Small-core potentials

Besides the reduction of frozen-core errors when going from large-core to medium-core or small-core potentials also the valence correlation energies obtained in pseudopotential calculations become more accurate since the radial nodal structure is partially restored [97,98]. Clearly the accuracy of small-core potentials is traded against the low computational cost of the large-core po-... 

A priori it is not clear if effective core potentieds, which have for example been adjusted to reproduce atomic energy differences in wave function based calculations or to reproduce the shape of the valence orbitals outside the core, can successfully be used in density functional calculations. For so-called small core potentieds, where the atomic core has been chosen such that core and valence densities have little overlap, test calculations have shown that results from allelectron and pseudopotential calculations were virtually the same [74]. A related investigation on gold compounds comes to the same conclusion [75]. It is however not recommended to perform density functional investigations with large-core pseudopotentials that have been adjusted in wave function calculations. One example for a leirge-core situation is a transition metal where the vedence d orbiteds are (of course) treated explicitly, while the s emd p orbitals of the same principal quantum number are considered core orbitals. From an energetic view, such a separation seems well justified. However, problems arise since the densites of the s,p, and d orbitals of the same principal quantum number have considerable overlap. 

The methods listed thus far can be used for the reliable prediction of NMR chemical shifts for small organic compounds in the gas phase, which are often reasonably close to the liquid-phase results. Heavy elements, such as transition metals and lanthanides, present a much more dilficult problem. Mass defect and spin-coupling terms have been found to be significant for the description of the NMR shielding tensors for these elements. Since NMR is a nuclear effect, core potentials should not be used. 

This chapter provides only a brief discussion of relativistic calculations. Currently, there is a small body of references on these calculations in the computational chemistry literature, with relativistic core potentials comprising the largest percentage of that work. However, the topic is important both because it is essential for very heavy elements and such calculations can be expected to become more prevalent if the trend of increasing accuracy continues. 

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]. 

The present work represents a preliminary attempt to incorporate many of these strategies in conjunction with the use of small-core relativistic effective core potentials for obtaining compact series of correlation consistent basis sets... 

Gropen,0., Wahlgren,U. and Pettersson,L.G.M. (1982), Effective core potential calculations on small molecules containing transition metal ions , Chem.Phys. 66, 459... 

The one-center approximation allows for an extremely rapid evaluation of spin-orbit mean-field integrals if the atomic symmetry is fully exploited.64 Even more efficiency may be gained, if also the spin-independent core-valence interactions are replaced by atom-centered effective core potentials (ECPs). In this case, the inner shells do not even emerge in the molecular orbital optimization step, and the size of the atomic orbital basis set can be kept small. A prerequisite for the use of the all-electron atomic mean-field Hamiltonian in ECP calculations is to find a prescription for setting up a correspondence between the valence orbitals of the all-electron and ECP treatments.65-67... 

Before any computational study on molecular properties can be carried out, a molecular model needs to be established. It can be based on an appropriate crystal structure or derived using any technique that can produce a valid model for a given compound, whether or not it has been prepared. Molecular mechanics is one such technique and, primarily for reasons of computational simplicity and efficiency, it is one of the most widely used technique. Quantum-mechanical modeling is far more computationally intensive and until recently has been used only rarely for metal complexes. However, the development of effective-core potentials (ECP) and density-functional-theory methods (DFT) has made the use of quantum mechanics a practical alternative. This is particularly so when the electronic structures of a small number of compounds or isomers are required or when transition states or excited states, which are not usually available in molecular mechanics, are to be investigated. However, molecular mechanics is still orders of magnitude faster than ab-initio quantum mechanics and therefore, when large numbers of... 

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. 

In general, for each acid HA, the HA-(H20) -Wm model reaction system (MRS) comprises a HA (H20) core reaction system (CRS), described quantum chemically, embedded in a cluster of Wm classical, polarizable waters of fixed internal structure (effective fragment potentials, EFPs) [27]. The CRS is treated at the Hartree-Fock (HF) level of theory, with the SBK [28] effective core potential basis set complemented by appropriate polarization and diffused functions. The W-waters not only provide solvation at a low computational cost they also prevent the unwanted collapse of the CRS towards structures typical of small gas phase clusters by enforcing natural constraints representative of the H-bonded network of a surface environment. In particular, the structure of the Wm cluster equilibrates to the CRS structure along the whole reaction path, without any constraints on its shape other than those resulting from the fixed internal structure of the W-waters. 

Relativistic effective small-core core potentials with triple-zeta... 

Use of the SBKJC and CRENBL ECPs appear to be less prevalent in the current literature. The SBKJC ECP, also called the consistent effective potential (CEP), developed by Stevens and coworkers is also large core. The CRENBL ECP developed by La John and coworkers is small core, where the 10 4d electrons are also classified as valence electrons, leaving 36 electrons to be treated as core electrons in the ECP. 

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