{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,10]],"date-time":"2025-06-10T18:45:22Z","timestamp":1749581122639},"publisher-location":"Berlin, Heidelberg","reference-count":19,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540632429"},{"type":"electronic","value":"9783642583605"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1999]]},"DOI":"10.1007\/978-3-642-58360-5_23","type":"book-chapter","created":{"date-parts":[[2011,7,22]],"date-time":"2011-07-22T13:25:05Z","timestamp":1311341105000},"page":"412-420","source":"Crossref","is-referenced-by-count":9,"title":["Symplectic Multiple-Time-Stepping Integrators for Quantum-Classical Molecular Dynamics"],"prefix":"10.1007","author":[{"given":"Peter","family":"Nettesheim","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sebastian","family":"Reich","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"23_CR1","doi-asserted-by":"crossref","unstructured":"A.I. Arnold. Mathematical methods of classical mechanics. Springer-Verlag, 1978.","DOI":"10.1007\/978-1-4757-1693-1"},{"key":"23_CR2","doi-asserted-by":"publisher","first-page":"1117","DOI":"10.1007\/BF02188219","volume":"74","author":"G Benettin","year":"1994","unstructured":"G. Benettin and A. Giorgilli. On the Hamiltonian interpolation of near to the identity symplectic mappings with application to symplectic integration algorithms. J. Statist Phys., 74: 1117\u20131143, 1994.","journal-title":"J. Statist Phys"},{"key":"23_CR3","doi-asserted-by":"publisher","first-page":"13464","DOI":"10.1021\/j100153a009","volume":"97","author":"HJC Berendsen","year":"1993","unstructured":"H.J.C. Berendsen and J. Mavri. Quantum simulation of reaction dynamics by density matrix evolution. J. Phys. Chem., 97: 13464\u201313468, 1993.","journal-title":"J. Phys. Chem"},{"key":"23_CR4","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1006\/jcph.1993.1220","volume":"109","author":"JJ Biesiadecki","year":"1993","unstructured":"J.J. Biesiadecki and R.D. Skeel. Dangers of multiple-time-step methods. J. Comput. Phys., 109: 318\u2013328, 1993.","journal-title":"J. Comput. Phys"},{"issue":"3","key":"23_CR5","doi-asserted-by":"publisher","first-page":"1074","DOI":"10.1063\/1.471952","volume":"105","author":"FA Bornemann","year":"1996","unstructured":"F.A. Bornemann, P. Nettesheim, and Ch. Sch\u00fctte. Quantum-classical molecular dynamics as an approximation for full quantum dynamics. J. Chem. Phys., 105(3): 1074\u20131083, 1996.","journal-title":"J. Chem. Phys"},{"key":"23_CR6","unstructured":"F.A. Bornemann and Ch. Sch\u00fctte. On the singular limit of the quantumclassical molecular dynamics model. Preprint SC 97\u201307, ZIB Berlin, 1997. Submitted to SIAM J. Appl. Math."},{"key":"23_CR7","doi-asserted-by":"publisher","first-page":"7242","DOI":"10.1063\/1.463550","volume":"97","author":"A Garc\u00eda-Vela","year":"1992","unstructured":"A. Garc\u00eda-Vela, R.B. Gerber, and D.G. Imre. Mixed quantum wave packet\/classical trajectory treatment of the photodissociation process ArHCl \u2192 Ar+H+Cl. J. Chem. Phys., 97: 7242\u20137250, 1992.","journal-title":"J. Chem. Phys"},{"key":"23_CR8","doi-asserted-by":"publisher","first-page":"3022","DOI":"10.1063\/1.444225","volume":"66","author":"RB Gerber","year":"1982","unstructured":"R.B. Gerber, V. Buch, and M.A. Ratner. Time-dependent self-consistent field approximation for intramolecular energy transfer. J. Chem. Phys., 66: 3022\u20133030, 1982.","journal-title":"J. Chem. Phys"},{"key":"23_CR9","doi-asserted-by":"publisher","first-page":"7099","DOI":"10.1063\/1.471428","volume":"104","author":"SK Gray","year":"1996","unstructured":"S.K. Gray and D.E. Manolopoulos. Symplectic integrators tailored to the timedependent Schr\u00f6dinger equation. J. Chem. Phys., 104: 7099\u20137112, 1996.","journal-title":"J. Chem. Phys"},{"key":"23_CR10","unstructured":"M. Hochbruck and Ch. Lubich. A bunch of time integrators for quantum\/classical molecular dynamics, this volume."},{"key":"23_CR11","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1007\/s002110050271","volume":"76","author":"E Hairer","year":"1997","unstructured":"E. Hairer and Ch. Lubich. The life-span of backward error analysis for numerical integrators. Numer. Math., 76: 441\u2013462, 1997.","journal-title":"Numer. Math"},{"key":"23_CR12","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1016\/0009-2614(96)00471-X","volume":"256","author":"P Nettesheim","year":"1996","unstructured":"P. Nettesheim, F.A. Bornemann, B. Schmidt, and Ch. Sch\u00fctte. An explicit and symplectic integrator for quantum-classical molecular dynamics. Chemical Physics Letters, 256: 581\u2013588, 1996.","journal-title":"Chemical Physics Letters"},{"key":"23_CR13","unstructured":"P. Nettesheim and Ch. Sch\u00fctte. Numerical integrators for quantum-classical molecular dynamics, this volume."},{"key":"23_CR14","doi-asserted-by":"crossref","unstructured":"S. Reich. Backward error analysis for numerical integrators. SIAM J. Numer. Anal., to appear, 1999.","DOI":"10.1137\/S0036142997329797"},{"key":"23_CR15","doi-asserted-by":"crossref","unstructured":"S. Reich. Preservation of adiabatic invariants under symplectic discretization. Applied Numerical Mathematics, to appear, 1998.","DOI":"10.1016\/S0168-9274(98)00032-4"},{"key":"23_CR16","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/0301-0104(96)00066-3","volume":"208","author":"U Schmitt","year":"1996","unstructured":"U. Schmitt and J. Brinkmann. Discrete time-reversible propagation scheme for mixed quantum classical dynamics. Chem. Phys., 208: 45\u201356, 1996.","journal-title":"Chem. Phys"},{"key":"23_CR17","unstructured":"U. Schmitt. Gemischt klassisch-quantenmechanische Molekulardynamik im Liouville-Formalismus. Ph.D. thesis (in german), Darmstadt, 1997."},{"key":"23_CR18","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-3093-4","volume-title":"Numerical Hamiltonian Systems","author":"JM Sanz-Serna","year":"1994","unstructured":"J.M. Sanz-Serna and M.P. Calvo. Numerical Hamiltonian Systems. Chapman and Hall, London, 1994."},{"key":"23_CR19","doi-asserted-by":"publisher","first-page":"1990","DOI":"10.1063\/1.463137","volume":"97","author":"M Tuckerman","year":"1992","unstructured":"M. Tuckerman, B.J. Berne, and G. Martyna. Reversible Multiple Time Scale Molecular Dynamics. J. Chem. Phys., 97: 1990\u20132001, 1992.","journal-title":"J. Chem. Phys"}],"container-title":["Lecture Notes in Computational Science and Engineering","Computational Molecular Dynamics: Challenges, Methods, Ideas"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-58360-5_23.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,24]],"date-time":"2020-11-24T03:33:18Z","timestamp":1606188798000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-58360-5_23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999]]},"ISBN":["9783540632429","9783642583605"],"references-count":19,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-58360-5_23","relation":{},"ISSN":["1439-7358"],"issn-type":[{"type":"print","value":"1439-7358"}],"subject":[],"published":{"date-parts":[[1999]]}}}