Electronic structure algorithms

Benzene has often been used as a test system for vibrational calculations using a variety of different electronic structure algorithms. The molecule exhibits regular hexagonal planar symmetry with six carbon atoms joined by a bonds and six remaining p-orbitals which overlap to form a delocalised n electron over all six carbon atoms. Table 1 shows comparisons of several different methods for benzene. 

We now describe a subset of all work done to parallelize electronic structure methods. The remainder of this section provides an outline of the work significant in the development of state-of-the-art electronic structure algorithms and codes. When appropriate, we focus on the algorithm and performance of applications. 

The past decade has seen an extraordinary growth in novel new electronic structure methods and creative implementations of these methods. Concurrently, there have been important advances in middleware , software that enables the implementation of efficient electronic structure algorithms. Combined with continuing improvements in computer and interconnect hardware, these advances have extended both the accuracy of computations and the sizes of molecular systems to which such methods may be applied. 

In Sect. 5.3 that follows, we report on the electronic structural characteristics of the C-based hexagonite structure from the point of view of the extended Hiickel molecular orbital method (EHMO), which is an approximate solid state electronic structure algorithm based upon the tight binding methodology (Hoffmann 1963 ... 

This algorithm alternates between the electronic structure problem and the nuclear motion It turns out that to generate an accurate nuclear trajectory using this decoupled algoritlun th electrons must be fuUy relaxed to the ground state at each iteration, in contrast to Ihe Car-Pairinello approach, where some error is tolerated. This need for very accurate basis se coefficients means that the minimum in the space of the coefficients must be located ver accurately, which can be computationally very expensive. However, conjugate gradient rninimisation is found to be an effective way to find this minimum, especially if informatioi from previous steps is incorporated [Payne et cd. 1992]. This reduces the number of minimi sation steps required to locate accurately the best set of basis set coefficients. 

In mesoscopic physics, because the geometries can be controlled so well, and because the measurements are very accurate, current under different conditions can be appropriately measured and calculated. The models used for mesoscopic transport are the so-called Landauer/Imry/Buttiker elastic scattering model for current, correlated electronic structure schemes to deal with Coulomb blockade limit and Kondo regime transport, and charging algorithms to characterize the effects of electron populations on the quantum dots. These are often based on capacitance analyses (this is a matter of thinking style - most chemists do not consider capacitances when discussing molecular transport junctions). 

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