# 4.2.43. POLY_ANISO¶

The POLY_ANISO program is a routine which allows a semi-ab initio description of the (low-lying) electronic structure and magnetic properties of polynuclear compounds. It is based on the localized nature of the magnetic orbitals (i.e. the d or f orbitals containing unpaired electrons [105][106]). For many compounds of interest, the localized character of magnetic orbitals leads to very weak character of the interactions between magnetic centers. Due to this weakness of the interaction, the metals’ orbitals and corresponding localized 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 Figure 4.2.43.1.

Figure 4.2.43.1 Fragmentation model of a polynuclear compound. The upper scheme shows a schematic overview of a tetranuclear compound and the resulting four mononuclear fragments obtained by diamagnetic atom substitution method. By this scheme, the neighboring magnetic centers, containing unpaired electrons are computationally replaced by their diamagnetic equivalents. As example, transition metal sites TM(II) are best replaced by either diamagnetic $$\ce{Zn(II)}$$ or $$\ce{Sc(III)}$$, in function which one is the closest. For lanthanides $$\ce{Ln(III)}$$ the same principle is applicable, $$\ce{La(III)}$$ or $$\ce{Lu(III)}$$ are best suited to replace a given magnetic lanthanide. Individual mononuclear metal framgents are then investigated by common CASSCF/CASPT2/RASSI/SINGLE_ANISO computational method. A single file 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. It can be considered 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.

The description of the magnetic exchange interaction is done within the Lines model [107]. 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 of interaction between magnetic sites with intermediate anisotropy, the Lines model represents an approximation. However, it was succesfully 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 information about each metal site already computed ab initio. In the case of strongly anisotropic lanthanide compounds, the dipole-dipole interaction is usualy the dominant one. Dipolar magnetic coupling is one kind of long-range interaction between magnetic moments. For example, a system containing two magnetic dipoles $$\mu_1$$ and $$\mu_2$$, separated by distance $$\vec{r}$$ have a total energy:

$E_{\text{dip}} = \frac{\mu_{\text{Bohr}}^{2}}{r^3} [\vec{\mu}_1 \cdot \vec{\mu}_2 - 3(\vec{\mu}_1 \vec{n}_{12}) \cdot (\vec{\mu}_2 \vec{n}_{12})],$

where $$\vec{\mu}_{1,2}$$ are the magnetic moments of sites 1 and 2, respectively; $$r$$ is the distance between the two magnetic dipoles, $$\vec{n}_{12}$$ is the directional vector connecting the two magnetic dipoles (of unit length). $$\mu_{\text{Bohr}}^2$$ is the square of the Bohr magneton; with an approximative value of 0.43297 in $$\text{cm}^{-1}/\text{T}$$. 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 (see the keyword COOR).

## 4.2.43.1. Files¶

### 4.2.43.1.1. Input files¶

The program POLY_ANISO needs the following files:

aniso_XX.input

This is an ASCII text file generated by the Molcas/SINGLE_ANISO program. It should be provided for POLY_ANISO 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.

chitexp.input

set directly in the standard input (key TEXP)

magnexp.input

set directly in the standard input (key HEXP)

### 4.2.43.1.2. Output files¶

zeeman_energy_xxx.txt