Semi-empirical treatments

The neglect of electron-electron interactions in the Extended Hiickel model has several consequences. For example, the atomic orbital binding energies are fixed and do not depend on charge density. With the more accurate NDO semi-empirical treatments, these energies are appropriately sensitive to the surrounding molecular environment. 

A common way to benefit from the ability to combine different molecular orbital methods in ONIOM is to combine a DFT or ab-initio description of the reactive region with a semi-empirical treatment of the immediate protein environment, including up to 1000 atoms. Due to the requirement for reliable semi-empirical parameters, as discussed in Section 2.2.1, this approach has primarily been used for non-metal or Zn-enzymes. Examples include human stromelysin-1 [83], carboxypeptidase [84], ribonucleotide reductase (substrate reaction) [85], farnesyl transferase [86] and cytosine deaminase [87], Combining two ab-initio methods of different accuracy is not common in biocatalysis applications, and one example from is an ONIOM (MP2 HF) study of catechol O-methyltransferase [88],... 

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>. 

Machlin (1974, 1977) developed a semi-empirical treatment which used a constant set of nearest-neighbour interactions and was one of the earliest semi-empirical attempts to obtain the relative enthalpies of formation between different crystal structures. This successfiilly predicted the correct ground states in a substantial number of cases, but the treatment was generally restricted to transition metal combinations and a limited number of crystal structures. 

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 explosion of interest in supercritical fluids during the past decade has seen a bridging of these extremes, a movement toward balance. Investigators have sought to understand and develop applications on the basis of underlying physicochemical principles, and recent reports of semi-empirical treatment of supercritical solvent properties have shifted these fluids squarely into the mainstream of chemical research. 

Linear stationary systems with regular fluxes are realized mostly in laboratory conditions, whereas technology deals with systems in nonsteady-state and/or random fluxes. Nevertheless, the linear stationary model is enough simple and sometimes effective for semi-empirical treatment of various experimental data (first of all adsorption-desorption) even obtained on materials obviously prepared in conditions of random fluxes. 

Comparison of the observed value of by with the known contact interaction constant of the Mn+ ion gives a value for cf of0.573. In other words the 3da and 4s hybridisation is a nearly perfect one-to-one mixture. The dipolar hyperfine constant c depends upon a sum of contributions from the 3d unpaired electrons in the 9atomic orbitals, a value which agrees well with the measured value of —48.199 MHz. As we have commented elsewhere, the quadrupole coupling constant involves all of the electrons, and is not readily amenable to a simple semi-empirical treatment. 

Barriers to internal rotation have been calculated using various semi-empirical treatments erratic results have been found in a number of... 

Our quantum chemical calculations were carried out with the Spartan 02 and Spartan 04 programs by Wavefunction, Inc., Irvine, California, USA. Spartan 02 was used only to obtain the Raman spectra. All other calculations were done with Spartan 04 using the RB3LYP method with the 6-3IIG base set. In most cases, the final geometry was computed directly from the initial construct. In other cases, the final calculation was preceded by MMFF molecular mechanics and PM3 semi-empirical treatments. 

Though the sum-over-states formalism of the previous section can be used in semi-empirical treatments, e.g. Pierce [29], it is not appropriate in ab initio calculations for anything but the smallest of chemical systems. This is because of the need for a highly extensive and highly electron-correlated pseudo-spectral series. Faute de mieux, one must turn to less accurate ab initio treatments. For... 

In 1956 Muller et al. presented a semi-empirical treatment based on a method suggested by Saika and Slichter for fluorine chemical shifts. This attributed major changes in P chemical shifts to variations in the magnitude of the second order paramagnetic term Since the contribution of s electrons was zero, and that of electrons in closed shells and valence electrons on other atoms could be neglected, the effect on the shielding constant for a single 3/> electron was expressed as equation (10)—... 

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 approximations introduced in the derivation of London s expression (orthogonality of the basis wave functions) were discussed by COOLIDGE and JAMES /29/ and more recently by SLATER /30/. It seems that the accuracy of calculation is lowered not too much by these approximations, as it is derived from a comparison with a more exact semi-empirical treatment of PORTER and KARPLUS /31/ based on the formulas (37.1), (38.1) and (39.1). 

K. P. Black and M. A. Rosenberg, Semi-empirical treatment of wave transformation outside and inside the breaker line. Coastal Eng. 16, 313-345 (1992). 

Semi-Empirical Treatment of Steady-State Mass Transfer For the cathode reaction of a reversible electrode reaction (Reaction 1.64), without considering migration and convection, the electrode reaction rate equals the diffusion rate of Ox at the electrode surface ... 

Surface Density Profile in Liquid Metals A Semi-empirical Treatment of the Screening Effect, in Proc. 6th Int. Conf. on Liquid and Amorphous Metals, Z. Phys. C 1S6S, 445-450. 

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