Computational Material Science Part II

Transcription

1 Computational Material Science Part II Ito Chao ( ) Institute of Chemistry Academia Sinica

2 Aim of Part II Get familiar with the computational methodologies often used and properties often predicted in molecular- or clusterbased research. With the basic understanding acquired, hopefully, you will have the ability to read literature and in conduct your own calculations when needed in research.

3 Outline Overview and comparison of methods Potential energy surface: energy minimization (Part I) and stationary point characterization Classical modeling: force field calculations (molecular mechanics; MM); solvation Quantum mechanical modeling (QM); qualitative molecular orbital analysis, various molecular orbitalbased methods, calculation of chemical and physical properties Molecular dynamic (MD) and Monte Carlo (MC) calculations QM/MM

4 Grading 25% -- take home assignments 25% -- final examination Useful Structure Database CSD -- organic and metal-organic crystal structure database (350,000 compounds) ICSD -- inorganic crystal structure database CRYSTMET -- metals (alloys, intermetallics and minerals) structure database --available at (NCHC: National Center for High-Performance Computing)

5 Useful Books Molecular Modelling: Principles and Applications, 2nd Ed., A. R. Leach / Prentice Hall (2001) Essentials of Computational Chemistry: Theory and Models, C. J. Cramer / Wiley (2004) Molecular Modelling for Beginners, A. Hinchliffe/Wiley (2003) Encyclopedia of Computational Chemistry, P. v. R. Schleyer, Ed. / Wiley (1998)

6 Program Used Gaussian 03 GaussView 1998 Nobel Prize Winner in Chemistry (with Walter Kohn). Home: Capability g_brochures/g03_intro.ht m

7 Gaussian Citation Gaussian 03, Revision C.02, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, and J. A. Pople, Gaussian, Inc., Wallingford CT, 2004.

8 Overview New tools in research (still under intensive development) Reliability changes when different methods used (choose the appropriate method for the property you care) Often use the important part to carry out the simulation

9 Molecule Bond forming/breaking? Force field parameter missing? Smaller than 150 atoms? Charges of interest? Orbital information needed? Excited state? Many structures of similar energies? Movement of surrounding molecules important? Need QM or MM for potential energy surface? QM MM MD/MC s p E r HΨ = EΨ E E = ½ kx 2 + r E <E> r

10 Chemical drawing H atoms next to C atoms are often omitted H N HO O H N HO O NH 2 H H H H NH 2 H Three-dimensional effects N HO O O OH N H NH 2 H 2 N H S-form R-form Same molecular formula, different optical activity

11 Stationary Points ( ) on Potential Energy Surface E Local maximum Gradient = 0 Negative curvature Local minimum Gradient = 0 Positive curvature Global minimum Gradient (force) = 0 Positive curvature (force constant) r

12 Characterization of Stationary Points An optimization procedure deemed converged E when ( ) 0 r 2 E 2 r Stationary points are further characterized by. Harmonic oscillator approximation of a diatomic molecule 2 E 2 r ω = = 1 2π k k µ If in a frequency analysis, imaginary frequency obtained not at a local minimum

13 Characterization of Stationary Points 2-D case At points (1,0) and (-1,0) eigenvalues of Hessian matrix all positive => minimum At point (0,0) eigenvalue eigenvector -4 (1,0) +4 (0,1) => maximum along x direction minimum along y direction One negative eigenvalue: 1st order saddle point (correspond to the transition state along a minimum energy path)

14 Significance of Stationary Points E Transition structure Ea = activation energy; related to reaction rate Ea E Product E = reaction energy Reactant r

15 Significance of Stationary Points E Transition structure E = rotational barrier E E Conformer 2 E = energy difference of conformers Conformer 1 Torsional angle

16 How can one model systems with numerous atoms? Grey: carbon Blue: nitrogen Red: oxygen

17 Molecular Mechanics (MM) Born-Oppenheimer approximation: motion of electrons can be decoupled from that of nuclei. No electron considered in MM Empirical fit to PE surface Force field: equations and parameters that define the energy surface Fundamental assumptions E(total) can be divided into parts Parameters are transferable between similar chemical systems

18 Force Field Bond stretch Morse function D e : dissociation energy α: force constant l o :equilibrium bond length Simplified approximation k l : force constant l o :equilibrium bond length

19 ¾Simplified forms does not describe bond dissociation ¾The cubic function deviates significantly from the true PES at long bond lengths so atoms may fly apart when bad initial geometry is given 4/21/2006 CMS II

20 Bond angles + higher order terms k θ : force constant θ o :equilibrium bond angle For highly strained systems, different sets of parameters have to be used e.g.

21 Dihedral angles (Torsional angles) n = 3 n = 1 n = 2 V n : related to rotational barrier height n: periodicity of rotation n = 2 is important for sp 2 species e.g. ethene H 2 C=CH 2 n = 3 is important for sp 3 species e.g. ethane H 3 C-CH 3 s: 1 or -1 ω: dihedral angle Note: the overall rotational barrier height also has contributions from non-bonded interations.

22 Non-bonded interactions distance dependent interactions calculated for all atoms with a 1,4 or greater separation van der Waals interactions Lennard-Jones potential Cut-off distance for Saving computing time ε: well depth r m : minimum energy interaction distance Buckingham potential Electrostatic interactions Coulomb s law q: atomic charge D: dielectric constant of solvent; sometimes as a function of distance

23 Other terms Stretch-bend not in all force fields Bend-bend Torsion-bend Out-of-plane bending χ: height above the plane Hydrogen bonding O-H O (Often not needed)

24 Other treatments not in all force fields π systems: MO calculations on the π systems => bond order => scale parameters (e.g. bond stretching) => minimization Heat of formation ( H f ): steric energy (Etotal) + group/bond increment (e.g. a methyl group contributes kcal/mol and a methylene group contributes kcal/mol) Strain energy: H f H f (strain free reference) strain-free reference: one that consists of the same numers of each different type of group

25 Solvation free energy based the Born model -Solvation: from vacuo to solvent -Born model of electrostatic component of solvation free energy of an ion vacuo solvent a: radius of solvent cavity ε: dielectric constant -Electrostatic component of solvation free energy of a group of atoms

26 Solvation free energy based on generalized Born equation: the GB/SA method G sol = G cav + G vdw + G elec G cav + G vdw = Σ σ k SA k SA k : solvent-accessible surface area σ k : empirical atomic solvation papmeter G elec = 1 1 q iq 1 2 ε i j fgb q : atomic charge f GB : function of r (interatomic distances) and a (or α; Born radii) j J. Am. Chem. Soc. 1990, 112, 6127; Leach 9.9.2

27 Calculated Calculated vs. vs. Experimental Experimental

28 Parameterization Need experimental (or ab initio) properties Gas phase structure Vibrational frequency Torsional barriers Crystal lattice constants Sublimation energies Hydrogen-bonding energies and geometries Liquid properties (density, heats of vaporization, radial distribution functions) Free energy of solvation

29 Advantages and Disadvantages of Molecular Mechanics Get structure, dipole moment, energy, frequency, heat of formation, etc, with little computational efforts If compounds belong to an unparameterized class, not reliable Electron-related events cannot be modeled. (electronic transition, bond breaking/forming, electron transport)

30 Docking with force field interaction potential

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32 MM MM performance performance on on bond bond length length

33 MM MM performance performance on on conformer conformer energy energy

34 Cautions Do not mix parameters from different FF Do not compare steric energies of compounds involving different combinations of functions e.g. steric energies from different FF e.g. steric energies of different molecules O O Do not overemphasize the contribution from each term for intramolecular terms

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