# Extending Libraries of Extremely Localized Molecular Orbitals to Metal Organic Frameworks: A Preliminary Investigation

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{3}(BTC)

_{2}}

_{n}, with BTC=1,3,5-benzenetricarboxylate) to quickly calculate electrostatic potential maps in the small and large cavities inside the network. On the basis of the obtained results, we envisage further improvements and applications of this strategy, which can be also seen as a starting point to perform less computationally expensive quantum mechanical calculations on metal organic frameworks with the goal of investigating transformation phenomena such as chemisorption.

## 1. Introduction

## 2. Theoretical and Computational Details

#### 2.1. Extremely Localized Molecular Orbitals and ELMO Libraries

#### 2.2. ELMO-Protocol for MOFs

_{3}(BTC)

_{2}}

_{n}(where BTC stands for 1,3,5-benzenetricarboxylate), which is also commonly known as HKUST-1 (see Figure 2) [108,109]. Since the current ELMO libraries cover only the basic fragments of the twenty natural amino acids, it was primarily necessary to obtain tailor-made ELMOs computed on suitable model molecules of the MOF subunits.

- Construct a library of ELMOs describing the elementary fragments of the most common linkers employed for MOFs design.
- For each MOF crystal structure, perform ad hoc QM/ELMO calculations on model systems consisting of a SBU (at QM level) and the connected linkers (using ELMOs computed at step 1).
- The ELMOs for the linkers (see point 1) and the localized molecular orbitals for the SBU (obtained from point 2) will be finally transferred to the symmetry-related positions of the crystal structure using the ELMOdb program [61], thus quickly obtaining an approximate wavefunction/electron density for the periodic system.

## 3. Results and Discussion

## 4. Conclusions and Perspectives

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Gordon, M.S.; Slipchenko, L.V. Introduction: Calculations on Large Systems. Chem. Rev.
**2015**, 115, 5605–5606. [Google Scholar] [CrossRef] - Jones, L.O.; Mosquera, M.A.; Schatz, G.C.; Ratner, M.A. Embedding Methods for Quantum Chemistry: Applications from Materials to Life Sciences. J. Am. Chem. Soc.
**2020**, 142, 3281–3295. [Google Scholar] [CrossRef] - Warshel, A.; Levitt, M. Theoretical Studies of Enzymic Reactions: Dielectric, Electrostatic and Steric Stabilization of the Car-bonium ion in the Reaction of Lysozyme. J. Mol. Biol.
**1976**, 103, 227–249. [Google Scholar] [CrossRef] - Field, M.J.; Bash, P.A.; Karplus, M. A Combined Quantum Mechanical and Molecular Mechanical Potential for Molecular Dynamics Simulations. J. Comput. Chem.
**1990**, 11, 700–733. [Google Scholar] [CrossRef] - Gao, J. Methods and Applications of Combined Quantum Mechanical and Molecular Mechanical Potentials. In Reviews in Computational Chemistry; Lipkowitz, K.B., Boyd, D.B., Eds.; VCH Publishers, Inc.: Weinheim, Germany, 1996; Volume 7, pp. 119–186. [Google Scholar] [CrossRef]
- Senn, H.M.; Thiel, W. QM/MM Methods for Biomolecular Systems. Angew. Chem. Int. Ed.
**2009**, 48, 1198–1229. [Google Scholar] [CrossRef] - Warshel, A. Multiscale Modeling of Biological Functions: From Enzymes to Molecular Machines (Nobel Lecture). Angew. Chem. Int. Ed.
**2014**, 53, 10020–10031. [Google Scholar] [CrossRef] [Green Version] - Levitt, M. Birth and Future of Multiscale Modeling for Macromolecular Systems (Nobel Lecture). Angew. Chem. Int. Ed.
**2014**, 53, 10006–10018. [Google Scholar] [CrossRef] - Karplus, M. Development of Multiscale Models for Complex Chemical Systems: From H+H
_{2}to Biomolecules (Nobel Lecture). Angew. Chem. Int. Ed.**2014**, 53, 9992–10005. [Google Scholar] [CrossRef] [PubMed] - Svensson, M.; Humbel, S.; Froese, R.D.J.; Matsubara, T.; Sieber, S.; Morokuma, K. ONIOM: A Multilayered Integrated MO + MM Method for Geometry Optimizations and Single Point Energy Predictions. A Test for Diels−Alder Reactions and Pt(P(t-Bu)
_{3})_{2}+ H_{2}Oxidative Addition. J. Phys. Chem.**1996**, 100, 19357–19363. [Google Scholar] [CrossRef] - Chung, L.W.; Sameera, W.M.C.; Ramozzi, R.; Page, A.J.; Hatanaka, M.; Petrova, G.P.; Harris, T.V.; Li, X.; Ke, Z.; Liu, F.; et al. The ONIOM Method and Its Applications. Chem. Rev.
**2015**, 115, 5678–5796. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Wesolowski, T.A.; Warshel, A. Frozen density functional approach for ab initio calculations of solvated molecules. J. Phys. Chem.
**1993**, 97, 8050–8053. [Google Scholar] [CrossRef] - Wesolowski, T.A. Embedding a multideterminantal wave function in an orbital-free environment. Phys. Rev. A
**2008**, 77, 012504. [Google Scholar] [CrossRef] [Green Version] - Wesolowski, T.A.; Shedge, S.; Zhou, X. Frozen-Density Embedding Strategy for Multilevel Simulations of Electronic Structure. Chem. Rev.
**2015**, 115, 5891–5928. [Google Scholar] [CrossRef] [Green Version] - Manby, F.R.; Stella, M.; Goodpaster, J.D.; Miller, T.F., III. A Simple, Exact Density-Functional-Theory Embedding Scheme. J. Chem. Theory Comput.
**2012**, 8, 2564–2568. [Google Scholar] [CrossRef] [Green Version] - Barnes, T.A.; Goodpaster, J.D.; Manby, F.R.; Miller, T.F., III. Accurate basis set truncation for wavefunction embedding. J. Chem. Phys.
**2013**, 139, 24103. [Google Scholar] [CrossRef] [Green Version] - Goodpaster, J.D.; Barnes, T.A.; Manby, F.R.; Miller, T.F., III. Accurate and systematically improvable density functional theory embedding for correlated wave functions. J. Chem. Phys.
**2014**, 140, 18A507. [Google Scholar] [CrossRef] [Green Version] - Bennie, S.J.; Stella, M.; Miller, T.F., III; Manby, F.R. Accelerating wavefunction in density-functional-theory embedding by truncating the active basis set. J. Chem. Phys.
**2015**, 143, 024105. [Google Scholar] [CrossRef] [Green Version] - Pennifold, R.C.R.; Bennie, S.J.; Miller, T.F., III; Manby, F.R. Correcting density-driven errors in projection-based embedding. J. Chem. Phys.
**2017**, 146, 084113. [Google Scholar] [CrossRef] [Green Version] - Welborn, M.; Manby, F.R.; Miller, T.F., IIII. Even-handed subsystem selection in projection-based embedding. J. Chem. Phys.
**2018**, 149, 144101. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Chulhai, D.V.; Goodpaster, J.D. Improved Accuracy and Efficiency in Quantum Embedding through Absolute Localization. J. Chem. Theory Comput.
**2017**, 13, 1503–1508. [Google Scholar] [CrossRef] - Chulhai, D.V.; Goodpaster, J.D. Projection-Based Correlated Wave Function in Density Functional Theory Embedding for Periodic Systems. J. Chem. Theory Comput.
**2018**, 14, 1928–1942. [Google Scholar] [CrossRef] - Bennie, S.J.; van der Kamp, M.W.; Pennifold, R.C.R.; Stella, M.; Manby, F.R.; Mulholland, A.J. A Projector-Embedding Approach for Multiscale Coupled-Cluster Calculations Applied to Citrate Synthase. J. Chem. Theory Comput.
**2016**, 12, 2689–2697. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lee, S.J.R.; Welborn, M.; Manby, F.R.; Miller, T.F., III. Projection-Based Wavefunction-in-DFT Embedding. Acc. Chem. Res.
**2019**, 52, 1359–1368. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Yang, W. Direct calculation of electron density in density-functional theory. Phys. Rev. Lett.
**1991**, 66, 1438–1441. [Google Scholar] [CrossRef] [PubMed] - Yang, W. Direct calculation of electron density in density-functional theory: Implementation for benzene and a tetrapeptide. Phys. Rev. A
**1991**, 44, 7823–7826. [Google Scholar] [CrossRef] - Dixon, S.L.; Merz, K.M., Jr. Semiempirical molecular orbital calculations with linear system size scaling. J. Chem. Phys.
**1996**, 104, 6643–6649. [Google Scholar] [CrossRef] - Dixon, S.L.; Merz, K.M., Jr. Fast, accurate semiempirical molecular orbital calculations for macromolecules. J. Chem. Phys.
**1997**, 107, 879–893. [Google Scholar] [CrossRef] - He, X.; Merz, K.M., Jr. Divide and Conquer Hartree−Fock Calculations on Proteins. J. Chem. Theory Comput.
**2010**, 6, 405–411. [Google Scholar] [CrossRef] [PubMed] - Gadre, S.R.; Shirsat, R.N.; Limaye, A.C. Molecular Tailoring Approach for Simulation of Electrostatic Properties. J. Phys. Chem.
**1994**, 98, 9165–9169. [Google Scholar] [CrossRef] - Sahu, N.; Gadre, S.R. Molecular Tailoring Approach: A Route for ab Initio Treatment of Large Clusters. Acc. Chem. Res.
**2014**, 47, 2739–2747. [Google Scholar] [CrossRef] - Kitaura, K.; Ikeo, E.; Asada, T.; Nakano, T.; Uebayasi, M. Fragment molecular orbital method: An approximate computational method for large molecules. Chem. Phys. Lett.
**1999**, 313, 701–706. [Google Scholar] [CrossRef] - Nakano, T.; Kaminuma, T.; Sato, T.; Akiyama, Y.; Uebayasi, M.; Kitaura, K. Fragment molecular orbital method: Application to polypeptides. Chem. Phys. Lett.
**2000**, 318, 614–618. [Google Scholar] [CrossRef] - Fedorov, D.G.; Kitaura, K. Theoretical development of the fragment molecular orbital (FMO) method. In Modern Methods for Theoretical Physical Chemistry and Biopolymers; Starikov, E.B., Lewis, J.P., Tanaka, S., Eds.; Elsevier: Amsterdam, The Netherlands, 2006; Chapter 1; pp. 3–38. [Google Scholar] [CrossRef]
- Fedorov, D.G.; Kitaura, K. Theoretical Background of the Fragment Molecular Orbital (FMO) Method and Its Implementation in GAMESS. In The Fragment Molecular Orbital Method: Practical Applications to Large Molecular Systems; Fedorov, D.G., Kitaura, K., Eds.; CRC Press-Taylor & Francis Group: Boca Raton, FL, USA, 2009; Chapter 2; pp. 5–36. [Google Scholar] [CrossRef]
- Huang, L.; Massa, L.; Karle, J. Kernel energy method illustrated with peptides. Int. J. Quantum Chem.
**2005**, 103, 808–817. [Google Scholar] [CrossRef] - Huang, L.; Massa, L.; Karle, J. Kernel energy method applied to vesicular stomatitis virus nucleoprotein. Proc. Natl. Acad. Sci. USA
**2009**, 106, 1731–1736. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Huang, L.; Bohorquez, H.; Matta, C.F.; Massa, L. The Kernel Energy Method: Application to Graphene and Extended Aromatics. Int. J. Quantum Chem.
**2011**, 111, 4150–4157. [Google Scholar] [CrossRef] - Zhang, D.W.; Zhang, J.Z.H. Molecular fractionation with conjugate caps for full quantum mechanical calculation of protein-molecule interaction energy. J. Chem. Phys.
**2003**, 119, 3599–3605. [Google Scholar] [CrossRef] - Gao, A.M.; Zhang, D.W.; Zhang, J.Z.H.; Zhang, Y. An efficient linear scaling method for ab initio calculation of electron density of proteins. Chem. Phys. Lett.
**2004**, 394, 293–297. [Google Scholar] [CrossRef] - He, X.; Zhang, J.Z.H. The generalized molecular fractionation with conjugate caps/molecular mechanics method for direct calculation of protein energy. J. Chem. Phys.
**2006**, 124, 184703. [Google Scholar] [CrossRef] - Li, S.; Li, W.; Fang, T. An Efficient Fragment-Based Approach for Predicting the Ground-State Energies and Structures of Large Molecules. J. Am. Chem. Soc.
**2005**, 127, 7215–7226. [Google Scholar] [CrossRef] - Walker, P.D.; Mezey, P.G. Ab Initio Quality Electron Densities for Proteins: A MEDLA Approach. J. Am. Chem. Soc.
**1994**, 116, 12022–12032. [Google Scholar] [CrossRef] - Exner, T.E.; Mezey, P.G. Ab Initio-Quality Electrostatic Potentials for Proteins: An Application of the ADMA Approach. J. Phys. Chem. A
**2002**, 106, 11791–11800. [Google Scholar] [CrossRef] - Exner, T.E.; Mezey, P.G. Ab initio quality properties for macromolecules using the ADMA approach. J. Comput. Chem.
**2003**, 24, 1980–1986. [Google Scholar] [CrossRef] [PubMed] - Breneman, C.M.; Thompson, T.R.; Rhem, M.; Dung, M. Electron density modeling of large systems using the transferable atom equivalent method. Comput. Chem.
**1995**, 19, 161–179. [Google Scholar] [CrossRef] - Chang, C.; Bader, R.F.W. Theoretical construction of a polypeptide. J. Phys. Chem.
**1992**, 96, 1654–1662. [Google Scholar] [CrossRef] - Bader, R.F.W.; Martín, F.J. Interdeterminancy of basin and surface properties of an open system. Can. J. Chem.
**1998**, 76, 284–291. [Google Scholar] [CrossRef] - Matta, C.F. Theoretical Reconstruction of the Electron Density of Large Molecules from Fragments Determined as Proper Open Quantum Systems: The Properties of the Oripavine PEO, Enkephalins, and Morphine. J. Phys. Chem. A
**2001**, 105, 11088–11101. [Google Scholar] [CrossRef] - Bader, R.F.W. Atoms in Molecules: A Quantum Theory; Oxford University Press: Oxford, UK, 1990. [Google Scholar]
- Stoll, H.; Wagenblast, G.; Preuβ, H. On the use of local basis sets for localized molecular orbitals. Theor. Chim. Acta
**1980**, 57, 169–178. [Google Scholar] [CrossRef] - Fornili, A.; Sironi, M.; Raimondi, M. Determination of Extremely Localized Molecular Orbitals and Their Application to Quantum Mechanics/Molecular Mechanics Methods and to the Study of Intramolecular Hydrogen Bonding. J. Mol. Struct.
**2003**, 632, 157–172. [Google Scholar] [CrossRef] - Sironi, M.; Genoni, A.; Civera, M.; Pieraccini, S.; Ghitti, M. Extremely localized molecular orbitals: Theory and applications. Theor. Chem. Acc.
**2007**, 117, 685–698. [Google Scholar] [CrossRef] - Genoni, A.; Sironi, M. A novel approach to relax extremely localized molecular orbitals: The extremely localized molecular orbital-valence bond method. Theor. Chem. Acc.
**2004**, 112, 254–262. [Google Scholar] [CrossRef] - Genoni, A.; Fornili, A.; Sironi, M. Optimal Virtual Orbitals to Relax Wave Functions Built Up with Transferred Extremely Localized Molecular Orbitals. J. Comput. Chem.
**2005**, 26, 827–835. [Google Scholar] [CrossRef] - Genoni, A.; Ghitti, M.; Pieraccini, S.; Sironi, M. A novel extremely localized molecular orbitals based technique for the one-electron density matrix computation. Chem. Phys. Lett.
**2005**, 415, 256–260. [Google Scholar] [CrossRef] - Genoni, A.; Merz, K.M., Jr.; Sironi, M. A Hylleras functional based perturbative technique to relax extremely localized molecular orbitals. J. Chem. Phys.
**2008**, 129, 054101. [Google Scholar] [CrossRef] - Sironi, M.; Ghitti, M.; Genoni, A.; Saladino, G.; Pieraccini, S. DENPOL: A new program to determine electron densities of poly-peptides using extremely localized molecular orbitals. J. Mol. Struct.
**2009**, 898, 8–16. [Google Scholar] [CrossRef] - Meyer, B.; Guillot, B.; Ruiz-Lopez, M.F.; Genoni, A. Libraries of Extremely Localized Molecular Orbitals. 1. Model Molecules Approximation and Molecular Orbitals Transferability. J. Chem. Theory Comput.
**2016**, 12, 1052–1067. [Google Scholar] [CrossRef] - Meyer, B.; Guillot, B.; Ruiz-Lopez, M.F.; Jelsch, C.; Genoni, A. Libraries of Extremely Localized Molecular Orbitals. 2. Comparison with the Pseudoatoms Transferability. J. Chem. Theory Comput.
**2016**, 12, 1068–1081. [Google Scholar] [CrossRef] [PubMed] - Meyer, B.; Genoni, A. Libraries of Extremely Localized Molecular Orbitals. 3. Construction and Preliminary Assessment of the New Databanks. J. Phys. Chem. A
**2018**, 122, 8965–8981. [Google Scholar] [CrossRef] - Genoni, A.; Bučinský, L.; Claiser, N.; Contreras-García, J.; Dittrich, B.; Dominiak, P.M.; Espinosa, E.; Gatti, C.; Giannozzi, P.; Gillet, J.-M.; et al. Quantum Crystallography: Current Developments and Future Perspectives. Chem. Eur. J.
**2018**, 24, 10881–10905. [Google Scholar] [CrossRef] [Green Version] - Grabowsky, S.; Genoni, A.; Bürgi, H.-B. Quantum crystallography. Chem. Sci.
**2017**, 8, 4159–4176. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Genoni, A.; Macchi, P. Quantum Crystallography in the Last Decade: Developments and Outlooks. Crystals
**2020**, 10, 473. [Google Scholar] [CrossRef] - Grabowsky, S.; Genoni, A.; Thomas, S.P.; Jayatilaka, D. The Advent of Quantum Crystallography: Form and Structure Factors from Quantum Mechanics for Advanced Structure Refinement and Wavefunction Fitting. In 21st Century Challenges in Chemical Crystallography II. Structure and Bonding; Springer International Publishing: Berlin/Heidelberg, Germany, 2020; pp. 65–144. [Google Scholar] [CrossRef]
- Macchi, P. The connubium between crystallography and quantum mechanics. Crystallogr. Rev.
**2020**, 26, 209–268. [Google Scholar] [CrossRef] - Massa, L.; Matta, C.F. Quantum crystallography: A perspective. J. Comput. Chem.
**2018**, 39, 1021–1028. [Google Scholar] [CrossRef] - Jayatilaka, D.; Dittrich, B. X-ray structure refinement using aspherical atomic density functions obtained from quantum me-chanical calculations. Acta Crystallogr. Sect. A
**2008**, 64, 383–393. [Google Scholar] [CrossRef] [PubMed] - Capelli, S.C.; Bürgi, H.-B.; Dittrich, B.; Grabowsky, S.; Jayatilaka, D. Hirshfeld atom refinement. IUCrJ
**2014**, 1, 361–379. [Google Scholar] [CrossRef] [Green Version] - Woińska, M.; Grabowsky, S.; Dominiak, P.M.; Woźniak, K.; Jayatilaka, D. Hydrogen atoms can be located accurately and pre-cisely by x-ray crystallography. Sci. Adv.
**2016**, 2, e1600192. [Google Scholar] [CrossRef] [Green Version] - Fugel, M.; Jayatilaka, D.; Hupf, E.; Overgaard, J.; Hathwar, V.R.; Macchi, P.; Turner, M.J.; Howard, J.A.K.; Dolomanov, O.V.; Puschmann, H.; et al. Probing the accuracy and precision of Hirshfeld atom refinement with HARt interfaced with Olex2. IUCrJ
**2018**, 5, 32–44. [Google Scholar] [CrossRef] [PubMed] - Wieduwilt, E.K.; Macetti, G.; Malaspina, L.A.; Jayatilaka, D.; Grabowsky, S.; Genoni, A. Post-Hartree-Fock methods for Hirshfeld atom refinement: Are they necessary? Investigation of a strongly hydrogen-bonded molecular crystal. J. Mol. Struct.
**2020**, 1209, 127934. [Google Scholar] [CrossRef] - Kleemiss, F.; Dolomanov, O.V.; Bodensteiner, M.; Peyerimhoff, N.; Midgley, L.; Borhis, L.J.; Genoni, A.; Malaspina, L.A.; Jayatilaka, D.; Spencer, J.L.; et al. Accurate Crystal Structures and Chemical Properties from NoSpherA2. Chem. Sci.
**2021**, 12, 1675–1692. [Google Scholar] [CrossRef] - Malaspina, L.A.; Wieduwilt, E.K.; Bergmann, J.; Kleemiss, F.; Meyer, B.; Ruiz-López, M.F.; Pal, R.; Hupf, E.; Beckmann, J.; Piltz, R.O.; et al. Fast and Accurate Quantum Crystallography: From Small to Large, from Light to Heavy. J. Phys. Chem. Lett.
**2019**, 10, 6973–6982. [Google Scholar] [CrossRef] [PubMed] - Johnson, E.R.; Keinan, S.; Mori-Sánchez, P.; Contreras-García, J.; Cohen, A.J.; Yang, W. Revealing Noncovalent Interactions. J. Am. Chem. Soc.
**2010**, 132, 6498–6506. [Google Scholar] [CrossRef] [Green Version] - Contreras-García, J.; Johnson, E.R.; Keinan, S.; Chaudret, R.; Piquemal, J.-P.; Beratan, D.N.; Yang, W. NCIPLOT: A Program for Plotting Noncovalent Interaction Regions. J. Chem. Theory Comput.
**2011**, 7, 625–632. [Google Scholar] [CrossRef] - Lefebvre, C.; Rubez, G.; Khartabil, H.; Boisson, J.-C.; Contreras-García, J.; Hénon, E. Accurately Extracting the Signature of In-termolecular Interactions Present in the NCI Plot of the Reduced Density Gradient versus Electron Density. Phys. Chem. Chem. Phys.
**2017**, 19, 17928–17936. [Google Scholar] [CrossRef] [PubMed] - Lefebvre, C.; Khartabil, H.; Boisson, J.-C.; Contreras-García, J.; Piquemal, J.-P.; Hénon, E. The Independent Gradient Model: A New Approach for Probing Strong and Weak Interactions in Molecules from Wave Function Calculations. ChemPhysChem
**2018**, 19, 724–735. [Google Scholar] [CrossRef] - Ponce-Vargas, M.; Lefebvre, C.; Boisson, J.-C.; Hénon, E. Atomic Decomposition Scheme of Noncovalent Interactions Applied to Host–Guest Assemblies. J. Chem. Inf. Model.
**2020**, 60, 268–278. [Google Scholar] [CrossRef] - Klein, J.; Khartabil, H.; Boisson, J.-C.; Contreras-García, J.; Piquemal, J.-P.; Hénon, E. New Way for Probing Bond Strength. J. Phys. Chem. A
**2020**, 124, 1850–1860. [Google Scholar] [CrossRef] [PubMed] - Arias-Olivares, D.; Wieduwilt, E.K.; Contreras-García, J.; Genoni, A. NCI-ELMO: A New Method to Quickly and Accurately Detect Noncovalent Interactions in Biosystems. J. Chem. Theory Comput.
**2019**, 15, 6456–6470. [Google Scholar] [CrossRef] - Wieduwilt, E.K.; Boisson, J.-C.; Terraneo, G.; Hénon, E.; Genoni, A. A Step toward the Quantification of Noncovalent Interactions in Large Biological Systems: The Independent Gradient Model-Extremely Localized Molecular Orbital Approach. J. Chem. Inf. Model.
**2021**. [Google Scholar] [CrossRef] [PubMed] - Macetti, G.; Genoni, A. Quantum Mechanics/Extremely Localized Molecular Orbital Method: A Fully Quantum Mechanical Embedding Approach for Macromolecules. J. Phys. Chem. A
**2019**, 123, 9420–9428. [Google Scholar] [CrossRef] [PubMed] - Macetti, G.; Wieduwilt, E.K.; Assfeld, X.; Genoni, A. Localized Molecular Orbital-Based Embedding Scheme for Correlated Methods. J. Chem. Theory Comput.
**2020**, 16, 3578–3596. [Google Scholar] [CrossRef] - Macetti, G.; Genoni, A. Quantum Mechanics/Extremely Localized Molecular Orbital Embedding Strategy for Excited States: Coupling to Time-Dependent Density Functional Theory and Equation-of-Motion Coupled Cluster. J. Chem. Theory Comput.
**2020**, 16, 7490–7506. [Google Scholar] [CrossRef] - Macetti, G.; Wieduwilt, E.K.; Genoni, A. QM/ELMO: A Multi-Purpose Fully Quantum Mechanical Embedding Scheme Based on Extremely Localized Molecular Orbitals. J. Phys. Chem. A. submitted.
- Wieduwilt, E.K.; Macetti, G.; Genoni, A. Climbing Jacob’s Ladder of Structural Refinement: Introduction of a Localized Molecular Orbital-Based Embedding for Accurate X-ray Determinations of Hydrogen Atom Positions. J. Phys. Chem. Lett.
**2021**, 12, 463–471. [Google Scholar] [CrossRef] [PubMed] - Furukawa, H.; Cordova, K.E.; O’Keeffe, M.; Yaghi, O.M. The Chemistry and Applications of Metal-Organic Frameworks. Science
**2013**, 341, 1230444. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Ockwig, N.W.; Delgado-Friedrichs, O.; O’Keeffe, M.; Yaghi, O.M. Reticular Chemistry: Occurrence and Taxonomy of Nets and Grammar for the Design of Frameworks. Acc. Chem. Res.
**2005**, 38, 176–182. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Yaghi, O.M.; O’Keeffe, M.; Ockwig, N.W.; Chae, H.K.; Eddaoudi, M.; Kim, J. Reticular Synthesis and the Design of New Materials. Nature
**2003**, 423, 705–714. [Google Scholar] [CrossRef] - Zagorodniy, K.; Seifert, G.; Hermann, H. Metal-organic frameworks as promising candidates for future ultralow-k dielectrics. Appl. Phys. Lett.
**2010**, 97, 251905. [Google Scholar] [CrossRef] - Boys, S.F. Construction of Some Molecular Orbitals to Be Approximately Invariant for Changes from One Molecule to Another. Rev. Mod. Phys.
**1960**, 32, 296–299. [Google Scholar] [CrossRef] - Foster, J.M.; Boys, S.F. Canonical Configurational Interaction Procedure. Rev. Mod. Phys.
**1960**, 32, 300–302. [Google Scholar] [CrossRef] - Edmiston, C.; Ruedenberg, K. Localized Atomic and Molecular Orbitals. Rev. Mod. Phys.
**1963**, 35, 457–464. [Google Scholar] [CrossRef] - Edmiston, C.; Ruedenberg, K. Localized Atomic and Molecular Orbitals. II. J. Chem. Phys.
**1965**, 43, S97–S116. [Google Scholar] [CrossRef] - Von Niessen, W. Density Localization of Atomic and Molecular Orbitals. I. J. Chem. Phys.
**1972**, 56, 4290. [Google Scholar] [CrossRef] - Pipek, J.; Mezey, P.G. A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions. J. Chem. Phys.
**1989**, 90, 4916–4926. [Google Scholar] [CrossRef] - McWeeny, R. The density matrix in many-electron quantum mechanics I. Generalized product functions. Factorization and physical interpretation of the density matrices. Proc. R. Soc. London. Ser. A Math. Phys. Sci.
**1959**, 253, 242–259. [Google Scholar] [CrossRef] - Adams, W.H. On the Solution of the Hartree-Fock Equation in Terms of Localized Orbitals. J. Chem. Phys.
**1961**, 34, 89. [Google Scholar] [CrossRef] - Huzinaga, S.; Cantu, A. A Theory of Separability of Many-Electron Systems. J. Chem. Phys.
**1971**, 55, 5543–5549. [Google Scholar] [CrossRef] - Gilbert, T.L. Multiconfiguration Self-Consistent-Field Theory for Localized Orbitals. II. Overlap constraints, Lagrangian multipliers, and the screened interaction field. J. Chem. Phys.
**1974**, 60, 3835–3844. [Google Scholar] [CrossRef] - Matsuoka, O. Expansion methods for Adams-Gilbert equations. I. Modified Adams-Gilbert equation and common and fluctuating basis sets. J. Chem. Phys.
**1977**, 66, 1245–1254. [Google Scholar] [CrossRef] - Smits, G.F.; Altona, C. Calculation and properties of non-orthogonal, strictly local molecular orbitals. Theor. Chem. Acc.
**1985**, 67, 461–475. [Google Scholar] [CrossRef] - Francisco, E.; Martín Pendás, A.; Adams, W.H. Generalized Huzinaga building-block equations for nonorthogonal electronic groups: Relation to the Adams–Gilbert theory. J. Chem. Phys.
**1992**, 97, 6504–6508. [Google Scholar] [CrossRef] - Ordejón, P.; Drabold, D.A.; Grumbach, M.P.; Martin, R.M. Unconstrained minimization approach for electronic computations that scales linearly with system size. Phys. Rev. B
**1993**, 48, 14646–14649. [Google Scholar] [CrossRef] - Couty, M.; Bayse, C.A.; Hall, M.B. Extremely localized molecular orbitals (ELMO): A non-orthogonal Hartree-Fock method. Theor. Chem. Acc.
**1997**, 97, 96–109. [Google Scholar] [CrossRef] - Philipp, D.M.; Friesner, R.A. Mixed Ab Initio QM/MM Modeling Using Frozen Orbitals and Tests with Alanine Dipeptide and Tetrapeptide. J. Comput. Chem.
**1999**, 20, 1468–1494. [Google Scholar] [CrossRef] - Chui, S.S.-Y.; Lo, S.M.-F.; Charmant, J.P.H.; Orpen, A.G.; Williams, I.D. Chemically Functionalizable Nanoporous Material [Cu
_{3}(TMA)_{2}(H_{2}O)_{3}]_{n}. Science**1999**, 283, 1148–1150. [Google Scholar] [CrossRef] [PubMed] - Scatena, R.; Guntern, Y.T.; Macchi, P. Electron Density and Dielectric Properties of Highly Porous MOFs: Binding and Mobility of Guest Molecules in Cu
_{3}(BTC)_{2}and Zn_{3}(BTC)_{2}. J. Am. Chem. Soc.**2019**, 141, 9382–9390. [Google Scholar] [CrossRef] [Green Version] - Guest, M.F.; Bush, I.J.; van Dam, H.J.J.; Sherwood, P.; Thomas, J.M.H.; van Lenthe, J.H.; Havenith, R.W.A.; Kendrick, J. The GAMESS-UK electronic structure package: Algorithms, developments and applications. Mol. Phys.
**2005**, 103, 719–747. [Google Scholar] [CrossRef] - Frisch, M.J.; Trucks, G.W.; Schlegel, H.B.; Scuseria, G.E.; Robb, M.A.; Cheeseman, J.R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G.A.; et al. Gaussian 09, Revision D.01; Gaussian, Inc.: Wallingford, CT, USA, 2009. [Google Scholar]
- Macchi, P.; Sironi, A. Chemical bonding in transition metal carbonyl clusters: Complementary analysis of theoretical and ex-perimental electron densities. Coord. Chem. Rev.
**2003**, 238–239, 383–412. [Google Scholar] [CrossRef] - Jahn, H.A.; Teller, E. Stability of polyatomic molecules in degenerate electronic states-I—Orbital degeneracy. Proc. R. Soc. London. Ser. A Math. Phys. Sci.
**1937**, 161, 220–235. [Google Scholar] [CrossRef]

**Figure 1.**Examples of extremely localized molecular orbitals computed for acetamide (see panel (

**A**)) using a localization scheme corresponding to the Lewis diagram of the molecule: (

**B**) ELMO describing the lone pair of the nitrogen atom, (

**C**) ELMO associated with one of the two N-H bonds, (

**D**) ELMO corresponding to the N-C bond, (

**E**) ELMO describing the C-C bond, (

**F**) ELMO associated with one of the three C-H bonds, (

**G**,

**H**) ELMOs corresponding to the C=O double bond ($\sigma $ and $\pi $ orbitals, respectively), (

**I**,

**J**) ELMOs for the lone pairs of the oxygen atom. All the orbitals were computed with the cc-pVDZ basis set and were plotted considering a 0.15 a.u. isosurface.

**Figure 2.**Crystal structure of {Cu

_{3}(BTC)

_{2}}

_{n}(HKUST-1): (

**left**panel) unit-cell content with large and small cavities highlighted by ochre and blue spheres, respectively; (

**right**panel) paddlewheel model system for the QM/ELMO calculations.

**Figure 3.**NCI plots at different levels of theory with basis set 6-311G(2d,2p) for the model system extracted from the HKUST-1 experimental crystal structure with water chemisorption degree of 14.3(6)%. All the reduced-density gradient isosurfaces correspond to the 0.4 a.u. isovalue and are colored according to the BGR (blue-green-red) scheme over the range −5.0 a.u < $\mathrm{sign}\left({\lambda}_{2}\right)\rho $ < 5.0 a.u.

**Figure 4.**Zoom on the Cu-Cu subunit of the NCI plots depicted in Figure 3. All the reduced-density gradient isosurfaces correspond to the 0.4 a.u. isovalue and are colored according to the BGR (blue-green-red) scheme over the range −5.0 a.u < $\mathrm{sign}\left({\lambda}_{2}\right)\rho $ < 5.0 a.u.

**Figure 5.**Electrostatic potential maps at different levels of theory with basis set 6-311G(2d,2p) for the model system extracted from the HKUST-1 experimental crystal structure with a water chemisorption degree of 14.3(6)%. The electrostatic potentials were plotted on the corresponding 0.05 a.u. electron density isosurfaces according to the RWB (red-white-blue) scheme over the range [−0.1 a.u., 0.1 a.u.].

**Figure 6.**Electrostatic potential maps for the large cavity of HKUST-1 (

**A**) without water molecules and (

**B**) in the presence of water molecules, plotted both on the 0.05 a.u. isosurface of the electron density and as isocontour lines in the middle of the pore. The color scale for the maps is given on the right-hand side of the figure.

**Figure 7.**Electrostatic potential maps for the small cavity of HKUST-1 (

**A**) without water molecules and (

**B**) in the presence of water molecules, plotted both on the 0.05 a.u. isosurface of the electron density and as isocontour lines in the middle of the pore. The color scale for the maps is given on the right-hand side of the figure.

**Table 1.**Properties at the bond critical point between the Cu atoms and between the Cu and O atoms, as obtained from the calculations performed at different levels of theory with basis set 6-311G(2d,2p) on the model system extracted from the HKUST-1 experimental crystal structure with a water chemisorption degree of 14.3(6)%.

^{(a)}

Interaction | Spin State | Calculation | ${\mathit{\rho}}_{\mathit{b}\mathit{c}\mathit{p}}$ | ${\nabla}^{\mathit{2}}{\mathit{\rho}}_{\mathit{b}\mathit{c}\mathit{p}}$ | $\left|{\mathit{V}}_{\mathit{b}\mathit{c}\mathit{p}}\right|/{\mathit{G}}_{\mathit{b}\mathit{c}\mathit{p}}$ | $-{\mathit{K}}_{\mathit{b}\mathit{c}\mathit{p}}$ | $\mathit{D}\mathit{I}$ |
---|---|---|---|---|---|---|---|

Cu-Cu | Diamagnetic | B3LYP/ELMO | 0.029 | 0.075 | 1.344 | −0.0098 | 1.031 |

Standard B3LYP | 0.036 | 0.069 | 1.423 | −0.0127 | 0.426 | ||

Anti-Ferromagnetic | B3LYP/ELMO | 0.029 | 0.074 | 1.348 | −0.0099 | 0.100 | |

Standard B3LYP | 0.035 | 0.070 | 1.410 | −0.0122 | 0.146 | ||

Ferromagnetic | B3LYP/ELMO | 0.029 | 0.074 | 1.348 | −0.0099 | 0.100 | |

Standard B3LYP | 0.035 | 0.070 | 1.409 | −0.0121 | 0.144 | ||

Cu-O | Diamagnetic | B3LYP/ELMO | 0.066 | 0.614 | 0.956 | 0.0065 | 0.227 |

Standard B3LYP | 0.095 | 0.462 | 1.140 | −0.0189 | 0.429 | ||

Anti-Ferromagnetic | B3LYP/ELMO | 0.065 | 0.626 | 0.943 | 0.0084 | 0.233 | |

Standard B3LYP | 0.093 | 0.477 | 1.127 | −0.0174 | 0.466 | ||

Ferromagnetic | B3LYP/ELMO | 0.065 | 0.626 | 0.943 | 0.0084 | 0.233 | |

Standard B3LYP | 0.093 | 0.478 | 1.127 | −0.0173 | 0.466 |

^{(a)}${\rho}_{bcp}$ and ${\nabla}^{2}{\rho}_{bcp}$ are, respectively, the electron density (e/bohr

^{3}) and the Laplacian of the electron density (e/bohr

^{5}) at the bond critical point; $\left|{V}_{bcp}\right|/{G}_{bcp}$ is the ratio between the potential and the kinetic energy density at the bond critical point; $-{K}_{bcp}$ is the total bond energy density at the bond critical point (hartree/bohr

^{3}); and DI is the delocalization index (electron pairs shared between two atoms).

**Table 2.**Bader charges and volumes (0.001 e/bohr

^{3}isosurface) for the Cu and O atoms, as obtained from calculations performed at different levels of theory with basis set 6-311G(2d,2p) on the model system extracted from the HKUST-1 experimental crystal structure with a water chemisorption degree of 14.3(6)%.

^{(a)}

Spin State | Calculation | ${\mathit{q}}_{\mathit{C}\mathit{u}\mathit{1}}$ | ${\mathit{q}}_{\mathit{C}\mathit{u}\mathbf{2}}$ | ${\mathit{q}}_{\mathit{O}}$ | ${\mathit{V}}_{\mathit{C}\mathit{u}\mathit{1}}$ | ${\mathit{V}}_{\mathit{C}\mathit{u}\mathit{2}}$ | ${\mathit{V}}_{\mathit{O}}$ |
---|---|---|---|---|---|---|---|

Diamagnetic | B3LYP/ELMO | 1.79 | 1.79 | −1.42 | 61.50 | 61.50 | 109.45 |

Standard B3LYP | 1.10 | 1.10 | −1.13 | 75.03 | 75.03 | 104.62 | |

Anti-Ferromagnetic | B3LYP/ELMO | 1.79 | 1.79 | −1.42 | 61.52 | 61.52 | 109.46 |

Standard B3LYP | 1.20 | 1.20 | −1.16 | 73.41 | 73.41 | 104.95 | |

Ferromagnetic | B3LYP/ELMO | 1.79 | 1.79 | −1.42 | 61.52 | 61.52 | 109.46 |

Standard B3LYP | 1.21 | 1.21 | −1.16 | 73.35 | 73.35 | 104.97 |

^{(a)}Charges in electrons (e) and volumes in bohr

^{3}.

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**MDPI and ACS Style**

Wieduwilt, E.K.; Macetti, G.; Scatena, R.; Macchi, P.; Genoni, A.
Extending Libraries of Extremely Localized Molecular Orbitals to Metal Organic Frameworks: A Preliminary Investigation. *Crystals* **2021**, *11*, 207.
https://doi.org/10.3390/cryst11020207

**AMA Style**

Wieduwilt EK, Macetti G, Scatena R, Macchi P, Genoni A.
Extending Libraries of Extremely Localized Molecular Orbitals to Metal Organic Frameworks: A Preliminary Investigation. *Crystals*. 2021; 11(2):207.
https://doi.org/10.3390/cryst11020207

**Chicago/Turabian Style**

Wieduwilt, Erna K., Giovanni Macetti, Rebecca Scatena, Piero Macchi, and Alessandro Genoni.
2021. "Extending Libraries of Extremely Localized Molecular Orbitals to Metal Organic Frameworks: A Preliminary Investigation" *Crystals* 11, no. 2: 207.
https://doi.org/10.3390/cryst11020207