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Rationale & objectiveRecent studies evaluated and proposed new race-neutral, creatinine-based glomerular filtration rate (GFR) estimation equations. The performance of these equations in diverse potential living kidney donors requires study.Study designCross-sectional study.Setting & participants637 potential living kidney donors from one tertiary hospital with serum creatinine concentration measurement and GFR measurement by iohexol plasma clearance between October 2016 and December 2020.ExposureCreatinine-based estimation of GFR by Chronic Kidney Disease Epidemiology Collaboration (2009, CKDEPI09; 2021, CKDEPI21) and Modification of Diet in Renal Disease equations with and without inclusion of race coefficient, where applicable.OutcomesEquation bias, precision, accuracy, and accurate classification of GFR as equal to and above or below 80 mL/min/1.73 m2.Analytical approachGFR estimation equation performance compared to measured GFR (mGFR) by iohexol clearance.ResultsThe median bias of the CKDEPI21 equation underestimated mGFR by 2.8 mL/min/1.73 m2. The bias in the Black subgroup underestimated mGFR by 9.0 mL/min/1.73 m2. Compared to CKDEPI09 with and without race adjustment, the accuracy of CKDEPI21 increased across all subgroups. On average, 3.9% of individuals were misclassified by CKDEPI21 as having a GFR greater than, and 8.9% misclassified less than, 80 mL/min/1.73 m2, compared to 3.1% and 13.2% for CKDEPI09 with race adjustment, respectively. Total misclassification (either above or below 80 mL/min/1.73 m2) was 16.3% for CKDEPI21 and 16.0% for CKDEPI09 (with race adjustment).LimitationsLimited sample of individuals identifying as Black. Lack of cystatin C data.ConclusionsIn our potential living donor sample, GFR estimation by creatinine-based CKDEPI21 is less biased and more accurate than previous creatinine-based estimated GFR equations. When evaluated by race, this summative improvement remains in individuals identifying as Asian, Hispanic, or White. More external validation is needed to assess whether the new equation is an improvement over the previous CKDEPI equation with a race coefficient.

The calculation of quantum effects on temperature dependence of bimolecular reaction rates is reported.

The convergence behavior of Mo\ller-Plesset (MP) perturbation series is governed by the singularity structure of the energy, with the energy treated as a function of the perturbation parameter. Singularity locations, determined from quadratic approximant analysis of high-order series, are presented for a variety of atoms and small molecules. These results can be used as benchmarks for understanding the convergence of low-order methods such as MP4 and for developing and testing summation methods that model the singularity structure. The positions and types of singularities confirm previous qualitative predictions based on functional analysis of the Schrödinger equation. [ABSTRACT FROM AUTHOR]

It has been suggested [F. H. Stillinger, J. Chem. Phys. 112, 9711 (2000)] that the convergence or divergence of Mo\ller-Plesset perturbation theory is determined by a critical point at a negative value of the perturbation parameter z at which an electron cluster dissociates from the nuclei. This conjecture is examined using configuration-interaction computations as a function of z and using a quadratic approximant analysis of the high-order perturbation series. Results are presented for the He, Ne, and Ar atoms and the hydrogen fluoride molecule. The original theoretical analysis used the true Hamiltonian without the approximation of a finite basis set. In practice, the singularity structure depends strongly on the choice of basis set. Standard basis sets cannot model dissociation to an electron cluster, but if the basis includes diffuse functions then it can model another critical point corresponding to complete dissociation of all the valence electrons. This point is farther from the origin of the z plane than is the critical point for the electron cluster, but it is still close enough to cause divergence of the perturbation series. For the hydrogen fluoride molecule a critical point is present even without diffuse functions. The basis functions centered on the H atom are far enough from the F atom to model the escape of electrons away from the fluorine end of the molecule. For the Ar atom a critical point for a one-electron ionization, which was not previously predicted, seems to be present at a positive value of the perturbation parameter. Implications of the existence of critical points for quantum-chemical applications are discussed. [ABSTRACT FROM AUTHOR]

Extrapolation methods that accelerate the convergence of coupled-cluster energy sequences toward the full configuration–interaction (FCI) limit are developed and demonstrated for a variety of atoms and small molecules for which FCI energies are available, and the results are compared with those from Møller–Plesset (MP) perturbation theory. For the coupled-cluster sequence SCF, CCSD, CCSD(T), a method based on a continued-fraction formalism is found to be particularly successful. It yields sufficient improvement over conventional CCSD(T) that the results become competitive with, and often better than, results from the MP4-qλ method (MP4 summed with quadratic approximants and λ transformation). The sequence SCF, CCSD, CCSDT can be extrapolated with a quadratic approximant but the results are not appreciably more accurate than those from the CCSD(T) continued fraction. Singularity analysis of the MP perturbation series provides a criterion for estimating the accuracy the CCSD(T) continued fraction. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Details the application of the perturbation theory to a pair of coupled oscillators with cubic anharmonicity. Large-order perturbation theory shown to be more efficient computationally than numerical diagonalization of the Hamiltonian; Quadratic Pade summation of the energy expansions yielding convergent results for the real and imaginary parts of resonance eigenvalues.

The 1/D expansion, where D is the dimensionality of space, offers a promising new approach for obtaining highly accurate solutions to the Schrödinger equation for atoms and molecules. The method typically employs an asymptotic expansion calculated to rather large order. Computation of the expansion coefficients has been feasible for very small systems, but extending the existing computational techniques to systems with more than three degrees of freedom has proved difficult. We present a new algorithm that greatly facilitates this computation. It yields exact values for expansion coefficients, with less roundoff error than the best alternative method. Our algorithm is formulated completely in terms of tensor arithmetic, which makes it easier to extend to systems with more than three degrees of freedom and to excited states, simplifies the development of computer codes, simplifies memory management, and makes it well suited for implementation on parallel computer architectures. We formulate the algorithm for the calculation of energy eigenvalues, wave functions, and expectation values for an arbitrary many-body system and give estimates of storage and computational costs. [ABSTRACT FROM AUTHOR]