An algorithm for the simultaneous superposition of a structural series

@article{Kearsley1990AnAF,
  title={An algorithm for the simultaneous superposition of a structural series},
  author={Simon K. Kearsley},
  journal={Journal of Computational Chemistry},
  year={1990},
  volume={11}
}
  • S. Kearsley
  • Published 1 October 1990
  • Chemistry
  • Journal of Computational Chemistry
A procedure is delineated for finding the optimal superposition of a series of chemical structures. Quaternions are used to represent the absolute orientation of the structures–rotations of the structures need never be carried out explicitly. The Rational Function Optimization method is used to minimize a simultaneous superposition residual similar to the one given by Gerber and Müller. The robustness of the method is illustrated by comparing a series of conformations of a polyene carotenoid. 

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References

SHOWING 1-10 OF 14 REFERENCES

Superimposing several sets of atomic coordinates

A procedure is described which determines the best rotations to superimpose M rigid n-point objects, such that the weighted sum of mutual squared deviations is minimized. Apart from providing an easy

On the orthogonal transformation used for structural comparisons

Rotation matrices that minimize or maximize the sum of the squared distances between corresponding atoms for two structures are found using a constrained least-squares procedure solved analytically

On the representatation of orientation space

New sets of variables are studied which should lead to significantly improved numerical stability and efficiency for computer stimulation studies of rigid classical molecules. The search for these

Comparison of the convergence characteristics of some iterative wave function optimization methods

The convergence properties of several iterative methods for the optimization of orbitals and configuration mixing coefficients in multiconfigurational electronic wave functions are compared. All of

A note on the rotational superposition problem

A rotation axis vector with magnitude tan (θ/2) for a rotation angle θ and a closely related unit vector of dimension 4 are used to show that : (i) the quadratic residual (weighted sum of squares of

Search for stationary points on surfaces

Algorithms for finding local minima, maxima, and saddle points on surfaces, starting from an arbitrary point are presented. These algorithms are based on making a local approximation to the surface

Singularity‐free static lattice energy minimization

Comparative analyses are made of static lattice energy minimization procedures based on Newton or quasi‐Newton algorithms with rigid body orientations being parametrized in terms of Euler angles or

A discussion of the solution for the best rotation to relate two sets of vectors

A method is discussed for obtaining the best proper rotation to relate two sets of vectors.

Practical Methods of Optimization

The aim of this book is to provide a Discussion of Constrained Optimization and its Applications to Linear Programming and Other Optimization Problems.