title: Explicit correlation and intermolecular interactions: Investigating carbon dioxide complexes with the CCSD(T)-F12 method

authors: de Lange, Katrina M.

subjects: carbon compounds

abstract: We have optimized the lowest energy structures and calculated interaction energies for the CO₂–Ar, CO₂–N₂, CO₂–CO, CO₂–H₂O, and CO₂–NH₃ dimers with the recently developed explicitly correlated coupled cluster singles doubles and perturbative triples [CCSD(T)]-F12 methods and the associated VXZ-F12 (where X = D,T,Q) basis sets. For a given cardinal number, we find that results obtained with the CCSD(T)-F12 methods are much closer to the CCSD(T) complete basis set limit than the conventional CCSD(T) results. The relatively modest increase in the computational cost between explicit and conventional CCSD(T) is more than compensated for by the impressive accuracy of the CCSD(T)-F12 method. We recommend use of the CCSD(T)-F12 methods in combination with the VXZ-F12 basis sets for the accurate determination of equilibrium geometries and interaction energies of weakly bound electron donor acceptor complexes.

text: Explicit correlation and intermolecular interactions: Investigating carbon dioxide complexes with the CCSD(T)-F12 method We have optimized the lowest energy structures and calculated interaction energies for the CO₂–Ar, CO₂–N₂, CO₂–CO, CO₂–H₂O, and CO₂–NH₃ dimers with the recently developed explicitly correlated coupled cluster singles doubles and perturbative triples [CCSD(T)]-F12 methods and the associated VXZ-F12 (where X = D,T,Q) basis sets. For a given cardinal number, we find that results obtained with the CCSD(T)-F12 methods are much closer to the CCSD(T) complete basis set limit than the conventional CCSD(T) results. The relatively modest increase in the computational cost between explicit and conventional CCSD(T) is more than compensated for by the impressive accuracy of the CCSD(T)-F12 method. We recommend use of the CCSD(T)-F12 methods in combination with the VXZ-F12 basis sets for the accurate determination of equilibrium geometries and interaction energies of weakly bound electron donor acceptor complexes.

year: 2011

title: Lie theory and separation of variables. 11. The EPD equation

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: We show that the Euler–Poisson–Darboux equation {∂tt -∂rr – [(2m+1)/r]∂r}Ө=0
separates in exactly nine coordinate systems corresponding to nine orbits of symmetric second-order operators in the enveloping algebra of SL(2,R), the symmetry group of this equation. We employ techniques developed in earlier papers from this series and use the representation theory of SL(2,R) to derive special function identities relating the separated solutions. We also show that the complex EPD equation separates in exactly five coordinate systems corresponding to five orbits of symmetric second-order operators in the enveloping algebra of SL(2,C).

text: Lie theory and separation of variables. 11. The EPD equation We show that the Euler–Poisson–Darboux equation {∂tt -∂rr – [(2m+1)/r]∂r}Ө=0
separates in exactly nine coordinate systems corresponding to nine orbits of symmetric second-order operators in the enveloping algebra of SL(2,R), the symmetry group of this equation. We employ techniques developed in earlier papers from this series and use the representation theory of SL(2,R) to derive special function identities relating the separated solutions. We also show that the complex EPD equation separates in exactly five coordinate systems corresponding to five orbits of symmetric second-order operators in the enveloping algebra of SL(2,C).

year: 1976-03

title: Mana Wahine reworking the power to name taonga

authors: Ringham, Sandra Lee

abstract: The capacity of Indigenous peoples to officially name taonga species (flora and fauna) within taxonomy signifies resilience and a reworking of western scientific processes and institutions. This article explores the ways in which Ngāti Kuri women contribute to environmental justice through the naming of taonga species. Ngāti Kuri were the first tribe in the world to install a tribal name into the co-authorship of a nomenclature. The article explores the ways in which Ngāti Kuri women, both past and present, rework environmental relationships and knowledge in both tribal and non-tribal spaces in Aotearoa's most northern region.

text: Mana Wahine reworking the power to name taonga The capacity of Indigenous peoples to officially name taonga species (flora and fauna) within taxonomy signifies resilience and a reworking of western scientific processes and institutions. This article explores the ways in which Ngāti Kuri women contribute to environmental justice through the naming of taonga species. Ngāti Kuri were the first tribe in the world to install a tribal name into the co-authorship of a nomenclature. The article explores the ways in which Ngāti Kuri women, both past and present, rework environmental relationships and knowledge in both tribal and non-tribal spaces in Aotearoa's most northern region.

year: 2023-01-01