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

Arbuscular mycorrhizal colonisation of roots of grass species differing in invasiveness

Recent research indicates that the soil microbial community, particularly arbuscular mycorrhizal fungi (AMF), can influence plant invasion in several ways. We tested if 1) invasive species are colonised by AMF to a lower degree than resident native species, and 2) AMF colonisation of native plants is lower in a community inhabited by an invasive species than in an uninvaded resident community. The two tests were run in semiarid temperate grasslands on grass (Poaceae) species, and the frequency and intensity of mycorrhizal colonisation, and the proportion of arbuscules and vesicles in plant roots have been measured. In the first test, grasses representing three classes of invasiveness were included: invasive species, resident species becoming abundant upon disturbance, and non-invasive native species. Each class contained one C3 and one C4 species. The AMF colonisation of the invasive Calamagrostis epigejos and Cynodon dactylon was consistently lower than that of the non-invasive native Chrysopogon gryllus and Bromus inermis, and contained fewer arbuscules than the post-disturbance dominant resident grasses Bothriochloa ischaemum and Brachypodium pinnatum. The C3 and C4 grasses behaved alike despite their displaced phenologies in these habitats. The second test compared AMF colonisation for sand grassland dominant grasses Festuca vaginata and Stipa borysthenica in stands invaded by either C. epigejos or C. dactylon, and in the uninvaded natural community. Resident grasses showed lower degree of AMF colonisation in the invaded stand compared to the uninvaded natural community with F. vaginata responding so to both invaders, while S. borysthenica responding to C. dactylon only. These results indicate that invasive grasses supposedly less reliant on AMF symbionts have the capacity of altering the soil mycorrhizal community in such a way that resident native species can establish a considerably reduced extent of the beneficial AMF associations, hence their growth, reproduction and ultimately abundance may decline. Accumulating evidence suggests that such indirect influences of invasive alien plants on resident native species mediated by AMF or other members of the soil biota is probably more the rule than the exception

Exploring Attitudes Toward “Sugar Relationships” Across 87 Countries: A Global Perspective on Exchanges of Resources for Sex and Companionship

The current study investigates attitudes toward one form of sex for resources: the so-called sugar relationships, which often involve exchanges of resources for sex and/or companionship. The present study examined associations among attitudes toward sugar relationships and relevant variables (e.g., sex, sociosexuality, gender inequality, parasitic exposure) in 69,924 participants across 87 countries. Two self-report measures of Acceptance of Sugar Relationships (ASR) developed for younger companion providers (ASR-YWMS) and older resource providers (ASR-OMWS) were translated into 37 languages. We tested cross-sex and cross-linguistic construct equivalence, cross-cultural invariance in sex differences, and the importance of the hypothetical predictors of ASR. Both measures showed adequate psychometric properties in all languages (except the Persian version of ASR-YWMS). Results partially supported our hypotheses and were consistent with previous theoretical considerations and empirical evidence on human mating. For example, at the individual level, sociosexual orientation, traditional gender roles, and pathogen prevalence were significant predictors of both ASR-YWMS and ASR-OMWS. At the country level, gender inequality and parasite stress positively predicted the ASR-YWMS. However, being a woman negatively predicted the ASR-OMWS, but positively predicted the ASR-YWMS. At country-level, ingroup favoritism and parasite stress positively predicted the ASR-OMWS. Furthermore, significant cross-subregional differences were found in the openness to sugar relationships (both ASR-YWMS and ASR-OMWS scores) across subregions. Finally, significant differences were found between ASR-YWMS and ASR-OMWS when compared in each subregion. The ASR-YWMS was significantly higher than the ASR-OMWS in all subregions, except for Northern Africa and Western Asia