Prediction of Reaction Barriers and Thermochemical Properties with Explicitly Correlated Coupled-Cluster Methods: A Basis Set Assessment

We assessed the performance of our perturbative explicitly correlated coupled-cluster method, CCSD­(T)_F12, for accurate prediction of chemical reactivity. The reference data included reaction barrier heights, electronic reaction energies, atomization energies, and enthalpies of formation from the following sources: (1) the DBH24/08 database of 22 reaction barriers (Truhlar et al.), (2) the HJO12 set of isogyric reaction energies (Helgaker et al.), and (3) a HEAT set of atomization energies and heats of formation (Stanton et al.). We performed two types of analyses targeting the two distinct uses of explicitly correlated CCSD­(T) models: as a replacement for basis-set-extrapolated CCSD­(T) in highly accurate composite methods like HEAT and as a distinct model chemistry for standalone applications. Hence, we analyzed in detail (1) the <i>basis set error</i> of each component of the CCSD­(T)_F12 contribution to the chemical energy difference in question and (2) the <i>total error</i> of the CCSD­(T)_F12 model chemistry relative to the benchmark values. Two basis set families were utilized in the calculations: the standard aug-cc-p­(C)­VXZ-F12 (X = D, T, Q) basis sets for the conventional correlation methods and the cc-p­(C)­VXZ-F12 (X = D, T, Q) basis sets of Peterson and co-workers that are specifically designed for explicitly correlated methods. Our conclusion is that the performance of the two families for CCSD correlation contributions (which are the only components affected by the explicitly correlated terms in our formation) are nearly identical with triple- and quadruple-ζ quality basis sets, with some differences at the double-ζ level. Chemical accuracy (∼4.18 kJ/mol) for reaction barrier heights, electronic reaction energies, atomization energies, and enthalpies of formation is attained on average with the aug-cc-pVDZ, aug-cc-pVTZ, cc-pCVTZ-F12/aug-cc-pCVTZ, and cc-pCVDZ-F12 basis sets, respectively, at the CCSD­(T)_F12 level of theory. The corresponding mean unsigned errors are 1.72 kJ/mol, 1.5 kJ/mol, ∼2 kJ/mol, and 2.17 kJ/mol, and the corresponding maximum unsigned errors are 4.44 kJ/mol, 3.6 kJ/mol, ∼5 kJ/mol, and 5.75 kJ/mol

Anatomy of molecular properties evaluated with explicitly correlated electronic wave functions

<p>Static electric dipole and quadrupole moments were evaluated at the explicitly correlated second-order Møller–Plesset (MP2-F12) level for BH, CO, H₂O, and HF molecules. The electron correlation contributions to the multipole moments were further decomposed into the direct (<i>unrelaxed</i>) and indirect (<i>orbital response</i>) components; we found that both components are equally important for the conventional (MP2) contribution, whereas the F12 correction to these properties originates primarily from the orbital response effects. Finally, the direct contribution dominates in the perturbative Hartree–Fock basis set incompleteness (CABS singles) correction. Two basis set families were employed: the standard aug-cc-pVXZ series and the cc-pVXZ-F12 series designed specifically for the F12 methods. The aug-cc-pVXZ MP2-F12 multipole moments usually have smaller basis set errors than the cc-pVXZ-F12 counterparts, albeit their differences are small at the triple (<i>X</i> = <i>T</i>) and quadruple (<i>X</i> = <i>Q</i>) zeta level. With the MP2-F12 calculations, the basis set errors of dipole and quadrupole moments can be reduced to ∼0.001 a.u., or roughly 0.1%, at the aug-cc-pVDZ and aug-cc-pVTZ levels, respectively.</p

Massively Parallel Implementation of Explicitly Correlated Coupled-Cluster Singles and Doubles Using TiledArray Framework

A new distributed-memory massively parallel implementation of standard and explicitly correlated (F12) coupled-cluster singles and doubles (CCSD) with canonical <i>O</i>(<i>N</i>⁶) computational complexity is described. The implementation is based on the TiledArray tensor framework. Novel features of the implementation include (a) all data greater than <i>O</i>(<i>N</i>) is distributed in memory and (b) the mixed use of density fitting and integral-driven formulations that optionally allows to avoid storage of tensors with three and four unoccupied indices. Excellent strong scaling is demonstrated on a multicore shared-memory computer, a commodity distributed-memory computer, and a national-scale supercomputer. The performance on a shared-memory computer is competitive with the popular CCSD implementations in ORCA and Psi4. Moreover, the CCSD performance on a commodity-size cluster significantly improves on the state-of-the-art package NWChem. The large-scale parallel explicitly correlated coupled-cluster implementation makes routine accurate estimation of the coupled-cluster basis set limit for molecules with 20 or more atoms. Thus, it can provide valuable benchmarks for the merging reduced-scaling coupled-cluster approaches. The new implementation allowed us to revisit the basis set limit for the CCSD contribution to the binding energy of π-stacked uracil dimer, a challenging paradigm of π-stacking interactions from the S66 benchmark database. The revised value for the CCSD correlation binding energy obtained with the help of quadruple-ζ CCSD computations, −8.30 ± 0.02 kcal/mol, is significantly different from the S66 reference value, −8.50 kcal/mol, as well as other CBS limit estimates in the recent literature

Additional file 1 of Application, knowledge and training needs regarding comprehensive geriatric assessment among geriatric practitioners in healthcare institutions: a cross-sectional study

Supplementary Material 1

Comprehensive Mitochondrial Metabolic Shift during the Critical Node of Seed Ageing in Rice

<div><p>The critical node (CN) in seed aging in rice (<i>Oryza sativa</i>) is the transformation from Phase I (P-I) to Phase II (P-II) of the reverse S-shaped curve (RS-SC). Although mitochondrial dysfunction plays a key role in seed ageing, the metabolic shift in the CN remains poorly understood. Here, we investigated the mitochondrial regulatory mechanisms during the CN of rice seed ageing. We showed that during the CN of seed ageing, the mitochondrial ultrastructure was impaired, causing oxygen consumption to decrease, along with cytochrome <i>c</i> (cyt <i>c</i>) oxidase and malate dehydrogenase (MDH) activity. In addition, the transcript levels for the alternative pathway of the electron transport chain (ETC) were significantly induced, whereas the transcripts of the cytochrome oxidase (COX) pathway were inhibited. These changes were concomitant with the down-regulation of mitochondrial protein levels related to carbon and nitrogen metabolism, ATP synthase (ATPase) complex, tricarboxylic acid cycle (TCA) cycle, mitochondrial oxidative enzymes, and a variety of other proteins. Therefore, while these responses inhibit the production of ATP and its intermediates, signals from mitochondria (such as the decrease of cyt <i>c</i> and accumulation of reactive oxygen species (ROS)) may also induce oxidative damage. These events provide considerable information about the mitochondrial metabolic shifts involved in the progression of seed ageing in the CN.</p></div

Transmission electron micrographs of rice embryos aged 0 d (A–C), 3 d (D–F), 4 d (G–I), and 7 d (J–L).

<p>N, nucleus; CW, cell wall; St, starch granule; V, vacuole; M, mitochondria; Cr, cristae; OM, outer membrane; IM, inner boundary membrane.</p

Western blot analysis of antioxidant enzymes in purified mitochondria from 0 d, 3 d, and 4 d aged seeds.

<p>Total 10 μg protein was separated by SDS gel electrophoresis and blotted to supported polyvinylidene difluoride, then probed with antibodies against catalase (CAT), glutathione reductase (GR) and manganese superoxide dismutase (MnSOD).</p

O₂ consumption by crude mitochondria from aged seeds.

<p>O₂ consumption rates are presented as means ± SD (n = 3).</p

Cytochrome <i>c</i> oxidase (COX, A) and malate dehydrogenase (MDH, B) activity in crude mitochondria from 0 d, 3 d, 4 d, 7 d, and 11 d aged seeds.

<p>Data represents mean ± standard deviation of 3 independent experiments. All treatment significantly differed from the control (<b><i>p</i></b>< 0.05, one-way ANOVA, n = 3).</p

Abundance of the transcripts of mitochondrial components in rice embryos during germination.

<p>For each of the 13 transcripts investigated, a value of 1.0 was assigned to 0 d aged seed after imbibition 48 h and message abundance at the 3 d, 4 d, 7 d and 11 d aged seed was calculated relative to it. Data represent the mean ± standard deviation of 3 independent experiments. Asterisks indicate significant differences to 0 d aged seed (Student’s t-test; *<b><i>p</i></b>< 0.05).</p