Electronic structure methods Koopmans’ theorem

The success of the Hartree-Fock method in describing the electronic structure of most closed-shell molecules has made it natural to analyze the wave function in terms of the molecular orbitals. The concept is simple and has a close relation to experiment through Koopmans theorem. The two fundamental building blocks of Hartree-Fock (HF) theory are the molecular orbital and its occupation number. In closed-shell systems each occupied molecular orbital... 

IP and EA express the readiness of a molecule to accept or donate electrons, respectively. Koopmans theorem is an approximation. It rests on the assumption that the electron wave function of remaining electrons does not change if one electron is removed or added. Indeed, the electron structure of an ionized molecule differs from that of a neutral one. further quantum chemical descriptors, like those related to electron delocalizability and polarizability, are described in [48]. It should be emphasized that the quantum chemical descriptors depend (sometimes drastically) on the selected method and approximation. An example is shown in [48] where different quantum chemical descriptors were calculated for set of 607 compounds. As a final nofe on quantum chemical descriptors, we emphasize that the information on electronic structures of molecules can be obtained from spectroscopic measurements. Eor example, the energies of individual electronic states can be directly measured in photo electron spectroscopy experiments. 

Koopmans Theorem. In contrast to many other spectroscopic methods, interpretation of photoelectron spectra requires the support of calculations. According the equation 3 it is in principle necessary to calculate the total energy of both the ground state and the various cationic states of a molecule. In most cases—for exceptions, see Section III—it is sufficient to calculate the electronic structure of the ground state of the molecule within the self-consistent-field (SCF) method. 

The most promising approaches for efficient electronic structure calculations on large molecules are generally based on density functional theory with Kohn-Sham orbitals [32-35]. The most efficient such method for CE-BEs is based on Koopmans theorem, but this approach has quite limited accuracy [36-39]. Better accuracy can be obtained from calculations based on an effective core potential [40-45], an equivalent core approximation [46-48], a fractionally occupied transition state [49-52], or with a ASCF approach [29, 31, 53-57]. Time-dependent density functional theory is also widely used for CEBE calculation [58-62], wherein the best results are usually given with functionals having a long-range correction [63, 64]. 

The next five chapters are each devoted to the study of one particular computational model of ab initio electronic-structure theory Chapter 10 is devoted to the Hartree-Fock model. Important topics discussed are the parametrization of the wave function, stationary conditions, the calculation of the electronic gradient, first- and second-order methods of optimization, the self-consistent field method, direct (integral-driven) techniques, canonical orbitals, Koopmans theorem, and size-extensivity. Also discussed is the direct optimization of the one-electron density, in which the construction of molecular orbitals is avoided, as required for calculations whose cost scales linearly with the size of the system. 

One of the main aims of such computations is the prediction and rationalization of the optoelectronic spectra in various steric and electronic environments by either semiempirical or ab initio methods or a combination of these, considering equilibrium structures, rotation barriers, vibrational frequencies, and polarizabilities. The accuracy of the results from these calculations can be evaluated by comparison of the predicted ionization potentials (which are related to the orbital energies by Koopman s theorem) with experimental values. 

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