Semiempirical cluster calculations

Theoretical treatments of the H—B and H—Al defects began with the semiempirical cluster calculations of DeLeo and Fowler (1985a, 1985b). Using the MNDO-cluster method, they found the hydrogen to be stable at the BC site in both the H—B and H—Al complexes. The fit along the (111) direction was tighter for the Al complex. In the calculations, it was... 

In recent years, there have been many attempts to combine the best of both worlds. Continuum solvent models (reaction field and variations thereof) are very popular now in quantum chemistry but they do not solve all problems, since the environment is treated in a static mean-field approximation. The Car-Parrinello method has found its way into chemistry and it is probably the most rigorous of the methods presently feasible. However, its computational cost allows only the study of systems of a few dozen atoms for periods of a few dozen picoseconds. Semiempirical cluster calculations on chromophores in solvent structures obtained from classical Monte Carlo calculations are discussed in the contribution of Coutinho and Canuto in this volume. In the present article, we describe our attempts with so-called hybrid or quantum-mechanical/molecular-mechanical (QM/MM) methods. These concentrate on the part of the system which is of primary interest (the reactants or the electronically excited solute, say) and treat it by semiempirical quantum chemistry. The rest of the system (solvent, surface, outer part of enzyme) is described by a classical force field. With this, we hope to incorporate the essential influence of the in itself uninteresting environment on the dynamics of the primary system. The approach lacks the rigour of the Car-Parrinello scheme but it allows us to surround a primary system of up to a few dozen atoms by an environment of several ten thousand atoms and run the whole system for several hundred thousand time steps which is equivalent to several hundred picoseconds. 

The electronic structure and chemical bonding in N vacancy containing TiN,(, ZrN,( and NbN, were first studied by Ivanovsky et al (1980) using the simplest semiempirical cluster calculations. As was found with the isostructural carbides, metalloid depletion of nitrides leads to the narrow-... 

A much more detailed and time-dependent study of complex hydrocarbon and carbon cluster formation has been prepared by Bettens and Herbst,83 84 who considered the detailed growth of unsaturated hydrocarbons and clusters via ion-molecule and neutral-neutral processes under the conditions of both dense and diffuse interstellar clouds. In order to include molecules up to 64 carbon atoms in size, these authors increased the size of their gas-phase model to include approximately 10,000reactions. The products of many of the unstudied reactions have been estimated via simplified statistical (RRKM) calculations coupled with ab initio and semiempirical energy calculations. The simplified RRKM approach posits a transition state between complex and products even when no obvious potential barrier... 

At the time of their inception, cluster calculations of adsorbate-zeolite systems were largely treated by using a semiempirical method. In the mid-... 

Perhaps the most accurate calculations performed to date are the MP2, LMP2, and LCCSD(TO) calculations on chorismate mutase (CM) and para hydroxy-benzoate-hydroxylase (PHBH) (the L in the acronyms indicates that local approximations were used, and TO is an approximate triples correction).41,42 These are coupled-cluster calculations that account for the effects of conformational fluctuations through an averaging over multiple pathways (16 for CM and 10 for PHBH). Initial structures were sampled from semiempirical QM/MM dynamics, using B3LYP/MM optimized reaction pathways. 

H. Bock, R. Dammel and B. Roth, Molecular state fingerprints and semiempirical hypersurface calculations, in Inorganic Rings and Clusters (Ed. A. H. Cowley), ACS Symp. Ser., 232, 139 (1983). 

The local interactions between the metal atoms and water molecules or ions have been obtained from semiempirical and ab initio quantum chemical cluster calculations (see below). This technique has been used by the groups of Spohr and Heinzinger, and later by Berkowitz and coworkers, for platinum surfaces with (100) and (111) surface geometry [48, 49, 52-54, 76] and also for mercury surfaces [40, 77-81]. 

At present, ab initio methods, density functional methods, and semiempirical methods serve as the major computational tools of quantum chemistry. There is an obvious trade-off between accuracy and computational effort in these methods. The most accurate results are obtained from high-level correlated ab initio calculations (e.g., multireference Cl or coupled cluster calculations with large basis sets) which also require the highest computational effort. On the other end of the spectrum, semiempirical MO calculations are very fast, and it is therefore realistic to... 

A bonding scheme for the (M u) clusters should account for the magnetic properties and observed electronic transitions. Several semiempirical MO calculations, for instance those of Cotton and Haas based on the Me group, or those of Robin and Kuebler on the (MeXi2) group, are available. A valence bond description has also been proposed. ... 

As in the FPLAPW method the further increasing of the superceU is sufficiently difficult that the dependence of the results on the superceU size was not studied in [718]. Such a study was made in semiempirical cyclic-cluster calculations of Li and... 

Semiempirical calculations of simple molecules on zeolite model clusters were carried out by Beran, Lochmann et al., Kustov et al. and Tasi et al. [64-69]. One of these procedures, the Self Consistent Charge (SCC)-Xa method has been successfully applied also to zeolites [70-76], because of its higher reliability in comparison to other methods in the determination of atomic charges within a reasonable computation time. A combination of semiempirical MO calculations and vibrational analysis supplies detailed information on zeolitic systems when consistently combined with experimental data [77, 78]. 

This work cast valuable light on these systems, as UV-vis spectroscopic analysis clearly identified a charge-transfer band centered at = 319 nm for 4b, for example, and excitation at this wavelength led to emission at Xeni = 480nm (Figure 15.3). Semiempirical (MNDO) calculations established that the highest occupied molecular orbital (HOMO) was primarily localized on the boron cage cluster, while the lowest occupied molecular orbital (LUMO) was mostly concentrated... 

This formalism was originally devised for single ionization of ground-state atoms, but has now been successfully applied to the calculation of electron impact ionization cross sections for a range of molecules, radicals, clusters, and excited state atoms. Like many of the semiempirical and semiclassical methods used to describe the electron impact process, the theory has its roots in work carried out by J.J. Thomson, who used classical mechanics to derive an expression for the atomic electron impact ionization cross section,2... 

At the low end of the hierarchy are the TS descriptors. This is the simplest of the four classes molecular structure is viewed only in terms of atom connectivity, not as a chemical entity, and thus no chemical information is encoded. Examples include path length descriptors [13], path or cluster connectivity indices [13,14], and number of circuits. The TC descriptors are more complex in that they encode chemical information, such as atom and bond type, in addition to encoding information about how the atoms are connected within the molecule. Examples of TC descriptors include neighborhood complexity indices [23], valence path connectivity indices [13], and electrotopological state indices [17]. The TS and TC are two-dimensional descriptors which are collectively referred to as TIs (Section 31.2.1). They are straightforward in their derivation, uncomplicated by conformational assumptions, and can be calculated very quickly and inexpensively. The 3-D descriptors encode 3-D aspects of molecular structure. At the upper end of the hierarchy are the QC descriptors, which encode electronic aspects of chemical structure. As was mentioned previously, QC descriptors may be obtained using either semiempirical or ab initio calculation methods. The latter can be prohibitive in terms of the time required for calculation, especially for large molecules. 

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