Analytical gradients Atomic orbitals

To discuss the form and cost of analytic gradient and Hessian evaluations, we consider the simple case of Hartree-Fock (HF) calculations. In nearly all chemical applications of HF theory, the molecular orbitals (MOs) are represented by a linear combination of atomic orbitals (LCAO). In the context of most electronic structure methods, the LCAO approximation employs a more convenient set of basis functions such as contracted Gaussians, rather than using actual atomic orbitals. Taken together, the collection of basis functions used to represent the atomic orbitals comprises a basis set. 

Ab-initio methods, 1 Analytical gradients (PCM-LRCC), 42 Apparent charges operator, 4, 9 Apparent surface charges (ASC), 3 Apparent surface charges method (ASC), viii Atomic orbitals (AO), 6... 

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