Presentation is loading. Please wait.

Presentation is loading. Please wait.

concepts, machinery & applications Gerrit Groenhof

Published byFelicia Geraldine Morrison Modified over 9 years ago

Similar presentations

Presentation on theme: "concepts, machinery & applications Gerrit Groenhof"— Presentation transcript:

1 mixed quantum-classical molecular dynamics simulations of biomolecular systems
concepts, machinery & applications Gerrit Groenhof dept. of biophysical chemistry University of Groningen Nijenborg 4, 9747 AG Groningen The Netherlands

2 biomolecular simulation
biomolecules - proteins, DNA, lipid membranes, … - biochemistry, biology, farmacy, medicine, … physical composition of biomolecules - molecules are composed of atoms - atoms are composed of electrons and nuclei laws of physics - interaction - motion computing properties of biomolecules - static: energies, structures, spectra, … - dynamic: trajectories, …

3 molecular simulation standard molecular dynamics example - forcefield
- single overall connectivity: no chemical reactions - single electronic state: no photo-chemical reactions example - aquaporin-1 mechanism B. de Groot & H. Grubmüller  Science 294: (2001)

4 molecular simulation QM/MM molecular dynamics examples
- combination of quantum mechanics and forcefield - connectivity varies: chemical reactions electronic state varies: photo-chemical reactions examples - Diels-Alder reaction cycloaddition of ethene and butadiene in cyclo-hexane (not shown)

5 molecular simulation QM/MM molecular dynamics examples
- combination of quantum mechanics and forcefield - connectivity varies: chemical reactions electronic state varies: photo-chemical reactions examples photo-isomerization QM/MM simulation of Photo-active yellow protein J. Amer. Chem. Soc. 126: (2004)

6 molecular simulation concepts & machinery applications
- molecular dynamics (MD) (5m) - molecular mechanics forcefield (MM) (5m) - molecular quantum mechanics (QM) (60m) - mixed quantum/classical mechanics (QM/MM) (30m) - geometry optimization (10m) applications - Photoactive Yellow Protein (45m) - Diels-Alderase enzyme (you!) (3h)

7 molecular dynamics nuclei are classical particles
- Newton’s equation of motion - numerically integrate equations of motion potential energy and forces - molecular mechanics - quantum mechanics

8 molecular dynamics numerically integrate eoms of atoms

9 molecular mechanics forcefield
approximation for energy V - analytical lower dimensional functions (n << N) bonded interactions - empirical parameters (pk) thermodynamic data & QM calculations

10 molecular mechanics forcefield
approximation for energy V - analytical lower dimensional functions (n << N) non-bonded interactions - empirical parameters (pk) thermodynamic data & QM calculations

11 molecular mechanics forcefield
bonded interactions: bonds , angles & torsions

12 molecular mechanics forcefield
non-bonded interactions: Lennard-Jones & Coulomb

13 molecular mechanics forcefield
popular forcefields - CHARMM, OPLS, GROMOS, AMBER, … advantages - fast large systems: proteins, DNA, membranes, vesicles disadvantages - limited validity only valid inside harmonic regime no bond breaking/formation - limited transferrability new molecules need new parametrization

14 fundamental quantum mechanics
subatomic particles Louis de Broglie Erwin Schrödinger Werner Heisenberg Paul Dirac Max Born Albert Einstein many others - wave character electron diffraction - energy quantization wavefunction - Schrödinger wave equation Intro on quantum mechanics time-dependent time-independent - Hamilton operator kinetic potential

15 molecular quantum mechanics
solving electronic Schrödinger equation - Born-Oppenheimer approximation electronic and nuclear motion decoupled - electrons move in field of fixed nuclei electronic hamiltonian Golffunctie aanpak: golffie benaderen. kinetic elec-nucl elec-elec nucl-nucl forces on classical nuclei

16 molecular quantum mechanics
applications for molecular modeling - electron density (charge distribution)

17 molecular quantum mechanics
applications for molecular modeling - reaction pathways Diels-Alder cyclo-addition mechanism

18 molecular quantum mechanics
Hartree approximation to wavefunction - product of one electron functions - hamiltonian with electron-electron term - hamiltonian without electron-electron term kinetic elec-nucl elec-elec - mean field approximation electron i in average static field of other electrons - iterative solution (self consistent field)

19 molecular quantum mechanics
Hartree approximation - illustration of mean-field approach electronic structure of O2; atom conf.: (1s22s22px2)2py12pz1

20 molecular quantum mechanics
Hartree approximation - illustration of mean-field approach electronic structure of O2; atom conf.: (1s22s22px2)2py12pz1

21 molecular quantum mechanics
Hartree approximation - illustration of mean-field approach electronic structure of O2; atom conf.: (1s22s22px2)2py12pz1

22 molecular quantum mechanics
Pauli principle - electrons are fermions (spin ½ particles) - electron wavefunction is anti-symmetric - no two electrons can occupy same state Hartree approximation - product of one electron functions: - not anti-symmetric: Hartree-Fock approximation - anti-symmetric combination of Hartee products

23 molecular quantum mechanics
anti-symmetric sum of Hartree products - e.g. product of two one electron functions Hartree approximation: Fock (Slater) correction: - anti-symmetric - no effect on wavefunction’s properties energy, density, …

24 molecular quantum mechanics
Hartree-Fock approximation - anti-symm. product of one electron wavefunctions - Slater determinant

25 molecular quantum mechanics
one electron wavefunctions - spatial & spin part - Ĥ does not operate on s, only on x,y,z - s(s) is a spinlabel - spatial part (x,y,z) is a molecular orbital max. two electrons (Pauli principle) - Slater determinant with molecular orbitals

26 molecular quantum mechanics
molecular orbitals - linear combination of atomic orbitals - e.g. H2 ;

27 molecular quantum mechanics
atomic orbitals - combination of simple spatial functions Slater-type orbitals: gaussian-type orbitals: - mimic atomic s,p,d,… orbitals - basisset: STO-3G, 3-21G, …, 6-31G*, …

28 molecular quantum mechanics
restricted Hartree-Fock wavefunction - Slater determinant - molecular orbitals - atomic orbitals (basisset) optimization of MO coefficents cji - variation principle - find cji that minimize the energy (just 3 slides)

29 molecular quantum mechanics
Hartree-Fock equations - minimization problem - HF equation for single moleclar orbital (meanfield) - nonlinear set of equations coulomb operator exchange operator - total electronic energy (1/3)

30 molecular quantum mechanics
Roothaan-Hall equations - HF equation for molecular orbitals - expressed in atomic orbitals - multiply by atomic orbital ci* and integrate - matrix equation - solution ({cja} and {ea}) if (2/3)

31 molecular quantum mechanics
self consistent field procedure - iterate until energy no longer changes (converged) e.g. Gaussian SCF output: Closed shell SCF: Cycle 1 Pass 1 IDiag 1: E= Cycle 2 Pass 1 IDiag 1: E= Delta-E= Rises=F Damp=T Cycle 3 Pass 1 IDiag 1: E= Delta-E= Rises=F Damp=F ...skipping... Cycle 12 Pass 1 IDiag 1: E= Delta-E= Rises=F Damp=F Cycle 13 Pass 1 IDiag 1: E= Delta-E= Rises=F Damp=F Cycle 14 Pass 1 IDiag 1: E= Delta-E= Rises=F Damp=F SCF Done: E(RHF) = A.U. after 14 cycles Convg = D V/T = S**2 = (3/3)

32 molecular quantum mechanics
Hartree-Fock based methods Hartree Fock wavefunction as starting point no electron correlation MCSCF (CI, CASSCF) perturbation theory (MP2, MP4, CASPT2) high demand on computational resources small to medium-size molecules in gas phase alternative methods semi-empirical methods density functional theory methods

33 molecular quantum mechanics
limitations of HF wavefunction no electron correlation dynamic: electronic motion is correlated static: electrons avoid each other improving HF wavefunction multi-configuration self-consistent field (mcscf) single, double, triple, quadruple, quintuple, … excitations resolves (part of) static correlation

34 molecular quantum mechanics
multi-configuration self-consisitent field size of sum

35 molecular quantum mechanics
limitations of HF wavefunction no electron correlation dynamic: electronic motion is correlated static: electrons avoid each other improving HF wavefunction perturbation theory Møller-Plesset (MP): MP2, MP4, CASPT2, …

36 molecular quantum mechanics
semi-empirical methods Roothaan-Hall equations zero differential overlap empirical parameters in Fij fitted to thermochemical data CNDO, INDO, NDDO, MINDO, MNDO, AM1, PM3

37 molecular quantum mechanics
density functional theory Hohenberg-Kohn Theorem (1964) electron density defines all ground-state properties Kohn-Sham equation (1965) Kohn-Sham orbitals exchange-correlation functional Exc[re(r)] - find cji that minimize the energy functional E[re(r)] self-consistent Roothaan-Hall equations

38 molecular quantum mechanics
summary solving electronic Schrödinger equation computational techniques Hartree-Fock and beyond (RHF, UHF, CASSCF, MP2,…) semi-empirical methods (INDO, AM1, PM3, …) density functional theory (Becke, BP87, B3LYP, …) forces on nuclei more accurate than any forcefield bond breaking/formation excited states, transitions between electronic states

39 molecular quantum mechanics
high demand on computational recources small to medium sized gas-phase systems

40 mixed quantum/classical methods
reaction in condensed phase - reactions in solution - enzymatic conversions subdivision of the total system - reactive center (QM) - environment (MM) QM/MM hybrid model - compromise between speed and accuracy - realistic chemistry in realistic system

41 QM/MM hybrid model QM subsystem embedded in MM system
A. Warshel & M. Levitt. J. Mol. Biol. 103: (1976)

42 QM/MM hybrid model application for molecular modeling
- catalytic Diels-Alderase antibody J. Xu et al. Science 286: (1999) (experimental)

43 QM/MM hybrid model interactions in QM subsystem
- QM hamiltonian interactions in the MM subsystem - forcefield interactions between QM and MM subsystems - QM/MM interface - forcefield bonded and dispersion interactions - QM hamiltonian electrostatic interactions

44 QM/MM hybrid model QM/MM bonded interactions bonds , angles & torsions

45 QM/MM hybrid model QM/MM dispersion interactions Lennard-Jones

46 QM/MM hybrid model QM/MM boundary link atom , frozen orbital

47 QM/MM hybrid model QM/MM electrostatic interactions point charges:

48 QM/MM hybrid model Roothaan-Hall equations forcefield terms
- HF equation for molecular orbitals - QM subsystem in cloud of pointcharges - polarization of QM subsystem forcefield terms - QM/MM (bonds, angles, torsions & LJ) - MM

49 QM/MM hybrid model

50 QM/MM hybrid model electrostatic QM/MM interaction
- QM subsystem in cloud of pointcharges core elec-MMatom nucl-MMatom - polarization of QM subsystem problems & inconsistencies - no polarization of MM subsystem implicitly incorporated in LJ and atomic charges - pointcharges of MM atoms forcefield dependent

51 alternative QM/MM interface
ONIOM F. Maseras & K. Morokuma, J. Comp. Chem. 16, 1170 (1995) two layer ONIOM energy

52 alternative QM/MM interface
multilayer ONIOM QM/QM/.../…/MM

53 geometry optimization
potential energy surface energy & forces MM (forcefield) QM (HF, DFT, …) QM/MM …

54 geometry optimization
stationary points reactants → products minima on PES reactants products saddle-points transition states reaction mechanism

55 geometry optimization
stationary points Hess matrix (Hessian) - matrix of second derivatives minima on potential energy surface Hessian has only positive eigenvalues saddle-points on potential energy surface Hessian has one negative eigenvalue

56 geometry optimization
locating minima - general procedure follow the gradient downhill locating saddle points - optimization with constraints one eigenvalue of Hessian is negative good guess TS geometry (intuition & experience) linear transit reaction coordinate interpolation between reactant and product geometries always check the eigenvalues of Hessian!!

57 geometry optimization
linear transit calculation - reaction coordinate (experience & intuition) e.g. Diels-Alder cycloaddition constrain/restrain reaction coordinate minimize/sample all other degrees of freedom Dvreact or even DGreact (potential of mean force)

58 geometry optimization
linear transit calculation - result for the Diels-Alder cycloaddition

59 end of part I coming up part II QM/MM concepts & machinery QM/MM
applications

Download ppt "concepts, machinery & applications Gerrit Groenhof"

Similar presentations

Introduction to Computational Chemistry NSF Computational Nanotechnology and Molecular Engineering Pan-American Advanced Studies Institutes (PASI) Workshop.

Introduction to Computational Chemistry NSF Computational Nanotechnology and Molecular Engineering Pan-American Advanced Studies Institutes (PASI) Workshop.
Introduction to Møller-Plesset Perturbation Theory

Introduction to Møller-Plesset Perturbation Theory
Quantum Mechanics Calculations II Apr 2010 Postgrad course on Comp Chem Noel M. O’Boyle.

Quantum Mechanics Calculations II Apr 2010 Postgrad course on Comp Chem Noel M. O’Boyle.
0 Jack SimonsJack Simons, Henry Eyring Scientist and Professor Chemistry Department University of Utah Electronic Structure Theory Session 7.

0 Jack SimonsJack Simons, Henry Eyring Scientist and Professor Chemistry Department University of Utah Electronic Structure Theory Session 7.
ChE 452 Lecture 16 Quantum Effects In Activation Barriers 1.

ChE 452 Lecture 16 Quantum Effects In Activation Barriers 1.
Statistical Mechanics and Multi- Scale Simulation Methods ChBE 591-009 Prof. C. Heath Turner Lecture 03 Some materials adapted from Prof. Keith E. Gubbins:

Statistical Mechanics and Multi- Scale Simulation Methods ChBE Prof. C. Heath Turner Lecture 03 Some materials adapted from Prof. Keith E. Gubbins:
CHE-30042 Inorganic, Physical & Solid State Chemistry Advanced Quantum Chemistry: lecture 4 Rob Jackson LJ1.16, 01782 733042

CHE Inorganic, Physical & Solid State Chemistry Advanced Quantum Chemistry: lecture 4 Rob Jackson LJ1.16,
Solvation Models. Many reactions take place in solution Short-range effects Typically concentrated in the first solvation sphere Examples: H-bonds,

Solvation Models. Many reactions take place in solution Short-range effects Typically concentrated in the first solvation sphere Examples: H-bonds,
Molecular Quantum Mechanics

Molecular Quantum Mechanics
Introduction to Molecular Orbitals

Introduction to Molecular Orbitals
Chapter 3 Electronic Structures

Chapter 3 Electronic Structures
Theoretical Models “The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely.

Theoretical Models “The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely.
Molecular Mechanics Force Fields Basic Premise If we want to study a protein, piece of DNA, biological membranes, polysaccharide, crystal lattice, nanomaterials,

Molecular Mechanics Force Fields Basic Premise If we want to study a protein, piece of DNA, biological membranes, polysaccharide, crystal lattice, nanomaterials,
Chemistry 6440 / 7440 Semi-Empirical Molecular Orbital Methods.

Chemistry 6440 / 7440 Semi-Empirical Molecular Orbital Methods.
Quantum Mechanics and Force Fields Hartree-Fock revisited Semi-Empirical Methods Basis sets Post Hartree-Fock Methods Atomic Charges and Multipoles QM.

Quantum Mechanics and Force Fields Hartree-Fock revisited Semi-Empirical Methods Basis sets Post Hartree-Fock Methods Atomic Charges and Multipoles QM.
Computational Chemistry

Computational Chemistry
Molecular Modeling: Semi-Empirical Methods C372 Introduction to Cheminformatics II Kelsey Forsythe.

Molecular Modeling: Semi-Empirical Methods C372 Introduction to Cheminformatics II Kelsey Forsythe.
Ion Solvation Thermodynamics from Simulation with a Polarizable Force Field Gaurav Chopra 07 February 2005 CS 379 A Alan GrossfeildPengyu Ren Jay W. Ponder.

Ion Solvation Thermodynamics from Simulation with a Polarizable Force Field Gaurav Chopra 07 February 2005 CS 379 A Alan GrossfeildPengyu Ren Jay W. Ponder.
Photoactivation of the Photoactive Yellow Protein chemistry department Imperial Colege London London SW7 2AZ United Kingdom Gerrit Groenhof, Berk Hess,

Photoactivation of the Photoactive Yellow Protein chemistry department Imperial Colege London London SW7 2AZ United Kingdom Gerrit Groenhof, Berk Hess,
Case Studies Class 5. Computational Chemistry Structure of molecules and their reactivities Two major areas –molecular mechanics –electronic structure.

Case Studies Class 5. Computational Chemistry Structure of molecules and their reactivities Two major areas –molecular mechanics –electronic structure.

Similar presentations

Ads by Google