Capturing the electron-electron cusp with the coupling-constant averaged exchange-correlation hole: A case study for Hooke's atoms.

In density-functional theory, the exchange-correlation (XC) energy can be defined exactly through the coupling-constant (λ) averaged XC hole n̄xc(r,r'), representing the probability depletion of finding an electron at r' due to an electron at r. Accurate knowledge of n̄xc(r,r') has been crucial for developing XC energy density-functional approximations and understanding their performance for molecules and materials. However, there are very few systems for which accurate XC holes have been calculated since this requires evaluating the one- and two-particle reduced density matrices for a reference wave function over a range of λ while the electron density remains fixed at the physical (λ = 1) density. Although the coupled-cluster singles and doubles (CCSD) method can yield exact results for a two-electron system in the complete basis set limit, it cannot capture the electron-electron cusp using finite basis sets. Focusing on Hooke's atom as a two-electron model system for which certain analytic solutions are known, we examine the effect of this cusp error on the XC hole calculated using CCSD. The Lieb functional is calculated at a range of coupling constants to determine the λ-integrated XC hole. Our results indicate that, for Hooke's atoms, the error introduced by the description of the electron-electron cusp using Gaussian basis sets at the CCSD level is negligible compared to the basis set incompleteness error. The system-, angle-, and coupling-constant-averaged XC holes are also calculated and provide a benchmark against which the Perdew-Burke-Ernzerhof and local density approximation XC hole models are assessed.

Testing the r2SCAN Density Functional for the Thermodynamic Stability of Solids with and without a van der Waals Correction.

A central aim of materials discovery is an accurate and numerically reliable description of thermodynamic properties, such as the enthalpies of formation and decomposition. The r2SCAN revision of the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (meta-GGA) balances numerical stability with high general accuracy. To assess the r2SCAN description of solid-state thermodynamics, we evaluate the formation and decomposition enthalpies, equilibrium volumes, and fundamental band gaps of more than 1000 solids using r2SCAN, SCAN, and PBE, as well as two dispersion-corrected variants, SCAN+rVV10 and r2SCAN+rVV10. We show that r2SCAN achieves accuracy comparable to SCAN and often improves upon SCAN's already excellent accuracy. Although SCAN+rVV10 is often observed to worsen the formation enthalpies of SCAN and makes no substantial correction to SCAN's cell volume predictions, r2SCAN+rVV10 predicts marginally less accurate formation enthalpies than r2SCAN, and slightly more accurate cell volumes than r2SCAN. The average absolute errors in predicted formation enthalpies are found to decrease by a factor of 1.5 to 2.5 from the GGA level to the meta-GGA level. Smaller decreases in error are observed for decomposition enthalpies. For formation enthalpies r2SCAN improves over SCAN for intermetallic systems. For a few classes of systems-transition metals, intermetallics, weakly bound solids, and enthalpies of decomposition into compounds-GGAs are comparable to meta-GGAs. In total, r2SCAN and r2SCAN+rVV10 can be recommended as stable, general-purpose meta-GGAs for materials discovery.

Comparative Density Functional Theory Study of Magnetic Exchange Couplings in Dinuclear Transition-Metal Complexes.

Multicenter transition-metal complexes (MCTMs) with magnetically interacting ions have been proposed as components for information-processing devices and storage units. For any practical application of MCTMs as magnetic units, it is crucial to characterize their magnetic behavior, and in particular, the isotropic magnetic exchange coupling, J, between its magnetic centers. Due to the large size of typical MCTMs, density functional theory is the only practical electronic structure method for evaluating the J coupling. Here, we assess the accuracy of different density functional approximations for predicting the magnetic couplings of eight dinuclear transition-metal complexes, including five dimanganese, two dicopper, and one divanadium with known reliable experimental J couplings spanning from ferromagnetic to strong antiferromagnetic. The density functionals considered include global hybrid functionals which mix semilocal density functional approximations and exact exchange with a fixed admixing parameter, six local hybrid functionals where the admixing parameters are extended to be spatially dependent, the SCAN and r2SCAN meta-generalized gradient approximations (GGAs), and two widely used GGAs. We found that global hybrids tested in this work have a tendency to over-correct the error in magnetic coupling parameters from the Perdew-Burke-Ernzerhof (PBE) GGA as seen for manganese complexes. The performance of local hybrid density functionals shows no improvement in terms of bias and is scattered without a clear trend, suggesting that more efforts are needed for the extension from global to local hybrid density functionals for this particular property. The SCAN and r2SCAN meta-GGAs are found to perform as well as benchmark global hybrids on most tested complexes. We further analyze the charge density redistribution of meta-GGAs as well as global and local hybrid density functionals with respect to that of PBE, in connection to the self-interaction error or delocalization error.

Exact constraints and appropriate norms in machine-learned exchange-correlation functionals.

Machine learning techniques have received growing attention as an alternative strategy for developing general-purpose density functional approximations, augmenting the historically successful approach of human-designed functionals derived to obey mathematical constraints known for the exact exchange-correlation functional. More recently, efforts have been made to reconcile the two techniques, integrating machine learning and exact-constraint satisfaction. We continue this integrated approach, designing a deep neural network that exploits the exact constraint and appropriate norm philosophy to de-orbitalize the strongly constrained and appropriately normed (SCAN) functional. The deep neural network is trained to replicate the SCAN functional from only electron density and local derivative information, avoiding the use of the orbital-dependent kinetic energy density. The performance and transferability of the machine-learned functional are demonstrated for molecular and periodic systems.

Construction of meta-GGA functionals through restoration of exact constraint adherence to regularized SCAN functionals.

The strongly constrained and appropriately normed (SCAN) meta-GGA exchange-correlation functional [Sun et al., Phys. Rev. Lett. 115, 036402 (2015)] is constructed as a chemical environment-determined interpolation between two separate energy densities: one describes single-orbital electron densities accurately and another describes slowly varying densities accurately. To conserve constraints known for the exact exchange-correlation functional, the derivatives of this interpolation vanish in the slowly varying limit. While theoretically convenient, this choice introduces numerical challenges that degrade the functional's efficiency. We have recently reported a modification to the SCAN meta-GGA, termed restored-regularized-SCAN (r2SCAN) [Furness et al., J. Phys. Chem. Lett. 11, 8208 (2020)], that introduces two regularizations into SCAN, which improve its numerical performance at the expense of not recovering the fourth order term of the slowly varying density gradient expansion for exchange. Here, we show the derivation of a progression of density functional approximations [regularized SCAN (rSCAN), r++SCAN, r2SCAN, and r4SCAN] with increasing adherence to exact conditions while maintaining a smooth interpolation. The greater smoothness of r2SCAN seems to lead to better general accuracy than the additional exact constraint of SCAN or r4SCAN does.

Self-Consistent Field Methods for Excited States in Strong Magnetic Fields: a Comparison between Energy- and Variance-Based Approaches.

Self-consistent field methods for excited states offer an attractive low-cost route to study not only excitation energies but also properties of excited states. Here, we present the generalization of two self-consistent field methods, the maximum overlap method (MOM) and the σ-SCF method, to calculate excited states in strong magnetic fields and investigate their stability and accuracy in this context. These methods use different strategies to overcome the well-known variational collapse of energy-based optimizations to the lowest solution of a given symmetry. The MOM tackles this problem in the definition of the orbital occupations to constrain the self-consistent field procedure to converge on excited states, while the σ-SCF method is based on the minimization of the variance instead of the energy. To overcome the high computational cost of the variance minimization, we present a new implementation of the σ-SCF method with the resolution of identity approximation, allowing the use of large basis sets, which is an important requirement for calculations in strong magnetic fields. The accuracy of these methods is assessed by comparison with the benchmark literature data for He, H2, and CH+. The results reveal severe limitations of the variance-based scheme, which become more acute in large basis sets. In particular, many states are not accessible using variance optimization. Detailed analysis shows that this is a general feature of variance optimization approaches due to the masking of local minima in the optimization. In contrast, the MOM shows promising performance for computing excited states under these conditions, yielding results consistent with available benchmark data for a diverse range of electronic states.

Fluid Loss in Recreational Surfers.

Surfing offers unique challenges to thermoregulation and hydration. The purpose of this study was to quantify fluid loss in recreational surfers, and to analyze the effects of water temperature, air temperature, exercise intensity, duration, and garment thickness on the total amount of fluid lost during a surf session. A total of 254 male and 52 female recreational surfers were recruited from San Diego, Costa Rica, and Australia to participate in the study. Participants' hydration status was assessed by comparing nude body mass pre- and post-surf session. Heart rate (HR), used as an index of exercise intensity, was measured throughout the session. Environmental conditions and surf characteristics were recorded. The difference between average pre-mass (73.11 ± 11.88 kg) and average post-mass (72.51 ± 11.78) was statistically significant (0.60 ± 0.55, p < 0.001). Surfers experienced a 0.82 ± 0.73% reduction in body mass. In multivariable linear regression, session duration and body mass index (BMI) were significantly associated with fluid loss. For every 10-minute increase in session duration, there was a 0.06 kg (SE = 0.001; p < 0.001) increase in fluid loss, and for every two unit increase in BMI, fluid loss increased by 0.05 kg (SE = 0.03; p = 0.02). Results suggest that prolonged surfing at high environmental temperatures in participants with high BMI's resulted in significant body water deficits. Since there is no opportunity to rehydrate during a surf session, surfers must properly pre-hydrate before surfing in order to avoid the detrimental effects of dehydration.

r2SCAN-D4: Dispersion corrected meta-generalized gradient approximation for general chemical applications.

We combine a regularized variant of the strongly constrained and appropriately normed semilocal density functional [J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015)] with the latest generation semi-classical London dispersion correction. The resulting density functional approximation r2SCAN-D4 has the speed of generalized gradient approximations while approaching the accuracy of hybrid functionals for general chemical applications. We demonstrate its numerical robustness in real-life settings and benchmark molecular geometries, general main group and organo-metallic thermochemistry, and non-covalent interactions in supramolecular complexes and molecular crystals. Main group and transition metal bond lengths have errors of just 0.8%, which is competitive with hybrid functionals for main group molecules and outperforms them for transition metal complexes. The weighted mean absolute deviation (WTMAD2) on the large GMTKN55 database of chemical properties is exceptionally small at 7.5 kcal/mol. This also holds for metal organic reactions with an MAD of 3.3 kcal/mol. The versatile applicability to organic and metal-organic systems transfers to condensed systems, where lattice energies of molecular crystals are within the chemical accuracy (errors <1 kcal/mol).

Accurate and Numerically Efficient r2SCAN Meta-Generalized Gradient Approximation.

The recently proposed rSCAN functional [ J. Chem. Phys. 2019 150, 161101] is a regularized form of the SCAN functional [ Phys. Rev. Lett. 2015 115, 036402] that improves SCAN's numerical performance at the expense of breaking constraints known from the exact exchange-correlation functional. We construct a new meta-generalized gradient approximation by restoring exact constraint adherence to rSCAN. The resulting functional maintains rSCAN's numerical performance while restoring the transferable accuracy of SCAN.

Patient and surgical prognostic factors for inpatient functional recovery following THA and TKA: a prospective cohort study.

BACKGROUND: The introduction of enhanced recovery pathways has demonstrated both patient and organisational benefits. However, enhanced recovery pathways implemented for total hip arthroplasty (THA) and total knee arthroplasty (TKA) vary between health-care organisations, as do their measures of success, particularly patient-related outcomes. Despite inpatient functional recovery being essential for safe and timely hospital discharge, there is currently no gold standard method for its assessment, and the research undertaken to establish prognostic factors is limited. This study aimed to identify prognostic factors and subsequently develop prognostic models for inpatient functional recovery following primary, unilateral THA and TKA; identify factors associated with acute length of stay; and assess the relationships between inpatient function and longer-term functional outcomes. METHODS: Correlation and multiple regression analyses were used to determine prognostic factors for functional recovery (assessed using the modified Iowa Level of Assistance Scale on day 2 post-operatively) in a prospective cohort study of 354 patients following primary, unilateral THA or TKA. RESULTS: For the overall cohort and TKA group, significant prognostic factors included age, sex, pre-operative general health, pre-operative function, and use of general anaesthesia, local infiltration analgesia, and patient-controlled analgesia. In addition, arthroplasty site was a prognostic factor for the overall cohort, and surgery duration was prognostic for the TKA group. For the THA group, significant prognostic factors included pre-operative function, Risk Assessment and Prediction Tool score, and surgical approach. Several factors were associated with acute hospital length of stay. Inpatient function was positively correlated with functional outcomes assessed at 6 months post-operatively. CONCLUSIONS: Prognostic models may facilitate the prediction of inpatient flow thus optimising organisational efficiency. Surgical prognostic factors warrant consideration as potential key elements in enhanced recovery pathways, associated with early post-operative functional recovery. Standardised measures of inpatient function serve to evaluate patient-centred outcomes and facilitate the benchmarking and improvement of enhanced recovery pathways.

Examining the order-of-limits problem and lattice constant performance of the Tao-Mo functional.

In their recent communication, Tao and Mo [Phys. Rev. Lett. 117, 073001 (2016)] presented a semi-local density functional derived from the density matrix expansion of the exchange hole localized by a general coordinate transformation. We show that the order-of-limits problem present in the functional, dismissed as harmless in the original publication, causes severe errors in predicted phase transition pressures. We also show that the claim that lattice volume prediction accuracy exceeds that of existing similar functionals was based on comparison to reference data that miss anharmonic zero-point expansion and consequently overestimates accuracy. By highlighting these omissions, we give a more accurate assessment of the Tao-Mo functional and show a possible direction for resolving the order-of-limits problem.

Staging achilles tendinopathy using ultrasound imaging: the development and investigation of a new ultrasound imaging criteria based on the continuum model of tendon pathology.

AIM: To develop a standardised ultrasound imaging (USI)-based criteria for the diagnosis of tendinopathy that aligns with the continuum model of tendon pathology. Secondary aims were to assess both the intra-rater and inter-rater reliability of the criteria. METHODS: A criteria was developed following a face validity assessment and a total of 31 Achilles tendon ultrasound images were analysed. Intra-rater and inter-rater reliability were assessed for overall tendinopathy stage (normal, reactive/early dysrepair or late dysrepair/degenerative) as well as for individual parameters (thickness, echogenicity and vascularity). Quadratic weighted kappa (kw) was used to report on reliability. RESULTS: Intra-rater reliability was 'substantial' for overall tendinopathy staging (kw rater A; 0.77, 95% CI 0.59 to 0.94, rater B; 0.70, 95% CI 0.52 to 0.89) and ranged from 'substantial' to 'almost perfect' for thickness (kw rater A; 0.75, 95% CI 0.59 to 0.90, rater B; 0.84, 95% CI 0.71 to 0.98), echogenicity (kw rater A; 0.78, 95% CI 0.62 to 0.95, rater B; 0.73, 95% CI 0.58 to 0.89) and vascularity (kw rater A; 0.86, 95% CI 0.74 to 0.98, rater B; 0.89, 95% CI 0.79 to 0.99). Inter-rater reliability ranged from 'substantial' to 'almost perfect' for overall tendinopathy staging (kw round 1; 0.75, 95% CI 0.58 to 0.91, round 2; 0.81, 95% CI 0.63 to 0.99), thickness (kw round 1; 0.65, 95% CI 0.48 to 0.83, round 2; 0.77, 95% CI 0.60 to 0.93), echogenicity (kw round 1; 0.70, 95% CI 0.54 to 0.85, round 2; 0.76, 95% CI 0.58 to 0.94) and vascularity (kw round 1; 0.89, 95% CI 0.79 to 0.99, round 2; 0.86, 95% CI 0.74 to 0.98). Inter-rater reliability increased from 'substantial' in round 1 (kw 0.75, 95% CI 0.58 to 0.91) to 'almost perfect' in round 2 (0.81, 95% CI 0.63 to 0.99). CONCLUSION: Intra-rater and inter-rater reliability were 'substantial' to 'almost perfect' when utilising an USI-based criteria to diagnose Achilles tendinopathy. This is the first study to use the continuum model of tendon pathology to develop an USI-based criteria to diagnose tendinopathy.

Competing stripe and magnetic phases in the cuprates from first principles.

Realistic description of competing phases in complex quantum materials has proven extremely challenging. For example, much of the existing density-functional-theory-based first-principles framework fails in the cuprate superconductors. Various many-body approaches involve generic model Hamiltonians and do not account for the interplay between the spin, charge, and lattice degrees of freedom. Here, by deploying the recently constructed strongly constrained and appropriately normed (SCAN) density functional, we show how the landscape of competing stripe and magnetic phases can be addressed on a first-principles basis both in the parent insulator YBa2Cu3O6 and the near-optimally doped YBa2Cu3O7 as archetype cuprate compounds. In YBa2Cu3O7, we find many stripe phases that are nearly degenerate with the ground state and may give rise to the pseudogap state from which the high-temperature superconducting state emerges. We invoke no free parameters such as the Hubbard U, which has been the basis of much of the existing cuprate literature. Lattice degrees of freedom are found to be crucially important in stabilizing the various phases.

Subtlety of TiO2 phase stability: Reliability of the density functional theory predictions and persistence of the self-interaction error.

TiO2 is an important material with broad applications that can exist in different phases with dramatically different properties. Theoretical prediction of their polymorph energetics is therefore critical for the material design and for identifying thermodynamically accessible structures. Determining TiO2 relative phase stabilities remains challenging for first-principles methods, and density functional theory is the only approach available for studying phase stabilities at finite temperatures with acceptable computational efficiency. Here, we show that density functional theory using the recently developed efficient strongly constrained and appropriately normed (SCAN) [Sun et al., Phys. Rev. Lett. 115, 036402 (2015)] exchange-correlation functional for the first time predicts the phase stability in qualitative agreement with the experimental results at realistic conditions. Further analysis shows that the self-interaction error intrinsic in the density functional persists in the stability prediction. By correcting the self-interaction error through an empirical approach, SCAN predicts the relative stability as well as defect properties in excellent agreement with the experimental results.

Physiological Profile of Male Competitive and Recreational Surfers.

Furness, J, Hing, W, Sheppard, JM, Newcomer, S, Schram, B, and Climstein, M. Physiological profile of male competitive and recreational surfers. J Strength Cond Res 32(2): 372-378, 2018-Surfing consists of both high- and low-intensity paddling of varying durations, using both the aerobic and anaerobic systems. Surf-specific physiological studies lack adequate group sample sizes, and V[Combining Dot Above]O2peak values are yet to determine the differences between competitive and recreational surfers. The purpose of this study was therefore to provide a comprehensive physiological profile of both recreational and competitive surfers. This multisite study involved 62 male surfers, recreational (n = 47) and competitive (n = 15). Anthropometric measurements were conducted followed by dual-energy x-ray absorptiometry, anaerobic testing and finally aerobic testing. V[Combining Dot Above]O2peak was significantly greater in competitive surfers than in recreational surfers (M = 40.71 ± 3.28 vs. 31.25 ± 6.31 ml·kg·min, p < 0.001). This was also paralleled for anaerobic power (M = 303.93 vs. 264.58 W) for competitive surfers. Arm span and lean total muscle mass was significantly (p ≤ 0.01) correlated with key performance variables (V[Combining Dot Above]O2peak and anaerobic power). No significant (p ≥ 0.05) correlations were revealed between season rank and each of the variables of interest (V[Combining Dot Above]O2peak and anaerobic power). Key performance variables (V[Combining Dot Above]O2peak and anaerobic power) are significantly higher in competitive surfers, indicating that this is both an adaptation and requirement in this cohort. This battery of physiological tests could be used as a screening tool to identify an athlete's weaknesses or strengths. Coaches and clinicians could then select appropriate training regimes to address weaknesses.

Connections between variation principles at the interface of wave-function and density-functional theories.

A recently proposed variation principle [N. I. Gidopoulos, Phys. Rev. A 83, 040502(R) (2011)] for the determination of Kohn-Sham effective potentials is examined and extended to arbitrary electron-interaction strengths and to mixed states. Comparisons are drawn with Lieb's convex-conjugate functional, which allows for the determination of a potential associated with a given electron density by maximization, yielding the Kohn-Sham potential for a non-interacting system. The mathematical structure of the two functionals is shown to be intrinsically related; the variation principle put forward by Gidopoulos may be expressed in terms of the Lieb functional. The equivalence between the information obtained from the two approaches is illustrated numerically by their implementation in a common framework.

A Performance Analysis of a Stand-Up Paddle Board Marathon Race.

Stand-up paddle boarding (SUP) is a rapidly growing sport and recreational activity in which little scientific research exists. A review of the literature failed to identify a single article pertaining to the physiological demands of SUP competition. The purpose of this study was to conduct a performance analysis of a national-level SUP marathon race. Ten elite SUP athletes (6 male and 4 female athletes) were recruited from the Stand Up Paddle Surfing Association of Australia to have their race performance in the Australian Titles analyzed. Performance variables included SUP speed, course taken, and heart rate (HR), measured with a 15-Hz global positioning system unit. Results demonstrated that there was a variation in distance covered (13.3-13.9 km), peak speed (18.8-26.4 km·h), and only moderate correlations (r = 0.38) of race result to distance covered. Significantly greater amounts of time were spent in the 5- to 10-km·h speed zones (p ≤ 0.05) during the race. Peak HR varied from 168 to 208 b·min among the competitors with the average HR being 168.6 ± 9.8 b·min. Significantly higher durations were spent in elevated HR zones (p ≤ 0.05) with participants spending 89.3% of their race within 80-100% of their age-predicted HRmax. Marathon SUP races seem to involve a high aerobic demand, with maintenance of near-maximal HRs required for the duration of the race. There is a high influence of tactical decisions and extrinsic variables to race results. These results provide a greater understanding of the physiological demands of distance events and may assist in the development of specialized training programs for SUP athletes.

Current Density Functional Theory Using Meta-Generalized Gradient Exchange-Correlation Functionals.

We present the self-consistent implementation of current-dependent (hybrid) meta-generalized gradient approximation (mGGA) density functionals using London atomic orbitals. A previously proposed generalized kinetic energy density is utilized to implement mGGAs in the framework of Kohn-Sham current density functional theory (KS-CDFT). A unique feature of the nonperturbative implementation of these functionals is the ability to seamlessly explore a wide range of magnetic fields up to 1 au (∼235 kT) in strength. CDFT functionals based on the TPSS and B98 forms are investigated, and their performance is assessed by comparison with accurate coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) data. In the weak field regime, magnetic properties such as magnetizabilities and nuclear magnetic resonance shielding constants show modest but systematic improvements over generalized gradient approximations (GGA). However, in the strong field regime, the mGGA-based forms lead to a significantly improved description of the recently proposed perpendicular paramagnetic bonding mechanism, comparing well with CCSD(T) data. In contrast to functionals based on the vorticity, these forms are found to be numerically stable, and their accuracy at high field suggests that the extension of mGGAs to CDFT via the generalized kinetic energy density should provide a useful starting point for further development of CDFT approximations.