Full-core ECPs

Generation of the REPs is perhaps the most critical step in the derivation of an ECP/valence basis set scheme. The major question is What core size to use The choice of orbitals to include in the core is fraught with uncertainty. One needs to strike a balance between chemical accuracy and the desire to replace as many core electrons as possible. Replacement of all core electrons by the potential (full-core ECPs) is most prevalent for p-block elements, but not replacing the outermost core electrons (semicore ECPs) is the norm for d- and f-block metals. -i° This issue is discussed in detail in the survey of ECP applications later in this chapter. 

Perhaps the main problem in ECP applications for s-block metals concerns core size, particularly for heavier members. - Core-valence correlation is large in these elements, and the use of full-core ECPs can be dangerous. A striking example is provided by CaO ( 2). Using an ECP that replaces the [Ar] core of Ca yields a CaO potential curve with no repulsion at short separations However, an ECP that explicitly includes the Ca 3s and 3p orbitals yields results nearly identical to those from all-electron calculations and displays the classic diatomic potential curve shape." ... 

The transition metals have been a very active area for effective core potential applications. Several monographs and reviews are available. Many ot the issues discussed for main group elements are also pertinent to computational TM chemistry, in particular, core size. For transition metals, most chemists would agree the valence orbitals are the nd, (n -I- l)s, and (n -I- l)p atomic orbitals. However, most ECP researchers have derived schemes in which the outer core orbitals are not replaced by the potential. -7 Hay and Wadt have derived semi- and full-core ECP schemes for the d-block metals, ... 

The ECP basis sets include basis functions only for the outermost one or two shells, whereas the remaining inner core electrons are replaced by an effective core or pseudopotential. The ECP basis keyword consists of a source identifier (such as LANL for Los Alamos National Laboratory ), the number of outer shells retained (1 or 2), and a conventional label for the number of sets for each shell (MB, DZ, TZ,...). For example, LANL1MB denotes the minimal LANL basis with minimal basis functions for the outermost shell only, whereas LANL2DZ is the set with double-zeta functions for each of the two outermost shells. The ECP basis set employed throughout Chapter 4 (denoted LACV3P in Jaguar terminology) is also of Los Alamos type, but with full triple-zeta valence flexibility and polarization and diffuse functions on all atoms (comparable to the 6-311+- -G++ all-electron basis used elsewhere in this book). 

Slovenia), using the DFT implementation in the Gaussian03 code. Revision C.02 (8). The orbitals were described by a mixed basis set. A fully uncontracted basis set from LANL2DZ was used for the valence electrons of Re (9), augmented by two / functions Q =1.14 and 0.40) in the full optimization. Re core electrons were treated by the Hay-Wadt relativistic effective core potential (ECP) given by the standard LANL2 parameter set (electron-electron and nucleus-electron). The 6-3IG basis set was used to describe the rest of the system. The B3PW91 density functional was used in all calculations. 

The ECP method dates back to 1960, when Phillips and Kleinman suggested an approximation scheme for discarding core orbitals in band calculations [1]. They replaced the full Fock-operator with the following operator ... 

Figure 40 displays the predicted ECP versus distance from the bottom of the core for full power, normal operation, which includes the injection of 5 mg kg-1 O2 into the feedwater. All of the sections, except Section 7, display ECP values that lie... 

Scalar relativistic effects (e.g. mass-velocity and Darwin-type effects) can be incorporated into a calculation in two ways. One of these is simply to employ effective core potentials (ECPs), since the core potentials are obtained from calculations that include scalar relativistic terms [50]. This may not be adequate for the heavier elements. Scalar relativity can be variationally treated by the Douglas-Kroll (DK) [51] method, in which the full four-component relativistic ansatz is reduced to a single component equation. In gamess, the DK method is available through third order and may be used with any available type of wavefunction. 

Model core potential (MCP) methods replace core orbitals by a potential just as in ECP. On the other hand, MCP valence orbitals preserve the nodal structure of valence orbitals, unlike ECP valence orbitals. The expectation values of (r ) for the valence orbitals show that the results of MCP are closer to those calculated with all-electron orbitals when comparing MCP, ECP, and the all electron case. Comparisons between MCP and an all electron basis utilizing the full Breit-Pauli spin-orbit Hamiltonian based on multiconfigura-tional quasidegenerate perturbation theory (MCQDPT) calculations show good agreement between the two methods for hydrides of P, As, and Sb. The MCP based spin-orbit calculation appears to be a promising technique, but systematic studies of many different molecular systems are still needed to assess its characteristics and accuracy. 

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