ECP

Unlike semiempirical methods that are formulated to completely neglect the core electrons, ah initio methods must represent all the electrons in some manner. However, for heavy atoms it is desirable to reduce the amount of computation necessary. This is done by replacing the core electrons and their basis functions in the wave function by a potential term in the Hamiltonian. These are called core potentials, elfective core potentials (ECP), or relativistic effective core potentials (RECP). Core potentials must be used along with a valence basis set that was created to accompany them. As well as reducing the computation time, core potentials can include the effects of the relativistic mass defect and spin coupling terms that are significant near the nuclei of heavy atoms. This is often the method of choice for heavy atoms, Rb and up. 

The energy obtained from a calculation using ECP basis sets is termed valence energy. Also, the virial theorem no longer applies to the calculation. Some molecular properties may no longer be computed accurately if they are dependent on the electron density near the nucleus. 

There are several issues to consider when using ECP basis sets. The core potential may represent all but the outermost electrons. In other ECP sets, the outermost electrons and the last filled shell will be in the valence orbital space. Having more electrons in the core will speed the calculation, but results are more accurate if the —1 shell is outside of the core potential. Some ECP sets are designated as shape-consistent sets, which means that the shape of the atomic orbitals in the valence region matches that for all electron basis sets. ECP sets are usually named with an acronym that stands for the authors names or the location where it was developed. Some common core potential basis sets are listed below. The number of primitives given are those describing the valence region. 

Dolg Also called Stuttgart sets, this is a collection of ECP sets currently under development by Dolg and coworkers. These sets are popular for heavy main group elements. 

Ah initio methods can yield reliable, quantitatively correct results. It is important to use basis sets with diffrise functions and high-angular-momentum polarization functions. Hyperpolarizabilities seem to be relatively insensitive to the core electron description. Good agreement has been obtained between ECP basis sets and all electron basis sets. DFT methods have not yet been used widely enough to make generalizations about their accuracy. 

The ah initio methods available include HF, DFT, MPn, MCSCF, Cl, and CC. In the version tested, the Cl methods were still under development. There are a large number of basis sets available, including ECP sets. Dynamic calculations can be performed at ah initio levels of theory. 

Laboratory experiments have shown that IGSCC can be mitigated if the electrochemical potential (ECP) could be decreased to —0.230 V on the standard hydrogen electrode (SHE) scale in water with a conductivity of 0.3 ]lS/cm (22). This has also been demonstrated in operating plants. Equipment has been developed to monitor ECP in the recirculation line and in strategic places such as the core top and core bottom, in the reactor vessel during power operation. 

Whereas addition of hydrogen to feedwater helps solve the O2 or ECP problem, other complications develop. An increase in shutdown radiation levels and up to a fivefold increase in operating steam plant radiation levels result from the increased volatiUty of the short-Hved radioactive product nitrogen-16, N, (7.1 s half-life) formed from the coolant passing through the core. Without H2 addition, the in the fluid leaving the reactor core is in the form of nitric acid, HNO with H2 addition, the forms ammonia, NH, which is more volatile than HNO, and thus is carried over with the steam going to the turbine. 

Basis sets for atoms beyond the third row of the periodic table are handled somewhat differently. For these very large nuclei, electrons near the nucleus are treated in an approximate way, via effective core potentials (ECPs). This treatment includes some relativistic effects, which are important in these atoms. The LANL2DZ basis set is the best known of these. 

Optimize these three molecules at the Hartree-Fock level, using the LANL2DZ basis set, LANL2DZ is a double-zeta basis set containing effective core potential (ECP) representations of electrons near the nuclei for post-third row atoms. Compare the Cr(CO)5 results with those we obtained in Chapter 3. Then compare the structures of the three systems to one another, and characterize the effect of changing the central atom on the overall molecular structure. 

Effective core potentials (ECP) replace the atomic core electrons in valence-only ab initio calculations, and they are often used when dealing with compounds containing elements from the second row of the periodic table and above. 

These ECPs were traditionally presented as a linear combination of functions of the type... 

Ab initio ECPs are derived from atomic all-electron calculations, and they are then used in valence-only molecular calculations where the atomic cores are chemically inactive. We start with the atomic HF equation for valence orbital Xi whose angular momentum quantum number is 1 ... 

Rappe, Smedley and Goddard (1981) Stevens, Basch and Krauss (1984) Used for ECP (effective core potentitil) calculations Dunning s correlation consistent basis sets (double, triple, quadmple, quintuple and sextuple zeta respectively). Used for correlation ctilculations Woon and Dunning (1993)... 

The gain by using ECPs is largest for atoms in die lower part of the periodic table, especially those where relativistic effects are important. Since fully relativistic results... 

F eCp(CsH4) 2SiCl2,6, 19 Fe2SnC,4Cl204 FeCp(CO)2 2SnCl2, 2,19 Fe2SnC16H664... 

Petrone A Grego S Chinellato S Puppin P ECP Enichem Polimeri (Crain Communications Ltd.)... 

Electric chemical polish (ECP) and electric chemical mechanical polish (ECMP) [53] have been developed as promising methods for global planarization of LSI fabrication and abrasive-free polish. 

Presently it is not possible to relax the Cu lattice at the SCF level, since from a computational point of view it is composed of two different kinds of Cu atoms (those with and without the ECP). Also questions of wetting, i.e. whether the chemisorbed Be4 would prefer to remain as a tetrahedron (or distorted tetrahedron) or to spread out to a single layer are still not amenable to ab initio study. These questions have not yet been investigated using the parameterized model approach, because of the problems associated with modeling Be2 and Beg as accurately as larger Be clusters. Nonetheless, these preliminary results show that the parameterized and ab initio calculations can be used to complement each other in a multicomponent system, just as for single component systems. 

---