COSMOS force field

Many problems in force field investigations arise from the calculation of Coulomb interactions with fixed charges, thereby neglecting possible mutual polarization. With that obvious drawback in mind, Ulrich Sternberg developed the COSMOS (Computer Simulation of Molecular Structures) force field [30], which extends a classical molecular mechanics force field by serai-empirical charge calculation based on bond polarization theory [31, 32]. This approach has the advantage that the atomic charges depend on the three-dimensional structure of the molecule. Parts of the functional form of COSMOS were taken from the PIMM force field of Lindner et al., which combines self-consistent field theory for r-orbitals ( nr-SCF) with molecular mechanics [33, 34]. 

TD-DFT) they calculated the transition energies and dipole moments for NMA both in vacuum and in an aqueous solution. Moreover, in the treatment of the solvent they compared two different approaches, i.e., a polarizable-continuum method (COSMO) and a supermolecule approach. For the latter, the authors performed molecular-dynamics calculations using a force-field model and, subsequently, extracted a cluster containing the solute and 3 water molecules that form hydrogen bonds to the solute. Averages over 90 such configurations were ultimately determined. 

Computational quantum mechanics continues to be a rapidly developing field, and its range of application, and especially the size of the molecules that can be studied, progresses with improvements in computer hardware. At present, ideal gas properties can be computed quite well, even for moderately sized molecules. Complete two-body force fields can also be developed from quantum mechanics, although generally only for small molecules, and this requires the study of pairs of molecules in a large number of separations and orientations. Once developed, such a force field can be used to compute the second virial coefficient, which can be used as a test of its accuracy, and in simulation to compute phase behavior, perhaps with corrections for multibody effects. However, this requires major computational effort and expert advice. At present, a much easier, more approximate method of obtaining condensed phase thermodynamic properties from quantum mechanics is by the use of polarizable continuum models based on COSMO calculations. 

Fig. 10. The three best COSMOS-NMR force field results of a peptide-zinc complex obtained with NOE as well as chemical shift pseudo-forces. Zn-X bonds are shown if the distance is shorter than 2.5 A. The force field search for the most stable complex was run with a free Ziv ion.

R. Witter. Three Dimensional Structure Elucidation with the COSMOS-NMR Force Field, thesis, 2003. dissertation.de. 

The COSMO method is also interesting as the basis of a very successful COSMO-RS method, which extends the treatment to solvents other than water [27,28]. The COSMO method is very popular in quantum chemical computations of solvation effects. For example, 29 papers using COSMO calculations were published in 2001. However, we are not aware of its use together with MM force fields. Compared with the BE method, COSMO introduces one more simplification, that of Eq. (22). On the other hand, the matrix A in Eq. (21) is positively defined [25], which makes solution of the system of linear equations simpler and faster. Also, because both A and B matrices contain only electrostatic potential terms, their computation in quantum chemistry is easier than calculation of the electric field terms in Eq. (12). Another potential benefit is that the long-range electrostatic potential contribution is easier to expand into multipoles than the electric field needed in BE methods, which may benefit linear-scaling approaches. 

The recently developed global optimization tool for the Calibration of molecular force fields by Simultaneous Modeling of Simulated data (CoSMoS) [56] uses a metamodeling procedure based on radial basis functions (RBFs). It has been shown in [56] that metamodel-based optimizers particularly suit the quest for quickly finding nearly optimal force-field parameters. The metamodels constmcted by CoSMoS describe functional dependencies between the force-field parameters and the relative deviations of the simulated properties to experimental data so that the minimization task is easier to solve. The RBFs are rational symmetric functions fl) M of the form (x) = (llx l) for x e M. For the present optimization... 

Several studies have combined force fields calculated in the presence of a dielectric continuum, most often the PCM [166, 167, 282, 283] or the COSMO model [284] in order to get an approximate treatment of the solvent effects on the ROA spectra. To the best of our knowledge, the only smdies in which the PCM has been apphed to all quantities determining the ROA spectrum are those of Pecul and co-workers [285, 286]. 

In Section 2.1 the theoretical concept of COSMO as a CSM is explained. In Section 2.2 the general technical strategy of the COSMO implementations is presented, while in Section 2.3 special details of the various implementations in force-field, semi-empirical, ab initio, and density functional codes are discussed. Section 2.4 gives a general outlook on future improvements and the potential of COSMO. 

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