On the use of a Hessian model function in molecular geometry optimizations

When a molecular equilibrium geometry is determined by minimizing the energy by a quasi-Newton-Raphson method, the number of iterations required depends critically on the choice of an approximate molecular Hessian matrix. We find that a simple 15-parameter function of the nuclear positions gives a good choice for any molecule with atoms from the first three rows of the periodic table. This Hessian is used for ab initio geometry optimizations with the quasi-Newton-Raphson method, with or without update. The equilibrium geometries of 30 molecules, with a variety of sizes and symmetries, is obtained with the new scheme, which is shown to converge significantly faster than other methods.