Context Anion-pillared metal–organic frameworks (APMOFs) have emerged as promising materials for natural gas purification, owing to the strong electrostatic fields generated by high-charge-density ionic pillars. However, accurately describing these highly localized interactions within classical force field frameworks remains challenging, as generic parameterizations such as the Universal Force Field (UFF) and DREIDING fail to capture the specific polarization effects of ionic active sites. In this work, we address this limitation for MoOFOUR-1-Ni, an APMOF exhibiting high CO<InlineEquation ID="IEq7"> <EquationSource Format="TEX">$_{{\textbf {2}}}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn mathvariant="bold">2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> selectivity over N<InlineEquation ID="IEq8"> <EquationSource Format="TEX">$_{{\textbf {2}}}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn mathvariant="bold">2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> and CH<InlineEquation ID="IEq9"> <EquationSource Format="TEX">$_{{\textbf {4}}}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn mathvariant="bold">4</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>, by developing a system-specific force field for the <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$[\text {MoO}_{{\textbf {4}}}]^{{\textbf {2}}-}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mo stretchy="false">[</mo> <msub> <mtext>MoO</mtext> <mn mathvariant="bold">4</mn> </msub> <mo stretchy="false">]</mo> </mrow> <mrow> <mn mathvariant="bold">2</mn> <mo>-</mo> </mrow> </msup> </math></EquationSource> </InlineEquation> pillar through a DFT-guided parametrization workflow. The optimized Lennard–Jones parameters were validated against experimental adsorption isotherms for all three gases, yielding a five-fold reduction in mean absolute error for CO<InlineEquation ID="IEq11"> <EquationSource Format="TEX">$_{{\textbf {2}}}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn mathvariant="bold">2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> relative to UFF+DREIDING, and very good agreement for N<InlineEquation ID="IEq12"> <EquationSource Format="TEX">$_{{\textbf {2}}}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn mathvariant="bold">2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> and CH<InlineEquation ID="IEq13"> <EquationSource Format="TEX">$_{{\textbf {4}}}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn mathvariant="bold">4</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>. The results highlight the inherent substrate-specificity of the derived parameters and the fundamental limitations of transferable force fields in chemically complex ionic environments. Methods Potential energy curves for the interactions between the <InlineEquation ID="IEq14"> <EquationSource Format="TEX">$[\text {MoO}_{{\textbf {4}}}]^{{\textbf {2}}-}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mo stretchy="false">[</mo> <msub> <mtext>MoO</mtext> <mn mathvariant="bold">4</mn> </msub> <mo stretchy="false">]</mo> </mrow> <mrow> <mn mathvariant="bold">2</mn> <mo>-</mo> </mrow> </msup> </math></EquationSource> </InlineEquation> anion and CO<InlineEquation ID="IEq15"> <EquationSource Format="TEX">$_{{\textbf {2}}}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn mathvariant="bold">2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>, N<InlineEquation ID="IEq16"> <EquationSource Format="TEX">$_{{\textbf {2}}}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn mathvariant="bold">2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>, and CH<InlineEquation ID="IEq17"> <EquationSource Format="TEX">$_{{\textbf {4}}}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn mathvariant="bold">4</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> were computed at the PBE-D3(BJ)/def2-TZVPD level of theory using ORCA 6.0.1. Partial charges were obtained via the CHELPG method as implemented in Multiwfn. Lennard–Jones parameters were optimized using the L-BFGS-B algorithm, minimizing a regularized objective function combining mean absolute deviation from DFT reference energies and a quadratic penalty term. Grand Canonical Monte Carlo (GCMC) adsorption isotherms were simulated using RASPA on a <InlineEquation ID="IEq18"> <EquationSource Format="TEX">$\varvec{2\times 2\times 2}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn mathvariant="bold">2</mn> <mo mathvariant="bold">×</mo> <mn mathvariant="bold">2</mn> <mo mathvariant="bold">×</mo> <mn mathvariant="bold">2</mn> </mrow> </math></EquationSource> </InlineEquation> supercell derived from a PBE-D3/Quantum ESPRESSO periodic DFT optimization, with TraPPE parameters employed for the adsorbate molecules. Pure-component adsorption isotherms were further fitted to Langmuir-based models and employed in Ideal Adsorbed Solution Theory (IAST) calculations to estimate binary CO<InlineEquation ID="IEq19"> <EquationSource Format="TEX">$_{{\textbf {2}}}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn mathvariant="bold">2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>/CH<InlineEquation ID="IEq20"> <EquationSource Format="TEX">$_{{\textbf {4}}}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn mathvariant="bold">4</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> and CO<InlineEquation ID="IEq21"> <EquationSource Format="TEX">$_{{\textbf {2}}}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn mathvariant="bold">2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>/N<InlineEquation ID="IEq22"> <EquationSource Format="TEX">$_{{\textbf {2}}}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn mathvariant="bold">2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> adsorption selectivities. Graphical abstract

DFT-guided Lennard–Jones parametrization for accurate $\text {CO}_{2}$, $\text {N}_{2}$, and $\text {CH}_{4}$ adsorption in MoOFOUR-1-Ni

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2026年8月1日

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Herick Ribeiro Torres,
Roberta Pereira Dias,
Heitor Avelino de Abreu,
Júlio Cosme Santos da Silva,
Guilherme Ferreira de Lima

摘要

Context

Anion-pillared metal–organic frameworks (APMOFs) have emerged as promising materials for natural gas purification, owing to the strong electrostatic fields generated by high-charge-density ionic pillars. However, accurately describing these highly localized interactions within classical force field frameworks remains challenging, as generic parameterizations such as the Universal Force Field (UFF) and DREIDING fail to capture the specific polarization effects of ionic active sites. In this work, we address this limitation for MoOFOUR-1-Ni, an APMOF exhibiting high CO $_{{\textbf {2}}}$ $_{2}$ selectivity over N $_{{\textbf {2}}}$ $_{2}$ and CH $_{{\textbf {4}}}$ $_{4}$ , by developing a system-specific force field for the $[\text {MoO}_{{\textbf {4}}}]^{{\textbf {2}}-}$ ${[{MoO}_{4}]}^{2 -}$ pillar through a DFT-guided parametrization workflow. The optimized Lennard–Jones parameters were validated against experimental adsorption isotherms for all three gases, yielding a five-fold reduction in mean absolute error for CO $_{{\textbf {2}}}$ $_{2}$ relative to UFF+DREIDING, and very good agreement for N $_{{\textbf {2}}}$ $_{2}$ and CH $_{{\textbf {4}}}$ $_{4}$ . The results highlight the inherent substrate-specificity of the derived parameters and the fundamental limitations of transferable force fields in chemically complex ionic environments.

Methods

Potential energy curves for the interactions between the $[\text {MoO}_{{\textbf {4}}}]^{{\textbf {2}}-}$ ${[{MoO}_{4}]}^{2 -}$ anion and CO $_{{\textbf {2}}}$ $_{2}$ , N $_{{\textbf {2}}}$ $_{2}$ , and CH $_{{\textbf {4}}}$ $_{4}$ were computed at the PBE-D3(BJ)/def2-TZVPD level of theory using ORCA 6.0.1. Partial charges were obtained via the CHELPG method as implemented in Multiwfn. Lennard–Jones parameters were optimized using the L-BFGS-B algorithm, minimizing a regularized objective function combining mean absolute deviation from DFT reference energies and a quadratic penalty term. Grand Canonical Monte Carlo (GCMC) adsorption isotherms were simulated using RASPA on a $\varvec{2\times 2\times 2}$ $2 \times 2 \times 2$ supercell derived from a PBE-D3/Quantum ESPRESSO periodic DFT optimization, with TraPPE parameters employed for the adsorbate molecules. Pure-component adsorption isotherms were further fitted to Langmuir-based models and employed in Ideal Adsorbed Solution Theory (IAST) calculations to estimate binary CO $_{{\textbf {2}}}$ $_{2}$ /CH $_{{\textbf {4}}}$ $_{4}$ and CO $_{{\textbf {2}}}$ $_{2}$ /N $_{{\textbf {2}}}$ $_{2}$ adsorption selectivities.

Graphical abstract

DFT-guided Lennard–Jones parametrization for accurate \(\text {CO}_{2}\), \(\text {N}_{2}\), and \(\text {CH}_{4}\) adsorption in MoOFOUR-1-Ni

摘要