Atomic natural orbital bases

Sources. Results taken from Ref. 69 the near-HF SCF Slater bases are from Ref. 70. The 6-31IG basis is that of Ref. 16. The contracted ANO (atomic natural orbital) bases [72] are indicated in [69], as well as the (13r 2d If) basis constructed with the help of van Duijneveldt s (13i 8p) basis [18] augmented with d and / functions taken from Ref. 17. 

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... 

Traditionally, the exact same basis set will be used to define atoms in varying chemical environments. The 6-310 carbon basis set is the same regardless of the nature of the carbon (alkane, olefin, alcohol, carbanion, ketone, carboxylic acid, etc.). The three-dimensional space of the carbon atom must be different in these molecules, yet the Mulliken procedure sums up the occupancy of identically defined orbitals in all these different chemical environments. The natural population analysis (NPA), developed by Reed, Weinstock, and Weinhold,i0 > 8 attempts to define atomic orbitals based on the molecular wavefunction, thereby obtaining different atomic orbitals depending on the chemical environment. 

Presently, the widely used post-Hartree-Fock approaches to the correlation problem in molecular electronic structure calculations are basically of two kinds, namely, those of variational and those of perturbative nature. The former are typified by various configuration interaction (Cl) or shell-model methods, and employ the linear Ansatz for the wave function in the spirit of Ritz variation principle (c/, e.g. Ref. [21]). However, since the dimension of the Cl problem rapidly increases with increasing size of the system and size of the atomic orbital (AO) basis set employed (see, e.g. the so-called Paldus-Weyl dimension formula [22,23]), one has to rely in actual applications on truncated Cl expansions (referred to as a limited Cl), despite the fact that these expansions are slowly convergent, even when based on the optimal natural orbitals (NOs). Unfortunately, such limited Cl expansions (usually truncated at the doubly excited level relative to the IPM reference, resulting in the CISD method) are unable to properly describe the so-called dynamic correlation, which requires that higher than doubly excited configurations be taken into account. Moreover, the energies obtained with the limited Cl method are not size-extensive. 

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