AH„ molecules

An electric dipole consists of two equal and opposite charges separated by a distance. AH molecules contain atoms composed of positively charged nuclei and negatively charged electrons. When a molecule is placed in an electric field between two charged plates, the field attracts the positive nuclei toward the negative plate and the electrons toward the positive plate. This electrical distortion, or polarization of the molecule, creates an electric dipole. When the field is removed, the distortion disappears, and the molecule reverts to its original condition. This electrical distortion of the molecule is caHed induced polarization the dipole formed is an induced dipole. 

Using these assumptions and a classical partitioning function, integrated over the coordinates and momenta of aH molecules, a universal function was defined ... 

This correlation only holds if charged and uncharged species are treated separately. Apparently, there is no direct relationship between D and the charge on the heavy atom of an AH molecule. It is expected that a more electronegative element is less likely to accommodate a positive charge, but AH species do not necessarily bear a positive charge on A CHj (C = -0.13 e), SiHj (Si = +1.13 e), GeH+ (Ge = +0.51 e), BH5 (B = -0.11 e), and AIH5 (A1 = +0.75 e). 

FIGURE 8. Correlation diagram for the trigonal bipyramidal (D3h) and square pyramidal (C4u) forms of an AH molecule, via a C structure... 

These curves are then used to explain and predict (ij the shapes and (ii) the electronic spectra and associated characteristics of A112 molecules. AH. molecules containing 4 valency electrons should be linear in their ground states. AH2 molecules containing 5—8 valency electrons should be bent in their ground states. 

Bent AH2 Molecules.—A bent AH molecule belongs to the symmetry class C2r. The definitions of the symbols appropriate to the non-localized orbitals of such a molecule are given below. The z axis bisects the HAH angle and lies in the molecular plane. The y axis also lies in the molecular plane and is parallel with the H H line. C2(z) means a rotation by 180° about the z axis. wave function does not or does change sign when one of the symmetry- operations C2(z) or av(y) is carried out. 

On going from one acid to another, IP(H) of course is constant and D(H—AR ) might be expected to be fairly closely correlated with AH°ion, particularly when the molecules HAR have similar electronic structures. Hence for any isoelectronic set of AH molecules the heat of ionization would be expected to be linearly related to the electron affinity of the... 

Another way of rationalizing these results is to treatx, y, z as px, py, p- orbitals of central atom A in an AH molecule. A molecule with C2v symmetry is H2S. A convention to set up the Cartesian coordinates for this molecule is as follows. Take the principle axis (C2 in this case) as the z axis. Since H2S is planar, we take the x axis to be perpendicular to the molecular plane. Finally, the y axis is taken so as to form a right-handed system. Following this convention, the px, py, p- orbitals on sulfur in a H2S molecule are shown in Fig. 6.3.2. When the orientations of these orbitals are examined, it is obvious that the p- orbital is symmetric with respect to all four operations of the C2v point group E, C2, other hand, the px orbital is symmetric with respect to E and arv(xz), but antisymmetric with respect to C2 and [Pg.182]

Recall that the character of an operation is equal to the number of vectors unshifted by that operation. Previously, for AH molecules, in determining 7h, the Is orbitals on the hydrogen atoms are spherically symmetric. In the present case, however, the 2p orbitals have directional properties. Take [Pg.222]

It is well known that proton transfer can be induced by electronic excitation of molecules which present a strong difference in acidity between their ground and excited states. Generally, the absorption spectrum of the hydrogen-bonded complex AH B is only slightly modifed compared with the free AH molecule. 

As the hydroxy-aromatic molecule is a weak acid in the ground state, one can assume that in all AH B clusters the equilibrium is mainly displaced towards the neutral form [AH(B) —process I]. When the AH molecule in the cluster is excited by a first photon (process II), two types of behavior can be observed ... 

Relaxation of the neutral excited complex towards the ground state with emission of fluorescence (process IV). The red shift in the absorption (excitation) spectra of the AH-B complex with respect to the absorption of the bare AH molecule will only measure the increase of the binding energy in the excited neutral form AH - B of the cluster. Then, the emission spectrum will be similar to the fluorescence of the free molecule. 

Analogous reasoning would make the AH molecule in AH"-BH a better proton acceptor, in comparison to the isolated AH molecule. 

Consider, for example, the pair of molecules AH and BH, each of which has a proton to donate in a H-bond, and each of which contains one or more lone electron pairs appropriate to accept a proton. If they form a H-bond of the type AH -BH, the proton of BH is still available to form a H-bond to another molecule, CH. But the CH molecule will encounter two different situations depending on whether the BH molecule is involved in the aforementioned dimer, or is a single isolated BH molecule. In fact, formation of the AH—BH complex will remove electron density from the BH subunit, density which is transferred across to AH. This loss of negative charge will make BH a more powerful proton donor so that one can expect the BH—CH interaction in the AH --BH--CH trimer to be stronger than in the simpler BH---CH dimer. Analogous reasoning would make the AH molecule in AH---BH a better proton acceptor, in comparison to the isolated AH molecule. 

Fig. 6.16 Molecuiar orfaita] picuires and qnalilalive energies of linear and beni AH molecules. Open and shaded areas represent differences in sign (+ or -) df the wave functions. Changes in shape which increase in-phase overlap lower the molecular orbital energy- Frum Cunarc.

Dipole polarizabilities for hydrides containing two first-row atoms reveal an interesting pattern [82]. The a values of these molecules tend to follow those of the AH molecules in the following sense. The a value of a given ABH molecule is well estimated (to within about 15%) by the sum of the a values for the A and B simple hydrides, diminished by about 6 a.u. if there is a double bond between A and B, or diminished by about 12 a.u. if there is a triple bond ... 

Figure 2. Isotropic dipole polarizability (a) (a.u.) of AH molecules versus the atomic number of A.

Table 4. Stabilization energy of tetrahedral and butterfly AH, molecules as a function of electron count...

Not ah molecules colhde with the walls at right angles, so we must average (using calculus) over ah the trajectories. This gives a proportionality constant of, and... 

AH molecules in this volume v cross in unit time. The number of moles in this volume = cv / c -f dc ... 

The emission of H3+O ions defines the acidity of the AH molecule. Dissociation depends on the value of the equilibrium constant, Ka, of the acid ... 

Figure 1.6. Molecular orbitals for AH molecules (with the electronic occupation appropriate for molecules with four valence electrons, such as BH or AIH in their lowest singlet state). 0-0 bonding (Ta-h MO...

The preceding examples show that one must always consider the atomic or molecular orbital on the ligand that allows a a bond to be formed with the metal. This orbital may be a nonbonding s orbital (H), a hybrid s-p orbital (AH3, AH2, and AH molecules), or ap orbital which points towards the metal centre (A atoms). When the atom bound to the metal also possesses nonbonding p orbitals perpendicular to the metal-ligand bond (AH2, AH, A), it is also necessary to consider them, since they lead to 7r-type interactions with the metal orbitals. 

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