EDRcal

This FORTRAN based code calculates the Electron Delocalization Range Function EDR(r;d), and Orbital Overlap Distance Function D(r) on entire molecule and generate output in Gaussian .cub file. Currently, it accepts the wavefunction in .wfn, .wfx file format that can be generated by nearly all mainstream quantum chemistry softwares. It also supports Gaussian formatted checkpoint files .fch and .fchk.

Basic Workflow

• Obtain .wfn, .wfx, .fch or .fchk files from a standard quantum chemistry calculation
• Boot up EDRcal and input the file generated in previous step
• Generate the total electron density .cub file by selecting the grid size
• Similarly, generate the overlap distance D(r) .cub file by selecting the EDR(r;d) exponents (default is OK)
• EDR(r;d) .cub can also be generated similarly by using appropriate length scale d
• The obtained EDR(r;d) can be visualized using the common visualizers such as GaussView, VMD, Avogadro etc., by choosing proper ISOvalue
• The D(r) can be used to map the obtained total electron density using standard ISOvalue of 0.001 e/bohr³.

How to Compile

Binary Package

The pre-compiled binary files for Win64 and Linux 64-bit are provided in bin folder. These are parallel versions and will use all available processors.

Source Code

The source code is provided in src folder along with Makefile which can be used to compile by using either Intel ifort and MPI Library or equally using GNU Fortran with OpenMPI libraries. Uncomment your favorite compiler section and hit make.

Theoretical Details

The Electron Delocalization Range Function, EDR(r;d), quantifies the extent to which an electron at point r in a calculated wave function overlaps over distance d. It is constructed from the one-particle density matrix γ(r,r')=Σ_in_iψ_i(r)ψ_i(r') of molecular orbitals ψ_i with nonzero occupancy n_i. At each point r, its overlap is evaluated with an s-orbital-like test function C_d exp(−|r – r'|²/d²) centered at point r and having width d:

The orbital overlap distance D(r) is the distance d that maximizes EDR(r;d) at point r. When plotted on molecular isosurfaces such as electron or spin density surfaces, D(r) distinguishes the compact regions on the surface of molecule from those regions which are relatively diffuse. Correspondingly, the chemically "hard" regions tend to give small D(r), whereas chemically "soft" regions tend to give larger D(r). For example, the figure on right shows that sulfur in mercaptoethanol is diffuse due to large value of D(r) relative to the chemically hard i.e., compact oxygen which has smaller value of D(r). Similarly, the left figure shows the EDR(r;d) of solvated electrons highlighting that the extra electron is delocalized in the center of two H₂O molecules.

For further details, please see the following publications.

1. Janesko, B. G.; Scalmani, G.; Frisch, M. J., How Far Do Electrons Delocalize? J. Chem. Phys. 2014, 141, 144104.
2. Janesko, B. G.; Wiberg, K. B.; Scalmani, G.; Frisch, M. J., Electron Delocalization Range in Atoms and on Molecular Surfaces. J. Chem. Theory Comput. 2016, 12, 3185–3194.
3. Mehmood, A.; Janesko, B. G., An Orbital-Overlap Complement to Atomic Partial Charge. Angew. Chem. Int. Ed. 2017, 56, 6878-6881.
4. Mehmood, A.; Jones, S. I.; Tao, P.; Janesko, B. G., An Orbital-Overlap Complement to Ligand and Binding Site Electrostatic Potential Maps. J. Chem. Inf. Model. 2018, 58, 1836-1846.
5. Mehmood, A.; Janesko, B. G., Extending the Marcus μ-Scale of Solvent Softness Using Conceptual Density Functional Theory and the Orbital Overlap Distance: Method and Application to Ionic Liquids. J. Solution Chem. 2020, 49, 614–628.

Technical Notes and Manuals

These tools can also be evaluated by using Multiwfn or cubegen utility of Gaussian 16. Our research group page provides the technical notes for calculations using Multiwfn and Gaussian 16.