Basis functions correlation consistent

There are several types of basis functions listed below. Over the past several decades, most basis sets have been optimized to describe individual atoms at the EIF level of theory. These basis sets work very well, although not optimally, for other types of calculations. The atomic natural orbital, ANO, basis sets use primitive exponents from older EIF basis sets with coefficients obtained from the natural orbitals of correlated atom calculations to give a basis that is a bit better for correlated calculations. The correlation-consistent basis sets have been completely optimized for use with correlated calculations. Compared to ANO basis sets, correlation consistent sets give a comparable accuracy with significantly fewer primitives and thus require less CPU time. 

Before leaving this topic, it should be mentioned that, in addition to the (Pople) basis sets discussed so far, there are others as well. The more popular ones include the Dunning-Huzinaga basis sets, correlation consistent basis sets, etc. These functions will not be described here. 

As usual, the (Gaussian) basis set (see Basis Sets Correlation Consistent Sets) selected for anharmonic force field calculations should be sufficiently complete to allow a reasonably good description of the wave function and moderate in size so that larger systems of interest can be handled at an acceptable computational cost. In case of anharmonic force field studies the computational cost can be substantial either in the case of a fully analytic calculation or if calculations are carried out at a large number of displaced geometries. In systematic studies of molecular families it is probably worthwhile choosing a basis set with which results have been obtained for similar species. 

AMI Basis Sets Correlation Consistent Sets Complete Active Space Self-consistent Field (CASSCF) Second-order Perturbation Theory (CASPT2) Configuration Interaction Coupled-cluster Theory Density Functional Theory (DFT), Hartree-Fock (HF) and the Self-consistent Field Diradicals Electronic Wavefunctions Analysis G2 Theory M0ller-Plesset Perturbation Theory Natural Bond Orbital Methods Spin Contamination. 

Basis Sets Correlation Consistent Sets Configuration Interaction Coupled-cluster Theory Density Functional Applications Density Functional Theory Applications to Transition Metal Problems G2 Theory Integrals of Electron Repulsion Integrals Overlap Linear Scaling Methods for Electronic Structure Calculations Localized MO SCF Methods Mpller-Plesset Perturbation Theory Monte Carlo Quantum Methods for Electronic Structure Numerical Hartree-Fock Methods for Molecules Pseudospectral Methods in Ab Initio Quantum Chemistry Self-consistent Reaction Field Methods Symmetry in Hartree-Fock Theory. 

Basis Sets Correlation Consistent Sets Benchmark Studies on Small Molecules Density Functional Applications ... 

Throughout the remainder of this article, differentiation between primitive or contracted basis functions will not be made unless specifically noted. However, the use of square brackets and parentheses for the integrals will be reserved exclusively for the primitive and the contracted basis functions, respectively. For details on basis sets, see the article by T. Dunning, Jr. on Basis Sets Correlation Consistent Sets. 

An extension of this last notation is aug—cc—pVDZ. The aug denotes that this is an augmented basis (diffuse functions are included). The cc denotes that this is a correlation-consistent basis, meaning that the functions were optimized for best performance with correlated calculations. The p denotes... 

Bauschlicker ANO Available for Sc through Cu (20.vl5/il0r/6/4 ). cc—pVnZ [n = D, T, Q, 5,6) Correlation-consistent basis sets that always include polarization functions. Atoms FI through Ar are available. The 6Z set goes up to Ne only. The various sets describe FI with from i2s p) to [5sAp id2f g) primitives. The Ar atoms is described by from [As pld) to ils6pAd2>f2g h) primitives. One to four diffuse functions are denoted by... 

Some of the basis sets discussed here are used more often than others. The STO—3G set is the most widely used minimal basis set. The Pople sets, particularly, 3—21G, 6—31G, and 6—311G, with the extra functions described previously are widely used for quantitative results, particularly for organic molecules. The correlation consistent sets have been most widely used in recent years for high-accuracy calculations. The CBS and G2 methods are becoming popular for very-high-accuracy results. The Wachters and Hay sets are popular for transition metals. The core potential sets, particularly Hay-Wadt, LANL2DZ, Dolg, and SBKJC, are used for heavy elements, Rb and heavier. 

Electron correlation studies demand basis sets that are capable of very high accuracy, and the 6-31IG set I used for the examples above is not truly adequate. A number of basis sets have been carefully designed for correlation studies, for example the correlation consistent basis sets of Dunning. These go by the acronyms cc-pVDZ, cc-pVTZ, cc-pVQZ, cc-pV5Z and cc-pV6Z (double, triple, quadruple, quintuple and sextuple-zeta respectively). They include polarization functions by definition, and (for example) the cc-pV6Z set consists of 8. 6p, 4d, 3f, 2g and Ih basis functions. 

A+B L -fl/2) have also been used. The theoretical assumption underlying an inverse power dependence is that the basis set is saturated in the radial part (e.g. the cc-pVTZ ba.sis is complete in the s-, p-, d- and f-function spaces). This is not the case for the correlation consistent basis sets, even for the cc-pV6Z basis the errors due to insuficient numbers of s- to i-functions is comparable to that from neglect of functions with angular moment higher than i-functions. 

We need to look at the convergence as a function of basis set and amount of electron correlation (Figure 4.2). For the former we will use the correlation consistent basis sets of double, triple, quadruple, quintuple and, when possible, sextuple quality (Section 5.4.5), while the sensitivity to electron correlation will be sampled by the HF, MP2 and CCSD(T) methods (Sections 3.2, 4.8 and 4.9). Table 11.1 shows how the geometry changes as a function of basis set at the HF level of theory. 

Stuttgart pseudopotential for Au with a uncontracted (lls/10p/7d/5f) valence basis set and a Dunning augmented correlation consistent valence triple-zeta sets (aug-cc-pVTZ) for both C and N, but with the most diffuse f function removed, was used. 

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