Atomic natural orbitals ANO basis sets

Atomic natural orbital (ANO) basis sets [44] are fonned by contracting Gaussian fiinctions so as to reproduce the natural orbitals obtained from correlated (usually using a configuration interaction with... 

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. 

Calculations of ionization energies and electron affinities were performed with a modified development version of Gaussian 99 [48], Pople and Effective Core Potential (ECP) basis sets are provided in this software [49], Dunning and Atomic Natural Orbital (ANO) basis sets were obtained from the EMSL Gaussian Basis Set Library [50],... 

Almlof, J., Taylor, P.R. Atomic natural orbital (ANO) basis-sets for quantum-chemical calculations. Adv. Quantum Chem. 1991, 22, 301-73. 

Pierloot, K., Dumez, B., Widmark, P.-O., Roos, B.O. Density-matrix averaged atomic natural orbital (ANO) basis-sets for correlated molecular wave-functions. IV. Medium-size basis-sets for the atoms H-Kr. Theor. Chim. Acta 1995, 90, 87-114. 

Knowles and Handy demonstrated the power of this approach by estimating the full Cl energy of NH3 in an atomic natural orbital (ANO) basis set of DZP quality.218 The full Cl expansion contains more than 209 million determinants, yet Knowles and Handy were able to obtain an apparently reliable variational energy of -56.4235 hartree using a Cl vector with only 665,247 nonzero elements (0.3% of the full Cl vector). Employing perturbation theory to estimate the remaining energy error (presumably via equation 135), Knowles and Handy arrived at a final estimate of -56.4236 0.0001 hartree.218... 

Having examined the performance of UGA based MP and EN MBPT schemes for a smaller DZ basis, where the comparison with the exact FCI results is possible, we can be reasonably confident that the MP2 and 3 methods, similarly as CCSD, will reproduce experimental results assuming that we employ a sufficiently large basis set. We have thus carried out a series of calculations at the MP2, MP3 and CCSD levels with different basis sets approaching the atomic natural orbital (ANO) basis set of (34). First, we... 

The basis sets described above are small and intended for qualitative or semiquantitative, rather than quantitative, work. They are used mostly for simple wave functions consisting of one or a few Slater determinants such as the Hartree-Fock wave function, as discussed in Sec. 3. For the more advanced wave functions discussed in Sec. 4, it has been proven important to introduce hierarchies of basis sets. New AOs are introduced in a systematic manner, generating not only more accurate Hartree-Fock orbitals but also a suitable orbital space for including more and more Slater determinants in the n-electron expansion. In terms of these basis sets, determinant expansions (Eq. (14)) that systematically approach the exact wave function can be constructed. The atomic natural orbital (ANO) basis sets of Almlof and Taylor [23] were among the first examples of such systematic sequences of basis sets. The ANO sets have later been modified and extended by Widmark et al. [24],... 

P. O. Widmark, P. A. Malmqvist, and B. 0. Roos, Theor. Chim. Acta, 77, 291 (1990). Density Matrix Averaged Atomic Natural Orbital (ANO) Basis Sets for Correlated Molecular Wavefunctions. I. First-Row Atoms. 

The DFT calculations presented here were obtained with B3P86, in combination with cc-pVDZ for Li clusters, and St-RECP for coinage metals, hence, UB3P86/St-RECP. Specifically, UB3P86/St-RECP was shown [2e,f to have a very small basis set superposition error (BSSE), and was compatible with the results of the extended augmented double zeta atomic natural orbital (ANO) basis set of Roos et al. [28] Other DFT methods were tried, and the results were similar to UB3P86 [2f. ... 

In a contracted scalar basis set, the core spin-orbit splitting must be accounted for, and the calculations become a little more difficult to do directly. The worst case for basis set size would be a basis set in which all functions are contracted, for example, a generally contracted basis set or an atomic natural orbital (ANO) basis set. Then, the large-component basis set would double in size, apart from the functions. The small-component basis set, however, would not change, provided the contractions were properly restricted for instance, the component was eliminated from the d functions for the small component of the p3/2 contracted functions. 

By far the two most commonly used families of basis sets in calibration studies are atomic natural orbital (ANO) basis sets (see Natural Orbitals) and the correlation consistent (cc) basis sets of the Dunning group (see Basis Sets Correlation Consistent Sets) ... 

There are two types of basis sets particularly useful for property calculations one is the polarizability consistent basis set of Sadlej (POL), and the other is the correlation consistent atomic natural orbital (ano) basis sets. 

Different basis set series for use in F12 calculations have been assessed by Bischoff, et al who confirmed the good performance of the cc-pVXZ-F12 basis sets. Another interesting alternative, atomic natural orbital (ANO) basis sets were investigated, too. ... 

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