Minimization of energy

Jack A and M Levitt 1978. Refinement of Large Structures by Simultaneous Minimization of Energy and R-factor. Acta Crystallographica A34 931-929. 

Hartree-Fock MO approach, the minimization of energy should provide the most accurate description of the electronic field. The mathematical problem is to define each of the terms, with being the most challenging. The formulation carmot be done exactly, but various approaches have been developed and calibrated by comparison with experimental data. The methods used most frequently by chemists were developed by A. D. Becke. " This approach is often called the B3LYP method. The computations can be done with... 

Jack A, Levitt M (1978) Refinement of large structures by simultaneous minimization of energy and R factor. Acta Crystallogr A 34 931-935... 

Majozi, T., 2009. Minimization of energy use in multipurpose batch plants using heat storage an aspect of cleaner production. J. Cleaner Prod., 17 945-950. 

Another important point deals with selectivity in the abstraction of -protons on equally substituted carbons. In a iyw-periplanar transition state as described above, the minimization of energy concept implies proton abstraction with a maximum of orbital overlap and a minimum of molecular deformation. Consequently, conformations possessing the more acute dihedral angles for bonds H —C—C—O wiU be favored (Scheme 2l/. 

Catalysis represents a possible tool to convert selectively carbohydrates through environmentally friendlier processes. Homogeneous catalysts are widely used in industry mainly because of their high activity, thus allowing a minimization of energy, cost, and labor. However, these catalytic processes present some problems... 

J.M. Ball and R.D. James. Fine phase mixtures as minimizers of energy. Arch. Rat. Mech. Anal., 100 13-52, 1987. 

Level 5 Energy Integration. This level involves a large spectrum of design activities dealing with the minimization of energy and material utilities. These can be classified as follows ... 

The determining principle in the formation of a structure is the principle of energy minimization which, for nondirectional forces, is expressed geometrically as the maximum filling principle. If the minimization of energy is attained when the structural units occupy low-symmetry positions, their proper symmetry does not completely coincide with the symmetry of the crystallographic positions. 

The overall approach to determining the structure of a protein is to use computational power to take into account concurrently (1) the known sequence of the amino acids in the protein (2) the known molecular structure of each of those amino acid residues, including bond distances and angles (3) the known planar structure of the peptide group (4) internuclear distances and interresidue bond angles, as determined from NMR data (5) correlations of chemical shifts and structural features and (6) minimization of energy and avoidance of unreasonable atomic contacts. There are a number of ways to handle the computations and to derive the molecular structure, but all of them depend critically on the data supplied by NMR. 

For any wave number in the Brillouin Zone we seek the lowest energy solution by minimizing K k iAk> with respect to in direct analogy to the minimization of energy for the system based upon two basis states, as taken up in... 

Density functional techniques are, in principle, based on minimization of energy as a functional of the electron density p(r). In practice the density is represented in terms of Kohn-Sham orbitals, and therefore the implementation takes the same broad form [Equation (2)] as Schrodinger based methods. We will forgo extensive discussion of specific forms of [ ] until Section 2 below, and consider simple examples to illustrate the use simulated annealing here. 

Keywords Green chemistry alternative feedstocks benign reagents catalytic synthetic pathways natural processes biocatalysis alternative solvents safer chemicals alternative reaction conditions minimization of energy consumption... 

Alternative reaction conditions for efficiency and selectivity Minimization of energy consumption. 

Ball J. M. and James R. D., Fine Phase Mixtures as Minimizers of Energy, Arch. Rational Mech. Anal. 100, 13 (1987). 

A co-generation plant to produce shaft power and steam Minimization of energy loss and total cost while maximizing shaft power. NIMBUS The process was simulated using BALAS. Hakanen et al. (2006)... 

Fig. 2.10. Optimized conformation of A-acetyl-Pro-Gly-Phe as obtained by the minimization of energy from the initial form as deduced from the REDOR experiment [18].

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