A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package

Consultants’ Perceptions of School Counselors’ Ability to Implement an Empirically-Based Intervention for Adolescent Social Anxiety Disorder

Social anxiety is highly prevalent but goes untreated. Although school-based CBT programs are efficacious when delivered by specialized psychologists, it is unclear whether school counselors can implement these interventions effectively, which is essential to promote sustainable school programs. We present an initial consultation strategy to support school counselor implementation of group CBT for social anxiety and an evaluation of counselors’ treatment fidelity. Counselors were highly adherent to the treatment, but competence varied based on measurement. Counselors and consultants demonstrated good agreement for adherence, but relatively modest correspondence in competence ratings. We discuss future directions for school-based implementation efforts informed by these initial findings