Pseudoconvexity of the atomic electron density: Lower and upper bounds

1993 ◽  
Vol 47 (2) ◽  
pp. 936-943 ◽  
Author(s):  
Rodolfo O. Esquivel ◽  
Jiqiang Chen ◽  
M. J. Stott ◽  
Robin P. Sagar ◽  
Vedene H. Smith
Keyword(s):  
Electron Density ◽  
Upper Bounds ◽  
Atomic Electron ◽  
Lower And Upper Bounds ◽  
Atomic Electron Density

scholarly journals Refinement of proteins at subatomic resolution withMOPRO

2001 ◽  
Vol 34 (2) ◽  
pp. 214-223 ◽  
Author(s):  
Benoit Guillot ◽  
Laurence Viry ◽  
Regis Guillot ◽  
Claude Lecomte ◽  
Christian Jelsch
Keyword(s):  
High Resolution ◽  
Supramolecular Chemistry ◽  
Electron Density ◽  
Structure Factor ◽  
Atomic Electron ◽  
Gradient Algorithm ◽  
Large Structures ◽  
Diagonal Approximation ◽  
Atomic Electron Density ◽  
Very High

Crystallography at subatomic resolution permits the observation and measurement of the non-spherical character of the atomic electron density. Charge density studies are being performed on molecules of increasing size. TheMOPROleast-squares refinement software has thus been developed, by extensive modifications of the programMOLLY, for protein and supramolecular chemistry applications. The computation times are long because of the large number of reflections and the complexity of the multipolar model of the atomic electron density; the structure factor and derivative calculations have thus been parallelized. Stereochemical and dynamical restraints as well as the conjugate gradient algorithm have been implemented. A large number of the normal matrix off-diagonal terms turn out to be very small and the block diagonal approximation is thus particularly efficient in the case of large structures at very high resolution.

Erratum: Pseudoconvexity of the atomic electron density: A numerical study [Phys. Rev. A47, 4735 (1993)]

1999 ◽  
Vol 61 (1) ◽  
Author(s):  
Rodolfo O. Esquivel ◽  
Robin P. Sagar ◽  
Vedene H. Smith ◽  
Jiqiang Chen ◽  
M. J. Stott
Keyword(s):  
Electron Density ◽  
Numerical Study ◽  
Atomic Electron ◽  
Atomic Electron Density

Pseudoconvexity of the atomic electron density: A numerical study

1993 ◽  
Vol 47 (6) ◽  
pp. 4735-4748 ◽  
Author(s):  
Rodolfo O. Esquivel ◽  
Robin P. Sagar ◽  
Vedene H. Smith ◽  
Jiqiang Chen ◽  
M. J. Stott
Keyword(s):  
Electron Density ◽  
Numerical Study ◽  
Atomic Electron ◽  
Atomic Electron Density

scholarly journals Optimal local axes and symmetry assignment for charge-density refinement

2008 ◽  
Vol 41 (6) ◽  
pp. 1140-1149 ◽  
Author(s):  
Sławomir Domagała ◽  
Christian Jelsch
Keyword(s):  
Transition Metal ◽  
Metal Complexes ◽  
Charge Density ◽  
Electron Density ◽  
Transition Metal Complexes ◽  
Atomic Electron ◽  
Local Geometry ◽  
Symmetry Constraints ◽  
Atomic Electron Density

In the perspective of building an expanded electron-density library based on multipolar modelling for common chemical atom types, new consistent local axes systems are proposed. Optimal symmetry constraints can consequently be applied to atoms and a large number of multipole populations can be fixed to a zero value. The introduction of symmetry constraints in the multipolar refinement of small compounds allows a reduction in the number of multipolar parameters stored in the library and required for the description of the atomic electron density. In a refinement where the symmetry constraints are not applied, the use of optimal axes enables the deviations from the local pseudo-symmetry to be highlighted. The application of symmetry constraints or restraints on multipoles is more effective when the axes are in accordance with the local geometry of the atom and can lead to improved crystallographicRfreeresiduals. The new local axes systems, based on two or three atom neighbours, can also be usefully applied to the description of transition metal complexes.

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