Condensed matter

Since solids do not exist as truly infinite systems, there are issues related to their temiination (i.e. surfaces). However, in most cases, the existence of a surface does not strongly affect the properties of the crystal as a whole. The number of atoms in the interior of a cluster scale as the cube of the size of the specimen while the number of surface atoms scale as the square of the size of the specimen. For a sample of macroscopic size, the number of interior atoms vastly exceeds the number of atoms at the surface. On the other hand, there are interesting properties of the surface of condensed matter systems that have no analogue in atomic or molecular systems. For example, electronic states can exist that trap electrons at the interface between a solid and the vacuum [1]. 

Mn is the mass of the nucleon, jis Planck s constant divided by 2ti, m. is the mass of the electron. This expression omits some temis such as those involving relativistic interactions, but captures the essential features for most condensed matter phases. 

One common approximation is to separate the nuclear and electronic degrees of freedom. Since the nuclei are considerably more massive than the electrons, it can be assumed that the electrons will respond mstantaneously to the nuclear coordinates. This approximation is called the Bom-Oppenlieimer or adiabatic approximation. It allows one to treat the nuclear coordinates as classical parameters. For most condensed matter systems, this assumption is highly accurate [11, 12]. 

Applying Flartree-Fock wavefiinctions to condensed matter systems is not routine. The resulting Flartree-Fock equations are usually too complex to be solved for extended systems. It has been argried drat many-body wavefunction approaches to the condensed matter or large molecular systems do not represent a reasonable approach to the electronic structure problem of extended systems. 

Perhaps the simplest description of a condensed matter system is to imagine non-interacting electrons contained within a box of volume, Q. The Scln-ddinger equation for this system is similar to equation Al.3.9 with the potential set to zero ... 

A key issue in describing condensed matter systems is to account properly for the number of states. Unlike a molecular system, the eigenvalues of condensed matter systems are closely spaced and essentially mfmite in... 

Knowing the energy distributions of electrons, (k), and the spatial distribution of electrons, p(r), is important in obtaining the structural and electronic properties of condensed matter systems. 

Another realistic approach is to constnict pseiidopotentials using density fiinctional tlieory. The implementation of the Kolm-Sham equations to condensed matter phases without the pseiidopotential approximation is not easy owing to the dramatic span in length scales of the wavefimction and the energy range of the eigenvalues. The pseiidopotential eliminates this problem by removing tlie core electrons from the problem and results in a much sunpler problem [27]. 

Since and depend only on die valence charge densities, they can be detennined once the valence pseudo- wavefiinctions are known. Because the pseudo-wavefiinctions are nodeless, the resulting pseudopotential is well defined despite the last temi in equation Al.3.78. Once the pseudopotential has been constructed from the atom, it can be transferred to the condensed matter system of interest. For example, the ionic pseudopotential defined by equation Al.3.78 from an atomistic calculation can be transferred to condensed matter phases without any significant loss of accuracy. 

Other methods for detennining the energy band structure include cellular methods. Green fiinction approaches and augmented plane waves [2, 3]. The choice of which method to use is often dictated by die particular system of interest. Details in applying these methods to condensed matter phases can be found elsewhere (see section B3.2). 

Surfaces are found to exliibit properties that are different from those of the bulk material. In the bulk, each atom is bonded to other atoms m all tliree dimensions. In fact, it is this infinite periodicity in tliree dimensions that gives rise to the power of condensed matter physics. At a surface, however, the tliree-dimensional periodicity is broken. This causes the surface atoms to respond to this change in their local enviromnent by adjusting tiieir geometric and electronic structures. The physics and chemistry of clean surfaces is discussed in section Al.7.2. 

Alavi A 1996 Path integrals and ab initio molecular dynamics Monte Carlo and Molecular Dynamics of Condensed Matter Systems ed K Binder and G Ciccotti (Bologna SIF)... 

Nitzan A 1988 Activated rate processes in condensed phases the Kramers theory revisited Adv. Chem. Phys. 70 489 Onuchic J N and Wolynes P G 1988 Classical and quantum pictures of reaction dynamics in condensed matter resonances, dephasing and all that J. Phys. Chem. 92 6495... 

Doll J D and Gubernatis J E (eds) 1990 Quantum Simuiations of Condensed Matter Phenomena (Singapore World Scientific)... 

Lovesey S W 1984 Theory of Neutron Scattering from Condensed Matter vo 1 (Oxford Oxford University Press)... 

Hamilton D C, Mitchell A C and Nellis W J 1986 Electrical conductivity measurements in shock compressed liquid nitrogen Shock M/aves in Condensed Matter (Proc. 4th Am. Phys. Soc. Top. Conf.) p 473... 

Schmidt S C, Dandekar D P and Forbes J W (eds) 1998 Shock Compression of Condensed Matter, 1997 (AlP Conf. Proc. vol 429) (College... 

The accuracy of most TB schemes is rather low, although some implementations may reach the accuracy of more advanced self-consistent LCAO methods (for examples of the latter see [18,19 and 20]). However, the advantages of TB are that it is fast, provides at least approximate electronic properties and can be used for quite large systems (e.g., thousands of atoms), unlike some of the more accurate condensed matter methods. TB results can also be used as input to detennine other properties (e.g., photoemission spectra) for which high accuracy is not essential. 

The general potential LAPW teclmiques are generally acknowledged to represent the state of the art with respect to accuracy in condensed matter electronic-structure calculations (see, for example, [62, 73]). These methods can provide the best possible answer within DFT with regard to energies and wavefiinctions. 

This chapter concentrates on describing molecular simulation methods which have a counectiou with the statistical mechanical description of condensed matter, and hence relate to theoretical approaches to understanding phenomena such as phase equilibria, rare events, and quantum mechanical effects. 

Binder K (ed) 1995 The Monte Carlo Method in Condensed Matter Physics vol 71 Topics in Applied Physics 2nd edn (Berlin Springer)... 

Perram J W, Petersen H G and DeLeeuw S W 1988 An algorithm for the simulation of condensed matter which grows as the 3/2 power of the number of particles Moi Phys. 65 875-93... 

Heermann D W and Burkitt A N 1995 Parallel algorithms for statistical physics problems The Monte Carlo Method In Condensed Matter Physios vol 71 Toplos In Applied Physios ed K Binder (Berlin Springer) pp 53-74... 

Heermann D W 1996 Parallelization of computational physics problems/Monfe Carlo and Moleoular Dynamlos of Condensed Matter Systems vol 49, ed K Binder and G CIccottI (Bologna Italian Physical Society) pp 887-906... 

Cluster research is a very interdisciplinary activity. Teclmiques and concepts from several other fields have been applied to clusters, such as atomic and condensed matter physics, chemistry, materials science, surface science and even nuclear physics. Wlrile the dividing line between clusters and nanoparticles is by no means well defined, typically, nanoparticles refer to species which are passivated and made in bulk fonn. In contrast, clusters refer to unstable species which are made and studied in the gas phase. Research into the latter is discussed in the current chapter. 

Moerner W E and Orrit M 1999 Illuminating single molecules in condensed matter Science 283 1670-6... 

In addition to their practical importance, colloidal suspensions have received much attention from chemists and physicists alike. This is an interesting research area in its own right, and it is an important aspect of what is referred to as soft condensed matter physics. This contribution is written from such a perspective, and although a balanced account is aimed for, it is inevitably biased by the author s research interests. References to the original literature are included, but within the scope of this contribution only a fraction of the vast amount of literature on colloidal suspensions can be mentioned. 

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