Molecular orbitals comparing theory with experiment

In this review we summarized our experience with the development and applications of semiempirical Pariser-Parr-Pople (PPP)-type and all-valence-electron methods to electronic spectra of radicals. After the era of PPP calculations on closed-shell molecules and the advent of semiempirical all-valence-electron methods, the electronic spectra of radicals represented a new challenge for molecular orbital (MO) theory. It was a time when progress in experimental techniques resulted in accumulation of a vast amount of data on the electronic spectra of radicals of various structural types. Compared to closed-shell molecules, the electronic spectra of some radicals exhibited peculiar features bands in the near infrared, many transitions in the whole UV/vis region, and some bands of extraordinary intensity. Clearly, without the help of MO theory, their interpretation seemed even harder than with closed-shell molecules. 

The UPS valence band spectra of multilayer and monolayer samples of phthalimide (pirn) and methyl-phthalimide (mpim) on copper have been compared with the calculated DOVS for corresponding systems. Very good agreement is found between theory and experiment for all the systems included in this study. This made it possible to interpret the features appearing in the UPS spectra in terms of specific molecular orbitals. Furthermore, by analyzing the MO s, the nature of the ligand-metal bonding is uncovered. 

Deformation density maps have been used to examine the effects of hydrogen bonding on the electron distribution in molecules. In this method, the deformation density (or electrostatic potential) measured experimentally for the hydrogen-bonded molecule in the crystal is compared with that calculated theoretically for the isolated molecule. Since both the experiment and theory are concerned with small differences between large quantities, very high precision is necessary in both. In the case of the experiment, this requires very accurate diffraction intensity measurements at low temperature with good thermal motion corrections. In the case of theory, it requires a high level of ab-initio molecular orbital approximation, as discussed in Chapter 4. 

Another possibility to obtain direct information from such a collision system is the observation of Molecular orbital (MO) X-rays resulting from electronic de-excita-tions between the molecular levels during the collision under emission of noncharacteristic photons. The result of our many-particle calculation is given in Fig. 10 where the spectrum of the collision system 20 MeV CP on Ar is compared with the experiment. In this calculation the radiation field was coupled to the system by first order perturbation theory but the wavefunctions were taken from the solution ot the time-dependent relativistic DV-Xa calculations . 

For molecules of chemical interest it is not possible to calculate an exact many-electron wave function. As a result, we have to make certain approximations. The most commonly made approximation is the molecular orbital approximation, which is outlined in the next section. Within such a framework, it is useful to define various levels of computational method, each of which can be applied to give a unique wave function and energy for any set of nuclear positions and number of electrons. If such a model is clearly specified and if it is sufficiently simple to apply repeatedly, it can be used to generate molecular potential energy surfaces, equilibrium geometries, and other physical properties. Each such theoretical model can then be explored and the results compared in detail with experiment. If there is sufficient consistent success, some confidence can then be acquired in its predictive power. Each such level of theory therefore should be thoroughly tested and characterized before the significance of its prediction is assessed. 

It is useflil to show the valence bond representations of the complexes [CoFe] and [Co(NH3)6], which can then be compared with representations from the crystal field and molecular orbital theories to be discussed later. First, we must know from experiment that [CoF ] contains four unpaired electrons, whereas [Co(NH3)g] has all of its electrons paired. Each of the ligands, as Lewis bases, contributes a pair of electrons to form a coordinate covalent bond. The valence bond theory designations of the electronic structures are shown in Figure 2.7. The bonding is described as being covalent. Appropriate combinations of metal atomic orbitals are blended together to give a new set of orbitals, called hybrid orbitals. 

Simple molecular aggregates are amenable to detailed ab initio molecular orbital calculations of vibrational modes, which can be compared to experiment to resolve structural dilemmas. For instance theory predicts that the linear-asymmetric H2O dimer is more stable than the cyclic-symmetric alternative. Consistent with theory, the low-temperature matrix spectrum can only be fitted to the linear structure. 

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