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J. Phys. Chem. A 2010, 114, 9782–9787
Explicitly Correlated Coupled Cluster Calculations for Propadienylidene (H2CCC)† Peter Botschwina* and Rainer Oswald Institut fu¨r Physikalische Chemie, UniVersita¨t Go¨ttingen, Tammannstraβe 6, D-37077 Go¨ttingen, Germany ReceiVed: March 25, 2010; ReVised Manuscript ReceiVed: May 19, 2010
Propadienylidene (H2CCC), a reactive carbene of interest to combustion processes and astrochemistry, has been studied by explicitly correlated coupled cluster theory at the CCSD(T)-F12x (x ) a, b) level. Vibrational configuration interaction (VCI) has been employed to calculate accurate wavenumbers for the fundamental vibrations of H2CCC, D2CCC, and HDCCC. The symmetric CH stretching vibration of H2CCC is predicted to occur at ν1 ) 2984 cm-1. Absorptions observed by argon matrix infrared spectroscopy at 3049.5 and 3059.6 cm-1 are reassigned to the combination tone ν2 + ν4, which interacts with ν1 and is predicted to have a higher intensity than the latter. Furthermore, IR bands detected at 865.4 and 868.8 cm-1 are assigned to ν6(HDCCC), and those observed at 904.0 and 909.8 cm-1 are assigned to the out-of-plane bending vibration ν8(HDCCC). An accurate value of 79.8 ( 0.2 kJ mol-1 is recommended for the zero-point vibrational energy of H2CCC. I. Introduction Reactive molecules of chemical formula C3H2 are important species in various areas of chemistry such as combustion processes or astrochemistry. Early ab initio calculations1–3 predicted that the energetically most favorable isomer is cyclopropenylidene in its closed-shell singlet state, followed by chain-like triplet propargylene, HCCCH. As was first demonstrated by Maier and co-workers,4 the latter may be photochemically produced from the former. A third C3H2 isomer, singlet propadienylidene (ethylidene carbene, vinylidene carbene), could be obtained in a similar way and was spectroscopically investigated by argon matrix isolation IR spectroscopy.5 In 1990, propadienylidene (H2CCC) was investigated in the gasphase by millimeter-wave spectroscopy,6 which opened the way for an astronomical detection of this molecule. Indeed, shortly later radio astronomical lines of H2CCC were observed in two famous astronomical sources (TMC-1 and IRC+10216) by means of the IRAM 30 m telescope.7 In a joint experimental/ theoretical study, the equilibrium (re) structure of H2CCC was determined by Gottlieb et al.;8 it was slightly revised with the aid of more accurate ab initio data by Gauss and Stanton in 1999.9 To the authors’ knowledge, no high-resolution IR spectra have yet been published for H2CCC and its deuterated isotopomers. Compared with the theoretical harmonic values for the symmetric CH stretching vibration (ω1 ) 3137.5 cm-1 from CEPA-1 calculations of ref 8 and ω1 ) 3123.2 cm-1 from CCSD(T) calculations of ref 9), the argon matrix values of 3049.5 and 3059.6 cm-1 given in ref 5 appear to be rather high. Typically, anharmonicity contributions to the symmetric CH stretching vibrations of comparable molecules are well above 100 cm-1. For example, recent calculations by means of vibrational configuration interaction (VCI) based on ab initio potential energy surfaces (PESs) yielded differences of 126-149 cm-1 for the molecules H2CO, H2CNH, and H2CCO.10 †
Part of the “Reinhard Schinke Festschrift”. * To whom correspondence should be addressed. E-mail: pbotsch@ gwdg.de.
The main goal of the present work consists in the calculation of accurate wavenumbers for all fundamental vibrations of H2CCC, D2CCC, and HDCCC. VCI in conjunction with PESs from explicitly correlated coupled cluster theory at the CCSD(T)F12x (x ) a, b)11,12 level is used for this purpose. The high efficiency and accuracy of this approach was recently demonstrated for nine test molecules by Rauhut et al.10 II. Details of Calculations Most of the calculations of the present work made use of explicitly correlated coupled cluster theory at the CCSD(T)F12x (x ) a, b) level.11,12 The fixed-amplitude approximation 3C(FIX) was employed in the density-fitting MP2-F12 calculations, which precede the explicitly coupled cluster computations. The newly developed systematically convergent basis sets of type cc-pVnZ-F12 (n ) D, T, Q), developed by Peterson et al.,13 were used as the atomic orbital basis sets. In the following, they will be denoted VnZ-F12. Following the recommendation of Peterson et al., the geminal exponents β were chosen as 0.9, 1.0, and 1.1 for n ) D, T, and Q, respectively. Optimized auxiliary basis sets termed VnZ-F12/OptRI were taken from the recent work of Yousaf and Peterson.14 JKFIT and MP2FIT basis sets were chosen as recommended in that work. Tight thresholds (10-9) were employed in the construction of the complementary auxiliary basis set (CABS); see ref 12 for details. The Hartree-Fock reference energies were improved by addition of the CABS singles correction. For comparison, a number of calculations was also carried out by standard CCSD(T),15 using Dunning-type basis sets either of the cc-pVnZ or of the cc-pCVnZ family, in both cases with n ) Q, 5, and 6.16–19 For brevity, we will denote them by VnZ or CVnZ, respectively. All electronic structure and VCI calculations of the present work were performed with the MOLPRO system of ab initio programs.20 Equilibrium geometrical parameters and harmonic vibrational wavenumbers were calculated either by automatic procedures inherent in MOLPRO or by means of appropriate least-squares fitting with polynomials and subsequent solution of the harmonic vibrational problem using self-written programs. A multimode expansion of the potential energy surface was used in the VCI
10.1021/jp102702n 2010 American Chemical Society Published on Web 06/01/2010
Vibrational Configuration Interaction for H2CCC Isotopomers
J. Phys. Chem. A, Vol. 114, No. 36, 2010 9783
TABLE 1: Calculated Equilibrium Geometrical Parameters and Total Energies for H2CCC (X˜ 1A1) CCSD(T)a b
re (C(1)H) Re (HC(1)H)b R1e (C(1)C(2))b R2e (C(2)C(3))b Ve (+115) /Eh a
CCSD(T*)-F12aa
n)Q
n)5
n)6
n)D
n)T
n)Q
1.08508 117.47 1.33134 1.29136 -0.144372
1.08479 117.52 1.33077 1.29042 -0.153471
1.08479 117.54 1.33054 1.29013 -0.156686
1.08540 117.57 1.33282 1.29209 -0.153959
1.08511 117.55 1.33119 1.29048 -0.163300
1.08485 117.55 1.33056 1.28995 -0.163837
Valence electrons are correlated. b Equilibrium bond lengths in Å, HC(1)H angle in degrees.
Figure 1. Dependence of CCSD(T) carbon-carbon equilibrium bond lengths of H2CCC on the size of the basis set (all electrons correlated).
calculation of anharmonic vibrational wavenumbers, employing the automated iterative interpolation procedure of MOLPRO.21 Up to three-mode contributions were considered, and all contributions were computed at the same level as theory. For further details we refer to refs 21 and 22. The vibrational selfconsistent field (VSCF) and VCI calculations make use of Watson’s rovibrational Hamiltonian for nonlinear molecules,23 with an approximation to the Coriolis term as described in ref 22. The VCI calculations include configurations from single up to quadruple excitations; see ref 24 for more details. III. Results and Discussion A. Equilibrium Structures. Calculated equilibrium structures, obtained by standard and explicitly correlated coupled cluster calculations and six different basis sets, are listed in Table 1. Among the different variants of CCSD(T)-F12x, results obtained by CCSD(T*)-F12a are quoted. This method includes scaling of the contributions of the connected triple substitutions as described in ref 12. Results obtained by CCSD(T)-F12a, CCSD(T)-F12b, and CCSD(T*)-F12b are supplied as Supporting Information, Table S1. According to Table 1, there are only very small differences among the equilibrium geometrical parameters obtained at levels CCSD(T)/V6Z and CCSD(T*)F12a/VQZ-F12. The maximum difference of 0.000 18 Å occurs
Figure 2. Variation of the CCSD(T*)-F12a/VQZ-F12 energy with the CCC angles for three different molecules, with the other geometrical parameters kept fixed at their equilibrium values.
for the terminal CC equilibrium distance, R2e. Basis set extension at the explicitly correlated coupled cluster level from cardinal number n ) T to n ) Q leads to reductions in R1e and R2e by only 0.00062 and 0.00053 Å, so that the values at n ) T are probably already within 0.001 Å of the valence basis set limit results. Mainly owing to the neglect of core-valence correlation effects, the equilibrium bond lengths obtained with the largest basis sets are still too long. For isoelectronic linear CCCO, CCSD(T*)-F12a calculations with the VQZ-F12 basis set overestimate the carbon-carbon equilibrium bond lengths by 0.0034 Å (inner CC bond) and 0.0025 Å (outer CC bond) with respect to an accurate mixed experimental/theoretical equilibrium structure.25 Assuming the same differences to apply for H2CCC, we arrive at R1e ) 1.3272 Å and R2e ) 1.2875 Å. Both agree well with the recommended values reported by Gauss and Stanton, R1e ) 1.328 ( 0.0005 Å and R2e ) 1.287 ( 0.001 Å.9 Results of standard CCSD(T) calculations, in which all electrons were correlated, are provided as Supporting Information (see Table S2). For the smaller basis sets up to CVQZ, data from ref 9 were taken. The convergence behavior of R1e and R2e with respect to the size of the basis set, measured by
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TABLE 2: Harmonic and Anharmonic Vibrational Wavenumbers (in cm-1) for H2CCC CCSD(T)
CCSD(T*)-F12a
vibration
VQZ
V5Z
V6Z
VDZ-F12
ω1 (a1) ω2 (a1) ω3 (a1) ω4 (a1) ω5 (b1) ω6 (b1) ω7 (b2) ω8 (b2) ω9 (b2) ν1 (a1) ν2 (a1) ν3 (a1) ν4 (a1) ν5 (b1) ν6 (b1) ν7 (b2) ν8 (b2) ν9 (b2) ZPE (harm.) ZPE (anh.)
3120 1996 1489 1117 1019 210 3210 1049 272
3119 1996 1488 1117 1017 207 3210 1049 270
3120 1998 1488 1118 1017 207 3210 1049 270
3116 1987 1486 1112 1008 198 3207 1048 262 2982 1944 1448 1104 993 212 3064 1030 272 6712 6630
6741
6737
6738
b
VTZ-F12b
VQZ-F12
3117 1994 1487 1116 1013 202 3208 1048 267 2984 1952 1448 1109 998 216 3069 1031 278 6726 6646
3119 1997 1487 1118 1015 206 3209 1048 269
exp.a Ar matrix
3049.5, 3059.6c 1952.2, 1963.2 1446.9, 1449.3 999.5, 1004.8 1025.0 6734
a
Reference 5. Two values are quoted in the case of site absorptions, with the more intense band being underlined. b VCI calculations are based on 8645 grid points and 45 330 configurations. c Questionable assignment (see the text).
cardinal number n, is displayed in Figure 1. The results from the CCSD(T) calculations with CVnZ basis sets may be extrapolated to R1e ) 1.3270 Å and R2e ) 1.2865 Å. At the CCSD(T) basis set limit, the CC equilibrium distances are thus probably too small by ca. 0.001 Å. Very likely, the omission of higher substitutions in the coupled cluster calculations is mainly responsible for the underestimation of the bond lengths. B. Harmonic and Anharmonic Fundamental Vibrations of H2CCC. Table 2 lists calculated and experimental wavenumbers for the fundamental vibrations of H2CCC. Standard CCSD(T) calculations with the large V6Z basis (602 contracted Gaussian-type orbitals, cGTOs) and CCSD(T*)-F12a calculations with the VQZ-F12 basis (329 cGTOs) exhibit maximum differences of 1-2 cm-1 in the harmonic wavenumbers. The largest difference between the results obtained with basis sets VQZ-F12 and VTZ-F12 is 4 cm-1 for the lower vibration of b1 symmetry, which is mainly CCC out-of-plane bending in character. Results from other explicitly correlated coupled cluster variants are given in Table S3 of the Supporting Information. The VCI calculations place the wavenumber of the symmetric CH stretching vibration (ν1) at 2984 cm-1 (VTZ-F12 basis). This value is 66 cm-1 smaller than the stronger matrix IR absorption assigned to this type of vibration.5 The calculated difference ω1 - ν1 is 133 cm-1, which falls well into the range of such differences as noted in the introduction. The correctness of the assignment made by the experimentalists thus appears to be highly questionable. The wavenumber of the asymmetric CH stretching vibration (ν7) is predicted at 3069 cm-1, 85 cm-1 above the present value for ν1. According to previous coupled cluster calculations by Gauss and Stanton,26 the absolute IR intensity of the ν7 band is very weak, and so it is not surprising that it has not been observed in the argon matrix IR spectrum. Experimental values for the difference in CH stretching vibrational wavenumbers νasymm - νsymm of H2CO, H2CNH, and H2CCO, calculated from Table 2 of ref 10, are 61, 110, and 95 cm-1, respectively. The corresponding value for H2CCC falls well within that range. The VCI wavenumbers for vibrations ν2 (∼ pseudo-antisymmetric CC stretch) and ν3 (∼ CH2 scissoring) are very close to
the more intense matrix absorptions. The remaining totally symmetric vibration ν4 is predicted at 1109 cm-1. The intensity of this band was calculated to be very small (only 1% of the most intense ν2 band26) and thus may well have escaped detection. Among the two vibrations of b1 symmetry, ν5 (∼ CH2 wagging) was predicted to have the second highest intensity (7% of the ν2 band,26 in good agreement with experiment). We predict the gas-phase wavenumber to occur at ν5 ) 998 cm-1, very close to the matrix absorptions at 995.5 and 1004.8 cm-1. For the nearby CH rocking vibration ν8, our calculations yield a wavenumber of 1031 cm-1, to be compared with the matrix value of 1025.0 cm-1. The CCC bending vibrations (ν6 and ν9) have wavenumbers outside the range of the previous argon matrix IR experiments.5 According to the coupled cluster calculations of Gauss and Stanton,26 their absolute IR intensities are also very weak. We predict the anharmonic wavenumbers at ν6 ) 216 and ν9 ) 278 cm-1. The substantial difference in wavenumbers for the out-of-plane (o.p.) and in-plane (i.p.) CCC bending vibrations may be traced back to the corresponding CCC bending potentials. These are displayed in Figure 1 together with CCC bending potentials for isoelectronic C3O and the triatomic molecule C3, which is well-known to have an extremely shallow bending potential.27 The experimental CCC bending vibrational wavenumbers of C3 and C3O are 63.4 cm-1 and 109 ( 8 cm-1, respectively.27,28 Accurate zero-point energies (ZPEs) of fundamental small molecules are of great interest to thermochemistry and reaction kinetics. For H2CCC, quite accurate values have been recently reported by Aguliera-Iparraguirre et al.29 and Va´zquez et al.30 The published values are 79.35 and 80.23 kJ mol-1, respectively. The latter is probably an overestimate since calculations at the CCSD(T)/VQZ level, with all electrons correlated, were employed. As may be seen from Table S4 of the Supporting Information, such calculations overestimate the harmonic ZPE by about 30 cm-1 (0.36 kJ mol-1) with respect to the present value of 6760 cm-1 from CCSD(T)/CV5Z calculations. The CCSD(T)/V6Z value from calculations, in which the valence electrons were correlated, is 6738 cm-1 and is very close to the
Vibrational Configuration Interaction for H2CCC Isotopomers corresponding CCSDT*)-F12a value of 6734 cm-1 (see Table 2). Owing to the overestimation of the equilibrium bond lengths and the corresponding effects on the harmonic force constants, the latter two values appear to be slightly too small. We recommend ZPE (harm.) ) 6750 cm-1, with an uncertainty of ca. 10 cm-1. The anharmonicity contribution to ZPE is calculated to be -80 cm-1 (-0.96 kJ mol-1) from the present VCI calculations with the larger basis set. The corresponding value from ref 29 is -0.83 kJ mol-1. Our final recommendation for ZPE (H2CCC) is 6670 cm-1 or 79.79 kJ mol-1, with a somewhat conservative error estimate of (0.2 kJ mol-1. We have still to look for an alternative assignment of the matrix absorptions at 3049.5 and 3059.6 cm-1.5 According to our VCI calculations, the combination tone ν2 + ν4 might be a suitable candidate. However, intensity considerations may also play an important role in proper assignments. Since the calculation of absolute IR intensities by full-dimensional VCI based on CCSD(T)-F12x potential and electric dipole moment functions is still an arduous task, we have adopted a simpler dimensionality-reduced approach. Only the totally symmetric vibrational modes are considered explicitly in a way that was introduced earlier in applications to protonated diacetylene (H2C4H+).31 In the case of H2CCC, we make use of a fourdimensional (4D) approximate vibrational Hamiltonian of the form (in atomic units) ∧
4
Hvib ) - 1/2
∑ ∂2/∂Qi2 + Vanh(S1,S2,S3,S4)
(1)
i)l
where Qi are the normal coordinates of the four totally symmetric vibrations. The mass-independent curvilinear symmetry coordinates S1-S4 are defined as follows:
J. Phys. Chem. A, Vol. 114, No. 36, 2010 9785 TABLE 3: Anharmonic Wavenumbers (in cm-1) and Absolute IR Intensities (in km mol-1, in Parentheses) for H2CCC from Dimensionality-Reduced (4D) Calculations band ν4 ν3 ν2 2ν4 ν3 + ν4 2ν3 ν1 ν2 + ν4
uncorr.
corr.a
1106 (2.0) 1468 (11.3) 1969 (251) 2207 (0.3) 2572 (0.004) 2917 (0.4) 3070 (8.0) 3056 (0.1)
1109 (2.0) 1448 (11.2) 1952 (249) 2213 (0.3) 2554 (0.004) 2869 (0.8) 2984 (2.9) 3048 (4.7)
Ar matrixb
1446.9 1952.2
3049.5c
a Underlined values refer to VCI calculations with CCSD(T*)-F12a/VTZ-F12 PES (see Table 2). The correction parameters (in cm-1) are: ∆4 ) 3, ∆3 ) -20, ∆2 ) -17, and ∆1 ) -85. b Reference 5. Most intense absorptions are quoted in case of site absorptions. c Assignment revised (see the text).
Analogous corrections have been applied earlier to several 32 33 molecules and complexes such as HN+ 2 , H3N · · · HF, or CH3/ + 34 CH3 . The corrections consist in a modification of the diagonal ˆ vib over a basis of harmonic elements Hii(V1, V2, V3, V4) of H oscillator product functions according to 4
∼
Hii(V1,V2,V3,V4) ) Hii(V1,V2,V3,V4) +
∑ ∆i(Vi + 21 ) i)1
1 S1 ) (∆r1 + ∆r2) √2 S2 ) -
32 ∆R
(4) (2a)
(2b)
S3)∆R1
(2c)
S4)∆R2
(2d)
In eqs 2a-2d, the difference coordinates are taken with respect to the corresponding equilibrium data as defined in Table 1. The 4D PES Vanh was obtained by least-squares fit to 183 CCSD(T*)-F12a/VQZ-F12 energy points and has the following analytical form:
V-Ve )
∑ CijklSi1Sj2Sk3Sl4
(3)
ijkl
Here, Ve is the total energy at equilibrium; the coefficients Cijkl are provided as Supporting Information (Table S5). In an analogous way, the electric dipole moment function (EDMF) is analytically represented in polynomial form (see Table S6). To improve the results of calculations with the approximate Hamiltonian of eq 1, a simple correction scheme is employed. Thereby, the anharmonic interaction with asymmetric vibrational modes of b1 and b2 symmetry is implicitly accounted for.
The parameters ∆i were determined through adjustment of the wavenumbers of the fundamental transitions, obtained via ˆ vib in a sufficiently large basis of harmonic diagonalization of H oscillator product functions, to the VCI data (VTZ-F12 basis) of Table 2. From the calculated vibrational wave functions and the analytical EDMF of Table S6, integrated molar absorption intensities for vibrational transitions arising from the vibrational ground state were calculated according to the formula
Af0 )
πNA ν |µ | 2 3pc0ε0 f0 f0
(5)
In eq 5, NA is the Avogadro constant, p is Planck’s constant divided by 2π, c0 is the speed of light in vacuum, ε0 is the electric constant, νjf0 is the vibrational wavenumber, and µf0 is the corresponding vibrational transition dipole moment. Results of the 4D calculations are given in Table 3. In agreement with the previous ab initio calculations,5,26 the ν2 band is by far the most intense totally symmetric vibration. Anharmonicity effects on the ν2, ν3, and ν4 bands are small, and the present values agree well with the previous CCSD(T) results of Gauss and Stanton.26 The corrected anharmonic 4D treatment predicts an intensity of only 2.9 km mol-1 for the symmetric stretching vibration ν1. Within the double-harmonic approximation, a significantly larger value of 4.5 km mol-1 is obtained. The anharmonic result is comparable in magnitude with that calculated for the ν4 band, which has not been assigned
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TABLE 4: Harmonic and Anharmonic Vibrational Wavenumbers and ZPEs (all in cm-1) for D2CCC CCSD(T)/V6Z
CCSD(T*)-F12a/VDZ-F12
CCSD(T*)-F12a/VTZ-F12
vibrational mode
harm.
harm.
anharm.
harm.
anharm.
exp. Ar matrixa
1a1 2a1 3a1 4a1 1b1 2b1 1b2 2b2 3b2 ZPE
2283 1975 1224 965 812 200 2391 843 249 5471
2279 1965 1219 962 804 192 2389 842 242 5447
2201 1925 1204 950 794 198 2309 830 246 5399
2281 1972 1222 964 808 195 2390 842 247 5460
2203 1930 1208 951 798 203 2311 831 251 5412
2200.5, 2212.5 1933.4, 1944.4 1208.7 950.8 800.3, 803.2
a
829.2, 832.6
Reference 5. Two values are quoted in case of site absorptions, with the more intense band being underlined.
TABLE 5: Anharmonic Wavenumbers (in cm-1) and Absolute IR Intensities (in km mol-1, in Parentheses) for D2CCC from Dimensionality-Reduced (4D) Calculations band ν4 ν3 ν2 2ν4 ν3 + ν4 2ν3 ν1 ν2 + ν4
uncorr.
corr.a
Ar matrixb
955 (0.05) 1211 (8.8) 1947 (228) 1908 (0.1) 2161 (2.2) 2422 (0.4) 2243 (26.1) 2897 (1.5)
951 (0.05) 1208 (8.8) 1930 (226) 1900 (0.3) 2152 (4.0) 2416 (0.3) 2203 (24.0) 2876 (1.5)
950.8 1208.7 1933.4
2212.5c
a Underlined values refer to VCI calculations with CCSD(T*)-F12a/VTZ-F12 PES (see Table 4). The correction parameters (in cm-1) are: ∆4 ) -4, ∆3 ) -3, ∆2 ) -17, and ∆1 ) -41. b Reference 5. Most intense absorptions are quoted in case of site absorptions. c The absorption at 2200.5 cm-1 is almost equally strong.
in the argon matrix spectrum. A higher intensity of 4.7 km mol-1 is predicted for the combination tone ν2 + ν4 at 3048 cm-1, which closely matches the band observed at 3049.5 cm-1. Apparently, the combination tone borrows some of its intensity through anharmonic interaction with the ν1 fundamental. C. D2CCC and HDCCC. Table 4 lists vibrational wavenumbers and ZPEs for D2CCC. Within the harmonic approximation, results from standard valence-only CCSD(T)
calculations with the large V6Z basis set as well as from CCSD(T*)-F12a calculations with two VnZ-F12 basis sets (n ) D and T) are quoted. Similar to the results of Table 2, CCSD(T*)-F12a/VQZ-F12a and CCSD(T)/V6Z produce results that differ by no more than 5 cm-1, which is the maximum difference obtained again for the out-of-plane CCC bending vibration (2b1). The VCI calculations of the present work at level CCSD(T*)F12a/VTZ-F12 yield results which are in almost perfect agreement with the assignments of argon matrix IR experiments made earlier.5 In particular, no discrepancy between theory and experiment is observed for the symmetric CD stretching vibration ν1. Results of 4D calculations for the totally symmetric modes of D2CCC are given in Table 5. We will discuss the data involving correction parameters in the following. Again, ν2 at 1930 cm-1 is the strongest band, with an absolute IR intensity only 9% smaller than for H2CCC. The symmetric CD stretching vibration (ν1) is predicted to be more intense than the symmetric CH stretching vibration of H2CCC by an order of magnitude. The intensity ratio A(ν2)/A(ν1) for D2CCC is calculated to be 9.4, which agrees well with argon matrix values of 14 and 10, depending on the absorption site. The CD2 scissoring vibration (ν3) has a calculated intensity of 8.8 km mol-1. This corresponds to 4% of the intensity of the ν2 band, and the matrix IR study5 reported a relative intensity of 8%. In agreement with experiment, the ν4 band is calculated to be the weakest of the four totally symmetric fundamentals. Calculated and experimental wavenumbers for the fundamentals of HDCCC are listed in Table 6. Again, the differences in both harmonic and anharmonic values obtained with the VDZ-F12 and VTZ-F12 basis do not exceed 7 cm-1. Agreement with the argon matrix values5 is very good for ν2(2a′), ν3(3a′),
TABLE 6: Harmonic and Anharmonic Vibrational Wavenumbers (in cm-1) for HDCCC CCSD(T*)-F12a/VDZ-F12
a
CCSD(T*)-F12a/VTZ-F12
vibrational mode
harm.
anh.
harm.
anh.
1a′ 2a′ 3a′ 4a′ 5a′ 6a′ 7a′ 1a′′ 2a′′ ZPE
3164 2329 1977 1361 1100 879 251 912 196 6085
3026 2260 1933 1329 1085 865 257 898 206 6019
3166 2331 1984 1362 1104 879 256 916 200 6098
3027 2263 1940 1331 1088 865 261 903 209 6019
exp. Ar matrixa 2254.5, 2266.5 1940.6, 1953.1 1331.6, 1335.5 865.4, 868.8b 904.0, 909.8b
Reference 5. Two values are quoted in the case of site absorptions, with the more intense band being underlined. b Assignment has been reversed (see the text).
Vibrational Configuration Interaction for H2CCC Isotopomers
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and ν4(4a′). The present calculations place the wavenumber of the totally symmetric vibration ν6(6a′) below that of the upper out-of-plane vibration ν8(1a′′). We therefore suggest a reassignment of the observed absorptions, which has already been carried out in Table 6. Then, almost perfect agreement is observed between theory and experiment.
(5) Maier, G.; Reisenauer, H. P.; Schwab, W.; Carsky, P.; Hess, B. A., Jr.; Schaad, L. J. J. Am. Chem. Soc. 1987, 109, 5183. (6) Vrtilek, J. M.; Gottlieb, C. A.; Gottlieb, E. W.; Killian, T. C.; Thaddeus, P. Astrophys. J. Lett. 1990, 364, L53. (7) Cernicharo, J.; Gottlieb, C. A.; Gue´lin, M.; Killian, T. C.; Paubert, G.; Thaddeus, P.; Vrtilek, J. M. Astrophys. J. Lett. 1991, 368, L39. (8) Gottlieb, C. A.; Killian, T. C.; Thaddeus, P.; Botschwina, P.; Flu¨gge, J.; Oswald, M. J. Chem. Phys. 1993, 98, 4478. (9) Gauss, J.; Stanton, J. F. J. Mol. Struct. 1999, 485-486, 43. (10) Rauhut, G.; Knizia, G.; Werner, H.-J. J. Chem. Phys. 2009, 130, 054105. (11) Adler, T. B.; Knizia, G.; Werner, H.-J. J. Chem. Phys. 2007, 127, 221106. (12) Knizia, G.; Adler, T. B.; Werner, H.-J. J. Chem. Phys. 2009, 130, 054104. (13) Peterson, K. A.; Adler, T. B.; Werner, H.-J. J. Chem. Phys. 2008, 128, 084102. (14) Yousaf, K. E.; Peterson, K. A. J. Chem. Phys. 2008, 129, 184108. (15) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. Chem. Phys. Lett. 1989, 157, 479. (16) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007. (17) Dunning, T. H., Jr.; Woon, D. E. J. Chem. Phys. 1995, 103, 4572. (18) Wilson, A. K.; van Mourik, T.; Dunning, T. H., Jr. J. Mol. Struct. (THEOCHEM) 1996, 388, 339. (19) Peterson, K. A.; Wilson, A. K.; Woon, D. E.; Dunning, T. H., Jr. Theor. Chem. Acc. 1997, 97, 251. (20) Werner, H.-J.; Knowles, P. J.; Lindh, R.; Manby, F. R.; Schu¨tz, M. MOLPRO Version 2009.1, a Package of ab Initio Programs; 2009; see http://www.molpro.net. (21) Rauhut, G. J. Chem. Phys. 2004, 121, 9313. (22) Rauhut, G.; Hrenar, T. Chem. Phys. 2008, 346, 160. (23) Watson, J. K. G. Mol. Phys. 1968, 15, 479. (24) Rauhut, G. J. Chem. Phys. 2007, 127, 184109. (25) Botschwina, P. J. Mol. Struct. (THEOCHEM) 2005, 724, 95. (26) Gauss, J.; Stanton, J. F. Phys. Chem. Chem. Phys. 2000, 2, 2060. (27) Mladenovic´, M.; Schmatz, S.; Botschwina, P. J. Chem. Phys. 1994, 101, 5891. (28) Garand, E.; Yacovitch, T. I.; Neumark, D. M. J. Chem. Phys. 2009, 131, 054312. (29) Aguilera-Iparraguirre, J.; Boese, A. D.; Klopper, W.; Ruscic, B. Chem. Phys. 2008, 346, 56. (30) Va´zquez, J.; Harding, M. E.; Gauss, J.; Stanton, J. F. J. Phys. Chem. A 2009, 113, 12447. (31) Botschwina, P.; Schramm, H.; Sebald, P. Chem. Phys. Lett. 1990, 169, 121. (32) Botschwina, P. Chem. Phys. Lett. 1984, 107, 535. (33) Botschwina, P.; Oswald, R. T. Z. Phys. Chem. 2005, 219, 399. (34) Cunha de Miranda, B. K.; Alcaraz, C.; Elhanine, M.; Noller, B.; Hemberger, P.; Fischer, I.; Garcia, G.; Soldi-Lose, H.; Gans, B.; Vieira Mendes, L. A.; Boye´-Pe´ronne, S.; Douin, S.; Zabka, J.; Botschwina, P. J. Phys. Chem. A 2010, 114, 4818.
IV. Conclusions Following the pioneering work of Rauhut et al.,10 VCI calculations involving potential energy surfaces from the efficient explicitly correlated coupled cluster method CCSD(T*)F12a have been carried out for H2CCC, D2CCC, and HDCCC. Comparison with experimental data from argon matrix IR isolation spectroscopy5 leads to two reassignments of spectral features. The symmetric CH stretching vibration of H2CCC, which has already only a small intensity within the doubleharmonic approximation, loses further intensity through anharmonic interaction with the combination tone ν2 + ν4. Thereby, the combination tone becomes the stronger band and the absorptions observed at 3049.5 and 3059.6 cm-1 are assigned to it. In the case of HDCCC, the present VCI calculations predict the order ν8(1a′′) > ν6(6a′) and, consequently, we recommend to reverse the assignments made in Table 4 of ref 5. Acknowledgment. Financial support from the Fonds der Chemischen Industrie is gratefully acknowledged. Supporting Information Available: Six tables with equilibrium geometrical parameters and harmonic vibrational wavenumbers from various methods and basis sets (S1-S4) and 4D potential energy and electric dipole moment functions for the totally symmetric vibrations (S5 and S6). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Hehre, W. J.; Pople, J. A.; Lathan, W. A.; Radom, L.; Wassermann, E.; Wassermann, Z. R. J. Am. Chem. Soc. 1976, 98, 4378. (2) Shepard, R.; Banerjee, A.; Simons, J. J. Am. Chem. Soc. 1979, 101, 6174. (3) Lee, T. J.; Bunge, A.; Schaefer III, H. F. J. Am. Chem. Soc. 1985, 107, 137. (4) Reisenauer, H. P.; Maier, G.; Riemann, A.; Hoffmann, R. W. Angew. Chem., Int. Ed. 1984, 23, 641.
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