12.1.1 Overview

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, Dr. Qinghui Ge, and Matthias Loipersberger 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:

• •

  Initial guess at the MOs as a superposition of the converged MOs on the isolated fragments (FRAGMO guess). ⁶⁸³ Khaliullin R. Z., Head-Gordon M., Bell A. T.
  J. Chem. Phys.
  (2006), 124, pp. 204105. Link

• •

  Constrained (locally-projected) SCF methods for molecular interactions (SCF MI methods) between both closed-shell ⁶⁸³ Khaliullin R. Z., Head-Gordon M., Bell A. T.
  J. Chem. Phys.
  (2006), 124, pp. 204105. Link and open-shell ⁵⁹⁷ Horn P. R. et al.
  J. Chem. Phys.
  (2013), 138, pp. 134119. Link fragments.

• •

  Single Roothaan-step (RS) correction methods that improve FRAGMO and SCF MI description of molecular systems. ⁶⁸³ Khaliullin R. Z., Head-Gordon M., Bell A. T.
  J. Chem. Phys.
  (2006), 124, pp. 204105. Link ^{, 597} Horn P. R. et al.
  J. Chem. Phys.
  (2013), 138, pp. 134119. Link

• •

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

• •

  The original version the ALMO-EDA method (energy decomposition analysis based on absolutely localized molecular orbitals), including the associated charge transfer analysis, ⁶⁸² Khaliullin R. Z. et al.
  J. Phys. Chem. A
  (2007), 111, pp. 8753. Link ^{, 680} Khaliullin R. Z., Bell A. T., Head-Gordon M.
  J. Chem. Phys.
  (2008), 128, pp. 184112. Link ^{, 597} Horn P. R. et al.
  J. Chem. Phys.
  (2013), 138, pp. 134119. Link and the analysis of intermolecular bonding in terms of complementary occupied-virtual pairs (COVPs). ⁶⁸⁰ Khaliullin R. Z., Bell A. T., Head-Gordon M.
  J. Chem. Phys.
  (2008), 128, pp. 184112. Link ^{, 681} Khaliullin R. Z., Bell A. T., Head-Gordon M.
  Chem. Eur. J
  (2009), 15, pp. 851. Link ^{, 597} Horn P. R. et al.
  J. Chem. Phys.
  (2013), 138, pp. 134119. Link

• •

  The second-generation ALMO-EDA method, ⁵⁹⁶ Horn P. R., Mao Y., Head-Gordon M.
  Phys. Chem. Chem. Phys.
  (2016), 18, pp. 23067. Link ^{, 896} Mao Y. et al.
  Annu. Rev. Phys. Chem.
  (2021), 72, pp. 641. Link ^{, 593} Horn P. R., Head-Gordon M.
  J. Chem. Phys.
  (2015), 143, pp. 114111. Link ^{, 595} Horn P. R., Mao Y., Head-Gordon M.
  J. Chem. Phys.
  (2016), 144, pp. 114107. Link ^{, 895} Mao Y. et al.
  Phys. Chem. Chem. Phys.
  (2020), 22, pp. 12867. Link including its extension to single-bond interactions ⁸¹⁰ Levine D. S. et al.
  J. Chem. Theory Comput.
  (2016), 12, pp. 4812. Link ^{, 808} Levine D. S., Head-Gordon M.
  J. Phys. Chem. Lett.
  (2017), 8, pp. 1967. Link ^{, 809} Levine D. S., Head-Gordon M.
  Proc. Natl. Acad. Sci. USA
  (2017), 114, pp. 12649. Link and the ALMO-EDA(solv) scheme ⁸⁹⁷ Mao Y. et al.
  Chem. Sci.
  (2021), 12, pp. 1398. Link for the inclusion of implicit solvents in EDA calculation.

• •

  The adiabatic ALMO-EDA method that analyzes the effects intermolecular interactions on molecular properties. ⁸⁹⁴ Mao Y., Horn P. R., Head-Gordon M.
  Phys. Chem. Chem. Phys.
  (2017), 19, pp. 5944. Link ^{, 857} Loipersberger M., Mao Y., Head-Gordon M.
  J. Chem. Theory Comput.
  (2020), 16, pp. 1073. Link

• •

  An extension of the ALMO-EDA to RI-MP2. ¹³⁵³ Thirman J., Head-Gordon M.
  J. Chem. Phys.
  (2015), 143, pp. 084124. Link ^{, 1354} Thirman J., Head-Gordon M.
  J. Phys. Chem. A
  (2017), 121, pp. 717. Link ^{, 856} Loipersberger M. et al.
  J. Phys. Chem. A
  (2019), 123, pp. 9621. Link

• •

  An extension of the ALMO-EDA to intermolecular interactions involving excited-state molecules (calculated by CIS or TDDFT/TDA). ⁴³⁵ Ge Q., Mao Y., Head-Gordon M.
  J. Chem. Phys.
  (2018), 148, pp. 064105. Link ^{, 434} Ge Q., Head-Gordon M.
  J. Chem. Theory Comput.
  (2018), 14, pp. 5156. Link

• •

  The variational explicit polarization (XPol) method, a self-consistent, charge-embedded, monomer-based SCF calculation. ¹⁵⁰⁵ Xie W. et al.
  J. Chem. Phys.
  (2008), 128, pp. 234108. Link ^{, 621} Jacobson L. D., Herbert J. M.
  J. Chem. Phys.
  (2011), 134, pp. 094118. Link ^{, 560} Herbert J. M. et al.
  Phys. Chem. Chem. Phys.
  (2012), 14, pp. 7679. Link

• •

  Symmetry-adapted perturbation theory (SAPT), a monomer-based method for computing intermolecular interaction energies and decomposing them into physically-meaningful components. ⁶⁴¹ Jeziorski B., Moszynski R., Szalewicz K.
  Chem. Rev.
  (1994), 94, pp. 1887. Link ^{, 1335} Szalewicz K.
  Wiley Interdiscip. Rev.: Comput. Mol. Sci.
  (2012), 2, pp. 254. Link

• •

  XPol+SAPT (XSAPT), which extends the SAPT methodology to systems consisting of more than two monomers. ⁶²¹ Jacobson L. D., Herbert J. M.
  J. Chem. Phys.
  (2011), 134, pp. 094118. Link ^{, 560} Herbert J. M. et al.
  Phys. Chem. Chem. Phys.
  (2012), 14, pp. 7679. Link ^{, 622} Jacobson L. D. et al.
  Annu. Rep. Comput. Chem.
  (2013), 9, pp. 25. Link

• •

  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. ⁷⁵⁹ Lao K. U., Herbert J. M.
  J. Phys. Chem. Lett.
  (2012), 3, pp. 3241. Link ^{, 760} Lao K. U., Herbert J. M.
  J. Chem. Phys.
  (2013), 139, pp. 034107. Link ^{, 762} Lao K. U., Herbert J. M.
  J. Phys. Chem. A
  (2015), 119, pp. 235. Link

• •

  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. ⁷⁶³ Lao K. U., Herbert J. M.
  J. Chem. Theory Comput.
  (2016), 12, pp. 2569. Link

• •

  The electrostatically-embedded many-body expansion ²⁹⁹ Dahlke E. E., Truhlar D. G.
  J. Chem. Theory Comput.
  (2007), 3, pp. 46. Link ^{, 1173} Richard R. M., Lao K. U., Herbert J. M.
  J. Chem. Phys.
  (2014), 141, pp. 014108. Link ^{, 1174} Richard R. M., Lao K. U., Herbert J. M.
  Acc. Chem. Res.
  (2014), 47, pp. 2828. Link ^{, 766} Lao K. U. et al.
  J. Chem. Phys.
  (2016), 144, pp. 164105. Link and the fragment molecular orbital method,^{691, 379} for decomposing large clusters into small numbers of monomers, facilitating larger calculations.

• •

  The Ab Initio Frenkel Davydov Model, ⁹⁶⁵ Morrison A. F., You Z.-Q., Herbert J. M.
  J. Chem. Theory Comput.
  (2014), 10, pp. 5366. Link ^{, 962} Morrison A. F., Herbert J. M.
  J. Phys. Chem. Lett.
  (2015), 6, pp. 4390. Link a low-order scaling, highly parallelizable approach to computing excited state properties of liquids, crystals, and aggregates.

• •

  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. ⁸⁴⁰ Liu J., Herbert J. M.
  J. Chem. Phys.
  (2015), 143, pp. 034106. Link ^{, 841} Liu J., Herbert J. M.
  J. Chem. Theory Comput.
  (2016), 12, pp. 157. Link ^{, 565} Herbert J. M. et al.
  Acc. Chem. Res.
  (2016), 49, pp. 931. Link

• •

  The ALMO-CIS and ALMO-CIS+CT models (also applicable to TDDFT/TDA) for computing a substantial number of excited states in large molecular clusters. ²⁵⁵ Closser K. D. et al.
  J. Chem. Theory Comput.
  (2015), 11, pp. 5791. Link ^{, 436} Ge Q. et al.
  J. Chem. Phys.
  (2017), 146, pp. 044111. Link

Other fragment-based approaches in Q-Chem include:

• •

  The Effective Fragment Potential (EFP) method ⁴³⁸ Ghosh D. et al.
  J. Phys. Chem. A
  (2010), 114, pp. 12739. Link developed by Prof. Lyudmila Slipchenko at Purdue University and Prof. Anna Krylov at USC (see Section 11.5)

• •

  Fragment-based approaches to diabatic states and electronic couplings (see Section 10.15.3)