8/9/2019 Molecular Modelling 2009-01-23
1/14
Department
of Chemistry
Molecular Modelling
Hans Martin Senn 2008/09
1Friday, 23 January 2009
8/9/2019 Molecular Modelling 2009-01-23
2/14
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
2Friday, 23 January 2009
8/9/2019 Molecular Modelling 2009-01-23
3/14
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.
3Friday, 23 January 2009
8/9/2019 Molecular Modelling 2009-01-23
4/14
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.
4Friday, 23 January 2009
8/9/2019 Molecular Modelling 2009-01-23
5/14
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
5Friday, 23 January 2009
8/9/2019 Molecular Modelling 2009-01-23
6/14
Molecular Modelling and Neighbouring Fields
Molecular modelling
Theoretical
chemistry
Chem-
informatics
Molecular
simulations
Molecular
graphics
Quantum
chemistry
Computational
chemistry
6Friday, 23 January 2009
8/9/2019 Molecular Modelling 2009-01-23
7/14
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
7Friday, 23 January 2009
8/9/2019 Molecular Modelling 2009-01-23
8/14
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
8Friday, 23 January 2009
8/9/2019 Molecular Modelling 2009-01-23
9/14
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
9Friday, 23 January 2009
8/9/2019 Molecular Modelling 2009-01-23
10/14
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
10Friday, 23 January 2009
8/9/2019 Molecular Modelling 2009-01-23
11/14
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.
11Friday, 23 January 2009
8/9/2019 Molecular Modelling 2009-01-23
12/14
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
12Friday, 23 January 2009
8/9/2019 Molecular Modelling 2009-01-23
13/14
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
13Friday, 23 January 2009
8/9/2019 Molecular Modelling 2009-01-23
14/14
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.
14Friday, 23 January 2009