Generation constrained

CONstrained GENeration (CONGEN) is software for generating all isomers for a given structure and is part of the DENDRAL project. 

We first describe formula-based generation of molecular structures. This starts with a molecular formula and takes further restrictions into account, which often allow an enormous and necessary - reduction of the search space. Then we discuss the handling of restrictions, i.e. constrained generation. 

In contrast to orderly generation, constrained generation does not use a fixed order of generation, rather it is controlled by the constraints. The strategy for adding bonds... 

R. Laue, T. Grllner, M. Meringer, and A. Kerber. Constrained Generation of Molecular Graphs, volume 69 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pages 319-332. American Mathematical Society, 2005. 

Monte Carlo simulations generate a large number of confonnations of tire microscopic model under study that confonn to tire probability distribution dictated by macroscopic constrains imposed on tire systems. For example, a Monte Carlo simulation of a melt at a given temperature T produces an ensemble of confonnations in which confonnation with energy E. occurs witli a probability proportional to exp (- Ej / kT). An advantage of tire Monte Carlo metliod is tliat, by judicious choice of tire elementary moves, one can circumvent tire limitations of molecular dynamics techniques and effect rapid equilibration of multiple chain systems [65]. Flowever, Monte Carlo... 

When the wave function is completely general and pennitted to vary in the entire Hilbert space the TDVP yields the time-dependent Schrodinger equation. However, when the possible wave function variations are in some way constrained, such as is the case for a wave function restricted to a particular functional form and represented in a finite basis, then the corresponding action generates a set of equations that approximate the time-dependent Schrodinger equation. 

Shielding and Stabilization. Inclusion compounds may be used as sources and reservoirs of unstable species. The inner phases of inclusion compounds uniquely constrain guest movements, provide a medium for reactions, and shelter molecules that self-destmct in the bulk phase or transform and react under atmospheric conditions. Clathrate hosts have been shown to stabiLhe molecules in unusual conformations that can only be obtained in the host lattice (138) and to stabiLhe free radicals (139) and other reactive species (1) similar to the use of matrix isolation techniques. Inclusion compounds do, however, have the great advantage that they can be used over a relatively wide temperature range. Cyclobutadiene, pursued for over a century has been generated photochemicaHy inside a carcerand container (see (17) Fig. 5) where it is protected from dimerization and from reactants by its surrounding shell (140). 

The primary photochemical act, subsequent to near-uv light (wavelengths <400 nm) absorption by Ti02 particles, is generation of electron—hole pairs where the separation (eq. 3) into conduction band electrons (e g ) and valence band holes (/lyB ) faciUtated by the electric field gradient in the space charge region. Chemically, the hole associated with valence band levels is constrained at... 

The steepest descent method is quite old and utilizes the intuitive concept of moving in the direction where the objective function changes the most. However, it is clearly not as efficient as the other three. Conjugate gradient utilizes only first-derivative information, as does steepest descent, but generates improved search directions. Newton s method requires second derivative information but is veiy efficient, while quasi-Newton retains most of the benefits of Newton s method but utilizes only first derivative information. All of these techniques are also used with constrained optimization. 

The reaction path formed by a sequence of points generated by constrained optimizations may be discontinuous. For methods where two points are gradually moved from the reactant and product sides (e.g. saddle and LTP), tliis means that tlie distance between end-points does not converge towards zero. 

---