Polarization basis sets

The most reliable results are obtained using ah initio methods with moderate-to large-sized polarized basis sets. The use of gauge-independent atomic orbitals (GIAO) removes gauge dependency problems. 

The alkali metals tend to ionize thus, their modeling is dominated by electrostatic interactions. They can be described well by ah initio calculations, provided that diffuse, polarized basis sets are used. This allows the calculation to describe the very polarizable electron density distribution. Core potentials are used for ah initio calculations on the heavier elements. 

Split Valence Basis Sets Polarized Basis Sets Diffuse Functions Pseudopotentials... 

Split valence basis sets allow orbitals to change size, but not to change shape. Polarized basis sets remove this limitation by adding orbitals with angular momentum beyond what is required for the ground state to the description of each atom. For example, polarized basis sets add d functions to carbon atoms and f functions to transition metals, and some of them add p functions to hydrogen atoms. 

So far, the only polarized basis set we ve used is 6-31G(d). Its name indicates that it is the 6-31G basis set with d functions added to heavy atoms. This basis set is becoming very common for calculations involving up to medium-sized systems. This basis set is also known as 6-31G. Another popular polarized basis set is 6-31G(d,p), also known as 6-31G, which adds p functions to hydrogen atoms in addition to the d functions on heavy atoms. 

Using local spin density functional (LSDF) theory, we obtain 70 kcal/mole for the rotational barrier of the ethylene molecule (35). In these calculations, we use the equivalent of a double-zeta+polarization basis set, i.e. for C two 2s functions. 

In particular the results of Ref. [16], obtained via a 4-3 Ig polarized basis set, have been reproduced on an 486 IBM compatible PC, with a hard disk memory of 100 Mbyte. As a matter of fact, in that calculation, only 1 180 752 symmetry unique two-electron integrals >1 X 10 a.u. had to be stored within our method. 

Karpfen published a study of trends in halogen bonding between a series of amines and halogens and interhalogens [171]. Iodine-containing electron acceptors were not included. This study involved the use of RHF, MP2, and various DFT methods using extended, polarized basis sets and made extensive use of pulsed-nozzle, FT-microwave spectroscopic data (similar to that... 

Although there is no strict relationship between the basis sets developed for, and used in, conventional ah initio calculations and those applicable in DFT, the basis sets employed in molecular DFT calculations are usually the same or highly similar to those. For most practical purposes, a standard valence double-zeta plus polarization basis set (e.g. the Pople basis set 6-31G(d,p) [29] and similar) provides sufficiently accurate geometries and energetics when employed in combination with one of the more accurate functionals (B3LYP, PBEO, PW91). A somewhat sweeping statement is that the accuracy usually lies mid-way between that of M P2 and that of the CCSD(T) or G2 conventional wave-function methods. 

IG and 6-3IG. These are commonly used split-valence plus polarization basis sets. These basis sets contain inner-shell functions, written as a linear combination of six Gaussians, and two valence shells, represented by three and one Gaussian primitives, respectively (noted as 6-3IG). When a set of six d-type Gaussian primitives is added to each heavy atom and a single set of Gaussian p-type functions to each hydrogen atom, this is noted as and... 

G. K.-L. Chan and M. Head-Gordon, Exact solution (within a triple-zeta, double polarization basis set) of the electronic Schrodinger equation for water. J. Chem. Phys. 118, 8551 (2003). 

Split-valence basis sets and polarization basis sets, respectively, have been formulated to address the two shortcomings. These are discussed in the following sections. 

As with hydrocarbons, accurate descriptions of equilibrium structures for molecules with heteroatoms from density functional and MP2 models requires polarization basis sets. As shown in Table A5-20 (Appendix A5), bond distances in these compounds obtained from (EDF 1 and B3LYP) density functional models and from MP2 models... 

IG, 6-3IG. The 6-3IG Basis Set in which non-hydrogen atoms are supplemented by d-type Gaussians and (for 6-3IG ) hydrogen atoms are supplemented by p-type Gaussians (Polarization Functions). 6-3IG and 6-3IG are Polarization Basis Sets. 

G, 6-31+G. Basis Sets that are identical to 6-31G and 6-3IG except that all non-hydrogen atoms are supplemented by diffuse s and p-type Gaussians (Diffuse Functions). 6-31+G and 6-31+G are supplemented Polarization Basis Sets. 

---