Theorectical methods

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Research group Thermodynamics (Dr. Liudmila Mokrushina)

The main goal in modelling is the prediction of phase equilibrium properties of mixtures based solely on the molecular structure of the mixture components. The group-contribution model (UNIFAC) and the a-priori COSMO-RS model based on quantum mechanics are of most interest due to their predictive ability.

Strategy of thermodynamic modelling

COSMO-RS

The COSMO-RS model (Conductor like Screening Model for Real Solvents) allows for an a priori prediction of thermodynamic properties such as activity coefficients based only on the molecular structure. The electrostatic interaction of a solute with the surrounding solvent is modelled with the continuum solvation theory. In this way, solvent effects are incorporated into quantum chemical calculation. The solvent is treated as a continuous media of dielectric constant ε. The solute is embedded inside an arbitrary shaped cavity in the continuum. Then, the dielectric medium of permeability ε is replaced with the scaled screening charges of a conductor. A COSMO calculation provides the screening charges on the surface of the cavity and is usually carried out at an adequate quantum level which is provided by the density functional theory. After quantum chemical self-consistency and geometry optimization loops, it gives the energy, the geometry, and the screening charge density σ on the surface of a solute molecule. The transfer from the state of the molecule embedded in a virtual conductor to a real solvent is done by applying the COSMO-RS concept based on statistical thermodynamics. Interactions between molecules are replaces by pair-wise interactions of small surface segments with a given surface density. As a result, a COSMO-RS calculation provides the chemical potential of a component in the mixture.

Group-contribution methods

In the group-contribution method UNIFAC (Universal Quasi-Chemical Functional-Group Activity Coefficient), the molecules of a compound are represented by structural groups which contribute additively to the properties of the system. Thus, a great variety of molecules is represented by a limited number of structural groups. The parameters of more than 50 groups (the number depends on the model modification) are tabulated (group-interaction parameters are estimated from experimental data). The UNIFAC-FV (UNIFAC Free Volume) model is extended with the so-called free-volume term (taking into account the difference in compressibilities of low and high molecular substances) and thus gives the possibility to calculate properties of systems containing polymers. The UNIFAC-IF (UNIFAC-InterFacial) model can be used for self-aggregated systems such as micellar and liposomal solutions, since it includes the interfacial contribution (in terms of Gibbs-Thomson theory) to regard the small size of the aggregates.

Molecular dynamics simulations

Molecular dynamics calculates the “real” dynamics of the system, from which time averages of properties can be calculated. Molecular dynamics combines energy calculations from force field methodology with the laws of Newtonian (as opposed to quantum) mechanics. The simulation is performed by numerically integrating Newton's equations of motion over small time steps (usually 10-15 sec or 1 fsec). The simulation is initialized by providing the location and assigning a force vector for each atom in the molecule. The acceleration of each atom is then calculated from the equation a = F/m where m is the mass of the atom and F the negative gradient of the potential energy function (the mathematical description of the potential energy surface). The Verlet algorithm is used to compute the velocities of the atoms from the forces and atom locations. Once the velocities are computed, new atom locations and the temperature of the assembly can be calculated. These values then are used to calculate trajectories, or time dependent locations, for each atom. Over a period of time, these values can be stored on disk and played back after the simulation has completed to produce a "movie" of the dynamic nature of the molecule. In our group, molecular dynamics is used to investigate the conformational properties of flexible molecules for the COSMO-RS model.