Article pubs.acs.org/JPCA

(π*,σ*), (σ*,π*) and Rydberg Triplet Excited States of Hydrogen Peroxide and Other Molecules Bearing Two Adjacent Heteroatoms J. Grant Hill† and Götz Bucher* WestCHEM, School of Chemistry, University of Glasgow, University Avenue, Glasgow G12 8QQ, United Kingdom S Supporting Information *

ABSTRACT: The properties of the lowest triplet excited states of a series of small molecules containing two or more adjacent heteroatoms have been investigated. Highlevel coupled cluster and MRCI+Q calculations were employed to probe the properties of the triplet excited states of hydrogen peroxide, hydrazine, hydroxylamine, fluoroamines, oxygen difluoride, hypofluorous acid, chlorine, fluorine, and disulfane. All of the molecules investigated except hydroxylamine are predicted to have bound lowest triplet excited states that are either (π*,σ*) or (σ*,π*) as in H2O2, HOF, OF2, H2S2, Cl2, NH2F, NHF2, or NF3, or are Rydberg states (hydrazine, also H2O2 and H2S2). The heteroatom−heteroatom bond dissociation enthalpies of the triplet states range from very small values as predicted for hydrogen peroxide or fluorine, to BDEs around 8−9 kcal mol−1 that should allow for an experimental observation of the triplet state, such as in disulfane or monofluoroamine. For all triplet minima investigated except NF3 and F2, CCSD(T) gave results in agreement with the multireference method MRCI+Q, and in excellent agreement with available experimental data (BDEs, ground-state geometries). Due to multireference problems, CCSD(T) does not provide a good description for longer heteroatom−heteroatom distances, and in some cases (e.g., Cl2) it wrongly predicts the presence of a transition state for bond formation on the triplet spin manifold, where the reaction is known experimentally and, as predicted by MRCI+Q, is known to be barrierless. Finally, the 3Πu state of F2 is poorly described by CCSD(T) theory, the equilibrium bond distance is significantly underestimated relative to MRCI+Q, and CCSD(T) places the triplet state above the energy of two fluorine atoms. The T1 diagnostic, frequently used to assess the quality of CCSD(T) calculations, does not appear to provide a valid criterion for the systems studied. The formation of H2O2 on the triplet potential energy hypersurface might possibly open up an additional channel for formation of hydrogen peroxide from two hydroxyl radicals. Due to a low density of states in triplet H2O2, and due to competing formation of water + O(3P) from a hydrogen-bridged HO···HO triplet radical pair, such a reaction channel probably only can play a role at low temperatures.

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exclusively results in weakening of a σ-bond, in a (π*,σ*) triplet excited state it leads to the concomitant strengthening of a π-bond. Correspondingly, the bond order is (1/2 π + 1/2 σ).3 Such a triplet state was initially shown to be observed in the case of lipoic acid, a cyclic disulfide ubiquitous in biological systems.3 Subsequent computational work revealed that the disulfide moiety can be replaced by heavier chalcogens and indicated that among cyclic disulfides, those incorporated into a five-membered ring are expected to show the longest triplet lifetimes.4 The relaxation of triplet disulfides such as the lowest triplet state of 1,2-dithiolane is rationalized to occur via a minimum energy crossing point (MECP) that is localized close to the reaction coordinate of ring-opening to an open-chain triplet dithiyl diradical.3 Other systems, for which the existence of triplet excited states of (π*,σ*) type had previously been established include molecular chlorine, Cl2.5−7 The purpose of the current contribution is to investigate whether a wider range of molecules bearing two adjacent heteroatoms might have (π*,σ*) triplet excited states. We will

INTRODUCTION Triplet excited states dominate the photochemistry of ketones and play a crucial role in the photochemical reactivity of annelated arenes.1 Typically, two types of triplet excited state are encountered when dealing with chromophores such as arenes and carbonyl groups. In a (π,π*) triplet excited state, an electron is excited from a doubly occupied π-orbital into an empty antibonding π* orbital. The other frequently observed type of triplet excited state is (n,π*), where the electron is excited from a nonbonding (lone pair-type) orbital.1 Triplet excited states of ketones often are of this type. Other types of triplet excited states are less common: (π,σ*) excited states are observed in the case of certain heteroaromatic compounds.2 (n,σ*) triplet excited states are usually repulsive, as the population of a strongly antibonding σ*-type orbital results in a large destabilization of a bond. In recent experimental3 as well as computational4 work on cyclic disulfides and related compounds, we have characterized a triplet excited state, where an electron is promoted from a doubly occupied antibonding π*-type orbital to an antibonding σ*-type orbital. Though such an electronic configuration is closely related to an (n,σ*) triplet excited state, it differs in an important aspect. Unlike an (n,σ*) triplet excited state, where excitation © 2014 American Chemical Society

Received: January 22, 2014 Revised: March 4, 2014 Published: March 4, 2014 2332

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Table 1. Structural Parameters of the Ground State of H2O2, Optimized at Various Levels of Theory, and Experimental Valuesa method

BDE

R(O−H)

r(O−O)

θ(OOH)

τ(HOOH)

CCSD(T)/aug-cc-pVDZ CCSD(T)/aug-cc-pVTZ CCSD(T)/aug-cc-pVQZ CCSD(T)/aug-cc-pV5Z UMP5/aug-cc-pVTZ MRCI+Q/aug-cc-pVQZ experiment

41.4 46.3 47.6 48.0b 45.0b 47.3 48.75c

0.9717 0.9665 0.9637 0.9633 0.9647 0.9634 0.9652d

1.4800 1.4609 1.4531 1.4512 1.4541 1.4563 1.464d

99.33 99.85 100.06 100.09 100.12 99.895 99.4d

112.52 112.20 112.36 112.56 111.86 112.22 111.8d

Bond lengths in Å, angles in degrees. Electronic bond dissociation energy in kcal mol−1, including zero point energy correction. bZPE correction from CCSD(T)/aug-cc-pVQZ. cReference 31. dReference 32.

a

Table 2. Structural Parameters of the Triplet States of H2O2, Optimized at Various Levels of Theorya method

PG

energy

r(O−H)

r(O−O)

θ(OOH)

CCSD(T)/aug-cc-pVDZ CCSD(T)/aug-cc-pVDZ CCSD(T)/aug-cc-pVTZ CCSD(T)/aug-cc-pVTZ CCSD(T)/aug-cc-pVQZ CCSD(T)/aug-cc-pVQZ CCSD(T)/aug-cc-pV5Z CCSD(T)/aug-cc-pV5Z UMP5/aug-cc-pVTZ UMP5/aug-cc-pVTZ MRCI+Q/aug-cc-pVQZ MRCI+Q/aug-cc-pVQZ

C2h C2v C2h C2v C2h C2v C2h C2vc C2h C2v C2h C2v

39.8 44.1 45.3 49.8 46.7 51.3 47.1b 51.8b 47.1b 51.7b 47.4 52.2

0.9781 0.9807 0.9722 0.9747 0.9696 0.9720 0.9692 0.9715 0.9686 0.9713 0.9699 0.9719

2.0270 2.0322 2.0007 2.0002 1.9906 1.9888 1.9864 1.9867 1.9779 1.9768 2.1012 2.1346

83.96 96.79 83.67 96.74 83.73 96.75 83.73 96.81 84.31 96.81 80.88 95.86

Bond lengths in Å, angles in degrees. Electronic triplet energy in kcal mol−1, including zero point energy correction. PG: point group. bZPE correction from CCSD(T)/aug-cc-pVQZ. cGeometry optimization using MOLPRO, with RHF reference wave function. Energy is of CCSD(T)(UHF)//CCSD(T)(RHF) single point energy calculation, using Gaussian. a

wave functions for all systems investigated are provided as Supporting Information. An aug-cc-pVQZ basis set was used for the MRCI+Q calculations. For calculation of the BDE of H2O2, Cl2, HOF, OF2, NH2F, NHF2, NF3, and F2 using MRCI +Q, well-separated (R = 1000 Å) radical pairs were calculated as reference points.

initially present data for the important case of hydrogen peroxide, but disulfane, oxygen fluorides, fluoroamines, hydrazine, and hydroxylamine will also be investigated. For comparison, the lowest triplet excited states of the dihalogen molecules Cl2 and F2 will be dealt with.

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COMPUTATIONAL DETAILS The small size of the molecules investigated meant that all could be treated at the coupled cluster with single, double and perturbative triple excitations [CCSD(T)] level of theory,8 using spin-unrestricted reference wave functions. For comparison, some calculations were performed using the UMP5 method.9 Unless indicated otherwise, a large aug-cc-pVQZ basis set10−13 was employed throughout this study. All CCSD(T) calculations except for the geometry optimization of the C2v triplet state of H2O2, employing an aug-cc-pV5Z basis, were performed by employing the Gaussian09 suite of programs.14 CCSD(T) optimization of the C2v triplet state of H2O2 with an aug-cc-pV5Z basis was performed by using MOLPRO version 2010.1.20,21 These calculations involved the use of an RHF reference wave function. All stationary points were fully geometry optimized, and most were characterized by performing a vibrational analysis. Geometries optimized at the CCSD(T)/aug-cc-pV5Z or UMP5/aug-cc-pVTZ levels of theory were not subjected to a vibrational analysis. For all stationary points optimized, the T1 diagnostic of Lee and Taylor was calculated (using the same T1 method for closed and open-shell systems).15 Internal contracted multireference configuration interaction with relaxed Davidson correction (MRCI+Q)16−19 calculations were performed by employing MOLPRO version 2010.1.20,21 Full details of the reference

RESULTS AND DISCUSSION

Hydrogen Peroxide. H2O2 is one of the simplest molecules bearing two adjacent heteroatoms. As a small molecule important in biochemistry and in atmospheric chemistry, it naturally has received considerable attention, and several studies about the nature of its excited states have been published. 22−29 Experimental evidence from EPR measurements indicates that a “repulsive triplet state” plays a role in the photochemistry of hydrogen peroxide.30 Previous computational studies had focused on vertical excitation energies.22−29 To the best of our knowledge, however, no detailed study has been published on the geometry of the lowest triplet excited state of H2O2 at its relaxed geometry. In the current work, the simple hydrogen peroxide molecule was used to investigate the influence of computational methodology on the ground- and triplet excited-state properties of H2O2. The C2-symmetric ground-state geometries optimized are consistent with previous computational studies. At the highest level of theory used (CCSD(T)/aug-cc-pV5Z), the HOOH dihedral is calculated as τ(HOOH) = 112.56°, which is in very close agreement with results (QCISD(T)/cc-pVTZ or CCSD(T)/aug-cc-pVQZ) of Watts and Francisco.27,29 The results are summarized in Table 1. 2333

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Unlike the singlet ground state, the lowest triplet excited states of H2O2 are predicted to be planar, with either C2h (trans isomer) or C2v (cis isomer) symmetry. Table 2 gives the calculated structural and energetic parameters of the triplet states. Tables 1 and 2 indicate that using CCSD(T) in combination with a large aug-cc-pVQZ basis set produces energies and geometries that are well converged with respect to the basis set. For ground state H2O2, the calculated O−O BDE is in close agreement (within 1.2 kcal mol−1) of the experimental value determined by Luo, Fleming, and Rizzo,31,33 and the ground state geometries obtained at the CCSD(T)/aug-cc-pVQZ and CCSD(T)/aug-cc-pV5Z levels of theory essentially are the same. As the calculations employing the huge augmented quintuple-ζ basis set were very costly, it was decided to employ CCSD(T)/aug-cc-pVQZ as the standard method for this and all other systems. It is noted that the use of basis sets augmented with diffuse functions is mandatory for the triplet states of H2O2. In most cases, calculations without additional diffuse functions led to meaningless (exceedingly high) triplet energies, and unreasonable force constants, as revealed by unrealistic vibrational frequencies. The UMP5 method, which could only be used in conjunction with a less flexible aug-ccpVTZ basis set, gave results that are in excellent agreement with CCSD(T) employing quadruple- or quintuple-ζ basis sets, if applied to the triplet excited states. When used on groundstate H2O2, UMP5 yielded a value for the O−O BDE that was too small, compared to experiment. At the CCSD(T)/aug-ccpVQZ level of theory, the triplet energy of H2O2 is calculated as 46.7 kcal mol−1 for the trans (C2h) triplet state and 51.3 kcal mol−1 for the cis (C2v) triplet state. Compared to two molecules of hydroxy radicals as a reference point, the value for the O−O BDE of the trans (C2h) triplet state of H2O2 is 0.9 kcal mol−1, using both quadruple- and quintuple-ζ basis sets. The cis (C2v) triplet state of H2O2, on the other hand, is considerably higher in energy than the C2h state (CCSD(T)/aug-cc-pVQZ: +3.7 kcal mol−1 relative to 2 × OH) and should therefore be unbound. The fact that it nevertheless is a minimum structure suggests the presence of a barrier for dissociation. To investigate this issue and to locate a transition structure for dimerization of OH on the triplet hypersurface, the latter was scanned systematically by performing a grid of constrained CCSD(T)/aug-cc-pVTZ geometry optimizations, varying the O−O distance from ROO = 1.3−2.2 Å in steps of 0.1 Å, and the H−O−O−H dihedral from τ = 0° to 180° in steps of 10°, and constraining the point group to C2.34 Both the O−H distance and the H−O−O angle were fully optimized for each point of the grid. The results are shown in Figure 1. On the HOOH triplet potential energy hypersurface, the energy is found to be consistently maximal at a HOOH dihedral of τ = 90°. Energy minima are only found at τ = 0° and 180°. In addition to the C2v- and C2h-(π*,σ*) triplet states, a Rydberg-type triplet state with C2v symmetry could be localized at a very short RO−O = 1.305 Å and at τ = 0°, with an OOH angle θ = 96.0°. Its energy is very high [CCSD(T)/aug-ccpVQZ: ΔUT = 111.4 kcal mol−1] relative to ground-state singlet H2O2. In C2h symmetry (τ = 180°), a stationary point is located with RO−O = 1.336 Å. It is a transition state for the identity reaction HOO + H → H + OOH and is very high in energy (ΔU = 126.1 kcal mol−1, relative to ground-state singlet H2O2). The geometry of the Rydberg triplet state of H2O2 is predicted to be similar to the geometry of its radical cation. In the case of the radical cation of H2O2, again two planar

Figure 1. Contour plot of the potential energy hypersurface of H2O2 in the triplet state (CCSD(T)/aug-cc-pVTZ), as a function of the HOOH dihedral and the O−O distance. Red (+110 kcal mol−1, relative to 2 × OH), green, and yellow (+80 kcal mol−1) indicate regions of high energy; dark blue or violet (ca. ±0 kcal mol−1, relative to 2 × OH, or slightly below) indicates regions of low energy. The C2h Rydberg minimum is seen in the very left bottom corner.

stereoisomers (C2v and C2h) could be located. At the CCSD(T)/aug-cc-pVQZ level of theory, the O−O distances are calculated as RO−O = 1.312 Å (RO−H = 0.992 Å, θOOH = 110.4°, C2v) or RO−O = 1.313 Å (RO−H = 0.992 Å, θOOH = 103.7°, C2h). We note that CCSD(T) optimization of triplet states of H2O2 consistently resulted in values of the T1 diagnostic that were above the accepted threshold for closed-shell species of T1 = 0.02,15 but below the value of T1 = 0.04535 (or even higher, if the T1 diagnostic as implemented in Gaussian09 is used)36 later published as a suggested upper limit for open-shell systems. To check for problems due to a multireference character of the wave function, we repeated the geometry optimizations of the triplet states using the MRCI+Q/aug-cc-pVQZ method. The results obtained using this method were very similar to those obtained using CCSD(T)/aug-cc-pVQZ (Tables 1 and 2), indicating that the CCSD(T) results should be reasonable. A triplet collision complex of two hydroxyl radicals does not necessarily have to result in formation of triplet states of H2O2. A hydrogen bridged triplet complex of two hydroxyl radicals HO···HO is found computationally (CCSD(T)/aug-cc-pVQZ) to be lower in energy than two separate hydroxyl radicals by 2.4 kcal mol−1, and hence also lower than the more favorable C2h triplet state by 1.5 kcal mol−1. This complex can disproportionate into water plus a ground-state triplet oxygen atom O (3P). At the CCSD(T)/aug-cc-pVQZ level of theory, the electronic barrier (including ZPE) for this reaction is obtained as ΔU‡ = 4.2 kcal mol−1. The reaction is exothermic by ΔU = −13.6 kcal mol−1. Figure 2 shows the optimized geometries for ground-state H2O2 and for stationary points on the triplet H2O2 hypersurface. Figure 3 shows the two singly occupied α-MOs of the C2h and C2v triplet states of hydrogen peroxide. The (π*,σ*) nature of both triplet states is clearly discernible. It is noted that the C2h (π*,σ*) triplet of H2O2 has a small degree of Rydberg character, as two higher (Rydberg-type) orbitals (HOMO+1, shown in Figure 3 and HOMO+2) have 2334

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Figure 2. Optimized geometries (CCSD(T)/aug-cc-pVQZ) of stationary points on the H2O2 hypersurface. Top left: ground-state singlet H2O2. Top right: trans-H2O2 triplet. Middle left: cis-H2O2 triplet. Middle right: transition state for formation of H2O + O(3P). Bottom left: Rydberg triplet state of H2O2. Bottom right: triplet radical pair of two hydroxy radicals. Distances in Å, angles in degrees. The dihedrals given refer to the HOOH dihedral (minima), or the HOHO dihedral (transition state). Electronic energies (in kcal mol−1, incl. ZPE correction) are relative to the ground-state singlet H2O2 = 0.0 kcal mol−1. The energy of two separated hydroxy radicals is 47.6 kcal mol−1, that of H2O + O(3P) is 31.6 kcal mol−1.

Figure 3. Highest occupied natural orbitals of the C2h (top, middle) and Rydberg (bottom) triplet states of hydrogen peroxide (CCSD(T)/aug-ccpVQZ). The isodensity surface value was set to 0.03 au. The values given are the occupation numbers of the natural orbitals.

two orbitals has been removed from the bonding σ and π orbitals of the O−O bond (HOMO−3 and HOMO−2).

population numbers of 0.04 and 0.02. According to the natural orbital population analysis, the electron density found in these 2335

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Hypofluorous Acid and Oxygen Difluoride. Hypofluorous acid, HOF can be synthesized by controlled oxidation of water with molecular fluorine and is used as a selective oxidant.37,38 A recent theoretical study had focused on a range of singlet excited states of HOF.39 At the CCSD(T)/aug-ccpVQZ level of theory, its first excited triplet (A″) state of (π*,σ*) type is calculated to be 42.2 kcal mol−1 above the singlet ground state. The O−F BDE of ground-state HOF is calculated as 46.8 kcal mol−1, resulting in an O−F BDE of triplet HOF of 4.6 kcal mol−1. Not surprisingly, the electronic barrier for disproportionation into HF and O(3P) is very small (ΔU‡ = 0.9 kcal mol−1), and this reaction is also highly exothermic by ΔU = −29.5 kcal mol−1. Unlike in the case of hydrogen peroxide, a Rydberg-type triplet state could not be localized for HOF, and the (π*,σ*) triplet state of HOF has no contribution from Rydberg-type orbitals. The radical cation of HOF has a calculated RO−F = 1.309 Å (CCSD(T)/aug-ccpVQZ), which is considerably shorter than the O−F bond length in neutral HOF calculated at the same level of theory (RO−F = 1.436 Å). Using the geometry of the radical cation as a starting point for optimization of a Rydberg triplet state, the geometry optimization converged to the geometry of the (π*,σ*) triplet state. At the MRCI+Q/aug-cc-pVQZ method, the optimized geometry of the lowest triplet-A″ state of HOF is in good agreement with the geometry obtained at the CCSD(T)/augcc-pVQZ level of theory (MRCI+Q: ROF = 1.905 Å, ROH = 0.975 Å, θ(FOH) = 84.25°). At the MRCI+Q/aug-cc-pVQZ level of theory, the calculated triplet energy is 41.5 kcal mol−1 (with ZPE correction), which is in very good agreement with the value obtained at the CCSD(T)/aug-cc-pVQZ level of theory (42.2 kcal mol−1). If the hydrogen atom in HOF is replaced by a second fluorine atom, as in oxygen difluoride, OF2, the electronic energy of the lowest triplet excited state is reduced to 36.6 kcal mol−1, with the O−F BDE of the OF2 molecule calculated as 38.4 kcal mol−1 (CCSD(T)/aug-cc-pVQZ). The resulting O−F BDE of the lengthened OF bond in triplet OF2 is 1.8 kcal mol−1. In the triplet excited state of OF2, the bond length of the shorter O−F bond is considerably shorter (RO−F = 1.342 Å) than the O−F bond length in ground-state singlet OF2 (RO−F = 1.406 Å). This value is approximately halfway between singlet OF2 and triplet OF+ (RO−F = 1.223 Å), is similar to the O−F bond length in doublet OF (RO−F = 1.353 Å), and suggests that triplet OF2 should be described as a complex of OF and a fluorine atom. In agreement with this picture, the calculated Mulliken atomic charges indicate only a small degree of negative charge (−0.03 au) at the distant F atom. Again, MRCI +Q gives a picture that agrees with the CCSD(T) results (Figure 4). At the MRCI+Q/aug-cc-pVQZ level of theory, the triplet energy calculated for OF2 is ΔUT = 35.8 kcal mol−1, which compares well with the CCSD(T) value. The geometries of both triplet HOF and triplet OF2, and the TS for disproportionation of triplet HOF are shown in Figure 4. Both the triplet states of HOF and OF2 are of (π*,σ*) type. The differences in geometry between 3HOF and 3OF2 lie mostly in the X−O−F angle (X = H or F), which is far larger for 3OF2, thus minimizing the dipole moment. Hydroxylamine. Like for hydrogen peroxide, a full scan was performed of the triplet excited state hypersurface of NH2OH (CCSD(T)/aug-cc-pVTZ), varying both the N−O distance and the HNOH dihedral, while optimizing all other parameters.

Figure 4. Optimized geometries (CCSD(T)/aug-cc-pVQZ) of the lowest triplet excited state of HOF (top left), the TS for disproportionation of triplet HOF into HF and O (3P) (top right), and the lowest triplet excited state of OF2 (bottom). Relevant distances in Å, angles in degree. In brackets: values calculated at the MRCI+Q/aug-cc-pVQZ level of theory.

No energy minimum could be localized. When the attempt was made to optimize the lowest triplet excited state of hydroxylamine without any contraints, no minimum could be localized, either. Instead, optimizations at both the CCSD(T)/aug-ccpVTZ and CCSD(T)/aug-cc-pVQZ levels of theory led to a hydrogen-bridged triplet radical pair H2N···HO. This finding agrees with earlier computational work on excited states of hydroxylamine and hydrazine, which stated that excited states of the two molecules should be dissociative.40 Figure 5 shows a

Figure 5. Contour plot of the potential energy of H2NOH in the triplet state (CCSD(T)/aug-cc-pVTZ), as a function of the HNOH dihedral and the N−O distance. Red (+38 kcal mol−1, relative to NH2 + OH), yellow (+29 kcal mol−1), and green (+20 kcal mol−1) indicate regions of high energy, and violet (ca. ±0 kcal mol−1, relative to NH2 + OH) indicates regions of low energy.

contour plot of the energy of the triplet H2NOH hypersurface as function of both N−O distance and the HNOH dihedral. The surface was computed by calculating a grid in steps of 0.1 Å/10°. Below RN−O = 1.5 Å, the hypersurface becomes dissociative, and formation of the HN−OH radical and a hydrogen atom occurs during restricted optimization. Fluoroamines. Mono- and difluoroamine, and nitrogen trifluoride were investigated. For all three compounds, bound 2336

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Figure 6. Highest occupied natural orbitals of the lowest triplet excited states of monofluoroamine (top), difluoroamine (middle), and nitrogen trifluoride (bottom), as calculated at the CCSD(T)/aug-cc-pVQZ level of theory. The isodensity surface value was set to 0.03 au. The occupation numbers of the natural orbitals are 1.00 in all cases.

Figure 7. Optimized geometries (CCSD(T)/aug-cc-pVQZ) of the lowest triplet excited states of fluoroamines. Top left: NH2F. Top right: NHF2. Bottom: NF3. All three triplet states are planar. Distances in Å, angles in degrees. In parentheses: values obtained at the MRCI+Q/aug-cc-pVQZ level of theory.

triplet excited states could be localized. In all three fluoroamine triplet states, the orbital occupation of the lowest triplet excited

state is 1 × π*, 1 × σ*. However, unlike in the triplet states of H2O2, HOF, and OF2, the singly occupied antibonding σ* 2337

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orbital is below the antibonding π* orbital in all haloamines investigated, resulting in a (σ*,π*) state. Where more than one halogen atom was present in the molecule, the spin density was essentially localized on one of the halogen atoms and the nitrogen atom, the remaining halogen atom(s) being tightly bound. Figure 6 shows the two singly occupied natural orbitals of the lowest triplet excited states of the three fluoroamines, and Figure 7 shows their optimized structures. The results on the haloamine triplet excited states are summarized in Table 3.

availability of literature data provides a basis for comparison with the coupled cluster data presented here, they were included in this study. Both molecules were optimized in their singlet ground and lowest triplet excited states using both CCSD(T)/aug-cc-pVQZ and MRCI+Q/aug-cc-pVQZ. The MRCI+Q calculations employed natural orbitals state-averaged over nine (including degenerates) singlet [1Σg+(2), 1Σu−, 1Πg, 1 Πu, 1Δg] and nine triplet [3Σu+(2), 3Σg−, 3Πg, 3Πu, 3Δu] states from a CASSCF reference, representing the molecular electronic states resulting from two separated 2P atoms. For molecular fluorine F2, a triplet excited state of (π*,σ*) type could be localized that is higher in energy than the singlet ground state of F2 by ΔUT = 39.2 kcal mol−1 (CCSD(T)/augcc-pVQZ) or 34.4 kcal mol−1 (MRCI+Q/aug-cc-pVQZ). It corresponds to the a 3Πu state, which is known to be very weakly bound, and is involved in the 157 nm emission of the F2 laser, which results from an f 3Πg → a 3Πu transition.48 Earlier calculations found this triplet state to be repulsive.47 At the CCSD(T) level of theory, the BDE of ground-state F2 is calculated as 36.3 kcal mol−1, which compares well with the experimental value of 38.0 kcal mol−1.51 MRCI+Q gives a BDE for F2 of 35.2 kcal mol−1. On the basis of the MRCI+Q calculations, triplet F2 (a 3Πu) therefore is lower in energy than two fluorine atoms by ΔU = 0.9 kcal mol−1, whereas the CCSD(T) calculation places it above 2 × F by 2.9 kcal mol−1, necessitating the presence of an electronic barrier. For F2 (a 3 Πu), the value for the CCSD(T) T1 diagnostic was 0.0265, which is above the recommended closed-shell threshold of 0.02, but a similar value had also been obtained for triplet H2O2. However, it has been previously noted that the ground state of F2 is a case where a low T1 value is produced for a molecule with not insignificant multireference character,53 and it has been shown to be a problematic case for a number of common multireference diagnostics,54 bringing into question the validity of the T1 diagnostic in the current triplet case. Figure 8b shows a plot of the electronic energy of F2 at the triplet spin manifold, vs the F−F distance, as calculated at the

Table 3. Energies and Geometrical Parameters of Haloamine Ground and Lowest Triplet Excited States (CCSD(T)/augcc-pVQZ) molecule H2NF HNF2 NF3 a

N−X BDE (S)a 67.5 64.3 57.1

a

E (T)

N−X BDE (T)

58.8 58.7 56.5

8.7 5.6 0.6

RN−X

RN− X′

Mulliken charge/spin at distant F

1.875 1.790 2.436

1.361 1.344

−0.20/0.8 −0.19/0.8 −0.01/1.0

For a compilation of computational values, see ref 41.

The results shown in Table 3 indicate that a significant attractive interaction must exist between the nitrogen and fluorine atoms in the lowest triplet excited state of NH2F. The calculated N−F bond length is comparatively short, and there is a partial negative charge on the fluorine atom, which, however, is smaller than that in ground-state NH2F (−0.38 eu). In the lowest triplet state of NF3, on the other hand, the long N−F bond is considerably longer than in triplet NH2F, and the distant fluorine atom is predicted to bear essentially no partial charge, but a full spin unit. Nevertheless, even in this system, the long N−F bond is significantly shorter than the sum of the van-der-Waals radii of nitrogen and fluorine, which amounts to RvdW = 2.89 Å. The lowest triplet excited state of NHF2, finally, is predicted to range between the properties of triplet NH2F and triplet NF3. It has Cs symmetry, with one fluorine atom tightly, the second loosely bound. A C2v symmetric structure is a transition state for exchange of the roles of the two fluorine atoms. To check the validity of the CCSD(T) calculations, the lowest triplet excited state of NH2F was also optimized at the MRCI+Q/aug-cc-pVQZ level of theory, where two singlet states and one triplet state were employed in the state-averaged CASSCF reference. The additional singlet state was required to properly describe the long N−F bond. The optimized geometry closely matches the results obtained at the CCSD(T)/aug-ccpVQZ level of theory (Figure 7). The triplet energy (MRCI +Q/aug-cc-pVQZ: ΔUT = 60.9 kcal mol−1) is also in reasonably good agreement with the value obtained by CCSD(T) theory. Similarly, MRCI+Q/aug-cc-pVQZ gave results in very good agreement with CCSD(T)/aug-cc-pVQZ when applied to the lowest triplet excited state of NHF2 (MRCI = Q/aug-cc-pVQZ: ΔUT = 62.6 kcal mol−1 (without ZPE)). If used on the lowest triplet excited state of NF3, however, MRCI+Q yields a result that significantly deviates from the result obtained by CCSD(T) theory (Figure 7). It should also be noted that the triplet energy in the MRCI+Q case is 93.1 kcal mol−1 (without ZPE correction), significantly higher than the CCSD(T) value reported in Table 3. Dihalogen Molecules. The triplet states of the dihalogen molecules F2 and Cl2 were previously thoroughly investigated, both experimentally and computationally.5−7,42−51 As the

Figure 8. Plot of the electronic energy of fluorine on the triplet (b) and singlet (a) spin manifolds vs the F−F distance, as calculated at the MRCI+Q/aug-cc-pVQZ level of theory.

MRCI+Q level of theory. The F−F potential obviously is very shallow in the region of the minimum geometry of the triplet state, and the optimized equilibrium geometries are very different between MRCI+Q and CCSD(T) (equilibrium distance of the triplet state: MRCI+Q, RF−F = 2.26 Å; CCSD(T), RF−F = 1.93 Å). Molecular chlorine Cl2 is predicted to have a bound triplet excited state of (π*,σ*) type (Cl2 a 3Πu), in agreement with 2338

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previous calculations.5−7 At the CCSD(T)/aug-cc-pVQZ level of theory, the electronic triplet energy is calculated as ΔUT = 49.4 kcal mol−1. At the same level of theory, the Cl−Cl BDE is obtained as 55.9 kcal mol−1 (exp 57.9 kcal mol−1),52 resulting in a Cl−Cl BDE of the lowest triplet state of chlorine of 6.5 kcal mol−1. Upon triplet excitation, the Cl−Cl bond length in Cl2 is predicted [CCSD(T)] to increase from RClCl = 2.003 Å in ground-state Cl2 to RClCl = 2.412 Å in triplet Cl2, which again agrees with previous results.5−7 The T1 diagnostic was calculated as T1 = 0.015 for Cl2 (3Πu), which is within the range where CCSD(T) should describe the problem correctly.15 When the calculation for Cl2 3Πu was repeated at the MRCI+Q/aug-cc-pVQZ + ZPE level of theory, a Cl−Cl distance of R = 2.494 Å was obtained (Figure 9b), and a triplet

agreement with the results obtained at the CCSD(T) level of theory. The potential energy as a function of the Cl−Cl distance is shown in Figure 9. The results indicate that the dimerization of two chlorine atoms must occur without barrier, also on the triplet spin manifold. It is noted that this is in contrast to the behavior observed when the potential energy diagram is calculated using the CCSD(T) method. Using CCSD(T), a transition-state structure could be optimized (Supporting Information, Cl−Cl distance of RCl−Cl = 3.62 Å, with an imaginary frequency of ν̃ = 95.9i cm−1, electronic energy higher than that of ground-state Cl2 by 60.5 kcal mol−1, resulting in an activation energy for dimerization of two chlorine atoms on the triplet hypersurface of ΔU‡ = 4.8 kcal mol−1, or an activation energy for dissociation of Cl2 (a 3Π1u) of ΔU‡ = 11.3 kcal mol−1). However, as the singlet and triplet potential energy hypersurfaces are energetically essentially degenerate at this Cl−Cl distance (Figure 9a,b), it is very likely that this transition state is an artifact due to the multireference character of the wave function. We note that the value of the T1 diagnostic for this TS is 0.022, which is well below the 0.045 guideline for open-shell systems.35,36 This gives further evidence for the failure of T1 as a diagnostic for validity of CCSD(T) calculations in these systems. Hydrazine. Two triplet excited states of hydrazine, H2NNH2, could be optimized. Both are nearly planar, with a slight pyramidalization at the nitrogen atoms. The pyramidalization is either syn or anti, resulting in two very similar triplet states with either C2h (anti) or C2v (syn) symmetry. The electronic triplet energies of both triplet states are calculated to be very high, with ΔUT = 88.7 kcal mol−1 for both triplet states (CCSD(T)/aug-cc-pVQZ), the C2v (syn) state being predicted to be very slightly lower in energy. At the same level of theory, the N−N BDE of ground-state singlet hydrazine is calculated as 61.8 kcal mol−1, which is in good agreement with the experimental value of 60 ± 3 kcal mol−1.55 The geometries of both triplet states are remarkable in that the N−N bond is not

Figure 9. Plot of the electronic energy of chlorine on the triplet (b) and singlet (a) spin manifolds vs the Cl−Cl distance, as calculated at the MRCI+Q/aug-cc-pVQZ level of theory.

energy of ΔUT = 48.5 kcal mol−1, in close agreement with the results obtained at the coupled-cluster level of theory. At this level of theory, the Cl−Cl BDE is obtained as BDE (1Σg) = 54.6 kcal mol−1, and BDE (3Πu) = 6.1 kcal mol−1, again in close

Figure 10. Optimised geometries (CCSD(T)/aug-cc-pVQZ) of stationary points on the H4N2 hypersurface. Top left: anti-H4N2 triplet. Top right: syn-H4N2 triplet. Bottom left: anti-H4N2 radical cation. Bottom right: ground-state singlet hydrazine. Distances in Å, angles in degrees. The dihedrals given refer to the HNNH dihedral. Electronic energies (in kcal mol−1, incl ZPE correction) are relative to ground-state singlet H4N2 = 0.0 kcal mol−1. The energy of two separated NH2 radicals is 61.8 kcal mol−1. 2339

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Figure 11. Highest occupied natural orbitals of the lowest triplet excited state of hydrazine, as calculated at the CCSD(T)/aug-cc-pVQZ level of theory. The isodensity surface value was set to 0.03 au. The occupation numbers of the natural orbitals are 1.00 in each case.

has Rydberg character, with significant contributions from higher s orbitals at the four hydrogen atoms (Figure 11). The same applies to the C2h triplet state. Figure 12 confirms that no (π*,σ*) triplet excited state exists for hydrazine, whereas the Rydberg minimum is considerably deeper than in the case of triplet hydrogen peroxide. Disulfane. Previous work3 had shown that the presence of two heavy chalcogen atoms (sulfur, selenium, or tellurium) is required to obtain maximum stabilization of (π*,σ*) triplet excited states in five-membered saturated heterocycles bearing two adjacent heteroatoms. In agreement with this expectation, the thermodynamic stability of the triplet state of disulfane is considerably larger than the stability of the triplet excited states of hydrogen peroxide. As in the case of hydrogen peroxide, two planar rotameric triplet excited states could be localized for disulfane, with C2h (trans) or C2v (cis) symmetry. The calculated (CCSD(T)/aug-cc-pVQZ) electronic triplet energies are ΔUT = 52.8 (C2h) or 53.6 (C2v) kcal mol−1. At the same level of theory, the S−S BDE of disulfane is calculated as 61.2 kcal mol−1, resulting in an S−S BDE of the triplet states of 8.4 (C2h) or 7.6 (C2v) kcal mol−1. Both triplet states of disulfane are (π*,σ*) triplet excited states, if a full population analysis (Gaussian: pop=full) is performed, whereas the ordering of the natural orbitals (Gaussian: pop=NO) is σ* below π*. Upon triplet excitation, the S−S bond length of disulfane is predicted to increase from RSS = 2.067 Å in ground-state disulfane to RSS = 2.534 (C2h) or RSS = 2.559 (C2v) Å. This 23% increase in S−S bond length is similar to what is predicted for cyclic disulfides.3 Figure 13 shows a potential energy hypersurface for H2S2 on the triplet spin manifold, as calculated at the CCSD(T)/aug-ccpVTZ level of theory. For the grid, both the S−S distance and the HSSH dihedral were varied, in steps of 0.1 Å/10°. At a shorter RS−S = 1.949 Å, a Rydberg triplet state (C2v symmetry) with a triplet energy ΔUT = 79.7 kcal mol−1 could be located. The geometries of stationary points of the triplet H2S2 hypersurface are shown in Figure 14. The results obtained indicate that the triplet states can be divided into two categories: first, we have triplet states with one singly occupied π* and σ* orbital each. These include hydrogen peroxide, oxygen difluoride, HOF, Cl2, fluoroamines, and disulfane. Normally, the π* orbital will be in energy below the σ* orbital ((π*,σ*) triplet state). In some cases (e.g., fluoroamines); however, the half-filled σ* orbital is predicted

lengthened relative to the ground state (as in most other triplet excited states in this work), but rather significantly shortened. In the case of both the C2h and C2v triplet states, it is calculated as RNN = 1.316 Å (Figure 10). Figure 11 shows natural orbitals for the syn-isomer of triplet hydrazine, and Figure 12 shows a scan of the triplet H4N2 hypersurface as a function of both the HNNH dihedral (in increments of 10°) and the N−N distance (in increments of 0.1 Å).

Figure 12. Contour plot of the potential energy hypersurface of N2H4 in the triplet state (CCSD(T)/aug-cc-pVTZ), as a function of the HNNH dihedral and the N−N distance. Red (+45 kcal mol−1, relative to 2 × NH2), yellow (+33 kcal mol−1), and green (+22 kcal mol−1) indicate regions of high energy, and violet (ca. ± 0 kcal mol−1, relative to 2 × NH2) indicates regions of low energy.

This value is exactly between the value for the N−N bond in neutral hydrazine (CCSD(T)/aug-cc-pVQZ: RN−N = 1.438 Å),56 and the NN bond in diprotonated diimine (or hydrazine dication), which at the CCSD(T)/aug-cc-pVQZ level of theory is calculated as RNN = 1.230 Å, and very close to the N−N distance in the radical cation of hydrazine (CCSD(T)/aug-cc-pVQZ: RNN = 1.309 Å). A look at the singly occupied natural orbitals of triplet hydrazine (C2v) reveals that the lower-lying of the two is a π* orbital, whereas the higher-lying singly occupied natural orbital 2340

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from two hydroxy radicals via the triplet spin manifold depends on the density of states available to dissipate the collisional energy. Given the extremely low bonding energy of the O−O bond in (π*,σ*) triplet excited H2O2, it appears unlikely that this very shallow minimum should accommodate sufficient energy states to effectively allow dissipation of the collisional energy, except possibly at very low temperatures. Under cryogenic conditions (and thus kinetic reaction control), the competing formation of water + O(3P), with a 4.2 kcal mol−1 barrier from the HO···HO complex, should be slower than the formation of the C2h triplet state of H2O2, which from HO··· HO is only uphill by 1.5 kcal mol−1. Due to its significantly deeper well, the lowest triplet state of disulfane could potentially play a role in the chemistry of the system H2S + S (3P). Previous high-level computational work on this system had not taken this species into account.57 Further, hydrogen peroxide is not the only molecule with two adjacent heteroatoms bearing lone pairs to play an important role in atmospheric chemistry. Given the results on oxygen fluorides presented here, it appears possible that chlorine oxides like Cl2O or ClO (which play a role in the degradation of ozone) could potentially have low-lying triplet or quartet excited states of (π*,σ*) character. Preliminary calculations on ClO indeed indicate that this is the case. Does single-reference CCSD(T) theory adequately describe the triplet excited states of the small molecules studied? Unfortunately, there is no simple answer to this question. The T1 diagnostic by Lee and Taylor,15 at least as implemented in Gaussian09, does not appear to provide a criterion, as we could not find any correlation between the value of T1 and agreement between CCSD(T) and MRCI+Q. As far as molecules involving third period heteroatoms are concerned, the answer is “yes”for triplet Cl2, the results obtained by the CCSD(T) and MRCI+Q methods show excellent agreement. However, even in these systems, bond-breaking or -formation processes will not be described well by a single-reference method like CCSD(T). As far as molecules involving second period heteroatoms are concerned, in many cases (like H2O2, NH2F, NHF2, HOF, OF2), CCSD(T) theory described the lowest triplet excited states well, failing only for the highly fluorinated species triplet F2 or triplet NF3.

Figure 13. Contour plot of the potential energy hypersurface of H2S2 in the triplet state (CCSD(T)/aug-cc-pVTZ), as a function of the HSSH dihedral and the S−S distance. Red (+80 kcal mol−1, relative to 2 × SH) and yellow (+50 kcal mol−1) indicate regions of high energy; dark blue (ca. ±0 kcal mol−1, relative to 2 × SH) and violet (ca. −10 kcal mol−1, relative to 2 × SH) indicate regions of low energy.

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Figure 14. Optimized geometries (CCSD(T)/aug-cc-pVQZ) of stationary points on the H2S2 hypersurface. Top left: singlet ground state. Top right: C2h-triplet state. Bottom left: C2v triplet state. Bottom right: C2v Rydberg triplet state. Distances in Å, angles in degrees, energies in kcal mol−1.

CONCLUSION Small molecules with at least two adjacent, lone pair-bearing heteroatoms X, Y are predicted to have lowest triplet excited states of (π*,σ*) character. Exceptions to this rule are hydroxylamine, where no bound triplet excited state could be localized, and hydrazine, which has a lowest triplet excited state of Rydberg character. The X−Y binding energies of the triplet excited states range between very small values (HOOH, C2h triplet: 0.9 kcal mol−1) and significant values that might allow for an experimental observation (e.g., NH2F 8.7 kcal mol−1, H2S2 (C2h) 8.4 kcal mol−1, all at CCSD(T)/aug-cc-pVQZ). With the exception of the lowest triplet excited states of fluorine and NF3, the triplet states investigated are described well by coupled-cluster theory and do not require multireference treatment.

to be energetically below the half-filled π* orbital ((σ*,π*) triplet state). The second category, Rydberg triplet states, includes hydrazine, and the higher Rydberg triplet states of H2O2 and H2S2. It is noted that a natural orbital population analysis indicates a very weak Rydberg character in some of the other triplet states belonging to category 1. The occupation number of the Rydberg type orbitals, however, always is very small (typically 0.01). How relevant are the triplet excited states of the molecules investigated? In the case of hydrogen peroxide, the presence of a bound triplet state could potentially open up a new reaction channel for dimerization of two hydroxy radicals. Normally, dimerization of two free radicals necessitates the presence of an encounter complex of singlet spin multiplicity. Triplet encounter complexes, which are more probable than singlet encounter complexes by a factor of 3, normally do not result in product formation. Whether hydrogen peroxide can be formed

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ASSOCIATED CONTENT

S Supporting Information *

Cartesian coordinates, energies, and value of T1 diagnostic for all stationary points calculated. Detailed information about 2341

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(18) Knowles, P. J.; Werner, H.-J. An Efficient Method For The Evaluation Of Coupling Coefficients In Configuration Interaction Calculations. Chem. Phys. Lett. 1988, 145, 514−522. (19) Knowles, P. J.; Werner, H.-J. Internally Contracted Multiconfiguration-Reference Configuration Interaction Calculations For Excited States. Theor. Chim. Acta 1992, 84, 95−103. (20) Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M.; Celani, P., Korona, T.; Lindh, R.; Mitrushenkov, A.; Rauhut, G.; et al. MOLPRO, Version 2010.1, A Package Of Ab Initio Programs; see http://www.molpro.net. (21) Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M. Molpro: A General-Purpose Quantum Chemistry Program Package. WIREs Comput. Mol. Sci. 2012, 2, 242−253. (22) Chevaldonnet, C.; Cardy, H.; Dargelos, A. Ab Initio CI Calculations On The PE And VUV Spectra Of Hydrogen Peroxide. Chem. Phys. 1986, 102, 55−61. (23) Reinsch, E.-A. A Theoretical Investigation Of The Excited States Of The H2O2 Molecule. Chem. Phys. Lett. 1987, 141, 369−371. (24) Takeshita, K.; Mukherjee, P. K. Theoretical Study On The Quasi-Bound State And UV Spectrum Of H2O2 With Inclusion Of The Vibrational Structure. Chem. Phys. 1994, 182, 195−202. (25) Mukherjee, P. K.; Senent, M. L.; Smeyers, Y. G. Half-Projected Hartree-Fock Calculations For The Spectroscopic Parameters, Frequencies, And Intensities Of The Torsional Mode Of The Lowest Lying Singlet Excited States Of Hydrogen Peroxide. Int. J. Quantum Chem. 1999, 75, 631−636. (26) Liu, Y.; Persson, P.; Lunell, S. Theoretical Study Of The Photodissociation Of Low Lying Excited States Of Hydrogen Peroxide. Mol. Phys. 2004, 102, 2575−2584. (27) Watts, J. D.; Francisco, J. S. Ground And Electronically Excited States Of Methyl Hydroperoxide: Comparison With Hydrogen Peroxide. J. Chem. Phys. 2006, 125, 104301. (28) Drozd, G. T.; Melnichuk, A.; Donahue, N. M. The HOOH UV Spectrum: Importance Of The Transition Dipole Moment And Torsional Motion From Semiclassical Calculations On An Ab Initio Potential Energy Surface. J. Chem. Phys. 2010, 132, 084304. (29) Linguerri, R.; Francisco, J. S. Coupled-Cluster And Multireference Configuration Interaction Study Of The Low-Lying Excited States Of The H2O2-H2O Complex. J. Chem. Phys. 2012, 137, 214312. (30) Bhattacharjee, B.; Das, R. Involvement Of Triplet State In The Photodissociation Of Hydrogen Peroxide: Experimental Evidence From Time-Resolved EPR Study. Mol. Phys. 2007, 105, 1053−1057. (31) Luo, X.; Fleming, P. R.; Rizzo, T. R. Vibrational Overtone Spectroscopy Of The 4νOH + νOH′ Combination Level Of HOOH Via Sequential Local Mode-Local Mode Excitation. J. Chem. Phys. 1992, 96, 5659−5667. (32) Koput, J. On The r0* Structure And The Torsional Potential Function Of Hydrogen Peroxide. J. Mol. Spectrosc. 1986, 115, 438− 441. (33) The remaining discrepancy may well be due to relativistic effects and higher-order correlation, see: Harding, M. E.; Vázquez, J.; Ruscic, B.; Wilson, A. K.; Gauss, J.; Stanton, J. F. High-Accuray Extrapolated Ab Initio Thermochemistry. III. Additional Improvements And Overview. J. Chem. Phys. 2008, 128, 114111. (34) Due to multireference character evolving at longer O−O bond distances, a limit of 2.2 Å was set. This value is based on the fact that the triplet state of NF3 with an N−F bond distance of 2.613 Å (MRCI +Q) was no longer adequately described by CCSD(T) theory, which gave a RN−F = 2.436 Å (see below). The same argument applies to Figures 5 (H2NOH) and 12 (H2NNH2). In the case of disulfane (Figure 13), the limit was set to RS−S = 2.7 Å. (35) Rienstra-Kieracofe, J. C.; Allen, W. D.; Schaefer, H. F., III. The C2H5 + O2 Reaction Mechanism: High-Level Ab Initio Characterizations. J. Phys. Chem. A 2000, 104, 9823−9840. (36) Thomas, L. H.; Kaltsoyannis, N. An Ab Initio Study Of The Electronic Structure Of BCl32+ And Its Decomposition Pathways. Phys. Chem. Chem. Phys. 2006, 8, 1271−1281. (37) Studier, M. H.; Appelman, E. H. Hypofluorous Acid. J. Am. Chem. Soc. 1971, 93, 2349−2351.

MRCI+Q calculations. This material is available free of charge via the Internet at http://pubs.acs.org

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AUTHOR INFORMATION

Corresponding Author

*G. Bucher: tel, +44 141 3308491; e-mail, [email protected]. uk. Present Address †

Department of Chemistry, University of Sheffield, Sheffield S3 7HF, United Kingdom. Notes

The authors declare no competing financial interest.

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dx.doi.org/10.1021/jp500766d | J. Phys. Chem. A 2014, 118, 2332−2343