Local density approximation many-body wavefunction

To obtain errors of 1 kcal/mol or better, it is essential to treat many-body effects accurately and, we believe, directly. Although commonly used methods such as the density functional theory within the local density approximation (LDA) or the generalized gradient approximation (GGA) may get some properties correctly, it seems unlikely that they, in general, will ever have the needed precision and robustness on a wide variety of molecules. On the other hand, methods that rely on a complete representation of the many-body wavefunction will require a computer time that is exponential in the number of electrons. A typical example of such an approach is the configuration interaction (Cl) method, which expands the wavefunction in Slater determinants of one-body orbitals. Each time an atom is added to the system, an additional number of molecular orbitals must be considered, and the total number of determinants to reach chemical accuracy is then multiplied by this factor. Hence an exponential dependence of the computer time on the number of atoms in the system results. 

One very successful method to solve this Hamiltonian is the density-functional theory (DFT). Within a DFT-based formalism one avoids constructing the many-body wavefunction of the system and instead computes directly ground-state properties from its charge density. However, the exact form of the functional embodied in the Hohenberg-Kohn theorem is unknown and, therefore, approximations are required. One of the most important, local-density approximation (LDA), developed by Kohn and Sham, works successfully for the ground-state properties of weakly... 

The calculation of the surface electronic structure is possible because many body effects can be neglected to a good approximation and the many electron Schrodinger equation is replaced by the one electron equation. An extra type of solution of the Schrodinger equation are wavefunctions which are localized at the surface. They cause the surface statesy which play an important role in the surface reconstruction of semiconductors. The local density of states at the surface is made of this surface states and of tails of bulk wave functions. 

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