Abstract
Optimal control theory (OCT) is a branch of mathematics that deals with the problem of finding optimal trajectories for dynamical systems. It can be used in combination with time-dependent quantum mechanical methods that describe the evolution of the electronic and/or nuclear wave functions of atoms, molecules, or materials in the presence of external perturbations, such as electromagnetic fields. OCT may then find the optimal shape of those external perturbations: the optimal character is defined in terms of a functional of the behavior of the system. This chapter provides a brief description of the basic elements of the theory and an overview of its applications to quantum dynamics and electronic structure.
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References
Attaccalite C, Moroni S, Gori-Giorgi P, Bachelet G (2002) Correlation energy and spin polarization in the 2D electron gas. Phys Rev Lett 88(25):256601
Beck M, Jackle A, Worth G, Meyer HD (2000) The multiconfiguration time-dependent hartree (mctdh) method: a highly efficient algorithm for propagating wavepackets. Phys Rep 324(1):1–105
Bellman R (1957) Dynamic programming, 1st edn. Princeton University Press, Princeton
Bloembergen N, Zewail AH (1984) Energy redistribution in isolated molecules and the question of mode-selective laser chemistry revisited. J Phys Chem 88(23):5459–5465
Boltyanskii VG, Gamkrelidze RV, Pontryagin LS (1956) On the theory of optimal processes (Russian). Dokl Akad Nauk SSSR (NS) 110:7
Brif C, Chakrabarti R, Rabitz H (2010) Control of quantum phenomena: past present and future. New J Phys 12(7):075,008
Brumer P, Shapiro M (1986a) Coherent radiative control of unimolecular reactions. Three-dimensional results. Faraday Discuss Chem Soc 82:177–185
Brumer P, Shapiro M (1986b) Control of unimolecular reactions using coherent light. Chem Phys Lett 126(6):541–546
Brumer P, Shapiro M (1989) Coherence chemistry: controlling chemical reactions [with lasers]. Acc Chem Res 22(12):407–413
Brumer P, Shapiro M (2003) Principles of the quantum control of molecular processes. Wiley, New York
Castro A (2016) Theoretical shaping of femtosecond laser pulses for molecular photodissociation with control techniques based on Ehrenfest’s dynamics and time-dependent density functional theory. ChemPhysChem 17(11):1601–1607
Castro A, Appel H, Oliveira M, Rozzi CA, Andrade X, Lorenzen F, Marques MAL, Gross EKU, Rubio A (2006) octopus: a tool for the application of time-dependent density functional theory. Phys Status Solidi (b) 243:2465–2488
Castro A, Werschnik J, Gross EKU (2012) Controlling the dynamics of many-electron systems from first principles: a combination of optimal control and time-dependent density-functional theory. Phys Rev Lett 109:153,603
Gaubatz U, Rudecki P, Becker M, Schiemann S, Külz M, Bergmann K (1988) Population switching between vibrational levels in molecular beams. Chem Phys Lett 149(5):463–468
Gómez Pueyo A, Budagosky M JA, Castro A (2016) Optimal control with nonadiabatic molecular dynamics: application to the coulomb explosion of sodium clusters. Phys Rev A 94:063421
Judson RS, Rabitz H (1992) Teaching lasers to control molecules. Phys Rev Lett 68:1500–1503
Kirk DE (1998) Optimal control theory. An introduction. Dover Publications, Inc., New York
Kosloff R, Rice SA, Gaspard P, Tersigni S, Tannor DJ (1989) Wavepacket dancing: achieving chemical selectivity by shaping light pulses. Chem Phys 139:201–220
Krausz F, Ivanov M (2009) Attosecond physics. Rev Mod Phys 81:163–234
Kuklinski JR, Gaubatz U, Hioe FT, Bergmann K (1989) Adiabatic population transfer in a three-level system driven by delayed laser pulses. Phys Rev A 40:6741–6744
Maiman TH (1960) Stimulated optical radiation in ruby. Nature 187:493–494
Marques MA, Maitra NT, Nogueira FM, Gross E, Rubio A (eds) (2012) Fundamentals of time-dependent density functional theory. Springer, Berlin/Heidelberg
Marques MAL, Castro A, Bertsch GF, Rubio A (2003) octopus: a first-principles tool for excited electron-ion dynamics. Comput Phys Commun 151:60–78
Mundt M, Tannor DJ (2009) Optimal control of interacting particles: a multi-configuration time-dependent Hartree-Fock approach. New J Phys 11(10):105038
Nest M, Klamroth T, Saalfrank P (2005) The multiconfiguration time-dependent Hartree-Fock method for quantum chemical calculations. J Chem Phys 122(12):124102
Newton I (1671) A letter of Mr. Isaac Newton, professor of the mathematics in the university of cambridge; containing his new theory about light and colors. Philos Trans 6:3075–3087
Peirce A, Dahleh M, Rabitz H (1988) Optimal control of quantum-mechanical systems: existence, numerical approximation, and applications. Phys Rev A 37(12):4950
Pontryagin LS, Boltyanskii VG, Gamkrelidze RV, Mishchenko EF (1962) The mathematical theory of optimal processes. Wiley, New York
Raab A (2000) On the Dirac-Frenkel/Mclachlan variational principle. Chem Phys Lett 319(5): 674–678
Rabitz H et al (2000) Whither the Future of Controlling Quantum Phenomena?. Science 288:824
Raghunathan S, Nest M (2011) Critical examination of explicitly time-dependent density functional theory for coherent control of dipole switching. J Chem Theory Comput 7(8):2492–2497
Räsänen E, Castro A, Werschnik J, Rubio A, Gross EKU (2007) Optimal control of quantum rings by terahertz laser pulses. Phys Rev Lett 98:157404
Rice SA, Zhao M (2000) Optical control of molecular dynamics. Wiley, New York
Runge E, Gross E (1984) Density-functional theory for time-dependent systems. Phys Rev Lett 52:997–1000
Shi S, Rabitz H (1989) Selective excitation in harmonic molecular systems by optimally designed fields. Chem Phys 139:185–199
Shi S, Woody A, Rabitz H (1988) Optimal control of selective vibrational excitation in harmonic linear chain molecules. J Chem Phys 88(11):6870
Tannor DJ, Rice SA (1985) Control of selectivity of chemical reaction via control of wave packet evolution. J Chem Phys 83(10):5013–5018
Tannor DJ, Kosloff R, Rice SA (1986) Coherent pulse sequence induced control of selectivity of reactions: exact quantum mechanical calculations. J Chem Phys 85(10):5805–5820
van Leeuwen R (1999) Mapping from densities to potentials in time-dependent density-functional theory. Phys Rev Lett 82(19):3863–3866
van Leeuwen R, Stefanucci G (2013) Nonequilibrium many-body theory of quantum systems. Cambridge University Press, Cambridge
Walkenhorst J, De Giovannini U, Castro A, Rubio A (2016) Tailored pump-probe transient spectroscopy with time-dependent density-functional theory: controlling absorption spectra. Eur Phys J B 89(5):128
Weiner AM (2000) Femtosecond pulse shaping using spatial light modulators. Rev Sci Instrum 71(5):1929–1960
Zhu W, Rabitz H (1998) A rapid monotonically convergent iteration algorithm for quantum optimal control over the expectation value of a positive definite operator. J Chem Phys 109(2):385–391
Acknowledgements
This work was supported by the Ministerio de Economía y Competitividad (MINECO) grants FIS2013-46159-C3-P2, FIS2017-82426-P and FIS2014-61301-EXP.
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Castro, A. (2018). Optimal Control Theory for Electronic Structure Methods. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling . Springer, Cham. https://doi.org/10.1007/978-3-319-42913-7_4-1
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DOI: https://doi.org/10.1007/978-3-319-42913-7_4-1
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