Water molecule, symmetry

As an example, we show that the water molecule symmetry-adapted orbital = V iiHa - V iiHb has a vanishing overlap with the oxygen 2s orbital. The symmetry species of the oxygen 2s orbital is a, and that of the symmetry-adapted orbital is bz. From the character table in Table A.26 of Appendix A,... 

The aluminium ion, charge -I- 3. ionic radius 0.045 nm, found in aluminium trifluoride, undergoes a similar reaction when a soluble aluminium salt is placed in water at room temperature. Initially the aluminium ion is surrounded by six water molecules and the complex ion has the predicted octahedral symmetry (see Table 2.5 ) ... 

The functions put into the determinant do not need to be individual GTO functions, called Gaussian primitives. They can be a weighted sum of basis functions on the same atom or different atoms. Sums of functions on the same atom are often used to make the calculation run faster, as discussed in Chapter 10. Sums of basis functions on different atoms are used to give the orbital a particular symmetry. For example, a water molecule with symmetry will have orbitals that transform as A, A2, B, B2, which are the irreducible representations of the C2t point group. The resulting orbitals that use functions from multiple atoms are called molecular orbitals. This is done to make the calculation run much faster. Any overlap integral over orbitals of different symmetry does not need to be computed because it is zero by symmetry. 

There is always a transformation between symmetry-adapted and localized orbitals that can be quite complex. A simple example would be for the bonding orbitals of the water molecule. As shown in Figure 14.1, localized orbitals can... 

The largest protonated cluster of water molecules yet definitively characterized is the discrete unit lHi306l formed serendipitously when the cage compound [(CyHin)3(NH)2Cll Cl was crystallized from a 10% aqueous hydrochloric acid solution. The structure of the cage cation is shown in Fig. 14.14 and the unit cell contains 4 [C9H,8)3(NH)2aiCUHnOfiiai- The hydrated proton features a short. symmetrical O-H-0 bond at the centre of symmetry und 4 longer unsymmetrical O-H - 0 bonds to 4... 

If a proton is removed from one COOH group, as shown in Fig. 466, and transferred to a distant water molecule to form (HjO)+, the symmetry of the molecule is lost. On the other hand, if the proton is now removed from the other COOH group and transferred to a water mole-... 

Fig. 15. Librated states of the L-Trp9 11-13-15 carbonyls to achieve interaction with Na+ at the binding site. The numbers in parentheses are the distances of the oxygen atoms and Na+ from the two fold symmetry axis of the channel. The water molecules are to indicate that water is expected to be bound on each side of the cation as it passes through the channel.

Fig. 8.—Packing arrangement of four symmetry-related 2-fold helices of mannan II (6). (a) Stereo view of two unit cells approximately normal to flic frc-plane. The two chains in the back (open bonds) and the two in the front (filled bonds) are linked successively by 6-0H-- 0-6 bonds. The front and back chains, both at left and right, are further connected by 0-2 -1V -0-2 bridges, (h) Projection of the unit cell along the c-axis the a-axis is down the page. This highlights the two sets of interchain hydrogen bonds between antiparallel chains, distinguished by filled and open bonds. The crossed circles are water molecules at special positions.

The water molecule possesses two mirror planes of symmetry, as shown in Fig. 6-3. One mirror plane lies in the plane of the diagram through which the whole molecule reflects into itself across the plane. The other, through the oxygen nucleus in the yz plane of the figure, and shown by the dotted line, reflects Ha into Hb and vice versa. 

Molecules or ions in crystals often occupy special positions. In that case the site symmetry may not be higher than the symmetry of the free molecule or ion. For example, an octahedral ion like SbClg can be placed on a site with symmetry 4 if its Sb atom and two trans Cl atoms are located on the fourfold axis a water molecule, however, cannot be placed on a fourfold axis. 

C2 Z = 4 Dx = 1.41 R = 0.102 for 4,115 intensities. The structure is a 3 2 complex of proflavine and CpG. The asymmetrical unit contains one CpG molecule, 1.5 proflavine molecules, 0.5 sulfate ion, and 11 5 water molecules. Two CpG molecules form an antiparallel, Watson-Crick, miniature duplex, with a proflavine intercalated between the base pairs through the wide groove. The double helix has exact (crystallographic), two-fold symmetry, and the crystallographic, two-fold axis passes through the C-9-N-10 vector of the intercalated proflavine. A second and a third molecule of proflavine are stacked on top of the C - G pairs ... 

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