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Cdt-2019-Day2 SBM CDT 2019 Computational Module Day 2 Dr Fernanda Duarte Department of Chemistry, University of Oxford http://fduartegroup.org 1 Workplan Tuesday Wednesday Friday 9:00-10:00 Lecture 2 Lecture 3* 10:30-12:00 Lecture 1 Project Work Project Work 14:00- 17:00 Lab session Project Work Presentations Lab session Project Work Presentations 2 Outline (Lecture 2) •Day 1 •The good side: Applications of DFT in Chemistry •The other side …. Challenges in DFT modelling •A bit more on Functionals and Basis sets !3 !3 Computational Chemistry Why should you care? Hˆ = Hˆ + Hˆ HEˆ Y = Y Born-Oppenheimer Approximation N e Y =y ey N ElectronicTheory Schrödinger Equation Modelling ˆ Hey e = Eey e 2 electrons electrons nuclei electrons ˆ -! 2 Z A 1 Hei= ååååÑ- + 2m iiAijrRiA- < rrij- Kinetic energy Coulomb attraction Electronic repulsion (nuclei-electrons) Experiments Synthesis Kinetics spectroscopy “Artificial Intelligence will not replace chemists. But chemists who doesn’t use (AI) will be replace by those who do” Willem Van Hoorn 4 Computational Chemistry What is - and why is it relevant? Which System Do I Have? What Do You Want to Compute (and Why)? Which Model /Method Should I Choose? Verify Approach (vs. Experiment) Interpret/Analyse 5 Computational Chemistry Which System Do I Have? 10 atoms – organic molecule – singlet 6 Computational Chemistry What Do I Want to Compute (and Why)? Asymmetric Induction via 1,2-Addition to Carbonyl Compounds Conformations for the starting material and TS Which product is preferred? What is the molecular origin of such preference? 7 Computational Chemistry Which Model /Method Should I Choose? Chemical Accuracy {φi} double hybrid: ωB97X-2, XYG3, B2PLYP HF/3-21G εx hybrid-GGA: hyper-meta-GGA: B3LYP, mPW1K M06-2X, M11,TPSSh NOT recommended Many known deficiencies τ or meta-GGA: … 2 ∇ ρ(r) τHCTH,TPSS, M06-L But fast… Simplicity Accuracy ∇ρ(r) GGA: Wong and Paddon-Row PBE, BLYP, OLYP, B97 Theoretical evidence in support of the Anh – Eisenstein electronic model in controlling π-facial stereoselectivity in nucleophilic additions to carbonyl compounds ρ(r) LDA: VWN, GPW92 J. Chem. Soc. Chem. Commun. 1990, 456 Hartree Fock theory 8 Computational Chemistry Which System Do I Have? What Do You Want to Compute (and Why)? Often the most Which Model /Method Should I Choose? interesting result is when the “calculation gets it wrong” Verify Approach (vs. Experiment/Previous studies) Interpret/Analyse 9 Computational Chemistry Conformational Analysis: 2 minima ΔG = -RTlnK K = exp[-(ΔΔG)/RT]/RT K = e-3.6 kcal/mol /(0.001987)(298) = [A]/[B] Thus % min1 = (0.0023/1.0023) x 100% = 99.8% T(K) = 298 R(kcal mol-1) = 0.001987 R(kJ K-1 mol-1) = 8.3144598 ×10−3 h(J*s) = 6.6262 x 10-34 kb(J/K) = 1.3807 x 10-23 10 Computational Chemistry Conformational Analysis: 2 minima k T k = B e-DG / RT h T(K) = 298 R(kcal mol-1) = 0.001987 R(kJ K-1 mol-1) = 8.3144598 ×10−3 -34 -23 h(J*s) = 6.6262 x 10 kb(J/K) = 1.3807 x 10 11 Computational Chemistry Asymmetric Induction via 1,2-Addition to Carbonyl Compounds Cornforth model J. Am. Chem. Soc. 1959 polar Felkin−Anh (PFA) model Tetrahedron Lett. 1968 Computational Organic Chemistry Steven M. Bachrach Paddon-Row, Rondan & Houk J. Am. Chem. Soc. 1982, 104, 7162. Houk, Paddon-Row, Rondan, Wu, Brown, Spellmeyer, Metz, Li & Longarich Science 1986, 231, 1108 Cee, Cramer & Evans J. Am. Chem. Soc. 2006, 128, 2920 12 Computational Chemistry Physical Organic Chemistry transforms slowly at room temperature O benzene benzene endo + O exo diastereomer RT Δ diastereomer O Kinetic Thermodynamic Product Product 13 https://pubs.rsc.org/en/Content/ArticleLanding/2016/CS/C6CS00573J Computational Chemistry transforms slowly at room temperature O benzene benzene endo + O exo diastereomer RT Δ diastereomer O Kinetic Thermodynamic Product Product 20.4 19.6 + + ΔΔG O O O O O O 0.0 + -6.7 + G -7.6 ΔΔ rxn + 14 https://pubs.rsc.org/en/Content/ArticleLanding/2016/CS/C6CS00573J Computational Chemistry 15 https://pubs.rsc.org/en/Content/ArticleLanding/2016/CS/C6CS00573J Computational Chemistry Conformations ΔG n = exp[-(ΔG2-ΔG1)/RT] ni/∑n (%) (kcal mol-1) 0.0 1.00 83.4 1.0 0.18 15.4 2.5 0.01 1.2 5.0 0.00 0.0 1.20 100.0 T(K) = 298 R(kcal mol-1) = 0.001987 R(kJ K-1 mol-1) = 8.3144598 ×10−3 16 http://www.metadynamics.cz/eyring/eyring.html Computational Chemistry Kinetics k T k = B e-DG / RT h T(K) = 298 R(kcal mol-1) = 0.00831 R(kJ K-1 mol-1) = 8.3144598 ×10−3 h(J*s) = 6.6262 x 10-34 kb(J/K) = 1.3807 x 10-23 ΔG‡ k t1/2 t1/2 (kcal mol-1) (s-1) (s-1) 12 9.8 x 103 7.1 x 10-5 70.5μs 17 2.11 3.3 x 10-1 327 ms 22 4.5 x 10-4 1.5 x 103 25min 27 9.8 x 10-8 7.1 x 106 81.1 days 30 6.2 x 10-10 2.4 x 10-6 35.5 years 17 http://www.metadynamics.cz/eyring/eyring.html Computational Chemistry When there are competing pathways leading from interconverting intermediates, the product ratio is determined by the relative heights of the highest energy barriers leading to the products" 18 http://www.metadynamics.cz/eyring/eyring.html Computational Chemistry Experimental Determinations of Activation Parameters ΔG‡ = ΔH‡ – TΔS entropy: energy associated with conformation, bond strength, vibrational states and how changes in these properties affect the overall energy of the system. enthalpy: can be related to the height of the surface while entropy is related to the width of the channels leading from one energy well to another 19 http://www.metadynamics.cz/eyring/eyring.html Computational Chemistry Experimental Determinations of Activation Parameters Experimental Determinations of Activation and Arrhenius Parameters ΔG‡ = ΔH‡ – TΔS The Eyring equation can be mathematically manipulated to give the equation of a line with a dependence on temperature kBT S H Eyring plot k = exp exp h R RT kh slope H ln k T kBT H S B ln k = ln – + h RT R y-intercept S kh H S ln = – + 1 / T (K-1) kBT RT R Similar manipulation of the Arrhenius equation allows one to experimentally determine values for Ea and A Arrhenius plot –E k = A exp a 20 RT slope Ea http://www.metadynamics.cz/eyring/eyring.htmlln k E y-intercept A ln k = ln A – a RT 1 / T (K-1) What is DFT useful for? Phosphate/sulfate hydrolysis Dissociative Associative 2.34 2.45 2.27 1.75 Bond Forming Bond P- Bond Breaking Olg !21 Neese et al. J. Chem. Phys. 2013, 138, 034106 Kumar et al. Chem. Sci. 2018, 9, 2655 What is DFT useful for? Phosphate/sulfate hydrolysis associative dissociative Linear Free energy Relationship (LFER) a. 3,5-NO -4 2 a. 3,5-NO2 -1.42±0.03 b. 4-NO2 NO -6 NO2 c. 3-NO -4-Cl O b. 4-NOO 2 2 O O O O O O 2 NO X d. 3-NO NO2 2 c. 3-NO -4-Cl P CH P P 2 O O O O O O O O S 2 O O 3 -8 O O X O O -1 O O e. 3,4-Cl P CH P d. 3-NO2 S 3 P / s f. 3-Cl O O O O O O e. 3,4-Cl k -10 O O g. 4-Cl f. 3-Cl log -12 h. H g. 4-Cl h. H -14 -16 -18 6 8 10 12 14 pKa !22 Duarte et al. J. Am. Chem. Soc. 2015, 137, 1081 (Cover article and Spotlight) Duarte et al. J. Am. Chem. Soc. 2016, 138, 10664 Edge Article Chemical Science 1 1 5 5 10 10 15 15 20 20 Fig. 2 Cation–p complexes analyzed in this work. Models of (A)/(B) lysine; (C)/(D), arginine; and (E)–(H), histidine sidechains interacting with benzene. 25 25 with one or three N–H atoms facing the aromatic ring.41 This complexes (A), (C), (E), and (G) CCSD(T) calculations were also binding mode is most prevalent in proteinWhat inter-residue is DFT inter- carrieduseful out using for? a dielectric constant of 4.2 (diethyl ether) and 30 actions.42 Guanidinium–benzene complexes can adopt at least 78.4 (water). 30 two conformations: perpendicular (T-shaped) or parallel. While In relation to the D6h symmetry of benzene, two vectors in the T-shaped geometries are preferred in gas-phase, parallel- plane of the ring represent extreme scenarios of displacement – complexes are preferred in solution and have been observedMagnitudesone towards a and C–H bond origins (angle displacement)of nonbonded and the other interactions more frequently in protein structures.43 We studied the parallel towards a C–C bond (side displacement). These vectors are 7,44 35 conguration, based on its biological relevance. For [C H ] related by a rotation of m 30 about the C axis (Fig. 3). By 35 6 6 ¼ 6 [Imi]+ complexes, both perpendicular and parallel arrange- plotting a potential energy curve (PEC) with vertical distance ments are found in protein interactions.45 We included both Cation–π interactions [C6H6][NH4]+ [C6H6][Gdm]+ interaction types in our analysis. We studied the interaction energy (Eint) of each model 40 cation–p complex as a function of intermolecular separation 40 ] and of horizontal displacement parallel to the aromatic plane.
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