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Accurate and Efficient ab Initio Calculations for Supramolecular Complexes: Symmetry-Adapted Perturbation Theory with Many-Body Dispersion Kevin Fenk, Ka Un Lao, Kuan-Yu Liu, and John M. Herbert J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.9b01156 • Publication Date (Web): 07 May 2019 Downloaded from http://pubs.acs.org on May 7, 2019
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The Journal of Physical Chemistry Letters
Accurate and Efficient ab Initio Calculations for Supramolecular Complexes: Symmetry-Adapted Perturbation Theory with Many-Body Dispersion Kevin Carter-Fenk,1 Ka Un Lao,2 Kuan-Yu Liu,1 and John M. Herbert1∗ 1
Department of Chemistry and Biochemistry, The Ohio State University, Columbus, OH 43210 2 Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853 (Dated: May 6, 2019)
ABSTRACT Symmetry-adapted perturbation theory (SAPT) provides a chemically meaningful energy decomposition scheme for non-bonded interactions that is useful for interpretive purposes. Although formally a dimer theory, we have previously introduced an “extended” version (XSAPT) that incorporates many-body polarization via self-consistent charge embedding. Here, we extend the XSAPT methodology to include nonadditive dispersion, using a modified form of the many-body dispersion (MBD) method of Tkatchenko and co-workers. Dispersion interactions beyond the pairwise atom–atom approximation improve total interaction energies even in small systems, and for large π-stacked complexes these corrections can amount to several kcal/mol. The XSAPT+MBD method introduced here achieves errors of . 1 kcal/mol (as compared to high-level ab initio benchmarks) for the L7 data set of large dispersion-bound complexes, and . 4 kcal/mol (as compared to experiment) for the S30L data set of host/guest complexes. This is superior to the best contemporary densityfunctional methods for non-covalent interactions, at comparable or lower cost. XSAPT+MBD represents a promising method for application to supramolecular assemblies, including protein/ligand binding.
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Non-covalent interactions are ubiquitous in chemistry, playing a major role in drug design,1–3 crystal structure prediction,4–6 synthesis of supramolecular host/guest complexes,7 and molecular organization at interfaces.8 Whereas in small systems composed of nonpolar monomers it may be possible to approximate the total intermolecular interaction energy in a pairwiseadditive way, this approximation quickly degrades for strongly-interacting molecules. In polar systems as small as water trimer, three-body (trimolecular) effects contribute 18% of the total interaction energy,9,10 and threebody polarization effects can be as large as 13 kcal/mol in magnitude for stable isomers of (H2 O)6 .11 These nonadditive polarization effects have long been a focal point in monomer-based approaches to supramolecular interaction energies,12–16 while nonadditive dispersion has been largely ignored. However, in systems such as π-stacked uracil dimer, the three-body (triatomic) van der Waals energy is estimated to contribute ∼ 30% of the total binding energy, with four-body (tetra-atomic) contributions of ∼ 10%.17,18 Here, we report a method that captures both nonadditive polarization and nonadditive dispersion, by combining the many-body dispersion (MBD) approach of Tkatchenko and co-workers19,20 with our “extended” version of symmetry-adapted perturbation theory (XSAPT).21–26 The SAPT approach affords a natural partition of intermolecular interaction energies into physicallyinterpretable contributions that include electrostatics, exchange repulsion, induction, and dispersion:27–29 SAPT Eint
=
(1) Eelst
+
(1) (2) (2) + Eexch + Eind + Eexch-ind (2) (2) Edisp + Eexch-disp + · · · .
(1)
(All terms through second order in intermolecular perturbation theory have been written out explicitly.) SAPT is normally used to investigate pairwise-additive interactions between dimers, as the calculation of nonadditive three-body interactions in trimers requires the use of triple excitations,30–33 which is computationally expensive. However, using monomer wave functions that include self-consistent charge embedding (“XPol” procedure13,16,34 ), the leading-order many-body polarization effects are incorporated into the zeroth-order SAPT wavefunctions. This is the basis of XSAPT.21–26 To date, nonadditive dispersion has been ignored. The SAPT framework provides varying levels of sophistication for the treatment of electron correlation and thus dispersion.28,35 Benchmark-quality description of dispersion interactions is not obtained at second order (eq. 1) and requires either higher-order perturbation theory (e.g., SAPT2+),35 which incurs O(N 7 ) scaling with respect to system size, or else SAPT(DFT),29,36–39 which computes the dispersion interaction based on frequencydependent density susceptibilities computed for each monomer. The cost of SAPT(DFT) can be reduced from O(N 6 ) to O(N 5 ) using density fitting,40,41 but even this remains prohibitively expensive for large systems.
Atom–atom dispersion potentials are a cost-effective alternative,23–25,42 and we have developed ab initio dispersion corrections for use in SAPT.24,25 These “+ai D” corrections26 are in some ways similar in spirit to empirical dispersion corrections used in density functional theory (DFT-D),43,44 but are fit directly to high-quality SAPT2+(3)(CCD)28 dispersion energies and thus represent pure dispersion at all length scales. In contrast, empirical dispersion in DFT must be attenuated as intermolecular distance R → 0, in order to avoid doublecounting of correlation effects in regions of space where the DFT exchange potential is significant.43 Our third-generation method, XSAPT+ai D3,25 affords accurate interaction energies for small clusters, with a mean absolute deviation (MAD) of just 0.3 kcal/mol versus complete-basis CCSD(T) benchmarks for the S66 data set of small dimers.45 The assumption of (atomic) pairwise additivity in the dispersion energy necessarily deteriorates in large systems,17 however, and this manifests as larger errors for supramolecular complexes involving large monomers.26 In such cases, one must account for screening of the atomic C6 coefficients in the presence of other, polarizable centers.46 An ab initio method to account for this effect within XSAPT+ai D3 has been introduced,47 but engenders O(N 4 ) cost. Alternatively, three-body dispersion corrections of the Axilrod-TellerMuto (ATM) variety can be introduced:26,48 EATM = atoms X A
