Difference electron density

Fig. 7.57 Plot of the isomer shift 5 of the 36.2 keV Mdssbauer transition of Os versus Dirac-Fock values for the electron density differences at the Os nuclei in free ion 5d configurations. The numbers of the data points refer to the numbering of the compounds in Table 7.9 (from [258])...

Fig. 11a and b. a) Total electron density of the systems HoO-Li+ in the plane of the water molecule, b) Electron density differences upon complex formation shown in the same plane (maps from Ref. 208))... 

Fig. 12. Integrated electron density and integrated electron density differences in the system HaO-Li+. (cf. Ref.

Fig. 15. Integrated electron density differences in the system H2CO-Li+ as a function of the 0-Li+ distance (cf. Ref. 109>. The spacing of the lines is 0.01 (eo) for continuous lines and 0.0025 ( o) for broken lines...

Fig. 20. Integrated electron density differences in the systems H2O-IJ+ and H2CO-Li+ calculated in the CNDO/2 approximation. (Wave functions taken from Ref. 224))...

Fig. 18. The active site region of the electron density difference map between N-carbobenzoxy-L-alanine-elastase at —SS C and native elastase at the same temperature. The resolution is 3.5 A. The bilobed feature is consistent with the binding of the alanyi portion of the substrate to the oxygen of the catalytic serine, with weak interaction of the carbobenzoxy group to the surface of the enzyme.

We do not distinguish here this density functional definition of exchange energy from that of Hartree-Fock (HF). This simplification is well-justified, if the HF electron density and the exact electron density differ only slightly [40]. Similarly, the coupling-constant averaged exchange-correlation hole is the usual... 

FIG. 11.11 Electron-density difference maps on Li2BeF4 calculated with all reflections < sin 6/1 = 0.9 A"1 (81 K). (a) Based on the neutral atom procrystal model, (b) based on the ionic model. Contour levels are drawn at intervals of 0.045 eA"3.1 Full lines for positive density, dashed lines for negative and zero density. The standard deviation, estimated from [2Lff2(F0)]1/2N, is 0.015 eA-3. Source Seiler and Dunitz (1986). 

After the crystal structure of the compound has been solved, or deduced, from the X-ray data, the initial parameters (atomic positions, bond lengths, and bond angles) are only approximate and have to be improved. The usual method employed is that of least-squares refinement, although electron-density difference-maps and trial-and-error procedures are also used. Electron-density difference-maps give the approximate difference between the actual structure and the trial structure. 

The development of synchrotron radiation as an X-ray source404 416 418 has permitted accumulation of data for electron density difference maps in less than 1 s and it is expected that such data can eventually be acquired in 1 ps.419-421 If a suitable photochemical reaction can be initiated by a picosecond laser flash, a substrate within a crystalline enzyme can be watched as it goes through its catalytic cycle. An example is the release of inorganic phosphate ions from a "caged phosphate" (Eq. 3-49) and study of the reaction of the released phosphate with glycogen phosphorylase (Chapter 12).422/423... 

FIGURE 24. Electron-density difference maps of207. (a) Section in the plane of atoms C1, C3 and C5, approximately perpendicular to the C2—C4 axis of the propellane unit. Note the density peaks in the centers of the three-membered rings, around the projection of C2 and C4. Contour lines are at 0.05 e A 3 intervals, (b) Section in the plane of the three-membered ring C2, C3, C4. Contour lines are at 0.025 e A 3 intervals. Full lines mark positive, dashed lines negative regions. Reproduced by permission of Verlag Helvetica Chimica Acta from Reference 319... 

Fig. 23. Stereodrawings of the dinucleotide phosphonate UpcA bound to RNase-S. Histidine 119 is in position IV where it is forced to be by the adenosine. Lysine 41 is in the position found in DNP-Lys 41 derivative. In the native protein it is lower and closer to the phosphate position, but it is not long enough to contact the phosphate. The UpcA is an interpretation of the 2-A resolution electron density difference map and the CH, which is bound to the phosphorus is crowding His 119. Some further adjustments may be necessary.

Fig. 15a-c. Scheme of the side chains arrangement of macromolecule (a), function of distribution of electron density Aq along a normal to the smectic plane (b) and one-dimensional correlation function Yi(x) for polymers V (1) and VI (2) (c),08) a) 1 — main chain 2 — mesogenic groups 3 — alkyl group b) Aq — electron density difference between ordered I, and disordered 12 regions E — width of the transitional region... 

As predicted by electron density difference plots (see text). o,p = ortho- and para-directing (relative to silicon) m = meta-directing (relative to silicon). 

Electron density difference matrices that correspond to the transition energies in the EP2 approximation may be used to obtain a virtual orbital space of reduced rank [27] that introduces only minor deviations with respect to results produced with the full, original set of virtual orbitals. This quasiparticle virtual orbital selection (QVOS) process provides an improved choice of a reduced virtual space for a given EADE and can be used to speed up computations with higher order approximations, such as P3 or OVGF. Numerical tests show the superior accuracy and efficiency of this approach compared to the usual practice of omission of virtual orbitals with the highest energies [27],... 

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