# Tag Info

16

It's a great question! Some of my answer will be taken from my answer to your question on the AI stack exchange, but cross-site questions are allowed and your question here is slightly different so my answer is slightly different. I'll address your points in reverse chronological order: (4) Most proteins don't have metals at all. It was estimated in 1999 ...

16

The Berry curvature is defined as: $$\Omega_{\mu\nu}(\mathbf{k})=\partial_{\mu}A_{\nu}(\mathbf{k})-\partial_{\nu}A_{\mu}(\mathbf{k}), \tag{1}$$ where $A_{\mu}(\mathbf{k})=\langle u_{\mathbf{k}}|i\partial_{\mu}u_{\mathbf{k}}\rangle$ is the Berry connection, $|u_{\mathbf{k}}\rangle$ is a Bloch state, and $\partial_\mu\equiv \frac{\partial}{\partial k_\mu}$, ...

15

Even for the simplest transition metal diatomic molecules, the most reliable way to know the ground-state spin configuration is often by doing experiments. I will give an example where it's easy to correctly determine the ground state spin configuration, and then an example where it has remained impossible as of the year 2020. Cr$_2$: Here we can accurately ...

12

Resolution for the time reversal symmetry: I need to demonstrate: $\Omega(-\mathbf{k})=-\Omega(\mathbf{k})$ (Berry's curvature is a odd function under time reversal symmetry) Berry's curvature: $$\Omega_{\mu\nu}(\mathbf{k})=\partial_{\mu}A_{\nu}(\mathbf{k})-\partial_{\nu}A_{\mu}(\mathbf{k})\tag{1}$$ If the system is time-reversally invariant: T|u_k\rangle=... 11 Often when one is asked for the number of spin states, we are interested in determining the spin state of metal complexes containing these ions, rather than the lone ion itself. If you are interested in just the lone ion itself, Nike Dattani's answer goes into depth about that. My answer will focus on the determination of spin states of ions within metal ... 11 \ce{Cu}^+ This ion has 28 electrons. If all of them are up (i.e. aligned with the +z axis), then since each electron has a spin of magnitude 1/2, we would have a total spin of +14. If all of them are down we would have a total spin of -14. We could also have 1 up and 27 down, meaning +\frac{1}{2} - \frac{27}{2} = -\frac{26}{2} = -13. The number of total ... 11 It's possible to estimate solution-phase dielectric constant from a molecular dynamics simulation using this formula:\epsilon_{r} = 1 + \frac{4\pi}{3Vk_{B}T}(\langle \mathbf{P}^{2} \rangle - \langle \mathbf{P} \rangle^{2}) Where $V$ is the volume, $k_{B}$ is Boltzmann's constant, $T$ is temperature, and $P$ is the dipole moment defined as: $\mathbf{P} ... 10 For computing the spin-state in a metal complex there are many methods available. I'll focus in DFT as one of the most used methodologies. In a single atom cluster (sometimes described as mononuclear complexes), DFT offers good results compared with wave-function multideterminantal methods. On the other hand, if the complex is formed by two or more ... 9 Difficulty in capturing enough electron correlation: The difference between the lowest states belonging to different electronic configurations can be small (for example, on the order of 1 kcal/mol). Traditional methods for full configuration interaction (FCI) calculations such as the Davidson method are unable to be used in any remotely accurate basis set ... 9 Just to add to Anyon's answer: Since there may be practical considerations for using DFT+$U$in a database like the Materials Project (i.e. a value you're confident will give you generally correct properties in high-throughput calculations, is there a literature reference or other justification for the value, etc.) I would in general not assume that they ... 9 I haven't had much experience with calculating chemical shifts, but I do have experience calculating J-coupling between P atoms on metal complexes. From this, I know that for chemical shifts and J-coupling calcs may require the use of specialized basis sets since most energy optimized basis sets (i.e. pople, dunning, karlsruhe) do not have an appropriate ... 8 If you're studying transition metal complexes, in short, there is no way to know except for to try the relevant physically plausible spin multiplicities and take the lowest energy solution as the ground state. For instance, an Fe(II) complex can have up to 4 unpaired electrons since it is$3d^6$. This is what we call the high-spin state and would be$2S+1=3$.... 8 The Karlsruhe def2 basis sets cover most of the periodic table and are based on effective core potentials for relativistic effects; these are a good starting point for whatever you are interested in, and are also available built-in in Gaussian. As to the functional, since you want to study slabs you probably want to use a pure functional since otherwise the ... 8 Quantum confinement can occur when the exciton (electron-hole quasiparticle) radius is larger than the size of the semiconductor. Due to this confinement, the energy levels which can be occupied by the exciton are quantized into discrete energy levels. This will spread the band gap due to missing states that would exist in the bulk material. This ... 7 I can't speak as to how the Materials Project selects what information to display, but it's clear that the Hubbard$U$(or rather the correlations/interactions it attempts to capture) generally is important for copper oxides. This is very clear in the cuprate high-$T_c$superconductors, which are often modeled as doped antiferromagnetic insulators. The$U$... 7 The word "splitting" seems to occur only in one sentence, over the course of the entire paper that you referenced: "The d-orbital spin-splitting energy is stronger than the weak crystal field splitting energy of the S ligand around the TM atoms" I can see why you had to ask this question here, because when I search "d-orbital spin-... 6 The main question here is whether the question makes sense for${\rm K}_3[{\rm Mn(CN)}_6]$as a molecular complex. Looks like the material has a solid state structure https://materials.springer.com/isp/crystallographic/docs/sd_1100190 which you could with solid state methods. As a complex it's not obvious where the potassiums would go, so you would probably ... 6 With metals, they can often exist as different multiplicities depending on the compound they are in and it is not always simple to predict the correct multiplicity. More often than not, determining the multiplicity of the ground state is either done experimentally or by comparing the energies of likely multiplicities computationally. In your case, it seems ... 6 d-block The extra difficulty of studying a d-block element/transition metal complex is that the "breaking of degeneracies of electron orbital states" can result in different stable configurations depending on the geometry and symmetry of the molecule. This is the simple linear combination of atomic orbitals (LCAO) picture, or if you want more ... 6 I can't help with the textbook, but the NIST-JANAF Thermochemical Tables are available here: https://janaf.nist.gov/ 5 Just to provide an answer to this question, my conclusion after all this is that in general, there is unfortunately not a great answer. I likely put too many constraints on the question. As noted in "Thirty Years of DFT" from the Head-Gordon group, ωB97X-V and the more expensive ωB97M-V are both excellent options for many tasks but are not widely ... 5 I do not have much experience with DFT, but have been digging into DFT in strong fields the last couple of months. The investigation of magnetic properties such as NMR shielding constant and the magnetisability in the context of DFT rely on an explicit dependence on the magnetic field. Magnetic-field DFT, known as BDFT (J. Chem. Theory Comput. 2017, 13, 9, ... 5 To obtain the spin multiplicity of the ground electronic state of a molecule, can be extremely hard. In your question you mentioned$\ce{UF6}$which has 7 atoms, and not all of them being of the same element. But even for a very simple homonuclear (all atoms being of the same element) diatomic molecule like$\ce{Fe2}\$, my answer to "Total spin and/or ...

5

Very briefly, in many cases d- and f- orbitals are (quasi)degenerate. So to accurately calculate energies we need to take into account all permutations of electrons over those orbitals (multireference calculations). If you want to know more there is a nice tutorial.

5

A band can either be expressed as a linear combination of plane waves, or as a linear combination of atomic orbitals. By asserting that the color of gold can be explained by relativistic shifts of atomic orbitals, one have implicitly expanded the conduction band wavefunctions into a linear combination of atomic orbitals. Then it follows easily that if an ...

4

I see now how your initial questions were related, as they all fall under the scope of crystal field theory. I wrote a bit about this in a previous answer. At least in the context of molecular crystal field theory, you will usually see the phrase pairing energy rather than "spin-splitting". The distinction is basically just the direction, where the ...

4

Quantum confinement is a kind of physical effect, which describes the change of electronic and optical properties when the material sampled is of sufficiently small size----typically 10 nanometers or less. For layered TMDC materials, when the materials are downsized to the 2D limit, the dielectric screening environment will be reduced significantly, and ...

3

Lets start with some data from Optical Transmission in Thin Metal Films where they deposited a range of metals on glass and measured their transmission. Sticking with their data on the noble metals, they see pretty much what one would expect - some changes in shape as the film thickness goes from 0.5 to 4nm of gold, coupled with the clear emergence of the ...

1

You are correct that the optimum geometry for one spin multiplicity will in general be different for another spin multiplicity. Therefore if you want to know the geometry of the lowest-energy state of a molecule, a pre-requisite is to first know the electronic configuration (spin multiplicity and spatial configuration) of the lowest-energy state of the ...

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