Van der Waals Clusters

Ar tetramer at T=0 - the "chemical picture"

Each Ar atom has an electronically closed shell. A description of Ar clusters therefore only requires treatment of the nuclear degrees of freedom of each atom. We assume an additive potential surface in our simulations. This figure shows the Ar tetramer cluster in its ground state using a schematic "chemical bond-type" representation. The pink balls show the equilibrium position of the atoms, and the green bars indicate the six van der Waals bonds. We obtain the equilibrium structure for the ground state from a diffusion quantum Monte Carlo (DMC) calculation, which simulates the many-body Schroedinger equation by switching to imaginary time. It's a very powerful method that allows us to describe ground state properties of weakly bound systems quite efficiently. This simple "chemical representation" of the system does not, of course, show the zero-energy motion. To visualize the "real density" of the system we have to go beyond the "stick ball representation".

Ar tetramer at T=0 - the "physical picture"

This picture shows the ground state of the Ar tetramer in a more realistic fashion: The "white blubs" show the quantum mechanical density of this 12-dimensional system (recall, each atom is described by 3 nuclear Cartesian coordinates, and the Ar tetramer consists of 4 Ar atoms). The input data for this figure are taken directly from a diffusion Monte Carlo calculation, which solves the Schroedinger equation stochastically. Basically, we're throwing dice to decide how to sample the configuration space. (This also explains the name "Monte Carlo".) Amazingly, throwing dice allows us to sample the configuration space just as required by the Hamiltonian of the many-body system. The spatial extend of the four "white blubs" are a direct measure of the zero point motion of the four atoms. The red bars show the equilibrium configuration, and are simply shown to guide the eye.

He trimer at T=0 - the much debated "physical picture"

He clusters are so diffuse and weakly bound that the "chemical picture" just doesn't do justice to the complexity of the system. In a sense, the system is so diffuse that using the word "geometry" is already a stretch. This figure shows the He trimer in its ground state. Again, the input data for this figure are obtained from a diffusion Monte Carlo calculation. As above, the white dots represent the density of the system. We've chosen a slightly different representation here than for the Ar tetramer (see above). However, without discussing the details, it is evident that the He trimer is extremely diffuse. For example, the equilibrium distance between two Ar atoms is 7.4a.u. (for the Ar trimer), and more than a factor of two larger between two He atoms, namely 18.1a.u. (for the He trimer). The diffuse character of the He trimer is reflected by its small binding energy of -0.087 inverse centimeters.

Our studies focuss on the characterization of excited states of van der Waals clusters. This is a highly non-trivial task since application of basis set expansion methods is typically limited to a few degrees of freedom only. Furthermore, Monte Carlo techniques, which describe ground state properties very successfully, are, without further modifications, intrinsically limited to the characterization of ground states. In our work, we focuss on the development of new algorithmic developments that will allow us to treat vibrationally and electronically excited states. In addition to pure clusters, we also study clusters with impurities, i.e., clusters that have one or more guest atom/molecule. These impurities can either be located on the surface of the cluster, or in the interior. Our theoretical efforts are closely linked to experimental work in this area. Many groups around the world operate, for example, He beam machines that allow the interesting and unique properties of superfluid bosonic He droplets to be studied.

Molecular Para-Hydrogen Clusters

More Molecular Para-Hydrogen Clusters

Additional Molecular Para-Hydrogen Clusters

Still More Molecular Para-Hydrogen Clusters

And Again More Molecular Para-Hydrogen Clusters

Yet More Molecular Para-Hydrogen Clusters

Back to Doerte's Main Page

Doerte Blume

Document Last Updated: 27 November, 2001