Atom basis sets, neutral

From a more quantitative point of view, it is more difficult to achieve accurate computations for DPEs than for PAs of neutral substrates, because molecular anions are involved in the former case. However, when using second-order perturbation theory (MP2), a coupled-cluster theory (CCSD(T)) or a density functional theory (DFT/B3LYP), in conjunction with a moderate atomic basis set including a set of diffuse and polarization functions, such as the 6-3114—FG(d,p) or cc-aug-pVDZ sets, the resulting DPE errors appear to be fairly systematic. To some extent, the accuracy rests on a partial but uniform cancellation of errors between the acid and its conjugate base. Therefore, use of appropriate linear regressions between experimental and calculated values allows the DPEs for new members of the series to be evaluated within the chemical accuracy of 4=0.1 eV or 4=10 kJmoD. ... 

Basis sets contraction coefficients from scalar-relativistic ground state calculation of the neutral atom (basis set A) or the anion (basis set B). Different contractions for and from... 

Kramers-restricted Hartree-Fock ground state calculations of the neutral atom (basis set C). The most diffuse primitives of the (7s7p) set were left uncontracted to generate the [nsnp] contracted sets. 

The very first application of the GCHF method was for the construction of universal atomic basis sets [17], culminating with very accurate Gaussian (GTO) and the construction of Slater (STO) bases for neutral and charged, ground and excited states for atoms H to Xe (see Ref. [18] and references therein). Contracted GTO sets were also introduced [19,20]. The extension of integral transforms other than for Is functions (Section 3) was also presented [21]. 

The pseudo-atomic basis functions (p j) are obtained by solving the Kohn-Sham equation for a spherical symmetric spin-unpolarized neutral atom selfconsistently. From this procedure, we obtain for each atom type optimized atomic basis sets and atomic densities p , which are used to... 

The conclusion is thus that the extension of the basis set with respect to the minimal atomic basis set is important (i) to distort the AOs in order to minimize the interatomic repulsion in the neutral forms, and (ii) to lower the energies of the ionic components of the VB wavefunction by important instantaneous repolarization and correlation effects. " " ... 

As mentioned above, HMO theory is not used much any more except to illustrate the principles involved in MO theory. However, a variation of HMO theory, extended Huckel theory (EHT), was introduced by Roald Hof nann in 1963 [10]. EHT is a one-electron theory just Hke HMO theory. It is, however, three-dimensional. The AOs used now correspond to a minimal basis set (the minimum number of AOs necessary to accommodate the electrons of the neutral atom and retain spherical symmetry) for the valence shell of the element. This means, for instance, for carbon a 2s-, and three 2p-orbitals (2p, 2p, 2p ). Because EHT deals with three-dimensional structures, we need better approximations for the Huckel matrix than... 

The first step in reducing the computational problem is to consider only the valence electrons explicitly, the core electrons are accounted for by reducing the nuclear charge or introducing functions to model the combined repulsion due to the nuclei and core electrons. Furthermore, only a minimum basis set (the minimum number of functions necessary for accommodating the electrons in the neutral atom) is used for the valence electrons. Hydrogen thus has one basis function, and all atoms in the second and third rows of the periodic table have four basis functions (one s- and one set of p-orbitals, pj, , Pj, and Pj). The large majority of semi-empirical methods to date use only s- and p-functions, and the basis functions are taken to be Slater type orbitals (see Chapter 5), i.e. exponential functions. 

All calculations are scalar relativistic calculations using the Douglas-Kroll Hamiltonian except for the CC calculations for the neutral atoms Ag and Au, where QCISD(T) within the pseudopotential approach was used [99], CCSD(T) results for Ag and Au are from Sadlej and co-workers, and Cu and Cu from our own work, using an uncontracted (21sl9plld6f4g) basis set for Cu [6,102] and a full active orbital space. 

The P3 approximation to the self-energy was applied to the atoms Li through Kr and to neutral and ionic molecular species from the G2 set [47]. For the atoms, a set of 22 representative basis sets was tested. Results for the molecular set were obtained using standard Pople basis sets as described below. 

The present basis sets for Y were developed using the 28 electron ECP of Andrae et al. (29), which leaves 11 electrons in the valence shell. A total of 3 electronic states of the neutral atom were considered in the optimizations. Specifically these corresponded to the Ad 5s (a D), AcF 5s (a F), and Acf (b F) states. The Hartree-Fock calculations on these states involved separate stateaveraging of all degenerate components so that the orbitals were fully symmetry equivalenced. Subsequent singles and doubles Cl (CISD) calculations were then carried out with these orbitals on only a single component of each state. 

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