Time-Dependent Properties and Real-Time Dynamics from Quasiclassical Quantum Simulations of Complex Systems

• Applicant: Professor Dr. Dominik Marx
• Subject Area: Theoretical Chemistry: Electronic Structure, Dynamics, Simulation
• Term: from 2001 to 2012
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5362432

• Final Report Year: 2012

Final Report Abstract

Computing and assigning the infrared spectra of molecules that undergo pronounced large–amplitude motion, which defines the class of so–called fluxional or floppy molecules, is a continuous challenge to theoretical chemistry once a sufficiently large number of coupled degrees of freedom is involved. The difficulty is to solve with sufficient accuracy the underlying quantum dynamics, which is traditionally done by solving the Schrödinger equation on a previously computed potential energy surface. In this project, a radical alternative to this in principle quasi–exact Schrödinger–based approach – relying instead on the Feynman–Kac formulation of quantum statistical mechanics in terms of path integrals – has been proposed, validated, and applied to key molecular spectroscopy problems. The formalism is based on the concept of ab initio path integral molecular dynamics as extended to quasiclassical time evolution. It allows one to compute infrared spectra at finite temperatures from the time–autocorrelation function of the dipole operator of systems involving on the order of 10 to 100 strongly coupled degrees of freedom. The potential energy surface and the dipole moment are not precomputed in terms of parameterized functions, but are generated “on the fly” as the molecular dynamics simulation proceeds, which avoids the “curse of dimensionality” also at this level. The novel quasiclassical method can not only be applied to floppy molecules or weakly–bound clusters in the gas phase, but also to liquids or solids, where the limitations of the involved approximations have also been delineated. In the analysis step, the generated trajectories are projected onto conformational and/or permutational contributions of the fluxional molecule via a consistent time correlation formalism. This allows one not only to assign infrared spectra of floppy molecules in terms of the motion of atoms, but also to compute approximately dynamical information such as transition rates and lifetimes. This machinery has been applied to protonated methane, CH+5, and all its H/D isotopologues and resulted into the reproduction of the experimental spectra as well as their assignment in terms of intra–molecular molecular motions and timescales. Furthermore, the technique has been successfully used to reproduce and to assign the experimental spectra of microsolvated Zundel and Hydronium cations, which have been measured by messenger vibrational spectroscopy using tagging with H2 molecules. Our “molecular dynamics approach to infrared spectroscopy” can be widely applied to problems tackled in modern experimental vibrational spectroscopy that addresses molecules and systems of ever increasing complexity including solvated molecules.

Publications

• Dem Geheimnis einer “Supersäure” auf der Spur. Akademie Aktuell
  A. Witt, S. D. Ivanov, and D. Marx
  
• Quantum corrections to classical time–correlation functions: Hydrogen bonding and anharmonic floppy modes. J. Chem. Phys. 121, 3973–3983 (2004)
  R. Ramírez, T. López–Ciudad, P. Kumar P, and D. Marx
  
• Understanding the Infrared Spectrum of Bare CH5+. Science 309, 1219–1222 (2005)
  O. Asvany, P. Kumar P, B. Redlich, I. Hegemann, S. Schlemmer, and D. Marx
  
• Understanding hydrogen scrambling and infrared spectrum of bare CH5+ based on ab initio simulations. Phys. Chem. Chem. Phys. 8, 573–586 (2006)
  P. Kumar P. and D. Marx
  
• Microsolvation of Protonated Methane: Structures and Energetics of CH5+ (H2 )n. J. Phys. Chem. A 112, 12510–12517 (2008)
  A. Witt, S. D. Ivanov, H. Forbert, and D. Marx
  
• On the applicability of centroid and ring polymer path integral molecular dynamics for vibrational spectroscopy. J. Chem. Phys. 130, 194510-1–15 (2009)
  A. Witt, S. D. Ivanov, M. Shiga, H. Forbert, and D. Marx
  
• Quantum–induced symmetry breaking explains infrared spectra of CH5+ isotopologues. Nat. Chem. 2, 298–302 (2010)
  S. D. Ivanov, O. Asvany, A. Witt, E. Hugo, G. Mathias, B. Redlich, D. Marx, and S. Schlemmer
  
• Theoretical Messenger Spectroscopy of Microsolvated Hydronium and Zundel Cations. Angew. Chem. Int. Ed. 49, 7346–7349 (2010)
  M. Baer, D. Marx, and G. Mathias
  
• Assigning Predissociation Infrared Spectra of Microsolvated Hydronium Cations H3O+ · (H2 )n (n = 0, 1, 2, 3) by Ab Initio Molecular Dynamics. ChemPhysChem 12, 1906–1915 (2011)
  M. Baer, D. Marx, and G. Mathias
  
• Quantum Molecular Dynamics Calculations of Ultrafast Timescales and Infrared Spectra of Protonated Methane: Quantifying Isotope-Specific Lifetimes. J. Phys. Chem. Lett. 2, 1377–1381 (2011)
  A. Witt, S. D. Ivanov, G. Mathias, and D. Marx
  
• Infrared Spectroscopy of Fluxional Molecules from (ab Initio) Molecular Dynamics: Resolving Large-Amplitude Motion, Multiple Conformations, and Permutational Symmetries. J. Chem. Theory Comput. 8, 224–234 (2012)
  G. Mathias, S. D. Ivanov, A. Witt, M. D. Baer, and D. Marx
  (See online at https://doi.org/10.1021/ct2006665)