Calculation of Spin Orbit Coupling of Tungsten (III) Complexes: A DFT Application

Introduction

Unlike the 1^st transition series metal ion complexes, there had, hardly, been any study done on the calculation of Spin Orbit Coupling (λ_complex) of the corresponding complexes of 2^nd and 3^rd transition series. The limitation would arise because  high λ_complex values^{( 1 )} of their complexes caused errors both  in the exact  determination of their Crystal Field Stabilization Energies (CFSE) as well as the ESR parameters (especially A _ten).They would, further, cause errors in  the g values if determined by experimental  methods. We applied Density Functional Theory (DFT) implemented in ADF 2010.02 software to its ESR/EPR Program which was run by giving Single Point, LDA, Default, Spin Orbit, Unrestricted, None, Collinear and ZORA commands using TZP Basis set with Nosym symmetry after definite Pre-optimization of five W (III) complexes to obtain their g _iso values ^(2-4). Five known relations (a-e) were used in a sequence. Magnetic moments (m_ADF) arising from the First Order Zeeman Effect were calculated from the g _iso values (a) . Magnetic moment values arising from the Second Order Zeeman Effect [Temperature Independent Paramagnetic Moments   (m _tip)] were calculated by (c) from their paramagnetic susceptibilities (χ_tip) as calculated by (b).  Sum of m_ADF and  m _tip would give effective magnetic moments (μ_eff) (d) .CFSE values of W (III) complexes were ≈1.75 times the reported CFSE values of the corresponding Cr (III) complexes ^(5-7).λ_Complex values ⁽⁸⁾ of W (III) complexes were calculated by (e).

Table 1 Click here to View table

*Multiply CFSE of corresponding Cr (III) Complex by 1.75

**Multiply by 10^6- c g s

μ_s.o=3.8729 B.M and χ_{s. o.} =6250 _* 10^{– 6}cgs for 3 unpaired electrons

(a)μ_ADF = [g_iso²s(s+1)]^1/2

(b) χ_tip = 8Nb²/10Dq

(c) μ_tip= χ_{tip *} m_s.o /c_s.o

(d)  μ_{t = mADF+m tip}

_(e)  μ_eff =m_so  (1-  σ _* λ _complex  /10Dq)

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