Lone-pair functions

A non-empirical alternative supporting a value X Anb close to 0.2 which has been adopted for lone-pair weights in the preceding treatment was presented later [59], using the concept of eccentric functions to enlarge the valence basis set of heteroatoms by means of lone-pair functions (LPF). The NH3 molecule was studied as a test without and with a LPF in the vicinity of nitrogen. A reference calculation with Slater orbitals of exponents = 1-90, ... 

The members of the /oqr set that are predominately - y and xy have some j z and A z character, respectively, mixed into them so that they are reoriented to lie between the M—L bonds. The Cg set is mainly az andyz. Thexy andx - character mixed into them provides maximal antibonding to the ligand lone-pair functions. The intermixing of atomic functions is due to nothing more than our choice of a coordinate system. It is certainly not the normal one for an octahedron however, it is the natural choice for a C v ML3 tmit. 

As an example of the results obtained consider correlated calculations on ammonia. Bartlett used three basis sets in his 1993 paper (1) was the Sadlej POL basis, (2) was POL with one set of d functions chosen to reproduce the molecular hyperpolarizability of hydrogen, and (3) was (2) plus lone pair functions, one s set and one p set located in the lone pair direction. 

Basis sets can be extended indefinitely. The highest MOs in anions and weakly bound lone pairs, for instance, are very diffuse maybe more so than the most diffuse basis functions in a spht valence basis set. In this case, extra diffuse functions must be added to give a diffuse augmented basis set. An early example of such a basis set is 6-31+G [26]. Basis sets may also be split more than once and have many sets of polarization functions. 

Molecular orbitals are not unique. The same exact wave function could be expressed an infinite number of ways with different, but equivalent orbitals. Two commonly used sets of orbitals are localized orbitals and symmetry-adapted orbitals (also called canonical orbitals). Localized orbitals are sometimes used because they look very much like a chemist s qualitative models of molecular bonds, lone-pair electrons, core electrons, and the like. Symmetry-adapted orbitals are more commonly used because they allow the calculation to be executed much more quickly for high-symmetry molecules. Localized orbitals can give the fastest calculations for very large molecules without symmetry due to many long-distance interactions becoming negligible. 

The next step is attack at the carbon carrying the carbonyl function by the lone pair of nitrogen atom, giving rise to a new cyclic intermediate... 

Neutral compounds such as boron trifluoride and aluminum chloride form Lewis acid-base complexes by accepting an electron pair from the donor molecule. The same functional groups that act as lone-pair donors to metal cations can form complexes with boron trifluoride, aluminum chloride, and related compounds. 

Diffuse functions are large-size versions of s- and p-type functions (as opposed to the standard valence-size functions). They allow orbitals to occupy a larger region of spgce. Basis sets with diffuse functions are important for systems where electrons are relatively far from the nucleus molecules with lone pairs, anions and other systems with significant negative charge, systems in their excited states, systems with low ionization potentials, descriptions of absolute acidities, and so on. 

In standard quantum-mechanical molecular structure calculations, we normally work with a set of nuclear-centred atomic orbitals Xi< Xi CTOs are a good choice for the if only because of the ease of integral evaluation. Procedures such as HF-LCAO then express the molecular electronic wavefunction in terms of these basis functions and at first sight the resulting HF-LCAO orbitals are delocalized over regions of molecules. It is often thought desirable to have a simple ab initio method that can correlate with chemical concepts such as bonds, lone pairs and inner shells. A theorem due to Fock (1930) enables one to transform the HF-LCAOs into localized orbitals that often have the desired spatial properties. 

The first correction is that due to diffuse sp basis functions. These are known to be important for anions and molecules with lone pairs. The correction is obtained at MP4 level, comparing the energy of the 6-311 -I-G and the 6-3IIG basis sets. 

The basic concept of activation in hetero-Diels-Alder reactions is to utilize the lone-pair electrons of the carbonyl and imine functionality for coordination to the Lewis acid. The coordination of the dienophile to the Lewis acid changes the FMOs of the dienophile and for the normal electron-demand reactions a decrease of the LUMO and HOMO energies is observed leading to a better interaction with... 

Nucleophiles have an electron-rich site, either because they are negatively charged or because they have a functional group containing an atom that has a lone pair of electrons. Electrophiles have an electron-poor site, either because they are positively charged or because they have a functional group containing an atom that is positively polarized. 

---