Geometry. Vibrations. Dissociation

X-ray diffraction of KPHg or RbPH2 single crystals gave an ionic radius of 2.12 or 2.13 A [1 ]. 

The geometrical structure of gaseous PH2 in its X Ai ground state appears to be similar to that of ground-state PH2 (with an internuclear distance of r=1.42 A and an interbond angle of a = 92° see p. 72). This was inferred from a sharp increase of the photodetachment cross section at threshold, measured by ion cyclotron resonance [2, 3] and from the predominance of the (0, 0, 0) -(0, 0, 0) transition in the PH2, X Bi PH, X A photoelectron spectrum [4]. r=1.34 0.05 A and a = 92 5 were taken from the isoelectronic H2S molecule (and used to calculate the thermodynamic functions of PH, see p. 109) [5]. r and a have also been theoretically calculated by several ab initio MO methods, i.e., at an MP2 [6, 7], a CEPA (coupled electron pair approximation) [8], and an HF level [9 to 15]. r was also obtained from a united-atom approximation [16] a was also calculated by a semiempirical (CNDO/2) method [17] and estimated by extended Huckel calculations [18]. 

X-ray structure determinations of crystalline LiPH2 DME at -120 3 C gave two P-H internuclear distances of 1.31 and 1.38 A and an HPH interbond angle of 85 [23]. Earlier work on UPH2 DME at 23 2 C [24] and on crystalline KPH2 at room temperature [25] could not determine the position of the H atoms. 

Complete sets of the fundamental vibrations Vi (symmetric stretching), V2 (bending), and V3 (antisymmetric stretching), all in cm , were obtained from IR absorption bands of MPH2 (M = K, Rb, Cs) in KBr pellets (and assigned to PHg by comparison with known vibrational frequencies of PH3, NH3, NH2, H2O, and H2S) [25] (see table on the next page). 

Ab initio MO calculations at the CEPA level yielded fundamental frequencies for PHj and PDi (in parentheses) of 2187 (1591), 1069 (773), and 2182 (1590) cm (for harmonic frequen- 

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Computational chemistry has reached a level in which adsorption, dissociation and formation of new bonds can be described with reasonable accuracy. Consequently trends in reactivity patterns can be very well predicted nowadays. Such theoretical studies have had a strong impact in the field of heterogeneous catalysis, particularly because many experimental data are available for comparison from surface science studies (e.g. heats of adsorption, adsorption geometries, vibrational frequencies, activation energies of elementary reaction steps) to validate theoretical predictions. 

The last decade has witnessed the establishment of quantum chemical methods as a standard tool for quantitative calculations of transition metal (TM) compounds, after numerous theoretical studies had proved that the calculated values are very accurate. The calculated data can be used to interpret experimental observations and to design new experiments and, thus, are very helpful for experimental chemistry. The theoretically predicted geometries, vibrational frequencies, bond dissociation energies, and other chemically important properties have become reliable enough to complement and sometimes even to challenge experimental data. This is particularly important for bond energies of TM compounds, which tend to be difficult to determine by experimental methods. 

Despite the fact that p in a molecule is not a slowly varying function of position, the LSDA works surprisingly well for calculating molecular equilibrium geometries, vibrational frequencies, and dipole moments, even for transition-metal compounds, where Hartree-Fock calculations often give poor results. (For detailed results, see Chapter 17.) However, calculated LSDA molecular atomization energies are very inaccurate. Accurate dissociation energies require functionals that go beyond LSDA. 

As we have reviewed here, the linear region is not fully repulsive, and transitions of the ground-state, linear conformer access vibrationally excited intermolecular levels that are delocalized in the angular coordinate. As depicted in Fig. 1, however, the internuclear distance is significantly longer in the excited state at the linear geometry. Consequently, there is favorable Franck-Condon overlap of the linear conformer with the inner-repulsive wall of the excited-state potential. It is therefore possible for the linear Rg XY conformers to be promoted to the continuum of states just above each Rg - - XY B,v ) dissociation limit. 

The anharmonic modes for both the a symmetric and 67 asymmetric CH stretching vibrations have been explored. In order to perform a reasonable anharmonic treatment, we had to take into account the stretching of the bonds to larger elongations than for the harmonic description where displacements can be confined close to the equilibrium geometry. Consequently, correlation effects were included in the determination of the potential surface. The electronic calculations were carried out at the MP2 level, which insures a good description of the CH bond potential towards dissociation. A double zeta... 

Another consequence of the stronger interactions upon ionization is that the equilibrium geometry of the ionized complex may differ signihcantly from that of the neutral states. Broadened ionization onsets are frequently attributed to the spectral superposition of ionization into several vibrational levels for which Franck-Condon factors are more favorable. As a result, the adiabatic ionization potential may be considerably lower than the vertical potential, and the observed ionization onsets may occur above the adiabatic potential. Another factor to be considered is the conformation-dependent efifect, due to the different conformations of the solvent molecules. The most populated form of a complex may involve a less stable form of the solvent. After photoionisation, the lowest-energy dissociation channel in the complex ion leads to the most stable form of isolated solvent, which has to be taken into account for the estimate of the binding energy. 

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