Computational Consideration

It has already been stated that the evaluation of the non-bonded energy is by far the most time-consuming. Consider a series of calculations of linear alkanes CH3(CH2)n-2CH3. The number of individual contributions to each energy term is given in Table 2.4. 

As can be seen from Table 2.4, the number of bonded contributions, bend and 

The introduction of a cut-off distance does not by itself lead to a significant computational saving, since all the distances must be computed prior to the decision of 

The use of a cut-off distance reduces the fonnal scaling in the large system limit from atom - atoni since the non-bonded contributions now only are evaluated within the locSl sphere determined by the cut-off radius. However, a cut-off distance of 10 A is so large that the large system limit is not achieved in practical calculations. The actual scaling is thus more like where n is perhaps 1.5-1.8. In static applications, 

Nevertheless, an R interaction requires a larger cut-off than the van der Waals 

The use of a cut-off distance reduces the formal scaling in the large system limit from atom atom since the non-bonded contributions now only are evaluated within the 

There are different ways of implementing the cut-off approximation. The simplest is to neglect all contributions if the distance is larger than the cut-off. This is in general not a very good method as the energy function becomes discontinuous. Derivatives of the energy function also become discontinuous, which causes problems in optimization 

From Table 2.7 it is clearly seen that vdw becomes small (less than -0.01 kj/mol) beyond a distance of -10 A. The electrostatic interaction reaches the same level of 

Distance (A) Svdw - dipole-dipole point charges net charges 

---

It is our purpose in this review to present a brief summary of some of the main results from the applications of our FOIST based approach to selective control of photodissociation. The formal and computational considerations of this method are summarised in section 2 and in section 3, we discuss some representative results from our applications. Some concluding remarks summarising the main results and avenues for further research are collected in section 4. 

Rodbard, D, Estimation of Molecular Weight by Gel Filtration and Gel Electrophoresis II. Statistical and Computational Considerations. In Methods of Protein Separation Catsimpoolas, ed. Plenum Press New York, 1976 Vol. 2, p 181. 

The first computational consideration is that of obtaining the solutions of the unperturbed problem, Eq. (15), and the approach taken in the present study is to utilize the Crystal program [1] as it has been successfully used for studies in molecular crystals [10-12,15], A given crystalline orbital, (k,r), such as that required for the matrix elements necessary given by the integral in Eq. (16), is expressed as a linear combination of Bloch functions, a ,(k) and atomic orbitals, (k,r) [1]... 

The computational considerations in the calculation of poles and corresponding FDAs may be outlined by rewriting the propagator eqn. (61) as... 

Natural Atomic Orbital and Natural Bond Orbital Analysis 230 9.7 Computational Considerations 232 9.8 Examples 232 References 234 10 Molecular Properties 235 104 Examples 236 References 294 12 Transition State Theory and Statistical Mechanics 296 12.1 Transition State Theory 296 12.2 Statistical Mechanics 298 12.2.1 ans 299 12.2.2 300... 

Computational Considerations grids approach saturation, i.e. in general the energy will depend on the number (and... 

If wavefunctions are calculated using semiempirical methods that assume zero overlap between atomic orbitals (AOs) on different atomic centers, then a MuUiken population analysis [84, 85] can be applied to the calculated TD to yield transition monopoles distributed over each atomic center. Such an approach has proven to be effective [82] an advantage being that the interaction between distributed monopoles can be computed considerably faster then that between TDCs. At the same time, the basic topology of the donor-acceptor... 

---