Double Hybrid Functionals and the Π-System Bond Length Alternation Challenge: Rivaling Accuracy of Post-HF Methods

Predicting accurate bond length alternations (BLAs) in long conjugated oligomers has been a significant challenge for electronic-structure methods for many decades, made particularly important by the close relationships between BLA and the rich optoelectronic properties of π-delocalized systems. Here, we test the accuracy of recently developed, and increasingly popular, double hybrid (DH) functionals, positioned at the top of Jacobs Ladder of DFT methods of increasing sophistication, computational cost, and accuracy, due to incorporation of MP2 correlation energy. Our test systems comprise oligomeric series of polyacetylene, polymethineimine, and polysilaacetylene up to six units long. MP2 calculations reveal a pronounced shift in BLAs between the 6-31G(d) basis set used in many studies of BLA to date and the larger cc-pVTZ basis set, but only modest shifts between cc-pVTZ and aug-cc-pVQZ results. We hence perform new reference CCSD(T)/cc-pVTZ calculations for all three series of oligomers against which we assess the performance of several families of DH functionals based on BLYP, PBE, and TPSS, along with lower-rung relatives including global- and range-separated hybrids. Our results show that DH functionals systematically improve the accuracy of BLAs relative to single hybrid functionals. xDH-PBE0 (N4 scaling using SOS-MP2) emerges as a DH functional rivaling the BLA accuracy of SCS-MP2 (N5 scaling), which was found to offer the best compromise between computational cost and accuracy the last time the BLA accuracy of DFT- and wave function-based methods was systematically investigated. Interestingly, xDH-PBE0 (XYG3), which differs to other DHs in that its MP2 term uses PBE0 (B3LYP) orbitals that are not self-consistent with the DH functional, is an outlier of trends of decreasing average BLA errors with increasing fractions of MP2 correlation and HF exchange.

The effectiveness of an online workshop on behavior management as a professional development tool for teachers

The current study examines the effects of an online workshop pertaining to classroom behavior management on teacher self-efficacy, attitudes, motivation, knowledge, and practices. In addition, information about teacher utilization of the Internet, their opinions about professional development, and experiences with classroom management were collected. Participants included 57 1 st through 5th grade special and regular education teachers. Eligible teachers were those who teach an academic subject and had at least one child in the classroom they considered as disruptive. Teachers were randomized to either a training or waitlist group. Classroom observations of teacher practices and questionnaires were utilized. Teachers in the training group participated in two assessment points, baseline and post-workshop, and received access to the online course immediately following the baseline assessment. Teachers in the waitlist group participated in three assessment points, baseline, post-workshop, and follow-up, and received access to the online course immediately following the post-workshop assessment. Findings show that all teachers had access to the Internet at home and at school and used it on a daily basis. The majority of teachers indicated having some past training on all the techniques that were presented in the online workshop. All teachers expressed satisfaction with the workshop, indicating that it should be offered again. Post-workshop, findings showed significant group differences in knowledge with a large effect for the training group scoring higher than the waitlist group on a quiz. Secondly, group differences in self-efficacy, knowledge, and attitudes with teachers’ past-training as a moderator, was examined. Past-training was not found to be a significant moderator of self-efficacy, knowledge, or attitudes. However, the main effect for training group was significant for attitudes. In addition, teacher attitudes, but not knowledge and self-efficacy, significantly predicted motivation to implement. Next, the moderating effect of barriers on motivation and classroom management skill implementation was examined. Barriers were not found to be a significant moderator. Lastly, the training group was observed to be significantly more effective at giving commands compared to the waitlist group. The current study demonstrates the potential of a low-intensity online workshop on classroom management to enhance the accessibility of teacher professional development. ^

A Transcriptome Atlas of Physcomitrella patens Provides Insights into the Evolution and Development of Land Plants

Post-print version of the article.