Spin Frustration Determines the Stability and Reactivity of Metal–Organic Frameworks with Triangular Iron(III)–Oxo Clusters

Density functional theory (DFT) is the standard approach for modeling MIL-101(Fe) and related Fe-based metal-organic frameworks, typically assuming a ferromagnetic high-spin configuration. However, this widely adopted approach overlooks a key electronic feature: Spin frustration in the triangular <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>Fe</mml:mi> <mml:mn>3</mml:mn></mml:msub> <mml:mrow><mml:mo>(</mml:mo></mml:mrow> <mml:msub><mml:mi>μ</mml:mi> <mml:mn>3</mml:mn></mml:msub> </mml:mrow> <mml:annotation>${\rm Fe}_{3}(\mu _{3}$</mml:annotation></mml:semantics> </mml:math> -O) nodes. Using flip-spin, broken-symmetry DFT, we identify the true ground state as an antiferromagnetic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mn>2</mml:mn> <mml:mi>S</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo>=</mml:mo> <mml:mn>6</mml:mn></mml:mrow> <mml:annotation>$2S+1=6$</mml:annotation></mml:semantics> </mml:math> state that standard DFT fails to capture. We demonstrate that neglecting spin frustration in MIL-101(Fe) leads to structural distortions, incorrect energetics, and misleading predictions of stability and reactivity. By explicitly accounting for spin frustration, we recover the correct structure and rationalize the temperature-dependent <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msub><mml:mi>N</mml:mi> <mml:mn>2</mml:mn></mml:msub> <mml:annotation>${\rm N}_{2}$</mml:annotation></mml:semantics> </mml:math> and CO binding. Spin frustration enhances <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msub><mml:mi>N</mml:mi> <mml:mn>2</mml:mn></mml:msub> <mml:annotation>${\rm N}_{2}$</mml:annotation></mml:semantics> </mml:math> fixation at room temperature, while its loss upon partial <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msup><mml:mi>Fe</mml:mi> <mml:mi>III</mml:mi></mml:msup> <mml:annotation>${\rm Fe}^{\mathrm {III}}$</mml:annotation></mml:semantics> </mml:math> reduction suppresses this activity but promotes CO adsorption via <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:semantics><mml:mi>π</mml:mi> <mml:annotation>$\pi$</mml:annotation></mml:semantics> </mml:math> -backbonding. These findings challenge current computational conventions and highlight spin frustration as a critical electronic feature in these frameworks.