text:
\section{Introduction}
\label{sec:intro}
One of the fundamental processes in molecular reaction dynamics is the unimolecular
dissociation of vibrationally excited
molecules.%
\cite{robinson_holbrook_book,baer_hase_book,schinke_book,stumpf_1995}
Depending on the molecular system, their decay dynamics can span the range from
mode-specific to statistical.
For intermediate cases, the dissociation mechanism
in terms of intramolecular
vibrational energy redistribution (IVR)
of bound and metastable resonance states provides considerable
insight into the dynamic properties of the molecular system under study.
{In the following, we use the term ``resonance'' both for vibrational
resonances and metastable states. The meaning should be clear from the
context and typically it will mean metastable state. Otherwise, we will point
out the meaning.}

One standard benchmark system is the formyl radical \ce{HCO} which plays an important
role in many combustion processes as well as in atmospheric and interstellar
chemistry; see, e.g., \lit{hco_astro_ocana_2017}.
In its electronic ground state $\widetilde{X}\,{}^2A'$, \ce{HCO} shows many
resonance states whose decays follow very systematic mode-specific pathways.

In contrast to \ce{HCO}, its deuterated counterpart \ce{DCO} shows more
statistical behavior.
This is due to an accidental, strong
$\nu_1\!:\!\nu_2\!:\!\nu_3\!\approx\!1\!:\!1\!:\!2$ Fermi
{(vibrational)} resonance in
the \ce{D-CO}  stretching  vibration $\nu_1$ ($\unit[1910]{cm^{-1}}$), the \ce{DC=O} stretching vibration $\nu_2$ ($\unit[1795]{cm^{-1}}$), and the \ce{D-C=O} bending vibration $\nu_3$ ($\unit[847]{cm^{-1}}$).
The Fermi resonance leads to strong mixing between zero-order states,
already for the lowest vibrational states.\cite{DCO_I_schinke,DCO_II_schinke,DCO_polyad_troellsch_2001,Jung2002}
Strong mixing is an essential prerequisite for
statistical dynamics. Keller \emph{et al.} thus consider \ce{DCO} a ``precursor of
`chaos'
in more complicated systems''.\cite{DCO_II_schinke}
Consequentially, the normal assignments in terms of the associated vibrational quantum
numbers ($v_1$, $v_2$, $v_3$) loose their meanings, although they may still be used
economically as ``nominal labels'' to indicate possible predominating vibrational
character. The only conserved quantity at short times is the polyad quantum
number, $P = v_1 + v_2 +v_3/2$, which describes the total vibrational excitation.%
\cite{polyad_quack_1984,polyad_quack_1985,polyad_rev_kellman_2007,DCO_I_schinke}

Due to their strikingly different characteristics, there has been strong interest in both \ce{HCO}
and \ce{DCO}, from both experiment and theory.
Due to the amount of work on these systems, we briefly mention only some
of the most important contributions.
Energies and widths of resonances of \ce{HCO} and \ce{DCO}
have
been measured to high
resolution by dispersed fluorescence and stimulated emission
pumping.%
\cite{HCO_exp_adamson_1993,HCO_exp_neyer_1993,HCO_exp_tobiason_1995,
DCO_exp_tobiason_1995,DCO_I_schinke,DCO_wei_2004}
For \ce{HCO}, Neyer \emph{et al.} also measured the rovibrational product distribution
of \ce{CO}.\cite{HCO_exp_neyer_1995}

Likewise, energies and widths of \ce{HCO} have been computed using
various methods, establishing this system as a benchmark for computing
resonance states.%
\cite{HCO_bowman_1986a,HCO_romanowski_1986,HCO_I_schinke,HCO_II_schinke,HCO_IV_schinke,
HCO_poirier_2002a, HCO_mandelshtam_2002,
HCO_tremblay_2005,HCO_mctdh_ndengue_2015,HCO_pes_ndengue_2016}
Rovibrational \ce{CO} state distributions and resonance decays have been
analyzed by various researchers, also for
nonzero total angular
momentum.\cite{HCO_qi_1996,HCO_yang_1997,HCO_I_schinke,HCO_II_schinke,HCO_III_schinke,
HCO_V_schinke,dixon_1992,gray_1992}
However, less attention has been paid to
\ce{DCO}.\cite{DCO_wang_1995,DCO_I_schinke,DCO_II_schinke,DCO_loettgers_1997,
stamatiadis_2001}
Although \ce{DCO} shows close to statistical behavior, it is not fully irregular.
The decay constants show strong state-to-state fluctuations. Microcanonical
statistical rate theory thus cannot predict the state-specific decay
constants.
Due to strong anharmonic couplings, an IVR analysis is much less straightforward but
still desirable.
Clear indications that remaining regularities may be strong enough for such an
approach were provided by the aforementioned %
polyad model
that turned out
to be applicable to \ce{DCO} and quite useful.\cite{DCO_II_schinke}
The group of Temps fitted an effective polyad Hamiltonian to experimental data and did an
analysis of different IVR pathways within this polyad
model.\cite{DCO_polyad_troellsch_2001,DCO_polyad_renth_2003}
This model Hamiltonian was then used for further semiclassical
analysis.\cite{jung_2002,huang_2007,DCO_semparithi_2003}
However, many of these analyses still lack comparison with quantum calculations on an
\emph{ab-initio} potential energy surface (PES).

Here, we make an initial attempt to fill this gap by a joint experimental and theoretical
study of the observed and calculated resonances of \ce{DCO} in polyads $5$ and $5.5$. In
particular, we present {experimental} kinetic energy
release (KER)
spectra of the \ce{D} atoms from the decay of the resonances and the associated \ce{CO}
vibration-rotation product state distributions. The results were obtained using the method
of Stimulated Emission Pumping (SEP)\cite{DCO_I_schinke} for the preparation of selected
excited \ce{DCO} resonance states in combination with velocity-map imaging
\cite{Eppink1997} of
the \ce{D} atoms. In addition, we computed the \ce{CO} state distributions using our
dynamically
pruned discrete variable representation (DP-DVR)
approach\cite{proDG_hartke_2006,pW_tannor_2016,pvb_rev_tannor_2017} and analyzed
the computed resonance decays. As critical tests of the theory, we compare our
computational results with the experimental data taking either the PES of Werner
\emph{et al.} (WKS)\cite{HCO_I_schinke,HCO_II_schinke}
or the PES of Song \emph{et al.} (SAG).\cite{HCO_pes_song_2013}

We thereby use this
study as a real-life
application of our new
method for performing molecular quantum dynamics.
The standard method in molecular quantum dynamics is to employ a direct-product basis of
discrete variable representation (DVR) functions.\cite{tannor_book}
However, this approach suffers from an exponential scaling of basis size with
dimensionality. Even for lower-dimensional problems like the one studied here, it is not
the most efficient method. For dissociation problems like \ce{DCO}, long
coordinate ranges need to be described, but the wavefunction typically does not
occupy the whole direct-product coordinate space. Such a problem is well-suited for
only using DVR grid points where the wavepacket has non-negligible amplitudes. This leads
to significant savings in computational resources (both regarding number of operations
and memory requirements). Since the wavepacket moves in time, the set of active basis
functions needs to be dynamically adapted. Exactly this capability is provided by our
dynamically pruned DVR
approach (DP-DVR).\cite{proDG_hartke_2006,pW_tannor_2016,pvb_rev_tannor_2017}
The accuracy is controlled by a so-called wave-amplitude
threshold.\cite{proDG_hartke_2006,pvb_algorithms_tannor_2016} The smaller the threshold,
the more basis functions are added and the more accurate the simulation becomes.
In \lit{pvb_rev_tannor_2017} we have introduced a very efficient algorithm for DP
simulations and have done careful benchmarks of the DP-DVR and other methods.
We have shown that DP-DVR can be more efficient than conventional dynamics
already for two-dimensional systems.

For the dissociation dynamics of \ce{DCO}, phase-space bases would be other useful
candidates
for our DP
approach.\cite{pvb_tannor_2012,pvb_math_tannor_2016,pW_tannor_2016,pvb_rev_tannor_2017}
One could use such a phase-space basis in the coordinate describing the dissociation.
However, efficient use of phase-space bases requires that the potential operator has the
form of a sum of products of one-dimensional terms (SOP form). This requires an
additional fitting of the potential into this form.

Recently, we have combined our DP approach with the Multiconfiguration
Time-De\-pen\-dent Hartree method (MCTDH), giving DP-MCTDH.\cite{dpmctdh_tannor_2017}
There, DP can be used either for pruning the time-dependent basis functions
(single-particle functions) or their DVR representation. The former is most useful for
higher-dimensional systems (see also
\lits{mctdh_selected_configurations_worth_2000,pruned_mctdh_carrington_2016,
pruned_mctdh_carrington_2017}) whereas the latter is useful whenever many DVR functions
are needed for describing the (multidimensional) single-particle functions.
This is the case for \ce{DCO} dissociation dynamics such that DP-MCTDH could be a useful
method for our study. MCTDH itself has been used for computing resonances of
\ce{HCO}.\cite{HCO_mctdh_ndengue_2015,HCO_pes_ndengue_2016}
However, the MCTDH algorithm is more complicated than a DVR code. Furthermore,
as with phase-space bases, an efficient use of MCTDH requires a SOP form of the potential.
Although methods for combining arbitrary potentials with MCTDH
exist,\cite{cdvr_manthe_1996,CMCTDH_wodraszka_2018} they are
less well established and require more careful convergence tests.
Further, MCTDH is most useful for weakly correlated systems and short-time dynamics, but
for \ce{HCO} \cite{HCO_mctdh_ndengue_2015} many single-particle functions are needed and
the wavepacket has to be propagated for tens of picoseconds.

Here, we resort to our standard DP-DVR algorithm to make our simulations as simple as
possible, without jeopardizing computational
efficiency, and also to test
the capabilities of our DP-DVR approach in an application involving resonances
and their decay.

The remainder of this Article is organized as follows:
The experimental and theoretical setups are described in Sections \ref{sec:exp} and
\ref{sec:theory}, respectively. The latter provides more details on the DP-DVR method
(\autoref{sec:dp-dvr}), on the methods to obtain resonance states
(\autoref{sec:filter_diag}) and asymptotic product distributions
(\autoref{sec:theory_rovib}), and on the employed PES (\autoref{sec:theory_pes}).
Our results are presented and discussed in \autoref{sec:results}.
The experimental velocity map images are presented in \autoref{sec:res_exp}.
\autoref{sec:res_params} details the simulation parameters and
\autoref{sec:energies} compares our computed resonance energies and widths with literature
values. The PES is analyzed in
terms of an adiabatic picture in \autoref{sec:adiabatic_repr}, the experimental and
theoretical asymptotic distributions are presented and compared in
\autoref{sec:rovib_distr}, and the decay processes of the studied resonances
are analyzed in
\autoref{sec:decay_processes}. We summarize in \autoref{sec:conclusion}.

\section{Experiment}
\label{sec:exp}
The {measurements} required four spatially and temporally controlled laser
pulses to be focused into a supersonic seeded molecular beam in a differentially pumped
stainless steel vacuum chamber.
\autoref{fig:setup} shows a sketch of the employed installation.
The SEP part of the setup for preparation of the \ce{DCO} ($ \widetilde X$) radicals
in
their
highly excited states \cite{DCO_I_schinke,DCO_wei_2004} and the photofragment imaging part
for measuring the kinetic energy release to the \ce{D}
atoms\cite{Wei2003,HCO_riedel_2005}
have been described in some detail separately before.
The exact experimental conditions varied slightly from those to record optimal SEP
spectra by the need of the present experiment for a high number density of highly
vibrationally excited radicals.\cite{riedel_thesis}

\begin{figure*}
        \includegraphics[width=.8\textwidth]{Figure1.pdf}
        \caption{%
Schematic diagram of the experimental setup. BBO: doubling crystal, DFR:
double-Fresnel rhomb, HS: harmonic separator, IO: ion optics electrode assembly, L: lens,
MCP: multi-channel plate, PS: phosphor screen, RP: Rochon prism, Sh: shutter, WP:
Wollaston prism.
        }
        \label{fig:setup}
\end{figure*}

A pulsed supersonic free jet containing $\sim \unit[0.5]{\%}$ deuterated acetaldehyde
(\ce{CD3CDO}) in \ce{He} was generated by flowing the carrier gas at a backing
pressure of
$\sim \unit[2]{bar}$ through a stainless steel reservoir with freshly distilled
\ce{CD3CDO}
(Fluka, $>\unit[99]{\%}$) at $\unit[-78]{^\circ{}C}$ and expanding it into the
first vacuum chamber of
the imaging apparatus through a 0.8 mm diameter solenoid-actuated valve (General Valve)
at \unit[20]{Hz} repetition rate.
Photolysis of the \ce{CD3CDO} with a \ce{XeCl} excimer laser at $\lambda = \unit[308]{nm}$
in the
high-pressure region of the free jet expansion $\sim \unit[3]{mm}$ behind the
pulsed nozzle
produced the desired \ce{DCO} radicals.
A molecular beam of the radicals shaped by a \unit[1.5]{mm} diameter conical skimmer then
entered
the test volume between the repeller and extractor plates of the imaging electrode
assembly in the second vacuum chamber, where it was crossed by the pump, dump and probe
laser beams. A liquid-\ce{N2} cryo-pump surrounding the assembly minimized the
background
ion signal.

Two dye lasers (Lambda Physik) were optically pumped by the dichroically separated third
resp.~second harmonic output beams of a Nd:YAG laser (Spectra Physics) and
frequency-doubled in BBO crystals to obtain the required $\sim\unit[259]{nm}$
pump (\unit[1.5]{mJ}) and
\unit[336\,--\,362]{nm} dump (\unit[5\,--\,7]{mJ}) pulses.
The precise wavelengths were set by recording the $ \widetilde B (^2A')\leftarrow
\widetilde X(^2A')$
fluorescence excitation and $ \widetilde B \rightarrow \widetilde X$ SEP spectra in a
separate molecular beam apparatus with fluorescence detection.
\cite{DCO_I_schinke,DCO_wei_2004}
Both beams were focused into the test volume at a small angle with respect to each other
through a $f=\unit[500]{mm}$ fused silica lens.
The \unit[308]{nm} excimer-pumped probe dye laser (both Lambda Physik) for imaging of the
\ce{D} atoms
from the \ce{D-CO} dissociation reaction by 2+1 resonance-enhanced multi-photon
ionization
(REMPI) via the $2\,{}^2S \leftarrow 1\,{}^2S$ transition was frequency-doubled to the
required $\lambda = \unit[243]{nm}\ (\unit[1]{mJ})$ and focused into the
detection region
counter-propagating to the pump and dump with a short delay of $\sim\unit[10]{ns}$.
The exact probe wavelength was set by optimizing the \ce{D^+} ion yield.
All laser polarizations were set parallel to the plane of the imaging detector using
combinations of Fresnel double rhombs and Rochon or Wollaston prisms.

The imaging measurements were made under velocity mapping conditions. \cite{Eppink1997}
The probe laser was periodically scanned over the Doppler profile of the recoiling \ce{D}
atoms.
The resulting \ce{D^+} ions were monitored on a microchannel plate (MCP) detector
coupled to
a phosphor screen.
The obtained signals were recorded on a CCD camera and accumulated over up to
$200\, 000$ laser shots using single ion counting and centroiding \cite{Chang1998} to
improve
the detection sensitivity
and spatial resolution and to discriminate against noise.
Background images with the dump laser blocked on alternate shots were subtracted to
eliminate contributions
to the \ce{D} atoms from the \ce{CD3CDO} photolysis and from predissociation of the
\ce{DCO}
($\widetilde B$) state.
Mass selectivity was achieved using a fast transistor switch (Behlke) to gate the MCP.
The timing of the pulsed valve, all lasers and the MCP voltage was controlled by a
digital delay generator (Stanford Research).

\section{Theory}
\label{sec:theory}

\subsection{Dynamically pruned discrete variable representation (DP-DVR)}
\label{sec:dp-dvr}
The propagation is performed in Jacobi coordinates $\{R,r,\theta\}$. $R$ is the distance
of \ce{D} to the center of mass of \ce{C-O}, $r$ is the \ce{C-O} distance and $\theta$
the angle between the corresponding vectors $\vec{R}$ and $\vec{r}$.
As usual,\cite{jacobi_coords_lequere_1990} the wavefunction is
divided by $R r$ such that the volume element takes the form of $\ensuremath{\mathrm{d}} V = \ensuremath{\mathrm{d}} R\, \ensuremath{\mathrm{d}} r\,
\sin(\theta) \ensuremath{\mathrm{d}} \theta$.
In our propagation, we consider only the $\widetilde{X}\,{}^2A'$ ground state and neglect
nonadiabatic and Renner-Teller couplings. The couplings only play an important role
if the wavefunction has non-negligible contributions at linear
geometries.\cite{HCO_I_schinke} This requires high excitation in the bending mode and
only occurs for a minority of the resonances studied; we will mention them in
\autoref{sec:decay_processes}.

The wavefunction is represented by a Gauß-Legendre DVR
for the angular coordinate and by a sinc DVR for the radial
coordinates.\cite{tannor_book,sinc_dvr_miller_1992}
This direct-product basis is then pruned using our DP-DVR
approach,\cite{pW_tannor_2016}
{which is related to previous pruning
methods.\cite{proDG_hartke_2006,proDG_hartke_2008,pruning_wyatt_2006,
  pruning_wyatt_2007,pruning_mccormack_2006}
In contrast to those,
we could show that our approach is actually faster than conventional methods.}
If the absolute value of a coefficient of a
direct-product basis function is larger than a predefined wave-amplitude threshold, this
basis function and its nearest neighbors become active. Otherwise, this function
is removed from the set of active functions. This procedure is repeated at each time
step, ensuring a compact representation of the wavefunction for all propagation times.
For further details we refer to \lit{pW_tannor_2016}.

In the following, we mention two improvements of our code introduced in
\lit{pW_tannor_2016} (the reader who is not interested in technical details may skip the
rest of this Subsection).
The first improvement is a (straightforward) implementation of standard shared-memory
parallelization. For the second improvement,
we take advantage of the fact that the momentum and kinetic energy operators in
sinc DVR representation give Toeplitz matrices with elements $T_{i,j} = T_{i+1,j+1} =
t_{i-j}$. Instead of storing all matrix elements $T_{i,j}$, we
only store one row $t_{i-j}$ of the matrix. This reduces the memory needed to be loaded
into the cache of the central processing units and thus gives large speed-ups, especially
for shared-memory parallelization. In standard molecular quantum dynamics
applications with basis
sizes smaller than 100, the storage of the one-dimensional matrices is negligible,
compared to the storage of the (pruned) multidimensional wavefunction. However, the
exploitation of the Toeplitz structure becomes useful whenever the one-dimensional basis
size is large. This is the case for the dissociation dynamics considered here.
For a basis that is not pruned, the action of a Toeplitz matrix onto a vector can be
implemented with a scaling of $\mathcal
O\bigl(N\log(N)\bigr)$ using fast Fourier transforms
(FFTs).\cite{toeplitz_nlogn_gohberg_1994} However, when the basis is pruned, some
structure
of the pruned matrix is lost and an implementation in terms of FFTs is not
straightforward.
Nevertheless, the matrix--vector product in a pruned basis is much faster than
a FFT in an unpruned basis if pruning reduces the size of the objects
sufficiently, which typically is the case.

\subsection{Retrieval of resonances}
\label{sec:filter_diag}
Previously, \ce{HCO} and \ce{DCO} resonances have been computed using, among others,
Lanczos procedures,\cite{HCO_poirier_2002a,HCO_tremblay_2005}
a log-derivative version of Kohn's variational
principle,\cite{DCO_II_schinke,HCO_II_schinke}
MCTDH,\cite{HCO_mctdh_ndengue_2015}
projection theory,\cite{HCO_wang_2017}
and filter diagonalization.\cite{HCO_mandelshtam_2002,HCO_V_schinke}
Many applications utilize the time-independent Schrödinger equation (TISE).
In principle, our DP-DVR code would work as well for the TISE using an algorithm that
iteratively adds and removes new basis
functions after each Lanczos iteration.\cite{pvb_algorithms_tannor_2016}
However, Lanczos and other iterative diagonalization algorithms require a good
preconditioner for efficient
usage,\cite{precond_huang_2000,precond_poirier_2001,HCO_poirier_2002a} especially when
eigenstates are searched in the middle of a dense eigenspectrum, as is the case in
this application. The search for a good preconditioner for a Hamiltonian is not trivial
and depends on the employed basis. We tested the
preconditioner proposed in \lit{precond_huang_2000} and some standard preconditioners
like
diagonal matrices but found no satisfying results.

Thus, instead of using a Lanczos approach, we use filter
diagonalization.\cite{filterdiag_neuhauser_1990,filterdiag_neuhauser_1991}
Since the standard form of filter diagonalization is based on propagation, it allows for
a straightforward integration into a DP code for solving the time-dependent Schrödinger
equation.
This worked without any adjustments or tuning of parameters, and the
bottleneck of our simulations was then not the retrieval of the eigenstates but the
subsequential simulation of their decay.
Thus, we did not try to use further improvements of filter
diagonalization.\cite{filterdiag_takatsuka_1995,filterdiag_taylor_1997,
HCO_mandelshtam_2002}

In standard filter diagonalization, a real-time dynamics of an initial wavepacket
with absorbing boundary conditions is performed and the wavepacket
is stored at intermediate times. Afterwards, the wavepacket is filtered at
(typically equidistantly spaced) energies $E_n$ \emph{via} Fourier
transform:\cite{filterdiag_neuhauser_1991}
\begin{equation}
 \ket{\Phi_F(E_n)} = \frac1{2\pi\hbar} \int_{0}^\infty \exp(\ensuremath{\mathrm{i}} E_n t/\hbar)
\ket{\Psi(t)} F(t)
\ensuremath{\mathrm{d}} t,
\end{equation}
where $F(t)$ is a filter function of the form
\begin{equation}
F(t) =   \exp[-(t-\tau)^2 W^2 / \hbar^2]. \label{eq:filterfunction}
\end{equation}
$W$ is the energy bandwidth, here taken as $E_{n+1}-E_{n}$.
The duration $\tau$ is set such that $W\tau \gg 1$.
Afterwards, the Hamiltonian is represented in the nonorthogonal basis
of filtered states $\{\ket{\Phi_F(E_n)}\}_{n=1}^N$ and diagonalized. The size of the
basis is typically less than $100$, such that diagonalization can be performed using
standard procedures.
{The obtained eigenvalues $E_n$ are complex-valued, including both the
resonance energies $\epsilon_n$ and resonance widths $\Gamma_n$ as
$E_n = \epsilon_n - \ensuremath{\mathrm{i}} \frac{\Gamma_n}{2}$.
}
{In the following, the width $\Gamma$ will be used for wavenumber quantities.}

\subsection{Rovibrational product distribution}
\label{sec:theory_rovib}

For obtaining the KER spectra of the \ce{D} atom and the asymptotic
rovibrational distributions of the \ce{CO} fragment, we employ the analysis-line method
developed by Balint-Kurti \emph{et
al}.\cite{analysis_line_balint-kurti_1990} %
It has previously been used for \ce{HCO} by both Gray and
Dixon.\cite{gray_1992,HCO_yang_1997,dixon_1992}
The retrieval of the asymptotic distribution is performed by Fourier-transforming
cuts of $\Psi(R,r,\theta; t)$ along the ``analysis line'' $R=R_\infty$, where the cuts
$\Psi(R_\infty, r,\theta;t)$ are represented in the basis of asymptotic rovibrational
states, $\{\ket{\psi_{vj}}\}$. $v$ and  $j$ are the \ce{CO} stretch and
rotational quantum numbers, respectively. The working expression is
\begin{align*}
C_{vj}(R_\infty,t) &= \bra{R_\infty}\braket{\psi_{vj}}{\Psi(t)},\\
A_{vj}(R_\infty,E) &= \frac1{2\pi} \int_0^\infty \exp(\ensuremath{\mathrm{i}} E t/\hbar)
C_{vj}(R_\infty,t)\ensuremath{\mathrm{d}} t.
\end{align*}
The KER spectrum $P(E_{\ce{D}})$ is then given by
\begin{align}
P(E_{\ce{D}}) &= \sum_{v,j=0}^{\infty}
P_{vj}(E_{\ce{D}}),\label{eq:P_Ed_analysis_line}\\
P_{vj}(E_{R}) &=
\lim_{t\to\infty}\bigl| \braket{\Psi^{(-)}_{kvj}}{\Psi(t)}\bigr|^2 %
\label{eq:P_Ed_analysis_line_vj}\\
&= \frac{16 \pi^3 k}{\mu_R} \left| A_{vj}(R_\infty,E_R)\right|^2, \\
E &= E_{vj} + E_R, \quad E_D = \frac{m_{\ce{CO}}}{m_{\ce{DCO}}}
E_R,\label{eq:ED_mass_weight}
\end{align}
where $k = \sqrt{2\mu_R E_{R}/\hbar^2}$ and  $E_R$ is the kinetic energy in the
internal Jacobi coordinate $R$. The corresponding kinetic energy of the \ce{D} atom
in the laboratory frame (without translation and rotation of the \ce{DCO} system)
is then given by mass-weighting $E_R$ (\autoref{eq:ED_mass_weight}), as obtained from the
standard center-of-mass transformation of a two-body system.\cite{bernath_book}
$E_{vj}$ is the internal energy of the \ce{CO} fragment.
$\mu_R$ is the reduced mass of $\ce{D-CO}$ in Jacobi
coordinates. $\ket{\Psi^{(-)}_{kvj}}$ is the outgoing scattering state for
dissociation into \ce{D} and \ce{CO}.\cite{schinke_book}
Integrating $P_{vj}(E_{R})$ over all $E_{R}$ gives the rovibrational
distributions of the \ce{CO} product.

Combining this method with our DP-DVR approach is straightforward because the only
quantity that needs to be stored during the dynamics calculation is the wavefunction
evaluated at
$R_\infty$ which is a DVR grid point in the asymptote. When no basis function at
$R_\infty$
is active at a specific time step, the wavefunction there is simply zero.

\subsection{Potential energy surfaces}
\label{sec:theory_pes}

To the best of our knowledge, there are three accurate and more recent potential energy
surfaces (PES) for \ce{HCO}. The (modified) WKS surface of Werner, Keller and
Schinke\cite{HCO_I_schinke,HCO_II_schinke} has been applied in many
studies; for example %
\lits{DCO_I_schinke,DCO_II_schinke,HCO_poirier_2002a,HCO_mandelshtam_2002,%
HCO_tremblay_2005,HCO_mctdh_ndengue_2015,HCO_wang_2017}.
This PES quite accurately describes both the dissociation and the interaction region,
including the
conical intersection at linear geometry. It is based on
multireference configuration interaction (MRCI) calculations.
Another recent PES is that developed by Song,
van der Avoird and Groeneboom (SAG).\cite{HCO_pes_song_2013} It is based on unrestricted
coupled-cluster calculations and focuses on the asymptotic and lower-energy
regions.
It has been used for scattering calculations.\cite{HCO_Scatt_song_2015}
The third recent PES was developed by Ndengu{\'e}, Dawes and Guo
and is based on explicitly correlated MRCI calculations.\cite{HCO_pes_ndengue_2016}
It was used for unraveling the effects of Renner-Teller coupling on the resonance
levels.

Only the WKS surface has been used in studies of
\ce{DCO}.\cite{DCO_I_schinke,DCO_II_schinke} To connect to those previous studies, we
mainly use this well-established PES in our calculations. In order to estimate the
sensitivity of the observables to changes of the potential, we also employed the SAG
surface for selected resonances.
Figures i and ii in the supplementary material show cuts of the two PES.
Since none of those PES were constructed with decay dynamics of
high-energy resonance {states} far out into the asymptote
in mind, none of the utilized
PES can be expected to give quantitative agreement between theoretical
and experimental results in this present application.

\section{Results and discussion}
\label{sec:results}

\subsection{Experimental Results}
\label{sec:res_exp}

Four \ce{DCO} ($\widetilde X$) resonances were picked at random for
investigating the KER spectra and \ce{CO} ($v, j$) product state
distributions by the \ce{D} atom velocity map imaging experiment.
Two states were taken from polyad $P = 5$ (at {wavenumbers} ${\tilde \nu_v}= 8\,902$ and
$\unit[8\,942]{cm^{-1}}$)
  and two from polyad $P = 5.5$ (${\tilde \nu_v} = 9\,896$ and $\unit[10\,065]{cm^{-1}}$).
SEP spectra illustrating the observed vibrational states belonging to both polyads are
shown in \autoref{fig:sep}.

\begin{figure}
        \includegraphics[width=\columnwidth]{Figure2}
        \caption{SEP scans over a) polyad 5.0 and b) polyad 5.5 with nominal assignments
of the observed resonances
        according to \lit{DCO_II_schinke}.
        The four resonances selected for \ce{D} atom imaging are highlighted by frames
around
the state labels.
With the pump laser tuned to the $\widetilde B \leftarrow \widetilde X,\ 0_0^0$,
$^qR_0(0)$ line at $\nu_{\text{pump}}= \unit[38\,631.60]{cm^{-1}}$,
state,
the dump transition can reach four different rotational states, $N_{K_aK_c} = 0_{00},\
2_{02},\ 1_{10}$ and $2_{12}$,
in each $\widetilde X$ vibrational state, explaining the four-line patterns observed in
the SEP scans.
}
        \label{fig:sep}
\end{figure}

Following Keller \emph{et al.},\cite{DCO_II_schinke} the four resonances are nominally
labeled
as (0,4,2), (0,5,0), (2,3,1) and (1,4,1), in order of increasing energy for
reference below.
We emphasize, however, that these ``assignments'' have to be taken with caution.
For example, the $\unit[8\,902]{cm^{-1}}$ resonance was reported as a mixture of
\unit[48]{\%} (2,2,2)
and \unit[32]{\%} (0,4,2), while the neighboring $\unit[8\,821]{cm^{-1}}$ resonance was
found as a
mixture \unit[41]{\%} (2,2,2) and \unit[32]{\%} (0,4,2).
Further, the resonance at ${\tilde\nu_v} = \unit[10\,065]{cm^{-1}}$ nominally assigned as (1,4,1)
is
special because it shows pronounced interpolyad mixing with a highly dissociative
resonance belonging to polyad $P = 6$, most likely (4,2,0).\cite{DCO_wei_2004}
{We note that we use the same notation $(v_1,v_2,v_3)$ for both zero-order
states and resonance states. Which state is meant should either be clear from
the context or the state is explicitly designated as resonance or zero-order
state.}

\begin{figure}
        \includegraphics[width=\columnwidth]{Figure3}
        \caption{a) Measured two-dimensional (2D) \ce{D} atom velocity map images after
excitation of the (0,4,2), (0,5,0), (2,3,1) and (1,4,1) DCO ($\widetilde X$) resonances
in
the 2$_{02}$ and 2$_{12}$ rotational states and b) reconstructed meridional slices
through
the respective three-dimensional (3D) \ce{D} atom recoil distributions. }
        \label{fig:images}
\end{figure}

The recorded D atom velocity mapped images after excitation of the 2$_{02}$ and 2$_{12}$
rotational states of the above four \ce{DCO} ($\widetilde X$) resonances are printed in
\autoref{fig:images} a) together with their Abel inversions in \autoref{fig:images} b).
The
depicted meridional slices through the three-dimensional (3D) \ce{D} atom recoil
distributions
were obtained using the iterative regularization method with the projected Landweber
algorithm.\cite{Renth2006} As can be seen, the raw images and the associated slices
through the 3D recoil distributions differ substantially from vibrational resonance to
resonance, while the results for the two rotational states are very similar, indicating
the good reproducibilty of the data. For (0,5,0) and (1,4,1), the 3D slices show \ce{D}
atoms  with comparably low recoil velocities. The allowed maximal available
energies
$E_{\text{avl}}$ is determined by the energy balance
\begin{equation}
  E_r +{ \unit{h} (\nu_{\text{pump}} - \nu_{\text{dump}})} = \Delta
  {E}_0^0\text{(\ce{D-CO})} +
E_{\text{avl}},
\end{equation}
where $E_r$ is the initial state's rotational state (here $E_r = 0$ for $N_{K_aK_c} =
0_{00}$),
$\Delta {E}_0^0\text{(\ce{D-CO})}$ is the asymptotic \ce{D-CO} dissociation
energy,
and $\nu_{\text{pump}}$ and $\nu_{\text{dump}}$ are the {frequencies} supplied by the pump and
dump laser pulses. Thus,
dissociation of the (2,2,2) and (0,5,0) resonances may lead to \ce{CO} in $v = 0$ and $v
= 1$,
while the (2,3,1) and (1,4,1) resonances may also give \ce{CO} in $v = 2$.
Evidently, however, (0,5,0) and (1,4,1) give mainly \ce{CO} in $v = 1$. Further, as
by the narrow recoil widths, the \ce{CO}\,($v = 1$) acquires relatively low rotational
excitation (quantum number $j$).
In contrast, the images obtained from the (2,2,2) and (2,3,1) resonances show the
formation of \ce{CO} in $v = 1$ and in $v = 0$, with broader rotational excitation in $v
= 0$.
The observed recoil anisotropies are negligible within experimental errors, consistent
with resonance lifetimes ($\tau=\unit[0.8\,\text{--}\,5]{ps}$ inferred from the measured
resonance
widths) longer than the DCO rotational period.

Subsequent integration of the D atom images over the angular coordinates and
transformation of the
resulting recoil velocity distributions to the recoil translational energies with account
of the fragment mass ratio and the appropriate Jacobian finally gave the total kinetic
energy release (KER) spectra for the decaying resonances.
The corresponding CO vibrational and rotational product state distributions follow by the
energy balance.
The experimental KER spectra will be presented and compared with the
present theoretical predictions in \autoref{sec:rovib_distr}.
The asymptotic \ce{D-CO} dissociation energy was assumed to have a value of
$\Delta {E}_0^0
= \unit[5\,450]{{h\, c\,}cm^{-1}}$.

\subsection{Simulation parameters}
\label{sec:res_params}

For the filter diagonalization, the initial wavefunction is taken from
\lit{DCO_II_schinke} and takes the form of the following Gaussian (excluding
normalization)
\begin{equation}
\begin{split}
 \Psi^{\text{FD}}&(R,r,\theta; t=0) \propto %
 \exp\{-[(R-R_0)/\alpha_R]^2\} \\
\times&\exp\{-[(r-r_0)/\alpha_r]^2\}\exp\{-[(\theta-\theta_0)/\alpha_\theta]^2\}
,
 \end{split}
\end{equation}
with the parameters $R_0 = \unit[3.05]{a_0}, r_0 = \unit[2.57]{a_0}, \theta_0 =
138^\circ, \alpha_R = \unit[0.256]{a_0},  \alpha_r = \unit[0.195]{a_0},$ and
$\alpha_\theta=7.19^\circ$. This initial wavepacket is propagated for $\unit[2]{ps}$.
The filter function is a Gaussian with duration of $\tau=\unit[1]{ps}$ (see
\autoref{eq:filterfunction}), and the energy region of
interest (see \autoref{sec:energies}) was divided into four regions, each with
a width of
$\sim\unit[400]{{h\, c\,}cm^{-1}}$ and with typically $10$ energy-filtered basis
functions. For each region, the number of
basis functions was adapted to avoid an overcomplete basis.

The DVR basis set parameters are given in \autoref{tab:basis_parameters}.
For the filter diagonalization, a smaller range in $R$ up to $R=\unit[10]{a_0}$ is used.
Due to a wrong
asymptote of the SAG potential, a smaller
coordinate range in $r$ was used for all simulations on that PES.
In coordinate $R$, we use the transmission-free complex absorbing potential
{(CAP)} of
\lit{cap_manolopoulos_2002} (taking the rational form, Eq.~(2.25) in that reference) with
a
width of $\unit[5]{a_0}$ for the filter diagonalization and a width of $\unit[10]{a_0}$
for the decay dynamics.
{This corresponds to starting positions of the CAP at $\unit[5]{a_0}$ and $\unit[18]{a_0}$, respectively. Similar values have been used previously for obtaining resonance states.\cite{DCO_II_schinke,HCO_mctdh_ndengue_2015,HCO_tremblay_2005}
For selected states, we have done simulations with other CAP positions and widths and found no significant deviations for neither the resonance energies/widths nor the decay distributions.}
We use the following atomic masses: $\unit[12.0096]{Da}$ for \ce{C},\cite{iupac_amu}
$\unit[15.99977]{Da}$ for \ce{O} and $\unit[2.01410178]{Da}$ for \ce{D}.\cite{ame2016}

The wave-amplitude threshold used for the pruning of the filter diagonalization
dynamics is $10^{-11}$, although a threshold of $10^{-8}$ would give the same results.
This looser threshold is used for the decay dynamics.
There, a {threshold} of $10^{-6}$ would have been sufficient.
The analysis line (\autoref{sec:theory_rovib}) is placed at $R_\infty =
\unit[16]{a_0}$.
For all propagations, we employ a short iterative Arnoldi
propagator\cite{sil_light_1986,mctdh_rev_meyer_2000} with an accuracy of
$10^{-10}$, in the form in which it is also
implemented in the Heidelberg MCTDH package.\cite{mctdh_package}
For each resonance, the final propagation time and the norm of the wavefunction at that
time can be found in Table i in the supplementary material.

We note that all parameters were chosen conservatively and are not well-optimized.
Especially, the employed coordinate ranges are probably too large. They do not require
an in-depth optimization because our DP algorithm does this automatically: If the
wavepacket will not enter a certain region in coordinate space, no basis function
will become active in that region during the propagation and computational
costs will not increase, compared to a carefully optimized coordinate range.
Further, this means that the CAP width needs not be tuned to increase computational
efficiency (although, the stronger the CAP, the earlier the wavefunction is absorbed in
the CAP region, and the fewer basis functions are needed).
This gives the DP-DVR algorithm
more of black-box character than conventional DVR dynamics. However, the other parameters
still
required convergence tests.
The number of DVR functions, which determines the maximum momentum that can be described,
can be easily determined by checking reduced densities of the wavefunction in momentum
space.
For the filter diagonalization and decay dynamics of
selected resonances, careful convergence tests with tighter parameters have been pursued
and the stated final parameters, {including $R_\infty$}, were chosen
based on conservative
conclusions from these tests.%
\footnote{To avoid unnecessary computational costs, not all the resonances
have been propagated with the final parameters. Further, the propagation for the filter
diagonalization has been performed with a larger basis but the results with the basis
from \autoref{tab:basis_parameters} are virtually identical.}

\begin{table}[!htbp]
\caption{Basis sizes $N$ and coordinate ranges for the three Jacobi coordinates $R, r$
and $\theta$
for the two employed PES. {The values in the ranges are given in units of
  the Bohr radius $a_0$.\cite{conventions_quack}}}
\label{tab:basis_parameters}
\begin{ruledtabular}
 \begin{tabular}{lll|ll|ll}
      &\multicolumn{2}{c|}{$R$} & \multicolumn{2}{c|}{$r$} &
\multicolumn{2}{c}{$\theta$}\\ \hline
 PES &$N$ & range & $N$ & range & $N$ & range\\
 \hline
 WKS\cite{HCO_I_schinke,HCO_II_schinke} & 210 & $[1.5,28]$ & 78 & $[1.5,6]$ & 60 &
$[0,\pi]$\\
 SAG\cite{HCO_pes_song_2013} & -"- & -"- & 34 & $[1.5,3.49]$ & -"- & -"- \\
 \end{tabular}
 \end{ruledtabular}
\end{table}

\subsection{Energies and widths}
\label{sec:energies}
The computed resonance energies and widths on the WKS surface are given in
\autoref{tab:energies} and compared with both
{the experimental and theoretical} values from
\lits{DCO_I_schinke,DCO_II_schinke}.

Note that some energetically low-lying resonances (below ${\tilde\nu} =
\unit[8770]{cm^{-1}}$, ${\tilde\nu}$ is the vibrational resonance {wavenumber} relative to the
ground state)
in polyad $5$ and one in polyad $5.5$
are not included in our simulations. They were
also not experimentally accessible. Here, we consider resonances in polyad $5$ and
$5.5$ that are within a {range} of $\unit[8770]{cm^{-1}}$ and
$\unit[10050]{cm^{-1}}$.

Compared to the computed {wavenumbers} from \lit{DCO_II_schinke}, ours are systematically
smaller but agree within $\sim\unit[5]{cm^{-1}}$. The decay widths have a better
agreement; there, except for
resonance (0,3,4), the maximal absolute deviation is $\unit[1]{cm^{-1}}$. Note that
Keller
\textit{et al.} reported that their basis was probably too small to
yield accurate calculations.\cite{DCO_II_schinke} Their basis used in the calculations
for \ce{HCO}\cite{HCO_II_schinke} was significantly larger.
To our knowledge, there are no further calculations done for \ce{DCO} on the WKS surface.
However, theoreticians have used resonance calculations for \ce{HCO} on the WKS surface
as a benchmark
case.%
\cite{HCO_IV_schinke,HCO_poirier_2002a,HCO_mandelshtam_2002,HCO_tremblay_2005,
HCO_mctdh_ndengue_2015,HCO_pes_ndengue_2016} There, the deviations from the results of
\lit{HCO_II_schinke} have a similar magnitude as the deviations shown here.
To conclude, our DP-DVR method with filter diagonalization gives results that are within
reasonable agreement with the results from Keller \text{et al.}
To allow for a better comparison, more extensive tests with \ce{HCO} should be done but
this is not within the scope of this work.

\begin{table*}[!htbp]
    \caption{Comparison of computed resonance {transition wavenumbers $\tilde{\nu}$} (relative to
the ground state) and widths $\Gamma$ from this work (DP) with the experimental
(Exp.) and theoretical (WKS) results from \lits{DCO_I_schinke,DCO_II_schinke}.}
\label{tab:energies}
\begin{ruledtabular}
    %
 \begin{tabular}{lc%
 rrrc|%
 rddl|%
 rclclclc %
 }
       &            &%
       \multicolumn{4}{c|}{$\tilde\nu/\unit{cm^{-1}}$} & %
        %
        \multicolumn{4}{c|}{$\Gamma / \unit{cm^{-1}}$}\\\cline{3-4}\cline{5-7}\cline{8-10}
     P.\footnotemark[1] & label\footnotemark[2] &  %
 %
     \multicolumn{1}{c}{Expt.\footnotemark[3]} & \multicolumn{1}{c}{WKS\footnotemark[2]} &
\multicolumn{1}{c}{DP\footnotemark[4]}  & $\Delta$\footnotemark[5]& %
     \multicolumn{1}{c}{Expt.\footnotemark[3]} & \multicolumn{1}{c}{WKS\footnotemark[2]} &
\multicolumn{1}{c}{DP\footnotemark[4]}  & $\Delta$\footnotemark[5]& %
     \multicolumn{8}{c}{decomposition of wavefunction\footnotemark[6]}\\\hline
 %
 %
 %
5 & ((034)) & 8778  & 8780 & 8775 & 5 &  3.50  & 7.6 & 5.6 & 2 &38:& 034 & 30:& (411) & 16:& 222 & 16:& 124  \\
5 & ((042)) & 8821  & 8832 & 8830 & 2 & {<}2.00  & 1.1 & 1.1 & 0 &41:& 222 & 32:& 042 & 23:& 132  \\
5 & ((222)) & 8902  & 8901 & 8895 & 6 &  1.06  & 1.9 & 1.2 & 0.7 &48:& 222 & 32:& 042  \\
5 & (050)   & 8942  & 8953 & 8950 & 3 &  1.79  & 0.14 & 0.13 & 0.01 &44:& 050 & 33:& (140) & 15:& 230  \\
5 & (132)   & 9050  & 9031 & 9029 & 2 &  0.34  & 0.28 & 0.28 & 0 &59:& 132 & 24:& 042 & 11:& 222  \\
5 & (230)   & 9099  & 9099 & 9096 & 3 &  0.20  & 0.32 & 0.32 & 0 &57:& 230 & 32:& 050  \\
     5.5 & 027 & \multicolumn{1}{c}{---}  & 9235 & 9234 & 1 &  \multicolumn{1}{c}{---}  & 14 & 13 & 1 &100:& 027\\
5 & ((140)) & 9272  & 9251 & 9248 & 3 &  0.29  & 0.32 & 0.31 & 0.01 &64:& 140 & 20:& 230 & 14:& 050  \\
    5.5 & ((321)) & \multicolumn{1}{c}{---}  & 9496 & 9494 & 2 &  \multicolumn{1}{c}{---}  & 17 & 17 & 0 &57:& (321) & 32:& 035  \\
5.5 & (043) & 9614  & 9630 & 9629 & 1 &  2.30  & 1.5 & 1.4 & 0.1 &38:& (223) & 29:& 043 & 27:& 133  \\
5.5 & (223) & 9686  & 9690 & 9688 & 2 & {<}5.00  & 5.6 & 5.5 & 0.1 &52:& (223) & 25:& 043 & 13:& 035  \\
5.5 & ((051)) & 9757  & 9764 & 9762 & 2 &  0.83  & 0.66 & 0.64 & 0.02 &26:& 051 & 24:& 231 & 22:& 141 & 22:& 043  \\
5.5 & ((133)) & 9819  & 9807 & 9805 & 2 & {<}3.00  & 1.9 & 1.8 & 0.1 &45:& 133 & 21:& 043 & 21:& 051 & 11:& (223)  \\
5.5 & (231) & 9896  & 9893 & 9891 & 2 &  1.22  & 1.6 & 1.6 & 0 &56:& 231 & 29:& 051  \\
5.5 & ((141)) & 10065  & 10046 & 10044 & 2 &  6.00  & 3.9 & 3.9 & 0 &46:& 141 & 21:& 420 & 21:& 231  \\
 \end{tabular}
\footnotetext[1]{Polyad quantum number.}
\footnotetext[2]{Assignment according to \lit{DCO_II_schinke}. The more parentheses the
assignment has, the more complicated the shape and the more difficult the assignment; see
\lit{DCO_II_schinke} for details.}
\footnotetext[3]{According to \lit{DCO_I_schinke} and as given in \lit{DCO_II_schinke}.}
\footnotetext[4]{This work with the PES from \lits{HCO_I_schinke,HCO_II_schinke}.}
\footnotetext[5]{Difference between the theoretical results from \lit{DCO_II_schinke} and
ours.}
\footnotetext[6]{Each entry: First part is contribution in percent, second part is
zero-order state assignment; taken from \lit{DCO_II_schinke}.}
 \end{ruledtabular}
\end{table*}

In \autoref{tab:energies_SAG}, vibrational {wavenumbers} and widths for five selected
resonances are
shown for the SAG surface and compared against experiment and results using the WKS
surface. For four of them, experimental KER spectra are available as well
(\autoref{sec:res_exp}).
Compared to our WKS results, the {wavenumbers} differ from those
obtained with the SAG surface by up to $\unit[54]{cm^{-1}}$. The widths differ by up to
$\unit[3]{cm^{-1}}$. The WKS {wavenumbers} are closer to the experimental values and so are
most of the widths --- except for resonance (0,5,0).
Note that some SAG states have components of the wavefunctions at linear geometries where
Renner-Teller coupling and a conical intersection occur; see
\autoref{sec:dp-dvr}. Using
single-reference coupled-cluster calculations, the SAG surface was not optimized for
linear geometries. %
Since both the {wavenumbers} and rovibrational distributions (\autoref{sec:rovib_distr}) from
the WKS surface are typically closer to the experiment, we focus in the following on the
WKS
surface but mention the SAG results where they are available.\footnote{The PES of
Ndengu{\'e} \textit{et al.} shows a better agreement to experimental data for many but
not all resonances in \ce{HCO}. Some {wavenumbers} and widths are actually still better
described by the WKS surface. Thus, it cannot be expected that this PES would give much
improved results than the two PES studied here.}

\begin{table*}[!htbp]
    \caption{Comparison of computed resonance {transition wavenumbers $\tilde \nu$} and widths
$\Gamma$ from this work with the PES from \lits{HCO_I_schinke,HCO_II_schinke} (WKS) and
the PES from \lit{HCO_pes_song_2013} (SAG), together with the experimental (Exp.) results
from \lits{DCO_I_schinke,DCO_II_schinke}.}
\label{tab:energies_SAG}
\begin{ruledtabular}
 \begin{tabular}{lc%
 rrrcc|%
 rdddd%
 }
       &            &%
        \multicolumn{5}{c|}{${\tilde\nu}/\unit{cm^{-1}}$} & %
        \multicolumn{5}{c}{$\Gamma / \unit{cm^{-1}}$}\\\cline{3-7}\cline{8-12}
P.\footnotemark[1] & Label\footnotemark[2] &  %
     \multicolumn{1}{c}{Expt.\footnotemark[3]} &
\multicolumn{1}{c}{DP:WKS\footnotemark[4]} & \multicolumn{1}{c}{DP:SAG\footnotemark[5]}  &
\multicolumn{1}{c}{$\Delta_\text{WKS}$\footnotemark[6]}&
\multicolumn{1}{c}{$\Delta_\text{SAG}$\footnotemark[7]} &
     \multicolumn{1}{|c}{Expt.\footnotemark[3]} & %
\multicolumn{1}{c}{DP:WKS\footnotemark[4]} & \multicolumn{1}{c}{DP:SAG\footnotemark[5]}  &
\multicolumn{1}{c}{$\Delta_\text{WKS}$\footnotemark[6]}&
\multicolumn{1}{c}{$\Delta_\text{SAG}$\footnotemark[7]} \\ \hline
5 & ((042)) & 8821  & 8830 & 8849 & -9 & -28 &  {<}2.00  & 1.1 & 0.77 & {<}0.90 & {<}1.2  \\
5 & ((222)) & 8902  & 8895 & 8925 & 7 & -23 &   1.06  & 1.2 & 0.53 & -0.2 & 0.5  \\
5 & (050) & 8942  & 8950 & 8957 & -8 & -15 &   1.79  & 0.13 & 1.2 & 1.7 & 0.59  \\
5.5 & (231) & 9896  & 9891 & 9928 & 5 & -32 &   1.22  & 1.6 & 0.36 & -0.38 & 0.86  \\
5.5 & ((141)) & 10065  & 10044 & 10098 & 21 & -33 &   6.00  & 3.9 & 0.85 & 2.1 & 5.2  \\
 \end{tabular}
\footnotetext[1]{Polyad quantum number.}
\footnotetext[2]{According to \lit{DCO_II_schinke}.}
\footnotetext[3]{According to \lit{DCO_I_schinke}.}
\footnotetext[4]{This work with the PES from \lits{HCO_I_schinke,HCO_II_schinke}.}
\footnotetext[5]{This work with the PES from \lit{HCO_pes_song_2013}.}
\footnotetext[6]{Difference between Exp. and WKS results.}
\footnotetext[7]{Difference between Exp. and SAG results.}
 \end{ruledtabular}
\end{table*}

\subsection{Adiabatic rovibrational states}
\label{sec:adiabatic_repr}

To shed more light on the coupling of the different states, we look at the adiabatic
potential energy curves in $R$ defined by the following eigenvalue problem in
$\{r,\theta\}$:
\begin{equation}
\begin{split}
\left[-\frac{\hbar^2}{2\mu_{\ce{CO}} r^2} \partdd{}{r} +
\left(\frac{1}{2\mu_{R} R^2} + \frac{1}{2\mu_r r^2}\right) \hat j^2 +
V(R,r,\theta)\right] \\
\Ket{\chi_{n}(r,\theta; R)} %
= E_{n}(R) \Ket{\chi_{n}(r,\theta; R)},
 \end{split}
 \label{eq:ad_hamilt}
\end{equation}
where $\hat j^2$ is the angular momentum operator in $\theta$ and $V(R,r,\theta)$ is the
WKS potential. $\mu_r$ is the reduced mass of \ce{CO}. A similar but
one-dimensional Hamiltonian, averaged over $\theta$, was
considered for \ce{HCO} in \lit{HCO_I_schinke}.
For \ce{DCO}, the agreement found with this angle-averaged potential is less
satisfactory.

\begin{figure*}%
 \includegraphics[width=.7\textwidth]{adiab_pes}
 \caption{Adiabatic potential energy curves for the \ce{CO} vibrational problem as a
function of
 \ce{D-CO} distance $R$ in Jacobi coordinates; see \autoref{eq:ad_hamilt}.
 The adiabatic curves are assigned \ce{DC=O} stretch $v_2$ and \ce{D-C=O} rotation
$v_3$ quantum numbers
 according to the character of the eigenstates.
 Note the occurrence of many avoided crossings where the character of the adiabatic
states
is ambiguous.
 Further, note that only a selection of curves ($v_2\le 5$ and $v_3\le 5$) is depicted,
 i.e., there are many more curves in this energy region.
 For $v_2 \ge 4$, only curves for $v_3 \le 3$ are shown and they should be regarded
as qualitative in the interaction region.
 }
 \label{fig:adiab_pes}
\end{figure*}

Selected adiabatic potential energy curves are shown in \autoref{fig:adiab_pes}. For
$R < \unit[4]{a_0}$, there are many avoided crossings and as such strong couplings
between states
that have a different $v_2$ number.
For example, the curve for $v_2=3, v_3=0$ shows a coupling with $v_2=0, v_3=5$ and, at
small $R$, even with $v_2=0, v_3=4$.
These curves can be used to qualitatively understand the mixing of the zero-order
states: {Resonance state} (0,5,1) has contributions of (2,3,1), (1,4,1) and
(0,4,3) (see
\autoref{tab:energies}).
The avoided crossing at $R\approx \unit[3.3]{a_0}$ for $v_2=5,
v_3=1$ and $v_2=4, v_3=3$ explains the mixing of states (0,5,1) and (0,4,3).
Although the curve also overlaps with $v_2=3, v_3=5$, the mixing is less significant
because the difference in the character of the two states is larger such that the
coupling is reduced.
Due to the excitation in $v_1$, states (2,3,1) and (1,4,1) mix with (0,5,1) as well.

It would strongly simplify the analysis of the decomposition of the states if the
adiabatic states $\Ket{\chi_{n}(r,\theta; R)}$ were (quasi-)diabatized such that the
character of the states does not change for all considered values of $R$.
A projection of the resonance states onto the diabatized states would give a quantitative
decomposition in terms of quantum numbers $v_2$ and $v_3$. However, we were not able to
obtain useful diabatic states that have a conserved nodal pattern for all values of
$R$; see Section iii in the supplementary material for more details.

\subsection{Product distributions}
\label{sec:rovib_distr}
The experimental and convoluted theoretical KER spectra
for resonance {states} (2,2,2), (0,5,0), (2,3,1) and (1,4,1) are shown in
\autoref{fig:KER}.
All theoretical KER spectra without convolution are shown in the supplementary
information (Figures iv -- x{i}v).
The agreement between the theoretical and the experimental spectra is good.
For (0,5,0) the spectrum from the SAG surface agrees better with experiment.
Whereas the spectrum from the WKS surface shows a bimodal distribution,
both experimental and SAG spectra show a monomodal rotational distribution for $v=0$.
This is in accord with the better agreement of the resonance width.  For
the WKS surface, the width is too small; compare with \autoref{tab:energies_SAG}.
However, for the other three resonances, the WKS surface shows better agreement with the
experiment, both in terms of peak positions and intensities. Compared to the experimental
results, some, but not all, peaks exhibit a minor shift. This cannot be explained simply
by a different asymptotic dissociation energy because there is no consistent trend.
Instead, the shifts probably arise because the KER spectra are very sensitive to the
shape of the PES, in particular near the transition region.

\begin{figure*}
 \includegraphics[width=.7\textwidth]{KER.pdf}
 \caption{
Experimental (Exp) and convoluted theoretical (WKS and SAG) total kinetic energy release
spectra $P(E_{\ce{D}})$ and corresponding \ce{CO} rovibrational product state
distributions
for the experimentally investigated \ce{DCO} ($\widetilde X$) resonance states.
WKS\cite{HCO_I_schinke,HCO_II_schinke} and SAG\cite{HCO_pes_song_2013} stands for the two
employed PES.
The vertical lines indicate the maximal available energies $E_{\text{avl}}$ for
formation of \ce{CO} in $v$ = 0, 1 and 2 and the energies of the \ce{CO} product
rotational ($j$) states.
The \ce{CO} rovibrational energies corresponding to the vertical lines are obtained from
computations with the WKS PES.
The theoretical curves are convoluted with a Gaussian, $\exp[-(E/\sigma)^2/2]$,
with an arbitrarily chosen width  of $\sigma=\unit[60]{{h\, c\,}cm^{-1}}$.
}
 \label{fig:KER}
\end{figure*}

To allow for a easier comparison of the theoretical results, we have converted the
energetically resolved
spectra to distributions resolved rovibrationally by the asymptotic \ce{CO}
fragment (see \autoref{sec:theory_rovib}).
Two of the distributions (for resonances (2,3,1) and (0,5,0)) are shown in
\autoref{fig:bars}
(black/darker
bars).
The rest of the distributions is shown in the supplementary material (Figures xv --
xx{i}v).
Except for (0,2,7), all computed resonances have major contributions for $v=1$ (compared
to $v=0$) and
negligible contributions for $v=2$. As in \ce{HCO},\cite{HCO_I_schinke,dixon_1992}
the distributions typically are multimodal. Especially the resonances with large initial
quantum
numbers in $v_2$ and $v_3$ show a complicated multimodal pattern for a \ce{CO}
stretch quantum number of $v=0$.
The multimodal pattern is in agreement with semiclassical
estimates used for \ce{H2O} and
\ce{HCO}.\cite{H2O_schinke_1991,HCO_I_schinke,HCO_III_schinke}

To evaluate the changes of these distributions during the decay, we projected the part of
the initial ($t=0$) resonance that lies in the dissociation region (we chose
$R\ge\unit[5]{a_0}$)
onto the asymptotic rovibrational states; see \autoref{eq:P_Ed_analysis_line_vj}.
Characteristic examples of such
distribution changes are shown as gray/brighter bars
in \autoref{fig:bars}.
The relative amount of the initial wavepacket that lies in this asymptotic region
ranges from $7\%$ (resonance (0,5,0)) to $33\%$ (resonance (3,2,1)). For most resonances,
this
ratio lies between  $13\%$ and $20\%$.
In most cases, the qualitative features of these asymptotic distributions
do not change during the dynamics, hence the projection at $t=0$ provides a very
reasonable estimate of the
rovibrational product distribution, even though the major part (typically more than
$80\%$) of the initial wavepacket resides in the interaction region.
Some resonances exhibit a shift to higher (lower) $j$ values for $v=0$
($v=1$).

Only for those resonances that have a small decay width ((0,5,0), (1,3,2), (2,3,0) and
(1,4,0); (2,3,1) on
the SAG surface), we see larger deviations, see, e.g., resonance (0,5,0) in
\autoref{fig:bars}. A small decay width means a {long} decay time and as
such more
time for interference processes etc.~which lead to these more
significant asymptotic pattern changes.
This follows from an investigation of the non-adiabatic coupling elements of the
adiabatic, $R$-dependent
rovibrational states (see \autoref{sec:adiabatic_repr}). It shows that the different
states couple with each other even for $R>\unit[4.5]{a_0}$, especially those with
the same quantum number $v_2$; compare with \autoref{fig:adiab_pes} and Section
iii in the supplementary material.
Further, the stated resonances are those where less than $10\%$ of the
initial wavepacket lies in the interaction region (naturally, a small decay width
causes a smaller fraction of that resonance in the asymptotic region).

\begin{figure}
\includegraphics[width=\columnwidth]{bars_321_050.pdf}
\caption{Asymptotic distributions resolved by \ce{CO} vibration-rotation
  quantum numbers, for resonances (2,3,1) (left) and (0,5,0) (right) using the WKS
PES.\cite{HCO_I_schinke,HCO_II_schinke}
The upper (lower) panels show the distributions for stretch quantum number $v=0$
($v=1$) versus
different rotational quantum numbers $j$ of the asymptotic \ce{CO} fragment (bend
quantum numbers for the undissociated state).
The distributions are scaled such that the maximal value is $1$.
The darker bars show the distributions for the final wavepacket,
$\ket{\Psi(t\to\infty)}$,
the brighter bars for the initial wavepacket,
$\ket{\Psi(t=0)}$, both in the asymptotic region.
}
\label{fig:bars}
\end{figure}

\subsection{Decay processes}
\label{sec:decay_processes}

We now analyze and discuss mechanisms of resonance decay, i.e.,
the occurrence of IVR during the decay.
{For that, the coordinate range in $R$ is increased (compare with
  \autoref{sec:res_params}) such that the resonance states obtained from filter
diagonalization are no longer eigenstates and will spread in $R$ and decay.}
{Note that we analyze here the part of the wavepacket that remains in the
interaction region during the decay. A loss in a
quantum number during the IVR means that the corresponding energy is moved from
the interaction region to the continuum.
}

Using a polyad model Hamiltonian, the Temps group has already done an IVR
analysis.\cite{DCO_polyad_troellsch_2001,DCO_polyad_renth_2003}
During dissociation, the bending motion (quantum number
$v_3$) turns into rotational motion of the \ce{CO} fragment (quantum number $j$).
Semiclassically,
four quanta
need to be transferred to the \ce{D-C} stretch degree of freedom. The \ce{C-O}
stretch quantum number $v_2$ remains (approximately) conserved and turns into $v$.

Here, we consider the \textit{ab initio} Hamiltonian, where an in-depth and quantitative
analysis is not possible.
As already mentioned in \autoref{sec:intro}, the assignment in terms of
zero-order
eigenstates and their vibrational quantum numbers is problematic. This was already
visible in \autoref{tab:energies} above, and it becomes even more obvious when
analyzing the time-dependent wavefunctions further: Already counting the
number of nodes (by plotting $\Re{(\Psi)}$) or counting  the number of pronounced lobes
(by plotting $|\Psi|^2$) can lead to different assignments because the intensities of the
lobes vary significantly.
In this sense, any assignment should be regarded as approximate, and
the IVR mechanism should be regarded as qualitative.

In the following, the assignment is performed based on counting the number of lobes.
Qualitatively, we reproduced the assignment from \lit{DCO_II_schinke} (see
\autoref{tab:energies}).
The assignment was done based on cuts of Jacobi coordinates that have been
shifted and rotated such that the first excited adiabatic state retained
its orientation for different cut values (see also \autoref{sec:adiabatic_repr}).
Further, we plotted cuts in Eckart bond coordinates, i.e., coordinates $\{X, Y,
\phi\}$, where $X$ ($Y$) is the \ce{C-D} (\ce{C-O}) distance and $\phi$ the angle
$\sphericalangle(\ce{DCO})$ between the corresponding vectors $\vec{X}$ and $\vec{Y}$.
Here, we solely show cuts of the wavefunction in Eckart coordinates, since
they provide clearer nodal patterns in the decisive interaction region.
Throughout, all cuts are performed along coordinate
values that show significant contributions to the wavefunction.

Note that we analyze the wavefunction in the interaction region, that is, we analyzed
that  part of the wavefunction that remains {bound} during the studied
propagation
times. Hence, the following analysis is not directly comparable with the rovibrational
product state distributions shown in \autoref{sec:rovib_distr}.
The direct conversion of the bound to the unbound part in the continuum
is hard to analyze since it happens over a wide coordinate range and over long
propagation times and since the initial wavefunctions already extends into the
dissociation region. Indeed, already the initial wavefunctions qualitatively contains all
required components in the asymptotic region (see \autoref{sec:rovib_distr}),
although these asymptotic parts typically contribute only 13--20\% to the
total resonance wavefunction.

\subsubsection{Polyad 5}
\label{sec:mech_5}

Cuts of the decay of the (0,3,4) resonance in the plane of \ce{C-O} stretching
(\ce{D-C} stretching) and \ce{D-C-O} bending are shown in Eckart bond coordinates in
\autoref{fig:decay_034} (\autoref{fig:decay_034_R}).
The upper left panel of \autoref{fig:decay_034} shows a part of the initial
resonance that can be assigned as $v_1 = 3$ and $v_3=4$ (there are four lobes in the
\ce{C-O} distance $Y$ and  five lobes in the bending angle $\phi$).
Here, the assignment is already ambiguous, because there is no contiguous nodal pattern.
However, an inspection of different cuts and in different coordinates (see
\autoref{sec:decay_processes}) verifies the assignment.
The upper left panel of \autoref{fig:decay_034_R} shows a part of the initial
resonance that can clearly be assigned as $v_{{1}}=0$ and $v_3=4$.
Note that the other zero-order components are typically visible in different coordinate
ranges such that there are regions where the different components do not significantly
overlap.

A distinctive change in the vibrational structure happens only after the norm
of the wavefunction has decreased to $0.15$ or less.
{A decrease of the norm means a decay of the wavefunction because it
  entered the region of the CAP.}
This is also the case for
the other resonances studied.
Before IVR takes place, there are oscillations between the different zero-order components
of the wavefunction, that is, the intensities of the lobes
change.
This can be seen in the plots shown in the upper two panels of
\autoref{fig:decay_034}, although the oscillations are typically less intensive.

At propagation times when the norm is below $0.15$,
a decrease of the bending quantum number $v_3$ from $4$ to $2$ happens; see
\autoref{fig:decay_034} and \ref{fig:decay_034_R}.
Neither an increase in $v_1$ nor a change in $v_2$ is visible in the interaction region.
This is valid also for other cuts of the wavefunction where other
zero-order states show contributions. For the zero-order $411$ contribution to the 034
resonance,
there is an additional decrease of $v_1$ to $2$.
The oscillations of the different zero-order states, the approximate
conversion of quantum number $v_2$ and the decay of $v_3$ are all in agreement with
the analysis done by a polyadic model
Hamiltonian.\cite{DCO_polyad_troellsch_2001,DCO_polyad_renth_2003}

\begin{figure}
 %
 %
 %
 %
 \includegraphics[width=\columnwidth]{034_Y.pdf}
 \caption{Contour values of $|\Psi(X,Y,\phi; t)|^2$ at $X=\unit[2.2]{a_0}$
and different times, for the (0,3,4) resonance. $X$ is the \ce{D-C} distance, $Y$
the \ce{C\bond{3}O} distance and $\phi$ the \ce{D-C=O} bending angle in Eckart bond
coordinates.
 For each panel, the shown function is normalized to have the maximal value of $1$. For
a comparison of the relative intensity, see the norm values in the panel captions.
 }
 \label{fig:decay_034}
\end{figure}

\begin{figure}
 %
 %
 %
 %
 \includegraphics[width=\columnwidth]{034_X.pdf}
 \caption{Same as \autoref{fig:decay_034} but showing cuts of $|\Psi(X,Y,\phi; t)|^2$
at $Y=\unit[2.53]{a_0}$.
$X$ is the \ce{D-C} distance, $Y$ the \ce{C\bond{3}O} distance and $\phi$ the \ce{D-C=O}
bending
angle in Eckart bond coordinates.
}
 \label{fig:decay_034_R}
\end{figure}

For the resonances (0,4,2), (2,2,2), (0,5,0), (1,3,2), (2,3,0), (1,4,0) (polyad 5) and
(0,4,3) (polyad 5.5),
only minor oscillations of the lobes occur.%
\footnote{
  For (0,4,2), the resonance {state} computed with the SAG PES does show an
IVR with a
decrease in $v_3$ to $2$ and $1$, but the initial state has a significant
contribution near the linear configuration of \ce{DCO}.
Since linear configurations are not properly described (see text), this result has to be
taken with caution.
}
No IVR is visible and the
oscillations are much less pronounced than that shown in the upper panels of
\autoref{fig:decay_034} for (0,3,4).
To some extent, this can be explained by the small decay rate of the
resonances. Except for (0,4,3) (polyad 5.5), they all have a decay width of $\Gamma \le
\unit[0.32]{cm^{-1}}$. In polyad 5.5, resonance (0,4,3) has the second smallest value of
$\Gamma$. A small reaction rate is correlated with a hindered
IVR.\cite{DCO_polyad_renth_2003} However, resonance (0,5,1), the resonance with the
smallest
value
of $\Gamma$ ($\unit[0.64]{cm^{-1}}$) in polyad 5.5, does show a decay
mechanism  (see \autoref{sec:mech_55}) but also lies higher in energy and has an evenly
spread-out distribution of four zero-order components such that the coupling to other
states may be larger; see also below.

To show how insignificant the temporal change in wavefunction structure can be, consider
the
cut of the (0,5,0) resonance shown in \autoref{fig:decay_050}.
Even after propagating for \unit[175]{ps} and after decay of the norm
to a value of $0.11$, the structure does not change.
For checking our results, we have propagated the (0,5,0) state using smaller coordinate
ranges
and
a higher propagator accuracy with a standard DVR code (without DP) until \unit[300]{ps},
where the norm has dropped down to a value of $0.02$. Even then, no significant change in
the
structure of the wavefunction is visible. Additionally,
our DP-DVR results are confirmed by this conventional DVR run.

For a polyadic model Hamiltonian, Temps \textit{et al.}~studied the decay
of a \emph{pure} (0,5,0) state.\cite{DCO_polyad_renth_2003} The state turned, among
others, into (1,4,0) and (2,3,0) within less than $\unit[0.5]{ps}$.
Here, already the \emph{initial} resonance state consists of these components
(not seen in the cuts shown in \autoref{fig:decay_050}); see \autoref{tab:energies}.
Hence, the \emph{initial} state already has all main zero-order
components needed for the IVR to happen. This explains the small
oscillations in the nodal pattern.

This further means that the zero-order states included in the initial
resonance states are strongly coupled whereas they couple weakly to other
states.
The strong coupling of the states within one polyad is stressed in \lit{DCO_I_schinke}.
Indeed, resonances (0,4,2), (2,2,2) and (1,3,2) consist of the corresponding zero-order
states and so do resonances (0,5,0), (1,4,0) and (2,3,0); see \autoref{tab:energies}.
In contrast, resonance (0,3,4) shows an IVR. However, its decay rate is much larger and
the resonance has components of (2,2,2) but also of the different zero-order states
(4,1,1) and (1,2,4).
The strong coupling between states $\{(0,4,2), (2,2,2), (1,3,2)\}$ and $\{(0,5,0),
(1,5,0), (2,3,0)\}$ is in
agreement with the parameters from the polyadic model
Hamiltonian.\cite{DCO_polyad_troellsch_2001}

\begin{figure}
 %
 %
 \includegraphics[width=\columnwidth]{050_Y.pdf}
 \caption{Same as \autoref{fig:decay_034} but showing cuts of $|\Psi(X,Y,\phi; t)|^2$
at $X=\unit[2.15]{a_0}$ for the (0,5,0) resonance.}
 \label{fig:decay_050}
\end{figure}

Considering the insignificant changes of the wavefunction within the interaction region,
it
may seem counterintuitive that for a subset of these states the asymptotic
rovibrational distributions of the \ce{CO} fragment do change significantly in
time. However, as pointed out in \autoref{sec:rovib_distr},
the rovibrational states still couple outside the typical interaction region where $R<
\unit[4.5]{a_0}$, such that the dynamics in the asymptote and in the interaction
regions are, to first order, not directly related. In fact, from
\autoref{fig:adiab_pes}, it may be argued that the distribution of the
adiabatic states on the energy axis, and thus also their couplings, strongly
change between $R<\unit[4.0]{a_0}$ and $R>\unit[4.0]{a_0}$, supporting
different dynamical behaviors.

As a side remark: On the SAG surface, resonance (0,5,0) does show an IVR with an
increase in $v_3$ to $1$ (with intermediate numbers up to $v_3=3$) and a
decrease in $v_2$ up to $v_2=2$.
However, the character of this resonance state also differs
from the state  computed on the WKS surface. Most importantly, the initial state already
has some  contributions of $v_3=1$ which the state on the WKS surface does not have (see
\autoref{tab:energies}).
Note that, in this case, $\Gamma$ is larger and, like the KER, closer to the experimental
value on the
SAG surface. Resonances with excitations in both $v_2$ and $v_3$ exhibit larger decay
rates than those with excitations only in $v_3$.\cite{DCO_II_schinke}

\subsubsection{Polyad 5.5}
\label{sec:mech_55}

In polyad 5.5, resonance (0,2,7) decays rapidly with a decrease in $v_2$. However, it has
a
strong contribution at the linear geometry. Due to the neglect of Renner-Teller coupling
in this simulation and since resonance {states} with high bending motion
are experimentally hard
to
measure, we have not analyzed this state further in the present study.

As already mentioned in \autoref{sec:mech_5}, resonance (0,4,3) shows only minor
oscillations
between the zero-order components of the initial state.
Resonance (2,2,3) shows a decrease in $v_3$ from $3$ to $\{1,0\}$ (both $1$ and $0$)
and an \emph{increase} in $v_2$ from $4$ to $5$.
However, due to a component of $v_3=5$, it shows also contributions at linear geometry
and the results have to be taken with caution.
As for the previous resonances
where a clear IVR takes place, (0,5,1) shows a decrease in
$v_3$
whereas $v_2$ remains mostly conserved. %
Likewise, 133 decays to $v_3=\{2,1\}$
and the zero-order (0,5,1) state initially
contributing by $\sim~21\%$ (\autoref{tab:energies}) gets more populated.

A decrease in $v_3$ to $0$ while the other quantum numbers are approximately conserved is
clearly seen also in state (2,3,1), see \autoref{fig:decay_231} and
\autoref{fig:decay_231_R}.
Both cuts in $Y$ and $X$ show a decrease in $v_3$ whereas the $v_2=3$ and $v_1=2$
components are constant. At $\unit[26]{ps}$, the cut shown in $Y$ (right panel in
\autoref{fig:decay_231_R}) is more difficult to analyze because contributions from other
zero-order states become more visible.

The corresponding state on the SAG surface shows no significant IVR. There, the state has
similar zero-order components except for a reduced $v_1=2$ component. This decreases
the decay width which is smaller, compared to experiment; see \autoref{tab:energies_SAG}).
The hindered IVR due to the smaller decay width ($\Gamma=\unit[0.36]{cm^{-1}}$) is in
agreement with the discussion in \autoref{sec:mech_5}.

\begin{figure}
 %
 %
 %
 \includegraphics[width=\columnwidth]{231_Y.pdf}
 \caption{Same as \autoref{fig:decay_034} but showing cuts of $|\Psi(X,Y,\phi; t)|^2$
at $X=\unit[1.85]{a_0}$ for the (2,3,1) resonance.}
 \label{fig:decay_231}
\end{figure}
\begin{figure}
 %
 %
 %
 \includegraphics[width=\columnwidth]{231_X.pdf}
 \caption{Same as \autoref{fig:decay_034} but showing cuts of $|\Psi(X,Y,\phi; t)|^2$
at
$Y=\unit[2.5]{a_0}$ for the (2,3,1) resonance.}
 \label{fig:decay_231_R}
\end{figure}

As (2,3,1), state (1,4,1) decays in $v_3$. Here, the $v_2=5$ component (see
\autoref{tab:energies}) becomes more pronounced.
The contribution of the (4,2,0) zero-order state shows a decay from $v_1=4$ to $v_1=1$,
see
\autoref{fig:decay_141_R}. There, the wavefunction looks like it has increased in $v_3$
but an inspection of the phase cannot clearly confirm this.

State (1,4,1) computed on the SAG surface shows a similar initial state (with a reduced
component of the (2,3,1) state) and a similar decay mechanism.
There, $\Gamma$ is lower ($\unit[0.85]{cm^{-1}}$ compared to the experimental value of
$\unit[6]{cm^{-1}}$; see \autoref{tab:energies_SAG}), but not too low for IVR, compared
to the resonances that show no pronounced IVR.

\begin{figure}
 %
 %
 \includegraphics[width=\columnwidth]{141_X.pdf}
 \caption{Same as \autoref{fig:decay_034} but showing cuts of $|\Psi(X,Y,\phi; t)|^2$
at $Y=\unit[2.09]{a_0}$ for the (1,4,1) resonance.}
 \label{fig:decay_141_R}
\end{figure}

A sequential decay from $v_1=3$ \emph{via} $v_1=2$ to $v_1=\{1,0\}$
in conjunction with
a decay of $v_3=1$ to $v_3=0$ can be observed for resonance (3,2,1).
Again, $v_2$ remains conserved.
Note that this resonance in polyad 5.5 has the highest \ce{D-C} stretch excitation.
Due to the large decay width of $\Gamma=\unit[17]{cm^{-1}}$, the IVR begins quickly and
there are intermediate states with contributions from many zero-order states that are
hard to analyze.
Note that this state has some contributions of $v_3=5$ and, due to this high excitation
in the bending mode, contributions at linear geometries.
However, they are less pronounced than for the other states with similar contributions.

While a decrease in bending quantum number $v_3$ can be seen in all resonances
where a clear IVR occurs, a decrease in \ce{D-C} stretch quantum number $v_1$ can only be
seen for $v_1>2$, namely in states (3,2,1), (1,4,1) and (0,3,4) where the latter two have
zero-order states with $v_1=4$.

\section{Conclusions}
\label{sec:conclusion}

To summarize, we have employed our newly developed dynamically pruned DVR (DP-DVR) for
computing resonance states in \ce{DCO} of polyads $5$ and $5.5$  using filter
diagonalization and for subsequential propagation to analyze their decay mechanisms.
For selected resonances, the kinetic energy release (KER) spectra were compared to
experimental
results obtained from velocity-map images.

For this challenging test case where the wavefunction has to be propagated in the
asymptotic region for up to 180 picoseconds, DP-DVR works well and the computed resonance
energies and widths show good agreement with results from the literature.
The computed KER spectra are in good agreement with the experimental spectra.
Two PES have been compared. For many states, the WKS surface\cite{HCO_I_schinke} gives
slightly better results than the SAG surface.\cite{HCO_pes_song_2013}
Since no PES was constructed with this particular application in mind (decay dynamics of
energetically high-lying resonances far out into the asymptote),
no quantitative agreement between
theoretical and experimental results can be expected.
Also, the importance of including $J>0$ and Renner-Teller couplings to higher
electronic states at linear geometries still has to be elucidated.

The rovibrational distribution of the asymptotic \ce{CO} states shows major contributions
only for \ce{C\bond{3}O} stretch quantum numbers $v=0$ and $1$. The distribution in the
\ce{CO} rotational quantum number $j$ is multimodal. For states with larger decay widths
of $\Gamma > \unit[0.6]{cm^{-1}}$, the initial state already shows the qualitatively
correct shape of the distributions.
Due to a coupling of the rovibrational states even in the near-asymptotic region, states
with smaller decay rates show qualitatively different distributions after long
propagation times.

Analyses of the decay processes confirm the results from a polyad model
Hamiltonian.\cite{DCO_polyad_troellsch_2001,DCO_polyad_troellsch_2001}
For the studied resonance states, the $v_2$ quantum
number typically is a conserved quantity while
the wavefunction part in the interaction region shows a
decrease in quantum number $v_3$. For high \ce{D-CO} stretch excitations with
corresponding quantum number $v_2 > 2$, a decay in this quantum number is possible as
well. In contrast to the polyad model, all resonance {states} show
significant mixing of zero-order states.

Some {zero-order states}, in particular in polyad $5$, show very strong
coupling with each other. Almost all zero-order components needed for an IVR are already
contained in the initial {resonance} state and, for these states, no
appearance or disappearance of
additional zero-order components can be observed.

The qualitative agreements between a polyad model and full quantum dynamics confirm that
there are analyzable residues of orderly IVR mechanisms present in
the strongly anharmonic \ce{DCO} system. However, not surprisingly, our full
quantum dynamics also indicate where and how a mechanistic understanding
has to transcend a zero-order model picture.

\section*{Supplementary material}
See supplementary material for plots of the PES, the propagation times, details on the
diabatization and the asymptotic distributions of all resonance {states}.

\begin{acknowledgments}
We thank R.~Schinke, L.~Song, A.~van der Avoird and G. C.~Groeneboom for providing us with
their PES.
H.~R.~L.~thanks R.~Welsch for helpful discussions.
H.~R.~L.~acknowledges support by the Studienstiftung des deutschen Volkes.
J.~R., J.~W.~and F.~T.~gratefully acknowledge the financial support of the
experimental part of this work by the Deutsche Forschungsgemeinschaft.
J.~R.~is indebted to F.~Renth for discussions regarding the analysis of the photofragment
images. J.~W.~thanks the Alexander von Humboldt-Stiftung for a research fellowship.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


This statistic shows the opinions on ads shown next to relevant content among individuals in Germany in 2018. According to the survey, eleven percent of respondents stated it would have a negative effect on their perception of the advertised brand, while 28 percent responded that it would have a positive effect.
* The source adds the following information: "The respondents have been selected from our Nordic, German, UK and US panels consisting of more than 1.5 million panelists and weighed to achieve representativity on the more than 14,000 respondents who completed the survey".


Miyamoto, Mick. "Open Opportunities: Get Your Tight End Involved in the Option Pass Game." American Football Monthly (April 2012):44-45.
Open Opportunities: Get Your Tight End Involved in the Option Pass Game.
Miyamoto, Mick. Friends from the Agora (charcoal). 2014.
Friends from the Agora (charcoal).
Miyamoto, Mick. Record Holder (pencil and ink). 2012.
Record Holder (pencil and ink).
"What is Greek about Greek Art?" Book project and show in the Bisignano Gallery for Art 368: Art and Culture of Greece, Spr '14, Prof. Garfield & Dr. Mick Miyamoto.
What is Greek about Greek Art?


One of the most important festival of the year is just around the corner, EID and on this occasion different companies are launching special packages for their users, and Hike Messenger has also joined the league and they had launched EID special stickers the under its 'Festival of India' sticker pack.for Hike Messenger users, which will allow Indians to wish each using special 'Eid' sticker.
In past we had seen Hike has launched lots of stickers in different festive occasions and other important session, at this time Hike Messenger has over 5000 stickers for every occasion and festival, which its users can download and use.
Hike also recently announced the launch of automatic Sticker Suggestions in its latest update Hike 4.0, which recommends the perfect sticker for every moment based on what users type making it extremely easy for consumers to discover and use stickers.
The latest update of hike is available free for android users on the Google Playstore and for IOS users on the Apple App store. The technology for exchanging stickers has also been designed in such a way that sending stickers is consumes minimal data and works extremely well on 2G, making it super data efficient and an attractive proposition for consumers across the country.


The feast that celebrates the noturnal visit of Prophet Mohammad pbuh (peace be upon him) to heaven.
Eid al-Fitr Also known as al-Eid al-Sagheer (the little feast).
It is a three-day celebration to mark the end of Ramadan, the month of fasting.
Eid al-Adha Known commonly as al-Eid al-Kabeer (the big feast).
It falls at the end of the month of Hajj (pilgrimage to Mecca). It commemorates the Prophet Ibrahim's offering of Isma'il for sacrifice.
Holidays: Holidays in Jordan are either religious (Islamic or Christian) or celebrations of important events in Jordanian or Arab history. Non-Islamic holidays are fixed, while Islamic holidays vary according to the lunar Muslim calendar, as well as some Christian holidays vary according to the liturgical year.
*Islamic Holidays: As the lunar Hijra calendar is 11 days shorter than the Gregorian calendar, each year Islamic holidays fall approximately 11 days earlier than in the previous year. The precise dates are known only shortly before they fall, however, as they depend on the sighting of the moon.
**Christian Holidays: The liturgical year, also known as the church year, consists of the cycle of liturgical seasons in Christian churches that determine when feast days, including celebrations of saints, are to be observed. The dates may vary between the different churches, though the sequence and logic is largely the same.


text:
Испа́нско-Португа́льская епа́рхия (, Мадри́дская и Лиссабо́нская епархия, ) — епархия Русской православной церкви, расположенная на территории Испании, Португалии и Андорры. Входит в состав Патриаршего экзархата Западной Европы.

История
В 1761 году в Мадриде открылась домовая церковь при Российском посольстве. В 1882 году эта церковь закрылась в первую очередь из-за прекращения финансирования. Немногочисленные православные христиане (в основном сотрудники дипломатических миссий), проживавшие в Испании, остались без пастырского окормления.

Распад Советского Союза и коммунистического блока породил массовую экономическую эмиграцию на Пиренейский полуостров. В Испанию ехали украинцы, русские, белорусы, болгары. Больше всего прибывало румын и молдаван. Открытые в Испании и Португалии приходы Русской православной церкви были объединены в Испано-Португальское благочиние Корсунской епархии.

28 декабря 2018 года Священный синод Русской православной церкви образовал Испанско-Португальскую епархию на территории Испании и Португалии, выделив её из Корсунской епархии и включив в состав созданного тогда же Западноевропейского экзархата. К тому времени в Испании проживали 73 тысячи российских граждан и 106 тысяч украинских. На территории Испании совершали служение 17 священников в 25 приходах Русской православной церкви. 11 приходов и общин действовали в Португалии. При этом по словам протоиерея Андрея Кордочкина: «Приходы располагаются зачастую за несколько сот километров друг от друга, координировать их служение из Франции едва ли возможно. Создание новой епархии призвано преодолеть эту изоляцию, укрепить единство среди священников, которые совершают служение вдали друг от друга. Кроме того, существует ряд вопросов, связанных с юридическим существованием приходов, и которые могут быть решены лишь в том случае, если их администрация будет в столице».

18 января 2019 года архиепископ Нестор подписал указ о придании храму святой равноапостольной Марии Магдалины статуса кафедрального собора епархии.

Правящие архиереи
 Нестор (Сиротенко) (28 декабря 2018 — 13 октября 2022), в/у с 13 октября 2022 года

Храмы и приходы

 Андорра
 община иконы Пресвятой Богородицы «Казанская» в Сан-Жулиа-де-Лория

 Испания
 Кафедральный собор в честь равноапостольной Марии Магдалины в Мадриде
 Храм Благовещения Пресвятой Богородицы в Барселоне
 приход в честь Сретения Господня в Адехе на острове Тенерифе
 Храм в честь Архангела Михаила в Альтее,
 Богородице-Рождественский храм в Торревьехе
 Храм Рождества Христова в Пальма-де-Майорке
 приход в честь великомученика Георгия в Валенсии
 Храм в честь святого великомученика Георгия и святой мученицы Анастасии в Калонже
 приход в честь Вознесения Господня в Марбелье
 приход в честь святителя Николая Чудотворца в Севилье
 приход в честь святых мучеников Кирика и Иулитты в Льорет-де-Мар
 Храм в честь иконы Божией Матери «Скоропослушница» в Таррагоне
 приход в честь преподобной Марии Египетской в Малаге
 приход преподобного Иова Почаевского в Мурсии
 приход в честь Покрова Божией Матери в Гранада
 приход в честь Иверской иконы Божией Матери в Аликанте

 Португалия
 Кафедральный собор в честь Всех святых в Лиссабоне
 приход приход Новомучеников и Исповедников Российских в Порту
 приход Блаженной Ксении Петербургской в Фару
 приход Святителя Иоанна Златоуста в Кашкайше
 домовая церковь при Международном Христианском Центре духовной культуры «Покров» в Албуфейре
 храм Святого Апостола Андрея в Сетубале
 община в честь священномученика Киприана Карфагенского в Лагуше
 община в честь великомученика Георгия в Алмаде
 община Святителя Спиридона Тримифунтского на острове Мадейра
 часовня в честь пророка Божия Ионы на Азорских островах

Примечания

Ссылки
 официальный сайт http://orthodoxspain.com/
 Испанско-Португальская епархия на сайте patriarchia.ru

Епархии Патриаршего экзархата Западной Европы
Православие в Андорре
Православие в Испании
Православие в Португалии
Организации, основанные в 2018 году
Появились в 2018 году в Португалии

redpajama_set_name: RedPajamaWikipedia


This entry was posted in History - Religion - Education, Uncategorized and tagged Against Our Better Judgement, Al Jazeera America, Alison Weir, American foreign policy, Balfour Declaration, Canaan, Imperialism, Israel, Judaism, Palestine, Religion, Religious extremism, Symptoms of war, U.S. Foreign Affairs, War casualties, World War One Through Arab Eyes, Zionism by Professor Taboo. Bookmark the permalink.
Alison Weir's story about how she became informed about the Israel-USA history and current ramifications is very interesting. Like any person who wants to become informed about any of a variety of issues, she did the research. It's truly shocking how the truth she's revealed hasn't become common knowledge, but that most Americans have views represented by their shallow analysis that "those people have been fighting over there for thousands of years, and there's nothing anyone can do to stop it". The talks and writings of Alison Weir should be studied by every U.S. citizen. Thanks for presenting such important information.
Jerry, agree on all your points!
There is one generalization I've learned through my deeper studies of American history and political sciences: True freedom, liberty, economic free-enterprise and its regulation, and dwindling government-by-representation, not only has an obvious quality of life for a certain number, but unfortunately it also fosters and allows — if the masses and their elected officials allow/neglect injustices — very influential oligarchies. There is no need for me to go into the consequences of diminshed government and much needed public services here. I've covered that subject comprehensively in a series of posts these last several months. But Alison Weir's work and book is one example of well-funded special-interest organizations that have had and do swing now a big hammer/gavel in Washington, D.C.
Many thanks Jerry for stopping by and for sharing your valued feedback. It is again appreciated Sir!


Walkin Date: 16-Mar-2019 - 16-Mar-2019 | Time: 10:00 AM - 12:00 AM | Venue: Infosys BPM Limited, #785, Ground Floor Axis Sai Jyoti, 15th Cross 100 Feet Road, Sarakki, 1st Phase J P Nagar, Bengaluru, Karnataka – 560078.
Job for application Support-Unix and Xamarin with Dot Net.
Walkin Date: 23-Feb-2019 - 23-Feb-2019 | Time: 10:00 AM - 12:00 AM | Venue: Bangalore Venue: Infosys BPM Limited No.785, Ground Floor, Axis Sai Jyoti, 15th Cross Road, Outer Ring Rd, Sarakki, 1st Phase, JP Nagar, Bengaluru, Karnataka 560078. Reporting Time : 10 am – 12 pm Recruiter : Pooja Sharma Pune interview Venue: Infosys BPM Ltd. Plot No 24/3, Rajiv Gandhi Infotech Park, Hinjewadi, Phase - II, Village - Man, Taluka - Mulshi, Pune - 411 057.


Wight Jewels have just completed the second of two practice hours at the Gothenburg rinks, allowing them to adjust to the difference in rink size. The Island's own rink measures a mere 44m by 22m, way short of the 60m by 30m of Gothenburg's Frölundaborg Arena, where the 2010 Junior World Challenge Cup takes place. The Jewels have to learn to scale up their two programmes to fill the ice area when they skate, making their task all the harder; the team often heads off to Basingstoke before most competitions to get a better sense of skating on big ice.


Take a tour of our Resource & Crisis Center to learn how you can help move people from crisis to hope.
You're also welcome to visit our Oakland County facility to talk with us in person.
Join us on Thursday, April 18th, from 5pm-10pm for a Live Trivia Night to benefit Common Ground at the Great Lakes Culinary Center in Southfield! Read more here.
Our Crisis Residential Unit helped Paul get his life back.
Survivors of Suicide Loss support group sessions helped Terri to heal.


Ravese Plumbing & Gas knows exactly what kind of plumbing maintenance and repairs you need around your home. Whether you have a leaking tap, blocked drain, or need a new hot water system, Ravese Plumbing & Gas offers affordable solutions and advice.
Leaking taps are one of the main sources of water wastage in the home and can cause long-term damage, so it's best to call in a professional plumber straight away. Both your budget and your plumbing may suffer if you ignore a leaking tap.
If you have a burst pipe, you need an expert to save your home from flooding. Call Ravese Plumbing & Gas - we'll come to your home with all the right equipment to deal with your burst pipe or water leak emergency.
Call Ravese Plumbing & Gas to clean your blocked gutters and drainpipes before water builds up and damages your property. We use a hydro-jet to flush away debris and leave your gutters and drains clean.
You don't need to put up with leaking or blocked toilets anymore. If you suspect a leak or hear a hiss, give us a call. Our plumbers are never far away. We can also clear any blockages so you can relax, knowing your plumbing is in good hands.
Gas is a clean, green option for cooking and heating your home. If you're looking to make the switch or need a local plumber to service, repair or install gas in your home, call Ravese Plumbing & Gas today.
When it comes to problems with sewer lines, we've seen it all before. This includes the unpleasant signs indicating a blocked or broken sewer line. Call us if you suspect any problems with your sewer lines.
Our plumbers have the latest equipment on hand to discover the cause of your blocked drain, including drain cameras and hydro-jets. No need to bring in other contractors - we do it all.
There's nothing like a cold shower to ruin your day. If your hot water system is faulty or leaking, call us straight away. Our qualified plumbers are here to repair or replace your hot water system so you can enjoy your next hot shower.
Our plumbers use the latest equipment including drain cameras and hydro-jets to detect and clear your blocked drains. This means we find and fix the problem quickly which saves you both time and money.
Our expert plumbers will come to your home to discuss your plumbing requirements.


text:
Church / Life Issues / Sin in our Lives / Social Media / Society
Internet, Online Porn seen as Enabling Sexual Exploitation of Children
by asiel · Published February 11, 2019 · Updated February 10, 2019
An illustration shows a teenager looking over her Facebook page. The internet facilitates sexual exploitation, a category of child abuse, experts in this field told Catholic News Service. (CNS photo/Mariana Bazo, Reuters)
The internet facilitates sexual exploitation, a category of child abuse, according to experts in this field interviewed by Catholic News Service.
The internet also, they say, enables near universal access to violent pornography, with a range of negative implications, including normalising sexual aggression and the dramatic increase in children abusing other children.
In a recent report on the role of technology in sex trafficking, as reported by the Justice Department's Domestic Minor Sex Trafficking studies and based on interviews with 260 survivors, Vanessa Bouche, a political science professor at Texas Christian University, found the internet facilitated prostitution, through online ads, in 75 percent of the cases.
The average age of entry was 15. Young victims, under 1 through age 10, were exploited by family members (76 percent), while older minors were exploited by members of their social network or strangers, far more often than by family.
According to Mary Anne Layden, director of the sexual trauma and psychopathology program in the University of Pennsylvania's Department of Psychiatry, our society is at the point of "almost universal exposure" of children to pornography, which gives them "massive mis-education about intimacy and sexuality."
Children "learn that sex is non-intimate, violent, adversarial, that it is non-relational, it is degrading and it is narcissistic," she told CNS. "Almost 90 percent of pornography coded by researchers is violent, so boys are being taught: Women like to be forced, women like to be raped, fisted, choked, gagged and slapped."
Women are depicted as enjoying, or having a neutral response, to maltreatment.
"Everything pornography says is a lie, but it is a massively effective teaching tool — of toxic learning," Layden explained.
Create in Me a Clean Heart
The U.S. Catholic bishops addressed these harmful effects on children in their 2015 pastoral letter on pornography, "Create in Me a Clean Heart."
"Being exposed to pornography can be traumatic for children and youth. Seeing it steals their innocence and gives them a distorted image of sexuality, relationships, and men and women, which may then affect their behaviour," they wrote. "It can also make them more vulnerable to being sexually abused, since their understanding of appropriate behaviour can be damaged."
One result of exposure to this violence of pornography is an "explosive" increase in children who are assaulting other children.
Layden said it is more likely for a daughter to be assaulted by her brother than by her stepfather in a "blended" household.
Dawn Hawkins concurs with Layden. Hawkins is senior vice president and executive director of the National Center on Sexual Exploitation, or NCOSE, known as Morality in Media until 2015.
"NCOSE believes the increase in children with 'harmful sexual behaviour' — a term that includes rape — is due to early exposure to hard-core porn," said Hawkins.
Hawkins said there's little data, for one reason, in school settings sexual abuse between children is not reported, but the damage to victims is real.
The lawyer for an 8-year-old girl raped multiple times by a 13-year-old male neighbour, consulted NCOSE recently. The boy — a consumer of violent pornography — had lined up his younger siblings, and the victim's sibling, to serve as an audience for his illicit performance.
"We know child sexual abuse leads to depression, anxiety, low self-esteem, self-harm, PTSD, risky sexual behaviours, poor physical health and other difficult struggles," summarized Hawkins. "It often predates an individual's entry into prostitution."
"So the trauma experienced by that group of children, caused by an immature brain's exposure to pornography, could take years, even decades, to unravel," she added.
Hawkins recommends the website Protect Young Minds, protectyoungminds.org, for guidance on inoculating them from harmful imagery online. Another such site is www.faithandsafety.org, created by the U.S. Conference of Catholic Bishops' Department of Communications and the Greek Orthodox Archdiocese of America.
Children abusing Children
A data set released Nov. 30 by Children's Mercy Hospital in Kansas City, Missouri, found that in almost half of its 2017 child abuse cases, boys ages 11 to 15 years were the perpetrators, physically and sexually attacking girls ages 4 to 8 years old. Nurses traced the phenomena to exposure to pornography.
One potentially positive note in the disturbing trend regarding peer assault is that, unlike adult perpetrators, young offenders who receive treatment do not appear to re-offend into adulthood.
"The good news on treatment means we need mandatory reporting of these cases, so kids get help," observed NCOSE's Hawkins.
She also is excited that after "many meetings" with Google, the internet giant has quietly added a "safe search" feature, allowing a setting that automatically screens out graphic sexual imagery from popping up.
Private companies as well are beginning to respond to evidence of the harmful impacts of pornography and to federal law enforcement crackdowns on it.
The social networking site Tumblr, now owned by Verizon, announced in early December it would block all pornography and "adult content" from its site beginning Dec. 17, as a result of child pornography — a federal crime treated with great severity– getting past its filters.
And Starbucks announced it will block customers from perusing pornography while on the store's free Wi-Fi, as a result of pressure from the South Carolina-based advocacy group Enough is Enough.
Some of these changes are a result of consumer pressure, according to Hawkins.
"The general public is becoming more aware of the public health harm," she told CNS. "Parents are concerned about the harm to their young kids."
She added, "There is a connection between pornography and violence against women. … The general public is becoming aware of this and demanding an end to the violence and sexual abuse of children."
Hawkins also cited 40 peer-reviewed studies since 2001 that stated the detrimental impacts of pornography. "There is much more widespread awareness of the harms, which have been swept under the rug and not talked about," she said. By Eleanor Kennelly Gaetan Catholic News Service
Latest posts by asiel (see all)
The Creed is the Bulwark of our Faith - July 16, 2019
How a Heresy Almost Won the Church - July 11, 2019
What We Catholics Believe – And Why - July 4, 2019
Abortion Raises Some Tough Questions Responding to Sexual Abuse Will Take Years – and it Should Pope: Don't Worry About Other's Faults, Own Up To Your Own Sins These Are The Questions Youth Have, and They're Not Trivial
Next story Annual Dominican Day: How to Cope Today Without Going Crazy
Previous story Bishop Boniface Tshosa Setlalekgosi of Gaborone Rest in Peace
More in Church, Life Issues, Sin in our Lives, Social Media, Society
Bishop Boniface Tshosa Setlalekgosi of Gaborone Rest in Peace
Bishop Boniface Tshosa Setlalekgosi of Gaborone diocese in Botswana died on Friday, January 25, at Gaborone Private Hospital at the...

redpajama_set_name: RedPajamaCommonCrawl