Magnetic exchange interactions in cyano‐bridged Mo^III binuclear complexes: Broken‐symmetry and density functional theory calculations

Abstract

Molecular tacnAN, NЈ, NЉ-trimethyl-1,4,7-triazacyclononane) has been calculated using Becke's three-parameter exchange functional and the gradient-corrected functional of Lee, Yang, and Parr (B3LYP), a hybrid density functional theory (DFT), combined with a modified broken symmetry (BS) approach and the post-Hartree-Fock (post-HF) method difference-dedicated configuration interaction (DDCI). We find B3LYP combined with broken-symmetry approach (DFT-BS) give the similar J values to those calculated by DDCI. So we use B3LYP combined with BS approach to investigate the magnetism above two molecules. Through calculations, we find that the absolute J values decrease with the increase of r (the Mo(2)-C brid and Mo(1)-N brid distances) and are linearly related to the differences of the squared spin populations [( HS 2 Ϫ BS2 )] on Mo III atoms between the highest-spin (HS) state and the broken symmetry (BS) state. Moreover, the absolute J values are linearly related to the sum of the square of the difference in energy of the unpaired electrons () with a limited variation of the r distance. We conclude that can be used to scale the degree of the antiferromagnetic coupling interactions. At the end of the paper, the spin density distributions and the mechanisms of magnetic coupling interactions are analyzed by us.

Relationship Between the Nearest‐Neighbor Exchange Coupling Constants and the Number of Exchange Interactions in the Cyano‐Bridged MnMo6(CN)18 Cluster: Density Functional Theory Calculations

“…The bridges are of the Mo-CN-Mn type and, therefore, the Mn atom with an N 6 coordination sphere is in a high-spin configuration. Models A 1 , A 2 , A 3 , A 4 , and A 5 (the superscript numbers denote the number of exchange interactions) (see Figure 2) were used to investigate the relationship between the nearest-neighbor exchange coupling constants J 12 and the number of exchange interactions. To investigate the relationship between J 12 and the θ angle (we use θ to represent the MoMnMo angle), we obtained three different structures that all include two of the exchange interactions A 2 , A 2Ј , and A 2ЈЈ (see Figure 3).…”

A Theoretical Study of the Nearest Cu···Cu Antiferromagnetic Exchange Coupling Interactions in [LaCu6] and [YCu6]

“…We have also used Equation (15) to evaluate binuclear Mo III complexes and also found that the J values are almost linearly related to -(ρ HS 2 -ρ BS 2 ). [55] The spin populations were obtained by PW91 calculations on the basis of a Mulliken population analysis [53] using the first approach. Due to the symmetry of the structures, we only give the results for one of the Cu II ions (Table 3).…”

Adolescent–Adult discrepancies on the eating disorder examination: A function of developmental stage or severity of illness?

“…In a recent work, Desplanches et al 4 succeeded in calculating the exchange coupling constants in metal complexes of the second transition series, using density functional theory (DFT) combined with Noodleman's broken‐symmetry (BS) approach 5–7. We 8 also selected two cyano‐bridged Mo III binuclear complexes [Mo 2 (CN) 11 ] 5− 1 and [(Me 3 tacn) 2 Mo 2 (CN) 5 ] + (Me 3 tacn = N , N ′, N ″‐trimethyl‐triaz‐acyclononane) 2 to analyze the magneto‐structural correlations and the mechanisms of the magnetic coupling interactions through the spin‐density maps, using DFT‐BS. In the above theoretical work, Desplanches et al 4 and Zhang et al 8 only investigated the homo‐binuclear second transition metal complexes.…”

“…We 8 also selected two cyano‐bridged Mo III binuclear complexes [Mo 2 (CN) 11 ] 5− 1 and [(Me 3 tacn) 2 Mo 2 (CN) 5 ] + (Me 3 tacn = N , N ′, N ″‐trimethyl‐triaz‐acyclononane) 2 to analyze the magneto‐structural correlations and the mechanisms of the magnetic coupling interactions through the spin‐density maps, using DFT‐BS. In the above theoretical work, Desplanches et al 4 and Zhang et al 8 only investigated the homo‐binuclear second transition metal complexes. However, we selected four cyano‐bridged hetero‐trinuclear and hetero‐polynuclear complexes to investigate the magnetic properties extending the research of magnetic coupling mechanism of 4 d systems.…”