Molecular dynamics, local density solutions

Substantial evidence suggests that in highly asymmetric supercritical mixtures the local and bulk environment of a solute molecule differ appreciably. The concept of a local density enhancement around a solute molecule is supported by spectroscopic, theoretical, and computational investigations of intermolecular interactions in supercritical solutions. Here we make for the first time direct comparison between local density enhancements determined for the system pyrene in CO2 by two very different methods-fluorescence spectroscopy and molecular dynamics simulation. The qualitative agreement is quite satisfactory, and the results show great promise for an improved understanding at a molecular level of supercritical fluid solutions. 

A problem with this interpretation relates to electrostriction, a process in which the density of the solvent changes about a solute. Shim et al. [243] noted evidence of electrostriction in molecular dynamics simulations of a model chromophore in an IL, and the degree of electrostriction was sensitive to the charge distribution of the solute. This observation does not necessarily contradict the framework above, as some local disruption of solvent structure due to dispersive interactions is inevitable. However, it is desirable to obtain a clearer understanding of the competition between these local interactions and the need to maintain a uniform charge distribution in the liquid. 

In this chapter, we will review some of the work that we have been doing in recent years in the context of solvation and dynamical properties in polar and non-polar supercritical solutions using molecular dynamics computer simulations. First we will discuss solvation of alkaloids in SC-CO2 and provide detailed molecular views of the main structural features of the local density augmentation around simple alkaloids... 

NMR spectroscopy is a very useful tool for determining the local chemical surroundings of various atoms. Komin et al studied theoretically this for the adenine molecule of Fig. 20 both in vacuum and in an aqueous solution using different computational approaches. In all cases, density-functional calculations were used for the adenine molecule, but as basis functions they used either a set of localized functions (marked loc in Table 45) or plane waves (marked pw). Furthermore, in order to include the effects of the solvent they used either the polarizable continuum approach (marked PCM) or an explicit QM/MM model with a force field for the solvent and a molecular-dynamics approach for optimizing the structure (marked MD). In that case, the chemical shifts were calculated as averages over 40 snapshots from the molecular-dynamics simulations. Finally, in one case, an extra external potential from the solvent acting on the solute was included, too, marked by the asterisk in the table. 

Knutson, B. L., D. L. Tomasko, C. A. Eckert, P. G. Debenedetti, and A. A. Chiavlo. 1992. Local density augmentation in supercritical solutions A comparison between fluorescence spectroscopy and molecular dynamics results. In ACS Symp. Ser., 488 60-72. 

A promising method, developed in recent years, is the use of first principles molecular dynamics as exemplified by the Car-Parrinello technique (8]. In these calculations the interatomic potentials are explicitly derived from the electronic ground-state within the density functional theory in local or non-local approximation. It combines quantum mechanical calculations with molecular dynamics simulations and, therefore, overcomes the limitations of both methods. Actual computers allow only simulations of aqueous solutions of about 60 water molecules for several ps (10 s). This limit is still at least one order of magnitude shorter than the fastest directly measured water exchange rate, k = 3.5 x 10 s for [Eu(H20)8], i.e. one exchange event every (8 x 3.5 x lO s ) = 36 ps [9]. Nevertheless, several publications appeared in the late 1990s on solvated Be [10], K+ [11] and Cu + [12] presenting mainly structural results. 

In order to ascertain whether the 3-regime behavior observed in the experimental vibrational lifetimes is indeed a result of local density enhancements, Goodyear and Tucker [12] computed both vibrational lifetimes and local density enhancements from molecular dynamics simulation for a model solute-solvent SCF solution. These authors considered a diatomic solute in a 2-dimensional supercritical Lennard-Jones fluid of 1150 atoms (Fig. 1). In this model, each of the solute atoms was designated as a Lennard-Jones site, and the Lennard-Jones parameters between solute and solvent atoms were taken to be the same as those between solvent atoms. The vibrational lifetimes were computed using the standard, classical Landau-Teller expression [69,70,72,73,78], i.e. 

This is the most sophisticated (and computationally demanding) approach and involves the explicit determination of the electronic wavefunctions for both the solvent and solute. At present serious approximations relating to the size of samples studied and/or the liquid structure, and/or the electronic wavefunctions are necessary. A very successful scheme is the local-density-functional molecular-dynamics approach of Car and Parrinello that treats the electronic wave functions and liquid structure in a rigorous and sophisticated manner but is at present limited to sample sizes of the order of 32 molecules per unit cell to represent liquid water, for example. Clusters at low temperatures are well suited to supermolecular approaches as they are intrinsically small in size and could be characterized on the basis of a relatively small number of cluster geometries. Often, however, liquids are approximated by low temperature clusters in supermolecular calculations with the aim of qualitatively describing the processes involved in a particular solvation process. Alternatively, semiempirical or empirical electronic structure methods can be used in supermolecular calculations, allowing for more realistic sample sizes and solvent structures. Care must be taken, however, to ensure that the method chosen is capable of adequately describing the intermolecular interactions. 

Both integral equation and molecular dynamics simulation methodologies have been applied to the question of local solvent structure around solutes in SCFs. These methods incorporate both the direct and indirect mechanisms in an inseparable way however, in molecular dynamics simulation the range of the indirect effects included is limited by the simulation cell size. Probably the first computational observation that the maximum in the local density enhancement (p /p) occurs... 

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