider the structures for defining properties of van der Waals molecules. 

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