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

Efficacy, safety, and immunogenicity of a booster regimen of Ad26.COV2.S vaccine against COVID-19 (ENSEMBLE2) : results of a randomised, double-blind, placebo-controlled, phase 3 trial

Background Despite the availability of effective vaccines against COVID-19, booster vaccinations are needed to maintain vaccine-induced protection against variant strains and breakthrough infections. This study aimed to investigate the efficacy, safety, and immunogenicity of the Ad26.COV2.S vaccine (Janssen) as primary vaccination plus a booster dose. Methods ENSEMBLE2 is a randomised, double-blind, placebo-controlled, phase 3 trial including crossover vaccination after emergency authorisation of COVID-19 vaccines. Adults aged at least 18 years without previous COVID-19 vaccination at public and private medical practices and hospitals in Belgium, Brazil, Colombia, France, Germany, the Philippines, South Africa, Spain, the UK, and the USA were randomly assigned 1:1 via a computer algorithm to receive intramuscularly administered Ad26.COV2.S as a primary dose plus a booster dose at 2 months or two placebo injections 2 months apart. The primary endpoint was vaccine efficacy against the first occurrence of molecularly confirmed moderate to severe–critical COVID-19 with onset at least 14 days after booster vaccination, which was assessed in participants who received two doses of vaccine or placebo, were negative for SARS-CoV-2 by PCR at baseline and on serology at baseline and day 71, had no major protocol deviations, and were at risk of COVID-19 (ie, had no PCR-positive result or discontinued the study before day 71). Safety was assessed in all participants; reactogenicity, in terms of solicited local and systemic adverse events, was assessed as a secondary endpoint in a safety subset (approximately 6000 randomly selected participants). The trial is registered with ClinicalTrials.gov, NCT04614948, and is ongoing. Findings Enrolment began on Nov 16, 2020, and the primary analysis data cutoff was June 25, 2021. From 34 571 participants screened, the double-blind phase enrolled 31 300 participants, 14 492 of whom received two doses (7484 in the Ad26.COV2.S group and 7008 in the placebo group) and 11 639 of whom were eligible for inclusion in the assessment of the primary endpoint (6024 in the Ad26.COV2.S group and 5615 in the placebo group). The median (IQR) follow-up post-booster vaccination was 36·0 (15·0–62·0) days. Vaccine efficacy was 75·2% (adjusted 95% CI 54·6–87·3) against moderate to severe–critical COVID-19 (14 cases in the Ad26.COV2.S group and 52 cases in the placebo group). Most cases were due to the variants alpha (B.1.1.7) and mu (B.1.621); endpoints for the primary analysis accrued from Nov 16, 2020, to June 25, 2021, before the global dominance of delta (B.1.617.2) or omicron (B.1.1.529). The booster vaccine exhibited an acceptable safety profile. The overall frequencies of solicited local and systemic adverse events (evaluated in the safety subset, n=6067) were higher among vaccine recipients than placebo recipients after the primary and booster doses. The frequency of solicited adverse events in the Ad26.COV2.S group were similar following the primary and booster vaccinations (local adverse events, 1676 [55·6%] of 3015 vs 896 [57·5%] of 1559, respectively; systemic adverse events, 1764 [58·5%] of 3015 vs 821 [52·7%] of 1559, respectively). Solicited adverse events were transient and mostly grade 1–2 in severity. Interpretation A homologous Ad26.COV2.S booster administered 2 months after primary single-dose vaccination in adults had an acceptable safety profile and was efficacious against moderate to severe–critical COVID-19. Studies assessing efficacy against newer variants and with longer follow-up are needed