Overview of Molecular Modelling

Molecular modelling is a very diverse subject, ranging from the acquisition and subsequent display of molecular coordinates through to highly accurate (i.e. better than experiment) numerical simulation using theoretically derived functions. Depending on the context and the rigour, the subject itself is also often referred to as "molecular graphics", "molecular visualisation", "computational chemistry", "computational quantum chemistry" or "theoretical chemistry". A related area known as "molecular simulation" relates the use of molecular modelling techniques to describing and understanding the statistical behaviour and properties of collections of molecules on a "macroscopic" scale. "Molecular dynamics" deals with those time-dependent properties of collections of molecules, and uses many of the techniques of molecule modelling and statistical mechanics. Both these last two methods are beyond the scope of this lecture course.

Six Characteristic Features and Classifications

Molecular Scales. Molecular modelling spans an enormous range of molecule size.
- Essentially complete solutions of the Quantum mechanical Schroedinger equation are only available for molecules with 2-6 atoms
- Acceptably accurate (ie as good as, or better than experimental measurement can provide) "QM" solutions are nowadays available for molecules with perhaps 150 atoms if large-scale computational resources are available.
- The "macromolecular" region of up to 10,000 atoms using semi-empirical methods
- Beyond this, in the region up to about 50,000 atoms, non-quantum mechanical solutions based on "Molecular Mechanics" methods can be used.
- For larger systems, the "atom" is replaced by "unified groups" of several atoms, or by simple descriptions (spheres, ellipsoids, etc) of entire molecules.
- In the "Mesoscopic" region, one can treat collections of perhaps a million molecules.
Molecular Coordinates. Molecular modellers were amongst the first to take full advantage of on-line databases and information sources, and were the first chemists to adapt to the modern Internet. 3D atom coordinates are an essential feature of many modelling methods. Accurate or approximate 3D coordinates can be obtained from several experimental sources:
- The Cambridge Crystal database centre
- NMR data (NOE experiments which determine how close eg to H atoms might be).
- Microwave, electron diffraction and other specialised spectroscopies
- Specialised databases deriving from archived calculations or algorithms (Corina)
- Sources such as electronic journals e.g. DOI: 10.1021/ja061400a or 10.1021/ic0519988
- Digital Repositories. These are only just now starting to be used.
1. Coordinate Systems: For N atoms in a system to be modelled, at least 3N-6 coordinates are needed to specify the system geometrically. These coordinates can either be XYZ (resulting in 3N coordinates, of which 6 are normally redundant, corresponding to translations and rotations of the molecule) or so-called Internal or "Z" matrix coordinates;
```
H
O  0.96  1
O  1.4   2   111   1
H  0.96  3   111   2   90    1
```
  Some simple modelling methods (Huckel) need only the atom connectivity, and not the geometric information. Other modelling methods abandon the atom as the smallest unit whose coordinate needs to be known, and use larger scale approximations such as protein backbone positions, or even spherical or ellipsoidal approximations to whole molecules. For specialised cases (where group theoretical information is used/required to e.g.speed up calculations) symmetry adapted coordinates can be specified using exact symmetry restrictions (Gaussview is a program that can symmetrize a coordinate set). A Web site for handling coordinate symmetry even allows you to determine the symmetry group by providing XYZ coordinates.
2. Coordinate File Types: Historically, various computer file formats were developed to described these coordinates, of which the best known are the "Molfile", the "PDB" and the "XYZ" formats. The first two are really database formats, not modelling formats, and can lead to difficulties for small molecule modellers. The "XYZ" file is used almost entirely for animating molecular vibrations.
```
h2o2.mol
  4  3  0  0  0                 1 V2000
    0.1332    0.6883    2.1950 O   0  0  0  0  0
    0.2562    0.6410    0.9013 O   0  0  0  0  0
    0.8290    1.3074    2.5089 H   0  0  0  0  0
    0.2935   -0.3133    0.6690 H   0  0  0  0  0
  1  2  1  6  0  0
  1  3  1  0  0  0
  2  4  1  0  0  0
M  END
```
  The PDB format contains much more information about bio-molecules (note that atom coordinates are specified to only 3 decimal places, in Angstroms).
```
SEQRES   1 A  467  GLY ALA MET ALA SER SER VAL LEU VAL THR GLN GLU PRO          
SEQRES   2 A  467  GLU ILE GLU LEU PRO ARG GLU PRO ARG PRO ASN GLU GLU                                                              
HET    COA    101      48                                                       
HETNAM     COA COENZYME A                                                       
HETNAM     MAH 3-HYDROXY-3-METHYL-GLUTARIC ACID                                 
FORMUL   5  COA    4(C21 H36 N7 O16 P3 S1)                                      
HELIX    1   1 PRO A  444  LEU A  449  1                                   6    
HELIX    2   2 SER A  463  LYS A  474  1                                  12    
SHEET    1   A 4 LYS A 549  ALA A 556  0                                        
SHEET    2   A 4 VAL A 530  LEU A 546 -1  N  GLY A 539   O  MET A 555           
CISPEP   1 GLY A  542    PRO A  543          0         0.61                     
CRYST1   75.297  130.182   92.547  90.00 106.48  90.00 P 1 21 1      8          
ATOM      1  N   PRO A 439      -7.194 -13.702  30.538  1.00 76.06           N  
ATOM      8  N   ARG A 440      -7.440 -15.246  28.234  1.00 76.37           N 
```
  A more modern example is the CML format, which is an extensible format which can carry as much (molecular modelling) information as is needed:
```
<cml:molecule xmlns:cml="http://www.xml-cml.org/schema/cml2/core">
<cml:metadataList title="generated automatically from Openbabel">
<cml:metadata name="dc:creator" content="OpenBabel version 1-100.1"/>
<cml:metadata name="dc:description" content="CCSD(T)//CCSD/6-31G(d) Gaussian 03 optimised geometries"/>
</cml:metadataList>
<cml:atomArray atomID="a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14" elementType="C C O O C C C C H H H H H H" formalCharge="0 0 0 0 0 0 0 0 0 0 0 0 0 0" x3="0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000100" y3="0.675900 -0.675900 -1.705300 1.705300 -1.701000 1.701000 -0.722800 0.722800 1.111600 -1.111600 -1.147000 1.147000 2.739700 -2.739700" z3="-1.572000 -1.572000 -0.678200 -0.678200 0.682200 0.682200 1.617300 1.617300 -2.568500 -2.568500 2.622800 2.622800 1.006400 1.006400"/>
<cml:bondArray atomRef1="a1 a1 a1 a2 a2 a3 a4 a5 a5 a6 a6 a7 a7 a8" atomRef2="a2 a4 a9 a3 a10 a5 a6 a7 a14 a8 a13 a8 a11 a12" order="2 1 1 1 1 1 1 2 1 2 1 1 1 1"/>
</cml:molecule>
```
  The advantage of such modern formats is that e.g. molecular coordinates and properties can be embedded in a variety of delivery systems, including podcasts!
Molecular Visualisation. Once 3D coordinates are available, they can be visualised, an important aid to interpretation of molecular modelling:
- Wireframe, Ball and Stick and Spacefill for small and medium sized molecules
- Ribbon for protein, nucleotide and carbohydrate structures to render the tertiary molecular structures.
- Isosurfaces, onto which can be colour coded properties such as MOs, charges etc.
- Animation to view molecular vibrations and the time dependent properties of molecules such as protein folding dynamics, etc.
- Integration and Scripting. Programs such as Jmol allow seamless integration of models as part of lecture courses, electronic journals, podcasts, etc, and increasingly elaborate scripting of the models to illustrate scientific points.
Molecular Structure Analysis. Once a visual model is available, simple "heuristics" can be applied. These can range from detecting close contacts due to e.g. hydrogen bonding, bond lengths and the pattern of bond length alternation (e.g. aromaticity), to e.g. stereoelectronic effects such as atom antiperiplanarity or ring planarity. This corresponds to the simple ideas of e.g.arrow pushing which organic chemists tend to develop (and carry around in their head). IsoSTAR is a "data mining" method which can detect structural patterns in a large number of related structures.
Molecular Structure and Property Prediction
- Simple rule-based (heuristic) methods (e.g. CORINA) for approximations to molecular structures. Can be applied to most of the known 33,000,000 molecules, but is unlikely to lead to "new effects".
- Molecular Mechanics methods for larger molecules such as organics, carbohydrates, peptides, DNA oligomers, metal ion binding and some organometallics, zeolites, and complex ionic lattices.
- Semi-empirical Quantum mechanics methods for molecules up to the size of medium sized enzymes.
- Ab initio Quantum Mechanics for accurate reproduction of geometries, and for e.g. weak molecular interactions such as hydrogen bonds, non-classical bonds (e.g. agostic interactions in organometallic species).
- Ab initio (density functional) and correlated theories, particularly for "difficult" molecules such as e.g ozone, FOOF, aromatics, transition states, etc.
Molecular Reactivity
- Huckel theories (heuristics) for aromaticity, frontier orbital analysis and simple relative energetics
- Extended Huckel theories for orbital correlation diagrams and metal systems.
- Semi-empirical and ab initio theories for reactions and bond formation/cleavage, potential energy surfaces and transition state modelling, electron density distributions and stereoelectronic properties, excited state properties and reactions, intermolecular properties, molecular surfaces and charge distributions (electrostatic potentials, etc).
The next two features are largely beyond the scope of this lecture course:
1. Molecular Solvation and Condensed phase properties Supermolecule and condensed phase models of specific and bulk solvation effects.
2. Molecular Dynamics and Simulations. Theories of free energies and reaction kinetics.

Typical Molecular Modelling Software Tools

The "tools of the trade" have gradually evolved from physical models (Dreiding, CPK, etc) and calculators, including the use of programmable computers (starting around 1956 with the introduction of the first scientific programming language called Fortran), computers as visualisation aids (around 1970-), computers running commercially written analysis "packages" such as e.g. Sybyl (around 1984-) and most recently integration using Internet based tools and Workbenches (1994-) based on languages such as HTML, JavaScript, Java and C++. A Forum for discussing such tools, and other general queries is the Computational Chemistry List (CCL).

A typical selection of molecular modelling teaching tools available within the department is listed below.

Mercury: A (free) Crystallographic unit cell viewer and editor.
Jmol: A (free) Web-browser applet that can display molecules, and some of their properties such as surfaces, spectra, vibrations, etc.
Ghemical: an OpenSource molecular editing and molecular mechanics program. Superceded by Avogadro.
ChemDraw/ChemBio3D: Molecule editor and 3D geometry molecular mechanics/quantum mechanics optimisation and display tool (STEREO ENABLED)
Gaussview+Gaussian 03: Ab initio quantum mechanics editors and programs.
DS Viewer Pro (STEREO ENABLED)
VMD visualisation of molecular dynamics (STEREO ENABLED)