Semi-Empirical Theoretical Treatments

The Wd estimated from the RASCI is compared with other theoretical calculations [46, 54] in Table V. The present DF estimate of Wd deviates by 21%(29%) from the SCF (RASSCF) estimate of Kozlov et al. [46] and by 17% from the semiempirical result of Kozlov and Labzovsky [54], while our RASCI result departs by 6% (3%) from the SCF-EO (RASSCF-EO) treatment of Kozlov et al. [46] and is in good agreement with the semi-empirical result of Kozlov and Labzovsky. At this juncture, we emphasize that our computed ground state dipole moment of BaF (p(. = 3.203 debyes) is also reasonably close to experiment p(. = 3.2 debyes (see Table 5 of Ref. 38). 

Thus, in contrast to preceding MM approaches explicit treatment of electronic polarisability is integral to a semi-empirical QM approach and promises excellent prospects for quantitative theoretical modelling of carbohydrates across a range of condensed phase environments. The results of the PM3CARB-1 model do however indicate in line with classical force field approaches [65, 73] that perhaps greater... 

Semi-empirical quantum-mechanical methods combine fundamental theoretical treatments of electronic behavior with parameters obtained from experiment to obtain approximate wavefunctions for molecules composed of hundreds of atoms20-22. Originally developed in response to the need to evaluate the electronic properties of organic molecules, especially those possessing unusual structures and/or chemical reactivity in organic chemistry,... 

A theoretical study of degenerate Boulton-Katritzky rearrangements concerning the anions of the 3-hydroxyimi-nomethyl-l,2,5-oxadiazole has been carried out by using semi-empirical modified neglect of diatomic overlap (MNDO) and ab initio Hartree-Fock procedures. Different transition structures and reactive pathways were obtained in the two cases. Semi-empirical treatment shows asymmetrical transition states and nonconcerted processes via symmetrical intermediates. By contrast, ab initio procedures describe concerted and synchronous processes involving symmetrically located transition states <1998JMT(452)67>. 

Physical Models. Two basic approaches are used to quantify secondary ion intensities physical models and empirical methods. The physical models consist of several theoretical or semi-empirical treatments developed to simulate secondary ion emission [3,48-50]. Although several models have been developed (see Werner L3j for a recent review) and continue to be applied, the use of calibration standards (empirical methods) consistently give better results, e.g., accuracies of a factor of 2-3 for physical models compared to 10-20% for empirical methods. 

The theoretical treatment of transport at the nanoscale (see introduction in [65-70]) requires the combined use of different techniques which range from minimal model Hamiltonians, passing through semi-empirical methods up to... 

An approximate treatment for taking into account a—it interaction has been developed in the case of long polyenes 126>, and non-empirical calculations have been carried out for the various transitions of formaldehyde along the same lines as for ethylene 127,128,129)n) jn view of the intricacies of theoretical considerations concerning excited states, it is rather fortunate that calculations limited to the 71-electron systems can be forced to agree with experiment by introducing semi-empirical corrections on well-chosen matrix elements. 

The methods used to estimate the effects of plasticization on Tg fall into two general classes namely, semi-empirical equations based on considerations of "free volume" and the much more sophisticated theoretical treatments based on statistical thermodynamics. Neither type of approach is able to provide accurate predictions on a consistent basis. The equations based on free volume [30,67,121] have generally been favored over the statistical mechanical methods (see [122] for an example) for use in practical applications, because of their greater simplicity. For example, the Tg of a plasticized polymer can be estimated very roughly by using the following two equations ... 

The idea of the quality of a theoretical calculation is difficult to quantify but can be notionally separated into two parts. First, and from a strictly computational viewpoint, one must discover how sensitive the computed quantities are to the user-defined features of a given computational scheme (e.g. basis set size and electron correlation treatment in ab initio methods, parameter values in empirical and semi-empirical methods). Secondly, how well does the method reproduce actual experiment. 

Two theoretical analyses of physicochemical parameters of carbon-containing molecules have been effected. " C(ls) core-electron binding energies, calculated from atomic charges obtained by an electronegativity equilization procedure, and enthalpies of formation, molecular geometries, dipole moments, and first ionization potentials, derived from an improved version (MINDO/3) of the MINDO semi-empirical SCF MO treatment," have all been shown to be in excellent agreeement with experimentally derived values. The results of a theoretical study... 

For a long time the excited states of I2 were a challenge to theoretical chemistry methods. The first reliable theoretical estimates of the excited states of I2 was done by Mulliken in 1940 [104], using a semi-empirical treatment with the help of experimental data. One of the first ab initio spectroscopic calculations was made by Li et al [105] using large-core and shape-consistent... 

The definition of the gas-phase acidity through reaction (7.3) implies that this quantity is a thermodynamic state function. Thus, one could use quantum chemical approaches to obtain gas-phase acidities from the theoretically computed enthalpies of the species involved. However, two points must be noted before one proceeds A chemical bond is being broken and an anion is being formed. Thus, one may anticipate the need for a proper treatment of electronic correlation effects and also of basis sets flexible enough to allow the description of these effects and also of the diffuse character of the anionic species, what immediately rules out the semi-empirical approaches. Hence, our discussion will only consider ab initio (Hartree-Fock and post-Hartree-Fock) and DFT (density functional theory) calculations. 

The kinds of cumulenes covered with this treatment include allenes, bu-tatrienes, and pentatetraenes on the one side, and ketenes, ketene imines, car-bodiimides, diazocompounds, and thioketenes on the other side. The molecular spectra under consideration include photoelectron (pe), electronic uv absorption spectra, C-, N- ( N-), and H-nmr spectra as well as molar rotations and optical rotatory dispersions (ORD). Molecular properties related to theoretical indices (not observables), such as electron densities, are discussed on a semi-empirical CNDO/S or at initio STO-3G MO level. 

Mathematical formalism has been developed using semi-empirical considerations [36, 37]. Computer simulation smdies show that resulting equation predicts oscillations. Attempt has been made to provide justification on the bases of Navier-Stokes equation but it is open to question. Dimensional analysis has recently been employed for investigating the phenomena [31]. Flow dynamics and stability in a density oscillator have been examined by Steinbock and co-workers [38], They have related it to Rayleigh-Taylor instability of two different dense viscous liquids. A theoretical description has been presented which is based on a one-fluid model and a steady state approximation for a two-dimensional flow using Navier-Stokes equation. However, the treatment is quite complex and cannot explain the generation of electric potential oscillations. 

The electronic structure and transitions of cyclic disulphides have been calculated by a semi-empirical method, which indicated that absorption at 250—300 nm was due to -> absorption maxima were related to the dihedral angles about the sulphur-sulphur bond. The optical properties of 1,2-dithiolans and 1,2-dithians have also been accounted for in a theoretical treatment, and the photo-catalysed homolytic scission of the sulphur-sulphur bond in cyclic disulphides has been investigated spectroscopically. Spectrophotometry indicated that there was particularly strong interaction between ethylene chloride and 1,2-dithian, compared to that observed for acyclic disulphides. ... 

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