13.1 Introduction

Molecular complexes and molecular clusters represent a broad class of systems with interesting chemical and physical properties. Such systems can be naturally partitioned into fragments each representing a molecule or several molecules. Q-Chem contains a set of methods designed to use such partitioning either for physical or computational advantage. Some of these methods (e.g. the ALMO-EDA method and its most recent updates/extensions) were developed and implemented by Dr. Rustam Z. Khaliullin, Dr. Paul R. Horn, Dr. Yuezhi Mao, Dr. Jonathan Thirman, Dr. Daniel S. Levine, and Qinghui Ge working with Prof. Martin Head-Gordon at the University of California–Berkeley. Other methods [e.g., the XSAPT family of methods and TDDFT(MI)] were developed by Drs. Leif Jacobson, Ka Un Lao, and Jie Liu working with Prof. John Herbert at Ohio State University.

The list of methods that use partitioning includes:

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  Initial guess at the MOs as a superposition of the converged MOs on the isolated fragments (FRAGMO guess).⁴⁶⁷

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  Constrained (locally-projected) SCF methods for molecular interactions (SCF MI methods) between both closed-shell⁴⁶⁷ and open-shell³⁹⁷ fragments.

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  Single Roothaan-step (RS) correction methods that improve FRAGMO and SCF MI description of molecular systems.^{467, 397}

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  Automated calculation of the BSSE with counterpoise correction method (full SCF and RS implementation).

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  The original version the ALMO-EDA method (energy decomposition analysis based on absolutely localized molecular orbitals), including the associated charge transfer analysis,^{466, 464, 397} and the analysis of intermolecular bonding in terms of complementary occupied-virtual pairs (COVPs).^{464, 465, 397}

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  An improved version (“second generation”) of the ALMO-EDA method,^{393, 394, 395, 396} including its extension to single-bond interactions.^{565, 564}

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  The “adiabatic" ALMO-EDA method that partitions the effects intermolecular interactions on molecular properties.⁶⁰⁸

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  An extension of the ALMO-EDA to RI-MP2.^{916, 917}

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  An extension of the ALMO-EDA to intermolecular interactions involving excited-state molecules (calculated by CIS or TDDFT/TDA). ^{291, 290}

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  The variational explicit polarization (XPol) method, a self-consistent, charge-embedded, monomer-based SCF calculation.^{1028, 417, 372}

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  Symmetry-adapted perturbation theory (SAPT), a monomer-based method for computing intermolecular interaction energies and decomposing them into physically-meaningful components.^{428, 906}

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  XPol+SAPT (XSAPT), which extends the SAPT methodology to systems consisting of more than two monomers.^{417, 372, 418}

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  Closed- and open-shell AO-XSAPT(KS)+D, a dispersion-corrected version of XSAPT in atomic orbital basis that affords accurate intermolecular interaction energies at very low cost.^{528, 529, 531}

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  A stable and physically-motivated energy decomposition approach, SAPT/cDFT, in which cDFT is used to define the charge-transfer component of the interaction energy and SAPT defines the electrostatic, polarization, Pauli repulsion, and van der Waals contributions.⁵³²

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  The electrostatically-embedded many-body expansion^{208, 793, 794, 534} and the fragment molecular orbital method,^{472, 259} for decomposing large clusters into small numbers of monomers, facilitating larger calculations.

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  The Ab Initio Frenkel Davydov Model,^{654, 651} a low-order scaling, highly parallelizable approach to computing excited state properties of liquids, crystals, and aggregates.

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  TDDFT for molecular interactions [TDDFT(MI)], an excited-state extension of SCF MI that offers a reduced-cost way to compute excited states in molecular clusters, crystals, and aggregates.^{581, 582, 374}

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  The ALMO-CIS and ALMO-CIS+CT models (also applicable to TDDFT) for computing a substantial number of excited states in large molecular clusters.^{179, 292}

Another fragment-based approach, the Effective Fragment Potential (EFP) method,²⁹³ was developed by Prof. Lyudmila Slipchenko at Purdue University and Prof. Anna Krylov at USC; this method is described in Section 12.5.