Interpreting atomic coordinates Atomic connectivity The calculation ...

Interpreting atomic coordinates A crystal structure refinement leads toestimates of model parameters– coordinates, temperature factors andoccupancies What matters chemically is atomicconnectivity (bonding) and packing Need interatomic distances and structuraldrawingsAtomic connectivity Interatomic distances can be used todetermine the presence of bonds– chemical bonds often lead to well definedinteratomic distances»Csp 3 -C sp 3 ~ 1.53A»Csp 2 -Csp 2 ~ 1.32A Distances are readily calculated fromatomic fractional coordinatesThe calculation of bond lengths Position of atom in unit cell– r =xa +yb +zc Vector between two atoms– r = xa + yb + zc Calculate length from In most space groups there is more than onesymmetry equivalent of an atom in the unitcell– you need to take this into account whencalculating bond lengths– r.r = |r| 2 Symmetry equivalent atomsBenzene Space group Pbca. Each molecule has itscenter at an inversion centerErrors on bond lengthsRefinement give estimate of errors on x,y,z– this information can be used to estimate errors onderived quantities such as bond lengthsFor two atoms each with a positional standarddeviation of 0.005A– bond length = [0.005 2 + 0.005 2 ] 1/2– assumes atomic positions are not correlatedBond length calculation programs take intoaccount correlations

Structural diagrams Many different types– ball and stick (PLUTO)– thermal ellipsoids (ORTEP)– coordination polyhedra (STRUPLO) Many different styles– perspective– projection–stereoORTEP ORTEP plots are standard for smallmolecules. The orientation and size of theellipse tells you about the presence ofthermal motion, static disorder, and errorsin the model.ORTEP plotsCoordination polyhedraMonoclinicZrMo 2 O 8TrigonalZrMo 2 O 8Bond valence sumsBond strength - bond length In general there is a correlation betweenbond length and bond strength Pauling recognized that for some types ofstructure you could associate a valence witheach ‘bond’ between a central atom and itsneighbors and that these bond valenciesshould sum to give a number equal to theatomic valence of the central atom

Brown’s work I.D. Brown developed the bond valencesum idea– analysis of databases allowed the determinationthe relationship between bond length and bondvalence for a given pair of atoms– bond valence s ij = exp(r 0 -r ij /B)»r 0 and B are parameters from data base analysis»r ij is experimentally observed interatomic distance They can be used to check the accuracy of acrystal structure They can be used to locate missing atoms They have been used aids to structuresolution– atomic valence V i = s ijUse of bond valence sums