https://www.quanty.org/ 2026-04-29T06:46:14+00:00 https://www.quanty.org/ https://www.quanty.org/_media/wiki/dokuwiki.svg text/html 2025-11-20T02:29:40+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_ligand_field/density_matrix_plot?rev=1763605780&do=diff Density matrix plot An intuitive way to look at eigenstates is to plot the charge density. For multi-electron wave-functions one can not plot the wave-function (it depends on $3\times n$ coordinates) but the charge density is a well defined simple quantity. We here use the rendering options of \textit{Mathematica} in combination with the package for \textit{Mathematica} (Quanty.nb) to plot the density matrix of the lowest three eigenstates in NiO.$S_z=-1$$S_z=0$$S_z=1$$3d$$x^2-y^2$$z^2$$S_z=0$ni… text/html 2025-11-20T02:29:43+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_ligand_field/energy_level_diagram?rev=1763605783&do=diff Energy level diagram In order to do temperature averaging it is important to understand the number of excited states that are important. One can learn a lot by looking at the energy level diagram. Here we plot one for Ni$^{2+}$.The input file is: Verbosity(0) -- In order to understand the physics / chemistry of a system it is often good -- to make energy level diagrams. i.e. plot the eigen-state energy as a function -- of some parameter one varies. -- Here we create the energy level diagram … text/html 2025-11-20T02:29:40+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_ligand_field/fy_l23m1?rev=1763605780&do=diff FY $L_{2,3}M_{1}$ In Fluoressence Yield spectroscopy one can focus on different decay channels. Each of them will yield a different spectrum. For a $2p$ to $3d$ excitation one can look at the $3s$ to $2p$ decay. The edge measured is thus the $L_{2,3}M_{1}$ edge.The input file is:$L_{2,3}M_{45}$$3s$$2p$$2p$$3d$nio_ligand_field index text/html 2025-11-20T02:29:41+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_ligand_field/fy_l23m45?rev=1763605781&do=diff FY $L_{2,3}M_{4,5}$ The absorption cross section is in principle measured using transmission. Transmission experiments in the soft-x-ray regime can be difficult as the absorption is quite high. Alternatively one can measure the reflectivity, which allows one to retrive the complete conductivity tensor using ellipsometry. As the x-ray wave-length is not large compared to the sample thickness this does not return the average sample absorption, but gives spatial information as well. Known as resona… text/html 2025-11-20T02:29:40+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_ligand_field/fy_rixs_nixs_include?rev=1763605780&do=diff FY RIXS nIXS include In order to shorten the examples, make them better readable and focus more on the new part introduced in the calculation we split the input file into several parts which are saved as separate files. The input file attached here defines all operators and calculates the ground-state. The tutorials use these to calculate spectra.nio_ligand_field index text/html 2025-11-20T02:29:41+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_ligand_field/groundstate?rev=1763605781&do=diff Groundstate The first example looks at the ground-state of NiO. Ni in NiO is $2+$ and thus has locally formal valence of $8$ electrons in the Ni $d$-shell. The lowest state has two holes in the $e_g$ orbitals with $S=1$ ($\langle S^2\rangle=1(2+1)=2$). Covalence allows the $d^8$ configuration to mix with a $d^9$$d^{10}$$d$$d^8$$10\times 10$$d^9L^9$$d^{10}L^8$nio_ligand_field index text/html 2025-11-20T02:29:42+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_ligand_field/nixs_l23?rev=1763605782&do=diff nIXS $L_{2,3}$ Besides low energy transitions nIXS can be used as a core level spectroscopy technique. One then measures resonances with non-resonant inelastic x-ray scattering :-).This tutorial uses Radial wave functions in order to calculate the length of q dependence. You can download them in a zip file here $2p$$3d$nio_ligand_field index text/html 2025-11-20T02:29:42+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_ligand_field/nixs_m45?rev=1763605782&do=diff nIXS $M_{4,5}$ Inelastic x-ray scattering IXS (non-resonant) nIXS or x-ray Raman scattering allows one to measure non-dipolar allowed transitions. A powerful technique to look at even $d$-$d$ transitions with well defined selection rules \cite{Haverkort:2007bv, vanVeenendaal:2008kv, Hiraoka:2011cq}, but can also be used to determine orbital occupations of rare-earth ions that are fundamentally not possible to determine using dipolar spectroscopy \cite{Willers:2012bz}.$d$$d$nio_ligand_field index text/html 2025-11-20T02:29:40+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_ligand_field/rixs_l23m1?rev=1763605780&do=diff RIXS $L_{2,3}M_{1}$ Instead of looking at low energy excitations one can use RIXS to look at core-core excitations. A powerful technique comparable to other core level spectroscopies like x-ray absorption and core-level photoemission at once.Here a script to calculate the Ni $2p$$3d$$L_{2,3}$$3s$$2p$$M_{1}$$L_{2,3}M_{4,5}$nio_ligand_field index text/html 2025-11-20T02:29:41+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_ligand_field/rixs_l23m45?rev=1763605781&do=diff RIXS $L_{2,3}M_{4,5}$ Using the function ResonantSpectra we can calculate inelastic x-ray scattering. (or other second order processess) Here we show the example of $d$-$d$ excitations in NiO using RIXS. Due to an ever increasing resolution this method gains rapidly in popularity and impact. See for example the combined work of Ghiringhelli \textit{et al.} For NiO see \cite{Ghiringhelli:2005kp}. $d$$d$nio_ligand_field index text/html 2025-11-20T02:29:42+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_ligand_field/start?rev=1763605782&do=diff NiO ligand field This section shows several calculations of NiO in the ligand-field approximation. The substructure follows the same line as the tutorial on Crystal-field. Noticeable differences are in the example calculating partial excitations. For ligand field one can also the projection to different configurations.nio_ligand_field index text/html 2025-11-20T02:29:40+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_ligand_field/temperature?rev=1763605780&do=diff Temperature The effect of temperature can be added by calculating excited states and expectation values of excited states. The temperature dependent expectation value is then created using Boltzmann statistics.A small example: -- Sofar we calculated eigenstates and expectation values (or spectra) of these -- eigenstates. At 0 K one would measure the expectation value of the lowest eigenstate -- at finite temperature one would measure an average over several states weighted by -- Boltzmann stat… text/html 2025-11-20T02:29:41+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_ligand_field/xas_l23_as_conductivity_tensor?rev=1763605781&do=diff XAS $L_{2,3}$ as conductivity tensor Absorption spectra are polarization dependent. In principle one can choose an infinite different number of polarizations. Calculating for each different experimental geometry (or polarization) a new spectrum is cumbersome and not needed. The material properties are given by the conductivity tensor. For dipole transitions a 3 by 3 matrix. The absorption spectra for a given experiment are then found by the relation:\begin{equation} I(\omega,\epsilon) = -\mathrm… text/html 2025-11-20T02:29:42+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_ligand_field/xas_l23_partial_excitations?rev=1763605782&do=diff XAS $L_{2,3}$ partial excitations In order to understand where a particular peak originates from one can look at the character of the excited state. Quanty works with Green's functions and we can not just look at the excited eigen-states as these are not really calculated. We can however modify the transition operator in order to understand where the spectra come from. The example below looks at excitations into the $t_{2g}$$e_g$$d$$j=1/2$$j=3/2$$2p$$d^9$$d^{10}$$2p$$3d$$3d$$e_g$$t_{2g}$$2p$$j=1… text/html 2025-11-20T02:29:41+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_ligand_field/xas_l23?rev=1763605781&do=diff XAS $L_{2,3}$ Once the ground-state is calculated one can calculate the spectra. This example shows the Ni $2p$ to $3d$ excitations in NiO. Note that these excitations have an energy of more than 800 electron Volt, which is much higher than the chemically relevant energy scales. Non-the-less these kind of spectroscopy contain useful information on the local ground-state wave-function and the low energy effective Hamiltonian. nio_ligand_field index