Correlation consistent basis sets state

It is noticeable that correlation-consistent basis sets are not able to accurately reproduce the bond distances and energies of the excited states in II symmetry, which may be attributed to the relatively inadequate p-space. The problem was eliminated in the case of H-73 basis set. The polarization set that was purposefully optimized to correlate with the 2p orhitals of hydrogen atoms greatly improved the bond lengths and excitation energies, and reduced the errors to be within 100 cmof exact values. 

Recently correlation consistent basis sets for the Ca atom have been reported by Koput and Peterson [28]. Analogous to adding p-type functions to the Mg sets at the HP level of theory, additional HP d-type functions were included and optimized for the 4s 3d excited state of Ca. Affer confracfion, these functions played a very similar role in molecular calculations as the tight d functions in the cc-pV(n + d)Z basis sets described above for fhe 3p main group atoms. 

The previous section outlined the development of correlation consistent basis sets involving mostly light, p-block elements. In the extension of these ideas to heavier elements, the effects of relafivify on fhe basis set should be introduced. In addition to relativistic effects, the influence of low-lying electronic states must also be considered in the cases of fhe fransifion metals. For most cases only scalar relativistic effects will be considered, i.e., even if spin-orbit coupling is included in the calculations, each i component will be described by the same contracted basis set. The exceptions are the correlation consistent basis sets of Dyall [29-33], which were developed in fully-relafivisfic, 4-component Dirac-Hartree-Fock calculations. These basis sets, which are of DZ-QZ quality, are currently available for the heavier p-block elements, as well as the 4d and 5d transition metals. 

Abstract The forward and reverse reactions Br + H2. O HBr + OH are important in atmospheric and environmental chemistry. Five stationary points on the potential energy surface for the Br - - H2O HBr -I- OH reaction, including the entrance complex, transition state, and exit complex, have been studied using the CCSD(T) method with correlation-consistent basis sets up to cc-pV5Z-PP. Contrary to the valence isoelectronic F -I- H2O system, the Br -I- H2O reaction is endothermic (by 31.8 kcal/mol after zero-point vibrational, relativistic, and spin-orbit corrections), consistent with the experimental reaction enthalpy. The CCSD(T)/cc-pV5Z-PP method predicts that the reverse reaction HBr -I- HO Br -I- H2O has a complex... 

Table 8.12 The Hartree-Fock eneigy hf and the CISD correlation energy faso — hf for the ground state of the carbon atom calculated using correlation-consistent basis sets. All energies are given in atomic units. The Hartree-Fock basis-set limit is —37.688619 Eh and the estimated CISD correlation-energy basis-set limit is —99.7 0.4 mEh...

Fig. 8.16. Errors (in mEh) relative to the basis-set limit in the Hartree-Fock energy (dotted line) and in the valence CISD correlation energy (full line) for the ground state of the carbon atom calculated using correlation-consistent basis sets cc-pVXZ. On the left, we have plotted the errors on a linear scale as a function of the cardinal number X on the right, we have plotted the errors on a logarithmic scale.

The correlation-consistent basis sets described in Section 8.3.3 have been designed for one particular purpose the accurate calculation of valence-correlated wave functions of ground-state neutral systems. The cc-pVXZ basis sets therefore do not have the flexibility required either for the investigation of core correlation discussed in Section 8.3.1 or for the study of anions and excited states with diffuse electron distributions. For such applications, additional AOs must be introduced. In the present subsection, we shall first discuss the correlation-consistent polarized core—valence sets cc-pCVXZ [24], where the standard cc-pVXZ sets have been extended for additional flexibility in the core region, and next the augmented correlation-consistent basis sets aug-cc-pVXZ and aug-cc-pCVXZ [25], where diffuse functions have been added so as to improve the flexibility in the outer valence region. 

We now turn our attention to the outer, diffuse regions of the electronic system. The valence and core-valence basis sets considered so far are inadequate for the description of the difiuse electron distributions characteristic of anionic systems and excited states. In addition, these sets do not have the flexibility required for a proper description of interactions with external electric fields and hence the accurate calculation of dipole moments and polarizabilities. For such calculations, additional functions must be added in the outer valence region. Within the framework of correlation-consistent basis sets, we proceed by adding primitive functions to the standard cc-pVXZ sets, with exponents adjusted so as optimize the energy of atomic anions. Diffuse functions are added in groups, with one set of functions for each angular momentum present in the root set. This procedure leads to the augmented correlation-consistent polarized valence basis sets aug-cc-pVXZ [25], the composition and size of which are listed in Table 8.13. The number of functions in the aug-cc-pVXZ sets may be calculated as... 

The performance of the correlation-consistent basis sets is furthca- illustrated in Hguie 8.18, where, for the analytical and numerical cc-pVXZ and n-cc-pVXZ sets, we have plotted the ground-state helium wave function with one electron fixed at a distance of 0.5oo froni the nucleus and with the other electron confined to a circle of radius 0.5ao about the nucleus. For comparison with the correlation-consistent basis sets, the Hylleraas and Hartree-Fock wave functions are plotted as well. 

Table 8.17 The correlation energies recovered by the analytical and numerical correlation-consistent basis sets for the ground-state helium atom. The exact correlation energy is —42.044 mEh...

Fig. 8.18. The ground-state helium wave function plotted on a circle of ladius 0.5oo about the nucleus with one electron fixed at the origin of the plot. The full and dotted black lines repiesent the wave functions generated by the analytical and numerical correlation-consistent basis sets cc-pVXZ and n-cc-pVXZ,...

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