The velocity and angular distributions of O 1D photofragments arising from UV excitation of the CH2OO intermediate on the B1A′ ← X1A′ transition are characterized using velocity map ion imaging. The anisotropic angular distribution yields the orientation of the transition dipole moment, which reflects the π* ← π character of the electronic transition associated with the COO group. The total kinetic energy release distributions obtained at several photolysis wavelengths provide detail on the internal energy distribution of the formaldehyde cofragments and the dissociation energy of CH2OO X1A′ to O 1D + H2CO X1A1. A common termination of the total kinetic energy distributions, after accounting for the different excitation energies, gives an upper limit for the CH2OO X1A′ dissociation energy of D0 ≤ 54 kcal mol−1, which is compared with theoretical predictions including high level multi-reference ab initio calculations.

Alkenes are an important tropospheric constituent, originating from biogenic and anthropogenic sources. A major atmospheric removal process for alkenes is ozonolysis.1,2 This is a highly exothermic process that produces a primary ozonide with a cyclic structure, which dissociates to form a carbonyl oxide, known as the Criegee intermediate, and an aldehyde (or ketone).1,3,4 The Criegee intermediates are generated with a large amount of internal excitation, which can lead to unimolecular decomposition or rearrangement, forming products such as OH, HO2, CO, CO2, CH3, and H2CO.2,4 The Criegee intermediate can also be collisionally stabilized and/or react with tropospheric species including H2O, NO2, and SO2.5–7 The rates for these bimolecular reactions are more rapid and conformer-specific than previously thought, which may substantially change predictions of their tropospheric chemistry.8 

Recent experiments in this laboratory have revealed an additional atmospheric decay pathway for the simplest Criegee intermediate CH2OO and other alkyl substituted carbonyl oxides, namely, solar photolysis in the UV region.9,10 For CH2OO, Beames et al. obtained the B1A′ ← X1A′ absorption spectrum in the UV region by measuring the UV-induced depletion of the ground state population and corresponding vacuum ultraviolet (VUV) photoionization signal at m/z = 46. The CH2OO B-X spectrum peaks at ∼335 nm with a breadth of ∼40 nm (fwhm) and a large absorption cross section of ∼5 × 10−17 cm2 molecule−1. Theoretical calculations indicate that this is a π* ← π transition primarily involving 4π e localized on the carbonyl oxide group in the Franck-Condon region.11 A very large depletion approaching 100% near the peak of the profile is indicative of rapid dynamics in the excited B1A′ electronic state and consistent with the repulsive B-state potential along the O–O coordinate computed theoretically.9,10,12 The UV absorption spectrum was combined with the solar actinic flux to estimate an atmospheric lifetime for CH2OO at midday on the order of ∼1 s with respect to solar photolysis.

In this Communication, we significantly extend the previous study of the UV B1A′ ← X1A′ absorption spectrum for the simplest Criegee intermediate CH2OO by probing the resultant dissociation dynamics using velocity map imaging (VMI). Specifically, we obtain the kinetic energy and angular distributions of the O 1D products from direct dissociation of CH2OO B1A′ to O 1D + H2CO X1A1 products. The ground X1A′ state of CH2OO also correlates with this same asymptotic limit. (The lower energy O 3P + H2CO X1A1 product channel is spin-forbidden.) Notably, the translational energy release is used to infer an upper limit for the ground state binding energy (D0) of CH2OO X1A1, which is then compared with the wide range of theoretical predictions for this important thermodynamic property.12–15 

Only recently have the CH2OO and CH3CHOO Criegee intermediates been observed directly in the gas phase utilizing VUV photoionization near threshold to provide isomer- and mass-selective detection;5,7,16 prior studies have relied on indirect methods for detection.17 These recent studies also introduced a new photosynthetic route for generating the Criegee intermediates from diiodo alkane precursors.5,7 The simplest Criegee intermediate CH2OO is generated in this laboratory in a similar manner.9,10 Specifically, a gas mixture of CH2I2 entrained in a 10% O2/Ar (15 psi) is irradiated along the length of a quartz capillary tube reactor using the 248 nm output from an excimer laser, initiating the photolysis of CH2I2 and subsequent reaction of CH2I with O2 to form CH2OO.

The Criegee intermediates are collisionally stabilized in the capillary tube, cooled in a supersonic expansion, and then travel ∼4 cm downstream into the interaction region of a VMI apparatus. The frequency-doubled output of a Nd:YAG pumped dye laser utilizing many dyes (∼0.5 mJ, ∼0.3 cm2, 7 ns) crosses the interaction region and excites CH2OO on the B-X transition in the 300–365 nm range (pump laser). After a short time delay (30 ns), the O 1D dissociation products are ionized via 2 + 1 resonance enhanced multiphoton ionization (REMPI) at 205.47 nm,18 which is generated by frequency-tripling the output of another Nd:YAG pumped dye laser (probe laser). This laser is scanned over the O-atom Doppler profile during image collection. The counter propagating probe laser is focused into the center of the interaction region (50 cm focal length lens) and spatially overlapped with the unfocused UV pump laser. Ions travel through a field free time-of-flight (TOF) region and are velocity focused onto a spatially sensitive MCP/phosphor screen coupled detector, which is gated for the O+ mass (m/z = 16). The pump and probe laser polarizations are aligned and both set parallel to the plane of the detector. The VMI apparatus design and calibration are discussed in detail in Ref. 19. TOF profiles along with the spatial images captured by a CCD camera, such as the example shown in Figure 1, are transferred to a laboratory computer for further analysis. Image reconstruction is performed using the BASEX program.20 The resultant radial distribution is then integrated over the angular coordinate to give the velocity distribution of the O 1D fragments.

FIG. 1.

Velocity mapped raw image with derived total kinetic energy release (TKER) and anisotropy parameter (β) distributions for O 1D products resulting from photolysis of the simplest Criegee intermediate CH2OO at 360 nm. The polarizations of the pump and probe lasers are vertical in the plane of the detector. The TKER distribution is fit to a polynomial expansion as a guide to the eye with baseline at zero. The anisotropic angular distribution in the raw image and associated β parameter arise from the interaction of the transition dipole moment (TDM, |$\vec \mu $|μ) with the pump laser polarization. In the molecular frame, the angle χ between the TDM of CH2OO and the recoil velocity (⁠|$\vec v$|v) of the O-atom fragment is evaluated from the anisotropy parameter.

FIG. 1.

Velocity mapped raw image with derived total kinetic energy release (TKER) and anisotropy parameter (β) distributions for O 1D products resulting from photolysis of the simplest Criegee intermediate CH2OO at 360 nm. The polarizations of the pump and probe lasers are vertical in the plane of the detector. The TKER distribution is fit to a polynomial expansion as a guide to the eye with baseline at zero. The anisotropic angular distribution in the raw image and associated β parameter arise from the interaction of the transition dipole moment (TDM, |$\vec \mu $|μ) with the pump laser polarization. In the molecular frame, the angle χ between the TDM of CH2OO and the recoil velocity (⁠|$\vec v$|v) of the O-atom fragment is evaluated from the anisotropy parameter.

Close modal

Following excimer photolysis, a large pump laser induced O+ signal is detected with resonant probe laser ionization. No O+ signal is seen when the probe laser is tuned off-resonance of the REMPI transition, demonstrating that the O+ signal arises exclusively from ionization of O 1D. In addition, a much smaller O+ signal is observed with the excimer and 2+1 REMPI probe lasers only; no signal is detected with the probe laser alone. Using velocity information from the image, this small signal is attributed to photodissociation of IO at 205.47 nm, producing I* (2P1/2) + O 1D, which is subsequently ionized by the same laser.21 In order to remove this small excimer + probe signal, an active background subtraction scheme was implemented for TOF and image data collection. This is achieved by operating the pump laser (5 Hz) at half the repetition of the other lasers (10 Hz).

Initially, the pump laser is stepped across a broad UV spectral range while monitoring the O+ signal arising from O 1D REMPI, yielding the UV action spectrum shown in the leftmost panel of Figure 2. The UV action spectrum with peak at ∼331 nm and breadth of ∼40 nm (fwhm) reproduces the UV absorption spectrum for CH2OO reported previously within experimental uncertainty.9 This close correlation indicates that the species generating O 1D is indeed CH2OO. The experimental uncertainties, derived from repeated measurements (error bars) and Gaussian fits, for the UV action and absorption spectra of CH2OO are sufficiently large to preclude determination of small changes in the O 1D quantum yield. The absolute O 1D quantum yield is not determined in this work. We note that there is another energetically accessible product asymptote, O 3P + H2CO a3A″, shown in Figure 2, but no information is currently available on the branching to this product channel.

FIG. 2.

(Left panel) CH2OO action spectrum is obtained by detecting O 1D products following UV excitation in the 300–365 nm range. The smooth curve is a fit to a Gaussian function with baseline at zero; the uncertainty is illustrated by the shaded area. A schematic repulsive potential for the CH2OO B-state in the Franck-Condon region is illustrated with arrows indicating the excitation wavelengths used for image analysis. (Right panel) Total kinetic energy release (TKER) distributions for O 1D + H2CO X1A′ products arising from photodissociation of CH2OO at 308 nm (black), 330 nm (purple), and 360 nm (blue) are plotted relative to the photon energy, Ehν. The common termination of the distributions at 54 kcal mol−1 corresponds to an upper limit for the CH2OO X1A′ dissociation energy. The gray shaded area represents the rotational energy of the H2CO product estimated using an impulsive model, which reduces the upper limit for the dissociation energy of CH2OO X1A′ to O 1D + H2CO X1A′ products to D0 ≤ 47 kcal mol−1. The other asymptotic limits are positioned accordingly. The rotational and vibrational excitation of the separating H2CO product is shown schematically.

FIG. 2.

(Left panel) CH2OO action spectrum is obtained by detecting O 1D products following UV excitation in the 300–365 nm range. The smooth curve is a fit to a Gaussian function with baseline at zero; the uncertainty is illustrated by the shaded area. A schematic repulsive potential for the CH2OO B-state in the Franck-Condon region is illustrated with arrows indicating the excitation wavelengths used for image analysis. (Right panel) Total kinetic energy release (TKER) distributions for O 1D + H2CO X1A′ products arising from photodissociation of CH2OO at 308 nm (black), 330 nm (purple), and 360 nm (blue) are plotted relative to the photon energy, Ehν. The common termination of the distributions at 54 kcal mol−1 corresponds to an upper limit for the CH2OO X1A′ dissociation energy. The gray shaded area represents the rotational energy of the H2CO product estimated using an impulsive model, which reduces the upper limit for the dissociation energy of CH2OO X1A′ to O 1D + H2CO X1A′ products to D0 ≤ 47 kcal mol−1. The other asymptotic limits are positioned accordingly. The rotational and vibrational excitation of the separating H2CO product is shown schematically.

Close modal

The VMI images collected (and reconstructed) following UV excitation of CH2OO at several wavelengths (308, 330, and 360 nm) provide a wealth of new information on the velocity distribution and anisotropic angular distribution of the O 1D photofragments. The total kinetic energy released (TKER) to the O 1D + H2CO X1A1 products in the photodissociation process is obtained through conservation of momentum based on the velocity distribution of the O 1D fragments. A representative image and corresponding TKER distribution resulting from 360 nm photolysis (pump laser) is shown in Figure 1. The TKER distribution peaks at ∼4000 cm−1, falling off to higher and lower energy, but is otherwise unstructured over its 9000 cm−1 span. Analogous TKER distributions are obtained following 308 and 330 nm photolysis of CH2OO with their properties listed in Table S1 of the supplementary material.22 

The VMI image of the O 1D fragments also exhibits an anisotropic angular distribution I(θ), which can be recast in terms of an anisotropy or β parameter I(θ) ∝ 1 + βP2(cos θ), where P2 is a second-order Legendre polynomial and θ is the angle between the recoil direction and the polarization of the UV photolysis laser.23 At 360 nm, a β parameter of 0.97(3) is obtained for O 1D fragments with kinetic energies near the peak of the TKER distribution shown in Figure 1. Analogous angular distributions are seen upon photolysis of CH2OO at 308 and 330 nm with the same value for β (Table S1 of the supplementary material22). The β parameter does not change with excitation energy or over the range kinetic energies observed at each excitation wavelength. In the molecular frame, the β parameter is related to the angle χ between the transition dipole moment (TDM, |$\vec \mu$|μ) and the velocity recoil |$\vec v$|v vectors via |$\beta = 2\left\langle {P_2 (\vec \mu \cdot \vec v)} \right\rangle = 2\left\langle {P_2 (\cos \chi)} \right\rangle$|β=2P2(μ·v)=2P2(cosχ).23 The experimentally derived β parameters yield an average χ of 35.7(2)°, thereby determining the angle between the TDM and the O 1D recoil along the original O–O bond axis as shown in Figure 1.

Complementary electronic structure calculations10 at the equation-of-motion coupled-cluster inclusive of single and double excitations (EOM-CCSD)/6-311++G(2d,2p) level of theory are used to evaluate the TDM for the B-X transition of CH2OO in the Franck-Condon region. The angle between the TDM and O–O bond is evaluated to be 30° and oriented as shown in Figure 1. The theoretically derived angle is in good agreement with that determined experimentally, demonstrating that the angular distribution of the O 1D products is a reflection of the π* ← π transition originating from the 4π e system of the COO group in the CH2OO intermediate. Early GVB calculations by Wadt and Goddard also placed the TDM at 30° from the O–O bond.24 The experimentally derived TDM, similar to that predicted theoretically, and the invariance of the anisotropy parameter with excitation energy and TKER are indicative of prompt dissociation. This is also in accord with the repulsive nature of CH2OO B1A′ potential along the O–O stretch coordinate in the Franck-Condon region based on high level electronic structure calculations.9,10,12

Using conservation of energy, |$E_{avl} = E_{h\nu } - D_0\break = {\textit {TKER}} + E_{int} ({\rm H}_{\rm 2} {\rm CO})$|Eavl=EhνD0=TKER+Eint(H2 CO ), the TKER distribution can be directly related to the internal energy distribution of the formaldehyde cofragment Eint(H2CO) using the photon energy Ehν and dissociation energy D0 to O 1D + H2CO X1A1 products or corresponding available energy Eavl. (The internal energy of the jet-cooled Criegee intermediate is assumed to be small and is neglected.) However, the dissociation energy for CH2OO or other Criegee intermediates has not been established in any prior experimental study and varies greatly among theoretical predictions as discussed below.12–15 Nevertheless, plotting the TKER distributions arising from photodissociation of CH2OO at 308, 330, and 360 nm as Ehν − TKER in Figure 2 shows the similar profiles of the distributions starting at Ehν and terminating at a common energy of ∼54 kcal mol−1. The lowest translational energies at Ehν correspond to the highest internal energies for H2CO; similarly, the highest translational energies at Ehν − TKER = 54 kcal mol−1 indicate the lowest internal (vibrational + rotational) energy for H2CO. Since the lowest internal energy of the H2CO fragment is its zero-point level, the 54 kcal mol−1 cutoff of the TKER distributions represents a rigorous upper limit for the CH2OO X1A′ binding energy relative to O 1D + H2CO X1A1 products.

The rotational energy of the nascent H2CO fragments can be separately estimated using a simple impulsive model, which assumes prompt dissociation, as seen experimentally, on the repulsive B-state potential in the Franck-Condon region. Specifically, a model developed by Butler and coworkers equates the rotational angular momentum imparted to formaldehyde as a result of impulsive O-O bond breakage with the orbital angular momentum arising from the recoiling O 1D atom product.25 The rotational energy of the H2CO fragments can then be related to the experimentally derived recoil kinetic energy using |$E_{rot}=\frac{\mu b^2}{I_c}E_T$|Erot=μb2IcET, where μ is the reduced mass of the H2CO + O system, b is the impact parameter, IC is the moment of inertia about the C inertial axis of the H2CO subunit, and ET is the total kinetic energy release (TKER). The factor μb2/IC is evaluated to be 0.20 based on the equilibrium geometry for CH2OO.26 This factor changes only slightly if the equilibrium geometry for the separated H2CO product is utilized,27 although the geometries differ as detailed below. Using the model, the rotational energy of the H2CO product is estimated to be ∼5 kcal mol−1 at the maximum TKER following 360 nm photolysis of CH2OO, and even greater rotational energies (up to 8 kcal mol−1) can result from 330 and 308 nm photolysis. It should be noted that zero-point vibrational motion of CH2OO, particularly the COO bend, will result in a range of impact factors and corresponding small changes (∼1 kcal mol−1) in the predicted rotational energies of the H2CO fragments. Using the estimated rotational energy for the H2CO product reduces the CH2OO binding energy to D0 ≤ 47 kcal mol−1.

The broad span of the TKER distributions is indicative of a high degree of vibrational excitation in the H2CO products. Vibrational excitation extending over 9000 to 13 500 cm−1 is evident following photolysis of CH2OO, corresponding to ∼80% of Eavl. This substantial vibrational excitation likely originates from changes in the equilibrium structure for CH2OO as compared to H2CO. In particular, the HCH angle decreases by close to 10° and the C–O bond length decreases by ∼0.07 Å upon dissociation, suggesting multiple quanta of CO stretch, HCH rock, and/or HCH bend excitation in the H2CO products. The TKER distribution lacks structure because of the substantial vibrational and/or rotational excitation of the H2CO fragments.

There are several theoretical predictions of the CH2OO X1A′ → O 1D + H2CO X1A1 dissociation energy or the bond dissociation energy (BDE) for the spin-forbidden channel of CH2OO X1A′ to ground state O 3P + H2CO X1A1 products. The latter value differs by the energy difference between the ground (3P) and excited (1D) states of atomic oxygen (45.4 kcal mol−1)28 as shown in Figure 1. Nguyen et al. reported a BDE for CH2OO of 5.8 kcal mol−1,15 corresponding to D0 = 51.2 kcal mol−1. Alpincourt et al. considered the dissociation of CH2OO X1A′ along the O–O coordinate, although a specific value for De was not reported.12 Another study by Anglada and co-workers14 computed a CH2OO X1A′ dissociation energy of D0 = 32.4 kcal mol−1. Earlier work by Cremer et al. predicted D0 to be 47.0 kcal mol−1.13 Additional high level multi-reference configuration interaction (MRCI) with a Davidson correction calculations performed in this group at the MRCI//CASSCF(12,11)/aug-cc-pVTZ level using the Molpro computational suite29 yield a dissociation energy of De = 51.7 kcal mol−1. Representative points along the O–O stretch coordinate generated using a larger active space [MRCI//CASSCF(18,14)/aug-cc-pVTZ] are consistent with this dissociation energy. The MRCI value for De is corrected for the reduction in zero-point energy upon dissociation using the anharmonic frequencies computed by Su et al. for CH2OO30 and the experimental frequencies for H2CO,31 giving D0 = 49.2 kcal mol−1. The experimental upper limit for the dissociation energy, D0 ≤ 54 kcal mol−1, as well as a best estimate obtained by accounting for impulsive rotational excitation imparted to the recoiling H2CO (D0 ≤ 47 kcal mol−1) are in very good agreement with the present MRCI results and prior calculations by Nguyen et al.15 and Cremer et al.13 described above.

The dissociation energy of CH2OO X1A′ relative to O 1D + H2CO X1A1 is greater than the bond energy of a typical O–O single bond, e.g., CH3OOH at D0 = 42.6 ± 1 kcal mol−1,32 reflecting the biradical and/or zwitterionic character of the COO group. Similarly, the O–O bond length of CH2OO, recently determined by Fourier transform microwave spectroscopy, rOO = 1.345 Å,26 is shorter than a typical O–O single bond. One should note that isomerization of CH2OO to dioxirane is predicted to have a barrier of 19.2 kcal mol−1 using CCSD(T)/6-31G(d,p),33 indicating that isomerization and subsequent decomposition to OH radicals and other products2,4 will be favored over O–O bond breakage for energized CH2OO intermediates.

The UV photolysis of CH2OO intermediates has potentially significant atmospheric implications since the O 1D products will react at a gas kinetic rate with H2O in the troposphere to generate secondary OH radicals.34 Under atmospheric conditions, Criegee intermediates formed by alkene ozonolysis will be rapidly photolyzed by solar radiation in the UV region9,10 to generate O 1D and secondary OH radicals. This mechanism is quite similar to the primary scheme for OH production in the troposphere, in which O 1D is generated from O3 photolysis with UV solar radiation,34 differing mainly in the requirement of an alkene-rich environment.

This research was principally supported by the U.S. Department of Energy, Basic Energy Sciences (DE-FG02-87ER13792). J.M.B. acknowledges support through the Dreyfus Postdoctoral Program in Environmental Chemistry. H.L. acknowledges partial support from NSF CHE-1112016.

1.
J. G.
Calvert
,
R.
Atkinson
,
J. A.
Kerr
,
S.
Madronich
,
G. K.
Moortgat
,
T. J.
Wallington
, and
G.
Yarwood
,
The Mechanisms of Atmospheric Oxidation of the Alkenes
(
Oxford University Press
,
Oxford
,
2000
).
2.
D.
Johnson
and
G.
Marston
,
Chem. Soc. Rev.
37
,
699
(
2008
).
3.
R.
Criegee
,
Angew. Chem., Int. Ed.
14
,
745
(
1975
).
4.
O.
Horie
and
G. K.
Moortgat
,
Acc. Chem. Res.
31
,
387
(
1998
).
5.
O.
Welz
,
J. D.
Savee
,
D. L.
Osborn
,
S. S.
Vasu
,
C. J.
Percival
,
D. E.
Shallcross
, and
C. A.
Taatjes
,
Science
335
,
204
(
2012
).
6.
C. A.
Taatjes
,
O.
Welz
,
A. J.
Eskola
,
J. D.
Savee
,
D. L.
Osborn
,
E. P. F.
Lee
,
J. M.
Dyke
,
D. W. K.
Mok
,
D. E.
Shallcross
, and
C. J.
Percival
,
Phys. Chem. Chem. Phys.
14
,
10391
(
2012
).
7.
C. A.
Taatjes
,
O.
Welz
,
A. J.
Eskola
,
J. D.
Savee
,
A. M.
Scheer
,
D. E.
Shallcross
,
B.
Rotavera
,
E. P. F.
Lee
,
J. M.
Dyke
,
D. K. W.
Mok
,
D. L.
Osborn
, and
C. J.
Percival
,
Science
340
,
177
(
2013
).
8.
L.
Vereecken
,
H.
Harder
, and
A.
Novelli
,
Phys. Chem. Chem. Phys.
14
,
14682
(
2012
).
9.
J. M.
Beames
,
F.
Liu
,
L.
Lu
, and
M. I.
Lester
,
J. Am. Chem. Soc.
134
,
20045
(
2012
).
10.
J. M.
Beames
,
F.
Liu
,
L.
Lu
, and
M. I.
Lester
,
J. Chem. Phys.
138
,
244307
(
2013
).
11.
J. M.
Anglada
,
J.
Gonzalez
, and
M.
Torrent-Sucarrat
,
Phys. Chem. Chem. Phys.
13
,
13034
(
2011
).
12.
P.
Aplincourt
,
E.
Henon
,
F.
Bohr
, and
M. F.
Ruiz-Lopez
,
Chem. Phys.
285
,
221
(
2002
).
13.
D.
Cremer
,
J.
Gauss
,
E.
Kraka
,
J. F.
Stanton
, and
R. J.
Bartlett
,
Chem. Phys. Lett.
209
,
547
(
1993
).
14.
J. M.
Anglada
,
J. M.
Bofill
,
S.
Olivella
, and
A.
Solé
,
J. Am. Chem. Soc.
118
,
4636
(
1996
).
15.
M. T.
Nguyen
,
T. L.
Nguyen
,
V. T.
Ngan
, and
H. M. T.
Nguyen
,
Chem. Phys. Lett.
448
,
183
(
2007
).
16.
C. A.
Taatjes
,
G.
Meloni
,
T. M.
Selby
,
A. J.
Trevitt
,
D. L.
Osborn
,
C. J.
Percival
, and
D. E.
Shallcross
,
J. Am. Chem. Soc.
130
,
11883
(
2008
).
17.
N. M.
Donahue
,
G. T.
Drozd
,
S. A.
Epstein
,
A. A.
Presto
, and
J. H.
Kroll
,
Phys. Chem. Chem. Phys.
13
,
10848
(
2011
).
18.
S. T.
Pratt
,
P. M.
Dehmer
, and
J. L.
Dehmer
,
Phys. Rev. A
43
,
4702
(
1991
).
19.
J. H.
Lehman
,
H.
Li
, and
M. I.
Lester
, “
Ion imaging studies of the photodissociation dynamics of CH2I2 at 248 nm
,”
Chem. Phys. Lett.
(submitted).
20.
V.
Dribinski
,
A.
Ossadtchi
,
V. A.
Mandelshtam
, and
H.
Reisler
,
Rev. Sci. Instrum.
73
,
2634
(
2002
).
21.
K. S.
Dooley
,
J. N.
Geidosch
, and
S. W.
North
,
Chem. Phys. Lett.
457
,
303
(
2008
).
22.
See supplementary material at http://dx.doi.org/10.1063/1.4824655 for the characteristics of each TKER distribution.
23.
B. J.
Whitaker
,
Imaging in Molecular Dynamics Technology and Applications
(
Cambridge University Press
,
2003
).
24.
W. R.
Wadt
and
W. A.
Goddard
,
J. Am. Chem. Soc.
97
,
3004
(
1975
).
25.
B. J.
Ratliff
,
C. C.
Womack
,
X. N.
Tang
,
W. M.
Landau
,
L. J.
Butler
, and
D. E.
Szpunar
,
J. Phys. Chem. A
114
,
4934
(
2010
).
26.
M.
Nakajima
and
Y.
Endo
,
J. Chem. Phys.
139
,
101103
(
2013
).
27.
L. V.
Gurvich
,
Pure Appl. Chem.
61
,
1027
(
1989
).
28.
C. E.
Moore
, in
CRC Series in Evaluated Data in Atomic Physics
, edited by
J. W.
Gallagher
(
CRC Press
,
Boca Raton, FL
,
1993
), p.
339
.
29.
H.-J.
Werner
,
P. J.
Knowles
,
F. R.
Manby
,
M.
Schütz
 et al, MOLPRO, version 2010.1, a package of ab initio programs,
2010
, see http://www.molpro.net.
30.
Y.-T.
Su
,
Y.-H.
Huang
,
H. A.
Witek
, and
Y.-P.
Lee
,
Science
340
,
174
(
2013
).
31.
T.
Nakanaga
,
S.
Kondo
, and
S.
Saeki
,
J. Chem. Phys.
76
,
3860
(
1982
).
32.
J.
Matthews
,
A.
Sinha
, and
J. S.
Francisco
,
J. Chem. Phys.
122
,
221101
(
2005
).
33.
R.
Gutbrod
,
E.
Kraka
,
R. N.
Schindler
, and
D.
Cremer
,
J. Am. Chem. Soc.
119
,
7330
(
1997
).
34.
Y.
Matsumi
and
M.
Kawasaki
,
Chem. Rev.
103
,
4767
(
2003
).

Supplementary Material