Alkanes, force-field parameters

Munoz Munoz, Y.M., Guevara-Carrion, G., Llano-Restrepo, M., Vrabec, J. Lennard-Jones force field parameters for cyelie alkanes from cyclopropane to cyclohexane. Fluid Phase Eq. 404, 150-160 (2015)... 

Table 1 Force-field parameters for alkanes, as obtained by number theory...

All of the values are in the expected range (see other force fields, such as MM3, Amber and Momec, e.g. in [9,10,13,18,29,45]), but by no means are they refined and do not define an accurate force field. The major difference between the number-theory parameters and the alkane force field derived by point-charge simulation occurs in the strain-free C-C bond length with = 1.53 A compared to 1.51 A. The optimized structural parameters of a series of aliphatic hydrocarbons, shown in Table 2, although less accurate than with a properly optimized force field, reflect the... 

We started our OFF analysis of hydrogen bonded crystals (Hagler, Huler and Lifson, 1974) about a decade ago, after we concluded a OFF analysis of intra- and intermolecular potentials for alkanes. The nonbonded interactions in the alkane force field were selected to be of the "n-6-1" type, namely composed additively from a Lennard-Jones ("n-6") potential, Eqs. (17) or (19), and a Coulomb ("1") potential (Eq. (21)). Atoms of the same molecule were considered as nonbonded if they were separated by at least 3 consecutive bonds. The Lennard-Jones (LJ) potential is commonly considered to be a "12-6" potential, that is, the exponent n in the repulsive term Ar is taken to be n = 12 (see above). Examining the LJ potential for alkanes, we found that the LJ parameters optimized for intramolecular interactions were too low for intermolecular interactions, while the LJ parameters optimized for intermolecular interactions were too high for intramolecular interactions. These trends -12... 

Three other all-atom force fields have also received much recent attention in the literature MMFF94 [36-40], AMBER94 [9] and OPLS-AA [41, 42] and are becoming widely used. The latter two force fields both use non-bonded parameters which have been adjusted in order to reproduce experimental liquid phase densities and heats of vaporisation of small organic molecules. For example, OPLS-AA includes calculations on alkanes, alkenes, alcohols. 

Results of parameter optimization and MD simulations of small model compounds have been published, including alcohols [63], alkanes [63], aromatic [64] and heteroaromatic [209] compounds and liquid amides [65], Studies of ions in aqueous solution were also performed [61, 88] and results from an MD simulation on a DPPC lipid monolayer have been reported (Harder, MacKerell, Roux, submitted). Notable from the monolayer study was the reproduction of the dipole potential across the monolayer, a value that cannot be reproduced using non-polarizable models. This exciting, unforeseen observation points to the types of results that may be obtained from polarizable macromolecular force fields that are not accessible to the present additive models. 

The subscript e means that the second derivatives are taken for internal parameters of the known or assumed molecular geometry.) It then follows that, in principle, to every molecule a F-matrix is assigned with molecule-specific force constants Fd.Transferability can only be expected for molecules which contain qualitatively and quantitatively very similar internal coordinates For instance, a force field which reproduces very well frequencies of n-al-kanes (from which it was derived) gives significantly worse results for branched alkanes... 

Bartell and coworkers investigated the structures of a series of noncyclic alkanes by means of gas electron diffraction (14, 44, 45) and invoked for the interpretation of their results a simple force field which contained to a high extent vibrational spectroscopic constants of Snyder and Schachtschneider. This force field reproduces bond lengths and bond angles of acyclic hydrocarbons well, energies of isomerisation satisfactorily. As an example, Fig. 8 shows geometry parameters of tri-t-butylmethane as observed by electron diffraction and calculated with this force field (14). 

The OPLS parameters (charges and Lennard-Jones terms) were obtained primarily via Monte Carlo simulations with particular emphasis on reproducing the experimental densities and heats of vaporization of liquids. Those simulations were performed iteratively as part of the parametrization, so better agreement with experiment is obtained than in previous studies where the simulations were usually carried out after the parametrization. Once the OPLS parametrization was completed, further simulations were also performed in order to test the new set of parameters in the calculation of other thermodynamic and structural properties of the system, besides its density and its heat of vaporization. Parameters have now been generated, among others, for water, alkanes, alkenes, alcohols, amides, alkyl chlorides, amines, carboxylic esters and acids, various sulfur and nitrogen compounds, and nitriles. A protein force field has been established as well. 

A short presentation of the Consistent Force Field is given, with emphasis on parametrization and optimization of energy function parameters. For best possible calculation of structure, potential energy functions with parameter values optimized on both structural and other properties must be used. Results from optimization with the Consistent Force Field on alkanes and ethers are applied to glucose, gentiobiose, maltose and cellobiose. Comparison is made with earlier and with parallel work. The meaning and use of conformational maps is discussed shortly. 

The EHM will require far fewer parameters. This is easy to see, because each atom requires just one parameter for each valence atomic orbital. For C, for example, we need an ionization energy for the 2s, and one for the 2p orbitals, just two parameters (strictly, valence state ionization energies, VSIEs - see Harder Question 9).3 Each H needs only one parameter, for its Is orbital. So for an EHM program that will handle hydrocarbons in general we need only three parameters (as in Hoffmann s pioneering paper on hydrocarbons [1]). In contrast, an early but viable molecular mechanics forcefield limited to alkanes had 26 parameters [2]. The Universal Force Field, which sacrifices accuracy for wide applicability, has about 800 parameters, and the accurate and quite broadly applicable Merck Molecular Force Field 1994 (MMFF94) has about 9,000 parameters [3]. 

Another important component of the COMPASS force-field development is the systematic fit to various types of compounds. First, alkane parameters are fit, and then held fixed while alkene parameters are derived. Each functional group is added by fitting to larger arrays of compounds, but the parameters derived in the previous level are not changed, so a self-consistent force field is created that describes a wide variety of functional groups. 

Koddermann et al. calculated the heats of vaporization for imidazolium-based ILs [Cnmim][NTf2] with n = 1, 2, 4, 6, 8 by means of MD simulations [81], The authors applied a force field which they had developed recently. Within this force field the authors reduced the Lennard-Jones parameters in order to reproduce experimental diffusion coefficients [81], The refined force field also led to absolute values of heats of vaporization as well as their increase with the chain length of the imidazolium cation such that this quantities were described correctly. The overall heats of vaporization were split in several contributions and discussed in detail. The authors observed that with increasing alkyl chain length, the Coulomb contribution to the heat of vaporization remained constant at around 80 kJ mol 1, whereas the van der Waals interaction increased continuously. The calculated grow of about 4.7 kJ mol"1 per CH2-group of the van der Waals contribution in the IL exactly matched the increase in the heats of vaporization for n-alcohols and n-alkanes, respectively. The results support the importance of van der Waals interactions even in systems completely composed of ions [81],... 

The fact that the second derivative, d U/db in Eq. [24], contains a slight contamination from nonbonded interactions and third-order terms is an example of how parameter correlation can arise because it is not a pure bond stretch. If this derivative were simply used as the bond-stretching force constant, as in spectroscopic force fields, it would not be transferable to other molecules where the coupling or nonbonded interaction may differ. This problem is a general one and can be quite serious. As already discussed in previous sections, one possible resolution of this problem lies in the use of many molecular environments to determine all contributing terms. If we simultaneously fit many different alkanes, i.e., ethane, propane, butane, etc., with the full force field and assume... 

Parameterization of force fields for lipids is at an early stage of development in comparison to what has been done for proteins and nucleic acids. Most simulations on lipid systems using force fields have employed parameter sets and parameterization procedures that have proven satisfactory for related systems (i.e., alkane simulations, etc.). This appears to be a reasonable approach, but there are clear cases warranting improvement in the model (e.g., obtaining accurate order parameter profiles). 

Transferability of the functional form and parameters is an important feature of a force field. Transferability means that tire same set of parameters can be used to model a series of related molecules, rather than having to define a new set of parameters for each individual molecule. For example, we would expect to be able to use the same set of parameters for all u-alkanes. Transferability is clearly important if we want to use the force field to make predictions. Only for some small systems, where particularly accurate work is required, may it be desirable to develop a model specific to that molecule. 

C C-based parameters (fcb and Tq) to one structure, that is, that of ethane, will not lead to a unique combination of parameters. For a general parameter set kb and h), which can be used to model a whole series of alkanes, the development of the force field has to be based on a broader body of experimental data. Since molecular mechanics modeling is an interpolative method, the choice of data for the development of the force field determines the appUcabUity of the parameter set. 

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