12 Fragment-Based Methods

12.1 Introduction

(June 30, 2021)

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). 548 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 548 Khaliullin R. Z., Head-Gordon M., Bell A. T.
    J. Chem. Phys.
    (2006), 124, pp. 204105.
    Link
    and open-shell 471 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. 548 Khaliullin R. Z., Head-Gordon M., Bell A. T.
    J. Chem. Phys.
    (2006), 124, pp. 204105.
    Link
    , 471 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, 547 Khaliullin R. Z. et al.
    J. Phys. Chem. A
    (2007), 111, pp. 8753.
    Link
    , 545 Khaliullin R. Z., Bell A. T., Head-Gordon M.
    J. Chem. Phys.
    (2008), 128, pp. 184112.
    Link
    , 471 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). 545 Khaliullin R. Z., Bell A. T., Head-Gordon M.
    J. Chem. Phys.
    (2008), 128, pp. 184112.
    Link
    , 546 Khaliullin R. Z., Bell A. T., Head-Gordon M.
    Chem. Eur. J
    (2009), 15, pp. 851.
    Link
    , 471 Horn P. R. et al.
    J. Chem. Phys.
    (2013), 138, pp. 134119.
    Link

  • The second-generation ALMO-EDA method, 470 Horn P. R., Mao Y., Head-Gordon M.
    Phys. Chem. Chem. Phys.
    (2016), 18, pp. 23067.
    Link
    , 717 Mao Y. et al.
    Annu. Rev. Phys. Chem.
    (2021), 72, pp. 641.
    Link
    , 467 Horn P. R., Head-Gordon M.
    J. Chem. Phys.
    (2015), 143, pp. 114111.
    Link
    , 469 Horn P. R., Mao Y., Head-Gordon M.
    J. Chem. Phys.
    (2016), 144, pp. 114107.
    Link
    , 716 Mao Y. et al.
    Phys. Chem. Chem. Phys.
    (2020), 22, pp. 12867.
    Link
    including its extension to single-bond interactions 657 Levine D. S. et al.
    J. Chem. Theory Comput.
    (2016), 12, pp. 4812.
    Link
    , 655 Levine D. S., Head-Gordon M.
    J. Phys. Chem. Lett.
    (2017), 8, pp. 1967.
    Link
    , 656 Levine D. S., Head-Gordon M.
    Proc. Natl. Acad. Sci. USA
    (2017), 114, pp. 12649.
    Link
    and the ALMO-EDA(solv) scheme 718 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. 715 Mao Y., Horn P. R., Head-Gordon M.
    Phys. Chem. Chem. Phys.
    (2017), 19, pp. 5944.
    Link
    , 695 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. 1085 Thirman J., Head-Gordon M.
    J. Chem. Phys.
    (2015), 143, pp. 084124.
    Link
    , 1086 Thirman J., Head-Gordon M.
    J. Phys. Chem. A
    (2017), 121, pp. 717.
    Link
    , 694 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). 346 Ge Q., Mao Y., Head-Gordon M.
    J. Chem. Phys.
    (2018), 148, pp. 064105.
    Link
    , 345 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. 1213 Xie W. et al.
    J. Chem. Phys.
    (2008), 128, pp. 234108.
    Link
    , 493 Jacobson L. D., Herbert J. M.
    J. Chem. Phys.
    (2011), 134, pp. 094118.
    Link
    , 445 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. 506 Jeziorski B., Moszynski R., Szalewicz K.
    Chem. Rev.
    (1994), 94, pp. 1887.
    Link
    , 1073 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. 493 Jacobson L. D., Herbert J. M.
    J. Chem. Phys.
    (2011), 134, pp. 094118.
    Link
    , 445 Herbert J. M. et al.
    Phys. Chem. Chem. Phys.
    (2012), 14, pp. 7679.
    Link
    , 494 Jacobson L. D. et al.
    Annu. Rep. Comp. 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. 612 Lao K. U., Herbert J. M.
    J. Phys. Chem. Lett.
    (2012), 3, pp. 3241.
    Link
    , 613 Lao K. U., Herbert J. M.
    J. Chem. Phys.
    (2013), 139, pp. 034107.
    Link
    , 615 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. 616 Lao K. U., Herbert J. M.
    J. Chem. Theory Comput.
    (2016), 12, pp. 2569.
    Link

  • The electrostatically-embedded many-body expansion 242 Dahlke E. E., Truhlar D. G.
    J. Chem. Theory Comput.
    (2007), 3, pp. 46.
    Link
    , 938 Richard R. M., Lao K. U., Herbert J. M.
    J. Chem. Phys.
    (2014), 141, pp. 014108.
    Link
    , 939 Richard R. M., Lao K. U., Herbert J. M.
    Acc. Chem. Res.
    (2014), 47, pp. 2828.
    Link
    , 619 Lao K. U. et al.
    J. Chem. Phys.
    (2016), 144, pp. 164105.
    Link
    and the fragment molecular orbital method, 553 Kitaura K. et al.
    Chem. Phys. Lett.
    (1999), 313, pp. 701.
    Link
    , 308 Fedorov D. G., Kitaura K.
    J. Phys. Chem. A
    (2007), 111, pp. 6904.
    Link
    for decomposing large clusters into small numbers of monomers, facilitating larger calculations.

  • The Ab Initio Frenkel Davydov Model, 774 Morrison A. F., You Z.-Q., Herbert J. M.
    J. Chem. Theory Comput.
    (2014), 10, pp. 5366.
    Link
    , 771 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. 680 Liu J., Herbert J. M.
    J. Chem. Phys.
    (2015), 143, pp. 034106.
    Link
    , 681 Liu J., Herbert J. M.
    J. Chem. Theory Comput.
    (2016), 12, pp. 157.
    Link
    , 447 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. 208 Closser K. D. et al.
    J. Chem. Theory Comput.
    (2015), 11, pp. 5791.
    Link
    , 347 Ge Q. et al.
    J. Chem. Phys.
    (2017), 146, pp. 044111.
    Link

Another fragment-based approaches in Q-Chem:

  • The Effective Fragment Potential (EFP) method 348 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)