Metastable states of dimethylammonium, (CH3)2NH2.

Article abstract of DOI:10.1021/jp964077e

Hypervalent dimethylammonium radical, (CH₃)₂NH₂^., and its deuterium-labeled isotopomers (CH₃)₂ND₂^., (CH₃)₂NHD^., (CD₃)₂

Full text of DOI:10.1021/jp964077e

J. Phys. Chem. A 1997, 101, 3789-3799
3789
•
Metastable States of Dimethylammonium, (CH3)2NH2
Viet Q. Nguyen, Martin Sadilek, Jordan Ferrier, Aaron J. Frank, and Frantisˇek Turecˇek*
Department of Chemistry, Bagley Hall, Box 351700, UniVersity of Washington,
Seattle, Washington 98195-1700
ReceiVed: December 16, 1996; In Final Form: March 19, 1997X
•
•
Hypervalent dimethylammonium radical, (CH3)2NH2 , and its deuterium-labeled isotopomers (CH3)2ND2 ,
(CH3)2NHD•, (CD3)2NH2 , and (CD3)2ND2 were generated as transient species by collisional neutralization
•
•
of their cations in the gas phase and studied by neutralization-reionization mass spectrometry, laser
photoexcitation, and ab initio theory. (CH3)2ND2 , (CH3)2NHD•, and (CD3)2NH2 gave fractions of metastable
•
•
•
•
species of g3.3 µs lifetimes, whereas (CH3)2NH2 and (CD3)2ND2 dissociated completely on the same time
•
•
scale. Metastable (CD3)2NH2 and (CH3)2ND2 were photoexcited but not photoionized with the combined
488 and 514.5 nm lines from an Ar-ion laser. Ab initio calculations with effective PMP4(SDTQ)/6-311++G-
(3df,2p) identified the (X˜ )2A1 ground state of vertical ionization energy, IEv ) 3.70 eV. RRKM calculations
on the ab initio potential energy surface of the (X˜ )2A1 state predicted predominant N-H and N-D bond
dissociations but did not allow for competitive loss of CH3 or CD3. The four lowest excited states of (CH3)2-
NH2 , (A˜ )2B1, (B˜)2A1, (C˜)2B2, and (D˜ )2A1, were characterized by CIS/6-311++G(3df,2p) calculations, and
•
their vertical ionization energies were calculated as 2.86, 2.57, 2.48, and 1.82 eV, respectively. The excited
states were calculated to be strongly bound with respect to N-H bond dissociations. The N-C bond
dissociations were interpreted by potential energy surface crossing of the B˜ and A˜ states and transitions via
conical intersection to the dissociative ground state.
Introduction
been studied recently by photodissociation and photoionization
experiments.15,16 Boldyrev and Simons used ab initio calcula-
•
Following Herzberg’s discovery of NH4 in discharge in
gaseous ammonia,1-3 the chemistry of hypervalent ammonium,4
oxonium,5 and sulfonium4d,6 radicals has been of much interest.
Hypervalent onium radicals have formally nine electrons at the
central heteroatom, and their electronic structures thus violate
the octet rule.7 Organic ammonium radicals derived from
aliphatic amines have been generated by collisional neutraliza-
tion of fast beams of ammonium cations and analyzed by
neutralization-reionization mass spectrometry (NRMS).8 Iso-
topomers of several radicals, such as ammonium,4a methyl-
ammonium,4b trimethylammonium,9 and pyrrolidinium,10 showed
metastability on the microsecond time scale. In contrast, organic
ammonium radicals that contained larger alkyl and aryl sub-
stituents11 or functional groups12 were found to dissociate
completely within a few microseconds. Unimolecular dissocia-
tions of organic ammonium radicals often showed unexpected
branching ratios in dissociations of N-H and N-C bonds that
were difficult to interpret or predict on the basis of the known
or estimated dissociation energetics9 or using conventional
reactivity rules.13
tions to study the ground electronic states of methylated
ammonium radicals from mono- through tetramethylammo-
nium.17 All these radicals were found to be thermodynamically
metastable with respect to exothermic dissociations by N-H
or N-CH3 bond cleavages. The first three members of the
series showed decreasing activation energies for N-H bond
dissociations, e.g., from 28 kJ mol-1 for methylammonium17
to -8 kJ mol-1 for trimethylammonium.9 The potential energy
barriers to N-CH3 bond cleavages were calculated to be within
50-60 kJ mol-1 for mono-, di-, and trimethylammonium.9,17
However, the calculated energetics of ground electronic states
in methylated ammonium radicals did not account completely
for the behavior of these species when formed by collisional
electron transfer. In particular, the microsecond metastability
of trimethylammonium was incompatible with the dissociative
energy profile along the N-H coordinate in the ground
electronic state.9 Furthermore, both N-H and N-C bond
cleavages were observed experimentally in methylammonium
and trimethylammonium, whose branching ratios were difficult
to explain by the calculated potential energy barriers. Formation
of excited states has been suggested to qualitatively explain the
experimental data.9 A metastable excited state has been found
recently by photoionization of the related dimethyldeuteroxo-
nium radical.6
The energetics of hypervalent ammonium radicals was also
•
addressed by several ab initio calculations.14 NH4 was found
2
to be weakly bound in its A1 ground electronic state due to a
∼40 kJ mol-1 potential energy barrier to exothermic dissociation
•
by loss of H•. This low stability of NH4 , as opposed to that of
NH4+, which requires 523 kJ mol-1 for N-H bond homolysis,
can be attributed to perturbation of the bonding orbitals in the
radical by the presence of the unpaired electron.14f The four
To complete the series of studies on methylated ammonium
radicals and provide experimental data for comparison with ab
initio theory, we address in the present work the metastability
•
lowest excited electronic states of NH4 were calculated to be
and dissociations of dimethylammonium, (CH3)2NH2 , 1H•, and
•
•
its isotopomers (CH3)2ND2 (1D•), (CH3)2NHD• (1HD•), (CD3)2-
bound, and the energy barriers to their dissociations were
predicted to increase as the odd electron was placed in Rydberg
orbitals of increasing principal (n) and angular (l) quantum
numbers.14f The ground and excited states of ammonium have
•
•
NH2 (2H•), and (CD3)2ND2 (2D•). The formation of hyper-
valent radicals by collisional electron transfer and their analysis
by NRMS have some specific features that have been discussed
in detail previously.8 Briefly, in NRMS a beam of precursor
ions of a kiloelectronvolt kinetic energy is allowed to undergo
X Abstract published in AdVance ACS Abstracts, May 1, 1997.
S1089-5639(96)04077-7 CCC: $14.00 © 1997 American Chemical Society

3790 J. Phys. Chem. A, Vol. 101, No. 20, 1997
Nguyen et al.
glancing collisions with thermal molecules or atoms that serve
as electron donors under single collision conditions. Electron
transfer from a molecular donor to an ammonium cation acceptor
is highly endothermic; for example, neutralization of dimethyl-
ammonium cations (1H+) with dimethyl disulfide is ∼5.3 eV
endothermic from the difference in the corresponding vertical
ionization energies.17,18 A small part of the ion kinetic energy
is converted to make up for the energy deficit.8 The interaction
time between the electron donor and acceptor is limited to within
∼5 × 10-15 s due to the ion velocity (1.85 × 105 m s-1 for
8200 eV 1H+) and the short interaction path of e10 Å. The
electron transfer can therefore be viewed as a vertical process.8
Electron capture by the cation is not subject to dipole selection
rules. Hence, excited electronic states in the radical are
accessible depending on the Franck-Condon factors that govern
the transition probabilities between the initial vibrational state
of the precursor cation and the vibrational state of the hyper-
valent radical in the particular electronic state. The effect of
the electron donor on the electron transition probabilities in fast
collisions has been addressed qualitatively but is not well
understood at present.19 The precursor ion internal energy is
known to have an effect on the formation of hypervalent
radicals; as a rule, neutralization of vibrationally hot cations
produces larger fractions of metastable radicals.5e-g,8
In this study we show that dimethylammonium radicals
exhibit an intriguing pattern of metastability that depends on
the presence and position of deuterium and the internal energy
of the precursor cation. We also probe the excited states in
2H• by laser photoexcitation at 2.41 and 2.54 eV and compare
the experimental data with configuration interaction singles
(CIS) calculations.20 The dissociation kinetics and branching
ratios are analyzed by Rice-Ramsperger-Kassel-Marcus
(RRKM) calculations21 on ab initio potential energy surfaces
of ground state 1H•-2D•.
Figure 1. Schematic view of the tandem mass spectrometer for
neutralization-photoexcitation-reionization. A, ion source; B,- quad-
rupole mass filter; C, acceleration lens; D, neutralization collision cell;
E, reflector lens; F, conduit lens; G, reionization collision cell; H,
deceleration lens; I, energy filter lens; J, quadrupole mass analyzer; K,
electron multiplier; L, Ar-ion laser; M, mirrors; W, Brewster angle
window.
NR conversions for 1H+ through 2D+, expressed as sums of
integrated reionized peak intensities (∑INR) relative to the
intensity of the incident precursor ion beam (I0), were ∑INR/I0
) (1.6 ( 0.4) × 10-5 from several measurements. The
reionized cations were decelerated to 78 eV kinetic energy,
energy filtered, and mass-analyzed by a quadrupole mass filter
operated at unit mass resolution. The ion currents were detected
by an electron multiplier, converted to voltages by a Keithley
Model 428 amplifier, and treated by a PC-based data system.22
Typically, 25-40 repetitive scans were accumulated per spec-
trum, and the spectra were reproduced in subsequent runs and
over a period of several weeks. The apparatus was tuned daily
•+
to maximize the signal of reionized CS2
.
For laser photoexcitation experiments, the tandem mass
spectrometer was equipped with an argon-ion laser, as described
recently (Figure 1).16,24 The neutralized beam passed through
a 16.5 kV/cm electrostatic field gradient to remove high Rydberg
states,24,25 and it was merged with polarized light from a Laser
Ionics 1400-12A Ar-ion laser operated in the power mode that
delivered a total of 11 W at the 488 and 514.4 nm main visible
lines. This corresponded to a 1019 photon/s flux of photons
with 2.54 and 2.41 eV energy. The contributions from the 457,
476, 496, 501, and 528 nm lines were weaker than 0.9 W and
extended the energy range from 2.36 to 2.72 eV. The laser
beam overlapped with at least 40% of the neutral beam profile
over the entire drift distance of 60 cm.16,24 In the photoexci-
tation experiments, the electrostatic potentials on the conduit
elements were scanned in link with the deceleration lens
potentials to allow detection of survivor and product ions formed
within the conduit between the deflector lens and the reionization
cell (Figure 1, F).16 This provided a 0.3-3.2 µs observation
window for the neutral intermediates to be photoionized or
collisionally reionized. This also increased the observation
window for ion dissociations by 2.9 µs.23
Experimental Section
Methods. Measurements were made on a tandem quadrupole
acceleration deceleration mass spectrometer, as described previ-
ously.22 Precursor cations were generated in a tight chemical
ionization source of our design. The ionization conditions were
as follows: electron current 1 mA, electron energy 100 eV,
ion source temperature 200-220 °C, ion energy 78-80 eV.
The pressure of the protonation or deuteronation reagent gas
was adjusted to obtain [M + H]+/ [M•+] or [M + D]+/[M•+]
ratios >20 in most instances. This allowed us to keep the
contributions from 13C and 15N isotopomers of dimethylamine
cation-radicals below 0.1% of the [M + H,D]+ ion intensities.
The cations were extracted from the ion source, transmitted
through a radio-frequency-only quadrupole mass analyzer, and
accelerated to 8200 eV kinetic energy. Stable cations of >25
µs lifetimes were neutralized by collisions with dimethyl
disulfide that was admitted to the collision cell at pressures such
as to achieve 70% transmittance of the ion beam. This
corresponded mostly (85%) to single-collision conditions. The
remaining ions were reflected by a cylindrical lens maintained
at +250 V, and the neutral products were allowed to drift
through an electrostatic lens system (conduit)23 to a downbeam
collision cell. In addition to removing the precursor ions, the
reflector lens also created a 16.5 kV/cm electrostatic field
gradient that the neutral intermediates passed through. The
lifetimes of the neutrals to be reionized and detected were 3.2-
3.4 µs for 1H• through 2D• in the conventional NR mass spectra.
The neutral intermediates were reionized by collisions with
dioxygen admitted to the downbeam cell at pressures such as
to achieve 70% transmittance of the precursor ion beam. The
The neutralization target is transparent at the wavelengths
used. The UV spectrum of dimethyl disulfide (λmax ) 258 nm,
ꢀmax ) 21 000 in methanol) showed no absorption above 350
nm. The molar absorptivity at 488 and 514.5 nm was negligible
(ꢀ , 1).
The laser beam entering the deceleration lens and the drift
region was slightly collimated by the ion injection lens mounted
on the quadrupole mass analyzer, whose internal diameter
matched the laser beam width. This resulted in desorption/
ionization of the adsorbed organics (mostly diffusion pump oil)
+
+
that gave rise to the peaks of C3H3 at m/z 39 and C3H5 at

Metastable States of Dimethylammonium
J. Phys. Chem. A, Vol. 101, No. 20, 1997 3791
TABLE 1: Ab Initio Energiesa
species
PMP2/6-31++G(d,p)
PMP4(SDTQ)/6-31++G(d,p)
-135.158 37c
PMP2/6-311++G(3df,2p)
PMP4b/6-311++G(3df,2p)
-135.281 39
1H+
1H+
1H•
1H•
1A1
-135.103 31c
-135.226 33
-135.225 23
-135.359 30
-135.358 15
-135.318 97
-135.305 76
(VI)d
(X˜ )2A1
(VN)e
(A˜ )2B1
(C˜)2B2
-135.232 94
-135.231 76
-135.192 89
-135.181 43
-135.288 71
-135.287 71
-135.248 74
-135.237 67
-135.415 07
-135.414 10
-135.375 82
-135.362 00
a In units of hartree, 1 hartree ) 2625.5 kJ mol-1
.
b From additivity approximation, eq 1. c From ref 17. d From vertical ionization of 1H•. e From
vertical neutralization of 1H+.
m/z 41, which did not interfere with the analyte peaks.16 The
m/z 39 and 41 peaks were observed in the absence of collision
gases and precursor ions and were removed from the spectra
by background subtraction. Over 100 repetitive scans were
accumulated with the laser on and off in order to correct for
reionization by background gas collisions. Raw data were
digitally subtracted to obtain net differences due to photoion-
ization or photodissociation. The differential ion currents were
not measured directly; we estimate from these and previous
measurements16,24 that >0.1% changes in the reionized intensi-
ties were detectable.
Materials. Methane (Matheson, 99.97%), ammonia (Mathe-
son, 99.99%), isobutane (Matheson, 99.5%), ND3 (Cambridge
Isotope Laboratories, 99% D), D3O (Cambridge Isotope Labo-
ratories, 99.5% D), isobutane-d10 (CND Isotopes, 99% D), and
dimethylamine (Matheson, 99.5%) were used as received.
(CD3)2NH (2) was prepared by methylation of p-toluenesulfon-
amide with CD3I (Cambridge Isotope Laboratories, 99.5% D)
in ethanolic NaOH. The N,N-di-(methyl-d6)-p-toluenesulfon-
amide, obtained in 67% yield, was hydrolyzed in refluxing 80%
H2SO4 for 6 h; the (CD3)2NH formed was liberated with NaOH
and purified by trap-to-trap vacuum distillation. Yield, 65%,
99% D.
approximation.30 The rotational states were treated adiabatically
in the RRKM calculations.31 The microscopic rate constants,
k(E,J,K), were Boltzmann-averaged over the thermal distribution
of rotational J and K states pertinent to the ion source
temperature. To this end, a short program was written to treat
the output files of the RRKM calculations.
Results and Discussion
Metastable Dimethylammonium Radicals by Collisional
Neutralization. Dimethylammonium cation 1H+ was prepared
+
by gas phase protonations with CH5+, H3O+, t-C4H9+, and NH4
and by self-chemical ionization with (CH3)2NH•+, 1•+. The
corresponding reaction exothermicities32 are given in eqs 2-6.
(CH3)2NH + CH5+ f 1H+ + CH4
-∆Hr ) 386 kJ mol-1 (2)
+ H3O+ f 1H+ + H2O
-∆Hr ) 240 kJ mol-1 (3)
+ t-C4H9+ f 1H+ + C4H8
-∆Hr ) 129 kJ mol-1 (4)
Calculations. Standard ab initio calculations were carried
out using the Gaussian 92 suite of programs (Table 1).26 The
UHF/6-31++G(d,p) optimized geometries of 1H• and the
•
transition states for loss of H• and CH3 were obtained from
previous calculations of Boldyrev and Simons17 and used for
vibrational analysis of 1H• and its isotopomers 1D•, 1HD•, 2H•,
and 2D•. The harmonic vibrational frequencies and optimized
geometries are available from the corresponding author upon
request. The spin-projected energies27 for 1H+, 1H•, and the
transition states were taken from the previous PMP4/6-31++G-
(d,p) + ZPVE data17 unless stated otherwise. The geometries
of 1H+ and 1H• were reoptimized with UMP2/6-31++G(2d,p).
Single-point energies for 1H+ and the (X˜ )2A1 ground state of
1H• were obtained from PMP2(frozen core)/6-311++G(3df,-
2p) calculations on the reoptimized geometries. Effective
PMP4(SDTQ)/6-311++G(3df,2p) energies were estimated from
the additivity approximation28 (eq 1).
+ NH4+ f 1H+ + NH3
-∆Hr ) 77 kJ mol-1 (5)
+ (CH3)2NH•+ f 1H+ + (CH3)2N•
-∆Hr ) 25 kJ mol-1 (6)
The protonations were carried out at reagent gas pressures
of ∼0.1 Torr allowing high conversions such as to achieve ion
abundance ratios [1H+]/[1•+] > 20 in most instances and similar
for the isotopomers. This precaution was important in order to
minimize contamination of 1H+ with 13C and 15N isotope
satellites of 1•+ which amounted to 2.6% of the latter ion
intensity. Working in the high-pressure regime resulted in some
cooling of the vibrationally excited cations, which underwent
on average 70-90 collisions with the reagent gas during their
calculated residence time in the ion source (5.9-8.2 µs). The
neutralization-reionization spectra of 1H+ from protonations
with CH5+, t-C4H9+, NH4+, and 1•+ are shown in Figure 2. The
spectra showed weak peaks at m/z 46 (0.5-0.9% of the sum of
reionized peak intensities, ∑INR) that corresponded by mass to
reionized 1H+. Two major dissociation channels were observed
(Scheme 1), i.e., loss of H• to give dimethylamine (1), which
appeared as 1•+ at m/z 45 following ionization, and loss of CH3
to give methylamine (3), which appeared as 3•+ at m/z 31. Other
products in the spectra were formed by ion dissociations of
reionized 1•+ (m/z 38-44, 26-29, 12-15) and 3•+ (m/z 26-
PMP4/6-311++G(3df,2p) ≈ PMP4(SDTQ)/6-31++G(d,p)
+ PMP2/6-311++G(3df,2p) - PMP2/6-31++G(d,p) (1)
Geometry optimizations and potential-energy mapping along
the N-H and N-C dissociation coordinates for the three lowest
excited states of (CH3)2NH2• were carried out with the config-
uration interaction singles (CIS) method20 using the 6-31++G-
(d,p) basis set. Single-point energies were obtained for the
stationary states with CIS/6-311++G(3df,2p). RRKM calcula-
tions were carried out using Hase’s program29 on a cluster of
Silicon Graphics Indigo workstations. Vibrational state densities
were obtained by direct count for internal energies up to 60 kJ
mol-1 above the dissociation threshold. At higher excitations,
the state densities were obtained from the Whitten-Rabinovitch

3792 J. Phys. Chem. A, Vol. 101, No. 20, 1997
Nguyen et al.
Figure 2. Neutralization (CH3SSCH3, 70% transmittance)-reionization
Figure 3. Neutralization-reionization spectra of 1D+ from deuter-
onation with (a) ND4+, (b) D3O+, and (c) 1HD+ from deuteronation
with t-C4D9+. Insets show the precursor ion relative intensities from
chemical ionization.
(O2, 70% transmittance) spectra of 1H+ from protonation with (a) CH5+
,
(b) t-C4H9+, (c) NH4+, (d) self-CI. Insets show the precursor ion relative
intensities from chemical ionization.
of high-energy 1H•. Hence, loss of methyl was an important
dissociation channel of 1H•.
SCHEME 1
The presence of surviving 1H+ in the spectra was examined
with regard to the possible contamination by 1•+ isotope
satellites. For example, NR of 1H+ from self-CI gave an 8 ×
10-8 ratio of survivor to incident ion intensities, whereas the
same ratio for 1•+ was measured as 6 × 10-5. Hence, even the
presence of a small fraction of 13C and 15N isotopomers of 1•+
coinciding by mass with 1H+ (0.07% from the chemical
ionization spectrum) contributed a large fraction (4 × 10-8
,
50%) to the survivor ion intensity. Likewise, isotope contami-
nation was calculated to amount to 50, 200, and 110% of the
survivor ion intensities in the NR spectra of 1H+ from
protonations with NH4+, t-C4H9+, and CH5+, respectively.
Considering the spread in the correction factors, it appeared safe
to conclude that no significant fractions of survivor 1H• were
detected in collisional neutralizations of 1H+.
30, 12-16) as deduced from their reference NR spectra.9,33 The
peak at m/z 15 was notably stronger in the spectra of 1H+ than
•
in those of 1•+ and 3•+ and may correspond to reionized CH3
from dissociation of neutral 1H•.
The effect of precursor ion internal energy manifested itself
in the relative abundances of secondary fragment ions, e.g.,
Ions 1D+ and 1HD+ were generated by deuteronations at
different exothermicities. 1D+ was prepared by deuteronation
HCN•+ and HCNH+, which were highest for the most energetic
with ND4 and D3O+ of dimethylamine-N-d, whereas 1HD+
+
+
1H+ from protonation with CH5
.
The [3•+]/[1•+] ratio
was prepared by deuteronation of 1 with t-C4D9+. The NR
spectra of 1D+ and 1HD+ produced substantial fractions of
survivor ions (Figure 3a,c). In this case, isotope corrections
amounted to only 8 and 16% of the reionized 1D+ and 1HD+
intensities, respectively.34 In contrast, 1D+ from the more
exothermic deuteronation with D3O+ gave a barely detectable
survivor ion in the NR spectrum (Figure 3b). The existence of
metastable 1D• in the latter case was indirectly indicated by
the peak at m/z 47, which was due to H• loss from reionized
1D+. Note that radical 1D• can be expected to eliminate D•
but not H•. In contrast, dissociations of 1D+ involved loss of
both H• and D•, as verified by its collision-induced dissociation
spectrum. The observation of H• loss in the NR spectrum of
increased monotonously with the precursor ion internal energy
from 0.13 for 1H+ from self-CI to 0.27 for 1H+ from
protonation with CH5+. To obtain approximate branching ratios
for the formation of neutral 1 and 3 from 1H•, the relative
abundances of 1•+ and 3•+ in the NR spectrum of 1H+ must be
scaled by their fractions in the NR spectra of the neutral
molecules, 1 and 3, respectively, and by the reionization yields.
These were estimated from the survivor to precursor ion intensity
ratios for 1•+ (6 × 10-5) and 3•+ (3.3 × 10-5) in their NR
spectra, giving a factor of 1.8 favoring 1•+. The corrected
branching ratios indicated a 19/81 ratio for loss of CH3• and H•
from low-energy 1H•, which increased to 33/67 for dissociations

Metastable States of Dimethylammonium
J. Phys. Chem. A, Vol. 101, No. 20, 1997 3793
Figure 5. Neutralization-photoionization spectrum of 2H+: (a) total
spectrum with laser on; (b) collisional background with laser off; (c)
background-corrected photoionization spectrum.
Laser Photoexcitation. We have further probed metastable
radicals 2H• and 1D• by laser photoexcitation. In one series of
+
experiments, metastable 2H• from neutralization of CH5
-
protonated 2 was exposed to the laser beam in the absence of
the reionization gas. The resulting spectrum (Figure 5a) showed
a small peak of 2H+ at m/z 52 due to photoionization, while
substantial peaks of fragment ions originating from 2H• were
observed. Subtraction of the collisional background (Figure 5b)
and the laser background gave a spectrum (Figure 5c) that
showed weak positive contributions from the dehydrogenation
products of 2H• at m/z 49-51 and negative contributions for
Figure 4. Neutralization-reionization spectra of 2H+ from protonation
with (a) CH5+, (b) t-C4H9+, (c) self-CI, and (d) 2D+ from deuteronation
with ND4+. Insets show the precursor ion relative intensities from
chemical ionization.
1D+ indicated unambiguously that a fraction of 1D• survived
for 3.3 µs and was reionized to 1D+. Hence, the spectral data
supported the existence of metastable 1D• and 1HD• but also
pointed to substantial effects of the precursor ion internal energy.
The corrected branching ratio for CH3• versus D• loss from 1D•
(30/70) was higher than that for CH3• versus H• loss from 1H•
(22/78) prepared from NH4+-protonated 1. The branching ratio
for the CH3• and H• loss from 1HD• (34/66) was similar to that
for 1H• (33/67) prepared from t-C4H9+-protonated 1H+. The
NR spectrum of 1HD+ also allowed us to evaluate the fractions
of (1HD - H)•+ and (1HD - D)•+ after correcting for the
consecutive loss of H• from the former ion. The corrected ratio,
[1HD - H]•+/[1HD - D]•+ ) 1.64, indicated a modest
intramolecular isotope effect35 favoring cleavage of the N-H
bond in 1HD•.
+
CDNH+ (m/z 29) and CD3 (m/z 18). The net contribution to
the peak of 2H+ due to photoionization was within the noise
level in the background-corrected spectrum (Figure 5c). Very
similar results were obtained for photoionization of 1D•, whose
background-corrected spectrum yielded a very small peak of
1D+ due to laser photoionization. The data thus showed that
photoionization of 1D• and 2H• was inefficient at the wave-
lengths used. This indicated that the vertical ionization energy
of metastable dimethylammonium was greater than 2.41-2.54
eV from the Ar-ion main lines or that metastable 2H• and 1D•
were photoionizable but the photoionization cross sections were
too small to permit ion detection.
In a second series of experiments, the beams of metastable
1D• and 2H• were exposed to the laser beam in the presence of
dioxygen which was admitted to the neutral drift region at a
pressure allowing mostly (>85%) single-collision conditions.
In this case, metastable 1D• or 2H• could undergo competitive
unimolecular dissociations and photoexcitation, both followed
by collisional reionization. Contributions from laser photoion-
ization were excluded by the previous experiments. Following
background corrections, the spectrum of 2H• (Figure 6) showed
positive contributions for reionized 2H+ and its dissociation
products due to irradiation. The increased intensity of 2H+ must
be due to interaction with photons of neutral 2H•, because
alkylammonium ions and the neutralization and reionization
gases are transparent at the wavelengths used.36 The increased
intensities of fragments may, in principle, be due to photodis-
sociation of reionized 1•+ and 3•+, which were exposed to the
laser beam for most of their path length through the mass
spectrometer (Figure 1). 1 and 3 show large gaps (>2.5 eV)
between the first and second bands in their photoelectron
spectra,37 which indicated that absorption of 2.41 and 2.54 eV
Substantial fractions of survivor ions were obtained from
neutralization-reionization of 2H+ prepared by protonations
of (CD3)2NH (2) with CH5+ and t-C4H9+ and by self-CI (Figure
4a-c). Isotope corrections to the intensity of survivor 2H+ were
<8% in each case. 2H+ from CH5+-protonated 2 gave the
largest fraction of metastable hypervalent dimethylammonium,
2H•, yielding 5% of reionized 2H+ relative to ∑INR, and the
highest branching ratio for loss of CD3• versus H• (42/58). The
other spectra (Figure 4b,c) showed lower fractions of survivor
2H+ (3.0-3.4% ∑INR) and increased fractions of 2•+ which was
formed by loss of H• followed by reionization.
In contrast to 2H+, no survivor ions were found for the fully
deuterated isotopomer 2D+ prepared by deuteronation of 2 with
+
ND4 (Figure 4d). The intermediate hypervalent radical 2D•
dissociated completely by CD3• and D• losses in a 32/68 ratio.
This result was qualitatively similar to the previous observation
•
for the C2H7O• system, where CD3CD2OD2 showed no meta-
stability whereas other isotopomers did.5g

3794 J. Phys. Chem. A, Vol. 101, No. 20, 1997
Nguyen et al.
SCHEME 2
tation followed by dissociation or collisional reionization of the
excited state P(1). Direct photoionization of P(0) was excluded
experimentally (vide supra). Photoionization of photoexcited
states would correspond to a two-photon process that was
deemed unlikely at the photon densities used. Under these
assumptions, the formation of P+ from P(0) was due entirely
to collisional ionization as described by eq 7, which gave eq 8
on integration.
Figure 6. Neutralization-photoexcitation-reionization spectrum of
2H+: (a) spectrum with laser on; (b) background-corrected spectrum.
dP+(0) ) P(0)l)0 exp(- k l/V)σ(0)N dl
(7)
P+(0) ) P(0)l)0 σ(0)N(V/ k )[1 - exp(- k L/V)] (8)
∑
i
i
∑
∑
i
i
i i
P(0)l)0 is the initial flux of neutral 1H• (or its isotopomers) in
the electronic state produced by neutralization, P+(0) is the flux
of reionized 1H+, σ(0) is the collisional ionization cross section,
ki are the unimolecular dissociation constants, N is the reion-
ization gas number density, V is the neutral velocity, dl is the
path length element for P(0), and L is the total neutral path
length. The dissociation kinetics of P(0) was approximated by
single exponential decay in this model. The effect of photo-
excitation on the population of P(0) was neglected. Following
photoexcitation, the excited state P(1) is collisionally ionized
to form P+ according to eqs 9-11, where ds is the path element
for P(1) (s + l ) L), ꢀ is the photoexcitation cross section, IhV
Figure 7. Neutralization-photoexcitation-reionization spectrum of
1D+ from deuteronation with D3O+: (a) spectrum with laser on; (b)
spectrum with laser off; (c) background-corrected spectrum.
P(1)l ) P(0)l)0ꢀI (V/ k )[1 - exp(- k l/V)] (9)
∑
∑
hV
i
i
i i
dP+(1) ) P(1)l σ(1)N ds
(10)
photons could occur only in vibrationally hot 2A′ and 2A ground
electronic states of 1•+ and 3•+, respectively. The excited states
of 1•+ and 3•+ are dissociative.33 We found that methyl,
dimethyl, and trimethylamine cation-radicals from neutralization
and reionization showed only small increases of fragment
relative intensities upon irradiation at 488 and 514.5 nm, which
were difficult to quantify.16
A large increase of survivor ion relative intensity was
observed for photoexcitation of 1D• from neutralization of
D3O+-deuteronated 1. In the absence of the laser beam the
spectrum showed no detectable survivor 1D+ for neutral
observation times of 3.3 µs (Figure 3b) or 0.3 µs (Figure 7b).
However, irradiation of 1D• in the neutral drift region resulted
in the formation of a fraction of survivor 1D+ (Figure 7a,c).
Since 1D• was not photoionized at the wavelengths used, the
increased intensity of survivor 1D+ must be due to photoexci-
tation of 1D• followed by collisional reionization of the
photoexcited state.
P+(1) ) P(0)l)0ꢀI σ(1)N(V/ k ){L - (V/ k )[1 -
∑
∑
hV
i
i
i i
exp(- k L/V)]} (11)
∑
i
i
is the light intensity, and σ(1) is the collisional ionization cross
section for P(1). Built in this model are the simplifying
assumptions that the excited state is not depleted by dissociations
and de-excitation. The flux of reionized P+ depends on several
parameters, in particular ∑iki, which determine the half-life of
P(0). For example, dissociations with rate constants >3 × 107
s-1 would leave <0.5% of nondissociated 1H• to be reionized
on the present time scale. However, the relatiVe enhancement
of P+ intensity upon irradiation, expressed as P+(1)/P+(0), which
is amenable to experimental measurements, showed some
general characteristics that are now discussed.
Photoexcitation of 1H•, in the form of its metastable isoto-
pomers 1D• or 2H•, must involve promoting the odd electron
from the diffuse, singly occupied, 7a1 molecular orbital to a
higher orbital of a Rydberg type.14,17 Considering for simplicity
hydrogen-like ns orbitals (n g 3), the effective orbital radius,
taken at the maximum of the radial distribution function,38 scales
roughly with the square of the principal quantum number, n2,
so that the collisional ionization cross section scales roughly
The processes involved in the previous photoexcitation
experiments are summarized in Scheme 2. Metastable radicals
P(0), formed by collisional neutralization in an initial electronic
state (0), can undergo competitive collisional reionization to
give survivor ions P+ or unimolecular dissociation to products.
Upon irradiation these two processes compete with photoexci-

Metastable States of Dimethylammonium
J. Phys. Chem. A, Vol. 101, No. 20, 1997 3795
Figure 8. Relative enhancement of ionization yields for ns f (n +
∆n)s excitations. t1/2 ) ln 2/∑ki is the neutral half-life.
with n4. Hence, a higher n state can be expected to have a
substantially larger ionization probability than a lower n state.
A very similar situation is encountered in multiphoton ionization,
where the photoionization cross sections of excited states are
several orders of magnitude greater than those of the corre-
sponding ground states.39 The relative enhancement, P+(1)/
P+(0), depends on the half-life of P(0) (t1/2 ) ln 2/∑iki) and the
photoexcitation yield. This is plotted in Figure 8 for n ) 3
and an arbitrary 1/10 ratio of photoexcitation and collisional
reionization yields for P(0). The relative enhancement increases
steeply for neutrals of half-lives in the 10-5-10-7 s range,
whereas the total fraction of surviving radicals decreases in the
same order. This means that short-lived but observable 1D• or
2H• will give the greatest relatiVe enhancement of survivor 1D+
or 2H+, respectively, upon photoexcitation. This was indeed
observed for photoexcitation of metastable 1D• and 2H•, where
the less abundant 1D+ gave a greater enhancement than the more
abundant 2H+ (Figures 6 and 7). Figure 8 also shows that the
enhanced reionization yield upon photoexcitation depends
strongly on the change in n and can exceed 102 for excitations
from n ) 3 to n ) 10. It is also pertinent to note that the
lifetimes of high Rydberg states scale with n3;40 photoexcitation
to high Rydberg states is therefore expected to increase the
metastable lifetimes and hence the probability for collisional
reionization.
Figure 9. Energy diagram for excitation, ionization, and dissociation
in 1H•. The ground-state ionization energy is from PMP4/6-311++G-
(3df,2p) calculations. The excited-state ionization energies are from
CIS/6-311++G(3df,2p) excitation energies and the ground-state ioniza-
a
tion energy. Ground-state energy data from ref 17.
and moments of inertia for the isotopomers and the relevant
transition states that were used in RRKM calculations of
unimolecular rate constants for dissociations of 1H•, 1HD•, 1D•,
2H•, and 2D•. A complicating factor was the finding that the
highest point on the potential energy surface along the N-CH3
dissociation coordinate was not a saddle point but a cusp that
was located at a bond length d(N-C) ) 1.81 Å. An analogous
discontinuity on the potential energy surface was obtained for
the N-CH3 bond dissociation in trimethylammonium.9 Nev-
ertheless, harmonic frequency analysis at the cusp gave a single
negative force constant for the motion along the N-C coordi-
nate, and so this point was used to approximate the transition
state for the methyl loss. The RRKM curves for the dissocia-
tions of 1H• (Figure 10a) showed that the loss of H• should be
preferred at all excitations. The experimental branching ratio
Although the experimental data provided a qualitative de-
scription of metastable dimethylammonium radicals, alone they
did not allow us to identify the electronic states responsible for
the observed metastability. To summarize the experiments, the
metastable state(s) were not photoionized with 2.41 and 2.54
eV photons, but underwent photoexcitation that caused a large
change in the ionization cross section. These results are now
examined in the light of ab initio and RRKM calculations.
Ground and Excited State Energetics. The energetics of
•
for CH3 versus H• loss (0.23) could be achieved in dissociations
of 1H• at excitations >100 kJ mol-1 above the dissociation
threshold, while much greater ratios were predicted by RRKM
rate constants for lower excitations (Figure 10). A similar
conclusion followed from the RRKM curves for 1D•. In
contrast, the experimental branching ratios for loss of CD3 versus
•
H• from 2H• (0.72) and loss of CD3 versus D• from 2D• (Figure
10b) could not be explained by the RRKM curves at excitations
<140 kJ mol-1 above the threshold. RRKM curves for the H•
versus D• loss from 1HD• predicted large intramolecular isotope
effects, as shown in Figure 11. The calculated kH/kD ratio
approached the experimental value (1.6) at excitation energies
2
the A1 ground electronic state of 1H• was studied previously
by Boldyrev and Simons at the UMP4(SDTQ)/6-31++G(d,p)
level of ab initio theory.17 The radical was found to be weakly
bound with respect to N-H bond cleavage, whereas an energy
barrier was found for the cleavage of the N-CH3 bond (Figure
9). Both dissociations were found to be exothermic; the
>140 kJ mol-1
.
In contrast, the metastability observed for 1HD•, 1D•, and
2H• required that there be a fraction of radicals with internal
energies below the activation barrier for the lowest energy
dissociation by N-H or N-D bond cleavage. The calculated
lowest activation energies for the (X˜ )2A1 state of 1H•, 1HD•,
1D•, 2H•, and 2D•, including zero-point corrections, e.g., 13,
calculated difference in the product enthalpies (72 kJ mol-1
,
Figure 9) was close to the difference in the product heats of
formation (77 kJ mol-1).18
We used the previous ab initio energies and optimized
structures to obtain zero-point corrections, harmonic frequencies,

3796 J. Phys. Chem. A, Vol. 101, No. 20, 1997
Nguyen et al.
sibility of a sharply bimodal internal energy distribution in 1HD•,
1D•, and 2H•, the ground state properties of the radicals could
not account for the observed metastability, dissociations, and
isotope effects.
The energetics of the electronic states in 1H• were further
investigated by ab initio calculations. The ground-state geom-
etry was reoptimized with UMP2(FULL)/6-31++G(2d,p) cal-
culations, which gave bond lengths and angles which were
similar to those from previous UHF/6-31++G(d,p) calcula-
tions.17 The optimized geometry was used for UMP2 single-
point calculations using the larger 6-311++G(3df,2p) basis set.
Population analysis of the HF/6-311++G(3df,2p) wave function
of the ground state indicated the electron configuration in 1H•
to be (a1)2(b2)2(a1)2(a1)2(b2)2(a1)2(b1)2(a1)2(b2)2(a2)2(a1)2(b1)2(b2)2-
(a1)1...(a1)0(b1)0(b2)0(a1)0(b1)0.... The energy of the 7a1 singly
occupied orbital was 12.80 eV above the highest doubly
occupied 4b2 orbital. This large separation made the system
suitable for calculations by the CIS method, because all single-
electron excitations involved exclusively the unpaired electron
and combinations of the 7a1 SOMO and the virtual orbitals.
Geometry optimizations with CIS/6-31++G(d,p) found the first
three excited states of 1H• as (A˜ )2B1, (B˜)2A1, and (C˜)2B2. The
optimized geometry of the A˜ state was similar to that of the
ground state; e.g., the respective N-H bond lengths were d(N-
H) ) 1.023 and 1.022 Å, while the respective N-C bond lengths
were d(N-C) ) 1.483 and 1.477 Å. The B˜ and C˜ states showed
shorter N-H bonds (1.005 and 1.005 Å, respectively) and longer
N-C bonds (1.499 and 1.498 Å, respectively). The CIS
energies are summarized in Table 2. The relative energies for
the equilibrium structures are given as the corresponding
ionization energies in Figure 9.
The calculations indicated that neutralization of 1H+ and
ionization of the ground and three lowest excited electronic
states of 1H• were subject to negligible Franck-Condon effects
(e3 kJ mol-1). The adiabatic ionization energy of (X˜ )2A1 1H•
was calculated by effective PMP4/6-311++G(3df,2p) as 3.70
eV, including zero-point energy corrections. In the absence of
Franck-Condon effects, the vibrational energy distribution in
the precursor ions must be largely preserved in the radicals
formed by vertical neutralization.33 The average vibrational
energy in thermal 1H+-2D+ ranged between 14.2 and 15.7 kJ
mol-1 at 473 K. Thus, even fully thermalized precursor ions
would produce dimethylammonium radicals with internal ener-
gies close to the dissociation barrier for the H or D loss from
the ground electronic state. Efficient tunneling for the H loss
could be expected.25b Moreover, neutralization of vibrationally
excited ions from the exothermic protonations should give
dimethylammonium radicals in dissociative vibrational states.
Hence the formation of metastable (X˜ )2A1 states of microsecond
lifetimes appeared highly improbable for the isotopomers of 1H•.
A chemical rationale for the weak N-HN bonds in the (X˜ )2A1
electronic state of 1H• can be inferred from the charge and spin
densities, obtained from Mullikan population analysis of the
UHF/6-311++G(3df,2p) wave function. The (X˜ )2A1 state
showed a large spin population on the HN atoms (+0.81). In
addition, the negative charge on HN (-0.54) and N (-0.57)
and the antibonding character of the 7a1 SOMO along the N-H
bond pointed to its facile dissociation.
Figure 10. RRKM rate coefficients for unimolecular dissociations of
1H• and 2D• on the ground-state potential energy surface: open squares,
N-(H,D) bond cleavage; full diamonds, N-C bond cleavage. The lower
parts of the curves show superimposed points from direct count
calculations.
The energies of the excited states were calculated by CIS/
6-311++G(3df,2p) as 0.84, 1.13, 1.22, and 1.88 eV above the
ground state for (A˜ )2B1, (B˜)2A1, (C˜)2B2, and (D˜ )2A1, respec-
tively. The potential energy surfaces for the A˜ , B˜, and C˜ states
were investigated by CIS/6-31++G(d,p) calculations along the
N-H and N-C coordinates; the bond lengths were changed
stepwise, while the other degrees of freedom were fully
Figure 11. RRKM isotope effect on N-H and N-D bond dissociations
in 1HD•: open circles, direct count; open squares, Whitten-Rabinovitch
approximation; dashed line, experimental value.
15, 21, 16, and 22 kJ mol-1, respectively, were very low and
did not suggest any particular stabilization of 1HD• and 2H•
nor destabilization of 2D•. Hence, barring the unlikely pos-

Metastable States of Dimethylammonium
J. Phys. Chem. A, Vol. 101, No. 20, 1997 3797
energya oscillator strength, fb
TABLE 2: CIS Energies and Oscillator Strengths
method
A˜
B˜
C˜
D˜
Optimized Structures
CIS/6-31++G(d,p)
CIS/6-311++G(3df,2p)
-134.713 040
-134.749 517
(0.226)
-134.702 460
-134.738 949
(0.102)
-134.699 305
-134.735 799
(0.201)
-134.712 363c
(0.048c)
Reaction Paths
d(N-H) (Å)
CIS/6-31++G(d,p)
CIS/6-31++G(d,p)
1.15
1.25
1.35
-134.701 459
(0.192)
-134.686 604
(0.079)
-134.683 371
(0.179)
-134.678 824
-134.661 537
-134.657 985
(0.123)
(0.064)
(0.139)
-134.649 484
(0.061)
-134.629 459
(0.054)
-134.625 563
(0.095)
d(N-C) (Å)
1.65
-134.701198
(0.246)
-134.695187
(0.093)
-134.690611
(0.178)
1.75
1.85
-134.687 366
-134.687 043
-134.679 132
(0.254)
(0.059)
(0.162)
-134.673 044
(0.243)
-134.685 876
(0.002)
-134.665 299
(0.145)
a In units of hartree. b Oscillator strength given in parentheses. c On optimized geometry of the A˜ state.
and state symmetries (2A1 f A′ for both X˜ and B˜) indicated
that the X˜ and B˜ states nonadiabatically mix in the vicinity of
the transition state for the N-C bond cleavage in 1H•, possibly
through a conical intersection.41 The interaction between the
X˜ and B˜ states gives a clue to the observed loss of methyl from
1H•. The (B˜)2A1 state of 1H• can lose a methyl through internal
conversion to the ground state at d(N-C) ≈ 1.85 Å. Since the
potential energy surface of the ground state has a negative
gradient at d(N-C) > 1.85 Å (Figure 9), the system cannot
recross the transition state and continues moving along the N-C
coordinate to break the bond and form CH3• and H2NCH3. The
•
overall dissociation, (B˜)2A1 f CH3 + H2NCH3, is >200 kJ
mol-1 exothermic (Figure 9) and should result in vibrational
excitation of the products. This is corroborated by the NR
spectra of 1H•, which show substantial dissociation of CH3-
•+
NH2 following collisional reionization of CH3NH2 (Figure
2).33 Since the A˜ and B˜ states cross upon stretching the N-C
bond to 1.75 Å, dissociation of 1H• starting in the A˜ state can
continue on the potential energy surface of the B˜ state and be
funneled to the dissociative part of the ground state surface as
discussed above. Hence, loss of methyl from both the A˜ and
B˜ states is kinetically and dynamically possible. In contrast,
N-H stretching faces large potential energy barriers in both A˜
and B˜ states, so that loss of H is prevented kinetically. It should
be noted that the computational methods used in this study did
not allow us to treat the ground and excited states at the same
level of theory, and so the potential energy surfaces in the
vicinity of the critical region of N-C bond cleavage could not
be investigated in detail. Multireference calculations including
perturbational treatment of electron correlation would be desir-
able to address these excited states comprehensibly and in more
detail.41,42
The energy data allowed us to interpret some features of the
neutralization-reionization and photoexcitation experiments.
Regarding photoionization, the calculated energies suggested
that the (D˜ )2A1 and higher states should be photoionizable by
2.41 and 2.54 eV photons, whereas the lower (A˜ )2B1 and (B˜)2A1
states should not. The ionization energy of the C˜ state lies in
between the photon energies. It should be noted that correlated
calculations with large basis sets typically give ionization
energies within 0.1 eV of accepted experimental values.17,43 The
0.03-0.06 eV differences between the calculated ionization
energies of the (B˜)2A1 and (C˜)2B2 states and the 488 nm photon
Figure 12. CIS/6-31++G(d,p) potential energy profiles along the
N-H (top) and N-C (bottom) coordinates in 1H•. The energies are
relative to those of the ground state at the given bond distances.
optimized. The calculations showed that the A˜ , B˜, and C˜ states
were strongly bound with respect to N-H bond cleavage.
Figure 12 shows that the excited state energies increased by
>180 kJ mol-1 relative to the ground state as the N-H bond
was stretched from the equilibrium length to 1.35 Å. The latter
distance corresponded to the transition state of N-H bond
dissociation on the ground-state potential energy surface.17
However, the excited state energies along the N-C coordinate
differed (Figure 12, bottom). The A˜ and C˜ state energies
roughly followed the ground state energy profile, indicating
potential energy barriers to N-C bond dissociations in these
excited states. Both states also showed substantial positive
energy gradients at d(N-C) ) 1.85 Å, indicating further
potential energy increase at larger separations. In contrast, the
B˜ state showed a small energy gradient upon stretching the N-C
bond, and its energy converged to that of the ground state. This
convergence also resulted in the A˜ and B˜ state potential energy
surfaces crossing at d(N-C) ≈ 1.75 Å. The energy convergence

3798 J. Phys. Chem. A, Vol. 101, No. 20, 1997
Nguyen et al.
energy are well within this uncertainty range. However, even
if the ionization energies of the B˜ and C˜ states had matched
the photon energy, threshold photoionizations would have been
expected to have very low cross sections.15 The fact that
metastable 1D• and 2H• were not photoionized at 2.41 and 2.54
eV excluded the (D˜ )2A1 and higher excited states and left the
A˜ , B˜, and C˜ states as the likely candidates for the observed
metastability.
H or D could not be explained by the properties of the (X˜ )2A1
electronic ground state alone. Formation of metastable excited
states is therefore suggested on the basis of experimental data
and limited ab initio calculations. The (B˜)2A1 state is predicted
to have radiative lifetimes compatible with the observed
metastability and can undergo methyl loss by nonradiative
transition to the dissociative part of the ground state potential
energy surface. A detailed theoretical investigation of the
potential energy surfaces in the excited states of dimethylam-
monium appears to be necessary to explain the subtleties of
this radical species’ unusual behavior.
The role of excited states in 1H• can be further discussed in
view of the possible spontaneous or laser-induced de-excitation.
The C2V symmetry of 1H• allows for all radiative transitions
except for A1 f A2 and B1 a B2. Higher excited states
therefore could be depopulated by spontaneous or stimulated
photon emission in the laser beam, depending on the corre-
sponding transition moments. The calculated oscillator strengths
for the A˜ f X˜ , B˜ f X˜ , and C˜ f X˜ transitions, 0.23, 0.10, and
0.20, respectively, indicated excited-state lifetimes of τ < 0.46
µs, according to eq 12, where me is the mass of electron, e is
the elementary charge, ꢀ0 is the permeability of vacuum, c is
the speed of light, ν˜ij is the transition wavenumber, and fij is
the oscillator strength.44
Acknowledgment. Support of this work by the National
Science Foundation (Grant CHE-9412774) is gratefully ac-
knowledged. The ab initio computations were conducted by
using the resources of the Cornell Theory Center, which receives
major funding from the National Science Foundation and New
York State with additional support from the Advanced Research
Projects Agency, the National Center for Research Resources
at the National Institutes of Health, IBM Corporation, and
members of the Corporate Research Institute. We also thank
Dr. A. I. Boldyrev for providing us with vibrational frequencies
of the transitions states.
ꢀ0mec
τ )
(12)
2
e2 πν˜ij fij
References and Notes
(1) Herzberg, G. Discuss. Faraday Soc. 1981, 71, 165.
(2) Schuller, H.; Michel, A.; Grun, A. E. Z. Naturforsch. 1955, 10A,
1.
(3) (a) Alberti, F.; Huber, K. P.; Watson, J. K. G. J. Mol. Spectrosc.
1984, 107, 133. (b) Watson, J. K. G.; Majewski, W. A. J. Mol. Spectrosc.
1986, 115, 82.
(4) (a) Williams, B. W.; Porter, R. F. J. Chem. Phys. 1980, 73, 5598.
(b) Gellene, G. I.; Cleary, D. A.; Porter, R. F. J. Chem. Phys. 1982, 77,
3471. (c) Jeon, S.-J.; Raksit, A. B.; Gellene, G. I.; Porter, R. F. J. Am.
Chem. Soc. 1985, 107, 4129. (d) Griffiths, W. J.; Harris, F. M.; Beynon, J.
H. Int. J. Mass Spectrom. Ion Processes 1987, 77, 233.
(5) (a) Gellene, G. I.; Porter, R. F. J. Chem. Phys. 1984, 81, 5570. (b)
Raksit, A. B.; Jeon, S.-J.; Porter, R. F. J. Phys. Chem. 1986, 90, 2298. (c)
Raksit, A. B.; Porter, R. F. J. Chem. Soc., Chem. Commun. 1987, 500. (d)
Raksit, A. B.; Porter, R. F. Org. Mass Spectrom. 1987, 22, 410. (e) Holmes,
J. L.; Sirois, M. Org. Mass Spectrom. 1990, 25, 481. (f) Sirois, M.; George,
M.; Holmes, J. L. Org. Mass Spectrom. 1994, 29, 11. (g) Wesdemiotis, C.;
Fura, A.; McLafferty, F. W. J. Am. Soc. Mass Spectrom. 1991, 2, 459.
(6) Sad´ılek, M.; Turecˇek, F. J. Phys. Chem. 1996, 100, 9610, 15027.
(7) (a) Lewis, G. N. J. Am. Chem. Soc. 1916, 38, 762. (b) Reed, A. E.;
Schleyer, P. v. R. J. Am. Chem. Soc. 1990, 112, 1434.
Hence the calculated lifetimes would allow for <0.1% of
metastable 1H• surviving for 3.3 µs on the experimental time
scale. It should be noted that oscillator strengths are difficult
to calculate accurately even for simple systems, and substantially
different values were obtained for ammonium radicals that
depended on the computational method used.14d,h However, the
oscillator strengths calculated for 1H• were found to depend
on the molecular geometry and decreased markedly upon
stretching the N-H and N-C bonds (Table 2). In particular,
the B˜ f X˜ transitions showed fij ≈ 0.06 at d(N-H) ) 1.25 Å
or d(N-C) ) 1.75 Å (Table 2), which pointed to τ ≈ 0.92 µs
and 3% of metastable 1H• surviving for 3.3 µs. The oscillator
strengths for the A˜ f X˜ and C˜ f X˜ transitions decreased to
0.06 and 0.1, respectively, at d(N-H) ) 1.35 Å, but remained
high at larger N-C separations. This dependence may give a
clue to the observed increase of the metastable 1H• fractions
with the precursor ion internal energy (vide supra). 1H• formed
by collisional electron transfer in a vibrationally excited B˜ state
can be expected to have a low probability for radiative transition
to the dissociative ground state.
The dramatic effect on metastability of deuterium isotope
substitution in 1H• is difficult to explain in the absence of
detailed information on the properties of the excited states. It
may be noted, however, that 1H• and 2D•, which were not
metastable, showed strong coupling between the N-H and C-H
or N-D and C-D stretching vibrational modes, respectively,
whereas the N-D and C-H modes in 1HD• and 1D• and the
N-H and C-D modes in 2H• were well separated. If vibronic
coupling plays a role in transitions through conical intersection
to the dissociative (X˜ )2A1 state, the separation of the N-H and
N-D modes may contribute to the observed metastability.
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