Riassunto
In this chapter ve shall discuss the calculation of potential energy associated vith molecular conforaations. Raving obtained cartesian atoaic coordinates defining conforaations. and lists of intraao- cular interactions, as described in Chapter 3, ve are ready to calculate a quantity which in the chemical literature is known as the total aolecular potential energy or the conforaational, steric, strain or intraaolecular energy. ~he conformational energy of a aolecule can be expressed as a function , of all internal coordinates and interatoaic distances, or as a function of atoaic positions specified by soae general coordi Dates. ~he function , is supposed to haye local ainiaa corresponding to the stable equilibrium conforaations of a aolecule in vacuo, Deglecting interaolecular interactions. ~he exact fora of Y is. of course, unknown. We assume that it can be suitably approximated by a sua of different types of energy contri hutions: , = Y ., +, +, ., be. nb e ~he teras represent cODtributions to the total aolecular potential energy , due to bond stretching and coapression teras Vb' valence aDgle bending teras 'e' iDterDal rotational or torsional teras V,. DOD-bonded interactions 'nb and electrostatic or Couloab iDter actions 'e. If there are other intraaolecular aechanisas affecting 79 V, sucD as hydrogen bonding, corresponding terms say be added.
Contenuti
Contests.- 1 Introduction.- 1.1 What the CFF is.- 1.2 Background.- 1.3 Pre-CFF.- 1.4 The ascent of CFF.- 1.5 In the wake of CFF.- 2 The Programming System.- 2.1 Introduction.- 2.2 Outline of the programming system.- 2.2.1 Section I.- 2.2.2 Section II.- 2.2.3 Section III.- 2.2.4 Section IV.- 2.2.5 section V.- 2.2.6 Section VI.- 2.2.7 Section VII.- 2.3 Other programmes.- 2.3.1 Utilities.- 2.3.2 CFFPLOT.- 2.3.3 CRYSTAL.- 2.3.4 EDITOR.- 2.3.5 ORTEP.- 2.3.6 MCNSTER.- 2.4 Organisation of the system.- 2.4.1 Overlay structure.- 2.4.2 JCL procedures.- 2.4.2.1 CFFCLIB.- 2.4.2.2 CFFG.- 2.4.2.3 CFFCLG.- 2.4.2.4 CFFECLG.- 2.4.2.5 Listing of CFFECLG.- 2.4.3 Input-output.- 2.5 Input manual.- 3 Molecular Topology and Geometry.- 3.1 Molecular topology.- 3.1.1 Topological representation of chemical structures.- 3.1.2 From structural formula to linear notation.- 3.1.3 Coding of formulae.- 3.1.3.1 Rules for coding line formulae.- 3.1.3.2 Limitations.- 3.1.3.3 Examples.- 3.1.4 Coordination compounds.- 3.1.5 Output from the programmes.- 3.1.5.1 Programme BRACK.- 3.1.5.2 Programme CODER.- 3.2 Lists of interactions.- 3.2.1 Programme MKLIST.- 3.2.2 Interaction codes.- 3.2.3 Coding and decoding of integer words of interaction.- 3.3 Molecular geometry.- 3.3.1 Construction of molecular geometry.- 3.3.2 Coordination compounds.- 3.3.3 Incomplete structures.- 3.3.4 Sideatom positions.- 3.3.5 Torsional angle specification.- 4 The Conformational Energy and its Derivatives.- 4.1 Introduction.- 4.2 Intermolecular forces.- 4.2.1 Non-bonded interactions.- 4.2.2 Electrostatic interactions.- 4.2.3 Hydrogen bonding.- 4.3 Intramolecular forces.- 4.3.1 Bond stretching.- 4.3.2 Bond torsion.- 4.3.3 Angle bending.- 4.3.4 Urey-Bradley potential.- 4.4 Force field parametrisation.- 4.4.1 Parameters and variables.- 4.4.2 Specification of energy functions and parameters.- 4.4.2.1 Global control parameters.- 4.4.2.2 Fonction subroutines.- 4.4.2.3 Energy parameter input.- 4.5 Energy calculations.- 4.5.1 Expansion of V in a Taylor series.- 4.5.2 Energy processing subprogrammes.- 4.5.3 First- and second-order derivative calculation.- 4.5.3.1 Derivatives of interatomic distances.- 4.5.3.2 Derivatives of valence angles.- 4.5.4 Derivatives of torsional angles.- 4.6 Numerical calculation of derivatives.- 5 Energy Minimisation.- 5.1 Statement of the problems.- 5.2 Minimisation algorithms.- 5.2.1 Direct search methods.- 5.2.2 Descent methods.- 5.3 Unified approach to gradient algorithms.- 5.4 Evaluation of minimisation methods.- 5.4.1 The method of steepest descent.- 5.4.2 The Davidon-Fletcher-Powell method.- 5.4.3 The modified Newton method.- 5.5 The minimisation programme.- 5.6 Concluding remarks.- 5.6.1 Minimisation methods in conformational analysis.- 5.6.2 Local versus global minimum.- 5.6.3 False minima.- 6 Vibrational Calculations.- 6.1 The vibrational problem.- 6.2 Normal coordinates.- 6.3 Programme VIBRAT.- 6.4 Practical considerations.- 7 Optimisation of Energy Parameters.- 7.1 The basic algorithm.- 7.2 The partial derivatives.- 7.2.1 Internal coordinates.- 7.2.2 Internal frequencies.- 7.3 Implementation of the optimisation.- 7.3.1 Beading of experimental data.- 7.3.2 Organisation of the optimisation.- 8 Developing A Force Field.- 8.1 The concept of energy functions.- 8.1.1 Bonded interactions.- 8.1.1.1 Bonds.- 8.1.1.2 Torsions.- 8.1.2 Non-bonded interactions.- 8.1.2.1 Atom-atom interactions.- 8.1.2.2 Geminal interactions.- 8.2 Examples.- 8.2.1 Pre-CFF, cyclcalkanes.- 8.2.2 Original CFF, n- and cycloalkanes.- 8.2.3 CFF, alkane crystals.- 8.2.4 CFF, amides and lactams.- 8.2.5 CFF, aaides.- 8.2.6 Flexible amino acids.- 8.2.7 Coordination Compounds.- 8.2.8 Saccharides.- 9 References.
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