Small-core approximation

In the present work, correlation consistent basis sets have been developed for the transition metal atoms Y and Hg using small-core quasirelativistic PPs, i.e., the ns and (nA)d valence electrons as well as the outer-core (nA)sp electrons are explicitly included in the calculations. This can greatly reduce the errors due to the PP approximation, and in particular the pseudo-orbitals in the valence region retain some nodal structure. Series of basis sets from double-through quintuple-zeta have been developed and are denoted as cc-pVwZ-PP (correlation consistent polarized valence with pseudopotentials). The methodology used in this work is described in Sec. II, while molecular benchmark calculations on YC, HgH, and Hg2 are given in Sec. III. Lastly, the results are summarized in Sec. IV. 

The 7600 used is located at Lawrence Berkeley Laboratory, is approximately ten years old and has 65 K of 60 bit word fast memory (small core). Because CLAMPS has dynamic memory allocation, it is possible to fit a simulation in fast memory of up to about 2000 atoms as long as the potential tables are not too extensive. The compiler used was the standard CDC FTN 4.8, 0PT=2. The only difference between the CDC coding of the pairwise sum and that in Table I is that the periodic boundary conditions (loop 3) are handled by Boolean and shift operations instead of branches. Branches on the 7600 causes all parallel processing to halt. 

Note that if a frozen core approximation is used a small difference will persist in the Full CI limit since the unrelaxed series converges to a limit with the core orbitals constrained to be those of the unperturbed system whereas in the relaxed series the relaxation contribution of the core orbitals is included. For electric (hyper)polarizabihties this effect is usually negligible. 

The calculations were carried out at B3LYP using a quasi-relativistic small-core ECP with a DZP-quality basis set for Pt and 6-31G(d) for C and H. The bond energies were approximated CCSD(T) values. For details see the original paper J. Uddin, S. Dapprich, G. Frenking and B. F. Yates, Organometallics, 1999,18,457. 

The results of this procedure for alkaline and alkaline-earth systems were quite good [186,187], at least for atoms, and pseudopotentials of this type were generated [188] and applied [189] for most of the main group elements. However, due to the limited validity of the frozen-core approximation when going from a medium or highly charged one-valence electron ion to a neutral atom or nearly neutral ion, the approach is bound to fail for most other elements. This is especially the case for transition metals, lanthanides and actinides, where small cores are indispensable for accurate pseudopotentials. More recent calibration studies of alkaline and alkaline earth elements exhibited however, that for accu-... 

There are generally some small leaks in the wind tunnel between the test core and the point of air mass flow rate measurement. These leaks, although small, are approximately independent of the air mass flow rate, and they represent an increasing fraction of the measured flow rate m at low air flows. A primary leak test is essential at the lowest encountered test airflow before any testing is conducted. 

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