97,566 research outputs found
Vibrational Density Matrix Renormalization Group
Variational approaches for the calculation of vibrational wave functions and
energies are a natural route to obtain highly accurate results with
controllable errors. However, the unfavorable scaling and the resulting high
computational cost of standard variational approaches limit their application
to small molecules with only few vibrational modes. Here, we demonstrate how
the density matrix renormalization group (DMRG) can be exploited to optimize
vibrational wave functions (vDMRG) expressed as matrix product states. We study
the convergence of these calculations with respect to the size of the local
basis of each mode, the number of renormalized block states, and the number of
DMRG sweeps required. We demonstrate the high accuracy achieved by vDMRG for
small molecules that were intensively studied in the literature. We then
proceed to show that the complete fingerprint region of the sarcosyn-glycin
dipeptide can be calculated with vDMRG.Comment: 21 pages, 5 figures, 4 table
Full dimensional (15D) quantum-dynamical simulation of the protonated water-dimer I: Hamiltonian setup and analysis of the ground vibrational state
Quantum-dynamical full-dimensional (15D) calculations are reported for the
protonated water dimer (H5O2+) using the multiconfiguration time-dependent
Hartree (MCTDH) method. The dynamics is described by curvilinear coordinates.
The expression of the kinetic energy operator in this set of coordinates is
given and its derivation, following the polyspherical method, is discussed. The
PES employed is that of Huang et al. [JCP, 122, 044308, (2005)]. A scheme for
the representation of the potential energy surface (PES) is discussed which is
based on a high dimensional model representation scheme (cut-HDMR), but
modified to take advantage of the mode-combination representation of the
vibrational wavefunction used in MCTDH. The convergence of the PES expansion
used is quantified and evidence is provided that it correctly reproduces the
reference PES at least for the range of energies of interest. The reported zero
point energy of the system is converged with respect to the MCTDH expansion and
in excellent agreement (16.7 cm-1 below) with the diffusion Monte Carlo result
on the PES of Huang et al. The highly fluxional nature of the cation is
accounted for through use of curvilinear coordinates. The system is found to
interconvert between equivalent minima through wagging and internal rotation
motions already when in the ground vibrational-state, i.e., T=0. It is shown
that a converged quantum-dynamical description of such a flexible, multi-minima
system is possible.Comment: 46 pages, 5 figures, submitted to J. Chem. Phy
Semiclassical statistico-dynamical description of polyatomic photo-dissociations: State-resolved distributions
An alternative methodology to investigate indirect polyatomic processes with
quasi-classical trajectories is proposed, which effectively avoids any binning
or weighting procedure while provides rovibrational resolution. Initial
classical states are started in terms of angle-action variables to closely
match the quantum experimental conditions and later transformed into Cartesian
coordinates, following an algorithm very recently published [J. Chem. Phys.
130, 114103 (2009)]. Trajectories are then propagated using the 'association'
picture, i.e. an inverse dynamics simulation in the spirit of the exit-channel
corrected phase space theory of Hamilton and Brumer [J. Chem. Phys. 82, 595
(1985)], which is shown to be particularly convenient. Finally, an approximate
quasi-classical formula is provided which under general conditions can be used
to add possible rotational structures into the vibrationally-resolved
quasi-classical distributions. To introduce the method and illustrate its
capabilities, correlated translational energy distributions from recent
experiments in the photo-dissociation of ketene at 308 nm [J. Chem. Phys. 124,
014303 (2006)] are investigated. Quite generally, the overall theoretical
algorithm reduces the total number of trajectories to integrate and allows for
fully theoretical predictions of experiments on polyatomics.Comment: 10 pages, 3 figures, submitted to Phys. Chem. Chem. Phys; v2:
corrects Fig. 3 and its discussio
Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations
In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the
smoothest invariant manifolds tangent to linear modal subspaces of an
equilibrium. Amplitude-frequency plots of the dynamics on SSMs provide the
classic backbone curves sought in experimental nonlinear model identification.
We develop here a methodology to compute analytically both the shape of SSMs
and their corresponding backbone curves from a data-assimilating model fitted
to experimental vibration signals. Using examples of both synthetic and real
experimental data, we demonstrate that this approach reproduces backbone curves
with high accuracy.Comment: 32 pages, 4 figure
Evidence for a gravitational Myers effect
An indication for the existence of a collective Myers solution in the
non-abelian D0-brane Born-Infeld action is the presence of a tachyonic mode in
fluctuations around the standard diagonal background. We show that this
computation for non-abelian D0-branes in curved space has the geometric
interpretation of computing the eigenvalues of the geodesic deviation operator
for U(N)-valued coordinates. On general grounds one therefore expects a
geometric Myers effect in regions of sufficiently negative curvature. We
confirm this by explicit computations for non-abelian D0-branes on a sphere and
a hyperboloid. For the former the diagonal solution is stable, but not so for
the latter. We conclude by showing that near the horizon of a Schwarzschild
black hole one also finds a tachyonic mode in the fluctuation spectrum,
signaling the possibility of a near-horizon gravitationally induced Myers
effect.Comment: LaTeX, 23 page
- …