An experimental and theoretical study of the HNCO+ ion

Article abstract of DOI:10.1016/S0301-0104(00)00160-9

The dissociations of energy-selected HNCO⁺ ions have been examined at ionisation energies up to 40 eV using photoelectron-photoion coincidence spectroscopy. The slow metastable dissociation to HCO⁺ is shown to occur from initial population of low vibrational levels within the doublet states corresponding to the third photoelectron band. Rate constants for the dissociation from several levels have been measured and the existence of an optical emission is predicted. High level calculations identify the third band in the photoelectron spectrum as an overlay of almost degenerate states arising from ionisation of the in-plane and out-of-plane bonding π-orbitals. The calculations suggest that at energies between 15.5 and 16 eV, the dominant pathway for dissociation involves slow internal conversion to the ground doublet state without surface crossing, followed by intersystem crossing to the quartet surface. At energies over 16 eV, two mechanisms are possible; intersystem crossing from the second excited doublet state to the lowest quartet surface in a cis-bent configuration, or internal conversion to the first excited doublet state via a surface crossing in the same region, followed by a second nonradiative transition to the doublet ground state and intersystem crossing to the quartet surface. In each case, the initial step is expected to be slow, consistent with the existence of an optical emission, and H-atom transfer occurs on the quartet surface via a 'loose' transition state leading to the direct formation of HCO⁺ and N(⁴S(u)). (C) 2000 Published by Elsevier Science B.V.

Full text of DOI:10.1016/S0301-0104(00)00160-9

Chemical Physics 258 (2000) 21±36
www.elsevier.nl/locate/chemphys
‡
An experimental and theoretical study of the HNCO ion
S. Wilsey, S.E. Thomas, J.H.D. Eland *
Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QZ, UK
Received 19 January 2000
Abstract
‡
The dissociations of energy-selected HNCO ions have been examined at ionisation energies up to 40 eV using
‡
photoelectron±photoion coincidence spectroscopy. The slow metastable dissociation to HCO is shown to occur from
initial population of low vibrational levels within the doublet states corresponding to the third photoelectron band.
Rate constants for the dissociation from several levels have been measured and the existence of an optical emission is
predicted.
High level calculations identify the third band in the photoelectron spectrum as an overlay of almost degenerate
states arising from ionisation of the in-plane and out-of-plane bonding p-orbitals. The calculations suggest that at
energies between 15.5 and 16 eV, the dominant pathway for dissociation involves slow internal conversion to the
ground doublet state without surface crossing, followed by intersystem crossing to the quartet surface. At energies over
16 eV, two mechanisms are possible; intersystem crossing from the second excited doublet state to the lowest quartet
surface in a cis-bent con®guration, or internal conversion to the ®rst excited doublet state via a surface crossing in the
same region, followed by a second nonradiative transition to the doublet ground state and intersystem crossing to the
quartet surface. In each case, the initial step is expected to be slow, consistent with the existence of an optical emission,
‡
and H-atom transfer occurs on the quartet surface via a ÔlooseÕ transition state leading to the direct formation of HCO
and N(4Su). Ó 2000 Published by Elsevier Science B.V. All rights reserved.
1. Introduction
gested the involvement of complex rearrangements
instead. The kinetic energy release in the slow re-
action has been measured by mass spectrometric
methods [3,4] using electron impact ionisation and
is found to have a rather sharp distribution. Its
most recent value is 0.863 eV [4], and the appear-
A strong metastable peak in the mass spectrum
of HNCO has been known for many years, prov-
ing the existence of a slow (microsecond) reaction
4
‡
‡
1
‡
‡
HNCO ! HCO ꢀX R † ‡ Nꢀ Su†:
ance potential of HCO is reported [2±4] to be
about 1 eV above the thermodynamic limit. If the
kinetic energy release has the same magnitude at
threshold, most of the excess energy appears as
translation, suggesting an activation barrier for the
reverse reaction.
The slowness of the reaction was ®rst attributed to
its spin-forbidden character [1], but early semi-
empirical molecular structure calculations [2] sug-
The photoelectron spectrum has also been re-
corded and analysed [5,6] and was initially inter-
preted by analogy with the spectrum of CO2. Later
* Corresponding author. Tel.: +44-1865-275436; fax: +44-
1865-275410.
E-mail address: eland@physchem.ox.ac.uk (J.H.D. Eland).
0301-0104/00/$ - see front matter Ó 2000 Published by Elsevier Science B.V. All rights reserved.
PII: S0301-0104(00)00160-9

22
S. Wilsey et al. / Chemical Physics 258 (2000) 21±36
semiempirical calculations [7] reassigned the third
band in the spectrum, which starts at 15.5 eV, as a
pr ionisation instead of the bonding p-orbital
ionisation originally assigned. The original assign-
ment is restored in this paper on the basis of much
higher level calculations. Another recent theoreti-
cal study using density functional theory (B3LYP/
6-311G**) [8] treated only the lowest doublet and
from the coincidence spectra in the data treat-
ment.
‡
Searches for optical emission from HNCO
were carried out using Penning ionisation by
metastable helium and also by electron beam ex-
citation. Emitted light was focused using quartz
optics into a 2M in-plane Ebert spectrometer
equipped with a cooled photomultiplier detector.
Wavelength scales were calibrated on the He lines
in Penning ionisation and on the known emissions
from H atoms, NH radicals and residual N2 under
electron impact conditions.
HNCO and DNCO samples were prepared by
the action of phosphoric acid (or perdeutero-
phosphoric acid) on an aqueous (or D2O) solution
of potassium cyanate under vacuum. The product
was puri®ed by distillation and repeated freeze±
thaw cycles with pumping at solid CO2 tempera-
ture to remove CO2, the dominant impurity.
‡
quartet surfaces of the [H,N,C,O] complex in
detail in connection with observations of the ion±
‡
molecule reaction of O with HCN [8,9].
In the experimental part of this work, we have
‡
examined all the dissociation pathways of HNCO
‡
and DNCO ions up to 40.8 eV ionisation energy
by photoelectron±photoion coincidence spect-
rometry. HCO formation is the lowest energy
‡
process, and the characteristics of its onset led to
the prediction of a new optical emission from the
second excited state of the parent ions. We have
searched for this emission and obtained a provi-
sional positive result. On the theoretical side, we
have made high level calculations of the doublet
and quartet ground states (using both CASSCF/6-
311+G** and QCISD/6-311+G** methods), of
the relevant doublet excited states (using CASS-
CF/6-311+G**) and of the couplings between the
surfaces, allowing interpretation of the photoelec-
tron spectrum and the low-energy dissociation
mechanisms.
3. Theoretical methods
All the structures located were optimised using
the complete active space (CAS) SCF method and
the 6-311+G** basis set in GAUSSIAN 94 [11]. A
multireference method is necessary for studying
several excited states simultaneously; CASSCF
was chosen as it gives a balanced representation
of ground and excited electronic states, and it
includes nondynamic correlation energy which
means near-degeneracies are well described.
However, the computed energies lack some dy-
namic correlation energy, which can lead to inac-
curacies. The energies can be partially corrected
using single point multireference CASMP2 calcu-
lations, but these were found to be prohibitively
expensive with CASSCF active spaces larger than
(7,6).
The large basis set was used in order to describe
the proton transfer on the quartet surface as ac-
curately as possible. The shape of the quartet
surface computed using CASSCF di€ered some-
what from the B3LYP surface described by
Morokuma and co-workers [8], who located sev-
eral stable species that could not be found at
the CASSCF level. Therefore, the structures on
the quartet surface were also optimised using the
2. Experimental methods
The PEPICO apparatus has been described in
detail before [10]. Light of wavelengths 30.4, 58.4
and 46.1 nm from discharges in helium and neon
was selected by a grazing incidence monochro-
mator and crossed an e€usive jet of sample gas in
the spectrometer source. Photoelectrons were de-
tected after dispersion in a hemispherical energy
analyser at a position-sensitive detector, with a
resolution set by the chosen pass energy. When a
photoelectron was detected, a pulsed ®eld ejected
the corresponding ion from the source into a time-
of-¯ight mass spectrometer. Accidental coinci-
dence spectra were measured during each run by
periodic random ®eld pulsing, and were subtracted

S. Wilsey et al. / Chemical Physics 258 (2000) 21±36
23
QCISD (quadratic con®guration interaction with
single and double excitations) method with the
same basis set. The surface topology was similar
at the CASSCF and QCISD levels of theory giv-
ing us some con®dence in the accuracy of our re-
sults.
occupied during the structural rearrangement on
the quartet surface. Therefore, the proton transfer
on the quartet surface was studied using an active
space of nine electrons in eight orbitals (CAS4).
Transition structures were optimised using an
initial guess for the Hessian generated using the
redundant coordinate code. Vibrational frequen-
cies were computed analytically at each stationary
point located at the CASSCF level of theory, both
to check the nature of the critical point and
to compute the zero-point energies. The conical
intersection structures were located using the
method within GAUSSIAN 94, which optimises the
lowest energy point on an n-2 crossing seam (n is
the number of degrees of freedom in the molecule)
where two surfaces are degenerate [12]. The sin-
glet/triplet crossing point was optimised using the
same method although the crossing seam is only
n-1 dimensional in this case. The spin±orbit
coupling calculations were performed using the
algorithm implemented in GAUSSIAN 94, which
uses the method of Koseki et al. [13] with a one-
electron approximation for the spin±orbit coupling
operator and e€ective nuclear charges.
The CASSCF active space used depended on
the part of the surface studied. For interpreting the
photoelectron spectrum, an active space of nine
electrons distributed in seven orbitals was used
and this is referred to as CAS1. This included the
doubly occupied axial pr orbital on the oxygen
atom and the six p orbitals (three in-plane and
three out-of-plane) spread over the NCO frag-
ment. There has been some controversy as to
whether ionisation from the pr orbital gives rise to
the third band in the spectrum [7]; our results
suggest that this ionisation actually gives rise to
the fourth band in the spectrum. Therefore, for the
mechanistic study on the doublet surface, the pr
orbital was left out of the active space. We call the
remaining seven electrons in the six p orbitals
CAS2. The spectrum computed in this smaller
active space gave essentially the same energies as
obtained with the larger active space. Multirefer-
ence CASMP2 calculations were also carried out
with the CAS2 active space to check for dynamic
correlation e€ects.
4. Experimental results
There is considerable N±C bond relaxation on
the quartet surface and therefore an active space of
nine electrons in eight orbitals (CAS2 ‡ the
N±C r and rà orbitals) was also used to compare
the doublet and quartet energies around the
crossing region. The geometries optimised with
this active space (CAS3) were very similar to those
obtained using the CAS2 calculations except for
slightly longer N±C bonds, as expected. The dif-
ferences in energies computed using the two active
spaces were generally small; the largest di€erence is
0.11 eV, which occurs at the relaxed quartet min-
imum.
4.1. Photoelectron spectra
Previous photoelectron spectra [5,6] have been
taken at 58.4 nm, and our spectrum of HNCO at
this wavelength adds nothing to existing mea-
surements. The spectrum of HNCO at 30.4 nm
(40.8 eV) contains weak features centred at 24, 27
and 29.5 eV, which are interpreted as satellite
bands of mixed con®guration gaining intensity
from the C 2s ionisation in this energy region.
Weak ionisation intensity extends to higher ener-
gies, but is masked by low energy electron scat-
tering.
Finally, the active space used for the proton
transfer on the quartet surface also included the r
orbitals in the H±N bond. In order for the calcu-
lations to be computationally feasible, the out-of-
plane bonding (pb) and antibonding (pab) orbitals
had to be removed from the active space. This was
justi®ed as these remain doubly occupied and un-
The photoelectron spectrum of HNCO at 73.6
nm, shown later in connection with the PEPICO
results (Fig. 5), has clear vibrational structure in
the third band. The structure is richer than the
single progression originally identi®ed in the 58.4
nm spectrum [5], with at least one additional set
of peaks. The prominent peaks seem to form a

24
S. Wilsey et al. / Chemical Physics 258 (2000) 21±36
progression in 136 meV (1100 cm 1), as at 58.4 nm
[5]. A weaker set of peaks between members of the
prominent progression may be a second progres-
sion of independent origin in a similar interval, or
may be subsidiary excitations of a low frequency
mode at about 74 meV (600 cm 1). As these peaks
are also visible in the spectrum at 58.4 nm [5], they
are de®nitely not due to the 74.4 nm Ne line, which
is weakly present in the lamp output and is at-
tenuated by the monochromator. At energies
above 16 eV, the spectrum is more complicated
with several components to each peak. Interpre-
tation of the band structure is made dicult by the
(theoretically) known presence of near-degenerate
electronic states, and is not clari®ed by comparison
with the corresponding band in the spectrum of
DNCO. Peak intensity in the band, which may be
interpreted as a vertical ionisation energy, is at
15:9 Æ 0:05 eV.
4.2. PEPICO spectra, mass spectra and appearance
energies
The full PEPICO spectra of HNCO and DNCO
at each wavelength are two-dimensional data sets
from which mass spectra at each ionisation energy
or photoelectron spectra coincident with each ion
can be extracted by projection. A two-dimensional
PEPICO spectrum is illustrated as a grey scale
image in Fig. 1; photoelectron spectra for partic-
ular masses are illustrated in Fig. 2 and mass
spectra for single excitation energies are shown in
Fig. 3. The formation of di€erent products is best
represented as a breakdown diagram, giving the
fractional branching to products of each mass as a
function of the ionisation energy; a breakdown
diagram for the principal ions at 58.4 nm is shown
in Fig. 4.
Overall photoionisation mass spectra and pho-
toelectron spectra at each wavelength are mea-
sured simultaneously with the PEPICO spectra.
The mass spectrum at 58.4 nm (21.2 eV) is similar
to the 70 eV electron impact mass spectrum [1,2],
while at 73.6 nm (16.85 eV) only parent ions,
The photoelectron spectrum of DNCO has not
been reported before. The overall intensity distri-
bution at 58.4 nm is similar to the spectrum of
HNCO. The vibrational ®ne structure shows only
slight e€ects of deuteration in the ®rst two bands.
In the ®rst band, the (0±0) peak is dominant as in
the spectrum of HNCO, and is followed by two
peaks with spacings from (0±0) of 153 Æ 10 meV
(1234 Æ 80 cm 1) and 261 Æ 10 meV (2105 Æ 80
cm 1). These are identi®ed as single quantal exci-
tations of the two NCO stretching modes with
frequencies almost unchanged from those of
‡
‡
HCO and NCO , remain. Appearance potentials
of the fragment ions can be estimated from the
‡
HNCO .
In the second band, a single partially resolved
progression is detectable with a mean interval of
about 700 cm 1, similar to the corresponding
‡
HNCO interval of 650 cm 1, which must be an
in-plane bending mode.
The third band in the spectrum of DNCO dif-
fers quite strongly from the third band in HNCO.
The vibrational structure is much less marked,
has a less sharp onset and appears to consist of
a single progression in an interval of about
730 cm 1. This does not relate in any simple way
1
to the main progression in 1100 cm
in the
spectrum of HNCO. It is not clear whether an
adiabatic onset is seen, though the ®rst distinct
peak, at 15.5 eV, is provisionally interpreted as the
(0±0) transition.
Fig. 1. Partial PEPICO spectrum of HNCO at 58.4 nm. Traces
of H2O (masses 18 and 17) and CO2 (mass 44) impurity can be
seen; they were used to calibrate the energy scale.

S. Wilsey et al. / Chemical Physics 258 (2000) 21±36
25
Fig. 2. Coincident photoelectron spectra for the principal ions,
taken as cuts from the PEPICO spectrum.
Fig. 4. Breakdown diagram for HNCO showing the most
abundant ions at 58.4 nm. There is no substantial change in this
energy range on going to DNCO or to 30.4 nm.
coincident photoelectron spectra or from the
breakdown diagram; the values obtained are listed
in Table 1 for comparison with thermodynamic
limits and previous results. The present values are
in general agreement with earlier ones, but we
believe them to be more accurate. The thermody-
‡
namic limit for NCO formation is uncertain be-
cause no precise heat of formation of this ion is
‡
available. The measured threshold for NCO for-
mation indicates that its heat of formation should
be 301 kcal mol 1 rather than the 308 kcal mol 1 in
the standard listing [14]. The appearance potential
‡
for NO reported by Bogan and Hand [2] is cer-
tainly wrong, because it is far below the thermo-
dynamic limit. For mass 30 at energies below 17
‡
eV, we ®nd only metastable ions and the H13CO
isotope peak corresponding to the main fragment
ion. A weak signal at mass 30 appears between
17.5 and 18.5 eV, and cannot be an isotope peak
Fig. 3. Coincident mass spectra for ionisation energies where
‡
‡
metastable ions are seen from slow HCO formation.
because the HCO signal is too weak at these

26
S. Wilsey et al. / Chemical Physics 258 (2000) 21±36
Table 1
Energetics of ion formation from HNCO
Ion
Appearance energy (eV)
This work
Thermodynamic limit (eV)
Ref. [2]
‡
HNCO
‡
11.61
NCO
HCO
16:46 Æ 0:03
15:55 Æ 0:03
19:60 Æ 0:2
19:60 Æ 0:2
26:30 Æ 0:3
34:00 Æ 0:4
17:20 Æ 0:05
23:00 Æ 0:2
30:60 Æ 0:3
19:00 Æ 0:5
16.66
15.76
16.71
14.54
‡
‡
CO
HNC
17.45
18.25
‡
‡
CN
HNCO
24.5 ꢀ‡H ‡ O†
‡‡
‡
NH
‡
17.26
15.76
17.33
N
21.6 ꢀ‡H ‡ CO†
29.5 ꢀ‡H ‡ N ‡ O†
18.6
‡
C
‡
H
‡
O
NO
19.4 ꢀ‡HCN†
17.46 ꢀ‡NH†
‡
17:50 Æ 0:2
‡
energies; we attribute it to NO , appearing just
above its thermodynamic threshold.
The phenomena of slow metastable dissociation
transverse velocities from the known kinetic
energy release. The mean lifetimes giving the best
®ts for dissociation at chosen energies between
15.5 and 15.95 eV in the third bands of the HNCO
and DNCO spectra are reported in Table 2.
There is no signi®cant di€erence, for equal internal
energy, between the lifetimes of the hydrogen and
deuterium isotopomers.
‡
to HCO can be seen in the PEPICO spectrum
(Fig. 1) at energies near the dissociation threshold
and also in the coincident mass spectrum corre-
sponding to the threshold energy zone (Fig. 3).
Slow decays appear in two regions of the mass
‡
spectrum, just above the fragment HCO and
Kinetic energy releases in ionic dissociations
can be deduced from coincident ion peak widths;
the methods used here have been explained in re-
around the parent mass, corresponding to disso-
ciation in the ion source or in the ¯ight tube, re-
spectively. The intensity of the metastable signal
from the source region is shown in Fig. 5 with the
parent and HCO ions in the energy range of the
third band of HNCO under 73.6 nm ionisation.
Slow dissociation is con®ned to a narrow energy
‡
cent articles [15,16]. For HCO ion formation,
Fig. 1 shows directly that the peak width is es-
sentially independent of the ionisation energy from
the threshold upwards. Because of the distortion
of the peak shape caused by the slow reaction, the
kinetic energy release in metasable decay can only
be estimated; our value (0:9 Æ 0:1 eV) is consistent
with the more precise result from mass spectral
measurements [4]. In contrast to the large kinetic
‡
‡
region above the HCO onset, with maximum
intensity at the second peak in the main progres-
sion. At energies between 16 and 16.5 eV, we infer
that the dissociation is still slow relative to con-
ventional bond-breaking processes, although too
fast to be measured, because above 16.5 eV simple
‡
energy release at onset in the HCO channel, the
‡
formation of NH ‡ CO has an energy release
‡
H±NCO bond-cleavage takes over.
that rises from zero at threshold (Fig. 1), which is
normal behaviour for a simple bond breakage
without a reverse activation barrier.
The observed relative intensities of parent,
metastable and daughter ions in Fig. 5 and in
similar data for the ¯ight-tube metastables and for
DNCO have been compared with relative intensi-
ties calculated for single exponential lifetime dis-
tributions at each energy by Monte Carlo
simulations, allowing for losses of ions due to
‡
4.3. HNCO emission spectrum
Fig. 5 shows that for ions in the state repre-
sented by the ®rst vibrational peak in the third

S. Wilsey et al. / Chemical Physics 258 (2000) 21±36
27
band, lifetimes of the order of microseconds are
available before dissociation. Since an optical
transition to the ground state from the state as-
signed to the third band is allowed by symmetry,
and emission lifetimes for comparable transitions
are no more than a few hundred nanoseconds (e.g.
‡
‡
~
~
~
~
A±X in CO2 is 124 ns, A±X in OCS is 93 ns) [17],
we predict the existence of an optical emission.
We examined emission spectra from samples of
HNCO excited by 1 keV electrons and by Penning
ionisation in the afterglow of a He discharge. In
electron impact, the spectra were dominated by
‡
~
~
~
~
emissions from CO2 (A±X) and NH(A±X), with H
Balmer lines also present; no conclusion could be
drawn from the spectra. In Penning ionisation,
cleaner spectra were obtained and a spectrum from
‡
which residual CO2 has been digitally subtracted
is shown in Fig. 6. The spectrum is weak and
noisy, but contains one very clear band centred at
335.8 nm, which matches the position predicted
‡
for the 201 emission of HNCO . At the positions of
other predicted emissions, the presence of bands
may be suspected. Because of the di€erence in
geometry (mainly N±C and C±O bond lengths),
the 000 band is not expected to be the strongest. We
believe our spectrum is provisional con®rmation of
the existence of the expected emission. De®nite
proof could be provided by better spectra or by
coincidence measurements between photons and
ions or electrons [18,19].
Fig. 5. Detail of coincident photoelectron spectra for parent,
metastable and daughter ions from HNCO at 73.6 nm and 50
meV resolution.
5. Theoretical results and discussion
5.1. Interpretation of the photoelectron spectrum
The energies of the ®rst four bands in the
photoelectron spectrum of HNCO computed at
the CASSCF and CASMP2 levels of theory are
given in Table 3 and compared with the experi-
mentally determined values. The CAS1 and CAS2
energies were calculated at the CASSCF(10,7) and
CASSCF(8,6) optimised geometries of HNCO in
its ground state (Fig. 7(a)), respectively. The
multireference CASMP2 calculations were com-
puted using the CAS2 active space to check for
dynamic correlation e€ects.
Table 2
Dissociation lifetimes in the third photoelectron band
‡
‡
Energy (eV)
HNCO (ns)
DNCO (ns)
15.5
15.55
15.6
5500 Æ 1000
2500 Æ 500
2300 Æ 500
1650 Æ 300
4800 Æ 500
3600 Æ 500
2500 Æ 500
1560 Æ 300
1250 Æ 300
770 Æ 200
15.65
15.7
15.75
15.8
15.95
900 Æ 200
700 Æ 200
330 Æ 200
490 Æ 200

28
S. Wilsey et al. / Chemical Physics 258 (2000) 21±36
‡
Fig. 6. Optical emission spectrum obtained in He* Penning ionisation from HNCO, after digital subtraction of a CO2 emission
spectrum obtained under identical conditions. The remaining sharp lines are atomic He emissions.
Table 3
Assignment of the photoelectron spectrum of HNCOa
harmonic. Unfortunately, the experimental values
are too imprecise to make comparison with the
State
CAS1
CAS2
CAS-
MP2
Experi-
ment
theoretical e€ect of deuteration meaningful.
The computed vertical excitation energy of the
12A0 state is about 0.65 eV higher in energy than
that of the 12A00 state (compared to 0.8 eV ex-
perimentally). In this state, the single electron is in
the in-plane pnb orbital. Once on this surface, the
molecules relax to a linear geometry, the 12A0 and
12A00 states become degenerate, and ecient in-
ternal conversion to the lower energy state can
occur. The lowest energy point where the two
surfaces cross (conical intersection) was fully op-
timised and the structure obtained is shown in Fig.
7(c).
12A000
12A0
22A00
22A0
32A
0.0
0.0
0.0
0.0
0.8
3.9
3.9
5.2
0.65
4.42
4.51b
6.05
0.63
4.41
4.46
0.63
4.55
4.59b
a Energies are given in eV computed at the equilibrium geom-
etry of the neutral HNCO molecule.
b Energy computed using state-averaged orbitals with equal
weights over 22A0 and 22A00.
The computed vertical excitation energies are in
reasonable agreement with the experimental re-
sults and do not change much with the level of
theory used. The additional dynamic correlation
does not appear to make much di€erence to the
computed spectrum as the CASMP2 results are
very similar to the CAS1 and CAS2 energies. The
calculations predict the00 lowest lying state of
The third band of the photoelectron spectrum
lies some 3.8 eV higher in energy. Our computa-
tions clearly indicate that this band is comprised
of two nearly degenerate states, which correspond
to having a single electron in either of the pb
orbitals. The in-plane state (22A0) lies marginally
below the out-of-plane state (22A00), although the
energy di€erence is only a few hundredths of an
eV. This is the band that gives rise to the ecient
HNCO to be the 12A state, with the single
‡
electron in the out-of-plane pnb orbital. This is in
agreement with previous experimental [5] and
theoretical [7,8] results. The equilibrium geometry
of the ion in this state (Fig. 7(b)) is similar to that
of the neutral molecule, as expected from the
narrow bandwidth. The vibrational frequencies of
the neutral molecule and the ion computed ana-
lytically using CAS2 compare well with the ex-
perimentally determined values (Table 4) and
reinforce the original frequency assignments [5].
The computed frequencies are not scaled and such
calculations normally predict frequencies to be too
high as they assume the vibrational motion to be
‡
production of N(4Su) and HCO , which will be
discussed in more detail in the next section. The
calculations suggest that a one-electron ionisation
from the pr orbital requires an extra 1.6 eV of
energy and is responsible for the fourth band in
the spectrum.
‡
5.2. Dissociation mechanisms and HCO formation
In this section, we discuss possible mechanisms
‡
for the formation of HCO and analyse their

S. Wilsey et al. / Chemical Physics 258 (2000) 21±36
29
‡
Fig. 7. Optimised geometries for HNCO and HNCO (CAS2 geometries in plain text with CAS3 parameters in parentheses), bond
lengths in Angstroms and angles in degrees: (a) ground-state minimum of HNCO (CAS1 geometry shown in italic), (b) 12A00 minimum
(CA0S0 4 (plain text) and QCISD (bold text) geometries shown below), (c) 12A00=12A0 conical intersection0, (d) 22A0 trans minimum, (e)
22A minimum, (f) 22A0 cis minimum, (g) 22A0=14A00 crossing point (not fully optimised) and (h) 22A =12A0 conical intersection.
Table 4
‡
‡
Vibrational frequencies of neutral HNCO and the ground-state HNCO and DNCO ionsa
Mode
Computed
HNCOb
Experiment
HNCO
‡ c
‡
‡
‡
DNCO
HNCO
DNCO
HNCO
In-plane bend
Out-of-plane
bend
590
624
496
489
453
473
N±H wag
Symmetric
stretch
805
1396
907
1200
767
1135
1327 Æ 80
2274 Æ 80
3531 Æ 80
1050 Æ 80
2020 Æ 80
3222 Æ 80
1234 Æ 80
2105 Æ 80
3222 Æ 80
Asymmetric
stretch
N±H stretch
2471
2303
3611
2296
2644
3910
a Vibrational frequencies given in cm±1
b Vibrational frequencies computed using CAS(8,6)/6-311+G**.
c Vibrational frequencies computed using CAS(7,6)/6-311+G**.
.
‡
4
feasibility using high level computations. The
experimental results provide four key pieces of
information: (i) slow dissociation of HNCO to
form HCO ‡ Nꢀ Su† occurs from the states
that give rise to the third band in the photoelec-
tron spectrum; (ii) at energies where simple H±N
‡

30
S. Wilsey et al. / Chemical Physics 258 (2000) 21±36
bond-breaking is possible, this process takes over
‡
observed decay rate, even though it seems to ®t the
variation of rate with energy.
from HCO formation; (iii) the lifetimes of the D-
and H-isotopomers are equal at energies below 16
eV, where the rate is particularly slow and (iv)
there is a reverse barrier for reaction from the
quartet products of about 0.9 eV. On the basis of
these results, we know that the mechanism for the
formation of HCO from HNCO is initiated on
the second excited doublet state (D2) and must
involve intersystem crossing to the quartet (Q1)
surface and an H-atom transfer. The absence of a
kinetic isotope e€ect on deuteration suggests
that the slow step of the reaction is not the H-at-
om transfer. The appearance of an optical
emission is consistent with slow reaction from
the zeroth level, and implies that internal conver-
sion to the ground-state surface is not a rapid ®rst
step.
There are two types of reaction pathway which
we can envisage in terms of the electronic states
involved. One involves crossing directly from the
initially excited doublet state to the lowest quartet
state, which is the only state leading to products.
The second mechanism involves internal conver-
sion from the initial doublet state by one or more
nonradiative transitions to the ground state (with
or without a surface crossing), followed by a fur-
ther nonadiabatic transition to the quartet surface.
In either pathway, rearrangement by H-atom
transfer could happen in the initial, intermediate
or ®nal electronic state. Our calculations, detailed
below, suggest that whichever pathway is fol-
lowed, this rearrangement always occurs on the
®nal quartet surface and that the ®rst step of the
reaction is rate determining. The ®rst excited
doublet state (D1) is so strongly coupled to the
ground state of the ion (degenerate in linear ge-
ometry) that it is not likely to provide a separate
alternative pathway.
‡
‡
Conventional statistical theory of mass spectra
might suggest that internal conversion to the
doublet ground state (D0) is fast for vibrational
levels of D2 above the zeroth level (where crossing
is observed). The bottleneck would then be the
accessibility of the crossing point between the
ground-state and quartet surfaces. If this were
true, then the experimental rate constants should
®t a statistical model. The measured lifetimes of
5.2.1. The 22A0 and 22A00 surfaces
The third band in the photoelectron spectrum
of HNCO arises from ionisation from two near-
degenerate p-bonding orbitals and it is likely that
both states will be populated on ionisation. The
equilibrium geometries of these states were opti-
mised with some diculty due to the proximity of
the surfaces. The geometries (shown in Fig. 7(d)
and (e)) are very similar, the main structural dif-
ferences being longer N±C and C±O bonds and a
smaller NCO angle in the0out-of-plane state (Fig.
7(e)). Two di€erent 22A =22A00 crossing points
were optimised between the two states, one close
to the equilibrium geometries and the second at a
geometry where the NCO fragment is almost lin-
ear. This suggests that the two surfaces cross over
a wide range of geometries and energy transfer
between them will be ecient.
‡
the HNCO ions (Table 2) decrease smoothly, at
least within their error limits, as the internal en-
ergy of the ions increases. The fragmentation rate
constants are well ®tted by the simplest quasi-
equilibrium theory (QET) model, with an e€ective
number of oscillators of 4 (i.e. s 1 ˆ 3) and a
frequency factor of 8 Â 108 s 1. Extrapolation lo-
cates the dissociation onset at 15:29 Æ 0:05 eV.
However, the ®tted frequency factor is about four
orders of magnitude smaller than the normal value
for a simple bond ®ssion, and is about ten times
smaller than typical values found for rearrange-
ment reactions [15]. The minimum rate constant
for a single quantum state at the observed onset is
1
calculated to be 2 Â 108 s using an exact-count
density of states based on the theoretical ground-
state harmonic vibrational frequencies. This is
three orders of magnitude faster than the observed
rate at onset. Thus, a purely statistical model, as-
suming fast internal conversion and reaction on
the ground-state surface, is unable to explain the
The possibility of an H-atom transfer occurring
on the 22A0 surface was considered but this was
found to be energetically unfavourable. The opti-
mised transition structure for such a process was
computed to lie some 2.77 eV above the excited
state minimum, far outside the energy range where

S. Wilsey et al. / Chemical Physics 258 (2000) 21±36
31
the reaction is actually observed. This implies that
the ®rst step of the reaction is a surface crossing
and that H-atom transfer occurs further along the
reaction coordinate.
5.2.2. Intersystem crossing from the second excited
doublet surface to the quartet surface
At the 22A0 and 22A00 equilibrium geometries,
the quartet state is signi®cantly higher in energy
than the doublet states. In order to identify what
type of geometric change leads to stabilisation of
the quartet state, a series of partial optimisations
were carried out starting from the equilibrium
geometry of the molecule in the 22A0 state and
constraining each of the bond lengths, bond angles
and the torsional angle in turn. These indicated
that both an HNCO twist and an in-plane NCO
bend lead to stabilisation of the quartet surface. In
addition, an in-plane NCO bend leads to a change
in con®guration of the doublet state along the D2
adiabat. The new state has the con®guration
Fig. 8. Contour plot of energy versus NCO bending and
HNCO torsional angles. The lines are spaced 0.1 eV apart and
are marked relative to the 22A0 trans minimum. The bold line
represents the seam of doublet/doublet crossing and the shaded
areas indicate regions of the surface where the quartet state lies
lower in energy than the doublet state.
2
2
2
0
1
0
00
00
ꢀp0b0† ꢀp0b† ꢀp † ꢀpn0 b† ꢀpa0 b† ꢀp † and we will refer
nb
ab
to it as the Ôp-antibondingÕ state because the un-
paired electron is in the in-plane antibonding p
orbital. It is not detected in the photoelectron
spectrum as it cannot be formed by a simple one-
electron ionisation from the neutral molecule. The
molecule changes con®gura0tion because as it
bends, the in-plane p0b and pab orbitals are stabi-
lised relative to the pnb orbital. The minimum of
the p-antibonding state has a cis geometry, where
the NCO angle is 118° and the HNCO dihedral
angle is 58° (Fig. 7(f)).
A sketch of a two-dimensional contour plot
showing how the energy of the D2 adiabat changes
with respect to the HNCO and NCO coordinates
is shown in Fig. 8. The plot is based on the mini-
mum energy pathways obtained from the con-
strained optimisations and three scans taken along
the HNCO coordinate at NCO angles of 125°,
130°, and 135°. The energies were all calculated
using CAS2 and the contour lines are spaced at
energy intervals of about 0.1 eV. The 22A0 equi-
librium minimum is shown as a well in the top
right-hand corner and the p-antibonding cis min-
imum is located in the bottom left-hand corner.
The plot shows how the two states intersect over a
range of geometries along the seam indicated by
the bold line. The results suggest that the mole-
cules can cross to the p-antibonding surface at
various points along this seam at energies above
the 22A0 equilibrium minimum. The scan taken
along the HNCO torsional angle with the NCO
angle ®xed at 130° indicated that the seam passes
through the point (NCO ˆ 130°, HNCO ˆ 95°),
which lies 0.09 eV above the vertical ionisation
potential of the 22A0 state. This energy may be
somewhat high as the point is not a fully optimised
stationary point. However, the results indicate that
the lowest energy point of the crossing seam must
lie close to the vertical ionisation energy of 15.9
eV.
Single point energies indicate that the quartet
1 4A00 surface falls below the doublet surface at cis
geometries where the NCO angle is less than 125°
or at trans geometries where the NCO angle is less
than 120°. These regions are indicated by the
shaded areas in Fig. 8. The lowest energy D2/Q1
crossing point was found at an NCO angle of 125°
and an HNCO angle of 63°, where the computed
energy di€erence between the two surfaces is only

32
S. Wilsey et al. / Chemical Physics 258 (2000) 21±36
5.2.3. Internal conversion to the ground-state sur-
face followed by intersystem crossing
0.01 eV (Fig. 7(g)). This point lies 0.02 eV above
the vertical ionisation potential. The lowest energy
point on this D2/Q1 crossing seam could not be
fully optimised because of the proximity of the
12A0 state, which crosses the 22A0 state further
along the NCO coordinate.
Internal conversion from the initial doublet
state to the doublet ground state could occur with
or without a surface crossing. No 12A0=22A00
crossing point could be located close to the 22A
trans minimum, suggesting that no fully ecient
mechanism for nonradiative transition back to the
doublet ground state exists, consistent with the
existence of an optical emission. The only 1 2A0/
2 2A0 conical intersection that could be located was
optimised in the region of the p-antibonding cis
minimum at a near-planar geometry where the
NCO angle is 108° (Fig. 7(h)). The conical inter-
section is marked as a dark area in the bottom left-
hand corner of Fig. 8. It lies marginally higher in
energy than the D2/Q1 crossing point and requires
more NCO compression and HNCO torsion in
order to access it. However, as with intersystem
crossing, internal conversion by this mechanism
must be preceded by crossing to the p-antibonding
doublet state involving the same barrier and will
only be accessed at energies near the vertical
ionisation potential.
The most likely pathway for dissociation at
energies below the ionisation potential involves
internal conversion from the excited doublet state
to the ground state without a surface crossing.
Some evidence for the feasibility of this reaction
mechanism can be adduced by closer examination
of the measured dissociation lifetimes (Table 2)
and by comparison with known rates of internal
conversion between doublet states in comparable
molecular ions. The only comparable tetratomic
molecular ions for which information of nonradi-
ative transitions is available are the haloacetylenes.
Their emitting A-states are coupled to the ground
states as evidenced by the nonexponential ¯uo-
rescence decays and low quantum yields [19]. Their
decay behaviour is typical of intermediate case
coupling, where the strength of the interaction
between initial states and the quasi-continuum
of the ground state varies from level to level. In
5-atom and 6-atom molecular ions, nonradiative
Therefore, intersystem crossing directly from
the excited doublet state to the quartet surface
involves a combination of NCO compression and
HNCO torsion leading to the p-antibonding
doublet state, followed by a nonradiative tran-
sition to the quartet surface close to the cis mini-
2
2
1
00
mum. The quartet con®guration is ꢀp0b0† ꢀpb0 † ꢀp †
nb
1
1
0
ꢀp0nb† ꢀpa0 b† ꢀp † , which means intersystem cross-
00
ab
ing is accompanied by an electron transition from
the out-of-plane nonbonding orbital to the per-
pendicular in-plane nonbonding orbital. This is a
favourable transition, which is re¯ected in the
large computed spin±orbit coupling (49 cm 1) and
intersystem crossing to the 1 4A00 surface is ex-
pected to be ecient. The reaction bottleneck will
be reaching the D2/Q1 crossing point; as the en-
ergy of the crossing seam leading to the p-anti-
bonding doublet state is close to the vertical
ionisation potential, nearly all of the internal en-
ergy of the molecule must be in the in-plane NCO
bending and HNCO torsional modes in order for
the crossing to occur. This is consistent with
the experimental results, which indicate that at
energies above 16 eV, the reaction is too fast to
measure, but is still slower than expected for a
normal unimolecular reaction. Similar results were
obtained using CAS3, with the D2/Q1 crossing
predicted to occur slightly earlier along the reac-
tion coordinate at an NCO angle of about
130° and 0.05 eV above the vertical excitation
energy.
The theoretical results suggest that molecules in
the vibrational levels of D2 below the vertical
ionisation energy cannot reach the crossing seam.
If they react by the D2 ! Q1 route, it would have
to be by tunnelling or by a nonradiative transition
without surface crossing, invoking very unfa-
vourable Franck Condon factors. This would im-
ply that although this mechanism will occur at
higher energies, there must be a competing process
that exists at energies below the vertical ionisation
energy.
rate constants for depleting excited A-state popu-
1
lations are of the order of 106
HNCO is a borderline case. The increased density
of states and lowered symmetry as compared with
s
[20]. Thus,
‡

S. Wilsey et al. / Chemical Physics 258 (2000) 21±36
33
a linear molecule may enhance the nonradiative
transition probability, providing competition with
optical emission; we would still expect emission to
be observable, though with reduced quantum
yield. The rate of internal conversion generally
rises exponentially with energy, consistent with the
experimentally observed rate constants. Therefore,
at energies below the vertical ionisation potential
(i.e. in the range 15.5±16 eV), it is most likely that
internal conversion occurs by this mechanism, and
that this is the only reaction path available leading
to dissociated products.
tions of Morokuma and coworkers suggest that
there is no simple barrier for such a process. The
‡
lowest energy route to HCO product involves the
‡
formation of the less stable HCNO molecule and
the highest energy transition structure along this
‡
pathway lies about 5.3 eV above the HCNO
minimum and >1 eV above 0t0he vertical excitation
energies of the 22A0 and 22A states. Therefore, we
are con®dent that H-atom transfer occurs exclu-
sively on the quartet surface, regardless of the
mechanism taken to get there.
The calculations indicate that once internal
conversion to the ground-state surface has oc-
curred, then subsequent intersystem crossing to the
quartet surface will be relatively facile. A D0/Q1
crossing point was optimised (Fig. 9(a)) and was
found to lie 3.33 eV above the ground-state mini-
mum and 0.8 eV below the 22A0 equilibrium
minimum. The geometry of the molecule at the
crossing point is trans with an elongated central
N±C bond. The computed spin±orbit coupling is
21.2 cm 1, which is lower than that obtained at the
D2/Q1 crossing point but still signi®cant.
5.2.4. Rearrangement on the quartet surface
After crossing to the quartet surface from either
the ground or excited doublet states, both the
CASSCF and QCISD calculations predict that
the molecule relaxes to an ion±molecule complex.
The complex (Fig. 9(b)), which is cis with a long
ꢀ
N±C bond (ꢁ1.9 A), lies 1.2 eV below the D2/Q1
crossing point and 0.3 eV below the D0/Q1 cross-
ing point. The CASSCF and QCISD results di€er
from the B3LYP results obtained previously [8],
which indicated the presence of stable cis and trans
ÔstrongÕ complexes where the N±C bond is around
ꢀ
The possibility of an H-atom transfer on the
doublet ground-state surface prior to intersystem
crossing was considered. However, the calcula-
1.3±1.4 A. These ÔstrongÕ complexes could not be
optimised as stable species at either of the levels of
theory used here.
‡
Fig. 9. Optimised quartet geometries for HNCO (CAS4 geometries in plain t0e0 xt, CAS3 geometries in parentheses and QCISD pa-
rameters in bold), bond lengths in Angstroms and angles in degrees: (a) 12A =14A00 crossing point, (b) 14A00 minimum, (c) 14A00
transition structure for H-transfer, (d) 14A00 ÔtightÕ trans transition structure for H-transfer and (e) 14A00 minimum leading to disso-
ciated products.

34
S. Wilsey et al. / Chemical Physics 258 (2000) 21±36
A transition structure (Fig. 9(c)) for proton
transfer from the nitrogen to the carbon leading to
(CAS4) and 1.2 eV (QCISD) higher in energy than
the ÔlooseÕ transition structures. The CAS4 fre-
quency calculation indicated that this structure is a
second-order saddle point with two imaginary
frequencies; one (2131 cm 1) corresponding to the
proton transfer and the second (236 cm 1) corre-
sponding to an out-of-plane bend. However, no
lower energy transition structure could be opti-
mised suggesting that the second frequency may
just be an artifact of the active space used.
‡
the direct formation of N(4Su) and HCO was
located using both methods although there is some
discrepancy in the energies obtained for this bar-
rier. At the CAS3 and CAS4 levels of theory, the
transition structure lies 0.8 eV above the quartet
minimum and 0.5 eV below the vertical excitation
energy of the 2 2A0 state. The CAS4 frequency
calculation indicates that the structure has one
imaginary frequency (331 cm 1) corresponding
predominantly to an HNC bend. At the QCISD
level, the same transition state lies about 1.5 eV
above the quartet minimum. Although the QCISD
value is not corrected for zero-point energy which
is expected to lower it by about 0.2 eV, this value is
still somewhat high. This ÔlooseÕ transition struc-
ture could not be optimised at the B3LYP level of
theory (Table 5).
Both the CAS4 and QCISD calculations predict
a shallow minimum (Fig. 9(e)) in the exit channel,
corresponding to a loosely bound complex which
lies only 0.07 (CAS4) and 0.25 eV (QCISD) below
the energy of the dissociated products. The reverse
‡
barrier to forming the HNCO ion complex is
computed to be about 2 eV at both levels of theory
which, although in qualitative agreement with the
experimental results, is somewhat higher than the
0.9 eV kinetic energy release observed experimen-
tally. However, the CASSCF energies are expected
to su€er from a lack of dynamic correlation which
will a€ect the energies of the complexes more than
A saddle point for a proton transfer via a ÔtightÕ
trans geometry was also optimised (Fig. 9(d)),
similar to the structure optimised using B3LYP
calculations [8], but this was found to lie some 2.4
Table 5
Energies of CAS/6-311+G** and QCISD/6-311+G** optimised structuresa
Structure
State
CAS2
CAS3
CAS4
QCISD
0.13
S0 minimum 7a
12A000
22A00
12A0
12A00
12A0
22A00
22A0
22A00
14A0
22A00
14A0
22A0
12A00
14A00
12A00
14A00
14A00
14A00
14A00
14A
0.18
4.59
0.14
4.53
D0 minimum 7b
D1/D0 conical intersection 7c
0.00 (0.00)
0.36
0.37
0.00 (0.00)
0.31
0.31
0.00 (0.00)
0.00
D2 trans minimum 7d
D2 trans minimum 7e
D2 cis minimum 7f
4.17 (4.26)
4.17 (4.20)
4.55 (4.50)
4.44
4.10 (4.09)
4.11 (4.15)
4.46 (4.39)
4.33
D2/Q1 crossing 7g
4.61
4.60
4.58
4.58
D2/D1 conical intersection 7h
4.67
4.67
4.66
4.63
4.42
4.34
D0/Q1 crossing 9a
3.33
3.33
Q1 minimum 9b
3.18 (3.12)
4.07 (3.89)
2.99 (2.92)
3.90 (3.71)
6.26 (5.99)
1.73 (1.63)
1.80 (1.70)
4.16 (3.91)
3.32
4.80
6.04
2.32
2.57
5.15
Q1 transition structure 9c
Q1 ÔtightÕ transition structure 9d
Q1 minimum 9e
4
‡
Nꢀ Su† ‡ HCO
‡
NH ‡ CO
a Energies in eV relative to the 12A00 minimum, with zero-point energy corrected values in parentheses.

S. Wilsey et al. / Chemical Physics 258 (2000) 21±36
35
those of the products and may lead to dissociation
products that appear to be too low in energy. The
experimental value for the energy of the products
is about 3 eV relative to the ground-state minimum
of the ion, which is only 0.7 eV below the transi-
tion state computed at the CAS4 level.
conversion to the 12A0 surface via the same p-
bonding doublet state may also compete. This
would be followed by fully ecient D1/D0 internal
conversion and fast D0/Q1 intersystem crossing.
However, the barrier leading from the 22A0 mini-
mum to the p-antibonding state is close to the
vertical ionisation potential which suggests that
these two mechanisms will only occur at energies
above 16 eV and if the correct vibrational modes
are populated. In all three cases, we expect the ®rst
step of the mechanism to be rate determining,
consistent with the existence of an optical emission,
and subsequent processes to be relatively fast.
The lack of a kinetic isotope e€ect when deu-
terium is substituted for hydrogen is evidence that
proton transfer cannot be the rate-determining
step of the slow reaction. The calculations indicate
that H-atom transfer occurs on the quartet sur-
face, regardless of the initial reaction path taken.
Once the quartet surface is populated, the system
will evolve towards its equilibrium geometry,
6. Conclusions
The experimental results show that the meta-
‡
‡
stable decay of HNCO forming HCO arises
from initial population of levels above the zeroth
level, with excitation of (mainly) NCO stretching
vibrations in the electronically excited states rep-
resented by the third photoelectron band. The
theoretical results clearly identify the electronic
states as the near-degenerate 22A0 and 22A00 states
derived from ionisation of a p-bonding electron.
‡
The measured lifetimes of the HNCO ions
indicate that dissociation is slow from the zeroth
vibrational level of the second excited doublet
state up to energies of about 16 eV. At energies
between 16 and 16.5 eV, the reaction is still slow
relative to conventional bond-breaking processes,
but is too fast to be measured. Above 16.5 eV,
‡
which resembles an [HN±CO] ion pair complex.
Rotation of the diatomic components in the
complex can bring them to the con®guration of a
secondary barrier, with height 0.8 eV above the
quartet minimum. The presence of this ®nal tran-
sition state is consistent with the appearance of
much of the available energy as relative transla-
‡
simple H±NCO bond breakage takes over.
An extensive mapping of the doublet and
quartet surfaces using high level calculations sug-
gests that three di€erent mechanisms may be re-
‡
tional energy of N(4Su) and HCO .
‡
sponsible for the slow formation of HCO from the
second excited doublet state. The ®rst occurs at
energies below 16 eV and involves slow internal
conversion to the doublet ground state without a
surface crossing, followed by fast intersystem
crossing to the quartet surface and subsequent H-
atom transfer leading to products. This mechanism
is supported by the rates of comparable internal
conversion processes in other molecular ions such
as the haloalkynes and the absence of any surface
crossings in the region of the reactants. The second
possible mechanism is intersystem crossing directly
from the 22A0 state to the quartet surface via a p-
antibonding doublet state. The spin±orbit coupling
between the states at the D2/Q1 crossing point is
calculated to be 49 cm±1, which will allow rather
rapid transition at this point. A D2/D1 conical in-
tersection in the same region suggests that internal
Acknowledgements
We thank C.G. Spalton for help with measure-
ments of the emission spectra. S.W. is grateful
to the Violette and Samuel Glasstone Trust for
®nancial support. S.W. also thanks the Royal So-
ciety for an equipment grant and the UK Compu-
tational Chemistry Facility for computer time on
Columbus. We acknowledge the support of the
EPSRC for the experimental aspects of this work.
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