Localized gaussian orbitals

In the present article, we report a study concerning the reaction mechanism of a prototype reaction using both static and dynamic approaches to explore a DFT potential surface. The static approach is the standard IRC model, while the dynamic one is based on a Carr-Parrinello method performed with localized (Gaussian) orbitals, the so-called atom-centered density matrix propagation (ADMP) model.25 Our aim is to elucidate the differences, and the common aspects, between the two approaches in the analysis of bond breaking/formation. To this end, we have chosen topological quantities as probe molecular descriptors. 

Plane wave basis sets of reasonable size (of the order of 100 plane waves per atom) can be used in surface calculations of semiconductors like Si, Ge, GaAs (Hebenstreit et al., 1991) and s-p bonded metals like Al (Needs and Godfrey, 1990). For transition and noble metals the d-elcctrons which participate in the bonding are relatively localized and correspondingly feci a stronger potential than the s- and p-electrons. A plane-wave basis for such systems is unwieldy, and localized Gaussian orbitals of the form ... 

The last approach dealt with in this section is the Floating Spherical Gaussian Orbital (FSGO) model and related methods. The original FSGO model introduced fay Frost is very simple. It treats chemical bonds in terms of localized orbitals, in a very close correspondence with chemical concepts. Each localized orbital (inner... 

While general basis sets lead to an 0(N2) pairs of basis-function products, localized basis sets decrease this number to O(NM) with M a characteristic number of neighbors. As discussed in Ref. [49], the number of points at which the density must be calculated is also linear in the number of atoms. However since each product of localized basis functions is also localized, the determination of the density is intrinsically an O(N) problem. Further simplification occurs when the gaussian orbitals are used. Since the product of a pair of gaussian functions can always be expressed as a single gaussian function, it follows that the total and spin densities can always be analytically expressed as an O(N) sum given by ... 

For the present studies, we have used state-of-the-art DFT-based methods with plane wave basis set, viz., VASP [30] with PAW potentials [31] for extended systems, and with localized atomic orbital or Gaussian basis set, viz., DMol3 [32] or GAUSSIAN03 [33] for molecular or cluster systems. In all our calculations, the ions are steadily relaxed toward equilibrium until the Hellmann-Feynman forces are converged to less than 10 eV/A. Available experimental structural data have been used as input for some of the hydrides whenever they are available. 

The elechonic shucture of isolated molecular systems is most naturally described by using Gaussian type atomic orbitals (AO s) as basis functions in contrast to plane waves, which represent the natural choice in extended periodic systems. Here we present the approach for the calculation of the nonadiabatic couplings using KS orbitals expandedin terms of localized Gaussian atomic basis sets. This formulation is particularly convenient since it can be coupled with commonly used quantum chemical DFT codes. 

The application of density functional theory to isolated, organic molecules is still in relative infancy compared with the use of Hartree-Fock methods. There continues to be a steady stream of publications designed to assess the performance of the various approaches to DFT. As we have discussed there is a plethora of ways in which density functional theory can be implemented with different functional forms for the basis set (Gaussians, Slater type orbitals, or numerical), different expressions for the exchange and correlation contributions within the local density approximation, different expressions for the gradient corrections and different ways to solve the Kohn-Sham equations to achieve self-consistency. This contrasts with the situation for Hartree-Fock calculations, wlrich mostly use one of a series of tried and tested Gaussian basis sets and where there is a substantial body of literature to help choose the most appropriate method for incorporating post-Hartree-Fock methods, should that be desired. 

We have extended the linear combination of Gaussian-type orbitals local-density functional approach to calculate the total energies and electronic structures of helical chain polymers[35]. This method was originally developed for molecular systems[36-40], and extended to two-dimensionally periodic sys-tems[41,42] and chain polymers[34j. The one-electron wavefunctions here are constructed from a linear combination of Bloch functions c>>, which are in turn constructed from a linear combination of nuclear-centered Gaussian-type orbitals Xylr) (in ihis case, products of Gaussians and the real solid spherical harmonics). The one-electron density matrix is given by... 

Haberlen, O.D. and Rdsch, N. (1992) A scalar-relativistic extension of the linear combination of Gaussian-type orbitals local density functional method application to AuFl, AuCl and Au2. Chemical Physics Letters, 199, 491-496. 

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