Quantum contributions to free energy changes in fluids

The list of fluids which exhibit important quantum effects is not large. Getting back to the original question of this chapter, it is clear that for liquids like helium and hydrogen, a full quantum treatment is necessary. Liquids such as neon and water, however, show modest quantum effects which can be modeled with approximate free energy methods. The quantum correction to the free energy of water is roughly 10% - this magnitude is large enough to warrant inclusion in calculations of free energies. As discussed in Sect. 11.1, there are experimentally observed isotope effects on the solubilities of small nonpolar molecules and biomolecules, and protein stability. The quasichemical calculations discussed above are a first major step toward determining the relative magnitudes of the various factors contributing to the excess chemical potential of water. The factors include packing effects, chemical contributions from local interactions, electrostatics, van der Waals interactions, molecular flexibility, electronic polarization, and quantum effects. Ab initio simulation methods, although computationally challenging, remove many of the uncertainties inherent in empirical force fields. It appears that rigid water models better reproduce experimental structural properties than flexible models, but the origin of this observation is not entirely clear [40]. An alternative to the rigid model would be to compute an intramolecular potential of mean force from the ground-state vibrational wave function of water and include this potential during classical propagation; this approach is consistent with the fact that it is easy to generate the exact intramolecular partition function q _α^int. Adding quantum effects for flexible water with path integral calculations requires handling two very different energy-scale quantum effects on the same footing. But the intermolecular quantum effects are modest, and in this chapter we have discussed evidence that the QFH approach can handle those effects quite well. Thus, it would be interesting to see free energy computations performed using a combination of ab initio simulation along with the approximate quantum models. Establishing quantitative conclusions concerning the factors contributing to the excess chemical potential of water is a major challenge for molecular fluid free energy calculations. An even bigger challenge is extending the quantum mechanical methods discussed here to problems as complex as biomolecule solvation and enzyme kinetics. At a practical level, what is the current status of methods for studying quantum effects on condensed-phase free energies? If the quantum effects are relatively large, path integral methods are required. These techniques are mature, and the convergence of the calculations with increasing numbers of quantum degrees of freedom can easily be monitored. As long as an underlying classical interaction potential is employed, the additional computational cost is directly proportional to the number of variables needed to describe the paths. Thus, systems with hundreds of atoms can be handled on single workstations. The combination of path integral simulation with ab initio DFT methods is extremely challenging, however, so systems with only tens of water molecules can be modeled for tens of ps. This is a frontier methods development problem for the computer simulation of liquids. Progress will involve both the further development of linear scaling algorithms for ab initio DFT and increased computer power. Improvements in DFT potentials should proceed in parallel with the development of more-efficient numerical methods. The effective potentials described in this chapter, on the other hand, are suited to relatively weak intermolecular quantum effects and require only a slight additional computational overhead - more terms in the potential - relative to routine classical simulations. Therefore, systems with tens of thousands of atoms can readily be modeled. This makes possible the large-scale simulation of biomolecule solvation with the inclusion of quantum effects. If the intermolecular effective potentials ride atop a classical ab initio DFT simulation the overall cost should be comparable to the purely classical DFT modeling, but that approach has not been worked out yet. To reiterate, a main obstacle to overcome is a useful partitioning of quantum effects into intra- and intermolecular contributions during the ab initio simulation of molecular fluids with minor quantum effects. Ab initio simulation of a liquid like water is necessary to treat the complex charge redistribution effects and perhaps chemical reactions which may occur in the condensed phase. And quantum effects cannot be entirely neglected since they have a significant magnitude. Therefore, development of new computational methods for this partitioning should open the door to the quantitative modeling of aqueous solutions and their interactions with biomolecules.