New integral transforms for molecular properties and application to a massively parallel GIAO-SCF implementation Original Research Article

We present several new Gaussian integral transforms to be used with the Rys quadrature numerical integration method. These transforms lead to an elegant unified methodology for the calculation of the atomic Gaussian integrals that enter the calculation of many molecular wavefunctions and properties. The unified methodology is highlighted for several types of integrals that are at the heart of other modern electronic structure theoretical developments, including electric and magnetic properties. We make use of these transforms in a massively parallel implementation of the Gauge-Invariant-Atomic-Orbital (GIAO) method for the calculation of chemical shifts at the ab initio HF SCF level of theory. The implementation follows the original GIAO theory that bypasses computational tasks that are not massively scalable. Indeed the response of the wavefunction to the magnetic field is calculated by means of the Derivative Hartree–Fock method (DHF). The DHF method is amenable to high parallel efficiency as it involves only the calculation of Fock-like matrices from density-like matrices. The computationally intensive steps are shown to be highly scalable.