Small-core ECPs

For the related [CpIr(PH3)(CH3)]+ system, four basis sets were used. Basis set one (BS1) is the same as the ones described above for Ir and P, but the C and H are described as D95. Basis set two (BS2) is the Stuttgart relativistic, small core ECP basis set (49) augmented with a polarization function for Ir, and Dunning s correlation consistent double-zeta basis set with polarization function (50) for P, C and H. Basis set three (BS3) is the same as BS1 except the d-orbital of Ir was described by further splitting into triple-zeta (111) from a previous double-zeta (21) description and augmented with a f-polarization function (51). Basis set four (BS4) is the same as BS2 for Ir, P, and most of the C and H, but the C and H atoms involved in the oxidative addition were described with Dunning s correlation consistent triple-zeta basis set with polarization. 

Initially, the level of theory that provides accurate geometries and bond energies of TM compounds, yet allows calculations on medium-sized molecules to be performed with reasonable time and CPU resources, had to be determined. Systematic investigations of effective core potentials (ECPs) with different valence basis sets led us to propose a standard level of theory for calculations on TM elements, namely ECPs with valence basis sets of a DZP quality [9, 10]. The small-core ECPs by Hay and Wadt [11] has been chosen, where the original valence basis sets (55/5/N) were decontracted to (441/2111/N-11) withN = 5,4, and 3, for the first-, second-, and third-row TM elements, respectively. The ECPs of the second and third TM rows include scalar relativistic effects while the first-row ECPs are nonrelativistic [11], For main-group elements, either 6-31G(d) [12-16] all electron basis set or, for the heavier elements, ECPs with equivalent (31/31/1) valence basis sets [17] have been employed. This combination has become our standard basis set II, which is used in a majority of our calculations [18]. 

A key issue in the construction of ECPs is just how many electrons to include in the core. So-called Targe-core ECPs include everything but the outermost (valence) shell, while small-core ECPs scale back to the next lower shell. Because polarization of the sub-valence shell can be chemically important in heavier metals, it is usually worth the extra cost to explicitly include that shell in the calculations. Thus, the most robust ECPs for the elements Sc-Zn, Y-Cd, and La-Hg, employ [Ne], [Ar], and Kr cores, respectively. There is less consensus on the small-core vs. large-core question for the non-metals. 

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. 

Large-core pseudopotentials are well known to lead to sizable errors [122-125] we thus recommend the use of small-core ECP s that include semicore orbitals in the valence space [120],... 

Bond distance (in pm) and vibrational frequencies (in cm ) of UFe obtained by various density functional methods quasi-relativistic frozen core Becke-Lee-Yang-Parr (QR-FC BYLP), Hay-Martin large core ECP hybrid DFT (HM ECP B3LYP and VWN), Stoll-Preuss small core ECP LDA (SP ECP VWN) and an all-electron scalar relativistic LDA (AE SR VWN). 

Other, scalar relativistic effects are usually minor. Among them, the most important is the contraction of s-orbitals caused by the increase in electron mass due to high velocity near the nucleus. Except in the most careful work, such effects are modeled using relativistic effective core potentials (ECPs), also called core pseudopotentials [76]. When an ECP is used, the corresponding valence basis set should be used for the remaining electrons. A small-core ECP, in which fewer electrons are replaced by the effective potential, is a weaker approximation and therefore more reliable than the corresponding large-core ECP. The selection of basis sets to accompany ECPs is more restricted than the selection of all-electron basis sets, but appropriate correlation-consistent basis sets are available for heavy p-block elements [77-80]. 

It is obvious from Table 1 that the quality of the valence basis sets of the available pseudopotentials varies considerably. The large-core ECPs by Hay and Wadt have a low number of electrons in the valence space. Also, the valence orbitals are described by a rather small basis set. We recommend use of the small-core ECPs, which give clearly better results.The same comment applies to the two sets of ECPs that have been published by Christiansen et al 85-88 xhe (n - l)s and (n - l)p electrons should be treated as part of the valence electrons (see also below). 

Quantum mechanical ab initio and DFT methods predict accurate geometries, bond energies, and vibrational frequencies for electionically saturated, closed-shell TM compounds. Relativistic small-core ECPs may be used with confidence in DFT and ab initio calculations. The valence basis... 

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