J. Phys. Chem. 1995,99, 13850-13864
13850
Acetaldehyde: Harmonic Frequencies, Force Field, and Infrared Intensities Kenneth B. Wiberg* and Yvonne Thielt Department of Chemistry, Yale University, New Haven, Connecticut 06520
Lionel Goodman and Jerzy Leszczynski$ Wright and Rieman Chemistry Laboratories, Rutgers University, New Brunswick, New Jersey 08903 Received: June 2. 1995@
The harmonic frequencies of acetaldehyde, acetaldehyde-dl , and acetaldehyde44 were obtained experimentally via a comprehensive analysis of the molecules’ infrared vibrational spectra. Specifically, the observed fundamental frequencies were corrected for anharmonicity by applying an extensive list of anharmonic factors derived from the overtone and combination bands assigned to features in the infrared spectra of CH3CH0, CH3CD0, and CD3CD0. An ab initio harmonic force field calculated at the MP2/6-31 l++G(3df,p) level of theory yielded fundamental frequencies that were an average of 1.6% too large relative to the experimentally obtained harmonic values. The theoretical force constants were subsequently refined through a least squares fit to the experimental harmonic frequencies. The results of the normal coordinate analysis were then used to convert the acetaldehyde-do, -dl,and -d4 isotopomers’ measured absolute intensities to atomic polar tensors. The final potential function was successfully used to predict the observed vibrational spectrum of acetaldehyded3 and led to the reassignment of the v5, v12,and vi3 vibrational bands in the CD3CH0 infrared spectrum.
Introduction Force field calculations that invoke a normal mode treatment usually incorporate a molecule’s observed anharmonic fundamental frequencies in the final potential function determination. While these frequencies are readily obtainable, they must be corrected for anharmonicity in order to be consistent with the normal coordinate approach. Anharmonic constants are experimentally derived through assignment of overtone and combination bands in vibrational spectra of a molecule’s isotopomers. The complexity of this task is then a function of molecular size and symmetry. As the degrees of freedom increase, a greater number of anharmonic factors must be generated, and the increased density of states implies that the level of rovibrational coupling may be enhanced, as dictated by symmetry constraints of the molecule. The focus of this study is the derivation of harmonic force fields for moderately-sized asymmetric top molecules based on a thorough reduction of the molecule’s experimental vibrational data complimented by ab initio calculation. Acetaldehyde was chosen as an appropriate model system to evaluate the limitations of computational methodology for the following reasons. Its size provides a rather large density of states, while a multitude of vibrational and rotational perturbations are allowed by its C, symmetry. Even in the absence of these Fermi and Coriolis resonances, going from experimental frequencies alone to a quadratic force field is often somewhat futile because of the well-known indeterminacy problem. I Further incentive for undertaking a vibrational analysis of acetaldehyde was furnished by previous work conducted by Walters et a1.* The ill-defined rotational structure exhibited by the fundamental and first overtone of the CH3CHO carbonyl stretching mode, v4, was ascribed to intermode coupling. Specifically, the C=O stretch is believed to be “linked” via Current address: Texaco Research Center, Beacon, NY 12508. Permanent address: Chemistry Department, Jackson State University, Jackson, MS 39217-0510. Abstract published in Advance ACS Abstracts, September 1, 1995. 7
@
0022-365419512099- 13850$09.00/0
Fermi resonance to the first overtone of the C-C stretch ( 2 Y g ) . A Fermi interaction between v g and the methyl rotor combination ( V I 4 v15) has long been established in the literat~re.~ Irregular band contours often reflect a high density of rovibrational states at the given energy region. Deuteration typically adds complexity to vibrational bands because the density of states increases relative to that of the parent molecule. Interestingly, this trend is not observed in the v4 fundamental and overtone spectra of the d4 species. The introduction of discrete rotational features upon deuteration implies the CH3CHO v4 band shape is dependent on factors other than the density of isoenergetic rovibrational levels. Consequently, an understanding and future modeling of the carbonyl stretch mode’s dynamics requires a knowledge of the molecule’s force field and of the anharmonic terms that govern vibrational state coupling. The calculations performed in this analysis are detailed in the following sections. The experimental techniques used to acquire the vibrational data are outlined below, but only listings of assigned frequencies are provided. Supporting information regarding assignment justifications may be obtained from the authors.
+
Experimental Section Acetaldehyde Gas Phase Infrared Spectra. The gas phase infrared spectra of CH3CH0, CH3CD0, and CD3CDO were measured with a BOMEM DA3.002 Fourier transform spectrometer. A 10 cm path length absorption cell fitted with KBr windows was used to obtain spectra of the acetaldehyde fundamental vibrations. Spectra of the low-intensity, higher order vibrational transitions were acquired with a variable long path length cell (0.75-20.0 m) using a variety of pressures dictated by oscillator strength and sample cell path length. The spectrometer was equipped with a Globar source, KBr beam splitter, and liquid-helium-cooled, copper-doped germanium detector to record spectra between 400 and 1800 cm-I. The 1800-5000 cm-I spectral range required the Globar source, a calcium fluoride beam splitter, and an InSb detector. The spectrometer’s internal light source was switched to a quartz 0 1995 American Chemical Society
Acetaldehyde halogen lamp to measure spectra at energies over 5000 cm-I. The resolution of the room temperature gas phase spectra ranged from 0.1 to 0.05 cm-I. In all cases, 100 scans were coadded and ratioed to an appropriate 100 scan background. The apodization function was BOXCAR. AcetaldehyddArgon Matrix Infrared Spectra. Matrix isolation techniques were employed in an effort to decipher severely overlapped regions of the gas phase acetaldehyde spectra. Trapped in a host matrix, the guest molecule no longer rotates freely. The rotational fine structure of vibrational bands collapses, leaving a spectrum comprised of sharp vibrational peaks. The spectrum is further simplified by removal of hot band activity at the low matrix temperatures (typically 20 K for an Ar host). Acetaldehyde/argon matrices were prepared using a Displex apparatus described el~ewhere.~Approximately 0.7 Torr of CH3CHO and 670 Torr of Ar were mixed in the 2.0 L ballast bulb of the Displex apparatus vacuum line and allowed to equilibrate for 2 h. The sample was allowed to deposit on a cesium iodide window (cooled to 20 K) for 3 h at a flow rate of approximately 1.2 Torr per min. This same procedure was followed for the dl and d4 isotopomers. Their respective mixtures were 0.85 Torr of CH3CD0/670 Torr of Ar and 1.0 Torr of CD3CD0/650 Torr of Ar. A second d4 matrix comprised of 3 Torr of CD3CD0/675 Torr of Ar was also prepared. The matrix assembly was lowered into the sample port of a Nicolet 7199 FTIR spectrometer equipped with a HgCdTe detector and KBr-Ge beam splitter. One hundred scan spectra were acquired at a resolution of 0.5 cm-’ and were ratioed to a 100 scan background of the cooled CsI window. The spectral region ran from 400 to 4200 cm-’, and the apodization function was Happ-Genzel. Acetaldehyde Intensity Measurements. Gas phase infrared intensities of acetaldehyde have been previously reported by Vakhlueva, Finkel, Sverdlov, and Andreevasa and by Rogers.5b These investigators only studied the CH3CHO isotopomer. Furthermore none of these investigations partitioned the intensity of an overlapped absorbance feature among the constituent vibrational bands. The gaps in the available experimental intensity data prompted us to measure absolute infrared intensities of the CHFHO, CH3CD0, and CD3CDO fundamental vibrational bands. The infrared intensities of CH3CH0, CH3CD0, and CD3CDO were obtained according to the Wilson-Wells-Penner-Weber method.6 The 72.5 mm path length brass high-pressure cell used in this study is similar to that of Dickson, Mills, and Crawford.’ The sample cell was filled with a given pressure of acetaldehyde as measured using a Wallace and Tiernan absolute pressure gauge, pressurized to 300 psi with nitrogen, and allowed to equilibrate for 30 min. Pressure-broadened acetaldehyde spectra were recorded from 400 to 4000 cm-’ at a resolution of 0.25 cm-I with a Nicolet 7199 FTIR spectrometer. Fifty scans were coadded and ratioed to a fifty scan background of the nitrogen-filled cell. The spectrometer was equipped with a Globar source, KBr-Ge beam splitter, and HgCdTe detector. The apodization function was Happ-Genzel. Integration of vibrational bands was accomplished using the instrument’s software package. Solution phase infrared spectra of CH3CH0, CH3CD0, and CD3CDO in CC4 were obtained as a means of resolving the congested regions of the pressure-broadened spectra. For these measurements we used a Nicolet 5-SX FT-IR spectrometer to record the solution phase spectra from 400 to 4000 cm-’ at 1 cm-’ resolution. The 1 mm path length sample cell was fitted with KBr windows. Thirty-two sample scans were coadded and ratioed to a thirty-two scan CC4 background spectrum.
J. Phys. Chem., Vol. 99, No. 38, I995 13851
Results and Discussion Assignment of Acetaldehyde Gas Phase Infrared Spectra. %le identifying a spectrum’s components is typically a “bootstrapping” process, an assignment hierarchy was followed in this study. Fundamental vibrational bands and their associated sequence band progressions, when present, were treated fist. Binary combinations, fust overtones, and difference bands emanating from vibrational states less than 1000 cm-’ were then assigned. The sums of appropriate fundamental vibrational frequencies provided a list of “predicted” origins for the binary states. Combination and overtone assignments were based on several factors. (i) The experimental and predicted transition frequencies had to agree within the ltmits of anharmonicity and potential resonance interactions. Anharmonicity generally produces a negative shift in transition energy relative to its predicted harmonic value. This displacement is most often on the order of 10 cm-’ but may be as high as 100 cm-I for combinations and overtones comprised of CH stretch modes. Strong resonance effects lead to a repulsion of the interacting states’ energy levels. The C, symmetry of acetaldehyde implies these perturbations can be Commonplace. Resonance interactions were suspected if an assignment seemed unambiguous but its experimental frequency fell well to the blue of its predicted value or if its shift to the red was beyond that typically associated with anharmonicity. The spectral region was then examined for vibrational states that could participate in a perturbation. (ii) The relative intensities of the fundamentals that comprise the combinations or overtones helped make an assignment choice between closely lying states. For example, if only one band was observed in a region where the overtone of a very weak fundamental and the combination of a strong fundamental were predicted, then the assignment of the combination was favored. (Intensities of binary transitions tend to fall by at least an order of magnitude relative to those of their constituent fundamentals.) (iii) A comparison of acetaldehyde isotopomer spectra facilitated the assignment of vibrational states that incorporate the motion of particular functional groups. (iv) Assignments made in the spectrum of one phase (vapor, liquid, solid, or matrix) often substantiated the assignments made in another phase. Transitions involving three or more vibrational quanta were considered when a band could not be reasonably attributed to a binary transition. In many instances, the experimental positions of higher level states could be calculated using fundamental frequencies and anharmonicity constants generated in the course of the assignment procedure. The CHFHO, CH3CD0, and CD3CDO gas phase vibrational spectra assignments are listed in Tables 1-3. Assignments that agree with those posed in earlier investigations are noted in the tables. Assignment of AcetaldehyddArgon Matrix Infrared Spectra. The assignment of acetaldehyde’s fundamental vibrational modes in the matrix was directed by the gas phase and solid phase data: as well as by the frequencies determined in a previous normal coordinate analysis conducted at the HartreeFock (HF) 6-31G(d) theory leveL9 The remaining bands were then assigned as binary combinations or overtones. Note that the detector used in this work has a cutoff of 400 cm-I, preventing observation of the torsional mode, ~ 1 5 in , all cases. Similarly, this fundamental has not been assigned in the solid phase spectra. The ~ 1 position 5 should undergo a substantial shift to the blue in the matrix spectra relative to gas phase values. This makes it impossible to even gain an estimate of its combinations’ positions in the matrix. As such, v~s-type
Wiberg et al.
13852 J. Phys. Chem., Vol. 99, No. 38, 1995 TABLE 1: CH3CHO Gas Phase IR Spectra Assignments and Ar Matrix Spectrum (Brackets) freq 106.5 114.4 116.1 122.0 141.0 142.6 143.8 155.8 162.7 506.8 507.5 508.2 508.8 [505.9] 622.2 651.2 722.8 764.1 [772.1] 766.8 777.2 865.9 [871.4] 866.9 885.9 908.2 911.1 919.8 11013.41 fio97.83 1113.8 11111.41 1203.1 1208.1 1236.0 1252.4 1259.1 1262.2 1265.9 1289.7 1351.9 1352.6 [1348.7] 1354.5 1389.1 1392.4 1393.6 1394.9 [1389.7] 1420.5 1433.5 [1427.0] 1436.3 1499.9 1529.8 [1546.4] 1550.2 1551.9 1576.7 1580.811579.1 1620.6 1631.2 1706.5 1745.2 1746.0 [1727.4] 1747.5 [1748.8] 1876.0 1888.6 1903.6 1976.8 [1976.9] 2025.2
assignmenp
just.6 I I I I I I I I I I1 I1 I1 I1 I1 I1 I1 I1 I1 IF I11 I1 I1 IId IVe I1 I1 I1 I1
I1 I1 I1 I1
I1 IVf 11, IV I11 I1 I11 I11 I1 118 I1 I11 Vh I11 I1 I1
2113.1
21 14.3 [2119.0] 2125.8 2159.5 2218.7 [2215.4] 2260.3 2268.4 2269.7 2271.0
I1 I1 I1 I1 I1 I1
freq 2299.1 2306.9 2455.7 2461.4 [2455.6] 2540.4 [2537.2] 2544.4 [2536.8] [2679.5] 2715.4 -2776 [28 17.01 2823.4 [2840. I] 2923.2 [2921.5] 2964.3 [2961.7] 2967.8 2968.7 2969.9 3014.3 [3022.8] 3079.8 3081.9 3093.8 3111.5 3476 [3463.0] 3573.3 3581.5 3682.6 3125.8 3826.3 3911.8 3924.4 3950.8 4005.8 4016.1 4024.4 4028.0 -4033 [4030.0] 4074.2 [4072] 4194.0 4275.5 4305.8 4312.3 4358.3 4383.0 4431.7 4400-4630 4684.0 4713.0 4759.0 -5192 5321.6 5607.9 5625.0 5682.3 5741.6 5759.2 5765.8 5787.1 5795.2 5906.7 5910.5 5974.2 5977.6 6068.2 6078.2 6093.1 6119.9 6150-6355 6423.0 6481.2 6592.0 6597.7 -6764.5?
assignmentu
just.6 i1
V
V‘
V 11 11 11 11 V 11 11 11 11 111
VI VI VI
VI
VI VI
1
The principal symmetry coordinates (Table 10) that contribute to each of the fundamentals are indicated. Justification: (I) Detector cutoff in this study is 400 cm-]. Frequency and assignment taken from Hollenstein and Winther.I5 (11) Assignment agrees with that of Hollenstein and Winther.’’ (111) Absorbance feature was not observed in this study. Frequency and assignment taken from Hollenstein and Winther.I5 (IV) State is Coriolis perturbed. See Hollen~tein.~~ (V) Assignment agrees with that of Hollenstein and Gii~~thard.~ (VI) Assignment agrees with that of Lucazeau and S a n d ~ r f y . ~Fundamental ~ is in Fermi resonance with V I 4 VIS. Combination is in Fermi resonance with v9. e va is in Coriolis resonance with ~ 1 3 . v8 obscures V13. f v5 and vi2 are Coriolis coupled. The v5 origin of this B-type band was determined from the difference band v5 - vI5. 8 Assignment is tentative. Fundamental is in Fermi resonance with 2V9. ‘ Fundamental undergoes a complex resonance interaction, principally with 2v6. Origin uncertain. (I
+
J. Phys. Chem., Vol. 99,No. 38, 1995 13853
Acetaldehyde
TABLE 2: CH3CDO Gas Phase IR Spectra Assignments and Ar Matrix Bands (Brackets) freq assignment just.a freq 139.5 500.0 [497.1] 663.5 676.0 803.0 849.5 852.0 [995.6] 1044.0 [1042.4] [ 1077.1] 1109.0 [1107.2] 1217.0 1343.5 t1347.11 1354.0 1356.5 [1354.3] 1359.5 1362.5 1432.0 [1425.7] [ 1427.61 [ 1721.21 1743.0 [1734.6] 1855.0 1910.3 1919.0 1955.0 1957.7 2059.5 [2070.6] [2096.4] [2099.0] 21 19.9 2149.9 [2154.4] 2186.6 [2185.3] 2212.7 [2212.3] 2240.0 2394.7 2397.3 2407.2 2417.1 2417.7 2418.3 2462.4 [2457.1] 2464.2 2475.9 [2464.81 [2498.2] 2542.8 2594.9 2690.5 2729.4 2780 2783 2816.9 2843.4 2845.8 2874.8
b I I I
assignment
just.a
2924.8 [2920.6] 2962.9 [2959.8] 2967.2 2969.3 3014.2 [3023.9] 3080.0 3092.0 3108.3 3151.3 3469.0 3470.1 347 1.O 35 14 3606.7 3638.2 3799.2 3855.5 3960.4 4062.0 4075.8 41 19.6? 4279.7 4301.2 4311.3 -4359 4422.7 4435.5 4664.4 4669.4 4705.3 4709.5 4755.8 5006.8 5021.2 5034.0 5048.0 5070.5 5606.8 5626.4 5637.0 5738.8 5742.2 5758.9 5766.7 5716.9 5781.8 5784.7 5903.4 5908.0 5975.0 5978.0 6069.4 6092.0 6102.5 6115.1
IC
Id
I
I1
I1 I I
I
I1 IIC
I
I1 I€f
I1 I1
I1
I1
i1 111 111 111 11 111 111 111
11
11
IV IV
Iv IV
IV
Iv IV
IV
Iv
Justification: (I) Detector cutoff in this study is 1800 cm-I. Frequency and assignment taken from Hollenstein and Winther.I5 (11) Assignment (111) Assignment agrees with that of Hollenstein and Winther.15 (IV) Assignment agrees with that agrees with that of Hollenstein and Gii~~thard.~ of Lucazeau and Sandorfy.33 Frequency determined from differencebands assigned by Hollenstein and Winther.I5 Combination is in Fermi resonance with v9. Fundamental is in Fermi resonance with v14 ~ 1 5 . Fundamental is in Fermi resonance with VI3 f v14. fFundamenta1 is in Fermi resonance with 2~13. (I
+
combinations and overtones (some of which have been reported in a recent jet studyi0) have not been considered in the vibrational analysis of the acetaldehyde-do, 41, and -d4 matrix spectra. Care was taken that assigned peaks were indeed those of acetaldehyde and not the result of residual water and carbon dioxide present in the matrices.
Experimentally Derived Harmonic Frequencies The observed fundamental frequencies are classically converted to harmonic frequencies in the following manner. The vibrational energy of a molecule may be expressed asli
G(v19v27v3****) =
i)
')
+ + x&i,k(vi + i)(vk + 2 + i k>i
(l)
where vi = vibrational quantum number associated with normal mode i, oi = harmonic frequency of normal mode i, and Xi,k = anharmonicity constant linking modes i and k. If a molecule possesses n normal modes, the n(n 1)/2 anharmonicity factors are determinable via eq 1 and from the assignment of higher order transitions in the vibrational spectrum. The number of transitions assigned in a particular isotopomer' s gas phase vibrational spectrum is usually insufficient
+
13854 J. Phys. Chem., Vol. 99,No. 38, 1995
Wiberg et al.
TABLE 3: CD3CDO Gas Phase IR Spectra Assignments and Ar Matrix Spectrum (Brackets)
freq 116 436 [433.3] 564.1 566.1 57 1.6 [542.4] 573.8 747.9 751.3 753.7 793.1 873.0 [868.0] 876.4 940.1 938.71 949.51 1029.7 1024.01 1046.3 1044.63 1050.5 1051.3 1144.2 1147.4 1151.0 1147.51 1187.1 1325.2 1511.3 1576.9 1581.2 1584.9 1596.1 1618.7 1701.2 1736.4 [1727.0] 1890.4 [ 1895.01 1896.3 [ 1960.81 [ 1984.21 [ 1991.61 [2039.2] 2054.5 [2062.9] [2085.2] [2098.5] 2127.7 [2127.2] 2171.4 [2158.2] 2194.1 2222.7 [2219.0]
assignment
just.a
freq
I I
2229.9 2262.2 [2267.0] 2412.2 2483.7 2489.2 2524.9 2559.8 2599.0 2618.0 2623.2 2625.4 2876.8 2884.0 2944.9 2941.7 295 1.7 2986.6 [2995.5] 3058.8 3072.4 3160.9 [3156.8] 3189.9 3193.3 [3199.4] 3239.4 3242.2 [3233.5] 3298.1 3318.7 3455.1 3456.3 [3436.2] 3788.4 [3784.2] 3957.2 3998.3 [3993.3] 4055.8 4177.6 4249.7 4305.5 4345.6 4368.9 4407.4 442 1.7 4474.9 449 1.O 5143.3 5 159.3
I1 I1
I1 I1 I1
assignment
just.a
11
V8
+ VI I
11 11
3v4
a Justification: (I) Detector cutoff in this study is 400 cm-I. Frequency and assignment taken from Hollenstein and Gii~~thard.~ (11) Assignment agrees with that of Hollenstein and Giinth~d.~Fundamental is in Fermi resonance with 2 ~ 1 2 . Origin unclear.
to calculate a complete set of anharmonic constants. Although some transitions may be too weak to be observed even when the spectra are obtained with a long path length static cell, the lack of gas-phase data is primarily the result of rovibrational band overlap. Weaker vibrational bands may be concealed within the rotational envelope of an intense transition. Consequently, additional anharmonic constants are provided through matrix spectra assignments by assuming Xi,k to be phase invariant.' It is virtually impossible to determine all n(n 1)/2 anharmonic constants from the gas-phase, liquid phase, solid phase, and matrix-isolated vibrational spectra of a single isotopomer. The missing anharmonic constants of one isotopic form of the molecule can be calculated from those of another isotopic species. According to Darling and Dennison,I3 the corresponding anharmonicity factors of the two isotopomers are related by an empirically established equation,
+
Here w1 equals the harmonic frequency of vibrational mode 1 and the superscript (i) distinguishes the parameters associated with the isotopically-substituted forms of the molecule. If eq
2 is the only means of completing the set of anharmonic constants required to generate harmonic frequencies for a particular isotopomer, then the W I values are obviously unavailable. The anharmonic experimental frequencies, vl,must then be applied as a first approximation to the W I values in eq 2. The anharmonic constants derived from analysis of the gas phase and matrix-isolated spectra of CH3CH0, CH3CD0, and CD3CDO are listed in Table 4. The 2j.k values were calculated with eq 1 from the transitions assigned in Tables 1-3 and the matrix-isolated spectra. As stated earlier, acetaldehyde's C, symmetry affords multiple opportunities for homogeneous and heterogeneous resonance interactions among its vibrational states. Therefore it is not feasible to determine all of the anharmonic constants from unperturbed vibrational bands. Severely perturbed bands were not used to generate the X i , k values. Eichelberger and Fisanick analyzed the multiphoton ionization spectra of CHFHO, CHFDO, CD3CH0, and CD3CD0.I4 Spectra of the two photon n-35 Rydberg transitions observed from 3580 to 3700 8, were obtained using a static cell as well as by molecular beam techniques. The MPI spectral assignments yielded an additional series of anharmonicity factors. These values are also included in Table 4. The following anharmonic constants could not be generated
J. Phys. Chem., Vol. 99, No. 38, I995 13855
Acetaldehyde
TABLE 4: Anharmonic Constants for Acetaldehyde (cm-l) xi,k
gas
x1.1
-25.5
CH3CHO matrix MPI"
CH3CDO CD3CDO matrix MPIa gas matrix MPI"
-25.2
x1,2 xl,3
Xi.4
gas
-16.7 -44.3
-3.2 -1.4 - 10.7
-1.3
x1.5
-0.3
x5.11
-8.6
-0.7
x1.8 x1.9 x1.10
x1.11 ~1.12 x1.13
-2.6 -4.4 -18.9
-9.0
-6.3
-10.0 -10.4
-2.4 -3.4
x2.g x2.9 x2.10
-0.3 -4.0
-2.9
-9.0 +1.5 -3.9 -44.9
- 105.9
~ 2 . 1 1 -100.4
x2.12 X2.13 x2.14 x2.15 ~3.3
x6.10
-0.1
x7.10 x7.11 x7.12 ~7.13 x7.14 x7.15 X8.8 ~8.9
-8.3 -1.6
-2.5
-8.4 +5.9 -3.0 -28.5 -3.3
-54.6
x3.4
X8.10
-26.6 -2.5
xg,]l ~8.12 xs.13
-5.7
X8.14
~8.1s
x3.5
gas
CD3CDO matrix MPP
-3.3
+o. 1 f3.5
-0.5
x7.g x7.9
x2.5 x2.6 x2.7
-0.6
X6.9
X6,15 ~7.7
-4.6
x2.4
-0.1
-2.4 -10.5
+1.0
-1.0 -2.1 f5.0 -3.2
x6. I2 x6, I3
x2.2
x2.3
CH3CDO . matrix MPP
-14.8
x6.7 x6.8
x 6 , ~
-1.5
gas
x 6 .I 1
x1.14
~i.15
CH3CHO matrix MPI"
x5.14
X5.15 x6.6
-11.7 -3.6 -8.2 -0.2 -2.1 -23.5
gas
x5.12 x5.13
x1.6
XI,^
xi,k
-4.1 +OS -8.3 -10.6 -5.0 +0.2 -0.7 -11.1 -12.9 -4.2 -2.4 +3.5
-2.9 -2.0 -3.9 -5.7
-8.9 -4.5 -4.7
-11.2 -3.1
-5.9
-1.5 -8.1 -5.5 -3.2 -9.4 +3.0 -2.6 -3.5
-1.1 -6.3
+3.9 +1.8
-1.8
-1.9 -6.5
-7.0 -12.0 -4.4 -10.2
-4.4 -1.9 -9.5
-5.2 -1.0 -1.9
-0.9 f0.9 +1.0 +7.0 -0.4
+0.2 -1.2
-3.0
x3.6 x3.7 X3.8
~3.9
-6.0 -8.0
-2.9 -8.0
-6.1
x9.13 x9.14 x9.15
-1.2 x3.12
~IO,IO
x3.13 x3.14 x3.15 ~4.4
-2.9 +0.3 -8.2 -8.9
-6.1 -7.5
-8.0
Xl0,ll
-3.1 +1.0 +1.7 -0.3 +4.4
+2.5
-4.8
x4.8 x4.9
-7.5 -6.2 +2.4 -3.0 -0.6
-0.3 -1.0 -1.9
-1.3 -1.0
-0.5 -0.6
f0.7
+0.8 +OS
+4.3 +6.0 -1.1 +0.5 +0.7 +3.3 +4.1
f1.1
-11.7
XlO,l3
-7.3
-3.4
x4.6
$3.5 -25.4
x10.12 x10.14
x4.5 ~4.7
x9.l I X9.12
-2.1
-7.5 -7.0 -11.2
-11.8
-0.7 +5.9
+3.9
-7.5 -0.5
-2.3
X5.5 xS.6
x5.7 x5.8
x5,9 x5.10
-8.7 -10.1 -6.9
-1.1 x13.13 x13.14
-4.6 -8.5
-9.0 -5.6
x13.15
-5.7
x14.14
Xi4.15 xis.15
$4.9
+1.4 -7.2' -14.7
+1.1
a Anharmonic constant values determined from MPI study by Eichelberger and Fisanick.I4 corrected for Fermi resonance.
from the acetaldehyde vibrational spectra:
+0.8
XI,& x 1 , 1 3 . x1.14. x2.2.
x2.5, x2,12, 23.57 X3,6* x3.7, x3.10, 23.12, x3,13, x4,5, x4,12, x4.13, X S S , X5.9, Xs,iz, X5,14, x9,9, X I I J ~ ,x12.12, and XI^. Of these, one constant, ~ 2 . 2 could , be estimated from the form of the v 2 normal
mode. This mode is the symmetric stretch of the methyl group's out-of-plane CH bonds. Since the v11 fundamental is the antisymmetric stretch of these bonds involving the same local oscillators, the x2.2 value was approximated by X I 1.1 I . A few comments regarding the acetaldehyde anharmonic frequencies are required at this stage. The ~ 1 vibrational 3 band is completely obscured by the Y 8 band envelope in the CH3-
+l.l -5.5 Anharmonic constant determined from
-4.6 -12.4 VI4
+
~ 1 5
CHO gas phase spectrum. Hollenstein established that these two normal modes undergo a Coriolis intera~ti0n.l~~ His treatment of the perturbation yielded a ~ 1 anharmonic 3 frequency of 1107.3 cm-l. This value was used to calculate the harmonic frequency of the ~ 1 fundamental. 3 The CH3CHO v9 fundamental is Fermi perturbed by the VI4 ~ 1 binary 5 combination. This fundamental's energy was corrected for the ~ 1 4 ~ 1 interaction 5 by Hollenstein and WintherISb following the first-order perturbation method of Winther.I6 The v9 harmonic frequency was determined with an unperturbed anharmonic frequency of 885.0 cm-I.
+
+
Wiberg et al.
13856 J. Phys. Chem., Vol. 99, No. 38, 1995
The 1.92 fundamental is concealed within the vg vibrational band (1432.0 cm-I) in the CH3CDO gas phase spectrum. These fundamentals are observed at 1425.7 and 1427.6 cm-I, respectively, in the dl matrix-isolated spectrum. Given the proximity of these fundamentals in the matrix, the v12 gas phase origin was approximated with that of v g in order to generate a v12 harmonic frequency for the dl isotopomer. The v6 fundamental was not identified in the CH3CDO gasphase infrared spectrum. The solid phase v6 frequency of 1080.0 cm-l was used as an estimate of this mode's anharmonic frequency. The v5 fundamental has not been observed in gas phase, solid phase, or matrix-isolated spectra of CD3CDO. As such, it was impossible to derive an experimental d4 harmonic frequency for this normal mode. The CD3CDO x i . 5 values, where i f 5 , were all derived from do or dl isotopomers. In this case, the v5 "anharmonic" frequency determined in the HF/6-3 1G(d) normal coordinate analysis9 served as a substitute for 0 5 in eq 2. The anharmonic constants listed in Table 4 were used to derive the experimental harmonic frequencies, wi, by correcting the observed CH3CH0, CHFDO, and CD3CDO fundamental frequencies, vi, with the equation (3) If a given anharmonicity factor was missing for one isotopic form of the molecule, then the constant was calculated from the corresponding xi,k value of another acetaldehyde isotopomer using Darling and Dennison's eq 2. In several instances it was possible to generate a given anharmonic constant for more than one isotopic species. The choice as to which isotopomer's x j , k value was best suited for the derivative under study was based on the following considerations. (i) The anharmonic constant associated with the more confident vibrational assignment was preferred. (ii) An anharmonic constant obtained from an unperturbed vibrational band was favored over one determined from a perturbed band. (iii) The Xj,k value associated with the isotopomer whose modes i and k most resembled the corresponding normal modes in the species under investigation was preferred. For example, CH3CDO anharmonic factors linking methyl group sensitive vibrations were converted from the CH3CHO values when possible. The outcome, do, dl, and d4 experimentally-derived harmonic frequencies, is given in Table 5.
MP2 Force Field There have been several acetaldehyde ab initio harmonic frequency calculations. The earliest were Hartree-Fock studies by Wiberg, Walters, and Colson9 using 4-31G and 6-31G(d) basis sets in 1984 and by Crighton and BellI7 in 1985 using a Huzinaga-Dunning double-5 (HD-DZ) basis'* for the a' normal modes. Crighton and Bell went beyond the standard HD-DZ function by complementing the HD-DZ function with diffuse s functions on the oxygen and carbonyl carbon atoms (HD-DZs). Thiel in her 1990 all electron second-order Moller-Plesset perturbation theory (MP2) c a l c ~ l a t i o nused ' ~ a 6-3 1G(d) basis set. The earlier HD-DZs basis set of Crighton and Bell is superior but lacks any correlation correction. The most recently published study is a set of calculations by Hadad, Foresman, and Wiberg20 comparing several methods, i.e., HF and MP2 and singles configuration interaction (CIS) all carried out with a 6-31G(d) basis. At all published levels the predicted frequencies range from 1 to 12% too large (the best calculation's average absolute deviation is >3%) when compared with the harmonized experimental values given in Table 5.
TABLE 5: Experimental Harmonic Frequencies for Acetaldehyde no.of CH3CHO CH3CDO CD3CDO mode ~,.f (cm-I) (cm-I) (cm-I) 3138.0 3138.6 2343.2 VI 12 v2 13 3056.4 3056.8 2197.2 2130.4 21 19.6 v3 9 2841.6 v4 12 1774.4 1772.2 1763.7 1457.0 1452.7 v5 8 1406.0b 1168.3 v6 13 1411.6 v7 14 1400.2 1097.4b 1070.4 1145.6 1128.2 970.0 V8 15 906.8 88 1.7 765.8 v9 13 519.2 443.2 VI0 14 521.0 307 1.8 2285.0 VI I 14 3072.8 1459.4 1058.7 VI? 10 1469.7 1066.4 964.4 VI3 10 1129.8 692.2 582.5 VI4 13 780.8 180.7 150.2 VIS 15 186.7 Number of X8.k terms used in converting the observed anharmonic frequencies to their harmonic counterparts. The isotope-induced frequency shifts suggest that the assignments for v6 and 117 of CH3CDO [15] should be reversed. Doing so will not affect the results of the normal coordinate analysis or the infrared intensity study but would affect the numbering of some of the anharmonicity constants. Because the methods used in the post HF investigations of acetaldehyde have employed relatively small basis sets, we carried out MP2 calculations of the acetaldehyde harmonic force field using an ascending series of basis sets: 6-31G(d), 6-31l+G(d,p), 6-31 1+G(2df,p), 6-311G(3df,2p), and 6-31l++G(3df,2p). The largest bases are valence-triple-l; quality augmented with additional (d and f) polarization functions on the carbon and oxygen atoms. The 6-311++G(3df,2p) basis additionally introduces diffuse functions on both hydrogen and heavy atoms. This basis set can be regarded as approaching the MP2 limit. We restrict our discussion to three bases which illustrate the basis set expansion effects: 6-3 lG(d), 6-31 1G(3df,2p), and 6-311++G(3df,2p). In this paper we do not discuss predictions for the low-frequency large-amplitude methyl internal rotation vibration, VIS. The large-amplitude motion inherent in this mode requires a separate treatments2' Geometries. The Gaussian 92 program package22was used to derive MP2 level minimum energy geometries and ab initio harmonic force fields for each of the bases. The MP2/6-31G(d), MP2/6-311G(3df,2p), and MP2/6-31 l++G(3df,2p) optimized geometric parameters are compared with the experimental bond lengths and angles of Harmony et al.23ain Table 6. That the ground state is s-cis (eclipsed) is shown by many experimental and theoretical studies of the ground state conformation. Hartree-FocW6-3 1G(d) calculated bond lengths (not shown in Table 6) are approximately 1-2% shorter than the experimental values, a discrepancy typical of calculations performed at this level of theory.24 The difference between the theoretical and experimental bond lengths is substantially reduced by including the correction for electron correlation using MP2 theory.25 This is particularly evident in the acetaldehyde CO bond length. As observed by P ~ p l e electron , ~ ~ correlation has a smaller effect upon the theoretical bond angles. The MP2/6-31 lG(3df,2p) calculated values for re(C=O) = 1.2092 8, and LCCHi, = 110So (see Table 6) are respectively smaller and larger than the smaller basis MP2 values. The largest effects of augmenting the basis with diffuse functions are found in the C=O bond length and in the methyl CCH in-plane angle, which increase by '0.002 8, and by 0.3", respectively. The 6-311++G(3df,2p) values closely match the experimental ro(C=O) and LCCHg values to within 0.001 8, and 0.2". This gives us confidence that the 6-3 1l++G(3df,2p) basis set yields an excellent description of the acetaldehyde geometry. It is interesting to note that all calculation levels predict that the methyl group's
J. Phys. Chem., Vol. 99, No. 38, 1995 13857
Acetaldehyde
TABLE 6: Calculated (rq) and Observed ( r ~Geometriee ) MP2/6-31G(d)
MP2/6-311G(3df,2p)
MP2/6-31 lG++(3df,2p)
obs
1.5017 1.2222 1.1090 1.0900 1.0948 124.39 109.84 109.86 115.27 -153.358 97
1.4993 1.2092 1.1068 1.0857 1.0906 124.37 110.47 109.48 115.42 -153.533 75
1.4982 1.2116 1.1063 1.0857 1.0908 124.45 110.75 109.32 115.51 -153.538 38
1.504 1.213 1.106 1.0856 1.0916 124.0 110.6 110.3 114.9
a Bond lengths in angstroms and bond angles in degrees. Observed values are from ref 23a. Experimental bond lengths23a have been reversed. See text. In plane methyl CH bond. Out of plane methyl CH bond.
TABLE 7: CH3CH0 Calculated and Experimental Fundamental Harmonic Frequencies (cm-ly mode a'
VI
v2 v3 v4
V5 v6 v7
v8 v9 VI0
a"
VI 1 VI2 VI3 VI4
a
MP2/6-31G(d)
MP2/6-311G(3df,2p)
MP2/6-311+SG(3df,2p)
expt
3338.1 ($6.4) 3106.8 ($1.6) 2992.2 ($5.3) 1800.8 (f1.5) 1527.5 (f4.8) 1467.8 (f4.0) 1439.6 (f2.8) 1167.9 ($2.0) 926.2 ($2.1) 515.3 (-1.1) 3187.2 ($3.7) 1535.4 ($4.5) 1170.1 ($3.6) 799.2 ($2.4)
3203.7 ($2.4) 3073.6 (f0.6) 2946.4 ($3.7) 1794.1 ($1.1) 1482.4 ($1.7) 1435.6 ($1.6) 1391.2 (-0.6) 1142.1 (-0.4) 904.2 (-0.3) 507.4 (-2.7) 3154.1 ( t 2 . 6 ) 1493.3 ($1.6) 1138.3 ($0.8) 778.8 (-0.3)
3204.0 ($2.4) 3072.6 (f0.5) 2955.1 ($4.0) 1778.0 (f0.2) 1481.1 ($1.6) 1431.0 ($1.4) 1390.9 (-0.7) 1142.9 (-0.3) 904.6 (-0.3) 508.1 (-2.5) 3153.2 (f2.6) 1491.4 (f1.5) 1136.5 (f0.6) 778.0 (-0.4)
3 138.0 3056.4 2841.6 1774.4 1457.0 1411.6 1400.2 1145.6 906.8 521.0 3072.8 1469.7 1129.8 780.8
Numbers given in parentheses are percent deviations from the experimental harmonic frequencies.
in-plane CH bond length should be shorter than the group's out-of-plane CH bond lengths in accord with the Nosberger et al.23b and M ~ K e a nstructures ~ ~ ~ obtained respectively from microwave rotational constants and infrared C-H stretching frequencies (but the converse of Harmony's conclusions). Given that both uncorrelated and all MP2 level calculations provide the same result, the methyl group's experimental in-plane and out-of-plane CH bond lengths have been reversed from Harmony's ordering in our subsequent refinement of the MP2 ab initio force fields. MP2/6-31G(d) Frequencies. Thirteen of the fourteen MP2/ 6-31(d) normal mode frequencies for CH3CHO (Table 7) are 19-200 cm-l above the experimental harmonic values (the largest errors occurring for the CH modes). The fourteenth mode, v10 falls 6 cm-' below the experimental harmonic frequency. The average error of 53 cm-' (3.4%) puts the MP2/ 6-3 1(d) harmonic frequencies outside the window of usefulness for spectroscopic studies. The large-amplitude intemal rotation vibration, ~ 1 5 ,is not included in these statistics. MP2/6-311G(3df,2p) Frequencies. Of the fourteen MP2/ 6-311G(3df,2p) CH3CHO frequencies shown in Table 7 (vi5 again excepted), nine lie 9-134 cm-' above the experimental harmonic frequencies. The remaining five modes lie 2-14 cm-l below the harmonic values. The average absolute frequency error for all modes is 29 cm-' (1.7%). Thus the MP216-311G(3df,2p) frequencies are substantially improved over the MP2/6-31G(d) ones. MP2/6-311++G(3df,2p) Frequencies. The most striking effect of diffuse function augmentation is found for the C=O stretching frequency, v4,which moves from 20 cm-I disparity with the experimental harmonic frequency at the 6-3 11G(3df,2p) level to 4 cm-' at the 6-311++G(3df,2p) level. The improvement for the aldehyde out-of-plane wag, V I Z ,is also significant. Other modes are not strongly affected, and the overall root mean squared error is only slightly improved to 27 cm-I (1.6%).
Comparison of MP2 Frequencies. Table 7 shows that all the MP2 frequencies decrease when the basis set size is increased beyond 6-3 1G(d). A particularly striking decrease, '100 cm-', is found for the methyl CH in-plane stretching mode, V I . Other large decreases, >30 cm-I, are for aldehyde CH stretching and out-of-plane wagging modes, v3 and v12,the two methyl deformation modes, v5 and v7, and both symmetric and antisymmetricmethyl out-of-plane CH stretches, v2 and V I I . Virtually all frequencies are significantly closer to the experimental harmonic frequencies for the large basis sets. The single exception is the CCO bend, V I O . The largest discrepancy is found for the aldehyde CH stretching mode, v3, which still ends up > 100 cm-' above the experimental harmonic frequency. MP2 is clearly a disaster for this mode! A noteworthy outcome of the MP2 calculations is that for the largest basis, 6-31 l++G(3df,2p), four mode frequencies are within 5 cm-l and an additional two are within 10 cm-] of the experimental harmonic frequencies. At the 6-3 1G(d) level only a single mode, v10,falls within the 10 cm-' window. However, see the next section for a further discussion of v10. At both the 6-31 1G(3df,2p) and 6-31 l++G(3df,2p) levels well more than half of the modes are within 25 cm-' of the experimental harmonic values. Only three modes end up above 50 cm-' from the harmonic values compared to seven for 6-31G(d). A graphic comparison of the three MP2 corrections is shown in Figure 1. The five lowest frequencies are shown in part a, and progressively larger frequencies are shown in parts b and c. Discussion. Despite the very considerable improvement in the ab initio MP2 harmonic frequencies using the 6-311++G(3df,2p) and 6-311++(3df,2p) basis set, a 27-29 cm-' root mean squared error remains. Part of this disparity is probably due to errors in the experimental harmonic frequencies. For example, the aldehyde group CH stretch mode suffers from complex Fermi resonance perturbations in all isotopic forms of the molecule. The large deviations between the experimental
Wiberg et al.
13858 J. Phys. Chem., Vol. 99, No. 38, 1995
I
3300 -
!1050 -
W
t
1750
1650
650
450
I
1
3300
t
3100 -
30 19%
k A
B
C
-
a900
aeoo
0
1350'
*
B
C
B
C
D
D
Figure 1. Harmonic frequencies (in cm-I) for CH3CHO: (a) MP2/6-31G(d); (b) MP2/6-31 lG(3df.2~);(c) 6-31 l++G(3df,2p); (d) empirical.
TABLE 8: CHJCDOFundamental Frequencies (cm-I) Calculated at the MP2/6-311++G(W,2p) Level mode calc freq expt harmonic fres %A 3204.8 3072.4 2181.7 1764.1 1480.8 1102.1 1392.8 1135.7 857.3 498.9 3153.2 1489.7 1068.7 685.7
3138.6 3056.8 2130.4 1172.2 1452.7 1097.4 1406.0 1128.2 881.7 5 19.2 3071.8 1459.4 1066.4 692.2
+2.1 +0.5 +2.4 -0.5 +1.9 +0.5 -0.9 +0.7 -2.7 -3.9 -0.9 +2.1 +0.2 -1.0
and theoretical v3 energies are believed to be a result of these interactions. Another part of the disparity may arise from the geometry that was used. Even though it is close to the experimental geometry, it is known that force constants and bond lengths are inversely related.26 The correspondence between experimental and theoretical frequencies generally improves as the number of Xi,k values used to correct the observed frequency for anharmonicity increases, implying that the vibrational assignments used to generate the anharmonic constants are correct. The large differences observed between the experimental and calculated methyl stretching, v1 and v11, CH3CHO frequencies may in part result from the limited number of xiJ values that could be determined from the vibrational spectra for these modes. The normal mode frequencies of CH3CDO and CD3CDO calculated with the 6-3 1 lf+G(3df,2p) ab initio harmonic force field are compared with the experimental harmonic frequencies in Tables 8 and 9, respectively. On average, the calculated energies are approximately 1.5% larger than the observed values, i.e. similar to those for CH3CHO. The acetaldehyde levels of agreement compare favorably with analogous studies of C&, CZHZ,C2&, C2H6, and CsH6.*' Ab initio MP2/6-31G(d) frequencies for the first four molecules differ from their corresponding experimentally estimated harmonic values by an
TABLE 9: CDJCDOFundamental Frequencies (cm-l) Calculated at the MP2/6-311++G(3df,2p) Level mode calc freq exut harmonic fres %A 2376.2 2209.6 2179.5 1759.7 1054.8 1184.2 1074.3 958.0 754.2 436.1 2331.8 1074.9 970.3 576.8
2343.2 2197.2 21 19.6 1763.7
$14 $0.6 $2.8 - 0.2
1168.3 1070.4 970.0 765.8 443.2 2285.0 1058.7 964.4 582.5
+1.4 +0.4 -1.2 -1.4 -1.6 +2.1 +1.5 +0.6 -1.0
average of 4%. Guo and Karplus derived an MP2/6-31G ab initio harmonic force field for benzene.*' Their theoretical frequencies for the in-plane vibrational modes varied by 2-3% relative to the experimental harmonic values of Goodman, Ozkabak and Thakur.28 The theoretical CH3CDO v 1 2 frequency is 22 cm-' greater than the experimental harmonic value. Recall the Y I Zband is not observed in the dl gas phase infrared spectrum. The v12 and v5 band origins are within 1.9 cm-I of one another in the dl matrix-isolated spectrum. As such, the v12 gas phase experimental anharmonic frequency was approximated with that of v5. This substitution may account for this rather large deviation.
Refinement of MP2/6-311G(3df,2p) ab Initio Force Field As previously mentioned a 27 cm-' root mean squared disparity between the highest level MP2 calculated harmonic frequencies and the experimental harmonic ones indicates that the MP2 harmonic force field is not sufficiently accurate to use as a starting point for theoretical calculation (e.g., of anharmonic constants) or for detailed vibrational assignment of combination bands. We therefore improved the ab initio calculated force constants by the following scaling procedure. Both the MP2/
J. Phys. Chem., Vol. 99, No. 38, 1995 13859
Acetaldehyde
TABLE 10: Symmetry Coordinates for Acetaldehyde
The refinement involved a least squares fit to the experimental harmonic fundamental frequencies using a program packagez9 H H 0 requiring as input a force constant scaling vector, the G matrices, \ P I a14 \‘“ R2 40RI and the three isotopomers’ experimental harmonic fundamental 4 c-c 1‘ C-c a2 H p 3 \ frequencies. The force constant scaling vector, p, consisted of 9% Hr3 H the following elements. Each diagonal element of the force constant matrix was multiplied by a separate scaling factor. Two a’ a” separate scaling factors were assigned to the off diagonal S I = Rl S I I= r5 - 1-6 elements of the a’ and a” symmetry blocks. All 17 elements Sz = R2 SI2 = p2 - p3 of the Q, vector were initially set equal to 1.0. The Q, vector S3 = r3 SI3 = y1 - y2 SI4 = E (out-of-plane angle at the carbonyl group) S4 = r4 was allowed to vary in an iterative least squares fit until the S5 = r5 + r6 Sl5 = r (sum of methyl group’s torsional angles) best correlation between the calculated and experimental s 6 = al frequencies was achieved. The CH3CH0, CHFDO, and CD3S7 = a2 CDO harmonic frequencies found in Tables 7-9 were all ss =PI included in the first (scaled) refinement of the MPU6-311Gs9 = p2 + p3 (3df,2p) ab initio force field. The least squares analysis using SI0 = yl + y2 6-31 1G(3df,2p) and the MF2/6-31 l++G(3df,2p) force constants the 44 experimental frequencies Produced a root n ~ a squared n were used as the starting points, and it was found that a slightly ~rrOrof 9.5 more satisfactory fit was obtained using the former force This series of calculated harmonic frequencies and the experimental normal mode frequencies compare well, but a few constants. The force constants in Cartesian coordinates as calculated substantial deviations exist. The calculated CH3CHO and CH3by Gaussian 92 were transformed into force constants for the CDO v3 energies still differ substantially from the experimental symmetry coordinates in Table 10, making use of the correvalues. Again, this may be the result of the complex v3 Fermi sponding B matrix augmented by the terms representing the resonance interactions. This mode gave the largest deviation Eckhardt conditions. The ab initio geometry was used in between observed and calculated frequencies and was deleted constructing this B matrix. In the subsequent refinement of the in the subsequent refinement. The difference, 28 cm-I, between force field, Harmony’s experimental geometry was used, but the CH3CDO vg calculated and experimental harmonic energies as discussed above, the methyl group’s in-plane and out-ofis also high. This state is Fermi perturbed by the (VI4 V I S ) plane CH experimental bond lengths were reversed in the binary combination. Unfortunately, the experimental data analysis. required to correct the observed vg origin for the perturbation TABLE 11: Final Adjusted MP2/6-311G(Mf,2p) Symmetrized Force Constant MatriP E
‘
+
Diagonal Elements matrix element
ab initio values
scaling factor
adjusted value
131 22 393 434 53 66 7 97 88 939 10,lO 11,ll 12,12 13,13 14.14 15,15
12.985 4.572 4.798 5.566 5.418 1.624 1.318 1.202 1.793 1.732 5.381 0.834 0.764 0.346 0.266
0.982 0.968 0.949 0.953 0.999 1.012 0.960 0.988 0.973 0.934 0.948 0.942 0.949 0.994 1.243
12.754 4.427 4.552 5.306 5.41 1 1.644 1.265 1.188 1.744 1.618 5.102 0.786 0.125 0.344 0.330
Off-Diagonal Elements a’ block (Scaling Factor = 0.912)
1 2 3 4 5 6
2
3
4
5
6
I
8
0.587
0.513 0.110
0.012 0.029 --0.004
-0.003 0.077 0.013 0.006
0.490 0.068 -0.194 -0.101 0.06 1
0.486 -0.216 -0.071 -0.035 -0.006 0.471
-0.015 0.277 0.027 0.118 -0.206 -0.178 -0.103
7
8 9
9
10
0.058 0.3 16 0.018
0.01 1 0.116 -0.007 0.164 -0.163 0.046 -0.006 0.769 1.102
O.Oo0
-0.149 0.196 0.036 0.765
a” Block (Scaling Factor = 0.968) 12 11 12 13 14 a
0.130
13 0.124 0.216
Units = mdyne/A. 41 experimental harmonic frequencies included in least squares fit.
14
15
0.027 0.010 -0.068
-0.03 1 0.287 0.243 0.330
Wiberg et al.
13860 J. Phys. Chem., Vol. 99, No. 38, 1995
The experimental CD3CDO V6 harmonic frequency is much lower than the calculated value. A perturbation is believed to be the source of the discrepancy. The Y6 vibrational band is suspiciously broad in the d4 matrix-isolated spectrum. The shoulders that appear to the red and to the blue of the fundamental peak are believed to be the absorbance features of 2vI4(a') and vg v,o(a'), respectively. A complex resonance interaction involving these three states is plausible in that the v6, vg, Y I O , and V I 4 normal modes share common oscillators. Furthermore, the x6,9 anharmonic constant derived from the CH3CDO gas phase spectrum is equivalent to -9.4 cm-' for the d4 isotopomer. This fairly large coupling factor suggests a significant interaction between v6 and v g Y I O . Accordingly, the CD3CDO v6 experimental harmonic frequency was eliminated from the final force field fit. The remaining frequencies were retained in the final least squares analysis. The force constant refinement procedure was repeated for CHsCHO, CH3CD0, and CD3CDO with this reduced set of 41 experimental harmonic frequencies. Once again, the seventeen q vector elements were initialized at 1.0. The final force constant matrix is given in Table 13. The harmonic frequencies produced with this force field are contrasted with the experimental harmonic energies in Table 12. The overall root mean
TABLE 12: Results of Final Normal Coordinate Analysis" CH3CHO mode
obs (cm-I)
calc (cm-I)
3138.0 3146.9 3056.4 3052.5 ~3 (2841.6) 2872.2 ~4 1774.4 1783.4 ~5 1457.0 1457.4 ~6 1411.6 1417.2 V, 1400.2 1399.6 It8 1145.6 1148.1 ~9 906.8 905.3 V ~ O 521.0 521.5 VII 3072.8 3075.3 vi2 1469.7 1465.4 ~ 1 3 1129.8 1132.3 vi4 780.8 782.3 vi5 186.7 189.4 rms dev = 4.3 cm-I VI
~2
CHjCDO
CDsCDO
obs calc obs calc (cm-I) (cm-I) (cm-I) (cm-I) 2343.2 2331.4 3138.6 3146.6 2197.2 2197.0 3056.8 3052.4 2125.7 2119.6 2124.3 2130.4 1761.3 1763.7 1772.2 1765.4 1452.7 1456.3 1037.1 1096.1 (1168.3) 1188.7 1097.4 1408.0 1070.4 1066.0 1406.0 970.0 958.6 1128.2 1140.2 753.7 765.8 (881.7) 850.9 450.1 511.9 443.2 519.2 3075.2 2285.0 2276.9 3071.8 1459.4 1464.0 1058.7 1058.2 964.4 962.4 1066.4 1065.1 581.6 582.5 692.2 691.2 143.6 150.2 180.7 183.0 rms dev = 5.4 cm-I rms dev = 7.2 cm-'
+
+
41 experimental harmonic frequencies included in least squares fit. Frequencies in parentheses were not included in the final fit.
as outlined by Winther16was unavailable. Therefore, the CH3CDO vg experimental harmonic frequency was not included in the final adjustment of the force constant matrix.
TABLE 13: CDXHO Anharmonic Constants X1.k
1,1 1,4 1,7 1.10 1,13 22 2,s 23 2,ll 2,14 3.3 36 399 3,12 3,15 4,4 437 4,lO 4,13 5s 53 5,ll 5,14 66 63 6,12 6,15 737 7,lO 7,13 83
8,ll 8,14 9,9 9,12 9,15 10,lO 10,13 11,ll 11,14 12.12 12,15 13,13 14,14 15,15 a
value (cm-I) -16.7 -0.3 -5.4 -1.7 -6.2" -2.5 -44.9 $3.9 -54.5 -6.8 f0.4 -8.0 -4.0 -1.0 -4.2 -7.8 +0.2 -12.1 -3.8 -8.7 - 14.6 -0.5 -3.3 -2.0 -2.5 -0.4 -1.9 -1.2 t0.5 -13.2 -6.0 -1.6 -0.1 +1.3 -13.7
Estimated value: see text.
source d4 d4 do do N.A. d4 N.A. do d4 di do N.A. do N.A. d4 do do d4 N.A. N.A. do do N.A. di di d4 d4 d4 do do di do d4 N.A. do d4 d4 d4 do do N.A. do N.A. d4 d4
X1.k
value (cm-I)
12 13
-44.3 -5.6 -9.3 - 10.0 N.A. -6.2 -7.7 +1.5
1,8 1.1 1 1,14 23 2,6 23 2,12 2,15 3,4 397 3,lO 3,13
-1.8 -4.5
source d4 di d4 d4
1,15 d4 di d4 N.A. di di N.A. N.A. N.A.
X1.k
1,3 1,6 13 1.12 -0.9 2,4 2,7 2,lO 2,13 3,5 38 3.1 1 3,14
value (cm-l) -3.2 -5.5
- 10.4
source di N.A. di d4
do
-2.5 -0.2 -4.0 -1.7 -2.5 +1.9 -7.6 -4.1 -0.3
di do d4 do
N.A. do do
N.A. di d4 d4 do N.A. N.A. do do d4 di
46 4,9 4,12 4,15 5,7 5,lO 5,13
-0.6 -6.0 +3.1 -0.1
d4 d4 N.A. d4 do do di
6,8 6,ll 6,14
-2.7 +5.9 +0.4
di d4 do
-3.6 -11.2 -6.3 -2.1 -3.5 -3.2 +3.7 +4.9
do d4 d4 do do d4 d4 d4
7,9 7,12 7,15 8,lO 8.13
+o. 1 -3.3 +2.3 -1.5 +1.1
do di do do d4
9,ll 9,14
-26.2 +0.7
d4 do
10.1 1 10.14 11,12 11,15 12,13
+3.4 -8.4 -9.4 +4.1 -2.6
d4
+4.2 -0.5
do d4 d4
10,12 10,15 11,13
d4 d4 N.A.
12,14
-1.2
di
13,14 14.15
-11.1 -4.7
d4 do
13.15
-4.6
di
435 48 4,11 4,14 5,6 5,9 5,12 5,15 67 6,lO 6,13
-0.3 +2.9 -2.5 -5.3
7,8 7,ll 7.14 83 8.12 8.15 9,lO 9.13
-5.4 -1.9 -0.6 -6.2
d4
J. Phys. Chem., Vol. 99, No. 38, 1995 13861
Acetaldehyde squared error for all three isotopomers is 5.8 cm-l, and that for CH3CHO was only 4.3 cm-'. The average scaling factor for the diagonal force constants was 0.968 0.020, which is a significant improvement over that for an MP2/6-31G* calculation (0.930 2 0.025).19 In contrast to the MPZcalculated frequencies,those obtained using HF/6-31G* had an average scaling factor of 0.86 using the harmonic frequencies and 0.81 using the anharmonic frequencies. The scaling factor for frequencies is approximately the square root of the force constant scaling factors, and 0.81 corresponds to the commonly used factor of 0.90 in comparing HFl6-3lG* frequencies with the observed anharmonic frequencies. Vibrational Spectrum of CD3CHO. The validity of the experimentally-determined acetaldehyde harmonic force field was tested by calculating the CD3CHO anharmonic fundamental frequencies. Essentially, the steps of the vibrational analysis were reversed for the d3 isotopomer. Darling and Dennison's equation was used to derive the CD3CHO anharmonic constants from either the 4,dl, or d4 values, and the calculated harmonic frequencies were applied in the conversion equation. In several cases, a given anharmonic constant had been generated for more than one isotopic derivative. The choice as to which isotopomer's X;,k value was best suited for the CD3CHO conversion was made under the aforementioned considerations. Isotopic substitution naturally introduces a change in the kinetic energy matrix. The diagonalization of each isotopomer's FG matrix product necessarily generates a different series of vibrational energies. The L matrices of the assorted isotopomers vary, since this transformation matrix is specific to a given FG matrix. Consequently, the normal mode descriptions of the isotopically-substituted species may change significantly relative to those of the parent molecule. The normal modes of a deuterated form of the molecule, QD,may be expressed in terms of those of the parent molecule, QH,by30
*
TABLE 14: CDjCHO Fundamental Frequencies Calculated at the MP2/6-311G(3df,2p) Level and Predicted Anharmonic Frequenciec mode
calc harmonic freq (cm-I)
calc harmonic freq (cm-I)
233 1.3 2197.8 2872.4 1777.7 1040.9 1407.7 1172.6 985.4 775.9 457.9 2276.9 1050.3 1079.1 634.2 151.3
2249.6 2130.2 2749.0 1749.1 1027.3 1385.8 1124.2 960.2 753.3 449.5 2214.8 1034.5 1061.2 619.0 114.1
VI v2 v3 v4 v5 v6 v7
VS v9
VI0 VI1
VI? VI3 VI4 VI5 (I
obs freq (cm-I) 2262 2120 (2720) 1754 1027 1387 1131 960 750 444 2224 1038 1062 624
Av (obs - calc) (cm-I) 18
- 10 5 0 1 7 0 -3 -6 9 -3 1 5 rms dev = 7.0
All observed frequencies taken from ref 2.
v5,v12,and cm;', and
fundamentalsto v5 = 1027.0cm-l, = 1062.0 cm-I.
vl2 = 1038.0
Experimental Atomic Polar Tensors
The intensities of the infrared bands were measured for pressure-broadened spectra of the three acetaldehyde isotopomers. In each case, the intensities were measured at four to five aldehyde pressures, and the intensities were derived from Beer's law plots of Apl vs pl, where p is the pressure and 1 is the path length. The slopes were determined using a least squares procedure, with the 0,O point included in each data set. Good linear plots were obtained, and the slopes are summarized in Table 15. As is often the case, some of the normal modes gave overlapping bands, and it was necessary to find a way in which to partition the total intensity into that for each of the modes. (4) With acetaldehyde, VI4 was not observed and its intensity was set to zero. The v g fundamental vibration is perturbed by the The matrix product LD-ILHis used to describe the level of mode binary combination ~ 1 4 ~ 1 5 . The intensities of the latter are mixing. This matrix product was calculated for the CD3CHO expected to be weak on the basis of the ab initio calculations isotopomer to ensure that the do, dl, or d4 anharmonic constants and suggest that the combination band should be quite weak would be correlated with the correct d3 harmonic frequency. and is observed because it borrows intensity from the fundaThe calculated CD3CHO anharmonic constants are listed with mental. Therefore the absorption between 823 and 959 cm-l their sources in Table 13. was assigned to vg. The CD3CHO calculated harmonic frequencies, mi, and the The v8 and ~ 1 fundamental 3 vibrational bands overlap in the appropriate anharmonic constants, X j , k , were substituted into the pressure-broadened spectrum, and the former obscures the latter equation in the gas phase and solution. The matrix spectrum gave a ratio of band intensities of 1:73, and it was assumed to apply to the 1 gas phase spectrum. The ,5'1 v.5, v7, and v 1 2 fundamentals vi = wi -&i,k + 2xi,i overlap in the gas phase spectrum, The relative intensities of v6 and v7 could be obtained from the solution spectrum. The to generate the d3 vibrational spectrum. The resulting CD3v5 and v12 band origins almost coincide and could be separated CHO calculated anharmonic fundamental frequencies are comonly in the matrix spectrum. Here, the ratio was 1.86:1. The pared with the observed frequencies in Table 14. The experiv3, v2, Y I Iand , fundamentals form the band between 2630 mental d3 energies are taken from Hollenstein and Gii~~thard.~ and 307 1 cm-' . The v3 band could be separated from the others. It is involved in a complex Fermi resonance interaction, and Overall, the agreement between theoretical and experimental the total intensity of this part of the band was assigned to v3. CD3CHO anharmonic frequencies is outstanding. In fact, while The solution phase spectra allowed the division of the remaining the CD3CHO calculation was intended to evaluate the success intensity among the V I , v2, and V I I fundamentals. of the normal coordinate analysis, it has served to challenge In the spectrum of CH3CD0, ~ 1 and 4 v.5 were not observed some of Hollenstein and Giinthard's d3 gas phase infrared and their intensities were set to zero. The band corresponding spectrum assignments. These investigators assigned the ~ 5 v12, , to a's conceals ~ 1 3and , the ratio of intensities observed in the and ~ 1 fundamentals 3 to vibrational bands centered at 1038.0, matrix spectrum (12.8:l) was used. The ~ 5 v7, , and ~ 1 1062.0, and 1027.0 cm-I, respectively. The CD3CHO spectrum fundamentals form a continuous absorption between 1303 and calculated in this study, along with the results of the mode 1525 cm-I. The solution spectrum allowed the relative intensity mixing program, offers strong evidence for reassignment of the
+
+
2
Wiberg et al.
13862 J. Phys. Chem., Vol. 99, No. 38, 1995 TABLE 15: Observed IR Band Intensities int region (cm-I) slope (kcaumol)
a
476-557 823-958 1056-1 168 1310- 1505 1686- 1816 2630-3071
8.27 6.14 17.43 36.83 108.29 97.53
473-539 812-896 1040-1177 1303-1525 1663- 1790 1986-2156 2880-3140
6.39 2.23 23.32 32.63 108.62 55.98 11.77
891-977 990-1082 1099- 1215 1690- 1777 1925-2 177 21 85-2300
4.49 3.95 25.86 94.02 54.00 2.34
% error in slope
corr coeff
a. CHlCHO 1.21 1.19 1.60 1.33 1.46 1.27 b. CH3CDO 1.22 1.46 0.64 1.09 0.94 0.92 2.05 C. CD3CDO 0.82 2.61 0.60 1.22 0.89 3.79
int partitioning"
0.9995 0.9997 0.9994 0.9995 0.9995 0.9996
VI0
0.9995 0.9990 0.9999 0.9997 0.99988 0.9998 0.9989
VI0
VI
(57.2), vz (27.3), Y I I (15.5)
0.9994 0.9960 0.9996 0.9930 0.9994 0.9970
v8
(84.0), VI3 (16.0) (31.9), ~7 (40.2), Y I Z(27.9)
v9
VE (98.7, vi3 (1.3) V5 (25.8), Vrj (26.4), v7
(5.6). v2 (13.8)
v4
VI
(5.61, vz (1.1), v3 ( 9 0 3 , ~
I
(2.8) I
v9
v8 (92.81, v13 (7.2) ~5 (35.5), ~7 (46.7), Y I Z (17.8) v4
v3
~5
v6 v4 ~q
(7.4), ~3 (92.6)
V I (51.6), V I I (48.4)
See text.
of v7 to be determined, and the ratio of v5 to v12 was obtained from the matrix spectrum (2.0:l). The V I , v2, and V I Ifundamentals also were overlapped, but the relative intensities could be obtained from the solution spectrum. In the spectrum of CD3CD0, the P branch of V I O extended outside the detection range of the spectrometer, and its intensity could not be determined. Neither v g nor VI4 could be observed because of their low intensity, and the ab initio values of 0.16 and 0.08 "01, respectively, were used. The band origins for vs and v13are within a few inverse centimeters of each other, and the ratio of intensities (5.24: 1) was obtained from the matrix spectrum. The v5, v7, and v12 bands overlap, and the ratio of (vg v7) to v12 could be obtained from the solution phase spectrum. It was not possible to separate vg and v7 even in the matrix spectrum, and so the ab initio ratio, 1:1.26, was used. The weak v2 band overlaps the high-energy wing of v3, but it was not possible to obtain the ratio of intensities from either the solution or matrix spectra. Therefore, the ab initio ratio of 0.08:1 was used. The v1 and 1 bands also overlap, but here the ratio could be obtained from the solution spectrum. Plots of the observed pressure-broadened absorption bands, Beer's law plots, and further details of the separation of the band intensities are a~ailab1e.I~ The absolute intensity of mode Qi's vibrational band is proportional to the square of the dipole moment derivative, (dp/dQi). In the harmonic oscillator-linear dipole approximation this relationship is expressed as3I
+
The absolute intensities of the fundamentals may be converted to experimental dipole moment derivative magnitudes with eq 6. The sign ambiguity of the (dp/dQi) factors is resolved by applying the sign sets of the ab initio calculated dipole moment derivatives. The (dp/dQi) terms may then be written in matrix form to give the polar tensors with respect to normal coordinates, where x , y, and z are the coordinate axes of the molecule and a, equals the sign of the dipole moment derivative. The total experimental dipole moment derivative is partitioned among the Cartesian axes as dictated by the ab initio calculated (dp/dQi). For example,
(7)
The PQmatrix may be transformed into the corresponding matrix with respect to internal coordinates, PR,by
P, = PQL-l
(8)
or it may be converted to the Cartesian coordinate framework by
Px = P,B
+ P&3
(9)
The last matrix product in eq 9 is a correctional term for rotation and t r a n ~ l a t i o n .The ~ ~ translational correction applies to ions, while the rotational correction must be included for molecules with a permanent dipole moment. The form of the 4, matrix may be found in ref 29. PX is the atomic polar tensor matrix that describes the change in the molecule's dipole moment upon the displacement of a single atom in the x , y , or z direction. The absolute intensity data, combined with the matrices produced in a normal coordinate analysis, provide a means of generating a molecule's experimental atomic polar tensors. The experimental intensities are compared with the ab initio MP2/ 6-31G(d) absolute intensities in Table 16. Because of the significant errors associated with the measurement and separation of the experimental intensities, we restrict the ab initio calculations to the economical 6-31G(d) level. Even at this modest level of MP2 theory the calculated and experimental intensity trends are consistent. The coordinate transformation matrices produced in the final normal coordinate calculation were used to convert the experimental absolute intensities to atomic polar tensors. The ab initio calculated sign sets were transferred to the observed dipole moment derivatives. The total dipole moment derivatives were divided among the three Cartesian coordinate axes according to the ab initio calculated ratios. Two approximations had to be made in the determination of the experimental atomic polar tensors. The ~ 1 fundamental 5 frequencies of the acetaldehyde-& -dl, and -d4 isotopomers were
Acetaldehyde
J. Phys. Chem., Vol. 99, No. 38, 1995 13863
TABLE 16: Absolute Intensities of Acetaldehyde CH3CHO mode
MP2/ 6-31G*
obs 5.63 1.14 92.38 110.05 9.66 9.84 12.96 17.69 6.29 8.45 2.84 5.22 0.24 0.00
a
CH3CDO MP2/ 6-31G*
obs
5.50 1.65 120.38 97.74 17.99 12.84 17.94 22.04 6.13 13.01 5.58 10.70 0.7 1 1.01 0.47
7.01 1.90 57.91 110.44 11.76 0.00 15.81 22.00 2.32 6.64 3.33 5.91 1.73 0.00
suggests that the experimental intensities were divided among the fundamental vibrational bands in a realistic manner, that the normal coordinate calculation was performed correctly, and that the MF'2/6-31G(d) ab initio dipole moment derivative sign set was an appropriate choice.
CD3CDO
4.39 1.50 87.86 95.72 17.81 0.56 24.89 25.12 2.32 12.14 5.58 10.48 1.69 0.05 0.19
obs 1.25 4.15 51.55 95.50 0.00 26.25 2.96 3.89 0.00 1.16 1.11 0.73 0.00
MP2/ 6-31G* 1.94 6.52 81.05 101.20 3.72 41.80 4.69 5.96 0.16 10.58 2.70 5.32 0.95 0.08 1.09
Conclusions An experimentally-determined harmonic force field for acetaldehydewas developed in this study. Ab initio force fields are reported at MP2/6-31G(d), MP2/6-31lG(3df,2p), and MP2/ 6-31 l++G(3df,p) levels of theory. The large improvements (as much as 100 cm-I) between 6-311G(3df,2p) and 6-31G(d) frequency calculations show the inadequacy of a modest polarization double-g basis set. The effect of including diffuse functions was relatively small. The 6-31 l++G(3df,2p) level calculation is believed to approach the limit of MP2 theory. These MP2/6-31l++G(3df,2p) frequencies range from -10 to +113 cm-l from the experimental harmonic values with an average error of 1.6%. The largest error is 4.0% for mode 3. The MP2/6-31lG(3df,2p) ab initio harmonic force constants were subsequently revised through a least squares fit to a series of experimental fundamental frequencies that had been corrected for anharmonicity. The success of this refinement has been evaluated in two ways. In the Fist test, the final force field was used to calculate the harmonic frequencies of CD3CH0, an isotopomer that had not been included in the normal coordinate analysis. The CD3CHO anharmonic constants were derived from their corresponding CH3CH0, CHsCDO, or CD3CDO values. The d3 anharmonic fundamental frequencies were then determined from the calculated harmonic frequencies with the transferred X L , ~ . The correlation between the calculated and experimentalanharmonic fundamental frequencies is excellent. The level of agreement is all the more remarkable in light of the C, symmetry of this molecule. Specifically, there are innumerable opportunities for vibrational interactions that may vary dramatically from one
Observed values corrected for anharmonicity.
beyond the range of the infrared spectrometer's detection system. The MP2/6-31G(d) ab initio intensities for the V I S band were applied in the atomic polar tensor calculation in order to complete the intensity data set. Similarly, the CD3CDO YIO vibrational band's P branch extends beyond the detection range of the spectrometer. Reliable integrated intensity values for the CD3CDO YIO vibrational band could not be obtained. The CH3CHO and CH3CDO ab initio Y I O intensities are roughly twice the experimental values. As such, 50% of the CDsCDO MPY 631G(d) calculated v10 intensity served as an ersatz experimental value in the atomic polar tensor derivation. The observed atomic polar tensors for CH3CH0, CHsCDO, and CD3CDO are compared with the corresponding theoretical values in Table 17. There is a fairly good correspondence between the experimental and theoretical MP2/6-3 1G(d) atomic polar tensors. The agreement between the experimental polar tensors of the three examined isotopomers is also good. This
TABLE 17: Experimental Atomic Polar Tensors for Acetaldehyde, Acetaldehyde-& and Acetaldehyde44 X
CH3CHO lx ly lz 2x 2y 22 3x 3y 32 4x 4y 4z 5x 5y 5z 6x 6y 6z 7x 7y 7z a
CD3CDO
CH3CDO
average
calc"
X
Y
Z
X
Y
2
X
V
7
X
V
7
X
Y
Z
-1.52 -0.01 0.78 3.70 0.01 -0.18 -0.95 0.00 -0.67 -1.47 0.00 0.46 -0.16 0.00 -0.38 0.20 0.01 -0.01 0.20 -0.01 0.01
0.00 -0.68 0.00 0.00 0.19 0.00 0.00 0.02 0.00 0.00 0.34
0.14 0.00 -3.92 -0.60 0.00 4.56 -0.42 0.00 -0.21 1.06 0.00 -0.81 -0.16 0.00 0.13 -0.01 0.35 0.12 -0.01 -0.35 0.12
-1.36 -0.02 0.79 3.25 0.01 -0.20 -0.83 0.01 -0.61 -1.60 0.00 0.57 0.04 0.00 -0.29 0.27 0.09 -0.13 0.28 -0.10 -0.11
0.00 -0.74 0.00 0.00 0.45 0.00 0.00 0.03 0.00 0.00 0.27 0.00 0.00 0.30
0.22 0.00 -3.64 -0.59 0.00 4.15 -0.32 0.00 -0.23 0.94 0.00 -0.49 -0.09 0.00 0.23 -0.08 0.30 0.00 -0.08 -0.30 0.00
- 1.48 0.00 0.81 3.67 -0.01 -0.30 -0.83 0.00 -0.61 - 1.70 0.00 0.40 -0.12 0.00 -0.26 0.25 0.19 -0.05 0.25 -0.19 -0.03
0.00 -0.68 0.00 0.00 0.38 0.00 0.00 -0.03 0.00 0.00 0.14 0.00 0.00 0.37 0.00 0.07 -0.09 0.22 -0.08 -0.09 -0.22
0.25 0.00 -4.00 -0.75 0.00 4.52 -0.3 1 0.00 -0.26 0.90 0.00 -0.5 1 -0.07 0.00 0.04 -0.01 0.38 0.10 -0.01 -0.38 0.10
-1.45 -0.01 0.79 3.54 0.00 -0.23 -0.87 0.00 -0.63 -1.59 0.00 0.48 -0.08 0.00 -0.31 0.24 0.10 0.06 0.24 -0.10 -0.04
0.00 -0.70 0.00 0.00 0.34 0.00 0.00 0.01 0.00 0.00 0.25 0.00 0.00 0.34 0.00 0.06 -0.10 0.16 -0.06 -0.10 -0.16
0.20 0.00 -3.85 -0.65 0.00 4.41 -0.35 0.00 -0.23 0.97 0.00 -0.60 -0.11 0.00 0.13 -0.03 0.34 0.07 -0.03 -0.34 0.07
-2.38 0.00 0.28 4.48 0.00 -0.14 -1.18 0.00 -0.56 -1.30 0.00 0.80 -0.11 0.00 -0.39 0.25 0.00 0.00 0.25 0.00 0.03
0.00 -1.42 0.00 0.00 0.64 0.00 0.00 0.26 0.00 0.00 0.26 0.00 0.00 0.39 0.00 0.18 -0.06 0.33 -0.18 -0.06 -0.33
0.25 0.00 -3.56 -0.79 0.00 4.37 -0.42 0.00 -0.42 1.01 0.00 -0.88 -0.14 0.00 0.09 0.05 0.41 0.20 0.05 -0.41 0.20
0.00 0.00 0.34 0.00 0.11 -0.10 0.15 -0.11 -0.10 -0.15
MP2/6-3 lG* calculated intensities.
0.00 0.00 -0.10 0.12 0.00 -0.10 -0.12
13864 J. Phys. Chem., Vol. 99, No. 38, 1995 isotopic species to another. On occasion the anharmonic constants may have been unwittingly generated from perturbed vibrational bands. This sort of error would have been propagated through the use of Darling and Dennison’s Xi,k conversion equation. Nevertheless, the observed CD3CHO vibrational spectrum is well predicted by the calculation. This lends credibility to the computational method applied in this work, even for molecules of such low symmetry as acetaldehyde. The experimental atomic polar tensors offered a second check of the quality of the normal coordinate calculation. The coordinate transformation matrices derived in this type of analysis enable the determination of the atomic polar tensors from the experimental dipole moment derivatives. If the absolute intensities of the fundamental vibrational bands have been properly obtained and the normal coordinate calculation has been performed correctly, then the experimental atomic polar tensors of the investigated isotopomers should be the same. As seen in Table 16 there is satisfactory correspondence between the CH3CH0, CHFDO, and CD3CDO atomic polar tensors. The few larger deviations in Table 16 are believed to be the result of the difficulties in resolving the methyl group’s deformation bands v5, V I , and v12in the pressure-broadened spectra.I9
Acknowledgment. This investigation was supported by grants from the National Science Foundation. We thank the Pittsburgh Supercomputing Center for an allocation of computer time. References and Notes (1) E.g.: (a) McKean, D. C.; Duncan, J. L. Spectrochim. Acta 1971, 27A, 1879. (b) Goodman, L.; Ozkabak, A. G.; Wiberg, K. B. J. Chem. Phys. 1989, 91, 2069. (2) Walters, V. A.; Colson, S. D.; Snavely, D. L.; Wiberg, K. B. J. Phys. Chem. 1985, 89, 3857. (3) Hollenstein, H.; Giinthard, Hs. H. Spectrochim. Acta 1971, 27A, 2027. (4) Artis, D. Ph.D. Thesis, Yale University, 1990. (5) (a) Vakhlueva, V. I.; Finkel, A. G.; Sverdlov, L. M.; Andreeva, A. I. Opt. Spectrosc. 1%8,25,234.(b) Rogers, J. D. General Motors Research Laboratories Research Publication GMR-4853, ENV-195, 1985. (6) (a) Wilson, B.; Wells, A. J. J. Chem. Phys. 1946, 14, 578. (b) Penner, S. S.; Weber, D. J. Chem. Phys. 1951, 19, 807. (7) Dickson, A. D.; Mills, I. M.; Crawford, B. J. J. Chem. Phys. 1957, 27, 445.
Wiberg et al. (8) Hollenstein, H.; Gunthard, Hs. H. Spectrochim. Acta 1971, 27A, 2027. (9) Wiberg, K. B.; Walters, V.; Colson, S. D. J. Phys. Chem. 1984, 88, 4723. (10) Gu,H.; Kundu, T.; Goodman, L. J. Phys. Chem. 1993, 97, 7194. (11) Herzberg, G. Molecular Spectra and Molecular Structure. Vol. 11, Infrared and Raman Spectra of Polyatomic Molecules; van Nostrand Reinhold: New York, 1945. (12) Durocher, G.; Sandorfy, C. J. Mol. Specrrosc. 1967, 22, 347. (13) Darling, B. T.; Dennison, D. M. Phys. Rev. 1940, 57, 128. (14) Eichelberger, T. S.; Fisanick, G. J. J. Chem. Phys. 1981, 74, 5962. (15) (a) Hollenstein, H. Mol. Phys. 1980, 39, 1013. (b) Hollenstein, H.; Winther, F. J. Mol. Spectrosc. 1978, 71, 118. (16) Winther, F. Z. Naturjorsch. 1970, 25A, 1912. (17) Crighton, J. S.; Bell, S. J. J. Mol. Spectrosc. 1985, 112, 285. (18) (a) Huzinaga, J. J. Chem. Phys. 1965, 42, 1293. (b) Dunning, T. H. J. Chem. Phys. 1970, 53, 2823. (19) Thiel, C. Y. Ph.D. Thesis, Yale University, 1990. (20) Hadad, C. M.; Foresman, J. B.; Wiberg, K. B. J. Phys. Chem. 1993, 97, 4293. (21) (a) Ozkabak, A. G.; Goodman, L. J. Chem. Phys. 1992,96,5958. (b) Goodman, L.; Leszczynski, J.; Kundu, T. J. Chem. Phys. 1994, 100, 1274. (22) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. GAUSSIAN 92, Revision A; Gaussian, Inc.: Pittsburgh, PA, 1992. (23) (a) Harmony, M. D.; Laurie, V. W.; Kuckowski, R. L.; Schwendeman, R. H.; Ramsay, D. A.; Lovas, F. J.; Lafferty, W. J.; Maki, A. G. J. Phys. Chem. Rej Data 1979, 8, 619. (b) Nosberger, P.; Bauder, A.: Giinthard, H. H. Chem. Phys. 1973, I , 418. (c) McKean, D. C. Chem. SOC. Rev. 1978, 7 , 399. (24) (a) Defrees, D. J.; Ragavachari, K.; Schlegel, H. B.; Pople, J. A. J. Am. Chem SOC. 1982, 104, 5576. (b) Wiberg, K. B. J. Org. Chem. 1985, 50, 5285. (25) (a) M@ller,C.; Plesset, M. S. Phys. Rev. 1934,46,618. (b) Binkley, J. S.; Pople, J. A. Int. J. Quantum Chem. 1975, 9, 229. (c) Pople, J. A,; Binkley, J. S.;Seger, R. Int. J. Quantum Chem. Symp. 1976, IO, 1. (26) Wilson, E. B.; Decius, J. C.; Cross, C. C. Molecular Vibrations; McGraw-Hill Book Co., Inc.: New York, 1955. (27) Guo, H.; K q l u s , M. J. Chem. Phys. 1988, 89, 4235. (28) Goodman, L.; Ozkabak, A. G.; Thakur, S. N. J. Phys. Chem. 1991, 95, 9044. (29) Dempsey, R. C. Ph.D. Thesis, Yale University, 1983. (30) Rava, R. P.; Philis, J. G.; Krogh-Jespersen. K.; Goodman, L. J. Chem. Phys. 1983, 79, 4664. (31) Bode, J. H.; Smit, W. M. A. J. Phys. Chem. 1980, 84, 198. (32) Person, W. B.; Newton, J. H. J. Chem. Phys. 1974, 61, 1040. (33) Lucazeau, G.; Sandorfy, C. Can. J. Chem. 1970, 48, 3694.
JP95 15 141
