Answer

The easiest of these is [Cu(NNN)₂]²⁺, which is d⁹ and only a single transition is expected.

The peak maximum is at 619 nm or 16200 cm^–1

For d⁹ the peak directly gives 10Dq = 16200 cm^–1

There is not enough information available to determine B.

The transition is ²T_2g ← ²E_g

[Ni(NNN)₂]²⁺ is a d⁸ complex, where there is no high-spin/low-spin option.

There are 4 labeled peaks in the spectrum so there are several possible assignments

Guess 1

ν₁ = 919 nm = 10900 cm^–1

ν_{spin-forbidden} = 800 nm = 12500 cm^–1

ν₂ = 585 nm = 17100 cm^–1

ν₃ = 555 nm = 18000 cm^–1

With this assignment, ν₁ = 10Dq = 10900 cm^–1

15B = ν₃ + ν₂ – 3ν₁ = 18000 + 17100 – 3(10900) = 2400 cm^–1 so B = 160 cm^–1

β = B_complex/B_{free ion} = 160/1080 = 0.148

B and β seem too low so this assignment is probably incorrect.

Guess 2

ν₁ = 919 nm = 10900 cm^–1

ν₂ = 800 nm = 12500 cm^–1

ν_{spin-forbidden} = 585 nm = 17100 cm^–1

ν₃ = 555 nm = 18000 cm^–1

With this assignment, ν₁ = 10Dq = 10900 cm^–1

15B = ν₃ + ν₂ – 3ν₁ = 18000 + 12500 – 3(10900) = –2200 cm^–1 so B = –147 cm^–1

B must be positive so this assignment is incorrect.

Guess 3

ν₁ = 919 nm = 10900 cm^–1

ν₂ = 800 nm = 12500 cm^–1

ν₃ = 585 nm = 17100 cm^–1

ν_{spin-forbidden} = 555 nm = 18000 cm^–1

With this assignment, ν₁ = 10Dq = 10900 cm^–1

15B = ν₃ + ν₂ – 3ν₁ = 17100 + 12500 – 3(10900) = –3100 cm^–1 so B = –207 cm^–1

B must be positive so this assignment is incorrect.

Guess 4: the closely spaced peaks arise from splitting because the complex is not O_h

ν₁ arises from splitting of the 919 nm and 800 nm features so (averaging) ν₁ = ½(10900 + 12500) = 11700 cm^–1

ν₂ arises from splitting of the 555 nm and 585 nm features so ν₂ = ½(17100 + 18000) = 17550 cm^–1

With this assignment, ν₁ = 10Dq = 11700 cm^–1

3B = (ν₂ – ν₁)(ν₂ – ν₁)/ (5ν₂ – 9ν₁) = (17550 – 2×11700)(17550 – 11700)/ (5×17550 – 9×11700) = 1950 cm^–1 so B = 650 cm^–1

β = B_complex/B_{free ion} = 650/1080 = 0.602

These values seem most reasonable so this assignment is likely correct.

In O_h the assignments are ν₁ ³T_2g ← ³A_2g

and ν₂ ³T_1g ← ³A_2g

Assuming an approximate D₃ symmetry the assignments would be: 919 nm ³E ← ³A₂, 800 nm ³A₁ ← ³A₂, 585 nm ³A₂ ← ³A₂, and 555 nm ³E ← ³A₂.

[Co(NNN)₂]²⁺ is a d⁷ complex, so the complex may be high-spin or low-spin.

Guess 1 - High Spin. This would be consistent with the small values of 10Dq for the other two complexes

ν₁ = 1095 nm = 9130 cm^–1

ν₂ = 544 nm = 18400 cm^–1

ν₃ = 482 nm = 20700 cm^–1

10Dq = ν₂ – ν₁ = 18400 – 9130 = 9270 cm^–1

15B = ν₃ + ν₂ – 3ν₁ = 20700 + 18400 – 3(9130) = 11710 cm^–1 so B = 781 cm^–1

β = B_complex/B_{free ion} = 781/1120 = 0.697

These seem reasonable

Guess 2 - Low Spin. This requires the use of the Tanabe-Sugano diagram.

ν₁ = 1095 nm = 9130 cm^–1

ν₂ = 544 nm = 18400 cm^–1

ν₃ = 482 nm = 20700 cm^–1

ν₂/ν₁ = 18400/9130 = 2.02

ν₃/ν₁ = 20700/9130 = 2.27

Looking at the Tanabe-Sugano diagram, at no point along the low spin side can the ν₂/ν₁ ratio be as high as 2. Thus, this assignment must be incorrect

Guess 3 - Low Spin. Assume that ν₁ and ν₂ overlap.

ν₁, ν₂ = 1095 nm = 9130 cm^–1

ν₃ = 482 nm = 20700 cm^–1

ν₃/ν₁ = 20700/9130 = 2.27

Looking at the Tanabe-Sugano diagram, this ratio (= 40/18) could be attained at 10Dq/B = 22 (right at the high-spin/low-spin transition)

This gives B = 20700/40 = 520 cm^–1 and B = 9130/18 = 510 cm^–1, averaging to 515 cm^–1

Then, 10Dq = 22B = 22(515) = 11300 cm^–1

β = B_complex/B_{free ion} = 515/1120 = 0.460

B and β are low but not completely unreasonable.

Based on the Irving-Williams series, 10Dq(Co²⁺) should be less than 10Dq(Ni²⁺). Both assignments fit this but the if the Co²⁺ complex is low spin, the values for 10Dq are essentially the same. Given the size of B and the Irving-Williams series, the assignment of the high-spin values is most likely.

Then, ν₁, 1095 nm, ⁴T_1g ← ⁴T_1g

Then, ν₂, 544 nm, ⁴T_2g ← ⁴T_1g

Then, ν₃, 482 nm, ⁴A_2g ← ⁴T_1g

Coordination is probably between the central amine N atom and the imine N atoms in the 5-membered ring. The π system at the imine sites allows for some back donation, accounting for the low B value. The low 10Dq values must arise from steric repulsion in the ring system since both amine and imine donors would predict a strong field.

 

The spectra are taken from N. P. Magwa, E. Hosten, G. M. Watkins, Z. R. Tshentu, Int. J. Nonferr. Metals, 2012, 1, 49 – 58.