Axel U. J. Lode
Physikalisch-Chemisches Institut
Universität Heidelberg

Alexej I. Streltsov
Physikalisch-Chemisches Institut
Universität Heidelberg

Kaspar Sakmann
Physikalisch-Chemisches Institut
Universität Heidelberg

Ofir E. Alon
Department of Physics
University of Haifa at Oranim, Israel

Lorenz S. Cederbaum
Physikalisch-Chemisches Institut
Universität Heidelberg

The tunneling process is a phenomenon which lies at the very heart of quantum mechanics. A rich variety of systems in nature undergo it - for many of them the characteristics of the process play a key role, e.g., alpha decay, fusion, fission, photoassociation, and -dissociation. The main aim of the study is to understand the process of quantum tunneling of initially-coherent ultracold one-dimensional many-boson systems with repulsive interactions to open space. We use the MCTDHB method ([Phys. Rev. Lett 99, 030402 (2007)], [Phys. Rev. A 77, 033613 (2008)] and http://MCTDHB.org) to solve the underlying many-boson time-dependent Schrödinger equation numerically exactly. The results reveal that the emission of the bosons to open space is accompanied by fragmentation - a dynamical loss of the coherence in a very non-trivial way - the source bosons remain coherent while the emitted ones do not. The mechanism behind the dynamical fragmentation is a quantum superposition of many single-particle processes taking place simultaneously. See Figure and arxiv:1202.3447 for more details. To assess the way of the loss of coherence during the dynamical fragmentation process, we provide a movie of the correlation function in momentum space around the emerging peak structure. It prooves that the coherence stays in the source while it is lost solely and quickly for the escaping particles. This is because only for the corresponding momenta the bosons become correlated and |g⁽¹⁾|²→ 0.

Link

• http://MCTDHB.org

Software

• OpenMPI, OpenMP, Gnuplot, Intel MKL, Intel Fortran

Publications

• Wave chaos as signature for depletion of a Bose-Einstein condensate, Iva Brezinova, Axel U. J. Lode, Alexej I. Streltsov, Ofir E. Alon, Lorenz S. Cederbaum, Joachim Burgdrfer, to appear in Phys. Rev. A. (2012). arxiv:1005.0093
• How does an interacting many-body system tunnel through a potential barrier to open space?, Axel U. J. Lode, Alexej I. Streltsov, Kaspar Sakmann, Ofir E. Alon, Lorenz S. Cederbaum, submitted to Proceedings of the National Academy of the Sciences (2012). arxiv:1202.3447
• Recursive formulation of the multiconfigurational time-dependent Hartree method for fermions, bosons and mixtures thereof in terms of one-body density operators, Ofir E. Alon, Alexej I. Streltsov, Kaspar Sakmann, Axel U.J. Lode, Julian Grond, Lorenz S. Cederbaum, J. Chem. Phys. (2011). http://dx.doi.org/10.1016/j.chemphys.2011.09.026
• The Multiconfigurational time-dependent Hartree for Bosons package, version 2.2, A. I. Streltsov, K. Sakmann, A. U. J. Lode, O. E. Alon, L. S. Cederbaum. http://MCTDHB.org
• Exact Decay and Tunneling of Interacting Few-Boson Systems, Poster at Center for Quantum Dynamics Poster Session, Heidelberg, Germany.
• Tunneling Dynamics of Open Ultracold Bosonic Systems, Poster at Quantum Science and Technologies, Rovereto, Italy.
• Tunneling Dynamics of Open Ultracold Bosonic Systems, Poster at Finite-Temperature Non-Equilibrium Superfluid Systems, Heidelberg, Germany.
• Recent Developments in the MCTDHB Package, Talk at Annual Colloquium of the HGS, Heidelberg, Germany.
• Tunneling Dynamics of Open Ultracold Bosonic Systems, Talk at Hybrid Quantum Systems, Heidelberg, Germany.

Lipi Thukral
Interdisciplinary Center for Scientific Computing (IWR)
University of Heidelberg

The folding mechanism of beta-hairpins, secondary structural elements in proteins, represents an issue of intense ongoing debate in current protein folding research. Small peptide folding simulations and experiments characterize the dynamics and molecular mechanisms of the early events of folding. Computationally, adequate sampling is required to cover the entire conformational space of the protein of interest. In our present work, we perform replica-exchange molecular dynamics (REMD) simulations of Peptide 1, a 15-residue beta-hairpin peptide.

We simulated ~650 ns each for 32 replica - for a total simulation time of 20.8 μs. The adjoining Figure shows the time evolution of conformational transitions at various temperatures. The map is colored according to R parameter, a conformational order parameter. A value of R ≈ 5 indicates formation of the native β-hairpin and a value ≈ 2-4 indicates an unfolded peptide. The trajectories were started from folded peptide and due to the inherent nature of REMD, the structures in each trajectory unfolds-folds again, providing multiple transitions.

Currently, we are analyzing the data in detail to extract thermodynamic quantities like melting curve, enthalpy, entropy, free energies, etc. The data will also be validated with already published experimental data. The results presented here reveal large-scale protein folding simulations and the work will characterize thermodynamic properties of peptide folding in detail.

Software

• Gromacs

Publications

• Thermodynamic properties of a 15-residue peptide revealed using replica-exchange molecular dynamics simulations. Thukral L, Alekozai E, Smith JC, Daidone I. in preparation.

Uzma Habib
Anorganisch-Chemisches Institut
Universität Heidelberg

Nitrate reductase (Nars), a molybdoenzyme, belongs to the DMSO reductase family. The first W-containing nitrate reductase was isolated from Pyrobaculum aerophilum, a hyperthermophilic denitrifying archeon. It contains W as the metal cofactor but is otherwise identical to Mo-Nar previously purified from Pyrobaculum aerophilum grown at low tungstate concentration.  It demonstrates that the type of the metal cofactor is dependent on the environmental metal concentration. Several studies show that W can replace Mo as the active site metal in E.coli TMAO reductase, the Desulfovibrio alaskensis formate dehydrogenase, and the Rhodobacter capsulatus DMSO reductase. Active site model complexes, derived from the protein X-ray crystal structure of the E.coli NarGH enzyme, are under investigations to find: (i) The Effect on the reduction of nitrate when W replaces the Mo. (ii) The Energy barriers on the potential energy surface. (iii) The reason for the activity loss of Nars in the presence of W.

Software

• Gaussian

Publications

• Poster presentation, "Effect of Molybdenum and Tungsten on the reduction of nitrate in Nitrate Reductase, a DFT study", MOLMOD 2011 "Modeling of Molecular Properties", Heidelberg University, Heidelberg, Germany.

Mie Hoejer Vilhelmsen
Organisch-Chemisches Institut
Universität Heidelberg

Novel experimental investigations show that gold(I) in some catalytic processes can take up a dual role. One such reaction is in the hydroarylating-aromatization of arene-diynes which form substituted naphthalene compounds. However, to fully understand the reaction mechanism and especially the steps involving gold transfer the reaction and others displaying the same experimental characteristics will be theoretically examined.

Software

• Gaussian, Turbomole, Jaguar, Spartan

Markus Schröder
Physikalisch-Chemisches Institut
Universität Heidelberg

Within the current project, proton transfer processes, which can be classified as large amplitude motions, are to be studied. Currently, we investigate the proton transfer in malonaldehyde (see figure), a prototype system for studying proton transfer processes, by computing the tunneling splitting of the vibrational degrees of freedom. The internal degrees of freedom are strongly coupled which prohibits studies in reduced dimensionality. Instead the full, 21-dimensional wavefunction has to be deployed to obtain sufficiently accurate results.

The calculations are performed using the multi-configuration time-dependent Hartree (MCTDH) algorithm which approximates the exact wave function in terms of a sum of Hartree products. Low lying eigenstates of the system Hamiltonian have already been calculated by 'improved relaxation', a special feature of the MCTDH algorithm which uses a Krylov space method, the Davidson diagonalization, followed by imaginary time propagation of the single-particle functions.

MCTDH, in general, requires any operators such as the system Hamiltonian to be  of product form, i.e., expanded in a sum of products of one- or low-dimensional operators. This is usually the case for the kinetic energy, but not for the potential energy. To transform potential energy surfaces (PESs) to product form we use an algorithm called Potfit, which can bee seen as a generalization of the singular value decomposition for 2D matrices to multi-dimensional tensors. Potfit, however, requires multiple integrals over all degrees of freedom which limits its applicability to eight to nine dimensions.

The 21-dimensional PES of malonaldehyde therefore cannot be treated with Potfit directly.  To circumvent this, the PES is decomposed into n-particle interaction terms which are small enough for Potfit.  One starts with the self-energy of each degree of freedom, then adds particle-particle interactions, three-particle interactions and so on and hopes that this type of expansion can be truncated at low orders. However, a prediction of the required order and which of the terms are actually important for the representation of the PES is not possible. Also, a brute-force calculation of all terms is not feasible due to the dimensionality of the problem.

For the previous studies we identified relevant terms using a Monte Carlo scheme which produced Boltzmann distributed sampling points. The distribution is according to the the PES which roughly resembles the ground state wavefunction. The sampling points have then be used to calculate expectation values of the n-particle interaction terms using a Monte Carlo integration scheme. The calculations, however, suggest that additional terms exist which could not be identified with this technique as the sampling points do not resemble the true ground state.

To identify additional relevant terms we currently perform large scale Diffusion Monte Carlo (DMC) calculations using the exact PES. Within DMC, a set of random walkers is stochastically propagated according to the time-dependent Schrödinger equation in imaginary time such that the random walkers are distributed such that the their density resembles the exact ground state wavefunction. Once having a sufficiently large set of random walkers the expectation values of the n-particle interaction terms can be calculated according to the true ground state wavefunction. We expect that additional terms can be identified with this technique.

Software

• MPI, C, Fortran, Python

Publications

• Markus Schröder, Fabien Gatti, and Hans-Dieter Meyer; Theoretical studies of the tunneling splitting of malonaldehyde using the multiconfiguration time-dependent Hartree approach; J. Chem. Phys. 134, 234307 (2011)

Frank Otto
Physikalisch-Chemisches Institut
Universität Heidelberg

The system of two hydrogen molecules (and its isotopic variants) is the electronically most simple four-atom system.  Nowadays, quantum theoretical methods for computing its electronic potential energy surface as well as for treating the corresponding nuclear dynamics are advanced enough to compute scattering cross sections for various inelastic collisions processes of this system with very high accuracy, even on the full quantum-theoretical level.  The aim of this project is to investigate the vibrational energy transfer between a hydrogen molecule and a deuterium molecule, and to compare the obtained thermal rate constants with available experimental data.  Using electronic potential surfaces from literature, we treat the multi-dimensional nuclear dynamics with a highly advanced method for solving the time-dependent Schrödinger equation, the Multi-Configuration Time-Dependent Hartree method (see mctdh.uni-hd.de). While this method is highly efficient, a large number of rotational states must be taken into account in order to obtain the averaged thermal rate constants, which leads to an overall high computational demand.

Software

• Fortran, C

Publications

• Frank Otto, Fabien Gatti, and Hans-Dieter Meyer: Rovibrational energy transfer in collisions of H2 with D2. A full-dimensional wave packet propagation study. Will be published in: Molecular Physics, special issue "Quantum Molecular Dynamics: A Festschrift in Honour of William H. Miller". online

Evgeniy Gromov
Physikalisch-Chemisches Institut
Universität Heidelberg

In this project, large-scale parallel electronic structure calculations will be applied to understand the initial photoevents for the Photoactive Yellow Protein (PYP) at the molecular level. We focus on the very earliest steps observed in the PYP photocycle that involve the trans-cis isomerization of the ethylenic double bond in the p-hydroxycinnamoyl chromophore. The mechanism of the process is strongly dependent on both the intrinsic properties of the chromophore and the protein environment. The electronic structure calculations will be performed for the isolated chromophore and for the chromophore embedded in the native and mutated protein environment. Special emphasis will be placed on the mechanism of the isomerization and unraveling the role of the active-site amino acids in triggering and controlling the process.

Software

• Turbomole, Molcas

Publications

• E. V. Gromov, I. Burghardt, H. Köppel and L. S. Cederbaum; J. Phys. Chem. A 115, 9237 (2011) online
• E. V. Gromov, I. Burghardt, H. Köppel and L. S. Cederbaum; J. Photochem. Photobiol. A 234, 123 (2012) online