量子化学材料计算简介.ppt

Unfortunately functions of this kind are not suitable for fast calculations of necessary two electron integrals. That is why the Gaussian Type Orbitals GTOs were introduced. You can approximate the shape of the STO function by summing up a number of GTOs with dierent exponents and coecients. Even if you use ten GTOs to represent STO you will still calculate your integrals much faster than if original STOs are used. The GTO called also cartesian gaussian is expressed as One-particle basis sets:STOs and GTOs Slater-Type Orbitals are H like STOs have cusp Gaussian Type Orbitals have no cusp GTOs decline more strongly a: ‘exponent’ Ab initio basis set： STO and GTO Basis sets: Why GTOs ? Use of atom-centered GTOs Products of two GTOs at centers A, B gives GTO at center E Hence: Ease of integration! Much faster than with STOs, despite increased number Situation in molecules: Atomic centers A,B Ab initio basis set： STO and GTO Basis sets: Radial shifts Higher principal quantum numbers n Higher angular momenta p,d,f … Radial shifts through prefactors General expression: Ab initio basis set： STO and GTO Basis sets: Nodal structure Linear combination of individual GTOs Introduction of signs Description of radial nodes through several GTOs Analogous for higher n, l Ab initio basis set： STO and GTO Basis sets: Polarization functions Polarization of atomic density upon formation of chemical bond Additional polarization functions for description Molecular field breaks atomic symmetry ! Use of higher angular-momentum functions E.g. pz for polarization of s functions (s.a.) Ab initio basis set： STO and GTO Standard basis sets: Overview STO-NG: N GTO per STO Split-valence 6-31G(**) sets: SZ (core)/DZ(valence), *: polarization functions Z(zeta): Number of contracted functions (aug)-cc-(p)VXZ: Correlation-consistent basis sets XZV(PP): similar to above, less systematic ANO (Atomic Natural Orbital) basis sets Pseudo wave function NUMBER of basis functions per atom RANGE of localizat