structures and properties,will include many cross-terms (e.g.stretch-bend):MM311-13 and MM414-16 are examples.Quantum mechanical calculations may give a guide to the"best" molecular force-field;also comparison of simulation results with thermophysical proper- ties and vibration frequencies is invaluable in force-field development and refinement.A separate family of force fields,such as AMBER7.18,CHARMM19 and OPLS20 are geared more to larger molecules(proteins,polymers)in condensed phases;their functional form is simpler,closer to that of Eq.(5),and their parameters are typically determined by quan- tum chemical calculations combined with thermophysical and phase coexistence data.This field is too broad to be reviewed here;several molecular modelling texts21-23(albeit target- ted at biological applications)should be consulted by the interested reader.The modelling 200 150 FENE+WCA 50 FENE ··WCA --harmonic 0 0.5 1.5 r/σ Figure 4.The FENE+WCA potential,with its separate FENE (attractive)and WCA (repulsive)components, between bonded atoms in a coarse-grained polymer chain.Also shown is the equivalent harmonic potential. Unlike the harmonic spring,the FENE potential cannot be extended beyond a specified limit,here Ro=1.5. For more details see Ref.24. of long chain molecules will be of particular interest to us,especially as an illustration of the scope for progressively simplifying and"coarse-graining"the potential model.Var- ious explicit-atom potentials have been devised for the n-alkanes25.More approximate potentials have also been constructed26-28 in which the CH2 and CHa units are represented by single "united atoms".These potentials are typically less accurate and less transfer- able than the explicit-atom potentials,but significantly less expensive;comparisons have been made between the two approaches29.For more complicated molecules this approach may need to be modified.In the liquid crystal field,for instance,a compromise has been suggested30:use the united-atom approach for hydrocarbon chains,but model phenyl ring hydrogens explicitly. In polymer simulations,there is frequently a need to economize further and coarse- grain the interactions more dramatically:significant progress has been made in recent years in approaching this problem systematically31.32.Finally,the most fundamental prop- erties,such as the entanglement length in a polymer melt33,may be investigated using a 5structures and properties, will include many cross-terms (e.g. stretch-bend): MM311–13 and MM414–16 are examples. Quantum mechanical calculations may give a guide to the “best” molecular force-field; also comparison of simulation results with thermophysical proper￾ties and vibration frequencies is invaluable in force-field development and refinement. A separate family of force fields, such as AMBER17, 18 , CHARMM19 and OPLS20 are geared more to larger molecules (proteins, polymers) in condensed phases; their functional form is simpler, closer to that of Eq. (5), and their parameters are typically determined by quan￾tum chemical calculations combined with thermophysical and phase coexistence data. This field is too broad to be reviewed here; several molecular modelling texts21–23 (albeit target￾ted at biological applications) should be consulted by the interested reader. The modelling 0 0.5 1 1.5 r / σ 0 50 100 150 200 v / ε FENE+WCA FENE WCA harmonic Figure 4. The FENE+WCA potential, with its separate FENE (attractive) and WCA (repulsive) components, between bonded atoms in a coarse-grained polymer chain. Also shown is the equivalent harmonic potential. Unlike the harmonic spring, the FENE potential cannot be extended beyond a specified limit, here R0 = 1.5σ. For more details see Ref. 24. of long chain molecules will be of particular interest to us, especially as an illustration of the scope for progressively simplifying and “coarse-graining” the potential model. Var￾ious explicit-atom potentials have been devised for the n-alkanes25 . More approximate potentials have also been constructed26–28 in which the CH2 and CH3 units are represented by single “united atoms”. These potentials are typically less accurate and less transfer￾able than the explicit-atom potentials, but significantly less expensive; comparisons have been made between the two approaches29 . For more complicated molecules this approach may need to be modified. In the liquid crystal field, for instance, a compromise has been suggested30: use the united-atom approach for hydrocarbon chains, but model phenyl ring hydrogens explicitly. In polymer simulations, there is frequently a need to economize further and coarse￾grain the interactions more dramatically: significant progress has been made in recent years in approaching this problem systematically31, 32 . Finally, the most fundamental prop￾erties, such as the entanglement length in a polymer melt33 , may be investigated using a 5