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When thinking about orbital energy levels, it is not a good idea to think of them as fixed energy 'levels' that can be filled with electrons. This kind of picture is often found in introductory textbooks, but it is wrong. For example, it is known that even for the Hartree-Fock theory, the energy of a molecule is not a sum of the orbital energies. In this ...


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IMHO, this particular comparison is a strange one. You reference "Comparison of DFT Methods for Molecular Orbital Eigenvalue Calculations" by Zhang and Musgrave, and there are other similar comparisons between density functional orbital methods and ionization potentials and electron affinities. In general, these Kohn-Sham DFT benchmark papers show that ...


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As far as I understand this is explained by Judd–Ofelt theory. When lanthanides are doped in the crystals, the crystal perturbation renders the Laporte selection rule inadequate to explain these transitions. The accumulated influence of the electrons and nucleus of the crystal host creates an electric field called crystal field. This crystal field generates ...


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Absorbing photons is just one of ways atoms and their electrons, or molecules, can gain energy. Other ways are e.g mechanical collisions and chemical reactions. Note that atoms do not reflect light they do not absorb, but let it pass through like if they were not there. If they had reflected it, air would have been an opaque fog. A very small number of ...


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It look like the expression is just the equivalent way of expression the matrix product. I've attached two pictures that might help.


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To solve the problem, think about what is the condition for a radial node- what happens to the density $|\Psi_{\textrm{3s}}|^2$ at a node? First some definitions: $r$ is the distance from the nucleus and $a_0$ is a constant distance called the Bohr radius (=0.5291 Å). How can this go to zero? Now what? The solution for the position of the nodes is The ...


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The reason we speak of orbitals as being exclusively inhabited by 2 (max) electrons (with opposing electron spin quantum number) is because electrons are fermions and therefore observe the exclusion principle. The exclusion principle constrains the allowed electron configurations, disallowing occupation of lower E orbitals by more than 2 electrons. In the ...


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Heat energy is distributed and some of the energy might match the amount required to excite an electron There are two parts to the answer. Firstly, there is more to emission than electrons leaping to a new energy level. Molecules can be excited by making them move faster (kinetic energy), vibrate at a different frequency (vibrational energy), rotate faster ...


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SAPT(O) is an amazing tool for partitioning the interaction energies, it yields meaningful values and data. ETS-NOCV is also very good for partitioning the interaction energy, but it does it in a much different way, it yields values that correspond more to the orbital interactions, and more so the sigma and pi orbital mixing (although orca will not partition ...


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