Solvation and Periodic Boundary Conditions

Solvation can have a profound effect on the results of a chemical calculation. This is especially true when the solute and solvent are polar or when they can participate in hydrogen bonding. The solvent effect is expressed in several ways, including these  

Be cautious when projecting the results of calculations in one solvent to those using a different environment. 

HyperChem uses the TIP3P water model for solvation.You can place the solute in a box of TIP3P water molecules and impose periodic boundary conditions. You may then turn off the boundary conditions for specific geometry optimization or molecular dynamics calculations. However, this produces undesirable edge effects at the solvent-vacuum interface. 

Jorgensen, W.L. Chandrasekhas, J. Madura, J.D. Impey, R.W. Klein, M.L. Comparison of simple potential functions for simulation liquid water. J. Chem. Phys. 79 926-935, 1983. 

Since the periodic images are exact copies of the original box, movements of atoms in the original box are duplicated in the images. When a particle leaves a box, its periodic image enters from the opposite box side and replaces it. This conserves the number of atoms in each box. 

---

Often yon need to add solvent molecules to a solute before running a molecular dynamics simiilatmn (see also Solvation and Periodic Boundary Conditions" on page 62). In HyperChem, choose Periodic Box on the Setup m en ii to enclose a soln te in a periodic box filled appropriately with TIP3P models of water inole-cii les. 

Molecular Dynamics Simulations With rapid evaluation of energies and gradients, molecular dynamics (MD) simulations can be carried out. For MD simulations in the gas phase, the complex was first heated to 300 K by 6,000 steps and equilibrated at that temperature for 100 ps. Then, a 5-ns NVE trajectory was generated by free dynamics. The time step was 0.1 fs to follow the fast proton motions. For simulations in explicit solvent, a 46.0 A x 46.0 A x 40.9 A box of CDCI3 was first generated with a density of 1.50 g/cm. The Pt[Cl2(6-DPPon)2l complex was then solvated and periodic boundary conditions were applied. A cutoff of 12 A was applied to the shifted electrostatic and switched van der Waals interactions. Before 1-ns free dynamics simulations, the system was heated to 300 K and then equilibrated for 10 time steps. 

Wood, R.H. Continuum electrostatics in a computational universe with finite cut-off radii and periodic boundary conditions Correction to computed free energies of ionic solvation. J. Chem. Phys. 103 (1995) 6177-6187. 

Very recently, we have developed and incorporated into the CHARMM molecular mechanics program a version of LN that uses direct-force evaluation, rather than linearization, for the fast-force components [91]. The scheme can be used in combination with SHAKE (e.g., for freezing bond lengths) and with periodic boundary conditions. Results for solvated protein and nucleic-... 

It is sometimes desirable to include the effect of the rest of the system, outside of the QM and MM regions. One way to do this is using periodic boundary conditions, as is done in liquid-state simulations. Some researchers have defined a potential that is intended to reproduce the effect of the bulk solvent. This solvent potential may be defined just for this type of calculation, or it may be a continuum solvation model as described in the next chapter. For solids, a set of point charges, called a Madelung potential, is often used. 

HyperChem allows solvation of arbitrary solutes (including no solute) in water, to simulate aqueous systems. HyperChem uses only rectangular boxes and applies periodic boundary conditions to the central box to simulate a constant-density large system. The solvent water molecules come from a pre-equilibrated box of water. The solute is properly immersed and aligned in the box and then water molecules closer than some prescribed distance are omitted. You can also put a group of non-aqueous molecules into a periodic box. 

As in classical simulations of biomolecules, there are two general frameworks for setting up QM/MM simulations for a biological system periodic boundary condition (PBC) and finite-size boundary condition (FBC). When the system of interest is small ( 200-300 amino acids), PBC is well suited because the entire system can be completely solvated and therefore structural fluctuations ranging from the residue level to domain scale can potentially be treated at equal footing, within the limit... 

Rao and Singh32 calculated relative solvation free energies for normal alkanes, tetra-alkylmethanes, amines and aromatic compounds using AMBER 3.1. Each system was solvated with 216 TIP3P water molecules. The atomic charges were uniformly scaled down by a factor of 0.87 to correct the overestimation of dipole moment by 6-31G basis set. During the perturbation runs, the periodic boundary conditions were applied only for solute-solvent and solvent-solvent interactions with a non-bonded interaction cutoff of 8.5 A. All solute-solute non-bonded interactions were included. Electrostatic decoupling was applied where electrostatic run was completed in 21 windows. Each window included 1 ps of equilibration and 1 ps of data... 

This potential was developed to ensure that the molecules inside the sphere never escape and maintain a fully solvated system during molecular dynamics. Here, es, Rs, ew and Rw are the van der Waals constants for the solvent and the wall and rj is the distance between the molecule i and the center of the water sphere, Ro is the radius of the sphere. The quantities A, B and Rb are determined by imposing the condition that W and dW/dr, vanish at r, = Ro. The restraining potential W is set to zero for r, < R0. The van der Waals parameters Es, ew, Rs and Rw can also be specifically defined for different solvents. The constants Awaii and Cwan are computed using a well depth of es = ew = 0.1 kcal and the radius of Rs = Rw = 1.25 A. For the other set of simulations, especially for the hydride ion transfer, we applied periodic boundary conditions by using a spherical boundary shell of 10.0 A of TIP3P40 water to cover the edges of the protein. 

Another approach is that of including dynamics in the calculations. A dynamical formalism of DFT was first developed by Car and Parrinello [31], and has been employed in a wide range of areas, e.g. solvation problems, reactions on surfaces, solid-state interactions, and a variety of biochemical applications. In CP-MD one normally uses a plane wave basis to reduce the computational requirements and enable easy implementation of periodic boundary conditions. Nonetheless, CP-MD simulations are rather costly, and are normally not applied to systems larger than, say, 1-200 atoms, and over relatively short time frames. 

The second approach was to employ periodic boundary conditions and molecular mechanics (COMPASS) to model the solvated SFA.55 73 These simulations were performed with Cerius2 4.2 (Accelrys, Inc.). Periodic boundary conditions create a bulk system with no surface effects and hence, this situation is more realistic compared to the experimental system of SFA dissolved in water. H20 molecules, however, must diffuse to allow motion of the SFA model, so that the SFA model conformations may be restricted due to this limited motion of the surrounding H20 molecules. Note also that periodic simulations must be charge neutral within the... 

---