Optimal distinctiveness theory

The developed theory of two-phase laminar flow with a distinct interface which is based on a one-dimensional approximation, takes into account the major features of the process the inertia, gravity, surface tension and friction forces and leads to the physically realistic pattern of a laminar flow in a heated micro-channel. This allows one to use the present theory to study the regimes of flow as well as optimizing a cooling system of electronic devices with high power densities. 

HPLC theory could be subdivided in two distinct aspects kinetic and thermodynamic. Kinetic aspect of chromatographic zone migration is responsible for the band broadening, and the thermodynamic aspect is responsible for the analyte retention in the column. From the analytical point of view, kinetic factors determine the width of chromatographic peak whereas the thermodynamic factors determine peak position on the chromatogram. Both aspects are equally important, and successful separation could be achieved either by optimization of band broadening (efficiency) or by variation of the peak positions on the chromatogram (selectivity). From the practical point of view, separation efficiency in HPLC is more related to instrument optimization, column... 

Double-slash indicates a distinction between the level of theory at which a geometry was optimized and the level for which the energy was computed. For example, MP2/6-31G(2d,2p)//SCF/6-31G indicates a MP2/6-31G(2d,2p) calculation of a structure optimized at the SCF/6-31G level. 

Several accurate potentials for the water dimer have been developed by the present authors and collaborators using the regular SAPT approach [48,63] and its DFT-based version [81]. The most extensively tested potential, dubbed SAPT-5s for the five symmetry-distinct sites used in the fit, was based on about 2500 ab initio grid points—a much larger number of points than in any previous work on this dimer. The calculations employed a medium-size, interaction-optimized spdf-symmetry basis set with bond functions. By comparisons to the most elaborate single-point calculations [184], the SAPT interaction energies have been estimated to be accurate to about 0.3 kcal/mol or 5% with respect to basis set and theory level extensions. Recent SAPT calculations... 

The Roothaan-Hall equations are not applicable to open-shell systems, which contain one or more unpaired electrons. Radicals are, by definition, open-shell systems as are some ground-state molecules such as NO and 02. Two approaches have been devised to treat open-shell systems. The first of these is spin-restricted Hartree-Fock (RHF) theory, which uses combinations of singly and doubly occupied molecular orbitals. The closed-shell approach that we have developed thus far is a special case of RHF theory. The doubly occupied orbitals use the same spatial functions for electrons of both a and spin. The orbital expansion Equation (2.144) is employed together with the variational method to derive the optimal values of the coefficients. The alternative approach is the spin-unrestricted Hartree-Fock (UHF) theory of Pople and Nesbet [Pople and Nesbet 1954], which uses two distinct sets of molecular orbitals one for electrons of a spin and the other for electrons of / spin. Two Fock matrices are involved, one for each type of spin, with elements as follows ... 

An alternative to the conventional methods of quanfum chemistry is the state-specific theory, useful especially for excited states [1,42,131,132]. Such a theory is based on the choice and optimization of the function spaces for each excited state of interest, both at the zeroth-order and at the correlation level. This allows the systematic inclusion of relaxation and correlation effects to a very good degree of accuracy and the reliable description of phenomena and calculation of properties with small wavefunctions. Furthermore, physical and chemical concepts become more transparent while aspects of transferability of parfs of fhe energy or of the wavefunctions and their distinct effects on spectroscopy, on properties, and on chemical bonding in excited states may be systematized. 

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