Molecules and Clusters

To introduce the subject of many atoms per cell, we apply the tail-cancellation theorem, Sect.2.1, to a collection of atoms. In the derivation it is convenient to consider the simplest case, i.e. a diatomic molecule, but the results will be valid for any molecule or cluster. Our starting point is the energy-independent muffin-tin orbitals (2.1) in the atomic-sphere approximation, i.e. 

In this approximation each individual atom of type t is surrounded by an atomic sphere of radius S., and the kinetic energy k in the region outside the spheres is zero. Hence, the spherical Bessel and Neumann functions which enter the theory become polynomials in (r/S) where S may be taken as a common radius different from S. The requirement of continuity and differentiability at the individual radii St determines the normalisation of and the function 

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Bonin K D and Kresin V V 1997 Electric-dipole Polarizabilities of Atoms, Molecules and Clusters (Singapore World Scientific)... 

Molecules and Clusters. The local nature of the effective Hamiltonian in the LDF equations makes it possible to solve the LDF equations for molecular systems by a numerical LCAO approach (16,17). In this approach (17), the atomic basis functions are constructed numerically for free atoms and ions and tabulated on a numerical grid. By construction, the molecular basis becomes exact as the system dissociates into its atoms. The effective potential is given on the same numerical grid as the basis functions. The matrix elements of the effective LDF Hamiltonian in the atomic basis are given by... 

It is important to note that the only physical approximation here is the LDA. All other approximations are of a numerical nature and their convergence can be monitored and improved in a systematic way. Thus, this method allows a probe of the LDA limit for molecules and clusters without any further approximations such... 

TOO Schwerdtfeger, P. (2006) Atomic Static Dipole Polarizabilities, in Computational Aspects of Electric Polarizability Calculations Atoms, Molecules and Clusters (ed. G. Maroulis), Imperial College Press, London, pp. 1-32. 

G. Maroulis (Ed.), Atoms, Molecules and Cluster in Electric Fields. London Imperial College Press, 2006. 

Y. Yamada, Y. Katsumoto, and T. Ebata, Picosecond IR UV pump probe spectroscopic study on the vibrational energy flow in isolated molecules and clusters. Phys. Chem. Chem. Phys. 10, 1170 1185 (2007). 

Schreiber, E. Femtosecond Real-Time Spectroscopy of Small Molecules and Clusters(Environmental Intelligence Unit) , Springer Berlin, 1998. 

Over the last years we have explored several advanced techniques for high-resolution rotational coherence spectroscopy (RCS [1]) in order to study the structures of molecules and clusters in the gas phase [2]. We have provided spectroscopic examples demonstrating (i) mass-selectivity (Fig. 1, [3]), (ii) that the rotational constants of the ground and electronic excited states can be obtained independently with high precision (lO MO"5, [4]), (iii) that the transition dipole moment alignment, (iv) centrifugal distortion constants, and (v) information on the polarizability tensor can be obtained (Fig.l, [5]). Here we review results pertaining to points (i), (ii), (iv) and (v) [2,3,5],... 

R. Gordon and S. Rice, Annu. Rev. Phys. Chem. 48 (1997) 601. S. Rice, Nature 403 (2000) 496. E. Charron and B. Sheehy, Molecules and clusters in intense laser fields, Cambridge University Press (2000). 

J. Manz Prof. H. J. Neusser has presented to us beautiful high-resolution spectra of medium-size molecules and clusters such as benzene and C6H6 At (see current chapter). The individual lines have been assigned to individual rovibronic eigenstates of the systems, and their widths have been interpreted in terms of various intramolecular processes between zero-order states (e.g., Coriolis coupling, anharmonic couplings between bright and dark states, and so on). 

Figure 5. Radial distribution function(RDF) of whole Xe molecules and clusters for w = 0.90 and 1.00 nm pores at 75.5 kPa. Solid and dotted lines denote RDFs of the whole Xe molecules and clusters.

Stillinger (1980) suggested that disconnected icebergs should not be present, but that a more likely model is that of a random, three-dimensional network of hydrogen bonds, rather than long-lived clusters of molecules. Such networks of hydrogen-bonded water molecules and clusters are present when hydrates form or dissociate. These clusters are discussed relative to nucleation of hydrates in the following chapter. 

J. Berkowitz and B. Ruscic, Photoionization Mass Spectrometric Studies of Free Radicals (C. Y. Ng, ed.) Vacuum Ultraviolet Photoionization and Photodissociation of Molecules and Clusters, World Scientific Singapore 1991, pp. 1-41. 

The calculations were performed employing either pure ab initio Hartree-Fock (HF) methods, or hybrid HF-DFT functionals, in particular B3LYP [22]. The hybrid functionals have several advantages. One is that they are commonly applied with great success in computational studies of molecules and clusters, thus making it possible to benefit from the gathered experience from molecular studies. Another is their recently noted ability to accurately model band gaps in semiconductor compounds [57]. 

A remarkable shape is calculated with Eq. (9.35) for (3 > 4. A region is obtained where the 0-versus-P curve has a negative slope (dotted curve in Fig. 9.7). This is physically nonsense The coverage is supposed to decrease with increasing pressure and for one pressure there are three possible values of 6. In reality this is a region of two-phase equilibrium. Single adsorbed molecules and clusters of adsorbed molecules coexist on the surface. The situation is reminiscent of the three-dimensional van der Waals equation of state which can be used to describe condensation. 

Bonin KD, Kresin VV (1997) Electric dipole polarizabilities of atom molecules and clusters. World Scientific, Singapore... 

Proceedings of the International Workshop on Positron Interactions with Atoms, Molecules and Clusters (held at Bielefeld, Germany, 1993) edited by W. Raith and R.P. McEachran, published in Hyperfine Interactions 89 (1994)... 

E. Brandas, Complex Symmetry, Jordan Blocks and Microscopic Selforganization An Examination of the Limits of Quantum Theory Based on Nonself-adjoint Extensions with Illustrations from Chemistry and Physics, in N. Russo, V. Ya. Antonchenko, E. Kryachko (Eds.), Self-Organization of Molecular Systems From Molecules and Clusters to Nanotubes and Proteins, NATO Science for Peace and Security Series A Chemistry and Biology, Springer Science+Business Media B.V., Dordrecht, 2009, p. 49. 

The present volume of the Advances in Quantum Chemistry is the sequel of the first volume, mentioned above, i.e., Unstable States in the Continuous Spectra, Part II Interpretation, Theory and Applications. It contains six chapters with contents varying from a pedagogical introduction to the notion of unstable states to the presence and role of resonances in chemical reactions, from discussions on the foundations of the theory to its relevance and precise limitations in various fields, from electronic and positronic quasi-bound states and their role in certain types of reactions to applications in the field of electronic decay in multiply charged molecules and clusters, as well. 

ATW90] Albiez A, Thoma M, Weber W and Mehlhorn W 1990 Z. Physik D - Atoms, Molecules and Clusters 16 97. 

HDM92] Hall RI, Dawber G, McConkey AG, MacDonald MA and King GC 1992 Z. Physik D -Atoms, Molecules and Clusters 23 377. 

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