Extended basis sets Polarized bases

To improve upon a double- basis, one generally adds polarization functions whose / values correspond to orbitals unoccupied in the free atoms. For example, to expand upon a double- basis for HjO, one would add 2p functions on H and 3d functions on O. Such functions are called polarization functions since they describe the polarization of atomic electron density arising from molecule formation. For example, if a H atom is placed in the electrostatic field of an O atom, its electron density will be polarized along the 0-H bond direction, a change that can be described by the mixing of H 2p character into the His wave function. 

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When using HF theory for the geometry optimization the use of two sets of polarization functions is necessary to reproduce the Si-O-Si angle. Methods which include electron correlation (i.e. MP2- or DFT-based methods) do not require such extended basis sets. 

Basch has criticized the work of Bender et and Ryan et al., the first especially because of the lack of M orbitals in the basis and that of Ryan in omitting possibly important functions from the basis set. Basch carried out MCSCF calculations and used both spatially extended basis functions and polarization functions. However, there was less Cl than in ref. 204. The results disagreed with those of Ryan and Whitten, but were in reasonable agreement with those of Bender et The state becomes increasingly valence-like with improvements in the configuration and orbital bases. However is still fairly large. 

The purpose of this chapter will be to review the fundamentals of ab initio MD. We will consider here Density Functional Theory based ab initio MD, in particular in its Car-Parrinello version. We will start by introducing the basics of Density Functional Theory and the Kohn-Sham method, as the method chosen to perform electronic structure calculation. This will be followed by a rapid discussion on plane wave basis sets to solve the Kohn-Sham equations, including pseudopotentials for the core electrons. Then we will discuss the critical point of ab initio MD, i.e. coupling the electronic structure calculation to the ionic dynamics, using either the Born-Oppenheimer or the Car-Parrinello schemes. Finally, we will extend this presentation to the calculation of some electronic properties, in particular polarization through the modern theory of polarization in periodic systems. 

High-accuracy calculations clearly require very flexible basis sets extended in a number of ways such as with multiple polarization sets, with diffuse basis function augmentation, and with other than atom-centered functions. Use of smaller bases goes along with less reliability however, with bases smaller than double-zeta in the valence plus one well-chosen set of polarization functions on all centers, including hydrogens, the reliability is so limited that results are not likely to be meaningful for most contemporary problems of weak interaction. 

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