Hartree-Fock calculation electron density with

A more complex set of functionals utilizes the electron density and its gradient. These are called gradient-corrected methods. There are also hybrid methods that combine functionals from other methods with pieces of a Hartree-Fock calculation, usually the exchange integrals. 

As a final note, be aware that Hartree-Fock calculations performed with small basis sets are many times more prone to finding unstable SCF solutions than are larger calculations. Sometimes this is a result of spin contamination in other cases, the neglect of electron correlation is at the root. The same molecular system may or may not lead to an instability when it is modeled with a larger basis set or a more accurate method such as Density Functional Theory. Nevertheless, wavefunctions should still be checked for stability with the SCF=Stable option. ... 

Complexes of bulky substituted phenanthrolines [Pt(N-N)LX2] (L, X both monodentate N-N, e.g. 2,9-dimethyl- 1,10-phenanthroline) can be 5-coordinate tbp when a good 7r-acceptor (e.g. C2H4) is present or 4-coordinate with monodentate phenanthrolines. Hartree-Fock calculations indicate that the 7r-acceptors reduce the electron density at platinum so that the metal can accept charge from another donor. Species of this kind may be involved in alkene hydrogenation [138]. 

To use Equation 2 to determine s electron density diflFerences, it must be "calibrated —i.e., source-absorber or absorber-absorber combinations must be found for which the 5 electron density diflFerence is known. The most common method for calibrating the isomeric shift formula is to measure isomeric shifts for absorbers with diflFerent numbers of outer shell 5 electrons—e.g., by using compounds with the absorbing atoms in different valence states. The accuracy of this method depends on how much is known about the chemical bonds in suitably chosen absorber compounds, in particular about their ionicity and their hybridization. t/ (0) 2 can be obtained for an outer 5 electron from the Fermi-Segre formula or preferably from Hartree-Fock calculations. 

A traditional object for testing new methods is germanium. The ehemieal bonding in Ge was studied by X-ray diffraction, Hartree-Fock methods and density functional theory for which good agreement of electron densities was reached. Hence the ESP calculated from eleetron diffraction were also compared with the above results obtained from other methods. 

Duncanson and Coulson [242,243] carried out early work on atoms. Since then, the momentum densities of aU the atoms in the periodic table have been studied within the framework of the Hartree-Fock model, and for some smaller atoms with electron-correlated wavefunctions. There have been several tabulations of Jo q), and asymptotic expansion coefficients for atoms [187,244—251] with Hartree-Fock-Roothaan wavefunctions. These tables have been superseded by purely numerical Hartree-Fock calculations that do not depend on basis sets [232,235,252,253]. There have also been several reports of electron-correlated calculations of momentum densities, Compton profiles, and momentum moments for He [236,240,254-257], Li [197,237,240,258], Be [238,240,258, 259], B through F [240,258,260], Ne [239,240,258,261], and Na through Ar [258]. Schmider et al. [262] studied the spin momentum density in the lithium atom. A review of Mendelsohn and Smith [12] remains a good source of information on comparison of the Compton profiles of the rare-gas atoms with experiment, and on relativistic effects. 

Two commonly used approximations are the Hartree-Fock approach and density-functional theory (DFT). The Hartree-Fock approach approximates the exact solution of the Schrodinger equation using a series of equations that describe the wavefunc-tions of each individual electron. If these equations are solved explicitly during the calculation, the method is known as ab initio Hartree-Fock. The less expensive (i.e., less time-consuming) semi-empirical methods use preselected parameters for some of the integrals. DFT, on the other hand, uses the electronic density as the basic quantity, instead of a many-body electronic wavefunction. The advantage of this is that the density is a function of only three variables (instead of 3N variables), and is simpler to deal with both in concept and in practice. 

There is another physical phenomenon which appears at the correlated level which is completely absent in Hartree-Fock calculations. The transient fluctuations in electron density of one molecule which cause a momentary polarization of the other are typically referred to as London forces. Such forces can be associated with the excitation of one or more electrons in molecule A from occupied to vacant molecular orbitals (polarization of A), coupled with a like excitation of electrons in B within the B MOs. Such multiple excitations appear in correlated calculations their energetic consequence is typically labeled as dispersion energy. Dispersion first appears in double excitations where one electron is excited within A and one within B, but higher order excitations are also possible. As a result, all the dispersion is not encompassed by correlated calculations which terminate with double excitations, but there are higher-order pieces of dispersion present at all levels of excitation. Although dispersion is not necessarily a dominating contributor to H-bonds, this force must be considered to achieve quantitative accuracy. Moreover, dispersion can be particularly important to geometries that are of competitive stability to H-bonds, for example in the case of stacked versus H-bonded DNA base pairs. ... 

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