In VBSCF method, the formula deduction and code implementation for the Hessian matrix are very tedious and complicated due to the use of nonorthogonal orbitals. To overcome this difficulty, the automatic formula/code generation (AFCG) technique is developed for nonorthogonal orbitals. It was written with the Python programming language.

The AFCG is composed of two modules, AFG (automatic formulas generator) and ACG (automatic code generator). AFG reads the Hamiltonian/Overlap matrix elements required to calculate as input, parses the input, and then accomplishes the formula deduction to get the resulting formulas by utilizing the enhanced Wick’s theorem. The output formulas can be printed either in the plain text form or in LaTeX input file format, by which a PDF file can be easily produced.

After generating the formulas, the ACG module will generate corresponding codes automatically. The output codes are in standard Fortran form and are compiled into the XMVB package with a general Fortran compiler such as GFortran or IFORT. The implementation details of AFCG are discussed in the Appendix of the following paper:

Chen, X.; Chen, Z.; Wu, W.,* Nonorthogonal Orbital Based N-body Reduced Density Matrices and Their Applications to Valence Bond Theory. IV. The Automatic Implementation of the Hessian Based VBSCF Method, J. Chem. Phys., 2014, 141, 194113.