(sec:poly.aniso.detailed)= # Interface to POLY_ANISO module (sec:poly.aniso.general.detailed)= ## General description The `POLY_ANISO` is a stand-alone utility allowing for a semi-*ab initio* description of the (low-lying) electronic structure and magnetic properties of polynuclear compounds. The model behind it is based on the *localised* nature of the magnetic orbitals (i.e. the $d$ and $f$ orbitals containing unpaired electrons). For many compounds of interest, the localised character of the magnetic orbitals leads to very weak character of the exchange interaction between magnetic centers. Due to this weakness of the inter-site interaction, the molecular orbitals and corresponding localised ground and excited states may be optimized in the absence of the magnetic interaction at all. For this purpose, various fragmentation models may be applied. The most commonly used fragmentation model is exemplified in {numref}`fig:ThumbnailFragment`: (fig:ThumbnailFragment)= ```{figure} ../../images/polyaniso1.* Fragmentation model of a polynuclear compound. ``` The upper scheme shows a schematic overview of a tri-nuclear compound and the resulting three mononuclear fragments obtained by *diamagnetic atom substitution method*. By this scheme, the neighbouring magnetic centers, containing unpaired electrons are computationally replaced by their diamagnetic equivalents. As example, transition metal (TM) sites are best described by either a diamagnetic Zn(II) or Sc(III), in function of which one is the closest (in terms of charge and atomic radius). For lanthanides (LN), the same principle is applicable, La(III), Lu(III) or Y(III) are best suited to replace a given magnetic lanthanide. Individual mononuclear metal fragments are then investigated by the common `CASSCF`+`SOC`/`NEVPT2`+ `SOC`/`SINGLE_ANISO` computational method. A single `datafile` for each magnetic site, produced by the `SINGLE_ANISO` run, is needed by the `POLY_ANISO` code as input. Magnetic interaction between metal sites is very important for accurate description of low-lying states and their properties. While the full exchange interaction is quite complex (e.g. requiring a multipolar description employing a large set of parameters {cite}`Vier2016,Iwahara2015`), in a simplified model it can be viewed as a sum of various interaction mechanisms: magnetic exchange, dipole-dipole interaction, antisymmetric exchange, etc. In the `POLY_ANISO` code we have implemented several mechanisms, which can be invoked simultaneously for each interacting pair. The description of the magnetic exchange interaction is done within the Lines model{cite}`LinesModel`. This model is exact in three cases: 1. interaction between two isotropic spins (Heisenberg), 2. interaction between one Ising spin (only S$_Z$ component) and one isotropic (i.e. usual) spin, and 3. interaction between two Ising spins. In all other cases when magnetic sites have intermediate anisotropy (i.e. when the spin-orbit coupling and crystal field effects are of comparable strengths), the Lines model represents an approximation. However, it was successfully applied for a wide variety of polynuclear compounds so far. In addition to the magnetic exchange, magnetic dipole-dipole interaction can be accounted exactly, by using the *ab initio* computed magnetic moment for each metal site (as available inside the `datafile`). In the case of strongly anisotropic lanthanide compounds (like Ho$^{3+}$ or Dy$^{3+}$), the magnetic dipole-dipole interaction is usually the dominant one. For example, a system containing two magnetic dipoles $\vec{\mu}_{1}$ and $\vec{\mu}_{2}$, separated by distance $\vec{\textit{r} }$ have a total energy: $$E_{dip} = \frac{\mu_{Bohr}^2}{r^3}[ \vec{\mu}_{1} \cdot \vec{\mu}_{2} - 3 (\vec{\mu}_{1} \vec{n}_{1,2}) \cdot (\vec{\mu}_{2} \vec{n}_{1,2})],$$ where $\vec{\mu}_{1,2}$ are the magnetic moments of sites 1 and 2, respectively; $r$ is the distance between the two magnetic dipoles, $\vec{n}_{1,2}$ is the directional vector connecting the two magnetic dipoles (of unit length). $\mu_{Bohr}^2$ is the square of the Bohr magneton; with an approximate value of 0.43297 in $cm^{-1}$/T. As inferred from the above Equation, the dipolar magnetic interaction depends on the distance and on the angle between the magnetic moments on magnetic centers. Therefore, the Cartesian coordinates of all non-equivalent magnetic centers must be provided in the input. In brief, the `POLY_ANISO` is performing the following operations: 1. read the input and information from the datafiles 2. build the exchange coupled basis 3. compute the magnetic exchange, magnetic dipole-dipole, and other magnetic Hamiltonians using the *ab initio*-computed spin and orbital momenta of individual magnetic sites and the input parameters 4. sum up all the magnetic interaction Hamiltonians and diagonalise the total interaction Hamiltonian 5. rewrite the spin and magnetic moment in the exchange-coupled eigenstates basis 6. use the obtained spin and magnetic momenta for the computation of the magnetic properties of entire poly-nuclear compound The actual values of the inter-site magnetic exchange could be derived from e.g. broken-symmetry DFT calculations. Alternatively, they could be regarded as fitting parameters, while their approximate values could be extracted by minimising the standard deviation between measured and calculated magnetic data. ## Files `POLY_ANISO` is called independently of ORCA for now. In the future versions of ORCA we will aim for a deeper integration, for a better experience. ```sh bash:$ bash:$ $ORCA/x86_64/otool_poly_aniso < poly_aniso.input > poly_aniso.output bash:$ ``` The actual names of the `poly_aniso.input` and `poly_aniso.output` are not hard coded, and can take any names. A bash script for a more convenient usage of `POLY_ANISO` can be provided upon request or made available on the Forum. ### Input files The program `POLY_ANISO` needs the following files: `aniso_i.input` : This is an ASCII text file generated by the `CASSCF`/`SOC`/ `SINGLE_ANISO` run. It should be provided for `POLY_ANISO` as `aniso_i.input` (i=1,2,3, etc.): one file for each magnetic center. In cases when the entire polynuclear cluster or molecule has exact point group symmetry, only `aniso_i.input` files for crystallographically non-equivalent centers should be given. This saves computational time since equivalent metal sites do not need to be computed *ab initio*. `poly_aniso.input` : The standard input file defining the computed system and various input parameters. This file can take any name. ### Output files (sec:poly.aniso.keywords.detailed)= ## List of keywords This section describes the keywords used to control the `POLY_ANISO` input file. Only two keywords `NNEQ`, `PAIR` (and `SYMM` if the polynuclear cluster has symmetry) are mandatory for a minimal execution of the program, while the other keywords allow customisation of the execution of the `POLY_ANISO`. The format of the "poly_aniso.input" file resembles to a certain extent the input file for `SINGLE_ANISO` program. The input file must start with "`&POLY_ANISO`" text. ### Mandatory keywords defining the calculation *Keywords defining the polynuclear cluster:* `NNEQ` This keyword defines several important parameters of the calculation. On the first line after the keyword the program reads 2 values: 1) the number of types of different magnetic centers (NON-EQ) of the cluster and 2) a letter `T` or `F` in the second position of the same line. The number of NON-EQ is the total number of magnetic centers of the cluster which cannot be related by point group symmetry. In the second position the answer to the question: "Have all NON-EQ centers been computed *ab initio*?" is given: T for True and F for False. On the following line the program will read NON-EQ values specifying the number of equivalent centers of each type. On the following line the program will read NON-EQ integer numbers specifying the number of low-lying spin-orbit functions from each center forming the local exchange basis. Some examples valid for situations where all sites have been computed *ab initio* (case T, True): ```orca NNEQ 2 T 1 2 2 2 ``` There are two kinds of magnetic centers in the cluster; both have been computed *ab initio*; the cluster consists of 3 magnetic centers: one center of the first kind and two centers of the second kind. From each center we take into the exchange coupling only the ground doublet. As a result, the $N_{exch}=2^{1}\times2^{2}=8$, and the two datafiles `aniso_1.input` (for-type 1) and `aniso_2.input` (for-type 2) files must be present. ```orca NNEQ 3 T 2 1 1 4 2 3 ``` There are three kinds of magnetic centers in the cluster; all three have been computed *ab initio*; the cluster consists of four magnetic centers: two centers of the first kind, one center of the second kind and one center of the third kind. From each of the centers of the first kind we take into exchange coupling four spin-orbit states, two states from the second kind and three states from the third center. As a result the $N_{exch}=4^{2}\times2^{1}\times3^{1}=96$. Three files `aniso_i.input` for each center ($i=1,2,3$) must be present. ```orca NNEQ 6 T 1 1 1 1 1 1 2 4 3 5 2 2 ``` There are six kinds of magnetic centers in the cluster; all six have been computed *ab initio*; the cluster consists of 6 magnetic centers: one center of each kind. From the center of the first kind we take into exchange coupling two spin-orbit states, four states from the second center, three states from the third center, five states from the fourth center and two states from the fifth and sixth centers. As a result the $N_{exch}=2^1\times4^{1}\times3^{1}\times5^{1}\times2^{1}\times2^{1}=480$. Six files `aniso_i.input` for each center ($i=1,2,...,6$) must be present. Only in cases when some centers have NOT been computed *ab initio* (i.e. for which no `aniso_i.input` file exists), the program will read an additional line consisting of NON-EQ letters ($A$ or $B$) specifying the type of each of the NON-EQ centers: $A$ - the center is computed *ab initio* and $B$ - the center is considered isotropic. On the following number-of-B-centers line(s) the isotropic $g$ factors of the center(s) defined as $B$ are read. The spin of the B center(s) is defined: $S=(N-1)/2$, where $N$ is the corresponding number of states to be taken into the exchange coupling for this particular center. Some examples valid for mixed situations: the system consists of centers computed *ab initio* and isotropic centers (case $F$, False): ```orca NNEQ 2 F 1 2 2 2 A B 2.3 2.3 2.3 ``` There are two kinds of magnetic centers in the cluster; the center of the first type has been computed *ab initio*, while the centers of the second type are considered isotropic with $g_X=g_Y=g_Z$=2.3; the cluster consists of three magnetic centers: one center of the first kind and two centers of the second kind. Only the ground doublet state from each center is considered for the exchange coupling. As a result the $N_{exch}=2^1\times2^2=8$. File `aniso_i.input` (for-type 1) must be present. ```orca NNEQ 3 F 2 1 1 4 2 3 A B B 2.3 2.3 2.0 2.0 2.0 2.5 ``` There are three kinds of magnetic centers in the cluster; the first center type has been computed *ab initio*, while the centers of the second and third types are considered empirically with $g_X=g_Y=$2.3; $g_Z$=2.0 (second type) and $g_X=g_Y=$2.0; $g_Z$=2.5 (third type); the cluster consists of four magnetic centers: two centers of the first kind, one center of the second kind and one center of the third kind. From each of the centers of the first kind, four spin-orbit states are considered for the exchange coupling, two states from the second kind and three states from the center of the third kind. As a result the $N_{exch}=4^{2}\times2^{1}\times3^{1}=96$. The file `aniso_i.input` must be present. ```orca NNEQ 6 T 1 1 1 1 1 1 2 4 3 5 2 2 B B A A B A 2.12 2.12 2.12 2.43 2.43 2.43 2.00 2.00 2.00 ``` There are six kinds of magnetic centers in the cluster; only three centers have been computed *ab initio*, while the other three centers are considered isotropic; the $g$ factors of the first center is 2.12 (S=1/2); of the second center 2.43 (S=3/2); of the fifth center 2.00 (S=1/2); the entire cluster consists of six magnetic centers: one center of each kind. From the center of the first kind, two spin-orbit states are considered in the exchange coupling, four states from the second center, three states from the third center, five states from the fourth center and two states from the fifth and sixth centers. As a result the $N_{exch}=2^{1}\times4^{1}\times3^{1}\times5^{1}\times2^{1}\times2^{1}=480$. Three files `aniso_3.input` and `aniso_4.input` and `aniso_6.input` must be present. There is no maximal value for `NNEQ`, although the calculation becomes quite heavy in case the number of exchange functions is large. `SYMM` Specifies rotation matrices to symmetry equivalent sites. This keyword is mandatory in the case more centers of a given type are present in the calculation. This keyword is mandatory when the calculated polynuclear compound has exact crystallographic point group symmetry. In other words, when the number of equivalent centers of any kind $i$ is larger than 1, this keyword must be employed. Here the rotation matrices from the one center to all the other of the same type are declared. On the following line the program will read the number 1 followed on the next lines by as many $3\times3$ rotation matrices as the total number of equivalent centers of type 1. Then the rotation matrices of centers of type 2, 3 and so on, follow in the same format. When the rotation matrices contain irrational numbers (e.g. $\sin\frac{\pi}{6}=\frac{\sqrt{3} }{2}$), then more digits than presented in the examples below are advised to be given: $\frac{\sqrt{3} }{2}=0.8660254$. Examples: ```orca NNEQ 2 F 1 2 2 2 A B 2.3 2.3 2.3 SYMM 1 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 2 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 -1.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 -1.0 ``` The cluster computed here is a tri-nuclear compound, with one center computed *ab initio*, while the other two centers, related to each other by inversion, are considered isotropic with $g_X=g_Y=g_Z=2.3$. The rotation matrix for the first center is $I$ (identity, unity) since the center is unique. For the centers of type 2, there are two matrices $3\times3$ since we have two centers in the cluster. The rotation matrix of the first center of type 2 is Identity while the rotation matrix for the equivalent center of type 2 is the inversion matrix. ```orca NNEQ 3 F 2 1 1 4 2 3 A B B 2.1 2.1 2.1 2.0 2.0 2.0 SYMM 1 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 0.0 -1.0 0.0 -1.0 0.0 0.0 0.0 0.0 1.0 2 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 3 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 ``` In this input a tetranuclear compound is defined, all centers are computed *ab initio*. There are two centers of type "1", related one to each other by $C_2$ symmetry around the Cartesian Z axis. Therefore the `SYMM` keyword is mandatory. There are two matrices for centers of type 1, and one matrix (identity) for the centers of type 2 and type 3. ```orca NNEQ 6 F 1 1 1 1 1 1 2 4 3 5 2 2 B B A A B A 2.12 2.12 2.12 2.43 2.43 2.43 2.00 2.00 2.00 ``` In this case the computed system has no symmetry. Therefore, the `SYMM` keyword is not required. `End of Input` Specifies the end of the input file. No keywords after this one will be processed. ### Keywords defining the magnetic exchange interactions This section defines the keywords used to set up the interacting pairs of magnetic centers and the corresponding exchange interactions. A few words about the numbering of the magnetic centers of the cluster in the `POLY_ANISO`. First all equivalent centers of the type 1 are numbered, then all equivalent centers of the type 2, etc. These labels of the magnetic centers are used further for the declaration of the magnetic coupling. `PAIR` or `LIN1` : This keyword defines the interacting pairs of magnetic centers and the corresponding exchange interaction. A few words about the numbering of the magnetic centers of the cluster in the `POLY_ANISO`. First all equivalent centers of the type 1 are numbered, then all equivalent centers of the type 2, etc. These labels of the magnetic centers are used now for the declaration of the magnetic coupling. Interaction Hamiltonian is: $$\hat{H}_{Lines} = -\sum_{p=1}^{N_{pairs} } J_{p}\hat{s}_{i}\hat{s}_{j},$$ where $i$ an $j$ are the indices of the metal sites of the interacting pair $p$; $J_{p}$ is the user-defined magnetic exchange interaction between the corresponding metal sites; $\hat{s}_{i}$ and $\hat{s}_{j}$ are the `ab initio` spin operators for the low-lying exchange eigenstates. ```orca PAIR 3 1 2 -0.2 1 3 -0.2 2 3 0.4 ``` The input above is applicable for a tri-nuclear molecule. Two interactions are antiferromagnetic while ferromagnetic interaction is given for the last interacting pair. `LIN3` : This keyword defines a more involved exchange interaction, where the user is allowed to define 3 parameters for each interacting pair. The interaction Hamiltonian is given by: $$\hat{H}_{Lines} = -\sum_{p=1}^{N_{pairs} } \sum_{\alpha} J_{p,\alpha}\hat{s}_{i,\alpha}\hat{s}_{j,\alpha},$$ where the $\alpha$ defines the Cartesian axis $x,y,z$. ```orca LIN3 1 1 2 -0.2 -0.4 -0.6 # i, j, Jx, Jy, Jz ``` The input above is applicable for a mononuclear molecule. `LIN9` : This keyword defines a more involved exchange interaction, where the user is allowed to define 9 parameters for each interacting pair. The interaction Hamiltonian is given by: $$\hat{H}_{Lines} = -\sum_{p=1}^{N_{pairs} } \sum_{\alpha,\beta} J_{p,\alpha,\beta} \hat{s}_{i,\alpha}\hat{s}_{j,\beta},$$ where the $\alpha$ and $\beta$ defines the Cartesian axis $x,y,z$. ```orca LIN9 1 1 2 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 # i,j,Jxx,Jxy,Jxz,Jyx,Jyy,Jyz,Jzx,Jzy,Jzz ``` The input above is applicable for a mononuclear molecule. `COOR` : The `COOR` keyword turns ON the computation of the dipolar coupling for those interacting pairs which were declared under `PAIR`, `LIN3` or `LIN9` keywords. On the NON-EQ lines following the keyword the program will read the symmetrised Cartesian coordinates of NON-EQ magnetic centers: one set of symmetrised Cartesian coordinates for each type of magnetic centers of the system. The *symmetrized Cartesian coordinates* are obtained by translating the original coordinates to the origin of Coordinate system, such that by applying the corresponding SYMM rotation matrix onto the input COOR data, the position of all other sites are generated. ```orca COOR 6.489149 3.745763 1.669546 5.372478 5.225861 0.505625 ``` The magnetic dipole-dipole Hamiltonian is computed as follows: $$\hat{H}_{dip} = \mu_{Bohr}^2 \sum_{p=1}^{N_{pairs}} \frac{ \hat{\mu}_{i}\hat{\mu}_{j} -3(\hat{\mu}_{i} \vec{n}_{i,j} ) (\hat{\mu}_{j} \vec{n}_{i,j})} { \vec{r_{i,j}^{3}}}$$ and is added to $\hat{H}_{exch}$ computed using other models. The $\hat{H}_{dip}$ is added for all magnetic pairs. ### Optional general keywords to control the input Normally `POLY_ANISO` runs without specifying any of the following keywords. However, some properties are only computed if it is requested by the respective keyword. Argument(s) to the keyword are always supplied on the next line of the input file. `MLTP` : The number of molecular multiplets (i.e. groups of spin-orbital eigenstates) for which $g$, $D$ and higher magnetic tensors will be calculated (default `MLTP`=1). The program reads two lines: the first is the number of multiplets ($N_{MULT}$) and the second the array of $N_{MULT}$ numbers specifying the dimension (multiplicity) of each multiplet. Example: ```orca MLTP 10 2 4 4 2 2 2 2 2 2 2 ``` `POLY_ANISO` will compute the EPR $g$ and $D$- tensors for 10 groups of states. The groups 1 and 4-10 are doublets ($\tilde{S} = |1/2\rangle$), while the groups 2 and 3 are quadruplets, having the effective spin $\tilde{S} = |3/2\rangle$. For the latter cases, the ZFS (D-) tensors will be computed. We note here that large degeneracies are quite common for exchange coupled systems, and the data for this keyword can only be rendered after the inspection of the exchange spectra. `TINT` : Specifies the temperature points for the evaluation of the magnetic susceptibility. The program will read three numbers: $T_{min}$, $T_{max}$, and $nT$. - $T_{min}$ - the minimal temperature (Default 0.0 K) - $T_{max}$ - the maximal temperature (Default 300.0 K) - $nT$ - number of temperature points (Default 301) Example: ```orca TINT 0.0 300.0 331 ``` `POLY_ANISO` will compute temperature dependence of the magnetic susceptibility in 331 points evenly distributed in temperature interval: 0.0 K - 330.0 K. `HINT` : Specifies the field points for the evaluation of the molar magnetisation. The program will read three numbers: $H_{min}$, $H_{max}$, $nH$. - $H_{min}$ - the minimal field (Default 0.0 T) - $H_{max}$ - the maximal filed (Default 10.0 T) - $nH$ - number of field points (Default 101) Example: ```orca HINT 0.0 20.0 201 ``` `POLY_ANISO` will compute the molar magnetisation in 201 points evenly distributed in field interval: 0.0 T - 20.0 T. `TMAG` : Specifies the temperature(s) at which the field-dependent magnetisation is calculated. Default is one temperature point, T = 2.0 K. Example: ```orca TMAG 6 1.8 2.0 2.4 2.8 3.2 4.5 ``` `ENCU` : The keyword expects to read two integer numbers. The two parameters (`NK` and `MG`) are used to define the cut-off energy for the lowest states for which Zeeman interaction is taken into account exactly. The contribution to the magnetisation coming from states that are higher in energy than $E$ (see below) is done by second order perturbation theory. The program will read two integer numbers: $NK$ and $MG$. Default values are: $NK=100, MG=100$. $$E=NK \cdot k_{Boltz} \cdot \texttt{TMAG}_{max} + MG \cdot \mu_{Bohr} \cdot H_{max}$$ The field-dependent magnetisation is calculated at the maximal temperature value given by `TMAG` keyword. Example: ```orca ENCU 250 150 ``` If $H_{max}$ = 10 T and `TMAG` = 1.8 K, then the cut-off energy is: $$E=250 \cdot k_{Boltz} \cdot 1.8 + 150 \cdot \mu_{Bohr} \cdot 10 = 1013.06258 (cm^{-1})$$ This means that the magnetisation arising from all exchange states with energy lower than $E = 1013.06258 (cm^{-1})$ will be computed exactly (i.e. are included in the exact Zeeman diagonalisation) The keywords `NCUT`, `ERAT` and `ENCU` have similar purpose. If two of them are used at the same time, the following priority is defined: `NCUT > ENCU > ERAT`. `UBAR` : With `UBAR` set to \"true\", the blocking barrier of a single-molecule magnet is estimated. The default is not to compute it. The method prints transition matrix elements of the magnetic moment according to the Figure below: ![image](../../images/singleaniso1.*) In this figure, a qualitative performance picture of the investigated single-molecular magnet is estimated by the strengths of the transition matrix elements of the magnetic moment connecting states with opposite magnetisations ($n+ \rightarrow n-$). The height of the barrier is qualitatively estimated by the energy at which the matrix element ($n+ \rightarrow n-$) is large enough to induce significant tunnelling splitting at usual magnetic fields (internal) present in the magnetic crystals (0.01-0.1 Tesla). For the above example, the blocking barrier closes at the state ($8+ \rightarrow 8-$). All transition matrix elements of the magnetic moment are given as $((|\mu_X|+|\mu_Y|+|\mu_Z|)/3)$. The data is given in Bohr magnetons ($\mu_{Bohr}$). Example: ```orca UBAR ``` `ERAT` : This flag is used to define the cut-off energy for the low-lying exchange-coupled states for which Zeeman interaction is taken into account exactly. The program will read one single real number specifying the ratio of the energy states which are included in the exact Zeeman Hamiltonian. As example, a value of 0.5 means that the lowest half of the energy states included in the spin-orbit calculation are used for exact Zeeman diagonalisation. Example: ```orca ERAT 0.333 ``` The keywords `NCUT`, `ERAT` and `ENCU` have similar purpose. If two of them are used at the same time, the following priority is defined: `NCUT > ENCU > ERAT`. `NCUT` : This flag is used to define the cut-off energy for the low-lying exchange states for which Zeeman interaction is taken into account exactly. The contribution to the magnetisation arising from states that are higher in energy than lowest $N_{CUT}$ states, is done by second-order perturbation theory. The program will read one integer number. In case the number is larger than the total number of exchange states($N_{exch}$, then the $N_{CUT}$ is set to $N_{SS}$ (which means that the molar magnetisation will be computed exactly, using full Zeeman diagonalisation for all field points). The field-dependent magnetisation is calculated at the temperature value(s) defined by `TMAG`. Example: ```orca NCUT 32 ``` The keywords `NCUT`, `ERAT` and `ENCU` have similar purpose. If two of them are used at the same time, the following priority is defined: `NCUT > ENCU > ERAT`. `MVEC` : `MVEC`, define a number of directions for which the magnetisation vector will be computed. The directions are given as vectors specifying the direction *i* of the applied magnetic field). Example: ```orca MVEC 4 # number of directions 1.0 0.0 0.0 # px, py, pz of each direction 0.0 1.0 0.0 0.0 0.0 1.0 1.0 1.0 1.0 ``` `ZEEM` : This keyword allows to compute Zeeman splitting spectra along certain directions of applied field. Directions of applied field are given as three real number for each direction, specifying the projections along each direction: Example: ```orca ZEEM 6 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 0.0 1.0 1.0 1.0 0.0 1.0 1.0 1.0 0.0 ``` The above input will request computation of the Zeeman spectra along six directions: Cartesian axes X, Y, Z (directions 1,2 and 3), and between any two Cartesian axes: YZ, XZ and XY, respectively. The program will re-normalise the input vectors according to unity length. In combination with `PLOT` keyword, the corresponding `zeeman_energy_xxx.png` images will be produced. `MAVE` : The keyword requires two integer numbers, denoted `MAVE_nsym` and `MAVE_ngrid`. The parameters `MAVE_nsym` and `MAVE_ngrid` specify the grid density in the computation of powder molar magnetisation. The program uses Lebedev-Laikov distribution of points on the unit sphere. The parameters are integer numbers: $n_{sym}$ and $n_{grid}$. The $n_{sym}$ defines which part of the sphere is used for averaging. It takes one of the three values: 1 (half-sphere), 2 (a quarter of a sphere) or 3 (an octant of the sphere). $n_{grid}$ takes values from 1 (the smallest grid) till 32 (the largest grid, i.e. the densest). The default is to consider integration over a half-sphere (since $M(H)=-M(-H)$): $n_{sym}=1$ and $n_{sym}=15$ (i.e 185 points distributed over half-sphere). In case of symmetric compounds, powder magnetisation may be averaged over a smaller part of the sphere, reducing thus the number of points for the integration. The user is responsible to choose the appropriate integration scheme. Note that the program's default is rather conservative. Example: ```orca MAVE 1 8 ``` `TEXP` : This keyword allows computation of the magnetic susceptibility $\chi T(T)$ at experimental points. On the line below the keyword, the number of experimental points $N_T$ is defined, and on the next $N_T$ lines the program reads the experimental temperature (in K) and the experimental magnetic susceptibility (in $cm^{3}Kmol^{-1}$). The magnetic susceptibility routine will also print the standard deviation from the experiment. ```orca TEXP 54 299.9901 55.27433 290.4001 55.45209 279.7746 55.43682 269.6922 55.41198 259.7195 55.39274 249.7031 55.34379 239.735 55.29292 229.7646 55.23266 219.7354 55.15352 209.7544 55.06556 ... ``` `HEXP` : This keyword allows computation of the molar magnetisation $M_{mol}(H)$ at experimental points. On the line below the keyword, the number of experimental points $N_H$ is defined, and on the next $N_H$ lines the program reads the experimental field intensity (in Tesla) and the experimental magnetisation (in $\mu_{Bohr}$). The magnetisation routine will print the standard deviation from the experiment. ```orca HEXP 3 1.0 5.3 2.4 # temperature values 10 # numer of field points 0.30 4.17 1.26 2.51 # H(T) and M for each temperature 1.00 5.47 3.57 4.82 1.88 5.79 4.54 5.30 2.67 5.92 4.96 5.54 3.46 5.97 5.20 5.70 4.24 6.00 5.36 5.81 5.03 6.01 5.48 5.88 5.82 6.02 5.57 5.93 6.61 6.02 5.65 5.97 7.40 6.03 5.72 5.99 ``` `ZJPR` : This keyword specifies the value (in $cm^{-1}$) of a phenomenological parameter of a mean molecular field acting on the spin of the complex (the average intermolecular exchange constant). It is used in the calculation of all magnetic properties (not for spin Hamiltonians) (Default is 0.0). ```orca ZJPR -0.02 ``` `XFIE` : This keyword specifies the value (in T) of applied magnetic field for the computation of magnetic susceptibility by $dM/dH$ and $M/H$ formulas. A comparison with the usual formula (in the limit of zero applied field) is provided. (Default is 0.0). Example: ```orca XFIE 0.35 ``` This keyword together with the keyword `PLOT` will enable the generation of two additional plots: `XT_with_field_dM_over_dH.png` and `XT_with_field_M_over_H.png`, one for each of the two above formula used, alongside with respective `gnuplot` scripts and gnuplot datafiles. `TORQ` : This keyword specifies the number of angular points for the computation of the magnetisation torque function, $\vec{\tau}_{\alpha}$ as function of the temperature, field strength and field orientation. ```orca TORQ 55 ``` The torque is computed at all temperature given by `TMAG` or `HEXP_temp` inputs. Three rotations around Cartesian axes X, Y and Z are performed. `PRLV` : This keyword controls the print level. - 2 - normal. (Default) - 3 or larger (debug) `PLOT` : Set to \"true\", the program generates a few plots (png or eps format) via an interface to the linux program *gnuplot*. The interface generates a datafile, a *gnuplot* script and attempts execution of the script for generation of the image. The plots are generated only if the respective function is invoked. The magnetic susceptibility, molar magnetisation and blocking barrier (`UBAR`) plots are generated. The files are named: `XT_no_field.dat`, `XT_no_field.plt`, `XT_no_field.png`, `MH.dat`, `MH.plt`, `MH.png`, `BARRIER_TME.dat`, `BARRIER_ENE.dat`, `BARRIER.plt` and `BARRIER.png`, `zeeman_energy_xxx.png` etc. All files produced by `SINGLE_ANISO` are referenced in the corresponding output section. Example: ```orca PLOT ```