1112
J. Phys. Chem. A 2003, 107, 1112-1118
Vibrational and Electronic Spectroscopy of Sulfuric Acid Vapor Paul E. Hintze,† Henrik G. Kjaergaard,‡ Veronica Vaida,*,† and James B. Burkholder§ Department of Chemistry and Biochemistry and CooperatiVe Institute for Research in EnVironmental Sciences, Campus Box 215, UniVersity of Colorado, Boulder, Colorado 80309, Aeronomy Laboratory, NOAA, 325 Broadway, Boulder, Colorado 80305-3328, and Department of Chemistry, UniVersity of Otago, P.O. Box 56, Dunedin, New Zealand ReceiVed: June 22, 2002; In Final Form: October 27, 2002
We have measured and analyzed the infrared (IR), near-infrared (NIR) and vacuum ultraviolet (VUV) absorption spectra of vapor-phase sulfuric acid (H2SO4). Transitions associated with the fundamental vibrations and the first and second OH stretching overtones of this molecule have been identified. Our measured vibrational spectrum extends and complements those in the literature and agrees well with ab initio calculated spectra. We have calculated the fundamental and overtone OH stretching intensities with the use of a simple anharmonic oscillator local-mode model with ab initio calculated dipole-moment functions. Theory and experiment have been used to investigate the OH stretching vibrational overtones of H2SO4 and indicate that the OH stretching mode in H2SO4 is an important aspect of the spectroscopy of this atmospheric chromophore. We have attempted to measure the VUV spectrum of vapor-phase sulfuric acid and, in the absence of observed bands, give upper bounds to the photoabsorption cross section. We conclude that H2SO4 absorbs in the IR and NIR regions, with the OH stretching vibration playing the dominant role, and that the electronic excitation of H2SO4 will only be significant at very high energies, well above those available from the sun in the earth’s atmosphere.
Introduction The fundamental spectroscopic properties of vapor-phase sulfuric acid are required to evaluate the role of this atmospheric chromophore. The technical challenge of obtaining the spectra of this molecule is twofold: the vapor pressure of sulfuric acid is very low,1 and spectra are complicated by the presence of SO3 and H2O, which are in equilibrium with H2SO4 and absorb radiation at similar energies. The low vapor pressure can be overcome by working at elevated temperatures, and subtraction of the reference spectra of SO3 and H2O can minimize the spectral interference. Despite the importance of H2SO4 in the atmosphere, only a few experimental spectroscopic studies have been reported. The structure of H2SO4 was determined by microwave spectroscopy.2 The studies in the IR region3,4 have identified many of the fundamental transitions of H2SO4. For the SO2 (SdO) symmetric stretching vibration alone, the integrated absorption coefficient has been reported.5 The electronic excited states of H2SO4 vapor have been elusive. The only previous UV study did not detect any absorption that could be attributed to sulfuric acid and set an upper bound for the H2SO4 absorption cross section of 10-21 cm2 molecule-1 in the 30 300-51 300 cm-1 range.6 In this paper, we present experimental and theoretical studies of H2SO4 vapor to complement and extend those available in the literature. We have measured the vibrational spectrum of vapor-phase sulfuric acid from 500 to 10 500 cm-1 and have assigned bands associated with fundamental stretching vibrations and the first and second OH stretching overtones. We have compared our recorded spectrum with results of ab initio * Corresponding author. E-mail:
[email protected]. † University of Colorado. ‡ On sabbatical at Cooperative Institute for Research in Environmental Sciences, University of Colorado. § NOAA.
calculated fundamental vibrational frequencies and intensities. We focused on developing an appropriate model for the OH stretching vibrations. Toward this end, we have calculated the OH stretching vibrational-band frequencies and intensities of H2SO4 with an anharmonic oscillator (AO) local-mode model. We used experimental local-mode parameters and ab initio calculated dipole-moment functions in our AO local-mode model. The large-amplitude motion associated with XH stretching vibrations, where X is C, N, or O, has been well explained by the harmonically coupled anharmonic oscillator (HCAO) localmode model.7-10 CH stretching overtone intensities have been successfully predicted with the use of vibrational wave functions obtained with the HCAO local-mode model and ab initio calculated dipole-moment functions.11-15 Kjaergaard and Henry previously found that accurate absolute overtone intensities can be obtained with the Hartree-Fock (HF) self-consistent-field method, provided a reasonably sized 6-311++G(2d,2p) basis set is used.16 The hybrid density functional theory, B3LYP, and quadratic configuration interaction including singles and doubles (QCISD) theory improve the calculated intensities primarily in the fundamental region.17,18 Here, we use ab initio calculations performed at the HF, B3LYP, and QCISD levels of theory with the 6-311++G(2d,2p) basis set. The calculated OH stretching frequencies and intensities are compared with experimental results and confirm that the local-mode model provides an appropriate description of the OH overtone vibrations of H2SO4. To search for the elusive electronic spectrum of H2SO4, we have extended previous measurements6 into the vacuum ultraviolet (VUV) region between 51 300 and 71 400 cm-1. We have compared our measurements with calculations of the H2SO4 electronic transition energy19 and found agreement in the conclusion that the electronic excitations in H2SO4 require very high energy.
10.1021/jp0263626 CCC: $25.00 © 2003 American Chemical Society Published on Web 01/31/2003
Sulfuric Acid Vapor
J. Phys. Chem. A, Vol. 107, No. 8, 2003 1113
Theory and Calculations
function as a series expansion in the OH displacement coordinate,15,21
The geometry of H2SO4 was optimized at the HF, B3LYP, and QCISD levels of theory with the 6-311++G(2d,2p) basis set. The vibrational transition intensities of the fundamental normal modes were calculated with the B3LYP/6-311++G(2d,2p) method and the harmonic-oscillator linear dipolemoment (HOLD) approximation within the Gaussian 94 suite of programs.20 We have used a simple AO local-mode model15 to describe the OH stretching vibrational modes in H2SO4. The coupling between the two OH stretching vibrations in H2SO4 will split the two OH stretching vibrations into symmetric and asymmetric vibrations. However, this coupling is small because of the significant spatial separation of the OH bonds. This splitting is not observed in our spectra; thus, we have neglected this coupling in our calculation of the OH stretching fundamental and overtone transitions within the AO local-mode model. The reported intensities are the sum of two OH stretches, which is the same as that seen in the experiment. The AO local-mode model Hamiltonian for an isolated OH stretching oscillator can be written as15
˜ - (V2 + V)ω ˜x (H - E|0〉)/hc ) Vω
(1)
where E|0〉 is the energy of the vibrational ground state and ω ˜ and ω ˜ x are the local-mode frequency and anharmonicity (in cm-1) of the OH oscillator. The eigenstates of the AO Hamiltonian are taken as Morse-oscillator wave functions and are denoted by |V〉, where V is the vibrational quantum number. The local-mode parameters, ω ˜ and ω ˜ x, can either be derived from a Birge-Sponer fit to the observed local-mode peak positions or calculated from an ab initio calculated potentialenergy curve.21 The Morse-oscillator frequency ω ˜ and anharmonicity ω ˜ x can be expressed in terms of the reduced mass of the oscillator and the second- and third-order ab initio calculated force constants Fii and Fiii by21
ω ˜ ) ω ˜x)
(FiiGii)1/2 ω ) 2πc 2πc
(2)
( )
hGii Fiii ωx ) 2πc 72π2c Fii
2
(3)
where Gii is the reciprocal of the reduced mass. The force constants are obtained from a least-squares fit to an ab initio calculated one-dimensional potential-energy curve V(q) as a function of the internal OH stretching displacement coordinate, q. We scale our ab initio calculated local-mode parameters to compensate for deficiencies in the ab initio method.21 The scaling factors were determined as the ratio of calculated to experimental local-mode parameters of H2O.21,22 The uncertainty in ω ˜ x will lead to a small variation in the calculated intensities. The oscillator strength f of a transition from the ground vibrational state |0〉 to a vibrationally excited state |V〉 is given by14,23
bV0|2 fV0 ) 4.702 × 10-7[cm D-2]ν˜ V0|µ
(4)
where ν˜ V0 is the wavenumber of the transition and b µV0 ) 〈V|µ b|0〉 is the transition dipole-moment matrix element in debye (D). The calculated dimensionless oscillator strengths can be converted to units of km mol-1 by multiplication by 5.33 × 106 km mol-1.14 The vibrational wave functions are determined by the Hamiltonian eq 1, and we express the dipole-moment
b µ (q) )
∑i bµiqi
(5)
where b µi is 1/i! times the ith-order derivative of the dipolemoment function with respect to q. The coefficients b µi are obtained from a least-squares fit to an ab initio calculated onedimensional dipole moment grid, b µ(q). The one-dimensional grid is calculated by displacing the OH bond by (0.2 Å from the equilibrium position in steps of 0.05 Å. At each grid point, the energy and dipole moment is calculated to provide both V(q) and b µ(q). The dipole moments are calculated with the use of the generalized density for the specified level of theory, which will provide dipole moments that are the correct analytical derivatives of the energies. The nine-point grid with a step size of 0.05 Å provides good convergence of the dipole-moment derivatives and force constants. The choice of grid and step size is based on previous work.21,24 The optimized geometries and all single-point calculations in the grids were calculated at a specified ab initio method with the use of Gaussian 94. The B3LYP optimizations and single-point calculations were run with an increased integration grid size (Keyword Int ) 99434) to improve the convergence of the dipole derivatives.25 The excited electronic states of sulfuric acid were calculated with the Gaussian 98 suite of programs.26 We have used the configuration interaction including singles (CIS) level of theory with the 6-311++G(d,p) basis set and the microwavedetermined geometry.2 Previously, a CIS/6-31G(d) calculation had been reported;19 however, it has been shown that diffuse functions in the basis set are important in the CIS calculations of excited states.27 Experimental Section The absorption spectrum of H2SO4 vapor was measured in the IR, near-infrared (NIR), and VUV regions with two separate instruments appropriate for the different energy regions studied. The temperature-controlled cells used for the two experiments were similar. The cell used in the IR/NIR regions had been used previously,6 and the VUV cell was designed as a smaller version of this cell. Each cell had four inlet ports, two for the reactants and two for purging the windows, as well as a fifth exit port. The windows were attached using Viton O-ring seals. The condensation on the windows was checked by carefully monitoring the absolute light intensity on successive scans. The cells were wrapped with heating tape, insulation, and a layer of aluminum foil. The longer IR/NIR cell had a layer of copper foil between the glass and the heating tape. Thermocouple gauges were placed on the cell walls between the glass or copper foil and the heating tape to monitor the external temperature. The temperature of the gas inside the cell was measured by inserting a thermocouple into the cell while gases were flowing through at conditions similar to those used in the experiment. Vapor-phase H2SO4 was generated in a 1:1 reaction of SO3 and H2O by titrating SO3 with H2O through a heated side arm of a temperature-controlled cell.6 The amount of vapor-phase H2SO4 formed is a function of temperature. The temperature determined the vapor pressure of H2SO4. High temperatures of 130-150 °C were required to allow a measurable concentration of H2SO4 to be present. However, at temperatures above 150 °C the reaction shifts to the reactants, reducing the amount of H2SO4 present.
1114 J. Phys. Chem. A, Vol. 107, No. 8, 2003 SO3 was acquired by distillation from fuming sulfuric acid (∼25% SO3 in sulfuric acid). The IR spectrum of the distilled SO3 showed no impurities of H2O (
