Vibronic spectroscopy of the peroxyacetyl radical in the near IR

The A 2A'<--X 2A" electronic transition of the peroxyacetyl radical (PA) is observed employing NIR/VUV ion enhancement, supersonic jet spectroscopy. Rotational envelope simulations yield a rotational temperature for ground state PA of ca. 55 K. Ab initio calculations of transition energies and vibrational frequencies for the A<--X transition assist in the assignment of the observed spectrum. A number of the vibrational modes of the A state are assigned to observed transitions (the O-O stretch 2(1), the COO bend 5(1), and the CCOO backbone bend 6(1)). The calculations and mass spectra suggest that the ground state of the PA ion is repulsive. An increase in rotational linewidth of the overtone of the O-O stretch (2(1)) is observed and discussed in terms of A state dynamics. The O-O stretch anharmonicity is estimated to be 13.35 cm(-1).     

Mechanistic studies of the pyrolysis of 1,3-butadiene, 1,3-butadiene-1,1,4,4-d4, 1,2-butadiene, and 2-butyne by supersonic jet/photoionization mass spectrometry

The thermal decomposition of 1,3-butadiene, 1,3-butadiene-1,1,4,4-d(4), 1,2-butadiene, and 2-butyne at temperatures up to 1520 K was carried out by flash pyrolysis on a approximately 20 mus time scale. The reaction products were isolated by supersonic expansion and detected by single-photon (lambda = 118 nm) vacuum-ultraviolet time-of-flight mass spectrometry (VUV-TOFMS). Direct detection of CH(3) and C(3)H(3), as well as C(3)H(4), C(4)H(4), and C(4)H(5) products, provides insight into the initial steps involved in the complex pyrolysis of these C(4)H(6) species below T = 1500 K. The similar pyrolysis product distributions for the C(4)H(6) isomers on such a short time scale support the previously proposed mechanism of facile isomerization of these species. Isomerization of 1,3-butadiene to 1,2-butadiene and subsequent C-C bond fission of 1,2-butadiene to produce CH(3) and C(3)H(3) (propargyl) are most likely the primary initial radical production channel in the 1,3-butadiene pyrolysis.     

Ab initio study of the electronic spectrum of peroxyacetyl nitrate

A theoretical study of the ground and excited states of peroxyacetyl nitrate (PAN), CH3C(O)OONO2, has been carried out using high level ab initio molecular orbital methods. The ground state geometry and vibrational frequencies are calculated using the coupled-cluster method. The vertical excitation energies for the lowest three excited states are calculated using the complete active space self-consistent field method along with the multireference internally contracted configuration interaction method. These results are compared with vertical excitation energies calculated with the coupled cluster equation of motion method. The calculation provides relevant insight into the origin of PAN absorption in the UV wavelength region from 200 to 300 nm. The nature of the electron transitions for these excited states is discussed.     

Generation and detection of alkyl peroxy radicals in a supersonic jet expansion

Alkyl peroxy radicals are synthesized in a supersonic jet expansion by the initial production of alkyl radicals and subsequent reaction with molecular oxygen. Parent ions CH3OO+/CD3OO+ are observed employing vacuum ultraviolet (VUV) single photon ionizationtime-of-flight mass spectroscopy (TOFMS). Employing infrared (IR) + VUV photofragmentation detected spectroscopy, rotationally resolved infrared spectra of jet-cooled CH3OO and CD3OO radicals are recorded for the A 2A' <-- X 2A" transition by scanning the IR laser frequency while monitoring the CH3 + and CD3 + ion signals generated by the VUV laser. The band origins of the A 2A'<--X 2A" transition for CH3OO and CD3OO are identified at 7381 and 7371 cm(-1), respectively. Rotational simulation for the CH3OO and CD3OO 0(0) 0 transitions of A<--X yields a rotational temperature for these radicals of approximately 30 K. With the aid of ab initio calculations, two and five vibrational modes for the A 2A' excited electronic state are assigned for CH3OO and CD3OO radicals, respectively. Both experimental and theoretical results suggest that the ground electronic state of the ions of ethyl and propyl peroxy radicals are not stable although their ionization energies (IE) are less than 10.5 eV. The C2H5OO+/C3H7OO+ cations can readily decompose to C2H5 +/C3H7 + and O2. This is partially responsible for the inability of IR+VUV photofragmentation spectroscopy to detect the near IR A<--X electronic transition for these radicals.     

Competing channels in the thermal decomposition of azidoacetone studied by pyrolysis in combination with molecular beam mass spectrometric techniques

The thermal decomposition of azidoacetone (CH3COCH2N3) was studied using a combined experimental and computational approach. Flash pyrolysis at a range of temperatures (296-1250 K) was used to induce thermal decomposition, and the resulting products were expanded into a molecular beam and subsequently analyzed using electron bombardment ionization coupled to a quadrupole mass spectrometer. The advantages of this technique are that the parent molecules spend a very short time in the pyrolysis zone (20-30 mus) and that the subsequent expansion permits the stabilization of thermal products that are not observable using conventional pyrolysis methods. A detailed analysis of the mass spectra as a function of pyrolysis temperature revealed the participation of five thermal decomposition channels. Ab initio calculations on the stable structures and transition states of the azidoacetone system in combination with an analysis of the dissociative ionization pattern of each channel allowed the identity and mechanism of each channel to be elucidated. At low temperatures (296-800 K) the azide decomposes principally by the loss of N2 to yield the imine (CH3COCHNH), which can further decompose to CH3CO and CHNH. At low and intermediate temperatures a process involving the loss of N2 to yield CH3CHO and HCN is also open. Finally, at high temperatures (800-1250 K) a channel in which the azide decomposes to a stable cyclic amine (CO(CH2)2NH) (after loss of N2) is active. The last channel involves subsequent thermal decomposition of this cyclic amine to ketene (H2CCO) and methanimine (H2CNH).     

Wavelength dependence of nitrate radical quantum yield from peroxyacetyl nitrate photolysis: experimental and theoretical studies

The photolysis wavelength dependence of the nitrate radical quantum yield for peroxyacetyl nitrate (CH(3)C(O)OONO(2), PAN) is investigated. The wavelength range used in this work is between 289 and 312 nm, which mimics the overlap of the solar flux available in the atmosphere and PAN's absorption cross section. We find the nitrate radical quantum yield from PAN photolysis to be essentially invariant; Phi(NO3)(PAN) = 0.30 +/- 0.07 (+/-2sigma) in this region. The excited states involved in PAN photolysis are also investigated using ab initio calculations. In addition to PAN, calculations on peroxy nitric acid (HOONO(2), PNA) are performed to examine general photochemical properties of the -OONO(2) chromophore. Equation of motion coupled cluster calculations (EOM-CCSD) are used to examine excited state energy gradients for the internal coordinates, oscillator strengths, and transition energies for the n --> pi* transitions responsible for the photolysis of both PNA and PAN. We find in both molecules, photodissociation of both O-O and O-N bonds occurs via excitation to predissociative electronic excited states and subsequent redistribution of that energy as opposed to directly dissociative excitations. Comparison and contrast between experimental and theoretical studies of HOONO(2) and PAN photochemistry from this and other work provide unique insight on the photochemistry of these species in the atmosphere.     

Insights into mechanistic photodissociation of acetyl chloride by ab initio calculations and molecular dynamics simulations

The potential energy surfaces of dissociation and elimination reactions for CH(3)COCl in the ground (S0) and first excited singlet (S1) states have been mapped with the different ab inito calculations. Mechanistic photodissociation of CH(3)COCl has been characterized through the intrinsic reaction coordinate and ab initio molecular dynamics calculations. The alpha-C-C bond cleavage along the S1 pathway leads to the fragments of COCl((2)A' ') and CH(3) ((2)A') in an excited electronic state and a high barrier exists on the pathway. This channel is inaccessible in energy upon photoexcitation of the CH(3)COCl molecules at 236 nm. The S1 alpha-C-Cl bond cleavage yields the Cl((2)P) and CH(3)CO(X(2)A') fragments in the ground state and there is very small or no barrier on the pathway. The S1 alpha-C-Cl bond cleavage proceeds in a time scale of picosecond in the gas phase, followed by CH(3)CO decomposition to CH(3) and CO. The barrier to the C-Cl bond cleavage on the S1 surface is significantly increased by effects of the argon matrix. The S1 alpha-C-Cl bond cleavage in the argon matrix becomes inaccessible in energy upon photoexcitation of CH(3)COCl at 266 nm. In this case, the excited CH(3)COCl(S1) molecules cannot undergo the C-Cl bond cleavage in a short period. The internal conversion from S1 to S0 becomes the dominant process for the CH(3)COCl(S1) molecules in the condensed phase. As a result, the direct HCl elimination in the ground state becomes the exclusive channel upon 266 nm photodissociation of CH(3)COCl in the argon matrix at 11 K.     

Proton affinity of peroxyacetyl nitrate. A computational study of topical proton affinities

The structure and energetics of the peroxyacetyl nitrate conformers syn- and anti-PAN and several cations formed by PAN protonation were investigated by a combination of density functional theory and ab initio calculations. syn-PAN is the more stable conformer that is predicted to predominate in gas-phase equilibria. The acetyl carbonyl oxygen was found to be the most basic site in PAN, the oxygen atoms of the peroxide and NO(2) groups being less basic. The 298 K proton affinity of syn-PAN was calculated as 759-763 kJ mol(-1) by effective QCISD(T)/6-311 + G(3df,2p) and 771-773 kJ mol(-1) by B3-MP2/6-311 + G(3df,2p). The calculated values are 25-39 kJ mol(-1) lower than the previous estimate by Srinivasan et al. (Rapid Commun. Mass Spectrom. 1998; 12: 328) that was based on competitive dissociations of proton-bound dimers (the kinetic method). The calculated threshold dissociation energies predicted the formation of CH(3)CO(+) + syn - HOONO(2) and CH(3)COOOH + NO(2)(+) to be the most favorable fragmentations of protonated PAN that required 83 and 89 kJ mol(-1) at the respective thermochemical thresholds at 298 K. The previously observed dissociation to CH(3)COOH + NO(3)(+) was calculated by effective QCISD(T)/6-311 + G(3df,2p) to require 320 kJ mol(-1). The disagreement between the experimental data and calculated energetics is discussed.     

Photodissociation dynamics of the ethoxy radical investigated by photofragment coincidence imaging

The photodissociation dynamics of the ethoxy radical (CH3CH2O) have been studied at energies from 5.17 to 5.96 eV using photofragment coincidence imaging. The upper state of the electronic transition excited at these energies is assigned to the C2A'state on the basis of electronic structure calculations. Fragment mass distributions show two photodissociation channels, OH + C2H4 and CH3 + CH2O. The presence of an additional photodissociation channel, identified as D + C2D4O, is revealed in time-of-flight distributions from the photodissociation of CD3CD2O. The product branching ratios and fragment translational energy distributions for all of the observed mass channels are nonstatistical. Moreover, the significant yield of OH + C2H4 product suggests that the mechanism for this channel involves isomerization on the excited-state surface. Photodissociation at a much lower yield is seen following excitation at 3.91 eV, corresponding to a vibronic band of the B2A' <-- X2A' transition.     

Thermal decomposition of peroxy acetyl nitrate CH3C(O)OONO2

The thermal decomposition of peroxy acetyl nitrate (PAN) is investigated by low pressure flash thermolysis of PAN highly diluted in noble gases and subsequent isolation of the products in noble gas matrices at low temperatures and by density functional computations. The IR spectroscopically observed formation of CH3C(O)OO and H2CCO (ketene) besides NO2, CO2, and HOO implies a unimolecular decay pathway for the thermal decomposition of PAN. The major decomposition reaction of PAN is bond fission of the O-N single bond yielding the peroxy radical. The O-O bond fission pathway is a minor route. In the latter case the primary reaction products undergo secondary reactions whose products are spectroscopically identified. No evidence for rearrangement processes as the formation of methyl nitrate is observed. A detailed mapping of the reaction pathways for primary and secondary reactions using quantum chemical calculations is in good agreement with the experiment and predicts homolytic O-N and O-O bond fissions within the PAN molecule as the lowest energetic primary processes. In addition, the first IR spectroscopic characterization of two rotameric forms for the radical CH3C(O)OO is given.     

Mechanistic and kinetic study of the CH3CO + O2 reaction

Potential-energy surface of the CH3CO + O2 reaction has been calculated by ab initio quantum chemistry methods. The geometries were optimized using the second-order Moller-Plesset theory (MP2) with the 6-311G(d,p) basis set and the coupled-cluster theory with single and double excitations (CCSD) with the correlation consistent polarized valence double zeta (cc-pVDZ) basis set. The relative energies were calculated using the Gaussian-3 second-order Moller-Plesset theory with the CCSD/cc-pVDZ geometries. Multireference self-consistent-field and MP2 methods were also employed using the 6-311G(d,p) and 6-311++G(3df,2p) basis sets. Both addition/elimination and direct abstraction mechanisms have been investigated. It was revealed that acetylperoxy radical [CH3C(O)OO] is the initial adduct and the formation of OH and alpha-lactone [CH2CO2(1A')] is the only energetically accessible decomposition channel. The other channels, e.g., abstraction, HO2 + CH2CO, O + CH3CO2, CO + CH3O2, and CO2 + CH3O, are negligible. Multichannel Rice-Ramsperger-Kassel-Marcus theory and transition state theory (E-resolved) were employed to calculate the overall and individual rate coefficients and the temperature and pressure dependences. Fairly good agreement between theory and experiments has been obtained without any adjustable parameters. It was concluded that at pressures below 3 Torr, OH and CH2CO2(1A') are the major nascent products of the oxidation of acetyl radicals, although CH2CO2(1A') might either undergo unimolecular decomposition to form the final products of CH2O + CO or react with OH and Cl to generate H2O and HCl. The acetylperoxy radicals formed by collisional stabilization are the major products at the elevated pressures. In atmosphere, the yield of acetylperoxy is nearly unity and the contribution of OH is only marginal.     

Quantum chemical and statistical rate study of the reaction of O(3P) with allene: O-addition and H-abstraction channels

The lowest-lying triplet and singlet potential energy surfaces for the O(3P) + CH2=C=CH2 reaction were theoretically characterized using the complete basis set model chemistry, CBS-QB3. The primary product distributions for the multistate multiwell reactions on the individual surfaces were then determined by RRKM statistical rate theory and weak-collision master equation analysis using the exact stochastic simulation method. The results predict that the electrophilic O-addition pathways on the central and terminal carbon atom are dominant up to combustion temperatures. Major predicted end-products for the addition routes include CO + C2H4, 3CH2 + H2CCO, and CH2=C*-CHO + H*, in agreement with experimental evidence. CO + C2H4 are mainly generated from the lowest-lying singlet surface after an intersystem crossing process from the initial triplet surface. Efficient H-abstraction pathways are newly identified and occur on two different electronic state surfaces, 3A' and 3A', resulting in OH + propargyl radicals; they are predicted to play an important role at higher temperatures in hydrocarbon combustion chemistry and flames, with estimated contributions of ca. 35% at 2000 K. The overall thermal rate coefficient k(O + C3H4) at 200-1000 K was computed using multistate transition state theory: k(T) = 1.60 x 10(-17) x T (2.05) x exp(-90 K/T) cm3 molecule(-1) s(-1), in good agreement with experimental data available for the 300-600 K range.     

Mechanism for the gas‐phase hydrogen fluoride‐mediated decomposition of peroxyacetyl nitrate (PAN) studied by DFT method

Density functional theory has been used to study the mechanism of the decomposition of peroxyacetyl nitrate (CH₃C(O)OONO₂) in hydrogen fluoride clusters containing one to three hydrogen fluoride molecules at the B3LYP/6‐311++G(d,p) and B3LYP/6‐311+G(3df,3pd) levels. The calculations clarify some of the uncertainties in the mechanism of PAN decomposition in the gas phase. The energy barrier decreases from 30.5 kcal mol^?1 (single hydrogen fluoride) to essentially 18.5 kcal mol^?1 when catalyzed by three hydrogen fluoride molecules. As the size of the hydrogen fluoride cluster is increased, PAN shows increasing ionization along the O? N bond, consistent with the proposed predissociation in which the electrophilicity of the nitrogen atom is enhanced. This reaction is found to proceed through an attack of a fluorine to the PAN nitrogen in concert with a proton transfer to a PAN oxygen. On the basis of our calculations, an alternative reaction mechanism for the decomposition of PAN is proposed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

An ab initio molecular orbital study of the mechanism for the gas-phase water-mediated decomposition and the formation of hydrates of peroxyacetyl nitrate (PAN)

There is uncertainty in the mechanism for the hydrolysis of peroxyacetyl nitrate (PAN), and experimental attempts to detect products of the direct reaction have been unsuccessful. Ab initio calculations are used to examine the energetics of water-mediated decomposition of gas-phase PAN into acetic acid and peroxynitric acid. On the basis of ab initio calculations, an alternative reaction mechanism for the decomposition of PAN is proposed. The calculations indicate that the barrier for one water addition to PAN is large. However, including additional water molecules reveals a substantially lower energy route. The calculations suggest that the formation of PAN hydrate complexes are energetically favorable and stable. Additional waters are increasingly efficient at stabilizing hydrated PAN.     

Mechanistic study of thermal decomposition of isoprene (2-methyl-1,3-butadiene) using flash pyrolysis supersonic jet VUV photoionization mass spectrometry

The thermal decomposition of isoprene up to 1400 K was performed by flash pyrolysis with an approximately 100 mus time scale. This pyrolysis was followed by supersonic expansion to isolate the reactive intermediates and initial products, and detection was accomplished by vacuum ultraviolet single photon ionization time-of-flight mass spectrometry (VUV-SPI-TOFMS) at lambda = 118.2 nm. Products CH(3), C(2)H(4), C(3)H(3), C(3)H(4), C(4)H(4), C(4)H(5), C(5)H(6), C(5)H(7), and C(6)H(6) were directly observed and provide mechanistic insights to the isoprene pyrolysis. At temperatures >or= approximately 1200 K, the molecular elimination of ethene to form C(3)H(4) and sigma bond homolysis producing C(4)H(5) and CH(3) radicals are competitive reaction pathways. The molecular elimination of acetylene to form C(3)H(6) was minimal and direct C(2)-C(3) sigma bond homolysis was not observed. The C(3)H(3) radicals are also observed, as a result of hydrogen loss of C(3)H(4) by pyrolysis or hydrogen abstraction by the CH(3) radical from C(3)H(4). Above approximately 1250 K, production of C(6)H(6) was observed and identified as the combination product of the C(3)H(3) radicals.     

Detection of peroxyacetyl nitrate in air using chemiluminescence aerosol detector

A method for the rapid and sensitive determination of peroxyacetyl nitrate (PAN) in air based on a chemiluminescence reaction with an alkaline solution of luminol in the chemiluminescence aerosol detector is described. The PAN is chromatographically separated from nitrogen dioxide and ozone in a packed column filled with 5 % OV-1 on Chromosorb 30/60 and the eluted PAN is detected via the direct reaction with the luminol solution consisting of 0.002 mol L^?1 luminol, 1 vol. % Brij-35 and 0.1 mol L^?1 KOH. The limit of detection is 14.9 ng m^?3 (3 ppt) of PAN. Alternatively, the PAN after separation is thermally converted to NO₂ which is detected by the chemiluminescence reaction with a solution consisting of 0.002 mol L^?1 luminol, 0.5 mol L^?1 KOH, 0.2 mol L^?1 Na₂SO₃, 0.1 mol L^?1 KI, 0.05 mol L^?1 EDTA and 0.5 vol. % triton X-100. The alternative approach affords the simultaneous determination of PAN and NO₂. The limit of detection is 50 ppt of PAN and 50 ppt of NO₂. The time resolution is 3 min. The method was applied to the measurement of ambient peroxyacetyl nitrate in air.     

Quantum chemical and theoretical kinetics study of the O(3P) + C2H2 reaction: a multistate process

The potential energy surfaces of the two lowest-lying triplet electronic surfaces 3A' and 3A' for the O(3P) + C2H2 reaction were theoretically reinvestigated, using various quantum chemical methods including CCSD(T), QCISD, CBS-QCI/APNO, CBS-QB3, G2M(CC,MP2), DFT-B3LYP and CASSCF. An efficient reaction pathway on the electronically excited 3A' surface resulting in H(2S) + HCCO(A2A') was newly identified and is predicted to play an important role at higher temperatures. The primary product distribution for the multistate multiwell reaction was then determined by RRKM statistical rate theory and weak-collision master equation analysis using the exact stochastic simulation method. Allowing for nonstatistical behavior of the internal rotation mode of the initial 3A' adducts, our computed primary-product distributions agree well with the available experimental results, i.e., ca. 80% H(2S) + HCCO(X2A' + A2A') and 20% CH2(X3B1) + CO(X1sigma+) independent of temperature and pressure over the wide 300-2000 K and 0-10 atm ranges. The thermal rate coefficient k(O + C2H2) at 200-2000 K was computed using multistate transition state theory: k(T) = 6.14 x 10(-15)T (1.28) exp(-1244 K/T) cm3 molecule(-1) s(-1); this expression, obtained after reducing the CBS-QCI/APNO ab initio entrance barriers by 0.5 kcal/mol, quasi-perfectly matches the experimental k(T) data over the entire 200-2000 K range, spanning 3 orders of magnitude.     

Ab initio study of the ground state and conformational stability of peroxyacetyl nitrate in internal rotation about the peroxide bond

The molecular and electronic structure of the ground state of peroxyacetyl nitrate (PAN) was calculated by the unrestricted Hartree-Fock-Roothaan method with the use of the standard 3–21G and 6–31G basis set. The potential curve of the internal rotation about the peroxide bond of PAN was calculated with the 6–31G basis set. The curve contains two maxima. The ground state of PAN is characterized by a structure in which groups of atoms adjacent to the peroxide bond lie in planes that are perpendicular to each other (the dihedral angle ϱ(COON) is 89.9°). The calculated barriers to rotation are 19.6 and 66.8 kJ mol⁻¹. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 600–604, April, 1998.     

Thermal decomposition of methyl 2-azidopropionate studied by UV photoelectron spectroscopy and matrix isolation IR spectroscopy: heterocyclic intermediate vs imine formation

Methyl 2-azidopropionate (N(3)CH(3)CHCOOCH(3), M2AP) has been synthesized and characterized by different spectroscopic methods, and the thermal decomposition of this molecule has been investigated by matrix isolation infrared (IR) spectroscopy and ultraviolet photoelectron spectroscopy (UVPES). Computational methods have been employed in the spectral simulation of both UVPES and matrix IR spectra and in the rationalization of the thermal decomposition results. M2AP presents a HOMO vertical ionization energy (VIE) of 9.60 ± 0.03 eV and contributions from all four lowest-energy conformations of this molecule are detected in the gas phase. Its thermal decomposition starts at ca. 400 °C and is complete at ca. 650 °C, yielding N(2), CO, CO(2), CH(3)CN, and CH(3)OH as the final decomposition products. Methyl formate (MF) and CH(4) are also found during the pyrolysis process. Analysis of the potential energy surface of the decomposition of M2AP indicates that M2AP decomposes preferentially into the corresponding imine (M2IP), through a 1,2-H shift synchronous with the N(2) elimination (Type 1 mechanism), requiring an activation energy of 160.8 kJ/mol. The imine further decomposes via two competitive routes: one accounting for CO, CH(3)OH, and CH(3)CN (ΔE(G3) = 260.2 kJ/mol) and another leading to CO(2), CH(4), and CH(3)CN (ΔE(G3) = 268.6 kJ/mol). A heterocyclic intermediate (Type 2 mechanism)-4-Me-5-oxazolidone-can also be formed from M2AP via H transfer from the remote O-CH(3) group, together with the N(2) elimination (ΔE(G3) = 260.2 kJ/mol). Finally, a third pathway which accounts for the formation of MF through an M2AP isomer is envisioned.     

IR/UV double resonant spectroscopy of the methyl radical: determination of nu3 in the 3p(z) Rydberg state

IR+UV double resonant ion-dip and ion-enhancement spectroscopies are employed to study the nu3 asymmetric CH stretch vibration fundamental of CH3 in the ground and 3p(z) Rydberg electronic states. CH3 radical is synthesized in the supersonic jet expansion by flash pyrolysis of azomethane (CH3NNCH3) prior to the expansion. The Q band of the 3(1) (1) 3p(z)<--X transition of CH3, not detected by conventional UV resonantly enhanced multiphoton ionization (REMPI) spectroscopy, is determined to lie at 59,898 cm(-1) using IR+UV REMPI spectroscopy. Energy of the asymmetric CH stretch of CH3 in the 3p(z) Rydberg state, nu3(3p(z)), is 3087 cm(-1), redshifted by approximately 74 cm(-1) with respect to ground state nu3(X).