Quantum Chemistry for Supramolecular Complexes

Size: px

Start display at page:

Download "Quantum Chemistry for Supramolecular Complexes"

Amber Cummings
6 years ago
Views:

1 Quantum Chemistry for Supramolecular Complexes Stefan Grimme Mulliken Center for Theoretical Chemistry, University of Bonn COSMO Symposium, March 2015

Concepts include: molecular recognition and self-assembly template-directed processes molecular machinery (motors,

2 Supramolecular chemistry: chemistry beyond the covalent bond Nobel Prize in 1987 pioneering work at Bonn University F. Vögtle molecular systems made of assembled components organized by noncovalent interactions. Concepts include: molecular recognition and self-assembly template-directed processes molecular machinery (motors, switches) mechanically-interlocked molecular architectures encapsulation bottom-up approaches to nanotechnology models for protein-ligand binding

3 Non-covalent interactions (termed non-bonding in the FF community)

4 Noncovalent networks In a biological (protein-ligand) system various types of NCI are present:

5 The complexity of supramolecular processes solvation/de-solvation entropy (conformations/flexibility)

6 Theoretical Methods

7 Supramolecular interactions in solution: The ( had no good idea ) Method Brute force approach: compute all parts accurately (thermodynamic cycle), no further empiricism In solvent X at temperature T for single structures in the reaction host + guest Ka supramolecular complex G a = E(gas) + E(gas) = GTRV T (gas) + δg }{{} solv(x T ) }{{} DFT or semiemp. harm. freq. COSMO RS low freq.mode approx. E } DFT {{} + E (2) disp + E (3) disp }{{} PW 6B95/QZ// TPSS D3/TZ D3 method applicable to any semi-rigid (a few conformers) system

8 Supramolecular interactions in solution: The ( had no good idea ) Method By reversing the basic equation, experimental gas phase data can be estimated: Theory only: G(theor.) = E(gas) + GTRV T (gas) + δg }{{} solv(x T ) }{{} harm. freq. COSMO RS low freq.mode approx. Reverse basic equation and use exptl. G: E(gas, est. exptl.) = G(exptl.) GTRV T (gas) δg }{{} solv(x T ) primary quantity in QM to compare

9 A typical example pincer complex (126 atoms) from S12L set

10 Results for this example contribution to interaction (kcal/mol) E DFT(TPSS) 5.5 (unbound) E (2) disp E DFT D3 (2) E (3) disp 1.8 E DFT D3 (3) (E G) TRV 17.6 G gas -6.4 (G gas G solv ) 5.4 = Gcalc G exptl Sum or large and oppositely signed terms (worst case scenario), the approach can only work if they are individually accurate

11 A consistency check Exchange of CH 3 CCl 3 guest in similar solvent (CH 2 Cl 2 ): contribution to interaction (kcal/mol) E DFT(TPSS) 4.8 E DFT D3 (3) (E G) TRV 14.1 G gas -6.6 (G gas G solv ) 4.3 = Gcalc G exptl. -3.7

Different solvents and energy/entropy Exptl. from Huber et al, JACS, DOI:10.1021/ja509705f interaction (kcal/mol) property(solvent) exptl. theory G(C 6 H 12 ) -5.3-4.

12 Different solvents and energy/entropy Exptl. from Huber et al, JACS, DOI: /ja509705f interaction (kcal/mol) property(solvent) exptl. theory G(C 6 H 12 ) G(C 6 H 6 ) G(CH 2 Cl 2 ) H(C 6 H 12 ) T S(C 6 H 12 ) Examples: PW6B95-D3/def2-QZVP(-gf)//TPSS-D3/def2-TZVP+freq@(PBEh-3c,DFTB3-D3,HF-3c)+COSMO-RS(12,13)

13 Important Opposed to many empirical (FF, alchemic) methods we try to compute absolute G (and not relative G which is much easier). This yields physical insight and eventually also leads to accurate G.

14 QM methods for E(gas) DHDF/QZ DLPNO CCSD(T) accuracy hybrid/tz cost GGA/TZ DFTB PBEh 3c HF 3c default alternatives London dispersion corrected (inclusive) DLPNO-CCSD(T) from the F. Neese group 1 as implemented in ORCA 1 domain local pair natural orbital CCSD(T): C. Riplinger, B. Sandhoefer, A. Hansen, F. Neese, JCP 139, (2013).

15 Supramolecular benchmarking

16 S30L test set (extended S12L) Deav. =45 kcal/mol, up to 205 atoms, version with counter-ions also available

17 { S12L results with various high-level methods. Is theory consistent? 0 dispersion correction in PBE E(gas) [kcal/mol] CC correction MP2/CBS Diffusion QMC (A. Tkatchenko) PBE/def2-TZVP DLPNO-CCSD(T)/def2-TZVP+δCBS(MP2) DFT-SAPT/est. CBS (A. Hesselmann) PW6B95-D3/QZVP +E3 2a 2b 3a 3b 4a 4b 5a 5b 6a 6b 7a 7b pi-stacked (C60/C70) charged{

18 { S12L results with various high-level methods. Is theory consistent to experiment? 0 dispersion correction in PBE E(gas) [kcal/mol] CC correction reference (est. exptl.) MP2/CBS Diffusion QMC (A. Tkatchenko) PBE/def2-TZVP DLPNO-CCSD(T)/def2-TZVP+δCBS(MP2) DFT-SAPT/est. CBS (A. Hesselmann) PW6B95-D3/QZVP +E3 2a 2b 3a 3b 4a 4b 5a 5b 6a 6b 7a 7b pi-stacked (C60/C70) charged{

19 S30L: Understanding the interations!? Contribution to G a /kcal mol nonpolar disp. DFT E el E (2) disp δg T solv π π stacking G T RRHO E (3) disp G a CH π int. halogen bonds H bonds charged (set including counter-ions) PW6B95-D3/def2-QZVP(-gf)//TPSS-D3/def2-TZVP+freq@(HF-3c)+COSMO-RS(12,13fine)

20 S30L: Effect of methods for the three parts ( G) (a) PW6B95-D3/QZ (b) ωb97x-d3/qz (c) B3LYP-D3/QZ SMD 4.5 (2.3 ) 4.3 (2.0 ) 4.8 (2.3) 5.1 (1.5 ) 4.8 (1.2 ) 5.5 (1.5) 4.6 ( 0.3) 4.8 ( 0.6) 4.9 ( 0.3) COSMO RS 14 fine 2.8 ( 0.4) 3.6 ( 0.8) 3.0 ( 0.5) 3.7 ( 1.2) 4.2 ( 1.6) 4.2 ( 1.3) 4.2 ( 3.0) 4.7 ( 3.4) 4.6 ( 3.0) COSMO RS ( 0.6) 3.3 ( 0.9) 3.3 ( 0.6) 3.3 ( 1.4) 3.8 ( 1.7) 3.7 ( 1.4) 4.6 ( 3.1) 5.0 ( 3.5) 5.1 ( 3.2) Solvation COSMO RS 13 fine COSMO RS 13 COSMO RS ( 0.7) 3.0 ( 1.1) 3.0 ( 1.0) 3.5 ( 1.0) 3.5 ( 1.4) 3.5 ( 1.3) 3.2 ( 0.7) 3.4 ( 1.1) 3.5 ( 1.0) 3.0 ( 1.5) 3.5 ( 1.9) 3.5 ( 1.8) 3.5 ( 1.8) 4.1 ( 2.2) 4.1 ( 2.1) 3.5 ( 1.5) 3.9 ( 1.9) 4.0 ( 1.8) 4.4 ( 3.2) 4.8 ( 3.6) 5.0 ( 3.6) 4.7 ( 3.6) 5.2 ( 4.0) 5.3 ( 3.9) 4.8 ( 3.3) 5.3 ( 3.7) 5.4 ( 3.6) HF 3c DFTB D3 PM6 D3 Frequencies (RRHO) (d) TPSS-D3/QZ HF 3c DFTB D3 PM6 D3 (e) PBE-D3/QZ HF 3c DFTB D3 PM6 D3 SMD COSMO RS 14 fine COSMO RS (1.9 ) 3.5 ( 0.8) 3.6 ( 1.0) 4.8 (1.6 ) 4.1 ( 1.2) 4.1 ( 1.3) 5.1 (1.9) 3.6 ( 0.8) 4.1 ( 1.0) 6.3 (4.7) 4.3 (3.3) 3.7 (3.0) 6.5 (4.4) 4.4 (3.0) 4.1 (2.7) 6.7 (4.7) 4.3 (3.3) 3.8 (3.0) MAD < MAD 5.0 COSMO RS 13 fine 3.8 ( 1.1) 4.5 ( 1.4) 4.2 ( 1.1) 3.8 (2.6) 4.6 (2.3) 3.7 (2.6) MAD > 5.0 COSMO RS 13 COSMO RS ( 1.4) 3.7 ( 1.4) 4.4 ( 1.8) 4.3 ( 1.7) 4.3 ( 1.5) 4.1 ( 1.4) 3.6 (2.4) 3.9 (2.7) 4.4 (2.1) 4.3 (2.3) 3.6 (2.4) 4.0 (2.6) (MD in parentheses) all values in kcal/mol HF 3c DFTB D3 PM6 D3 HF 3c DFTB D3 PM6 D3

21 S30L: Choice of the best solvation model COSMO-RS outperfoms SMD, but which parameters are the best? Experimental G a /kcal mol overbinding R= nonpolar solvent water underbinding Calculated G a /kcal mol 1 27 COSMO-RS(12): good for nonpolar solvents, but bad for water

22 S30L: Choice of the best solvation model COSMO-RS outperfoms SMD, but which parameters are the best? Experimental G a /kcal mol overbinding 24 R= nonpolar solvent water underbinding Calculated G a /kcal mol 1 COSMO-RS(12), COSMO-RS(13fine) for water

23 S30L: DFT-D3 results vs. experiment for G 12 Ga (exptl.) / kcal mol G a (theor.) / kcal mol -1 PW6B95-D3/def2-QZVP(-gf)//TPSS-D3/def2-TZVP+freq@(HF-3c)+COSMO-RS(12,13fine)

24 Back-correct experimental G a for reference E emp gas E emp gas = Ga exp GRRHO(HF-3c) δg T solv(x T )(COSMO-RS(12/13f)) Binding Energy E /kcal mol nonpolar disp. reference π π stacking CH π int. halogen bonds H bonds charged

25 S30L: results for E(gas) with DFT-D3 Binding Energy E /kcal mol reference PW6B95 D3/QZ nonpolar disp. π π stacking MAD=3.4 MD= 2.3 CH π int. halogen bonds H bonds charged

26 S30L: results for E(gas) with DFT-D3 Binding Energy E /kcal mol reference wb97x D3 D3/QZ nonpolar disp. π π stacking MAD=4.0 MD= 3.1 CH π int. halogen bonds H bonds charged

27 S30L: results for E(gas) with DFT-D3 Binding Energy E /kcal mol nonpolar disp. reference TPSS D3/TZ π π stacking MAD=4.3 MD= 3.7 CH π int. halogen bonds H bonds charged

28 S30L: simple methods HF-3c: minimal basis set, D3-dispersion- and BSSE(geometrical CP)-corrected Hartree Fock 2 DFTB3-D3: dispersion-corrected tight-binding, approximates a GGA in a minimal basis set, third-order self-consistent charge (monopole) treatment 3 PM6-D3H2: dispersion- and hydrogen-bond corrected NDDO-MO-SCF 4 PBEh-3c: polarized double-ζ basis set, D3-dispersion- and BSSE(geometrical CP)-corrected hybrid DFT 5 M06-2x/SV(P): highly parameterized DF with small basis (often used in this combination), includes medium-range dispersion (and gcp) 2 R. Sure & SG, JCC 34 (2013), Elstner et al, JCTC 9 (2013), 338; G. Brandenburg & SG, JPCL 5, (2014), Hobza et al, JCTC 6 (2010), 344; J. J. P. Stewart, J. Mol. Mod. 13 (2007), to be published

29 S30L: results for E(gas) with simple methods Binding Energy E /kcal mol nonpolar disp. reference PBEh 3c/SVP π π stacking MAD=3.7 MD=1.1 CH π int. halogen bonds H bonds charged

30 S30L: results for E(gas) with simple methods Binding Energy E /kcal mol reference M06 2X/SVP+gCP nonpolar disp. π π stacking MAD=6.2 MD=5.0 CH π int. halogen bonds H bonds charged

31 S30L: results for E(gas) with simple methods Binding Energy E /kcal mol nonpolar disp. reference HF 3c π π stacking MAD=6.8 MD= 5.5 CH π int. halogen bonds H bonds charged

32 S30L: results for E(gas) with simple methods Binding Energy E /kcal mol nonpolar disp. reference DFTB D3 π π stacking MAD=6.9 MD= 4.3 CH π int. halogen bonds H bonds charged

33 S30L: results for E(gas) with simple methods Binding Energy E /kcal mol nonpolar disp. reference PM6 D3H2 π π stacking MAD=6.4 MD= 5.2 CH π int. halogen bonds H bonds charged

34 S30L statistics summary ωb97x D3/QZ Probability Density TPSS D3/TZ PM6 D3H2 DFTB D3 PW6B95 D3/QZ PBEh 3c M06 2X/SVP+gCP HF 3c Relative Error in E /%

35 Recipe to calculate accuracte G a use HF-3c or DFTB3-D3 for initial pree-screening re-optimize with TPSS-D3/TZ and include counter ions if nessecary compute E with PW6B95-D3/QZ (or ωb97x-d3/qz as alternative or when counter ions are present) calculate GRRHO T with HF-3c employ COSMO-RS(13fine) to get δgsolv T (X ) for water and if counter ions are present and COSMO-RS(12) otherwise only prerequisites: certain rigidity and charges not higher/lower than +4/-2

36 Conclusions Solid 5-10 % accuracy of DFT-D3 for non-covalent interactions Tailored levels of QM accuracy, similar for structures (not discussed) Three-body dispersion effects are important for binding energies of large systems (about 5 % of E (2) disp ) Semi-empirical methods are useful (typical % error), MP2-type methods are problematic Charged systems (and their charge state under the experimental conditions) are somewhat problematic (solvation terms) Remaining error for G a is mainly due to E(gas) and δg(solv) Similar accuracy for molecular crystals in periodic calculations (errors for H vap of about 1 kcal, about 1-2% cell volume error)

37 Acknowledgement Rebecca Sure (supramolecular complexes) Dr. Andreas Hansen (ORCA, DLPNO-CC, administration) DFTB: Prof. M. Elstner, KIT ORCA: Prof. F. Neese, MPI (CEC) Mühlheim TURBOMOLE team/cosmologic (Dr. A. Klamt, Dr. Uwe Huniar) Financial support: DFG, Fonds der chemischen Industrie, Bayer AG

38 Key References 1. DFT-D3: SG, J. Antony, H. Krieg, S. Ehrlich, J. Chem. Phys. 132 (2010), ; DFT-D3(BJ): SG, S. Ehrlich, L. Goerigk, J. Comput. Chem. 32 (2011), Supramolecular benchmarks: SG, Chem. Eur. J, 68, (2012) ; T. Risthaus, SG, JCTC, 9, (2013) ; J. Antony, R. Sure, SG, Chem. Comm. 51, (2015) ; R. Sure, J. Antony, SG, J. Phys. Chem. B, 118 (2014) Low-cost D3 methods: J. G. Brandenburg, M. Hochheim, T. Bredow, SG, J. Phys. Chem. Lett. 5 (2014) DFT-D3 for molecular crystals: J. G. Brandenburg, SG Top. Curr. Chem 345 (2014) 1-23; J. G. Brandenburg, SG J. Phys. Chem. Lett. 5 (2014) ; J. Moellmann, SG J. Phys. Chem. C 118 (2014)

Supporting Information: Predicting the Ionic Product of Water

Supporting Information: Predicting the Ionic Product of Water Eva Perlt 1,+, Michael von Domaros 1,+, Barbara Kirchner 1, Ralf Ludwig 2, and Frank Weinhold 3,* 1 Mulliken Center for Theoretical Chemistry,