Object
Title: Global optimization using automatic differentiation: Application to quantum chemistry
Contributor:
Subtitle:
Shape Optimization and Scientific Computations
Group publication title:
Abstract:
We present a new optimization method and one of its applications in quantum chemistry. The problem is to find the most stable configurations of sodium clusters. We have to minimize a weighted sum of eigenvalues of the Hamiltonian operator which corresponds to the energy of the molecules. According to the Rellich theorem, the eigenvalues/eigenvectors are analytic when the matrix follows an analytic path. ; Using automatic differentiation, we compute higher-order derivatives of the matrix. The eigenvalue/eigenvector derivatives are calculated by solving several factorized linear systems. The higher-order derivative method is used to obtain an explicit solution of the cost function (Taylor's expansion). ; This approach leads to a new global optimization algorithm whose idea is as follows: if we apply the optimality condition to the approximated cost function, we obtain a polynomial equation. We find its roots. The "best" zeros are used to restart the algorithm with a new search direction. ; This algorithm presents a natural way of parallelization: computation of Taylor's expansion and its minima in many directions can be performed independently. This method applied to our chemical problem gives very promising results. All the lowest energies of small sodium clusters have been found. This optimization algorithm can also be applied in dynamics of mechanical structures.
Publisher:
Zielona Góra: Uniwersytet Zielonogórski
Resource Identifier:
Pages:
Source:
AMCS, volume 6, number 2 (1996) ; click here to follow the link
Language:
Rights:
Biblioteka Uniwersytetu Zielonogórskiego
Object collections:
- Repository > Faculties > Faculty of Computer, Electrical and Control Engineering
- Repository > Types of work > Articles
- Repository > Scientific journals and UZ publishing series > International Journal of Applied Mathematics and Computer Science (AMCS)
- Repository > Scientific journals and UZ publishing series > International Journal of Applied Mathematics and Computer Science (AMCS) > International Journal of Applied Mathematics and Computer Science (AMCS) (1996)
Last modified:
Sep 2, 2021
In our library since:
Nov 17, 2020
Number of object content hits:
59
All available object's versions:
https://zbc.uz.zgora.pl/repozytorium/publication/64447
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International Journal of Applied Mathematics and Computer Science (AMCS)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 26 (2016)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 25 (2015)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 24 (2014)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 23 (2013)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 22 (2012)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 21 (2011)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 20 (2010)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 19 (2009)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 18 (2008)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 17 (2007)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 16 (2006)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 15 (2005)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 13 (2003)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 12 (2002)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 11 (2001)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 10 (2000)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 9 (1999)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 8 (1998)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 7 (1997)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 6 (1996)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 6, number 1 (1996)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 6, number 2 (1996)
- Thickness optimization of a geometrically non-linear arch at a limit point
- Mathematical modelling and numerical simulation of induction heating processes
- Theoretical and numerical estimates of instantaneous Lyapunov exponents of quasi-geostrophic ocean dynamics
- Shape optimal design for a fluid-heat coupled system
- Global optimization using automatic differentiation: Application to quantum chemistry
- Domain optimization problems for parabolic control systems
- Sensitivity analysis of buckling loads of physically non-linear frames using dynamic and static criteria
- A full-stress technique for structural shape optimization
- A simple method for improving the accuracy and convergence of FEM computations
- Handling the chemical part in large air pollution models
- Domain optimization problem for stationary heat equation
- LAPACK for Fortran 90
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 6, number 3 (1996)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 6, number 4 (1996)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 6, number 1 (1996)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 5 (1995)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 4 (1994)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 3 (1993)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 2 (1992)
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International Journal of Applied Mathematics and Computer Science (AMCS),volume 1 (1991)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 26 (2016)
| Edition name | Date |
|---|---|
| Global optimization using automatic differentiation: Application to quantum chemistry | Sep 2, 2021 |
