Atom-centered basis sets

The distinction between atomic orbitals and basis functions in molecular calculations has been emphasized several times now. An illustrative example of why the two should not necessarily be thought of as equivalent is offered by ammonia, NH3. The inversion barrier for interconversion between equivalent pyramidal minima in ammonia has been measured to be 5.8 kcal mol However, a HF calculation with the equivalent of an infinite, atom-centered basis set of s and p functions predicts the planar geometry of ammonia to be a minimum-energy structure ... 

In addition to the cluster calculations, we report details of recent first-principles calculations based on the density functional formalism. These calculations employ periodic boundary conditions to allow investigation of the entire zeolite lattice, and therefore the use of a plane-wave basis set is applicable. This has a number of advantages, most notably that the absence of atom-centered basis functions results in no basis set superposition error (BSSE) (272), which arises as a result of the finite nature of atom-centered basis sets. Nonlocal, or gradient, corrections are applicable also, just as they are in the cluster calculations. 

The main purpose of this chapter is to present the basics of ab initio molecular dynamics, focusing on the practical aspects of the simulations, and in particular, on modeling chemical reactions. Although CP-MD is a general molecular dynamics scheme which potentially can be applied in combination with any electronic structure method, the Car-Parinello MD is usually implemented within the framework of density functional theory with plane-waves as the basis set. Such an approach is conceptually quite distant from the commonly applied static approaches of quantum-chemistry with atom-centered basis sets. Therefore, a main... 

The Car-Parinello MD approach is usually applied in combination with plane wave based electronic structure methods. Use of plane waves in Car-Parinello MD is in many ways easier than the atom-centered basis sets (Gaussian-type or Slater-type... 

Periodic quantum chemical calculations can be carried out either with the atom-centered basis set or planewave basis set. First calculations of the electronic structure of periodic models of zeolites were carried out with atom-centered basis sets (e.g., Ref. [28-30]). First applications of the periodic model of zeolites employing a planewave basis set appeared just a year later [31-33], Majority of applications use the planewave basis sets at present. 

Becomes computational demanding for systems with large unit cell tplanewave calculations) or large number of atoms (atom-centered basis set)... 

The operator X is proportional to p thus, it can neither be represented accurately with a common atom-centered basis set nor with the DKH momentum basis of the eigenvectors [30]. Hence, an iterative solution for the matrix... 

Most of the cluster calculations for molecule/surface interactions are performed by means of finite atom-centered basis sets, in particular Gaussian basis sets. Since such basis sets are incomplete, the results have to be corrected for the so called basis set superposition error (BSSE). This error arises since the basis set centered at one fragment A helps to improve the description of the other fragment B and vice versa, as soon as the two fragments are brought to a finite separation R. This error is unavoidable in the supermolecule approach of intermolecular interactions and leads to an overestimation of the calculated binding energies. 

When atom-centered basis sets are used, a very simple procedure to assign the electrons among the atoms of the molecule comes from Mulliken s approach [26]. Within this method, the number of electrons assigned to the atom A is given by... 

Basis sets are constructed from atomatom-centered functions, or a combination of both. For condensed phase simulations, non-atom-centered basis sets such as plane waves are currently the most popular... 

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