Effective core potentials presence

To explore the dyotropic rearrangement of silyl hydroxylamines, Schmatz, Klinge-biel and colleagues studied the behaviour of 0-lithium-Af,Af-bis(f-butyldimethylsilyl) hydroxylamine 207 in the presence of chlorotrimethylstannane (equation 62). They found that the primarily formed Af,Af-bis(f-butyldimethylsilyl)-0-(trimethylstannyl)hydroxyl-amine 208 underwent a dyotropic rearrangement to form 209. This reaction mechanism is corroborated by quantum chemical calculations partly employing an effective core potential for tin. 

This analysis has been tested for Xe2+ and Au2 within the effective core potential approximation (65). Four sets of calculations have been carried out nonrelativistic, first-order relativistic, fully relativistic, and first-order nonrelativistic (relativistic wave function with nonrelativistic Hamiltonian). The computed Rc values were 3.01, 2.67, 2.58, and 3.14 A, respectively, for Au2 and 3.24, 3.18, 3.19, and 3.24 A for Xe2+. For these cases then, the analysis of Schwarz et al. is clearly inappropriate. It may be the case that the nonrelativistic electronic contraction stabilized in first-order calculations is independent of the usual relativistic AO contraction. However since the contraction is only stable in the presence of the relativistic Hamiltonian, it is still a relativistic orbital contraction, but now at a molecular level. 

Despite this ubiquitous presence of relativity, the vast majority of quantum chemical calculations involving heavy elements account for these effects only indirectly via effective core potentials (ECP) [8]. Replacing the cores of heavy atoms by a suitable potential, optionally augmented by a core polarization potential [8], allows straight-forward application of standard nonrelativistic quantum chemical methods to heavy element compounds. Restriction of a calculation to electrons of valence and sub-valence shells leads to an efficient procedure which also permits the application of more demanding electron correlation methods. On the other hand, rigorous relativistic methods based on the four-component Dirac equation require a substantial computational effort, limiting their application in conjunction with a reliable treatment of electron correlation to small molecules [9]. 

Some scalar relativistic effects are included implicitly in calculations if pseudopotentials for heavy atoms are used to mimic the presence of core electrons there are several families of pseudopotentials available the effective core potentials (ECP) (Cundari and Stevens 1993 Hay and Wadt 1985 Kahn et al. 1976 Stevens et al. 1984), energy-adjusted pseudopotentials (Cao and Dolg 2006 Dolg 2000 Peterson 2003 Peterson et al. 2003), averaged relativistic effective potentials (AREP) (Hurley et al. 1986 Lajohn et al. 1987 Ross et al. 1990), model core potentials (MCP) (Klobukowski et al. 1999), and ab initio model potentials (AIMP) (Huzinaga et al. 1987). 

The intrinsically relativistic nature of the electronic structure of the halogen monoxides is dictated by the presence of two spin-orbit components in the ground electronic state. Any accurate characterization of the XO Xj and X2 rii/2 potentials must therefore treat relativistic effects explicitly. However, diis requirement greatly increases the cost and complexity of the ab initio effort(26), resulting in few relativistic potential surface calculations such as the 10 study by Roszak et al.(21) One more frequently finds relativistic effects incorporated as corrections to non-relativistic energies or treated through the use of effective core potentials (23). 

The Pauli repulsion must also be simulated the problem that the valence shell orbitals are not simply the lowest solutions of the effective Schrodinger (or Hartree-Fock) equation in the presence of the electrostatic core potential must be addressed. 

Although certain of the above-mentioned theories are moderately successful in representing the experimental data of CF4 -t- CH and other fluorocarbon + hydrocarbon mixtures, experimental values of and x are required. At present there is no satisfactory method of obtaining these parameters a priori. Scott, in his 1958 review, considered the various possible factors that could lead to a weakening of the unlike interactions in such mixtures. He concluded that the three most significant were the presence of non-central forces, differences in ionization potential, and differences in size of the two component molecules. The use of the Kihara potential together with the Hudson and McCoubrey rule takes account of all these effects and thus the undoubted success of the Knobler treatment is not surprising. Criticisms could be levelled at his use of a spherically symmetric potential for substances such as n-hexane but the use of a more realistic potential such as the Kihara line-core potential is hardly justified until reliable experimental values for the ionization potentials of the fluorocarbons become available. 

An analogous situation is encountered in a theta-solution, with the quantity of interest now being the effective interaction potential between two solute molecules, or in the polymer case, between two monomers. The curve (b) in Fig. 2.11 represents the situation in a good solvent, where the potential is repulsive at all distances. Each solute molecule is surrounded by a hydrate-shell of solvent molecules and this shell has to be destroyed when two solvent molecules are to approach each other. The situation in a poor solvent is different, due to there being a preference for solute-solute contacts. Here, the solute molecules effectively attract each other and repulsion occurs only at short distances, then for the same reason as for the real gases, namely the presence of hard core interactions. For poor solvents, therefore, u r) has an appearance similar to the pair interaction potential in a van-der-Waals gas and a shape like curve (a) in Fig. 2.11. 

---