Rulis, PaulAlzahrani, Nuha2024-06-052024-06-052024-05-10https://hdl.handle.net/20.500.14154/72249Toward the long-term goal of predicting the figure of merit of complex thermoelectric materials, we introduce the computational and theoretical groundwork for the calculation of interatomic forces in ab initio calculations using the Orthogonalized Linear Combination of Atomic Orbitals (OLCAO) method. The approach is based on the Hellmann-Feynman (HF) theorem and Pulay forces in the presence of an atomic orbital basis set. To accomplish this, we offered a thorough derivation of a HF theorem that holds for all quantum mechanical systems. This theorem serves as a valuable tool for understanding the nature of chemical bonding in quantum chemistry and solid-state physics. We follow Pulay's suggestion [Mol. Phys.17, 153 (1969)] to update the HF theorem by including contributions from changes in the wave function with respect to nuclear sites. Additionally, we developed the Obara–Saika scheme for evaluating the derivative of different molecular integrals that contribute to the HF force using Gaussian-type orbitals, i.e., electron repulsion integrals, kinetic energy integrals, and nuclear attraction integrals. Once the force calculation was implemented in the OLCAO method, we applied this method to compute the interatomic forces between various pairs of atoms in diatomic molecules such as N2, H2, O2, F2, Cl2, I2, CO, and NO.131en-USHellmann-Feynman theoremInteratomic forcesObara–Saika schemeOLCAO methodPulay forcesThermoelectricThesis