Valence Correlation Effects

NASA Ames Research Center, Moffett Field, CA, USA 

5 Core-Valence Effects for Systems Containing First Row Atoms B-F 586 

ACPF = averaged CPF ANO = atomic natural orbital CCSD(T) = singles and doubles coupled-cluster approach with a perturbational estimate of the triples excitation Cl = configuration interaction CPF = coupled pair functional CPP = core polarization potential CVCI = core-valence Cl FCI = full configuration interaction ICACPF = internally contracted ACPF ICMRCI = internally contracted MRCI MCPF = modified CPF MRCI = multi-reference configuration interaction NHF = numeric Hartree-Fock SDCI = singles plus doubles Cl. 

---

Optimization of augmenting functions for the description of electron affinities, weak interactions, or core-valence correlation effects. 

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 addition, none of these calculations involve correlation of more than ten electrons, so no correlation effects from the core electrons axe included at all. Explicit inclusion of the core electrons at the CPF level was found to increase De by about 0.7 kcal/mol in calculations by Ahlrichs and co-workers [69], while in calculations by Almlof and co-workers [68] the same increase was obtained by a completely different technique (inclusion of only core-valence correlation effects, as described in Sec. 6.2). Hence it appeared safe to assume that core correlation would increase De by less than 1 kcal/mol. However, recent calculations by Werner and Knowles [70] give a larger effect of about 1.5 kcal/mol, so this question is not yet settled. 

Several empirical corrections are added to the resulting energies in the CBS methods to remove the systematic errors in the calculations (see Table 10). The CBS-Q method contains a two-electron correction term similar in spirit to the higher level correction used in G2 theory, a spin correction term to account for errors resulting from spin contamination in UHF wavefunctions for open-shell systems, and a correction to the sodium atom to account for core-valence correlation effects. The CBS-4 and CBS-q methods also contain a one-electron... 

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. 

Figure 15. First (IPj) and second (IP2) ionization potentials of the lanthanide elements j La -2jLu. Experimental values are compared to results from 4f-in-core pseudopotential (PP) calculations with and without account of core-valence correlation effects by means of a core polarization potential (CPP) [95].

What remedies do we have The brute-force device tried in pioneer days, of incorporating core- and core-valence correlation effects into pseudopotentials just by fitting to experimental reference data containing these effects, does not work since the one-electron/one-center PP ansatz is insufficient for this purpose, cf. below. Certainly more reliable is a DFT description of core contributions to correlation effects which is possible with (and actually implied in) the non-linear core corrections discussed in Section 1.4. Another device, which has shown excellent performance in the context of quantum-chemical ab initio calculations180 and has later been adapted to PP work cf. e.g. refs. 139, 181-184), is that of core-polarization potentials (CPP)... 

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. 

Next, an adjustment [A (CV)] for core-valence correlation effects is made through an MP2(EC1) aug-cc-pCVTZ computation... 

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. 

Relativistic core-valence correlation effects on molecular properties of the hydrogen halide molecules ... 

Non-Bom-Oppenheimer (BODC), relativistic, and core-valence correlation corrections, tacitly neglected in most quantum chemical studies, result in small shifts of the calculated PES values. BODC and relativistic correction to the force constant are usually negligble for species involving first- and second-row. atoms. On the other hand, advances in the continuing development of quantitatively accurate ab initio methods have revealed the necessity of a full understanding of the consequences of core-core and core-valence electron correlation (see Core-Valence Correlation Effects) on calculated force fields. It has been found that (a) equilibrium bond distances of first-row diatomic molecules experience a considerable contraction, about 0.002 A for multiple bonds and 0.001 A for single bonds, reducing the errors in Rq predictions... 

---