Development of MagSaki(Tetra) Software for the Magnetic Analysis of Tetranuclear High-spin Cobalt(II) Complexes

Keywords:
Magnetic analysis,
Octahedral high-spin cobalt(II) complex,
Spin-orbit coupling,
Ligand field,
Tetranuclear cobalt(II) complex,
MagSaki software series

2016 Volume 2 Article ID: 2016-0001

Details

Abstract

MagSaki(Tetra) software was developed for the purpose of analyzing the magnetic
susceptibility data of tetranuclear octahedral high-spin cobalt(II) complexes. The
software enables the analyses six types of tetranuclear cobalt(II) structures, including
cubane and defect dicubane structures, to obtain magnetic parameters: the interaction
parameters, *J*, *J*’, *J*”, and
*J*”’, the spin-orbit coupling parameter, *λ*, the orbital
reduction factor, *κ*, and the axial splitting parameter,
*Δ*.

1 INTRODUCTION

The magnetic properties of some high-spin cobalt(II) complexes are difficult to interpret because of the effects of the ligand field and the spin-orbit coupling [1]. Earlier, Lines [2] and Figgis [3] developed a way to analyze

the magnetic properties of mononuclear octahedral high-spin cobalt(II) complexes by considering an axially distorted ligand field and spin-orbit coupling. Although they showed the importance of considering the distorted ligand field, the distortion had never been considered for dinuclear octahedral high-spin cobalt(II) complexes until Sakiyama developed susceptibility equations for the dinuclear systems [4,5,6,7].

For the purpose of analyzing the magnetic properties of high-spin cobalt(II) complexes conveniently, a series of computational programs, MagSaki software series, has been developed for mononuclear, dinuclear, and trinuclear systems [8,9,10]. A magnetic susceptibility equation was recently developed for tetranuclear octahedral high-spin cobalt(II) complexes [11], including the cubane and defect dicubane structures (Figure 1). In this paper, a MagSaki(Tetra) software is reported, which was developed for the purpose of analyzing the magnetic properties of tetranuclear high-spin cobalt(II) complexes.

Figure 1.

Tetranuclear cubane (left) and defect dicubane (right) structures.

2 MAGNETIC PARAMETERS

The main symbols for the magnetic parameters are summarized in Table 1.

Table 1.
List of the main symbols [1,4,5,6,7,8,9,10,11].

Symbol | Unit | Meaning |

J, J’,
J”, J”’ |
cm^{–1} |
Interaction parameters |

T |
K | Absolute temperature |

TIP | cm^{3} mol^{–1} |
Temperature-independent paramagnetism |

v |
– | Distortion parameter defined as
Δ/(κλ) |

Δ |
cm^{–1} |
Axial splitting parameter |

κ |
– | Orbital reduction factor |

λ |
cm^{–1} |
Spin-orbit coupling parameter |

μ_{eff} |
μ_{B} |
Effective magnetic moment |

χ_{A} |
cm^{3} mol^{–1} |
Atomic magnetic susceptibility |

χ_{M} |
cm^{3} mol^{–1} |
Molar magnetic susceptibility |

3 METHOD

The software was developed using REALbasic software [12] on a KOHJINSHA SA5 SX04A computer (OS: Windows XP Home edition).

4 FUNCTION OF MAGSAKI(TETRA) SOFTWARE

As well as the previous MagSaki software series [8,9,10], the MagSaki(Tetra) software imports the temperature dependence data of
magnetic susceptibility, *χ*_{A} versus *T *data
(*χ*_{A} = *χ*_{M}/4 for tetranuclear
cobalt(II) complexes), and displays a *χ*_{A} versus *T
*graph and an effective magnetic moment *μ*_{eff} versus
*T *graph. The software can calculate theoretical
*χ*_{A} and *μ*_{eff} values for six types
of tetranuclear cobalt(II) structures, including cubane and defect dicubane structures, and
also displays the theoretical curves of *χ*_{A} and
*μ*_{eff} on the graph. The software can optimize magnetic
parameters to fit the theoretical curve to the observed data.

5 CALCULATION MODES

In addition to the calculation modes of the MagSaki(A) software, the MagSaki(Tetra)
software has six calculation modes for tetranuclear high-spin cobalt(II) species. The most
symmetrical tetranuclear structure belongs to a *T _{d}* point group
(Figure 2), and in this case, six interactions
between cobalt(II) ions are equivalent. Hereafter, the interaction pattern of the

Figure 2.

Main deformation patterns of tetranuclear structure.

Table 2.
Types of interactions for main tetranuclear structures.

Symmetry | Number of types of interactions | Type of interactions | Abbreviation of the pattern |

T_{d} |
1 | 6J |
<6> |

C_{3}_{v} |
2 | 3J, 3J’ |
<33> |

D_{3}_{h} |
2 | 3J, 3J’ |
<33> |

S_{4} |
2 | 4J, 2J’ |
<42> |

D_{4}_{h} |
2 | 4J, 2J’ |
<42> |

D_{2} |
3 | 2J, 2J’,
2J” |
<222> |

D_{2} − 1_{h} |
3 | 2J, 2J’,
2J” |
<222> |

C_{2}_{v} |
3 | J, 4J’,
J” |
<141> |

D_{2} − 2_{h} |
3 | J, 4J’,
J” |
<141> |

C_{2} |
4 | J, 2J’,
2J”, J”’ |
<1221> |

C_{2}_{h} |
4 | J, 2J’,
2J”, J”’ |
<1221> |

- ^{a} |
1 | 5J, J’ |
<51> |

- ^{a} |
3 | 3J, 2J’,
J” |
<321> |

a Not for any realistic structures, but useful for analysis; for example, <51>
corresponds to the *J* = *J*' case for <141>, and
<321> corresponds to the *J* = *J*' case for
<1221>.

6 MAGNETIC SIMULATIONS

Some of the theoretical *χ*_{A}*T* versus *T
*curves have been already reported for the tetranuclear cobalt(II) complexes of mode
<6> [11]. In this paper, some other theoretical
curves for square-shaped and parallelogram-shaped tetranuclear cobalt(II) complexes (Figure 3) are demonstrated in Figures 4 and 5. It is noted that the
*χ*_{A}*T *value is temperature-dependent due to the
spin-orbit coupling even when there are no interactions between cobalt(II) ions; the
no-interaction curve is shown in black in each graph. In the case of square-shaped
tetranuclear cobalt(II) complexes of
*D*_{4}* _{h}* symmetry, mode <42> is
appropriate, considering four

Figure 3.

Square-shaped (a) and parallelogram-shaped (b) models.

Figure 4.

Theoretical *χ*_{A}*T *versus *T
*curves for tetranuclear cobalt(II) complexes of square shape with the variation
of *J* when *J*’ > 0 (a) and when *J*’
< 0 (b). [The curves represent from the bottom (*J*/ cm^{–1},
*J*’/ cm^{–1}) = (−10, +10), (−5, +10), (0,0), (0, +10), (+5,
+10), and (+10, +10), respectively for (a) and (*J*/ cm^{–1},
*J*’/ cm^{–1}) = (−10, −10), (−5, −10), (0, −10), (+5, −10),
(+10, −10), and (0,0), respectively for (b), when *λ* =
−170 cm^{–1}, *κ* = 0.9, and *Δ* =
0 cm^{–1}.]

In the case of parallelogram-shaped tetranuclear cobalt(II) complexes, mode <1221> is
appropriate, considering one *J* interaction, two *J*’
interactions, two *J*” interactions, and one *J*”’ interaction
(Figure 3b). When only *J*’ is
negative, the complex is considered as two coupled dinuclear cobalt(II) complexes.
Therefore, the *χ*_{A}*T *curve is exactly equal to
that of a dinuclear complex, and the *χ*_{A}*T *value
reaches zero in the low-temperature range (the red curve in Figure 5a). On the other hand, when only *J* is
negative, the complex is considered as one coupled dinuclear cobalt(II) complex and two
magnetically isolated mononuclear cobalt(II) complexes. In this case, the
*χ*_{A}*T *value (one quarter of
*χ*_{M}*T *value) reaches one half of the monomer,
corresponding to two magnetically isolated cobalt(II) ions, in the low-temperature range
(the orange curve in Figure 5a).

Figure 5.

Theoretical *χ*_{A}*T *versus *T
*curves for tetranuclear cobalt(II) complexes of parallelogram shape. [The
curves represent from the bottom (*J*/ cm^{–1},
*J*’/ cm^{–1}, *J*”/ cm^{–1},
*J*”’/ cm^{–1}) = (0, −10, 0, 0) [red], (−10, 0, 0, 0)
[orange], and (0, 0, 0, 0) [black] when *λ* = −170 cm^{–1},
*κ* = 0.9, and *Δ* = 0 cm^{–1 }(a),
(*J*/ cm^{–1}, *J*’/ cm^{–1},
*J*”/ cm^{–1}, *J*”’/ cm^{–1}) = (−50,
−10, 0, 0) [blue], (−40, −10, 0, 0), (−30, −10, 0, 0), (−20, −10, 0, 0), (−10, −10, 0,
0), (0, −10, 0, 0) [red], and (0, 0, 0, 0) when *λ* =
−170 cm^{–1}, *κ* = 0.9, and *Δ* = 0 cm^{–1
}(b), when *λ* = −170 cm^{–1}, *κ* = 0.9, and
*Δ* = −1530 cm^{–1 }(c), and when *λ* =
−170 cm^{–1}, *κ* = 0.9, and *Δ* =
+1530 cm^{–1 }(d).]

When *J*’ is fixed to −10 cm^{–1} in a parallelogram-shaped
tetranuclear cobalt(II) complex, the variation of *J *(−50 to
−10 cm^{–1}) was demonstrated (Figure
5b). When *J* becomes smaller and the antiferromagnetic interaction
becomes larger, a characteristic two-step shape appears due to the two thermally distributed
states, while *χ*_{A}*T *decreases monotonously when
*J* is close to zero due to only one thermally distributed state. The axial
splitting parameter, *Δ*, is zero in Figure 5b, but when *Δ* changes, the shapes of the curves change
(Figures 5c and 5d). The *Δ*
parameter is negative in Figure 5c, and positive
in Figure 5d. Since the curve shape depends on the
*Δ* parameter, which indicates the degree of distortion, considering the
distortion of the octahedral ligand field is important in magnetic data analysis.

7 OPTIMIZATION OF PARAMETERS

The software can optimize magnetic parameters to fit the theoretical curve to the observed data. Using the software, several data have been analyzed [11,13].

8 REQUIREMENTS

The software (MagSaki(Tetra) 2100W) will run on Windows computers.

This work was supported by JSPS KAKENHI Grant Number 15K05445. Financial support by Yamagata University is also acknowledged.

REFERENCES

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