# Stacking Calculation Tutorial

### What is Pi-Pi stacking?

Pi-Pi stacking is a special spatial arrangement of aromatic compounds. It refers to a kind of weak interaction that often occurs between aromatic rings. It usually exists between two relatively electron-rich and electron-deficient molecules. Hydrogen bonds are also important non-covalent interactions. There are two common stacking methods: face-to-face and face-to-side. Face-to-face stacking can be divided into full face-to-face stacking and partial face-to-face stacking. The face-to-edge interaction can be regarded as a weak hydrogen bond formed between a slightly electron-deficient hydrogen atom on an aromatic ring and an electron-rich π electron cloud on another aromatic ring.

### Characterization of Pi-Pi Stacking

Two physical quantities are generally used to characterize Pi-Pi accumulation, distance and angle. The distance is the distance from the centroid or center of a group of atoms to the plane of another group of atoms, and the angle is the angle between the planes of the two groups of atoms. Calculate this Two quantities need to know how to calculate the plane equation of a group of atoms. For a completely rigid plane group of atoms, three non-collinear atoms can determine the plane equation (plane three-point equation). For an approximately rigid atom Group, it is necessary to determine the plane equation by multivariate linear fitting.

### Calculation of Pi-Pi Accumulation

gmx analyze can perform multiple linear fitting to get the plane equation. Just call it by script. Here we use vmd plus tcl math library for calculation. vmd does not come with this library, you must install it yourself. We only need the linear algebra library linalg.tcl, which contains the singular value decomposition algorithm leastSquaresSVD for multiple linear fitting, after adding the math library of tcl to vmd, all kinds of analysis can be basically carried out.

### Methods

After obtaining the trajectory, first process the trajectory: complete the molecule, and then calculate the amount of Pi-Pi accumulation.

Run MD simulation to get trajectory

Process the trajectory: first complete the molecule with gmx trjconv -pbc whole, and then superimpose the molecule in the center by gmx trjconv -center -fit rot+trans

Modify the two atom groups in pistack.tcl

vmd command window execute source pistack.tcl

Analyze the output file pistack.xvg, you can also play the track, view the calculation results of each frame

### Example

Simulation of two benzene molecules

Each row of data in the output file pistack.xvg will be listed in turn

Track frame number

The center of each group of atoms in each frame: Xcnt(1) Ycnt(1) Zcnt(1), Xcnt(2) Ycnt(2) Zcnt(2)

The coefficients of the plane equation where each group of atoms are: a(1) b(1) c(1), a(2) b(2) c(2)

The angle between two planes: A(n1,n2)

The distance from the center of the first group of atoms to the plane of the second group of atoms: D(c1,p2)

The distance from the center of the second group of atoms to the plane of the first group of atoms: D(c2,p1).

* For Research Use Only.
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