Comprehensive Benchmark of Association (Free) Energies of Realistic Host-Guest Complexes.

The S12L test set for supramolecular Gibbs free energies of association ΔGa (Grimme, S. Chem. Eur. J. 2012, 18, 9955-9964) is extended to 30 complexes (S30L), featuring more diverse interaction motifs, anions, and higher charges (-1 up to +4) as well as larger systems with up to 200 atoms. Various typical noncovalent interactions like hydrogen and halogen bonding, π-π stacking, nonpolar dispersion, and CH-π and cation-dipolar interactions are represented by "real" complexes. The experimental Gibbs free energies of association (ΔGa exp) cover a wide range from -0.7 to -24.7 kcal mol-1. In order to obtain a theoretical best estimate for ΔGa, we test various dispersion corrected density functionals in combination with quadruple-ζ basis sets for calculating the association energies in the gas phase. Further, modern semiempirical methods are employed to obtain the thermostatistical corrections from energy to Gibbs free energy, and the COSMO-RS model with several parametrizations as well as the SMD model are used to include solvation contributions. We investigate the effect of including counterions for the charged systems (S30L-CI), which is found to overall improve the results. Our best method combination consists of PW6B95-D3 (for neutral and charged systems) or ωB97X-D3 (for systems with counterions) energies, HF-3c thermostatistical corrections, and Gibbs free energies of solvation obtained with the COSMO-RS 2012 parameters for nonpolar solvents and 2013-fine for water. This combination gives a mean absolute deviation for ΔGa of only 2.4 kcal mol-1 (S30L) and 2.1 kcal mol-1 (S30L-CI), with a mean deviation of almost zero compared to experiment. Regarding the relative Gibbs free energies of association for the 13 pairs of complexes which share the same host, the correct trend in binding affinities could be reproduced except for two cases. The MAD compared to experiment amounts to 1.2 kcal mol-1, and the MD is almost zero. The best-estimate theoretical corrections are used to back-correct the experimental ΔGa values in order to get an empirical estimate for the "experimental", zero-point vibrational energy exclusive, gas phase binding energies. These are then utilized to benchmark the performance of various "lowcost" quantum chemical methods for noncovalent interactions in large systems. The performance of other common DFT methods as well as the use of semiempirical methods for structure optimizations is discussed.

[1]  Nicolaas A. Vermeulen,et al.  Ex(2)Box: interdependent modes of binding in a two-nanometer-long synthetic receptor. , 2013, Journal of the American Chemical Society.

[2]  Donald G Truhlar,et al.  Design of density functionals that are broadly accurate for thermochemistry, thermochemical kinetics, and nonbonded interactions. , 2005, The journal of physical chemistry. A.

[3]  A. Hesselmann,et al.  Intermolecular symmetry-adapted perturbation theory study of large organic complexes. , 2014, The Journal of chemical physics.

[4]  Christopher A. Hunter,et al.  Hydrogen-bond recognition of cyclic dipeptides in water , 1998 .

[5]  Liping Cao,et al.  Cucurbit[7]uril⋅guest pair with an attomolar dissociation constant. , 2014, Angewandte Chemie.

[6]  Peter Pulay,et al.  CAN (SEMI) LOCAL DENSITY FUNCTIONAL THEORY ACCOUNT FOR THE LONDON DISPERSION FORCES , 1994 .

[7]  David L. Mobley,et al.  The SAMPL4 host–guest blind prediction challenge: an overview , 2014, Journal of Computer-Aided Molecular Design.

[8]  S. H. Vosko,et al.  Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis , 1980 .

[9]  James J. P. Stewart,et al.  Optimization of parameters for semiempirical methods VI: more modifications to the NDDO approximations and re-optimization of parameters , 2012, Journal of Molecular Modeling.

[10]  L. T. Scott,et al.  Concave polyarenes with sulfide-linked flaps and tentacles: new electron-rich hosts for fullerenes. , 2005, The Journal of organic chemistry.

[11]  Pavel Hobza,et al.  A Transferable H-Bonding Correction for Semiempirical Quantum-Chemical Methods. , 2010, Journal of chemical theory and computation.

[12]  Jae Wook Lee,et al.  Cucurbituril homologues and derivatives: new opportunities in supramolecular chemistry. , 2003, Accounts of chemical research.

[13]  Pavel Hobza,et al.  Advanced Corrections of Hydrogen Bonding and Dispersion for Semiempirical Quantum Mechanical Methods. , 2012, Journal of chemical theory and computation.

[14]  D. Truhlar,et al.  The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals , 2008 .

[15]  Stefan Grimme,et al.  Effect of the damping function in dispersion corrected density functional theory , 2011, J. Comput. Chem..

[16]  M. Elstner SCC-DFTB: what is the proper degree of self-consistency? , 2007, The journal of physical chemistry. A.

[17]  S. Grimme Supramolecular binding thermodynamics by dispersion-corrected density functional theory. , 2012, Chemistry.

[18]  Jean-Marie Lehn,et al.  Supramolecular Chemistry: Concepts And Perspectives , 2014 .

[19]  L. Goerigk How Do DFT-DCP, DFT-NL, and DFT-D3 Compare for the Description of London-Dispersion Effects in Conformers and General Thermochemistry? , 2014, Journal of chemical theory and computation.

[20]  Jean-Marie Lehn,et al.  Dynamic devices. Shape switching and substrate binding in ion-controlled nanomechanical molecular tweezers. , 2004, Journal of the American Chemical Society.

[21]  J. F. Stoddart,et al.  Experimentally-based recommendations of density functionals for predicting properties in mechanically interlocked molecules. , 2008, Journal of the American Chemical Society.

[22]  Steven C. Zimmerman,et al.  Molecular Tweezers as Synthetic Receptors: Molecular Recognition of Electron‐Deficient Aromatic Substrates by Chemically Bonded Stationary Phases , 1999 .

[23]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[24]  Andrew T. Fenley,et al.  Bridging Calorimetry and Simulation through Precise Calculations of Cucurbituril–Guest Binding Enthalpies , 2014, Journal of chemical theory and computation.

[25]  S. Grimme,et al.  A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. , 2010, The Journal of chemical physics.

[26]  C. Bannwarth,et al.  The Thermochemistry of London Dispersion-Driven Transition Metal Reactions: Getting the ‘Right Answer for the Right Reason’ , 2014, ChemistryOpen.

[27]  Jeng-Da Chai,et al.  Long-Range Corrected Hybrid Density Functionals with Improved Dispersion Corrections. , 2012, Journal of chemical theory and computation.

[28]  H. Stoll,et al.  Systematically convergent basis sets with relativistic pseudopotentials. II. Small-core pseudopotentials and correlation consistent basis sets for the post-d group 16–18 elements , 2003 .

[29]  Stefan Grimme,et al.  Blind prediction of binding affinities for charged supramolecular host-guest systems: achievements and shortcomings of DFT-D3. , 2014, The journal of physical chemistry. B.

[30]  José M. Pérez-Jordá,et al.  A density-functional study of van der Waals forces: rare gas diatomics. , 1995 .

[31]  Jan M. L. Martin,et al.  The melatonin conformer space: benchmark and assessment of wave function and DFT methods for a paradigmatic biological and pharmacological molecule. , 2013, The journal of physical chemistry. A.

[32]  A. Klamt Conductor-like Screening Model for Real Solvents: A New Approach to the Quantitative Calculation of Solvation Phenomena , 1995 .

[33]  S. Grimme,et al.  Using dispersion-corrected density functional theory to understand supramolecular binding thermodynamics. , 2015, Chemical communications.

[34]  Michael K. Gilson,et al.  Quantum Mechanical Calculation of Noncovalent Interactions: A Large-Scale Evaluation of PMx, DFT, and SAPT Approaches , 2014, Journal of chemical theory and computation.

[35]  S. Grimme,et al.  The inhibition of iridium-promoted water oxidation catalysis (WOC) by cucurbit[n]urils. , 2012, Dalton transactions.

[36]  Yu Liu,et al.  Thermodynamics of the molecular and chiral recognition of cycloalkanols and camphor by modified beta-cyclodextrins possessing simple aromatic tethers. , 2004, The Journal of organic chemistry.

[37]  M. Monthioux,et al.  Encapsulated C60 in carbon nanotubes , 1998, Nature.

[38]  Sándor Suhai,et al.  Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties , 1998 .

[39]  J. Reimers,et al.  Efficient Methods for the Quantum Chemical Treatment of Protein Structures: The Effects of London-Dispersion and Basis-Set Incompleteness on Peptide and Water-Cluster Geometries. , 2013, Journal of chemical theory and computation.

[40]  Michael K Gilson,et al.  New ultrahigh affinity host-guest complexes of cucurbit[7]uril with bicyclo[2.2.2]octane and adamantane guests: thermodynamic analysis and evaluation of M2 affinity calculations. , 2011, Journal of the American Chemical Society.

[41]  A. Tkatchenko,et al.  Accurate and efficient method for many-body van der Waals interactions. , 2012, Physical review letters.

[42]  S. Grimme,et al.  A geometrical correction for the inter- and intra-molecular basis set superposition error in Hartree-Fock and density functional theory calculations for large systems. , 2012, The Journal of chemical physics.

[43]  S. Grimme,et al.  Dispersion-corrected density functional theory for aromatic interactions in complex systems. , 2013, Accounts of chemical research.

[44]  A. Schäfer,et al.  Fully optimized contracted Gaussian basis sets of triple zeta valence quality for atoms Li to Kr , 1994 .

[45]  Alexandre Tkatchenko,et al.  Hard Numbers for Large Molecules: Toward Exact Energetics for Supramolecular Systems. , 2014, The journal of physical chemistry letters.

[46]  S. Grimme,et al.  Benchmarking DFT and semiempirical methods on structures and lattice energies for ten ice polymorphs. , 2015, The Journal of chemical physics.

[47]  Thomas Williams,et al.  Gnuplot 4.4: an interactive plotting program , 2010 .

[48]  Marco Häser,et al.  Auxiliary basis sets to approximate Coulomb potentials (Chem. Phys. Letters 240 (1995) 283-290) , 1995 .

[49]  Michael K Gilson,et al.  Symmetry numbers for rigid, flexible, and fluxional molecules: theory and applications. , 2010, The journal of physical chemistry. B.

[50]  S. Grimme,et al.  Benchmarking density functional methods against the S66 and S66x8 datasets for non-covalent interactions. , 2011, Chemphyschem : a European journal of chemical physics and physical chemistry.

[51]  S. Grimme,et al.  Effects of London dispersion correction in density functional theory on the structures of organic molecules in the gas phase. , 2013, Physical chemistry chemical physics : PCCP.

[52]  J. Klimeš,et al.  Perspective: Advances and challenges in treating van der Waals dispersion forces in density functional theory. , 2012, The Journal of chemical physics.

[53]  C. Sherrill,et al.  Communication: resolving the three-body contribution to the lattice energy of crystalline benzene: benchmark results from coupled-cluster theory. , 2014, The Journal of chemical physics.

[54]  R. Ahlrichs,et al.  Efficient molecular numerical integration schemes , 1995 .

[55]  S. Grimme,et al.  Cooperativity in noncovalent interactions of biologically relevant molecules. , 2009, Physical chemistry chemical physics : PCCP.

[56]  Pavel Hobza,et al.  The relative roles of electrostatics and dispersion in the stabilization of halogen bonds. , 2013, Physical chemistry chemical physics : PCCP.

[57]  Donald J. Cram The Design of Molecular Hosts, Guests, and Their Complexes (Nobel Lecture)† , 1988 .

[58]  P. Anzenbacher,et al.  Anion binding modes in meso-substituted hexapyrrolic calix[4]pyrrole isomers. , 2014, Journal of the American Chemical Society.

[59]  Stefan Grimme,et al.  Corrected small basis set Hartree‐Fock method for large systems , 2013, J. Comput. Chem..

[60]  Lyle Isaacs,et al.  The cucurbit[n]uril family. , 2005, Angewandte Chemie.

[61]  Jan M. L. Martin,et al.  Halogen Bonds: Benchmarks and Theoretical Analysis. , 2013, Journal of chemical theory and computation.

[62]  Walter Thiel,et al.  Orthogonalization corrections for semiempirical methods , 2000 .

[63]  Alexandre Tkatchenko,et al.  First-Principles Modeling of Non-Covalent Interactions in Supramolecular Systems: The Role of Many-Body Effects. , 2012, Journal of chemical theory and computation.

[64]  Jochen Heil,et al.  Quantum chemistry in solution by combining 3D integral equation theory with a cluster embedding approach. , 2008, The journal of physical chemistry. B.

[65]  G. Scuseria,et al.  Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids. , 2003, Physical review letters.

[66]  Y. Inoue,et al.  Complexation Thermodynamics of Cyclodextrins. , 1998, Chemical reviews.

[67]  A. Becke,et al.  Density-functional exchange-energy approximation with correct asymptotic behavior. , 1988, Physical review. A, General physics.

[68]  Anthony J. Stone,et al.  The Theory of Intermolecular Forces , 2013 .

[69]  W. L. Mock,et al.  Dynamics of molecular recognition involving cucurbituril , 1989 .

[70]  C. Bannwarth,et al.  The Association of Two “Frustrated” Lewis Pairs by State-of-the-Art Quantum Chemical Methods , 2015 .

[71]  F. Weigend,et al.  Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. , 2005, Physical chemistry chemical physics : PCCP.

[72]  A. Tkatchenko,et al.  Many-body van der Waals interactions in molecules and condensed matter , 2014, Journal of physics. Condensed matter : an Institute of Physics journal.

[73]  J. Stewart Optimization of parameters for semiempirical methods V: Modification of NDDO approximations and application to 70 elements , 2007, Journal of molecular modeling.

[74]  S. Grimme Density functional theory with London dispersion corrections , 2011 .

[75]  D. Ugarte Curling and closure of graphitic networks under electron-beam irradiation , 1992, Nature.

[76]  J. Šponer,et al.  Density functional theory and molecular clusters , 1995, Journal of Computational Chemistry.

[77]  T. Park,et al.  A highly stable quadruply hydrogen-bonded heterocomplex useful for supramolecular polymer blends. , 2005, Journal of the American Chemical Society.

[78]  A. Klamt,et al.  Fast solvent screening via quantum chemistry: COSMO‐RS approach , 2002 .

[79]  Stefan Grimme,et al.  Inclusion complexes of buckycatcher with C(60) and C(70). , 2010, Physical chemistry chemical physics : PCCP.

[80]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[81]  S. Grimme,et al.  Highly strained phenylene bicyclophanes. , 2013, Angewandte Chemie.

[82]  Pavel Hobza,et al.  On the performance of the semiempirical quantum mechanical PM6 and PM7 methods for noncovalent interactions , 2013 .

[83]  Michael K. Gilson,et al.  A synthetic host-guest system achieves avidin-biotin affinity by overcoming enthalpy–entropy compensation , 2007, Proceedings of the National Academy of Sciences.

[84]  C. David Sherrill,et al.  Wavefunction methods for noncovalent interactions , 2012 .

[85]  Denis Jacquemin,et al.  A DFT-D evaluation of the complexation of a molecular tweezer with small aromatic molecules , 2012 .

[86]  Kwang Soo Kim,et al.  Molecular Clusters of pi-Systems: Theoretical Studies of Structures, Spectra, and Origin of Interaction Energies. , 2000, Chemical reviews.

[87]  F. Diederich,et al.  Cycloalkane and alicyclic heterocycle complexation by new switchable resorcin[4]arene-based container molecules: NMR and ITC binding studies. , 2011, Chemistry.

[88]  S. Grimme,et al.  Accurate Modeling of Organic Molecular Crystals by Dispersion-Corrected Density Functional Tight Binding (DFTB). , 2014, The journal of physical chemistry letters.

[89]  Wesley R. Browne,et al.  Molecular Switches: FERINGA:MOL.SWIT.2ED 2VOL O-BK , 2011 .

[90]  S. Grimme,et al.  A thorough benchmark of density functional methods for general main group thermochemistry, kinetics, and noncovalent interactions. , 2011, Physical chemistry chemical physics : PCCP.

[91]  S. Huber,et al.  Toward molecular recognition: three-point halogen bonding in the solid state and in solution. , 2014, Journal of the American Chemical Society.

[92]  A. Becke Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[93]  M. Frisch,et al.  Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields , 1994 .

[94]  J. Dobson Beyond pairwise additivity in London dispersion interactions , 2014 .

[95]  A. Becke,et al.  A post-Hartree-Fock model of intermolecular interactions. , 2005, The Journal of chemical physics.

[96]  Lyle Isaacs,et al.  The cucurbit[n]uril family: prime components for self-sorting systems. , 2005, Journal of the American Chemical Society.

[97]  Jirí Cerný,et al.  Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs. , 2006, Physical chemistry chemical physics : PCCP.

[98]  Tjerk P. Straatsma,et al.  NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations , 2010, Comput. Phys. Commun..

[99]  D. York,et al.  Extension of the self-consistent-charge density-functional tight-binding method: third-order expansion of the density functional theory total energy and introduction of a modified effective coulomb interaction. , 2007, The journal of physical chemistry. A.

[100]  J. Perdew,et al.  Van der waals coefficients for nanostructures: fullerenes defy conventional wisdom. , 2012, Physical review letters.

[101]  Andreas Hansen,et al.  Co-C Bond Dissociation Energies in Cobalamin Derivatives and Dispersion Effects: Anomaly or Just Challenging? , 2015, Journal of chemical theory and computation.

[102]  H. W. Kroto,et al.  The formation of quasi-icosahedral spiral shell carbon particles , 1988, Nature.

[103]  M. Elstner The SCC-DFTB method and its application to biological systems , 2006 .

[104]  David A Leigh,et al.  An AAAA–DDDD quadruple hydrogen-bond array. , 2011, Nature chemistry.

[105]  Donald G Truhlar,et al.  Free Energies of Solvation with Surface, Volume, and Local Electrostatic Effects and Atomic Surface Tensions to Represent the First Solvation Shell. , 2010, Journal of chemical theory and computation.

[106]  F. Weigend Accurate Coulomb-fitting basis sets for H to Rn. , 2006, Physical chemistry chemical physics : PCCP.

[107]  Pavel Hobza,et al.  Noncovalent interactions in biochemistry , 2011 .

[108]  Frank Neese,et al.  The ORCA program system , 2012 .

[109]  M. Head‐Gordon,et al.  Beyond Energies: Geometries of Nonbonded Molecular Complexes as Metrics for Assessing Electronic Structure Approaches. , 2015, Journal of chemical theory and computation.

[110]  Stefan Grimme,et al.  Benchmarking of London Dispersion-Accounting Density Functional Theory Methods on Very Large Molecular Complexes. , 2013, Journal of chemical theory and computation.

[111]  P. Pulay,et al.  The accuracy of quantum chemical methods for large noncovalent complexes. , 2013, Journal of chemical theory and computation.

[112]  Dmitrij Rappoport,et al.  Property-optimized gaussian basis sets for molecular response calculations. , 2010, The Journal of chemical physics.

[113]  A. Becke,et al.  A density-functional model of the dispersion interaction. , 2005, The Journal of chemical physics.

[114]  B. Sumpter,et al.  Density-functional approaches to noncovalent interactions: a comparison of dispersion corrections (DFT-D), exchange-hole dipole moment (XDM) theory, and specialized functionals. , 2011, The Journal of chemical physics.

[115]  Conrad C. Huang,et al.  UCSF Chimera—A visualization system for exploratory research and analysis , 2004, J. Comput. Chem..

[116]  K. Burke,et al.  Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)] , 1997 .

[117]  A. Klamt,et al.  COSMO : a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient , 1993 .

[118]  Jean-Marie Lehn,et al.  Supramolecular Chemistry—Scope and Perspectives Molecules, Supermolecules, and Molecular Devices (Nobel Lecture) , 1988 .

[119]  S. Grimme,et al.  DFT-D3 Study of Some Molecular Crystals , 2014 .

[120]  T. Kawase,et al.  Complexation of a carbon nanoring with fullerenes. , 2003, Angewandte Chemie.

[121]  T. Kawase,et al.  Cyclic [5]paraphenyleneacetylene: synthesis, properties, and formation of a ring-in-ring complex showing a considerably large association constant and entropy effect. , 2007, Angewandte Chemie.

[122]  S. Kast,et al.  Three-Dimensional RISM Integral Equation Theory for Polarizable Solute Models. , 2013, Journal of chemical theory and computation.

[123]  T. Frauenheim,et al.  DFTB+, a sparse matrix-based implementation of the DFTB method. , 2007, The journal of physical chemistry. A.

[124]  J. Perdew,et al.  Density-functional approximation for the correlation energy of the inhomogeneous electron gas. , 1986, Physical review. B, Condensed matter.

[125]  Pavel Hobza,et al.  S66: A Well-balanced Database of Benchmark Interaction Energies Relevant to Biomolecular Structures , 2011, Journal of chemical theory and computation.

[126]  Martin Korth,et al.  Third-Generation Hydrogen-Bonding Corrections for Semiempirical QM Methods and Force Fields , 2010 .

[127]  William L. Jorgensen,et al.  The many faces of halogen bonding: a review of theoretical models and methods , 2014 .

[128]  Michael K. Gilson,et al.  Thermodynamics of Water in an Enzyme Active Site: Grid-Based Hydration Analysis of Coagulation Factor Xa , 2014, Journal of chemical theory and computation.

[129]  C. Cramer,et al.  Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions. , 2009, The journal of physical chemistry. B.