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X-ray-excited Auger and Photoelectron Spectroscopy
Published in M. Prutton, Electronic Properties of Surfaces, 2018
So far the analysis has only included the limited amount of electron correlation implicit in the Hartree–Fock method. One way to include other correlations is to adopt the CI approach and expand ψi (N) and ψf(Ν) as combinations of Slater determinants including excited-state orbitals in the basis set. Such an expansion naturally leads to a more complicated expression for the transition moment than (2.8) as discussed by Martin and Shirley (1977). Deciding the degree of ci appropriate to a particular case and the choice of one-electron orbitals to include in the basis set requires some insight into the nature of the satellites involved. Martin and Shirley (1976, 1977) have performed an extensive analysis of the Ne+[1s] satellites concentrating on those states which can be approximately described as Ne 1s22s22p6 to Ne+1s12s22p5np1 excitations, lines 3–9 in figure 2. Their results are shown in table 2. In order to get such good agreement with the energies and particularly the intensities of the satellites Martin and Shirley (1976) found it essential to include CI in the initial state of the Ne atom, indicating that electron correlation has important effects even in such a simple closed-shell system.
Orbital Tuning of Ruthenium Polyimine Complexes by Ligand Design: From Basic Principles to Applications
Published in Ajay Kumar Mishra, Lallan Mishra, Ruthenium Chemistry, 2018
Joe Otsuki, Guohua Wu, Ryuji Kaneko, Yayoi Ebata
Theoretical interpretation or prediction of properties of metal complexes is done by density functional theory (DFT) computation most of the cases at the research level. Still, further interpretation of the results of the theoretical calculations by a human brain requires basic understanding of molecular orbital theory. Ligand field theory is molecular orbital theory as applied to metal complexes. Before going into the ligand field theory, we briefly summarize the basics of molecular orbital theory. The Hartree–Fock method is the standard theory in molecular orbital theory. This method incorporates electron–electron repulsion terms as an electron interacting with the average field the other electrons produce. As this theory is already complicated enough for back-of-the-envelope treatments, we restrict ourselves more or less on the extended Hückel theory level of molecular orbital theory. As the extended Hückel theory does not include electron–electron repulsion terms explicitly, which are hidden in the parameters used, the treatment is greatly simplified and the qualitative understanding becomes easier.
Computer Simulation Methods to Visualize Nanofillers in Polymers: Toward Clarification of Mechanisms to Improve Performance of Nanocomposites
Published in Toshikatsu Tanaka, Takahiro Imai, Advanced Nanodielectrics, 2017
Masahiro Kozako, Atsushi Otake
In the 1980s, ab initio molecular orbital simulation became generally available, and many software applications for Hartree– Fock approximation using Gaussian basis functions were developed. The reason why the Gaussian basis functions were adopted is explained in the following. In general, the existence probability of electrons around an atom forms a Slater-type distribution (exp[−α·x]). Because analytically solving the integral generated during the calculation process is difficult, numerical integration with a high computational load is used. When a Gaussian function (exp[−β·x2]) is linearly combined with the existence probability to form an almost Slater-type distribution, analytical integration becomes possible and the number of calculations is reduced. For general molecules, the calculation accuracy is increased by using a sufficient number of Gaussian functions, but significant errors may be generated for some molecules. In addition, the Hartree–Fock method has a drawback in that the many-body interaction of electrons (electron correlation) is not taken into consideration.
Speeding up density fitting Hartree–Fock calculations with multipole approximations
Published in Molecular Physics, 2020
The Hartree–Fock (HF) method is one of the most important approaches in quantum chemistry. Currently, it is rarely used as a standalone method, but it is usually employed for generating molecular orbitals (MOs) for a subsequent correlation calculation. Though the formal scaling of its computation time with the system size is better than that for conventional correlation methods, due to the rapid development of reduced-scaling correlation approaches [1–3], the HF calculation has become the bottleneck for large molecules. The other core approximation in quantum chemistry is Kohn–Sham (KS) density functional theory (DFT) [4], which is the most widely used method in computational chemistry these days. If the KS approach is employed in conjunction with a hybrid functional [5], the complexity of the resulting equations is very similar to that of the HF method. Consequently, considerable effort has been invested into the improvement of HF algorithms.
Parametrisation of the optimised effective potential method based on the Coulson–Fischer wave function for excited states
Published in Molecular Physics, 2020
Within the TI-DFT approach, the so-called constrained OEP (COEP) method has been proposed by Glushkov and Levy [47–49]. This method builds on the variational time independent DFT bifunctional formulation of Levy and Nagy [39, 40] for individual excited states and can be easily implemented using an asymptotic projection (AP) technique [55, 56] for taking orthogonality constraints into account. This method has been applied to small atoms and molecules [49, 57] using exchange-only approximation within the Hartree–Fock method for excited state. However, it is known that Hartree–Fock theory possesses a number of shortcomings. It gives an inadequate description of chemical binding both qualitatively and quantitatively – molecules in their ground states often dissociate into ions. These shortcomings are shared by Kohn–Sham-based density functional theory.