Atomic efficiency calculation

Two useful measures of the potential environmental acceptability of chemical processes are the E factor [12-18], defined as the mass ratio of waste to desired product and the atom efficiency, calculated by dividing the molecular weight of the desired product by the sum of the molecular weights of all substances produced in the stoichiometric equation. The sheer magnitude of the waste problem in chemicals manufacture is readily apparent from a consideration of typical E factors in various segments of the chemical industry (Table 1.1). 

Figure P32 shows four routes to 2-methylhept-2-ene-6-one, an important synthon for terpenoid preparation. These routes are taken from the schemes shown in Figures 9.6, 9.7, 9.9 and 9.11 in Chapter 9. What is the atom efficiency of each route (For the present purposes, consider only stoichiometric reagents and ignore solvents and catalysts.) If these routes were the result of a brainstorming exercise by your development team, what would be your priority order for testing them out in the laboratory How would this choice be affected by the atom efficiency calculations ...

The size of the move in step 3 of the above procedure will affect the elhciency of the simulation. In this case, an inefficient calculation is one that requires more iterations to obtain a given accuracy result. If the size is too small, it will take many iterations for the atom locations to change. If the move size is too large, few moves will be accepted. The efficiency is related to the acceptance ratio. This is the number of times the move was accepted (step 5 above) divided by the total number of iterations. The most efficient calculation is generally obtained with an acceptance ratio between 0.5 and 0.7. 

The atom utilization or atom efficiency concept is a useful tool for rapid evaluation of the amount of waste that will be generated by alternative routes to a particular product. It is calculated by dividing the molecular weight of the desired product by the sum total of the molecular weights of all the substances produced in the stoichiometric equation of the reaction(s) in question. The comparison is made on a theoretical (i.e. 100% chemical yield) basis. Fig. 2.8 shows a simple illu.stration of the concept for ethylene oxide manufacture. 

G. Gaigalas, Z. Rudzikas, Ch. Froese Fischer, An efficient approach for spin-angular integrations in atomic structure calculations, J. Phys. B At. Mol. Opt. Phys., 30, 3747-3771 (1997). 

Sun YY, Kim YH, Lee K, Zhang SB (2008) Accurate and efficient calculation of van der Waals interactions within density functional theory by local atomic potential approach. J Chem Phys 129 154102... 

B. Robson, E. Platt. Refined models for computer calculations in protein engineering. Calibration and testing of atomic potential functions compatible with more efficient calculations. J Mol Biol. 1986, 188, 259-281. 

In the calculations based on effective potentials the core electrons are replaced by an effective potential that is fitted to the solution of atomic relativistic calculations and only valence electrons are explicitly handled in the quantum chemical calculation. This approach is in line with the chemist s view that mainly valence electrons of an element determine its chemical behaviour. Several libraries of relativistic Effective Core Potentials (ECP) using the frozen-core approximation with associated optimised valence basis sets are available nowadays to perform efficient electronic structure calculations on large molecular systems. Among them the pseudo-potential methods [13-20] handling valence node less pseudo-orbitals and the model potentials such as AIMP (ab initio Model Potential) [21-24] dealing with node-showing valence orbitals are very popular for transition metal calculations. This economical method is very efficient for the study of electronic spectroscopy in transition metal complexes [25, 26], especially in third-row transition metal complexes. 

To turn the LCMTO method into an efficient calculational technique, in the following we introduce the atomic-sphere approximation and parametrise the energy dependence of the one-, two-, and three-centre or overlap integrals appearing in (5.40) by means of the results in Sect.3.5. The resulting procedure constitutes the so-called linear muffin-tin orbital (LMTO) method. 

As expected, the performance of all competing order-N methods depends on the system under investigation, the accuracy needed, the amount of experimental information available, the questions that need to be answered, and also computer-related parameters (processors, parallel architectures, etc.). All approaches have their pluses and minuses. It is also clear that the increased mathematical effort will "pay off" if at all) only beyond a critical number of atoms (around 100-1000 or so) below that, the normal route with cubic scaling is faster. Nonetheless, the same locality arguments may be used to derive linear-scaling methods for the extremely efficient calculation of electronic correlation (see Section 2.13). 

AE atom efficiency and F C value for common biomass primary products and some derivatives. Calculated straight from pentose or glucose-based biomass. Cell cellulose, Hcell hemicellulolse, G glucose, X xylose, Mw. molecular weight, co-r co-reagents, co-p co-products, GVL y-valerolactone, LA Levulinic acid, dimethylTHF dimethyltetrahydrofuran stoichiometry of product formation with respect to the feedstock... 

---