The laplacian of the electron density is the trace of the Hessian matrix. Or in other words,
the sum of the diagonal elements of the second derivative matrix of the density. The laplacian provides interesting information about the chemical bond.
Hessian matrix
✓ In regions where the Laplacian is negative, the potential energy is dominant and the negative charge
is concentrated.
✓ In regions where the Laplacian is positive, the kinetic energy density dominates and a depletion of
negative charge occurs.
Download Multiwfn from Multiwfn official website. Link
Drag the formchk file into Multiwfn. How to produce the formchk file?
Select the options. To do the Laplacian analysis, we usually follow these step:
✓ Topology Analysis
→ (2) Topology Analysis
→ (2) Search CPs from nuclear positions
→ (3) Search CPs from midpoint of atom pairs
→ (0) Print and visualize all generated CPs, paths and interbasin surfaces
→ click return
→ (7) Show real space function values at specific CP or all CPs
→ (0) Input the index of the CP that you are interested in
→ (-10) Return to main menu
✓ Laplacian of electron density
→ (4) Output and plot specific property in a plane
→ (3) Laplacian of electron density
→ (2) Contour line map
→ (Enter) Grids in the two dimensions
→ (2) Define the plane to be plotted How?
→ (0) Input Y value in Bohr
→ Right click
→ (-8) Change length unit of the graph to Angstrom
→ (6) Generate and show interbasin paths
✓ Other (not necessary)
→ (3) Change setting of contour lines
→ (13) Set color for negative contour lines, current
→ (9) Orange
→ (1) Save setting and return
→ (-2) Set stepsize in X and Y axes
→ (2,2) Input the stepsize between the labels in X and Y axes
→ (1) Disable showing atom labels and reference point
→ (1) Enable showing atom labels and reference point
→ (3) Blue
→ (-1) Show the graph again
→ (0) Save the graph to a graphical file in current folder
What is the Hessian matrix?
Laplacian Density at Bond Critical Point
The Laplacian of the Electron Density