Level-density parameterization

In O Fig. 5.9 the experimentally observed 0 level distances in the transmission resonance groups of Pu (fiiU circles) are compared to calculations of the level density in the first minimum according to different mcxlels. The soUd fine on the left side of the figure corresponds to the level distances in the first minimum calculated in the framework of the back-shifted Fermi gas model in the parameterization by Rauscher et al. (1997). In order to reproduce the experimentally observed 0 level distances, this curve has had to be shifted by 2.25 MeV, corresponding to the ground-state energy in the second minimum of Pu. For comparison, also shown are the level distances in the first minimum calculated with the Bethe formula and within the constant temperature formalism in a parameterization by von Egidy et al. (1988). 

One disadvantage is that the lower levels of theory must be able to describe all atoms in the inner regions of the molecule. Thus, this method cannot be used to incorporate a metal atom into a force field that is not parameterized for it. The effect of one region of the molecule causing polarization of the electron density in the other region of the molecule is incorporated only to the extent that the lower levels of theory describe polarization. This method requires more CPU time than most of the others mentioned. However, the extra time should be minimal since it is due to lower-level calculations on smaller sections of the system. 

In the original MIT bag model the bag constant B 55 MeV fm-3 is used, while values B 210 MeV fm-3 are estimated from lattice calculations [34], In this sense B can be considered as a free parameter. We found, however, that a bag model involving a constant (density independent) bag parameter B, combined with our BHF hadronic EOS, will not yield the required phase transition in symmetric matter at pr 6po 1/fm3 [28]. This can only be accomplished by introducing a density dependence of the bag parameter. (The dependence on asymmetry is neglected at the current level of investigation). In practice we use a Gaussian parameterization,... 

During last decades the DFT based methods have received a wide circulation in calculations on TMCs electronic structure [34,85-88]. It is, first of all, due to widespread use of extended basis sets, allowing to improve the quality of the calculated electronic density, and, second, due to development of successful (so called - hybrid) parameterizations for the exchange-correlation functionals vide infra for discussion). It is generally believed, that the DFT-based methods give in case of TMCs more reliable results, than the HER non-empirical methods and that their accuracy is comparable to that which can be achieved after taking into account perturbation theory corrections to the HER at the MP2 or some limited Cl level [88-90]. 

In summary, semiempirical methods such as AMI or PM3 have the advantage of being computationally very fast and allowing large molecules to be computed with minimal computer resources. The semiempirical methods are not nearly as accurate as the ab initio methods or even density functional methods. Some disadvantages of these methods include the following (1) they can be applied only to molecules containing elements for which they have been parameterized, (2) the errors are less systematic than at an ab initio level of calculation, and (3) semiempirical methods depend on the availability of accurate experimental data (or reliable ab initio data). 

Parameterizing the Bond Stretching Term A forcefield can be parameterized by reference to experiment (empirical parameterization) or by getting the numbers from high-level ab initio or density functional calculations, or by a combination of both approaches. For the bond stretching term of Eq. 3.2 we need stretch ancl 4q-Experimentally, stretch could be obtained from IR spectra, as the stretching frequency of a bond depends on the force constant (and the masses of the atoms involved) [8], and Zeq could be derived from X-ray diffraction, electron diffraction, or microwave spectroscopy [9],... 

To properly parameterize a molecular mechanics forcefield by calculations only high-level ab initio (or density functional) calculations would actually be used, but this does not affect the principle being demonstrated... 

Another approach to treating the boundary between covalently bonded QM and MM systems is the connection atom method, 125,126 in which, rather than a link atom, a monovalent pseudo-atom is used. This connection atom is parameterized to give the correct behaviour of the partitioned covalent bond, and has been implemented at semi-empirical molecular orbital (AMI and PM3)125 and density functional theory 126 levels of QM theory. It has been suggested that the connection atom approach is more accurate than the standard link atom approach.125... 

Measured size distributions of salt particles are monomodal and can by parameterized by the power law, with the index varying within 0.97-4.2 (average 2.3-2.6). The density of MSA particles is close to 2.35 — 2.40 g/m The spatial distribution of Cn MSA (r > 1 pm) for different regions of the world ocean can be illustrated by the following values in the Pacific Ocean Cn = (1.2-1.5) cm in the Indian Ocean (0.9-1.0) cm" near the Australian coastline 0.4 cm near the boundaries of the Antarctic ice sheet (1.8-2.1) cm" and near the Black Sea coastline (0.32-1.93) cm" [8]. The vertical distribution of Cn MSA has some specific features. A maximum of Cn distribution is often observed at altitudes of several hundred meters (apparently, because of a decrease in the Cn MSA near the water surface, resulting from the capture of salt particles by sea waves). At altitudes 2-3 km the value of Cn MSA constitutes < 1 % of the total Cn value, which is explained by the cloud filter . However, over land, near the coastline, at an altitude of 3 km, Cn MSA is somewhat higher than at the same level over the sea surface. This is connected with a more intensive turbulence over land. In general, sea-salt aerosol particles have to be chemically composed of dried sea water 88.7% chlorides, 70.8% sulfates, 0.3% carbonates, and 0.2% other salts. 

---