Heats of formation of the criegee formaldehyde oxide and dioxirane (2)

Available online at www.sciencedirect.com Chemical Physics Letters 448 (2007) 183–188 www.elsevier.com/locate/cplett Heats of formation of the Criegee formaldehyde oxide and dioxirane Minh Tho Nguyen a a,* , Thanh Lam Nguyen a, Vu Thi Ngan a,b , Hue Minh Thi Nguyen b Department of Chemistry and Mathematical Modeling and Computational Science Centre, University of Leuven, B-3001 Leuven, Belgium b Faculty of Chemistry, Hanoi National University of Education, Hanoi, Vietnam Received 19 August 2007; in final form October 2007 Available online 12 October 2007 Abstract CCSD(T)/CBS calculations plus corrections predict the heats of formation of formaldehyde O-oxide and dioxirane 2: DH 0f CH2 OO; 1ị ẳ 28:1 and 26.4 kcal/mol, and DH 0f CH2 O2 ; 2ị ẳ 3:0 and 1.2 kcal/mol at K and 298 K, respectively The adiabatic ionization energies are IEa(1) = 9.98 eV and IEa(2) = 10.82 eV Protonation of carbonyl oxide takes place at terminal oxygen with a proton affinity of PA(1) = 203.5 ± 1.0 kcal/mol The vertical triplet state 3A of is located at 1.82 eV above the ground state (with errors of ±1.0 kcal/mol or ±0.05 eV) The parent Criegee intermediate is unstable with respect to O–O bond cleavage but becomes more stable upon ionization Ó 2007 Elsevier B.V All rights reserved Introduction Nearly 60 years ago, Criegee [1,2] postulated a mechanism, summarized in Scheme 1, to rationalize the isolation of 1,2,4-trioxolanes from the reaction of ozone with olefins and the incorporation of external aldehydes into these fivemembered products This mechanism has rapidly been endorsed by chemists, and the molecules ˜COO formed by cyclo-reversions of the primary ozonides were named as ‘Criegee carbonyl oxides’ [3] While formation of Criegee intermediates (CI’s) in solution has been demonstrated by trapping agents [2], the cyclic isomer dioxiranes have often been identified in the gas phase The first evidence for the existence of the CI’s in the gas phase was obtained in 1983 from time-resolved laser spectroscopic studies [4], and the primary ozonides were only more recently trapped by using strained allylic alcohols [5] It now appears that both the CI’s and dioxiranes, are involved as short-lived intermediates in a number of photo-oxidation reactions and enzymatic processes [6–9] When formed from fast reaction of a carbene with molecular oxygen without the * Corresponding author Fax: +32 16 32 79 92 E-mail address: minh.nguyen@chem.kuleuven.be (M.T Nguyen) 0009-2614/$ - see front matter Ó 2007 Elsevier B.V All rights reserved doi:10.1016/j.cplett.2007.10.033 presence of another substrate, a CI could undergo a multi-step unimolecular rearrangement forming first a cyclic dioxirane, and then a carboxylic acid and finally CO2 or CO [10] In fact, the ozonolysis of olefins remains the main source of carboxylic acids in the atmosphere [8] In the presence of hydrogen compounds, carbonyl oxides contribute to production of the OH and HO2 radicals, which undergo important chemical processes in the troposphere [11] Due to the fact that the CI’s were not directly detected and characterized during the ozonolyses, most information on their molecular structure, basic spectroscopic and thermochemical properties have been derived from quantum chemical calculations The simplest parent CI, formaldehyde carbonyl O-oxide CH2O2, has been the subject of several theoretical studies [12–19], but these rather disagree with each other about its heat of formation In fact, the reported theoretical values for DHf(CH2O2) at 298 K range from 27 to 48 kcal/ mol [12–19] As far as we are aware, the experimental heat of formation of dioxirane is not available, and the theoretical values vary from À0.3 to 6.0 kcal/mol [15] Although relative energies between both isomers with respect to formic acid have repeatedly been calculated using different levels of theory, their heats of formation have been determined with high accuracy Note that formic acid is 184 M.T Nguyen et al / Chemical Physics Letters 448 (2007) 183–188 O O O O O * O O O O Scheme the most stable isomer of the (CH2O2) system for which the experimental heat of formation has been well established As it is now possible to perform higher level calculations with basis sets that can be extrapolated to the complete basis set limit for such species, we have calculated the heats of formation of the three (CH2O2) isomers using current state-of-the-art electronic structure calculations In addition their ionized state and the protonated form have been considered Extensive investigations on theoretical thermochemistry [20–23] have demonstrated that total atomization energies (TAE) of small molecules and radicals can be predicted within ±1.0 kcal/mol, when coupled-cluster CCSD(T) electronic energies obtained with the correlation-consistent basis sets and extrapolated to the complete basis set limit (CBS), can be used, and other smaller corrections can be included For the sake of comparison, we have also used the W1 approach [24] to evaluate these thermochemical parameters Computational methods Electronic structure calculations were carried out using the GAUSSIAN 03 [25] and MOLPRO 2002 [26] suites of programs Geometry parameters of each structure were fully optimized using molecular orbital theory at the secondorder perturbation theory MP2 and coupled-cluster theory CCSD(T) levels [27], with the correlation-consistent aug-ccpVTZ basis set [28] For open shell electron configurations, the fully unrestricted formalism was used for calculations done with GAUSSIAN 03 Single-point electronic energies were also calculated using the restricted coupled-cluster R/UCCSD(T) formalism in conjunction with the correlation-consistent aug-cc-pVnZ (n = D, T, Q, 5) basis sets at the (U)CCSD(T)/aug-cc-pVTZ optimized geometries For simplicity, the basis sets are denoted hereafter as aVnZ In the R/UCCSD(T) approach, a restricted open shell Hartree–Fock (ROHF) calculation is initially performed and the spin constraint is relaxed in the coupled-cluster calculation The CCSD(T) energies were extrapolated to the complete basis set (CBS) limit using the following expressions [29]: Exị ẳ ACBS ỵ B expẵx 1ị ỵ C expẵx 1ị ; 1ị where x = 2, 3, and for the aVnZ basis, D, T, and Q, respectively; and [30]: Exị ẳ ECBS ỵ B=x3 ; where x = and for aVQZ and aV5Z, respectively ð2Þ After the valence electronic energy, the largest contribution to the TAE is the zero-point energy (ZPE) The ZPE’s are based on that of formic acid whose experimental vibrational fundamentals were well known To evaluate the TAE’s, smaller corrections were also included Corevalence corrections (DECV) and relativistic corrections (DESR) were evaluated together from CCSD(T) calculations using a smaller basis set and the spin-free one-electron Douglas–Kroll Hamiltonian [31] These corrections can be derived from the W1 procedure [24] The atomic spin–orbit correction is 0.085 kcal/mol for C and 0.223 kcal/mol for O from the excitation energies of Moore [32] Results and discussion Table lists the different components of the TAE’s of the seven structures that we studied These include carbonyl oxide (CI) (1A ), dioxirane (1A1), formic acid (1A ), ionized carbonyl oxide 1Å+ (2A ), ionized dioxirane 2Å+ (2A2), ionized formic acid 3Å+ (2A ) and the O-protonated form of carbonyl oxide 1H+ (1A ) Table lists the calculated heats of formation of all structures considered at both K and 298 K All other thermochemical parameters were derived from the corresponding heats of formation The spin-contamination in the ionized state of (CH2O2) is negligible, as shown by the expectation values ỈS2ỉ of $0.76 in UHF wavefunctions Except for 1, the T1 diagnostic for the CCSD wavefunctions are acceptable, ranging from 0.015 to 0.029 (Table 1) 3.1 The electronic structure of carbonyl oxide There has been a longstanding issue over the electronic structure of carbonyl oxide Goddard and Harding [12] argued on the basis of GVB calculations with a double-zeta basis set that should be considered as a singlet 1,3-biradical, which attains a zwitterionic character only by substitution and/or solvent effects, and such intrinsic biradical character also accounts for its reactivity as a 1,3-dipole From a limited (6 · 6) configuration interaction wave function, Hiberty [13] found that the 1A (4p) ground state of has major component of the (n2,p2) orbital configuration mixed with the doubly excited ðp2 ! pÃ3 Þ configuration and to a lesser extent, the singly excited ðp2 ! pÃ3 Þ configuration This picture was in part confirmed by subsequent more elaborated complete active space CASSCF(10,10) calculations [17] Cremer et al [14] argued that the biradical character of mainly came from a shortcoming of the methods such as the GVB and MP2, which tend to exaggerate the biradical contributions This results in the nearly equal O–O and C–O bond distances obtained by the latter ˚ , respectively, at the methods (being 1.284 and 1.293 A MP2/aVTZ level) In contrast, coupled-cluster theory CCSD(T) or multi-configurational CASSCF calculations provide a shorter C–O bond and a longer O–O bond ˚ by CCSD(T)/aVTZ, respec(namely 1.275 and 1.349 A tively) Density functional theory also gives the distances 185 M.T Nguyen et al / Chemical Physics Letters 448 (2007) 183–188 Table Calculated atomization energies of the (CH2O2) structures considered (kcal/mol) Molecule CH2OO 1( A ) CH2O2 2(1A1) CH(O)OH 3(1A ) CH2OO 1Å+(2A ) CH2OO 2Å+(2A2) CH(O)OH 3Å+(2A ) + + CH2OOH 1H ( A ) a b c d e CBS (DTQ)a CBS (Q5)b DEZPEc DECV + DESRd DESOe RD0 (0 K) (DTQ) T1 Diagnostic 381.86 408.05 500.28 466.19 473.02 551.87 593.39 382.10 408.31 500.49 À19.15 À20.08 À20.82 À19.80 À20.96 À20.33 À27.39 0.89 0.76 1.01 0.69 0.63 0.91 0.77 À0.52 À0.52 À0.52 À0.52 À0.52 À0.52 À0.52 363.08 388.21 479.95 446.56 452.30 531.93 566.25 0.043 0.015 0.016 0.029 0.015 0.022 0.024 From CCSD(T)/CBS energies extrapolated using Eq (1) with n = D, T and Q and the CCSD(T)/aVTZ optimized geometries, unless otherwise noted From CCSD(T)/CBS energies extrapolated using Eq (2) with n = Q and and the CCSD(T)/aVTZ optimized geometries Estimated from calculated ZPE by MP2/aVTZ frequencies and scaled by a factor of 0.9844 obtained from values for formic acid Core-valence corrections and scalar relativistic correction (DKH were obtained at the CCSD(T)/MTsmall (W1) level) Spin orbit atomic values Table Calculated heats of formation for the CH2O2 structures considered (kcal/ mol) Structure DHf (0 K) DHf (0 K) DHf (298 K) DHf (298 K) (DTQ)a (W1)b (DTQ)a (W1)b CH2OO 1(1A ) 28.1 CH2CO2 2(1A1) 3.0 CH(O)OH 3(1A ) À88.7 258.2 CH2OOÅ+ 1Å+(2A ) CH2OOÅ+ 2Å+(2A2) 252.5 172.9 CH(O)OH 3Å+(2A ) CH2OOH+ 1H+(1A ) 190.2 a b 27.0 1.7 À89.9 257.0 250.2 171.7 188.7 26.4 1.2 À90.5 256.5 250.8 171.3 189.1 25.3 À0.1 À91.6 255.3 248.5 170.1 187.8 See footnotes of Table for definitions Values obtained from calculations using the W1 method ˚ close to the CCSD(T) results, namely 1.254 and 1.351 A using the popular hybrid B3LYP functional with the same basis set To verify further the validity of single-reference methods for 1, we have carried out CASSCF(12,11) calculations whose 11 orbitals employed include orbitals of a symmetry and orbitals of a00 symmetry, with the aVTZ basis set In agreement with earlier results [17], the wavefunction of is composed mainly by doubly excitations having the following CI-vectors: 0.94[ .(10a )2(1a00 )2(2a00 )2] À 0.20[ .(10a )2(1a00 )2(3a00 )2] À 0.10[ .(11a )2(1a00 )2(2a00 )2] À 0.11[ .(10a )1(11a )1(1a00 )1 (2a00 )2(3a00 )1] The singly excited configurations corresponding to biradical forms have negligible contributions Thus, the large value T1 = 0.044 for (Table 1) results from contributions of zwitterionic resonance forms rather than from biradical counterparts However, in view of the large CIcoefficient of the ground configuration, it appears that the single-reference CCSD(T) method can sufficiently describe the electronic structure of the carbonyl oxide Recently we showed that the CCSD(T) method accounts best for the energy of the singlet methylene (CH2), which has a formal two-configurational wavefunction [22] The NBO populations of also indicate a more bipolar com- pounds with a positive charge on C(H2) (0.14 electron) and a large negative charge on the terminal O (À0.41 electron) The bond indices amount to 1.5 for the CO bond and 1.1 for the OO bond 3.2 Heats of formation The zero-point energy (ZPE) of formic acid can be estimated as the average of one-half the sum of the calculated harmonic vibrational frequencies and one-half the sum of the experimental fundamentals which include anharmonic corrections For 3, the average of these two values gives an estimate of ZPE(3) = 20.82 kcal/mol [20] Evaluation of the ZPE’s for other isomers is less straightforward as no experimental information is available The CCSD(T)/aVTZ harmonic vibrational frequencies of the CI are (in cmÀ1): a : 529, 935, 1231, 1306, 1483, 3137, 3290, and a00 : 632, 862 The ZPE of amounts to 19.4, 19.5 and 19.2 kcal/mol at the B3LYP, MP2 and CCSD(T) levels, respectively, using the aVTZ basis set Comparison of the calculated and experimental results for formic acid yields a scaling factor, obtained as the ratio of the ZPE estimate to the calculated 0.5Rxi at a given level of theory We used the scaling factor of 0.9844 derived from and applied to the ZPE’s obtained from (U)MP2/ aVTZ harmonic vibrational frequencies for remaining structures For example, we obtained a value ZPE(1) = 19.1 kcal/mol, whereas the values of 18.7, 18.9 and 19.5 kcal/mol have been used for this quantity in previous studies [14–18] By combining our computed RD0 values with the known heats of formation at K for the elements (DH 0f Hỵ ị ẳ 365:2 ặ 0:01 kcal=mol, DH 0f Hị ẳ 51:63ặ and 0:001 kcal=mol; DH f Cị ẳ 169:98 ặ 0:1 kcal=mol DH 0f Oị ẳ 58:99 ặ 0:1 kcal=mol), we have derived DH 0f values at K for the molecules under study in the gas phase and convert them to 298 K using the calculated thermal corrections For three isomers 1, and 3, their TAE’s were calculated from CCSD(T)/CBS energies extrapolated using both Eqs (1) and (2) In all cases, the differences between two calculated values amount to $0.2 kcal/mol For formic 186 M.T Nguyen et al / Chemical Physics Letters 448 (2007) 183–188 acid 3, the calculated TAE’s of 480.0 and 480.2 kcal/mol from CCSD(T)/CBS energies extrapolated using Eqs (1) and (2), respectively, are essentially the same as the experimental value of 479.9 kcal/mol (experimental heat of formation of formic acid is À88.7 kcal/mol at K and À90.5 kcal/mol at 298 K) [33] For the sake of consistency, we have considered in Table only the values derived from Eq (1) We note that W1 approach results in the heats of formation of À89.8 kcal/mol at K and À91.6 kcal/mol at 298 K for formic acid 3, which represent thus a deviation of $1.1 kcal/mol, but more negative, with respect to the experimental results For the heat of formation of carbonyl oxide 1, Goddard and Harding [12] derived a value of 48 kcal/mol, which was later revised down to 29 kcal/mol (values at 298 K) On the basis of MBPT(2) calculations, Cremer et al [14] predicted a value of 38 kcal/mol at K Later, using CCSD(T)/ TZ + P calculations in conjunction with the energies of two decomposition reactions, this group of authors [14] derived the values of 31.7 kcal/mol at K and 30.2 kcal/ mol at 298 K Olzmann et al [16] used DFT B3LYP/ 6-31 G(d,p) calculations and obtained a value of 22.1 kcal/mol Subsequent CCSD(T) and CASPT2 calculations by Crehuet et al [17] making use of larger basis sets with f-type polarization functions led to an empirical correction of $4 kcal/mol on the heat of formation of 1, giving a smaller value of 27.0 kcal/mol at 298 K [15,17] This was the recommended value by Cremer and coworkers [16,17] Our values for DH 0f CH2 OO;1ị ẳ 28:1 and 26.4 kcal/ mol at K and 298 K, respectively, obtained from TAE[CCSD(T)/CBS] calculations compare well with the previous estimate of 27.0 kcal/mol at 298 K by Cremer and coworkers [17] The corresponding W1 results of 27.0 and 25.3 kcal/mol are again lower by about kcal/mol Similarly, our results for dioxirane DH 0f ðCH2 O2 ; 2Þ of 3.0 kcal/mol at K and 1.2 kcal/mol at 298 K differ by about 1.3 kcal/mol from the relevant W1 results of 1.7 and À0.1 kcal/mol (Table 2) For this cyclic isomer, Cremer et al [15] obtained a value of À0.3 kcal/mol at 298 K Thus it is of interest to note a consistent overestimation of $1 kcal/mol by the W1 heats of formation with respect to our CBS results Overall, the CI and dioxirane are predicted to be 116.8 and 91.7 kcal/mol higher in energy than formic acid 3, respectively Using the heats of formation DHf,0 K (CH2,3B1) = 93.4 kcal/mol and DHf,0 K(CH2O) = À25.1 kcal/mol, the stability of carbonyl oxide can be evaluated as: 3 CH2 OO 1ð A0 Þ ! CH2 ð B1 ị ỵ O2 R gị BDECOị ẳ 65:3 kcal=mol 1 ð3Þ CH2 OO 1ð A Þ ! CH2 O A1 ị ỵ O Pị BDEOOị ẳ 5:8 kcal=mol ð4Þ Both reactions are endothermic, but the O–O bond dissociation energy via (4) is peculiarly small The process (4) is seemingly prohibited by a barrier arising from an intercrossing between both lowest-lying singlet and triplet states It appears however that CI is unstable with respect to bond cleavage Such stability is in line with the nonobservation of the parent CI during the ozonolysis of ethylene 3.3 Ionization energies and proton affinity The corresponding calculated results are derived using the heats of formation listed in Table As for a calibration, let us first consider the adiabatic ionization energy of formic acid The calculated value of IEa(3) = 11.34 eV, by both CCSD(T)/CBS and W1 approaches, is nearly identical with respect to the experimental result of 11.33 eV [34] For both isomers and 2, the CBS results of IEa(1) = 9.98 eV and IEa(2) = 10.82 eV are also in good agreement with the W1 counterparts of 9.97 and 10.78 eV Nevertheless, as in the previous cases, the CBS heats of formation at K and 298 K of DH 0f 1ỵ ị ẳ 258:2 and 256.5 kcal/mol, DH 0f 2ỵ ị ẳ 252:5 and 250.8 kcal/mol, and DH 0f 3ỵ ị ẳ 172:9 and 171.3 kcal/mol again differ by 1–2 kcal/mol from the W1 results (Table 2) Following ionization, the energy differences between isomers are reduced, with the radical cations 1Å+ (2A ) and 2Å+ (2A2) being 85.3 and 79.6 kcal/ mol about 3Å+ (2A ) In particular, the energy difference between both ionized isomers CI 1Å+ and dioxirane 2Å+ is reduced to about 5.7 kcal/mol as compared with the gap of 25.1 kcal/mol in the neutral form Using the heats of formation DH f;0 K CHỵ ị ẳ 332:8 kcal/mol and DHf,0 K (CH2OÅ+) = À25.1 kcal/mol, the BDE’s of carbonyl oxide radical cation 1Å+ are evaluated in (5) and (6): CH2 OOỵ 1ỵ ! CHỵ ỵ O2 BDECOị ẳ 74:6 kcal=mol 5ị CH2 OOỵ 1ỵ ! CH2 Oỵ ỵ O BDEOOị ẳ 27:1 kcal=mol 6ị Thus, following ionization, the CI becomes more stable with respect to bond cleavages It is of interest to probe the electron reorganization accompanying the ionization process of the CI Fig displays the iso-surface maps of the electron localization function (ELF [35]) of in the neutral ground state (Fig 1a) and the difference between the ELF’s of the vertical radical cation and the ground neutral state (Fig 1b) The integrated populations in the basins show a large concentration of non-bonding electrons around the terminal O-atom, and ionization of is basically a removal of electron centered on this atom, and at a lesser extent at the carbon center The CI has three possible protonation sites Calculations clearly show that the terminal O-atom represents the most basic site of the molecule, in agreement with the charge distribution The protonated form 1H+ is favored by $55 kcal/mol over the C-protonated form The CBS heats of formation of the O-protonated carbonyl oxide M.T Nguyen et al / Chemical Physics Letters 448 (2007) 183–188 187 n) triplet 3A00 formed from the dominant tical (p* 00 (3a 10a ) transition (C0 = 0.98) lies higher in energy, at 2.30 eV above the 1A state In previous studies [18,19], only the higher-lying 3A00 state has been considered Due to the fact that both triplet states undergo out-of-plane distortion, the corresponding potential energy surface is rather complex and exploration needs appropriate methods Fig 1c illustrates the difference between the ELF’s of the vertical triplet 3A00 state and the ground neutral state Upon transition, electron is moving from the terminal O-atom and C–O1 bond to the CH2 group and O1 atom (sum of basin populations is À1.24 electrons) In the terminal Oatom, electron is partly moving from the in-plane orbital to the perpendicular orbital The 3(p* n) transition gives rise to an increase in negative charges of both C and O1 atoms from +0.14 to À0.18 e and À0.07 to À0.19e, respectively In the mean time, the negative charge on terminal O2 significantly decreases from À0.41 to +0.01e The movements of electron away from C–O1 and O1–O2 bonds reduce in the WI indices of these bonds, from 1.52 to 1.06 and 1.11 to 1.07, respectively In the singlet manifold, the 1A00 and 1A states have multi-reference character and their vertical positions are 2.39 and 3.52 eV above the ground state, respectively These results are in qualitative agreement with the previous values of 2.14 and 3.96 eV [19], and 2.22 and 3.18 eV [18], obtained from the CASPT2(8,8) calculations with different basis sets Summary Fig Iso-surfaces of the electron localization function (ELF) of carbonyl oxide in (a) ELF = 0.81 of (1A ), (b) ELF-differences between both singlet neutral and vertical ionized states DELF = ± 0.15, and (c) ELF-differences between singlet and vertical triplet states of the neutral Red color represents the iso-surface DELF = 0.15 and yellow color DELF = À 0.15 (For interpretation of the references in colour in this figure legend, the reader is referred to the web version of this article.) 1H+ are listed in Table The corresponding proton affinity is calculated to be PA(1) = 203.3 kcal/mol (203.5 kcal/mol by W1 calculations) This is substantially larger than the proton affinities of formaldehyde PA(CH2O) = 170.4 kcal/ mol, and acetaldehyde PA(CH3CHO) = 184.4 kcal/mol [20,34] Concerning the triplet states, our results are at variance with earlier results Using the CASSCF(12,11)/CASPT2/ aVTZ calculations, we found that the lowest-lying vertical triplet state of corresponds to a 3A (p* p) state arising from the dominant (3a00 2a00 ) transition (C0 = 0.97), and it is located at 1.8 eV above the ground 1A state The ver- Using CCSD(T)/CBS calculations of atomization energies, heats of formation of carbonyl oxide (the parent Criegee intermediate) and dioxirane (the cyclic isomer of formic acid) are predicted to be DH 0f CH2 OO; 1ị ẳ 28:1 and 26.4 kcal/mol at K and 298 K, respectively, and DH 0f ðCH2 O2 ; 2ị ẳ 3:0 and 1.2 kcal/mol at K and 298 K, respectively The adiabatic ionization energies are evaluated as IEa(1) = 9.98 eV and IEa(2) = 10.82 eV Protonation of carbonyl oxide occurs at the terminal oxygen with a proton affinity of PA(1) = 203.3 kcal/mol The error bar of our calculated results is expected to be about ±1.0 kcal/mol or ±0.05 eV, mainly due to the uncertainty in the evaluation of zero-point energies Overall, the CI is unstable with respect to the OO bond cleavage, in line with its non-observation in the gas phase The stability of the CI is enhanced following ionization Concerning the computational methods, we note that the W1 results for heats of formation differ from our CBS values by about À1 kcal/mol (being more negative) Acknowledgements We thank the KULeuven Research Council (GOA program and postdoctoral fellowship) and the Flemish FWO- 188 M.T Nguyen et al / Chemical Physics Letters 448 (2007) 183–188 Vlaanderen for continuing support V.T.N is grateful to the Vietnam Ministry of Education for a doctoral scholarship (program MOET 322) References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] R Criegee, G Wenner Justus, Liebigs Ann Chem 546 (1949) R Criegee, Rec Chem Progress 18 (1957) 111 P.D Bartlett, T.G Traylor, J Am Chem Soc 84 (1962) 3408 T Sugawara, H Iwamura, H Hayashi, A Sekiguchi, W Ando, M.T.H Liu, Chem Lett (1983) 1261 M.E Jung, P Divodov, Org Lett (2001) 627 R.W Murray, Chem Rev 89 (1989) 1187 R.I Martinez, R.E Hui, J.T Herron, J Chem Phys 75 (1981) 5975 G.E Orzechowska, H.T Nguyen, S.E Paulson, J Phys Chem A 109 (2005) 5366 D Johnson, A.G Lewin, G Marston, J Phys Chem A 105 (2001) 2933 J.T DePinto, W.A deProphetis, J.L Menke, R.J McMahon, J Am Chem Soc 129 (2007) 2308 H.J Tobias, P.J Ziemann, J Phys Chem A 105 (2001) 6129 L.B Harding, W.A Goddard, J Am Chem Soc 100 (1978) 7180, and references therein P.C Hiberty, J Am Chem Soc 98 (1976) 6088 D Cremer, J Gauss, E Kafka, J.F Stanton, R.J Bartlett, Chem Phys Lett 209 (1993) 547 D Cremer, E Kraka, P.G Szalay, Chem Phys Lett 292 (1998) 97 M Olzmann, E Krafka, D Cremer, R Gutbrod, S Andersson, J Phys Chem A 101 (1997) 9421 R Crehuet, J Anglada, D Cremer, J.M Bofill, J Phys Chem A 106 (2002) 3917, and references therein [18] P Aplincourt, E Henon, F Bohr, M.F Ruiz-Lopez, Chem Phys 285 (2002) 221 [19] J.M Anglada, J.M Bofill, S Olivella, A Sole, J Am Chem Soc 118 (1996) 4636 [20] D Feller, D.A Dixon, J Chem Phys 115 (2001) 3484 [21] D.A Dixon, D Feller, K.A Peterson, J Chem Phys 115 (2001) 2576 [22] M.H Matus, M.T Nguyen, D.A Dixon, J Phys Chem A 110 (2006) 8864 [23] M.H Matus, M.T Nguyen, D.A Dixon, J Phys Chem A 111 (2007) 113 [24] J.M.L Martin, G de Oliveira, J Chem Phys 111 (1999) 1843 [25] M.J Frisch et al., GAUSSIAN 03, Revision D.02, Gaussian, Inc., Wallingford CT, 2004 [26] H.J Werner, P.J Knowles, et al., MOLPRO-2006, a package of initio programs, Universitaăt Stuăttgart, Stuăttgart, Germany and University of Birmingham, Birmingham, United Kingdom, 2006 [27] R.J Bartlett, M Musial, Rev Mod Phys 79 (2007) 291 [28] R.A Kendall, T.H Dunning Jr., R.J Harrison, J Chem Phys 96 (1992) 6796 [29] K.A Peterson, D.E Woon, T.H Dunning Jr., J Chem Phys 100 (1994) 7410 [30] D.E Woon, T.H Dunning Jr., J Chem Phys 98 (1993) 1358 [31] M Douglas, N.M Kroll, Ann Phys 82 (1974) 89 [32] C.E Moore, Atomic Energy Levels (NSRDS-NBS 35), National Bureau of Standard, Washington, DC, 1971 [33] J.B Pedley, R.D Naylor, S.P Kirby, Thermodynamic Data for Organic Compounds, second edn., Chapman and Hall, New York, 1986 [34] NIST, [35] A.D Becke, K.E Edgecombe, J Chem Phys 92 (1990) 5397  ... formic acid 3Å+ (2A ) and the O-protonated form of carbonyl oxide 1H+ (1A ) Table lists the calculated heats of formation of all structures considered at both K and 298 K All other thermochemical parameters... to 1.5 for the CO bond and 1.1 for the OO bond 3.2 Heats of formation The zero-point energy (ZPE) of formic acid can be estimated as the average of one-half the sum of the calculated harmonic... isomers and 2, the CBS results of IEa(1) = 9.98 eV and IEa(2) = 10.82 eV are also in good agreement with the W1 counterparts of 9.97 and 10.78 eV Nevertheless, as in the previous cases, the CBS heats