molecular modelling 2009-01-23

8/9/2019 Molecular Modelling 2009-01-23

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Department

of Chemistry

Molecular Modelling

Hans Martin Senn 2008/09

1Friday, 23 January 2009


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Assessment

MSci students: Exam

PhD students: Attendance

Time table

1112 slot?

Administrative Notes

Semester 217 18 19 20 21 22 23

12 Jan 19 Jan 26 Jan 02 Feb 09 Feb 16 Feb 23 Feb 0

A6 A6 O4 O4 O7 O8 O8

O5 O5 O1 O1

C8 C8 A2 A2

A3/O3 A 3/O3 A 5/O6 A 5/O6 O9 O2 O2

O O O

C 3/A6 A6 A 4/O4 A4 /O4 O 7 A1/ O8 A 1/ O8

O5 O5 O1 O1

C8 C8 A2 A2

A3/O3 A 3/O3 A 5/O6 A 5/O6 O9 O2 O2

C 3/A6 A6 A 4/O4 A4 /O4 O 7 A1/ O8 A 1/ O8P P/O5 O5 O 1 O1 P

C8 C8 A2 A2 P

A3/O3 A 3/O3 A 5/O6 A 5/O6 O9 O2 O2

C 3/A6 A6 A 4/O4 A4 /O4 O 7 A1/ O8 A 1/ O8

O5 O5 O1 O1

C8 C8 A2 A2

A3/O3 A 3/O3 A 5/O6 A 5/O6 O9 O2 O2

C3 O7 A4/O7 A4/O7 O7 A1 A1

O9 O9 O9 O9



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Further Reading

Lecture notes

Slides and notes: http://www.chem.gla.ac.uk/staff/senn/

Text books

A. R. Leach, Molecular Modelling: Principles and Applications, 2nd ed., Pearson

Education, Harlow, 2001; Chem BL, Biochem B35 2001-L.

A. Hinchliffe, Molecular Modelling for Beginners, Wiley, Chichester, 2003; Chem BL,

Biochem B35 2003-H.

H.-D. Hltje, W. Sippl, D. Rognan, G. Folkers, Molecular Modeling: Basic Principlesand Applications, 3rd ed., Wiley-VCH, Weinheim, 2008; Chem BL, Biochem B35

2008-H.

G. H. Grant, W. G. Richards, Computational Chemistry, Oxford Chemistry Primers,

Vol. 29, OUP, Oxford, 1995; Chem BL, Chemistry D O3O 1995-G.

F. Jensen, Introduction to Computational Chemistry, 2nd ed., Wiley, Chichester, 2007;

Chem BL, Chemistry D030 2007-J. C.J. Cramer, Essentials of Computational Chemistry, 2nd ed., Wiley, Chichester,

2004; Chem BL, Chemistry D030 2008-C.



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Molecular Models: Historical Perspective

Mechanical molecular models

Widely used since the 1950s: X-ray crystallography makes structures of organic

molecules routinely accessible.

Intuitive and quantitative information about 3D properties: Distances, angles,

volumes, rigidity, steric hindrances, etc.



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Definitions of Terms

A model is

A simplified or idealized description or conception of a particular system,

situation, or process, often in mathematical terms, that is put forward as a basis

for theoretical or empirical understanding, or for calculations, predictions, etc.; a

conceptual or mental representation of something. (Oxford English Dictionary)

A model must be wrong, in some respects, else it would be the thing itself. The

trick is to see where it is right. (Henry A. Bent)

Features of a model

1. Simplified approximation

2. Didactical illustration

3. Mechanical analogy

4. Mathematical model



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Molecular Modelling and Neighbouring Fields

Molecular modelling

Theoretical

chemistry

Chem-

informatics

Molecular

simulations

Molecular

graphics

Quantum

chemistry

Computational

chemistry



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Molecular Modelling as a Discipline

Molecular models and modelling today

Use of computers to represent and manipulate 3D models of molecular

systems and their properties.

Broad sense: Manipulating molecules in/on/with/at the computer.

More narrowly: Computational classical-mechanical models

(molecular mechanics).

Electronic structure not considered, no quantum mechanics (no electrons). Shares common ground and boundaries with

Molecular simulations: Molecular dynamics and Monte Carlo simulations

Computational chemistry: Implementations, algorithms

Theoretical chemistry: Theories and models, often QM-based

Quantum chemistry: Applied molecular QM

Molecular graphics: Visualization

Cheminformatics: Data mining, statistics



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Course Overview

1. Representing molecular structure: Coordinate systems

2. Molecular potential-energy surfaces

3. Molecular mechanics

4. Molecular dynamics

5. Sampling from statistical-mechanical ensembles

6. Monte Carlo simulations

7. Docking



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Coordinate Systems / Cartesians

Basic requirements of coordinate information

What: Element type

Where: Position in 3D space (absolute or relative)

Cartesian coordinates

Absolutexyzposition

Example: Xmol xyz format9 1 C 0.000000 0.000000 0.0000002 C 0.000000 0.000000 1.4500003 O 1.319933 0.000000 -0.4666674 H 1.319933 0.000000 -1.4166675 H-0.513360 0.889165 -0.3630006 H-0.513360 -0.889165 -0.3630007 H-1.026719 0.000000 1.8130008 H 0.513360 0.889165 1.8130009 H 0.513360 -0.889165 1.813000

H4

O3

C1

C2

H7

H6 H5

H8

H9

No. of atomsAtom numberAtom symbolxcoordinate ycoordinate z coordinate



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Internal Coordinates

Definition

Position of an atom defined by internal distances, angles, dihedrals relative to

other atoms.

An example:Z-matrix

Each position specified by 1 distance, 1 angle, 1 dihedral

First 3 atoms define absolute frame

H4

O3

C1

C2

H7

H6 H5

H8

H9

1 c 2 c 1 1.450000 3 o 1 1.400000 2 109.471 4 h 3 0.950000 1 109.471 2180.0005 h 1 1.089000 3 109.471 2120.0006 h 1 1.089000 3 109.471 2240.0007 h 2 1.089000 1 109.471 3180.0008 h 2 1.089000 7 109.471 1120.0009 h 2 1.089000 7 109.471 1240.000

Atom numberAtom symbol

Ref. atom for distance

Distance Angle Dihedral

Ref. atom 2 for angle Ref. atom 3 for dihedral



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Internal Coordinates

Comments on internal coordinates

Absolute position and orientation in space of molecule as a whole are not

explicitly specified.

However:Z-matrix defines absolute position/orientation by convention via first 3atoms.

Distances, angles, dihedrals are usually taken as bonded but do not have to be.

Anycombination of (a suffcient number of) distances, angles, dihedrals can beused to define the positions.



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Degrees of freedom

Number of coordinates required

Absolute positions: 3Ncoordinates (N: no. of atoms)

Internal degrees of freedom

Absolute position and rotation of whole molecule remain undefined.

General molecule: 3N 6 degrees of freedom

Linear molecule: 3N 5 degrees of freedom



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Comparison of Coordinate Systems

All coordinate systems are equivalent

Cartesians and internals (with defined origin and orientation) carry identical

information

Transformation between coordinate systems always possible; can be expensive

Practical considerations

Smaller (< 1000 atoms), discrete molecules: Internals

Larger molecules, collections of molecules: Cartesians

Programs usually define appropriate internals automatically, user deals with

Cartesians

Cartesian coordinates Internal coordinates

Straightforward

General (equally suited for discrete

molecules or assemblies)

Unique

Coupled

Can be chosen decoupled

Implicit information about

connectivity

Not unique, need to be defined for

each case



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Potential Energy Surfaces (PES)

BornOppenheimer approximation

Electrons and nuclei are in principal quantum objects.

Motion of nuclei and electrons are adiabatically decoupled becausemp >>me.

Electrons adapt instantaneously to classical nuclear configuration (structure) R.

BO caricature: Clamped nuclei approximation.

Therefore: Energy (for chosen electronic state) is a function of R, E(R).

Mapping E(R) for all R: Potential energy surface (PES).

In principle: E(R) obtained by solving molecular electronic Schrdinger equation at

given R.

For the moment: Assume black box computing E(R); does not have to be QM.

Dimensionality of the PES

Considering only internal degrees of freedom:

E(R) is a (3N 6)-dimensional function.


molecular modelling 2009-01-23

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