# STM: Electronic Structure

The STM codes are a suite of application codes and AVS modules is available to display both the geometric structure and electronic properties. Electronic and structural information is obtained from either Density Functional Theory (DFT) or Schrödinger Theory, using a variety of computational or experimental approaches.

Electron densities are obtained from Density Functional Theory (DFT) via the Kohn-Sham (KS) orbital-density equations:

where Ck is the basis function and the C k are the expansion coefficients

Electron densities are obtained from wave function functional via the Schrödinger equation;

where the Fock matrix Fmn is given by,
where Dls = S i ci l ci s is the density matrix and Smn is the overlap matrix which arises from the non-orthogonality of the basis functions.

Some of the molecular electronic properties are

1. the Highest Occupied Molecular Orbital (HOMO)
2. the electronic charge density computed from the sum of the squares of the molecular orbitals namely,
   where N is the number of electrons in the molecule, ni is the number of electrons in the ith molecular orbital
3. the electrostatic potential (ESP) which is written as,
   where, Za is the nuclear charge on the ath nuclear center in the molecule and r(r1) is the electron density
4. the Laplacian of the density, whose zero-envelope defines a reactivity surface.

STM is designed to read GAUSSIAN cube output, GAUSSIAN chkpnt files (next release) and specialized GAMESS output files for electronic information. For more information on the visualization modules see the description of the AVS/Express STM modules.