Anisotropic systems¶

In this tutorial, the H-NMR relaxation rates \(R_1\) and \(R_2\) are measured for water confined within a nanoslit composed of silica. This system illustrates an anisotropic case, where all three correlation functions, \(G^{(1)}\), \(G^{(2)}\), and \(G^{(3)}\), must be evaluated, and the rates must be calculated from Eq. (1). The hydrogen atoms of interest include those in the water molecules and those in the surface hydroxyl (-OH) groups of the silica. The individual contributions to \(R_1\) and \(R_2\) – namely, intra-molecular, inter-molecular, and water-hydroxyl interactions – are computed separately.

Note

If you are new to NMRDfromMD, it is recommended to begin with the simpler tutorial on Isotropic system.

MD system¶

Water confined in silica slit with GROMACS - Dipolar NMR relaxation time calculation

The system consists of 602 \(\text{TIP4P}-\epsilon\) water molecules confined within a silica slit nanopore. The trajectory was recorded during a \(10\,\text{ns}\) production run performed using the open-source GROMACS software, in the anisotropic \(NP_zT\) ensemble, with a timestep of \(1\,\text{fs}\). To balance the surface charge, 20 sodium ions were added to the slit. The system was maintained at a temperature of \(T = 300\,\text{K}\) and a pressure of \(p = 1\,\text{bar}\). Atomic positions were saved to the prod.xtc file every \(2\,\text{ps}\).

Note

If you are interested in learning GROMACS and generating your own trajectories, beginner tutorials are available here.

File preparation¶

To access the GROMACS input files and pre-computed trajectory data, download the zip archive, or clone the water-in-silica dataset repository using:

git clone https://github.com/NMRDfromMD/dataset-water-in-silica.git

The necessary trajectory files for this tutorial are located in the data/ directory.

Create a MDAnalysis universe¶

Open a new Python script or a new notebook, and define the path to the data files:

datapath = "mypath/water-in-silica/raw-data/N50/"

Then, import NumPy, MDAnalysis, and NMRforMD:

import numpy as np
import MDAnalysis as mda
import nmrformd as nmrmd

From the trajectory files, create a MDAnalysis universe by loading the configuration file and the trajectory:

u = mda.Universe(datapath + "prod.tpr", datapath + "prod.xtc")

Next, extract some basic information from the universe, such as the number of molecules, the timestep, and the total duration:

n_molecules = u.atoms.n_residues
print(f"The number of molecules is {n_molecules}")
timestep = np.int32(u.trajectory.dt)
print(f"The timestep is {timestep} ps")
total_time = np.int32(u.trajectory.totaltime)
print(f"The total simulation time is {total_time} ps")

Running this will return:

>> The number of molecules is 623
>> The timestep is 2 ps
>> The total simulation time is 10000 ps

Launch the NMR analysis¶

Let us create three atom groups corresponding to: the hydrogen atoms of the silica, the hydrogen atoms of the water, and all the hydrogen atoms combined:

H_H2O = u.select_atoms("name HW1 HW2")
H_SIL = u.select_atoms("name H")
H_ALL = H_H2O + H_SIL

Then, let us run three separate NMR analyses: one for the water-silica interaction only, one for the intra-molecular interaction of water, and one for the inter-molecular interaction of water:

nmr_H2O_SIL = nmrmd.NMR(u, atom_group = H_H2O,
                    neighbor_group = H_SIL, number_i=40, isotropic=False)
nmr_H2O_INTRA = nmrmd.NMR(u, atom_group = H_H2O, neighbor_group = H_H2O, number_i=40,
                        type_analysis = 'intra_molecular', isotropic=False)
nmr_H2O_INTER = nmrmd.NMR(u, atom_group = H_H2O, neighbor_group = H_H2O, number_i=40,
                        type_analysis = 'inter_molecular', isotropic=False)

Note the use of isotropic=False, which is required here because the system is anisotropic.

Extract the NMR spectra¶

Let us access the NMR relaxation rate \(R_1\):

R1_spectrum_H2O_SIL = nmr_H2O_SIL.R1
R1_spectrum_H2O_INTRA = nmr_H2O_INTRA.R1
R1_spectrum_H2O_INTER = nmr_H2O_INTER.R1
f = nmr_H2O_SIL.f

NMR results obtained from the GROMACS simulation of water in silica

Figure: NMR relaxation rates \(R_1\) for the water confined in a silica slit.

Note that the \(\text{H}_2\text{O}-\text{silica}\) contribution is much smaller than the intra- and intermolecular contributions from the water. This is due to the relatively small number of hydrogen atoms from the silica (92), compared to the 1204 hydrogen atoms from the water.