scholarly journals Quantum alchemy beyond singlets: Bonding in diatomic molecules with hydrogen

2021 ◽  
Author(s):  
Emily Eikey ◽  
Alex Maldonado ◽  
Charles Griego ◽  
Guido Falk von Rudorff ◽  
John Keith
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Chemical Space ◽  
Diatomic Molecules ◽  
Taylor Series Expansion ◽  
Electron Affinities ◽  
Thermodynamic Cycles ◽  
Error Cancellation ◽  
Wide Range ◽  
Taylor Series Expansions

Bonding energies are key for the relative stability of molecules in chemical space. Therefore methods employed to search for relevant molecules in chemical space need to capture the bonding behavior for a wide range of molecules, including radicals. In this work, we investigate the ability of quantum alchemy to do so for exploring hypothetical chemical compounds, here diatomic molecules involving hydrogen with various electronic structures. We evaluate equilibrium bond lengths, ionization ener- gies, and electron affinities of these fundamental systems. We compare and contrast how well manual quantum alchemy calculations, i.e. quantum mechanical calculations in which the nuclear charge is altered, and quantum alchemy approximations using a Taylor series expansion can predict these molecular properties. We also investigate the extent of error cancellation of these approaches in terms of ionization energies and electron affinities when using thermodynamic cycles. Our results suggest that the accuracy of Taylor series expansions are greatly improved by error cancellation in thermodynamic cycles, and errors also appear to be generally system-dependent. Taken together, this work provides insights into how quantum alchemy predictions us- ing a Taylor series expansion may be applied to future studies of non-singlet systems as well as which challenges remain open for these cases.

scholarly journals Evaluating quantum alchemy of atoms with thermodynamic cycles: Beyond ground electronic states

2021 ◽  
Author(s):  
Emily Eikey ◽  
Alex Maldonado ◽  
Charles Griego ◽  
Guido Falk von Rudorff ◽  
John Keith
Keyword(s):  
Taylor Series ◽  
Reference Data ◽  
Chemical Space ◽  
Taylor Series Expansion ◽  
Finite Basis ◽  
Basis Set ◽  
Thermodynamic Cycles ◽  
Computational Screening ◽  
Method Accuracy ◽  
Net Charges

Due to the sheer size of chemical and materials space, high throughput computational screening thereof will require the development of new computational methods that are accurate, efficient, and transferable. These methods need to be applicable to electron configurations beyond ground states. To this end, we have systematically studied the applicability of quantum alchemy predictions using a Taylor series expansion on quantum mechanics (QM) calculations for single atoms with different electronic structures arising from different net charges and electron spin multiplicities. We first compare QM method accuracy to experimental quantities including first and second ionization energies, electron affinities, and multiplet spin energy gaps for a baseline understanding of QM reference data. We then investigate the intrinsic accuracy of an approach we call "manual" quantum alchemy schemes compared to the same QM reference data, which employ QM calculations where the basis set of a different element is used for an atom as the limit case of quantum alchemy. We then discuss the reliability of quantum alchemy based on Taylor series approximations at different orders of truncation. Overall, we find that the errors from finite basis set treatments in quantum alchemy are significantly reduced when thermodynamic cycles are employed, which points out a route to improve quantum alchemy in explorations of chemical space. This work establishes important technical aspects that impact the accuracy of quantum alchemy predictions using a Taylor series and provides a foundation for further quantum alchemy studies.

Full-Scale Bounds Estimation for the Nonlinear Transient Heat Transfer Problems with Interval Uncertainties

2021 ◽  
pp. 2150026
Author(s):  
Ruifei Peng ◽  
Haitian Yang ◽  
Yanni Xue
Keyword(s):  
Heat Transfer ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Transient Heat Transfer ◽  
High Fidelity ◽  
Interval Scale ◽  
Nonlinear Transient ◽  
Transfer Problems ◽  
Derivatives Of

A package solution is presented for the full-scale bounds estimation of temperature in the nonlinear transient heat transfer problems with small or large uncertainties. When the interval scale is relatively small, an efficient Taylor series expansion-based bounds estimation of temperature is stressed on the acquirement of first and second-order derivatives of temperature with high fidelity. When the interval scale is relatively large, an optimization-based approach in conjunction with a dimension-adaptive sparse grid (DSG) surrogate is developed for the bounds estimation of temperature, and the heavy computational burden of repeated deterministic solutions of nonlinear transient heat transfer problems can be efficiently alleviated by the DSG surrogate. A temporally piecewise adaptive algorithm with high fidelity is employed to gain the deterministic solution of temperature, and is further developed for recursive adaptive computing of the first and second-order derivatives of temperature. Therefore, the implementation of Taylor series expansion and the construction of DSG surrogate are underpinned by a reliable numerical platform. The parallelization is utilized for the construction of DSG surrogate for further acceleration. The accuracy and efficiency of the proposed approaches are demonstrated by two numerical examples.

scholarly journals Weighted Measurement Fusion Particle Filter for Nonlinear Systems with Correlated Noises

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3242 ◽  
Author(s):  
Ke Wei Zhang ◽  
Gang Hao ◽  
Shu Li Sun
Keyword(s):  
Nonlinear Systems ◽  
Particle Filter ◽  
Series Expansion ◽  
Taylor Series ◽  
Asymptotic Optimality ◽  
Taylor Series Expansion ◽  
Full Rank ◽  
Expansion Method ◽  
Least Square ◽  
Correlated Noises

The multi-sensor information fusion particle filter (PF) has been put forward for nonlinear systems with correlated noises. The proposed algorithm uses the Taylor series expansion method, which makes the nonlinear measurement functions have a linear relationship by the intermediary function. A weighted measurement fusion PF (WMF-PF) was put forward for systems with correlated noises by applying the full rank decomposition and the weighted least square theory. Compared with the augmented optimal centralized fusion particle filter (CF-PF), it could greatly reduce the amount of calculation. Moreover, it showed asymptotic optimality as the Taylor series expansion increased. The simulation examples illustrate the effectiveness and correctness of the proposed algorithm.

scholarly journals Bounds on the Third Order Hankel Determinant for Certain Subclasses of Analytic Functions

2017 ◽  
Vol 25 (3) ◽  
pp. 199-214
Author(s):  
S.P. Vijayalakshmi ◽  
T.V. Sudharsan ◽  
Daniel Breaz ◽  
K.G. Subramanian
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Analytic Functions ◽  
Unit Disc ◽  
Taylor Series Expansion ◽  
Upper Bounds ◽  
Hankel Determinant ◽  
Third Order ◽  
The Third

Abstract Let A be the class of analytic functions f(z) in the unit disc ∆ = {z ∈ C : |z| < 1g with the Taylor series expansion about the origin given by f(z) = z+ ∑n=2∞ anzn, z ∈∆ : The focus of this paper is on deriving upper bounds for the third order Hankel determinant H3(1) for two new subclasses of A.

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