Core-valence correlation effects basis set

In the case of core-valence correlation effects, correlating functions were optimized at the CISD level of theory using the weighted core-valence scheme (5). In this case a cc-pwCVTZ-PP set consisted of the cc-pVTZ-PP basis set with the addition of 2.y2p2(5fl/core-valence correlating functions. 

In our calculations we associate to each Li atom a (10s2p) atomic centered gaussian basis set contracted to [4s,2p] (Table 3). We treat only the valence electrons at the VB level and keep the inner shell electrons (LiIs) in a core obtained by HF calculations. Therefore we are neglecting the core-core and core-valence correlation effects, which are small for these small lithium clusters (Fig.5). 

The use of CPPs to account for core-valence correlation effects of inner shells in combination with accurate relativistic small- or medium-core ECPs (Yu and Dolg 1997) may be a useful direction for future developments, especially in view of the large computational effort for an explicit treatment of core-valence correlation in case of d and/or f shells and the significant basis-set superposition errors occurring at the correlated level (Dolg et al. 2001). 

ANO basis set used gives a separation in good agreement with, but smaller than, the value deduced from a combination of theory and experiment. From the convergence of the result with expansion of the ANO basis set, it is estimated that the valence limit is about 9.05 + O.lkcal/mole. The remaining discrepancy with experiment is probably mostly due to core-valence correlation effects. However, as the valence correlation treatment is nearly exact, finer effects such as Bom-Oppenheimer breakdown and relativity must also be considered. While FCI calculations have shown that a very high level of correlation treatment is required for an accurate estimate of the CV contribution to the separation, theoretical calculations indicate that CV correlation will increase the separation by at most 0.35 kcal/mole (see later discussion). Therefore, it is now possible to achieve an accuracy of considerably better than one kcal/mole in the singlet-triplet separation in methylene. 

DeYonker, N., Peterson, K.A., Wilson, A.K. Systematically convergent correlation consistent basis sets for molecular core-valence correlation effects the third row atoms gaUium through krypton, J. Phys. Chem. A, submitted. 

To summarize this section one should say that an effective Hamiltonian treatment of the core electron effect faces a contradiction between the necessity to use extended valence basis sets for the extraction and the risk of appearance of core excited intruder states. One should also recognize that this approach leads to p-electron operators for atoms involving p valence electrons and seems much more difficult to handle than the monoelectronic core pseudopotentials extracted by simulation techniques and discussed in Section IV of the present contribution. As a counterpart one should mention that this core effective Hamiltonian would be much superior, since it would include for instance the core-valence correlation effects which play such an important role in alkali- or alkaline-earth-containing molecules. 

Basis Sets Correlation Consistent Sets Classical Trajectory Simulations Final Conditions Complete Active Space Self-consistent Field (CASSCF) Second-order Perturbation Theory (CASPT2) Configuration Interaction Configuration Interaction PCI-X and Applications Core-Valence Correlation Effects Density Functional Applications Density... 

Basis Sets Correlation Consistent Sets Benchmark Studies on Small Molecules Complete Active Space Self-consistent Field (CASSCF) Second-order Perturbation Theory (CASPT2) Configuration Interaction Configuration Interaction PCI-X and Applications Core-Valence Correlation Effects Coupled-cbister Theory Density Functional Applications Density Functional Theory (DFT), Har-tree-Fock (HF), and the Self-consistent Field Density Functional Theory Applications to Transition Metal Problems Electronic Structure of Meted and Mixed Nonstoi-chiometric Clusters G2 Theory Gradient Theory Heats of Formation Hybrid Methods Metal Complexes Relativistic Effective Core Potential Techniques for Molecules Containing Very Heavy Atoms Relativistic Theory and Applications Semiempiriced Methetds Transition Metals Surface Chemi-ced Bond Transition Meted Chemistry. 

Peterson KA, Yousaf KE. Molecular core-valence correlation effects involving the post-d elements Ga-Rn Benchmarks and new pseudopotential-based correlation consistent basis sets. J Chem Phys. 2010 133 174116. 

For the very highest accuracy, the effect of at least core-valence correlation should be explored. This must be accompanied by some serious effort to extend the basis so that core-correlating functions are included. Using valence-optimized basis sets and including core correlation is not only a waste of computer time, but a potential source of problems, as it can substantially increase BSSE. This point is not well appreciated the prevailing view appears to be that no harm can come of correlating the core when the basis set is inadequate. This is not so. 

Another series of composite computational methods, Weizmann-n (Wn), with n = 1-4, have been recently proposed by Martin and co-workers W1 and W2 in 1999 and W3 and W4 in 2004. These models are particularly accurate for thermochemical calculations and they aim at approximating the CBS limit at the CCSD(T) level of theory. In all Wn methods, the core-valence correlations, spin-orbit couplings, and relativistic effects are explicitly included. Note that in G2, for instance, the single-points are performed with the frozen core (FC) approximation, which was discussed in the previous section. In other words, there is no core-valence effect in the G2 theory. Meanwhile, in G3, the corevalence correlation is calculated at the MP2 level with a valence basis set. In the Wn methods, the core-valence correlation is done at the more advanced CCSD(T) level with a specially designed core-valence basis set. 

The first iteration of the ccCA methodology modeled the popular and successfiil Gn methods [79]. In fact, similar to the G3 method, the initial formulation of ccCA sought as its effective level of theory QCISD(T) with large basis sets and some aceount of core-valence correlation. However, ccCA utilized the larger and more flexible correlation consistent basis sets instead of the Pople-style sets adopted by the Gn authors, which we felt would enable the more systematic behavior of the... 

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