Article pubs.acs.org/JPCA
Vibrational Overtone Spectroscopy, Energy Levels, and Intensities of (CH3)3CCCH Yasnahir Perez-Delgado, Jenny Z. Barroso, Lauren A. Garofalo, and Carlos E. Manzanares* Department of Chemistry and Biochemistry, Baylor University, 101 Bagby Avenue, Baylor Sciences Building E-216, Waco, Texas 76706, United States S Supporting Information *
ABSTRACT: The vibrational overtone spectra of the acetylenic (Δυ = 4, 5) and methyl (Δυ = 5, 6) C−H stretch transitions of tert-butyl acetylene [(CH3)3C−CC−H] were obtained using the phase shift cavity ring down (PS-CRD) technique at 295 K. The C−H stretch fundamental and overtone absorptions of the acetylenic (Δυ = 2 and 3) and methyl (Δυ = 2−4) C−H bonds have been obtained using a Fourier transform infrared and near-infrared spectrophotometer. Harmonic frequency ω(ν1) and anharmonicities x(ν1) and x(ν1, ν24) are reported for the acetylenic C−H bond. Molecular orbital calculations of geometry and vibrational frequencies were performed. A harmonically coupled anharmonic oscillator (HCAO) model was used to determine the overtone energy levels and assign the absorption bands to vibrational transitions of methyl C−H bonds. Band strength values were obtained experimentally and compared with intensities calculated in terms of the HCAO model where only the C−H modes are considered. No adjustable parameters were used to get order of magnitude agreement with experimental intensities for all pure local mode C−H transitions.
1. INTRODUCTION The acetylenic C−H fundamental (Δυ = 1) and first overtone (Δυ = 2) region for tert-butylacetylene [(CH3)3C−CC−H] and tert-butylacetylene-d9 [(CD3)3C−CC−H] have been studied previously in a molecular beam absorbing infrared radiation. An optothermal detection method was used to observe the line widths of the rotational transitions and relate them to intramolecular vibrational energy relaxation.1−3 A theoretical study of IVR has been reported for these molecules.4 The low temperature infrared (77 K) and Raman (10 K) spectra of polycrystalline (CH3)3C−CC−H have been recorded.5 Normal coordinate analysis has been done with gas phase infrared frequencies6 and liquid phase Raman frequencies at room temperature.7 Rotational lines have been obtained with microwave spectroscopy to determine the structural parameters of the molecule.8,9 Vibrational frequencies and structural parameters have been calculated.10 Fundamental and overtone studies of acetylenes have acquired new importance because of the discovery of the presence of organic molecules and aerosol particles in the atmosphere, and precipitating solids and liquids on the surface of Titan, the largest satellite of Saturn. The main components are N2 (90%) and CH4 (1−5%), but after being subjected to electric discharge and UV radiation, a large number of different saturated and unsaturated organic molecules are formed. Methods of analysis such as gas chromatography−mass spectrometry (GC-MS) have been used to determine the rich variety of molecules in the atmosphere.11 Infrared (IR) studies alone are hampered because of the large concentrations of © 2012 American Chemical Society
methane in the atmosphere that interfere with the absorption of other hydrocarbons in smaller concentrations. There are advantages using near IR and visible radiation because of the energy separation of the C−H bands in the order methylene < methyl < olefin < acetylenic in different regions of the near IR and visible spectra. Modeling the atmosphere of Titan will require the knowledge of high vibrational levels for identification and band intensities for concentration determinations. These measurements will complement analysis by IR and GC-MS methods. In this paper, we present a complete study of the fundamental and overtone spectra corresponding to the C−H acetylenic stretch (Δυ = 1−5) and the C−H methyl stretch (Δυ = 1−6) of tert-butyl acetylene. The high overtone levels were obtained using the phase-shift cavity ring down technique which allowed the determination of the peak positions and intensities of the bands. The study includes the determination of (1) spectroscopic constants such as harmonic frequencies and anharmonicities of the different C−H bonds, (2) ab initio calculation of molecular geometry and vibrational frequencies, (3) the use of the harmonically coupled anharmonic oscillator (HCAO) model to obtain energy levels and assign vibrational transitions, and (4) the use of a molecular orbital calculation of dipole moments as a function of the vibrational coordinates to Received: August 25, 2011 Revised: January 20, 2012 Published: January 21, 2012 2071
dx.doi.org/10.1021/jp208225g | J. Phys. Chem. A 2012, 116, 2071−2079
The Journal of Physical Chemistry A
Article
respectively. The internuclear distances and angles of the most stable configuration were obtained (Table S1). The structure of this molecule involves three equivalent C−Hs bonds in σv planes that contain the methyl carbon and the C−CC−H linear fragment. The remaining six equivalent C−Ha bonds exist in pairs on opposite sides of each σv plane. The calculated C−Hs bond length is 0.10859 nm (0.10942 nm) and the C−Ha bond length is 0.10843 nm (0.10924 nm). The acetylenic C−H bond length is 0.10548 nm (0.10622 nm). The number in parentheses is from the DFT calculation. The configuration with C3v symmetry possesses 3N − 6 = 42 normal modes with the symmetry representations 10A1 + 4A2 + 14E. The calculated frequencies were scaled (Table S2) and compared with the observed IR frequencies.5,6 3.2. FT-IR: Acetylenic C−H Stretch. The spectra shown in Figure 1 correspond to transitions from υ = 0 to levels 1, 2, and
obtain the oscillator strengths that are compared with experimental intensities.
2. EXPERIMENTAL SECTION The vibrational overtone spectra of the acetylenic and methyl C−H stretches of tert-butyl acetylene (C6H10) were obtained for the Δυ = 1−3 and Δυ = 1−4 transitions, respectively. These spectral regions were measured using a Thermo-Nicolet (Nexus 670) Fourier transform spectrophotometer with a resolution of 1 cm−1 and a multiple reflection cell with an optical path length of 6.6 m at T = 295 K. The overtone spectra (Δυ = 4 and 5) for the C−H acetylenic and for the methyl C−H stretches (Δυ = 5 and 6), were also obtained at 295 K using the phase Shift Cavity Ring Down (PS-CRD) technique. The experimental set up for the PS-CRD technique has been given in previous publications12,13 and only a short summary will be given here. Briefly, a laser system consisting of a continuous wave Nd:YAG laser was used to pump a Titanium Sapphire ring laser with a scanning range between 12200 and 14300 cm−1 or a dye laser (Rhodamine 610) to excite the molecules in the range from 14800 to 16700 cm−1. The excitation laser beam was modulated with an electro-optic modulator. The modulated beam passes through the optical cavity and is detected with a photomultiplier. The phase difference between the signal exiting the cavity and the signal entering the cavity is measured with a dual phase lock-in amplifier. The phase angle is recorded as a function of wavenumber (ν). The phase shift (ϕ) is related to the time that the light spends in the cavity or ring-down time (τ) by the equation: tan ϕ = 2πfτ, where f is the modulation frequency. For a cavity filled with an absorbing gas, the ringdown time is τ(ν) =
S c[(1 − R ) + α(ν)S]
(1)
The time (τ) is related to the reflectivity of the mirrors (R), the speed of light (c), the absorption coefficient (α) of the sample, and the length (S ) of the optical cavity. The absorption spectrum of the background or empty cavity [τo(ν)c]−1 = [(1 − R)/S ] is subtracted from the absorption spectrum of the sample plus the background (τ(ν)c)−1 to obtain the absorption of the sample. The sample (98%) was purchased from Aldrich. Calibration of the laser dye was done obtaining the optogalvanic spectrum of a hollow cathode lamp filled with neon. The advantage of the phase shift technique is that no signal averaging is necessary and the spectra can be obtained in a very short time. We have shown12 that if the laser bandwidth is smaller than the absorption band, the measured cross sections are as good as the ones obtained with conventional absorption techniques. In this investigation the absorption bands are obtained at different pressures and the integrated bands are plotted versus the density of the gas sample to obtain the experimental cross section to be compared with theoretical calculations.
3. RESULTS 3.1. Molecular Structure and Fundamental Frequency Calculations. tert-Butylacetylene (C6H10) is a symmetric top molecule that belongs to the C3v point group. Computations of molecular structure (Figure S1) and vibrational frequencies were performed using the Gaussian 03 program package.14 The Hartree−Fock (HF) and DFT (B3LYP) methods were used with the standard 6-311G (3d,p) and 6-311G(d,p) basis sets,
Figure 1. Infrared spectra of the acetylenic C−H absorptions of C6H10 at 295 K. The spectra were recorded with a FT-IR spectrophotometer in a 6.6 m sample cell at a pressure of 0.2 Torr for the fundamental (Δυ1 = 1), a pressure of 9.2 Torr for the first overtone (Δυ1 = 2), and a pressure of 200 Torr for the second overtone (Δυ1 = 3). 2072
dx.doi.org/10.1021/jp208225g | J. Phys. Chem. A 2012, 116, 2071−2079
The Journal of Physical Chemistry A
Article
3 of the acetylenic C−H stretch. These spectra were taken using the FT spectrophotometer. Figure 1 (top) shows the PQR structure for the acetylenic C−H fundamental centered at ν1 = 3328 cm−1, and a small shoulder at the low frequency end of the P branch. The fundamental spectrum looks similar to other molecules of the type R−CC−H such as trifluoropropyne15,16 and propyne.17 Also, the fundamental acetylenic C−H stretch of tert-butylacetylene and these similar molecules nearly coincide in frequency, and all show a characteristic hot band on the lower energy side. This weaker band centered at 3308 cm−1 could be assigned as a hot band originating from the ν24 vibrational frequency at 634 cm−1 or the transition ν24 → (ν1 + ν24). This band arises from nonresonant intramolecular coupling of the acetylenic C−H stretch (ν1) and the CC−H bending mode (ν24). In trifluoropropyne,15,18 hot band transitions appear with overtones of ν1, mainly the CC−H bend (ν7 = 686 cm−1) and the C−CC bend (ν10 = 171 cm−1). In propyne,19−21 the hot band transitions associated with overtones of ν1 are ν9 = 633 cm−1 and ν10 = 327 cm−1. In general, the hot bands involving the CC−H bend are well separated from overtones of ν1, while the ones that include the C−CC bend can only be observed at high resolution because they overlap the main band. Duval and Quack18 in a high resolution (variable temperature) study of C−H acetylenic bands of trifluoropropyne measured the hot band transitions: nν10 → (υν1 + nν10), with n = 1−5 and υ = 1−3. The first overtone (2ν1) is shown in Figure 1 (middle) and exhibits the strong narrow acetylenic C−H absorption (Q branch), as well as a small peak to the low frequency side. A similar low frequency absorption is observable for the 3ν1 transition in Figure 1 (bottom). Because of its lower frequency relative to the ν1 overtones and its proximity to them, it is most probably a hot band corresponding to one observed in the fundamental. In addition, the separation in energy between the maximum of main absorption and the low-frequency peak increases by a multiple of the vibrational quantum number of the excited level. 3.3. FT-IR: Methyl C−H Stretch. It is expected that this molecule will show two overtone bands in the methyl C−H regions corresponding to the two nonequivalent C−H bonds (C−Hs and C−Ha) calculated previously in section 3.1. The fundamental and first overtone (Δυ = 1 and 2) of the methyl C−H regions are shown in Figure 2. The main peak in the fundamental (Δυ = 1) region is at 2978 cm−1. The asymmetric methyl C−H frequencies associated with vibrations in this region are ν2 = 2977 cm−1, ν15 = 2978 cm−1, and ν16 = 2976 cm−1. The first overtone (Δυ = 2) is usually the region where the transition from normal to local mode occurs. It shows several peaks besides the ones labeled tentatively in Figure 2 as the local mode frequencies 2νa and 2νs. To the left of 2νs the peak at 5679 cm−1 could be assigned to ν2 + 2ν6 = 5703 cm−1 or ν16 + 2ν6 = 5702 cm−1. The first peak to the right of 2νa at 5939 cm−1 could be ν2 + 2ν5 = 5928 cm−1 or ν16 + 2ν5 = 5927 cm−1. The double peak at the right-hand side of the spectrum at 5948 cm−1 could be 2ν15 = 5956 cm−1 or 2ν16 = 5952 cm−1. The second and third overtones (Δυ = 3 and 4) are shown in Figure 3. The two C−H bonds have different anharmonicity constants. Their separation increases as a function of the quantum number. Complete assignments of local modes, local mode notation, and energies will be presented later in section 4.2. 3.4. PS-CRD: Acetylenic and Methyl C−H Spectra. Using the PS-CRD technique, the absorption spectrum of the
Figure 2. Infrared spectra of the methyl C−H absorptions of C6H10 at 295 K. The spectra were recorded with a FT-IR spectrophotometer in a 6.6 m sample cell at a pressure of 0.2 Torr for the fundamental (Δυ = 1) and a pressure of 9.2 Torr for the first overtone (Δυ = 2).
4ν1 acetylenic C−H stretch and the (Δυ = 5) methyl transitions of C6H10 is shown in Figure 4 (top). The strong acetylenic C−H absorption is shown on the left-hand side. The band is identified as 4ν1, and the small peak at the low frequency side is the hot band indicated in Figure 4 as 4ν* that corresponds to the transition ν24 → (ν24 + 4ν1). On the righthand side of the spectrum, the methyl C−H transitions (Δυ = 5) are shown. The spectrum of Figure 4 (bottom) was also obtained using the PS-CRD technique. It shows similar transitions to Figure 4 (top) for the acetylenic 5ν1 and methyl (Δυ = 6). The bands do not overlap but become closer in energy.
4. DISCUSSION 4.1. Spectroscopic Parameters: Acetylenic C−H Stretch. The energy difference corresponding to a pure local-mode transition 0 → υ for the acetylenic C−H bond of tert-butylacetylene is described by the equation ΔE /υ = ω(ν1) − (υ + 1)x(ν1)
(2)
Similarly, for a hot-band transition, the energy difference is given by ΔE /υ = ω(ν1) − (υ + 1)x(ν1) − x(ν1, ν24)
(3)
where ω(ν1) is the acetylenic harmonic frequency (in cm−1), x(ν1) is the local-mode anharmonicity, and x(ν1, ν24) is the local mode−normal mode anharmonicity. 2073
dx.doi.org/10.1021/jp208225g | J. Phys. Chem. A 2012, 116, 2071−2079
The Journal of Physical Chemistry A
Article
Figure 4. Deconvoluted PS-CRD spectra of the acetylenic and methyl C−H absorptions of C6H10 at 295 K. (Top) The acetylenic overtone is indicated as 4ν1 and the hot band transition as 4ν* that means (ν24 → (ν24 + 4ν1)), the in-plane methyl absorption as 5νs and the out-ofplane as 5νa. The pressure was 200Torr. (Bottom) The acetylenic overtone is indicated as (5ν1) and the hot band transition as 5ν* (or ν24 → (ν24 + 5ν1)), the in-plane methyl absorption as 6νs and the outof- plane as 6νa . The pressure was 200 Torr.
Figure 3. Deconvoluted infrared spectra of the methyl C−H absorptions of C6H10 at 295 K. The spectra were recorded with a FT-IR spectrophotometer in a 6.6 m sample cell at a pressure of 200 Torr for the second and third overtones (Δυ = 3 and 4).
The observed wavenumbers for transitions 0 → υν1 of the acetylenic C−H bands are presented in Table 1. With the experimental points, a Birge−Sponer plot of (ΔE/υ) versus (υ + 1) was obtained using eq 2. From the slope and intercept of the straight line (Figure S2), the spectroscopic constants ω(ν1) and x(ν1) are obtained for the acetylenic C−H. A similar plot was made with the experimental energies assigned as transitions ν24 → (ν24 + υν1) obtained for the small absorption on the low energy side of each acetylenic band. Using eq 3, a straight line was obtained. The constants: ω(ν1) and x(ν1) and x(ν1, ν24) were calculated. The harmonic frequency and anharmonicities have been directly associated with the acetylenic C−H vibration (ν1) because this vibrational mode behaves like a local mode even for the fundamental and first overtone transitions (Δυ = 1 and 2) that usually behave like normal modes. A summary of experimental peak positions, calculated wavenumbers, and local mode assignments are presented in Table 1. 4.2. Methyl C−H Transitions: HCAO Model and Energy Levels. Following the equations and notation given by Henry and co-workers22−24 for methyl groups, the pure local mode C−H transitions are described by the Birge−Sponer equation: ΔE /υ = ωi − (υ + 1)ωi
xi i = 1, 2, and 3
methyl peak wavenumbers. Harmonic and anharmonicity constants are shown in Table 2. The harmonically coupled anharmonic oscillators (HCAO) model was used to obtain suitable vibrational energies for the methyl groups. According to Kjaergaard et al.,23 the model neglects interactions among the three methyl groups of the molecule. In a methyl group, the coupling between the C−H stretching modes and the bending modes is also neglected, and the Hamiltonian is the sum of three (two of which are identical) Morse oscillators that are harmonically coupled. The states in each methyl group are described by three quantum numbers with the notation |υ1υ2⟩±|υ3⟩, where υ1 and υ2 are the vibrational quanta in the two C−Ha oscillators, respectively, and υ3 is the number of vibrational quanta in the C−Hs oscillator. The ± refers to the symmetry of the two equivalent C−H, wave functions with respect to reflection in the skeletal plane. The zeroth-order Hamiltonian H0 can be written as
(4)
((H 0 − E|000|0⟩)/hc)
The harmonic frequencies ω1 = ω2 and anharmonicities ω1x1 = ω2x2 correspond to the two C−Ha or out-of-plane C−H oscillators, and the constants ω3 and ω3x3 are assigned to the single C−Hs or the in-plane C−H oscillator. Table 1 shows the
= (υ1 + υ2)ω1 − (υ12 + υ22 + υ1 + υ2)ω1x1 + υ3ω3 − (υ32 + υ3)ω3x3 2074
(5)
dx.doi.org/10.1021/jp208225g | J. Phys. Chem. A 2012, 116, 2071−2079
The Journal of Physical Chemistry A
Article
and
Table 1. Observed and Calculated Peak Position of Acetylenic and Methyl Local Mode Transitions of C−H Bonds of tert-Butylacetylene (C6H10) Δυ
observed
calculated
3308.3 3328.3 5729.2 5763.5 6517.0 6555.9 8434.7 8469.6 9622.3 9682.0 10998.2 11063.5 12643.6 12724.0 13489.0 13574.5 15517.5 15624.0 15841.6 15926.8
2922 2937 3309 3329 5731 5761 6517 6557 8427 8473 9623 9684 11011 11072 12628 12710 13483 13559 15531 15636 15842 15933
1
2
3
4
5
6
1 Hinter * (a a + a +a +) − γ* (a a + a +a + = − γ12 1 2 1 2 1 3 13 1 3 hc
assignment/transition νs νa ν24 → (ν24 0 → ν1 2νs 2νa ν24 → (ν24 0 → 2ν1 3νs 3νa ν24 → (ν24 0 → 3ν1 4νs 4νa ν24 → (ν24 0 → 4ν1 5νs 5νa ν24 → (ν24 0 → 5ν1 6νs 6νa
+ a2a3 + a2+a3+) + ν1)
where the coupling parameters are defined by ′ = ( γ − ϕ )ω γ12 12 1 12
HF/6-311G (3d,p)
DFT/6-311G(d,p)
ω(ν1) = 3430 ± 3 (cm−1) ωi ωixi iso νCH ν|00⟩ |1⟩ ν|10⟩+|0⟩
x(ν1) = 50.4 ± 0.8 C−Ha 3050 ± 4 56.3 ± 0.8 3219
ν|10⟩−|0⟩
3240
γ′12 γ′13 iso νCH ν|00⟩ |1⟩ ν|10⟩+|0⟩
* = ( γ + ϕ )ω γ12 12 1 12
γij = −
+ 4ν1)
+ 5ν1)
x(ν1, ν24) = 19 ± 1 C−Hs 3034 ± 4 56.2 ± 0.8 3199 3163
3197 3163
3225 3236
γ′12 γ′13
23
20
o The energy E|00⟩|0⟩ is the zeroth-order energy of the ground state. States that have the same total number of vibrational quanta υ = υ1 + υ2 + υ3 are said to belong to the same manifold. The HCAO local model includes in the perturbation only terms that are quadratic in the momentum or the position operators. Henry et al.24,25 introduced the creation a+ and annihilation a operators in place of the momentum and position operators. Thus, the perturbation can be written as 1 1 + Hinter , where H1 = Hintra
1 Hintra = − γ′12 (a1a2+ + a1+a2) − γ′13 (a1a3+ + a1+a3 hc
+ a2a3+ + a2+a3)
* = (γ + ϕ ) ω ω γ13 1 3 13 13
(9)
1 2
Gijo GijoGijo
and
ϕij =
1 2
23,26
Fij FiiFij
(10)
where the Gijo are the elements of the Wilson G matrix calculated at the optimized geometry and the Fij are the force constants. Kjaergaard et al.23 assume that the operators a+ and a, to good approximation, have the step-up and step-down properties known from harmonic oscillators even though they operate here on Morse oscillators.26 Within this approximation, 1 Hintra couples states within the same manifold. The coupling occurs between states that differ by one vibrational quantum 1 number in two C−H oscillators. Hinter is the contribution to the energy from the coupling between vibrational manifolds. It has been shown25 that this second contribution to the perturbation is very small because it couples states where υ is changed by ±2, 1 which are states that are well separated in energy. Hence, Hinter is neglected in the present calculation. The problem of obtaining peak positions is reduced to diagonalization of a block diagonal Hamiltonian matrix with one block for each manifold. The intramanifold coupling parameters γ′ can usually be obtained from the observed frequencies of the fundamental peaks and/or some of the observed peak frequencies in the first CH-stretching overtone. However, in the present work the intramanifold coupling parameters (γ′) were obtained from calculated ab initio frequencies using the same method that was used for dimethyl ether.23 The isolated fundamental C−Ha and C−Hs stretching frequencies for (CD2H) (CD3)2C3D and the fundamental CH stretching frequencies of (CH3) (CD3)2C3D were calculated at the Hartree−Fock 6-311G (3d,p) and DFT (B3LYP)/ 6-311G(d,p) levels of theory. The results are presented in Table 2. Since the calculated isolated fundamental frequencies, C−Ha and C−Hs, for (CD2H) (CD3)2C3D are independent of any coupling, these two C−H frequencies are made equal to the pure local mode frequencies, (ω1 − 2ω1x1) = 3219 cm−1 and (ω3 − 2ω3x3) = 3199 cm−1, respectively. These values were obtained when the HF/6-311G (3d,p) level of theory was used. The latter calculation produces three frequencies (ν) that correspond in increasing order to the energies of the states ν|00⟩|1⟩ = 3163 cm−1, ν|10⟩+|0⟩ = 3228 cm−1, ν|10⟩−|0⟩ = 3240 cm−1 of the HCAO model. The parameter γ′12 is calculated from the equation
21
ν|10⟩−|0⟩
(8)
The parameters γ and ϕ are defined by
+ 3ν1)
3228
25 3216
′ = (γ − ϕ ) ω ω γ13 1 3 13 13
and
+ 2ν1)
Table 2. Local Mode Parameters (cm−1) and Calculated iso Isolated Frequencies νCH acetylenic C−H methyl C−H local mode parameters
(7)
′ = ν|10⟩ |0⟩ − (ω − 2ω x ) γ12 1 1 1 −
(6) 2075
(11)
dx.doi.org/10.1021/jp208225g | J. Phys. Chem. A 2012, 116, 2071−2079
The Journal of Physical Chemistry A
Article
Table 3. Calculated HCAO Frequencies (cm−1) and Tentative Assignments of Methyl C−H of tert-Butylacetylene: (HF/6311G(3d,p) and B3LYP/6-311G(d,p)) HCAO
HCAO
υ
assignment
HF
B3LYP
1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4
|00⟩ |1⟩ |10⟩+|0⟩ |10⟩−|0⟩ |00⟩ |2⟩ |20⟩+|0⟩ |20⟩−|0⟩ |10⟩+|1⟩ |10⟩−|1⟩ |11⟩ |0⟩ |00⟩ |3⟩ |30⟩+|0⟩ |30⟩−|0⟩ |10⟩+|2⟩ |20⟩−|1⟩ |21⟩+|0⟩ |20⟩+|1⟩ |10⟩−|2⟩ |21⟩−|0⟩ |11⟩ |1⟩ |00⟩ |4⟩ |40⟩+|0⟩ |40⟩−|0⟩ |00⟩ |3⟩+2ν6 |10⟩+|3⟩ |10⟩−|3⟩ |30⟩+|1⟩ |30⟩−|1⟩ |31⟩+|0⟩ |31⟩−|0⟩ |20⟩±|2⟩ |20⟩−|2⟩ |22⟩ |0⟩ |21⟩+|1⟩
2883 2954 2958 5702 5741 5751 5858 5889 5902 8410 8454 8458 8599 8640 8660 8730 8730 8757 8828 10997 11058 11058 11274 11302 11336 11355 11382 11396 11422 11517 11540 11560 11569
2887 2952 2957 5704 5741 5752 5857 5889 5900 8412 8455 8459 8601 8642 8660 8728 8728 8756 8827 10998 11059 11059 11154 11305 11339 11355 11382 11396 11422 11516 11537 11560 11568
observed frequencies
5729 5764 5865 5908 8435 8470 8589 8645 8696 8738
8794 10998 11063 11124
11399
and γ′13 is obtained from the calculated frequencies of the inplane fundamental |00⟩|1⟩ and the following energy matrix ′ |10⟩+|0⟩ ω1 − 2ω1x1 − γ12
|00⟩|1⟩
′ − 2 γ13
assignment
HF
B3LYP
4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6
|11⟩ |2⟩ |21⟩−|1⟩ |00⟩ |5⟩ |50⟩+|0⟩ |50⟩−|0⟩ |10⟩+|4⟩ |10⟩−|4⟩ |40⟩+|1⟩ |40⟩−|1⟩ |41⟩+|0⟩ |41⟩−|0⟩ |20⟩+|3⟩ |20⟩−|3⟩ |32⟩+|0⟩ |30⟩+|2⟩ |11⟩ |3⟩ |30⟩−|2⟩ |32⟩−|0⟩ |31⟩+|1⟩ |31⟩−|1⟩ |21⟩+|2⟩ |21⟩−|2⟩ |22⟩ |1⟩ |30⟩−|2⟩+ν6 |32⟩−|0⟩+ν6 |21⟩−|2⟩+ν7 |22⟩ |1⟩+ν7 |00⟩ |6⟩ |60⟩±|0⟩ |10⟩±|5⟩ |10⟩−|5⟩ |50⟩±|1⟩ |51⟩±|0⟩
11675 11678 13470 13546 13546 13903 13943 13950 13957 14002 14009 14126 14141 14172 14254 14276 14278 14300 14333 14347 14452 14502 14516 15710 15732 15770 15784 15830 15921 16382 16424 16463 16506
11672 11677 13471 13546 13546 13905 13945 13952 13959 14002 14010 14127 14142 14173 14256 14272 14276 14298 14331 14346 14450 14500 14512 15647 15669 15721 15733 15831 15921 16384 16425 16464 16505
observed frequencies
13489 13575
15668 15721 15750 15801 15842 15927
assignments corresponding to the most intense high energy overtone (C−Ha) are denoted by |υ0⟩±|0⟩, where υ = 3−6 is the vibrational quantum number. Assignments of pure local modes were also confirmed with the help of the Birge−Sponer plot. Some observed transitions are tentatively assigned as local mode-normal mode combination bands. 4.3. Band Strengths. In Figure 4 (top), the acetylenic and methyl absorption bands are well separated. The spectrum in this region was obtained as a function of the density (ρ) of the gas at 295 K. The acetylenic 4ν1 band was integrated and the deconvoluted methyl (Δυ = 5) band was also integrated separately to get integrated intensity (S). This information was used to calculate the band strength (S0) value for each, the acetylenic and methyl transitions. The plot of S versus ρ give the straight lines shown in Figure 5, where the points of highest molecular density correspond to integrated intensities from FTIR bands. All the lower densities are from PS-CRD measurements. The S0 value (Δυ = 4) for the acetylenic band (C−H (ν1)) is the slope of the line and is equal to (3.0 ± 0.1) × 10−22 cm2 cm−1 molecule−1. The acetylenic S0 values were also obtained for the fundamental and overtones (Δυ = 2, 3, and 5) in a similar manner. To obtain the band strength for methyl C− H stretch (C−Hm), integrated band values (total band) were plotted as a function of the molecular density. The S0
′ − 2 γ13
ω3 − 2ω3x3
υ
(12)
which involves the two symmetric states |10⟩+|0⟩ and |00⟩|1⟩ and their interaction through γ′13. The ab initio calculated fundamental frequencies are higher than the experimental ones but because the present analysis depends only on the differences in frequencies between (CD2H) (CD3)2C3D and (CH3) (CD3)2C3D, it is expected that the calculated parameters (γ′) are as reliable as the ones obtained from experimental frequencies. The analysis yields values of γ′12 = 21 cm−1 and γ′13 = 25 cm−1. The matrices for each vibrational manifold from υ = 1 to 6 were obtained using the local mode parameters and the coupling parameters γ′12 and γ′13. The frequencies corresponding to pure local modes were calculated from the matrices. Table 3 summarizes the calculated peak positions and the tentative assignments of experimental results. The local mode states are labeled |υ1υ2⟩±|υ3⟩. Pure local mode assignments corresponding to the least intense low energy overtone (C−Hs ) are denoted by |00⟩|υ⟩ and 2076
dx.doi.org/10.1021/jp208225g | J. Phys. Chem. A 2012, 116, 2071−2079
The Journal of Physical Chemistry A
Article
4.4. Calculated Intensities of Methyl C−H Transitions. The oscillator strength (f) for a vibrational transition from the ground state g to an excited state e within the same electronic state is given by25 fe ← g = 4.70165 × 10−7(cm D−2)ν̃eg |μ⃗eg |2
(13)
where ν̃eg is the transition frequency for a particular eigenstate in cm−1 and |μ⃗ eg| = ⟨e|μ⃗ |g⟩ is the transition dipole moment in debye (D). Because the transition frequencies are known from the measured spectra, determination of numerical values for the transition dipole moment is required. For the methyl transitions, the dipole moment function (DMF) is expressed as a polynomial expansion around the equilibrium configuration:23,25,27 μ⃗(q1, q2 , q3) =
∑ μ⃗i , j , kq1iq2jq3k i ,j,k
Figure 5. Acetylenic C−H (4ν1) and methyl C−H (Δυ = 5) absorptions. Integrated absorption S (cm−2) as a function of the molecular density ρ (molecules cm−3). The highest density points were obtained with the FT-IR.
(14)
where qn coordinates represent the displacement of the appropriate H atom from its equilibrium position and μ⃗ i,j,k are the DMF derivates:
value (Δυ = 5) obtained is (4.14 ± 0.09) × 10−22 cm2 cm−1 molecule−1. This value is larger than the sum of C−Ha and C− Hs integrated absorptions because it includes combination bands. The deconvolution indicates that 72.5% of the total band should be assigned to the methyl C−H absorption giving S0 = (3.00 ± 0.09) × 10−22 cm2 cm−1 molecule−1. The S0 values for the methyl bands with Δυ = 3, 4, and 6 were obtained in a similar manner. The individual contributions for the C−Ha and C−Hs bands were also obtained from the deconvoluted bands of the methyl group absorptions.
μ⃗i , j , k =
1 ∂ i + j + kμ⃗ i! j! k! ∂q i∂q j∂q k 1 2 3
(15)
The μ⃗ i,j,k coefficients were obtained by calculating twodimensional grids of the dipole moment both as a function of (q1, q2) and of (q1, q3). The grid was calculated by changing the two coordinates in steps of 0.05 Å from −0.20 to 0.20 Å about the equilibrium bond length and keeping the rest of the molecule at its optimized geometry. The convergence criterion was default. The derived coefficients were obtained by fitting
Figure 6. Three dimensional representation of the calculated methyl dipole moment as a function of the C−H displacements (q1, q2) obtained using the DFT method with 6-311G(d,p) basis set. 2077
dx.doi.org/10.1021/jp208225g | J. Phys. Chem. A 2012, 116, 2071−2079
The Journal of Physical Chemistry A
Article
Table 4. Observed and Calculated Band Strengths (cm2 cm−1 molecule−1) for Methyl C−H Stretch Transitions of tertButylacetylene (HF/6-311G(3d,p) and B3LYP/6-311G(d,p)) calculated ΔυCH
state
bond
3
|00⟩ |3⟩ |30⟩±|0⟩
CHs CHa
|00⟩ |4⟩ |40⟩±|0⟩
CHs CHa
|00⟩ |5⟩ |50⟩±|0⟩
CHs CHa
|00⟩ |6⟩ |60⟩±|0⟩
CHs CHa
total 4 total 5 total 6
HF 6.62 1.16 1.82 9.76 1.55 2.53 1.38 2.09 3.47 2.15 3.14 5.29
total
× × × × × × × × × × × ×
B3LYP
10−21 10−20 10−20 10−22 10−21 10−21 10−22 10−22 10−22 10−23 10−23 10−23
4.93 1.03 1.52 7.44 1.54 2.29 1.08 2.23 3.31 1.73 3.52 5.25
× × × × × × × × × × × ×
observed
10−21 10−20 10−20 10−22 10−21 10−21 10−22 10−22 10−22 10−23 10−23 10−23
9.06 1.19 2.10 1.38 1.71 3.09 6.99 2.30 3.00 1.29 5.22 6.51
× × × × × × × × × × × ×
10−21 10−20 10−20 10−21 10−21 10−21 10−23 10−22 10−22 10−23 10−23 10−23
Table 5. Observed and Calculated Band Strengths (cm2 cm−1 molecule−1) for Acetylenic C−H Stretch Transitions of tertButylacetylene HF ΔυCH
6-311G(3d,p)
1 2 3 4 5
8.22 2.11 1.11 1.11 1.52
× × × × ×
10−18 10−19 10−20 10−21 10−22
B3LYP 6-311++G(3d,p) 8.70 2.41 1.10 8.86 3.31
× × × × ×
6-311G(d,p)
10−18 10−19 10−20 10−21 10−21
8.30 3.35 1.29 1.03 3.89
e2 4 × 10−2ε0mc 2
10−18 10−19 10−20 10−20 10−21
6-311++G(d,p) 8.31 2.45 8.06 4.81 4.45
× × × × ×
10−18 10−19 10−21 10−22 10−23
observed 3.19 2.45 5.11 3.00 4.83
× × × × ×
10−18 10−19 10−21 10−22 10−23
Å from −0.4 to 0.4 Å about the equilibrium geometry. The dipole derivatives were obtained for fitted polynomials of different orders (n = 4−8). Although the results of intensity calculations were similar for all polynomials, the eight order polynomial was selected. Initially, the one-dimensional DMFs were calculated using HF/6-311G(3d,p) and B3LYP/6-311G(d,p) levels of theory for acetylenic C−H bonds. However, the results obtained did not have a reasonable agreement with experimental values (see Table 5). Because of this, calculations were done using HF/6-311++G(3d,p) and B3LYP/6-311+ +G(d,p) levels of theory. The observed and calculated band strength values for the fundamental and overtones with Δυ = 2−5 of the acetylenic C−H stretch are shown in Table 5. The results show that the B3LYP/6-311++G(d,p) is better than the HF/6-311++G(d,p) method to get the correct order of magnitude for all C−H acetylenic transitions. This result for tert-butyl acetylene is in agreement with previous calculations done by Kjaergaard and co-workers31−33 for other molecules.
the two-dimensional dipole moment surface to a fourth order polynomial using the MATLAB system of programs. Figure 6 shows the dipole moment surface as a function of (q1, q2). The band strength and the oscillator strength are related by the equation28 S0 =
× × × × ×
f = 8.85269 × 10−13f (16)
Table 4 shows the observed and calculated band strength values for methyl transitions with Δυ = 3−6. The experimental and calculated total methyl band values are also included. The order of magnitude agreement between experimental and calculated values with the total methyl band is very good. Agreement for all transitions with individual C−Ha or C−Hs bands is more difficult to obtain because the deconvolution could show several results depending on the number of bands used to fit the absorption band when there are also overlapping local mode-normal mode combination bands in the methyl region. The assignment of combination bands is tentative and this is the reason why the intensities of combination bands were not obtained. Finally, the barrier hindering internal rotation of the methyl groups in tert-butylacetylene has been estimated to be the same as in isobutene (≈1400 cm−1).8,29 It is not expected that internal rotations will have any effect on the shape of the overtone bands of tert-butylacetylene as has been found for methyl groups of molecules with low (
