Kirstin D.
Doney
*^{a},
Dongfeng
Zhao
^{b},
John F.
Stanton
^{c} and
Harold
Linnartz
^{a}
^{a}Sackler Laboratory for Astrophysics, Leiden Observatory, Leiden University, Leiden, The Netherlands. E-mail: doney@strw.leidenuniv.nl; Tel: +31 (0)71 527 8413
^{b}CAS Center for Excellence in Quantum Information and Quantum Physics and Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui, P. R. China
^{c}Department of Chemistry, University of Florida, Gainesville, Florida, USA
First published on 3rd November 2017
The full cubic and semidiagonal quartic force fields of acetylene (C_{2}H_{2}), diacetylene (C_{4}H_{2}), triacetylene (C_{6}H_{2}), and tetraacetylene (C_{8}H_{2}) are determined using CCSD(T) (coupled cluster theory with single and double excitations and augmented by a perturbative treatment of triple excitations) in combination with the atomic natural orbital (ANO) basis sets. Application of second-order vibrational perturbation theory (VPT2) results in vibrational frequencies that agree well with the known fundamental and combination band experimental frequencies of acetylene, diacetylene, and triacetylene (average discrepancies are less than 10 cm^{−1}). Furthermore, the predicted ground state rotational constants (B_{0}) and vibration–rotation interaction constants (α_{i}) are shown to be consistent with known experimental values. New vibrational frequencies and rotational parameters from the presented theoretical predictions are given for triacetylene and tetraacetylene, which can be used to aid laboratory and astronomical spectroscopic searches for characteristic transitions of these molecules.
HC_{2n}H + C_{2}H → HC_{2n+2}H + H, | (1a) |
HC_{2}H + C_{2n}H → HC_{2n+2}H + H, | (1b) |
HC_{2n}H^{+} + HC_{2}H → HC_{2n+2}H_{2}^{+} + H, | (2a) |
HC_{2n+2}H_{2}^{+} + e^{−} → HC_{2n+2}H + H. | (2b) |
Although long carbon chain molecules (e.g., HC_{n} and HC_{n}N for n ≤ 9)^{36–39} and small polyynes (HC_{2n}H for n ≤ 3) have been detected in carbon-rich astronomical sources,^{20,21,39} tetraacetylene has yet to be observed. One limiting factor is that as centrosymmetric molecules, polyynes lack a permanent dipole moment, and cannot be detected by radioastronomy using pure rotational transitions, unlike, e.g., HC_{n}N. Therefore, ro-vibrational spectra in the infrared (IR) region are the most important spectroscopic tools to detect polyynes both in the laboratory and in space. In particular, detection of acetylene, diacetylene, and triacetylene in planetary atmospheres and protoplanetary nebulae has been realized primarily through observation of the strongest perpendicular band (ν_{5}, ν_{8}, and ν_{11}, respectively, at ∼13–17 μm) and the second strongest parallel band (ν_{4} + ν_{5}, ν_{6} + ν_{8}, and ν_{8} + ν_{11}, respectively, at ∼8 μm).^{11,12,20,21} However, accurate line positions for tetraacetylene are lacking, from either laboratory or theoretical studies.
Extensive theoretical and experimental studies have been carried out for acetylene and diacetylene in the past few decades, including high-resolution spectroscopic studies of all the fundamental bands and a significant number of the combination bands,^{29,40–50} and high level ab initio calculations that take into account anharmonic effects.^{51–54} The combination of these studies shows that current quantum chemical theory, particularly coupled cluster theory with single and double excitations and augmented by a perturbative treatment of triple excitations (CCSD(T)),^{55} is able to accurately reproduce equilibrium geometries, experimental vibrational frequencies, vibration–rotation interaction constants (α_{i}), and ground state rotational constants (B_{0}).
Triacetylene and tetraacetylene are not as thoroughly studied, notably in terms of rotational information. While all of the fundamental vibrational modes of triacetylene have been measured, there is only rotational information for the IR active fundamental modes,^{56} and the strongest IR combination band (ν_{8} + ν_{11}).^{57–61} However, theoretical studies of triacetylene do give rotational information for the remaining modes from CCSD(T) calculations of the vibration–rotation interaction constants^{62} and the equilibrium geometry.^{63} In addition, the harmonic frequencies of triacetylene were calculated using partial fourth-order many-body perturbation theory [SDQ-MBPT(4)].^{63} Conversely though, to the authors' knowledge, there is almost no rotational information for tetraacetylene. There has been only one low-resolution spectroscopic study of tetraacetylene, which measured three of the fundamentals (ν_{6}, ν_{8}, and ν_{14} at 3329.4, 2023.3, and 621.5 cm^{−1}, respectively), and one combination band (ν_{10} + ν_{14} at 1229.7 cm^{−1}), and gives an estimate for the electronic ground state rotational constant, B_{0}.^{64} Unfortunately, the theoretical knowledge of tetraacetylene is equally limited, with only two studies of the equilibrium geometry (at the Hartree–Fock^{65} and B3LYP^{66} level of theory), and a calculation of the harmonic vibrational frequencies at the SVWN level of theory.^{64} While the two modes that are most useful for astronomical identification (ν_{14} and ν_{10} + ν_{14}) were measured, the uncertainty associated with the line positions is too large to allow for an unambiguous assignment. Moreover, some high-resolution IR searches have been attempted,^{50,61,62,67} but so far no transitions have been assigned to tetraacetylene.
In this paper, we report the ab initio calculations for acetylene, diacetylene, triacetylene, and tetraacetylene. Due to the centrosymmetric nature of these molecules, observations in the laboratory and in space are most easily accomplished through their infrared spectra. As such, the properties computed and presented here are those related to that technique: fundamental vibrational frequencies, ground state rotational constants, and intramolecular interactions. The computational approach is calibrated using the well studied acetylene and diacetylene, and then extended to make predictions for triacetylene and tetraacetylene.
However, it is well known that correlation-consistent basis sets, such as cc-pCVQZ, tend to underestimate the vibrational frequencies of symmetric bending modes (π_{g}) of conjugated molecules, e.g., polyynes, due to their susceptibility to an intramolecular variant of basis set superposition error (BSSE).^{54,80} It has been shown that one way to avoid this problem is to use basis sets with a large number of Gaussian primitives (particularly f-type), such as the atomic natural orbital (ANO) basis set (with the primitive basis set (13s8p6d4f2g) for non-hydrogen atoms and (8s6p4d2f) for hydrogen).^{52,81,82} The basis set has two common truncations: [4s3p2d1f] for non-hydrogen atoms and [4s2p1d] for hydrogen (hereafter known as ANO1), and [5s4p3d2f1g] (non-hydrogen atoms) and [4s3p2d1f] (hydrogen) (hereafter known as ANO2).^{74,75,81} In addition, only the valence electrons of carbon are considered in the correlation treatment, i.e., standard frozen-core (fc) calculations. (fc)-CCSD(T)/ANO1 has been shown to accurately reproduce experimental frequencies and intensities for small molecules.^{52,83,84} Using the (fc)-CCSD(T)/ANO1 optimized geometry, second-order vibrational perturbation (VPT2) theory calculations were determined from full cubic and the semidiagonal part of the quartic force fields obtained by numerical differentiation of analytic CCSD(T) second derivatives.^{70,85} All calculations were performed with the development version of the CFOUR program.^{86}
Fig. 1 AE-CCSD(T)/cc-pCVQZ equilibrium geometries (Å) for HC_{2n}H. Experimentally determined equilibrium bond lengths for acetylene,^{87} diacetylene,^{53} and triacetylene^{88} are given in italics below. |
The equilibrium rotational constants, B_{e}, obtained from the AE-CCSD(T)/cc-pCVQZ equilibrium geometries are summarized in Table 1, and agree well with experimental ground state rotational constants (B_{0}). As such, the equilibrium rotational constants suggest that the calculations predict the correct ground state geometry, because for linear molecules with more than three atoms the summation of vibration–rotation interaction constants (α_{i}) is expected to be close to zero, and from
(3) |
HC_{2}H | HC_{4}H | HC_{6}H | HC_{8}H | |
---|---|---|---|---|
Calc. | ||||
B _{e} | 1.181053 | 0.146248 | 0.044064 | 0.018823 |
B _{0} | 1.175319 | 0.146167 | 0.044092 | 0.018844 |
D _{e}(×10^{8}) | 160 | 1.5 | 0.086 | 0.012 |
Expt. | ||||
B _{0} | 1.17664632(18)^{90} | 0.1464123(17)^{50} | 0.0441735(12)^{61} | 0.020(3)^{64} |
D _{0}(×10^{8}) | 159.8(9)^{90} | 1.56825(20)^{29} | 0.107(7)^{61} |
In addition, as seen for other carbon chains (e.g., HC_{n}, HC_{2n+1}N, and H_{2}C_{n})^{89} the centrifugal distortion constant (D_{e}) decreases with increasing molecular size, with a theoretical D_{e} = 1.6 × 10^{−6} cm^{−1} for acetylene, D_{e} = 1.5 × 10^{−8} cm^{−1} for diacetylene, D_{e} = 8.6 × 10^{−10} cm^{−1} for triacetylene, and D_{e} = 1.2 × 10^{−10} cm^{−1} for tetraacetylene. These values are consistent with those found experimentally for the respective vibrational ground states (Table 1). As noted by Thaddeus et al.^{89} this behavior of increasing stiffness with chain length is a distinguishing characteristic associated with bona fide chains.
CCSD(T)/ANO1^{a} | Experimental | ||
---|---|---|---|
ω | ν | ν | |
a Intensities in km mol^{−1} are given in parentheses. | |||
ν _{1}(σ_{g}^{+}) | 3514.2(0) | 3375.2(0) | 3372.851^{41} |
ν _{2}(σ_{g}^{+}) | 2001.5(0) | 1964.8(0) | 1974.317^{41} |
ν _{3}(σ_{u}^{+}) | 3414.6(84.7) | 3285.9(74.8) | 3288.58075^{48} |
ν _{4}(π_{g}) | 600.5(0) | 600.6(0) | 612.871^{42} |
ν _{5}(π_{u}) | 752.3(90.5) | 734.7(91.7) | 730.332^{42} |
ν _{4} + ν_{5}(σ_{u}^{+}) | 1352.8 | 1329.2(10.8) | 1328.074^{42} |
ν _{2} + ν_{5}(π_{u}) | 2753.8 | 2698.3(0.1) | 2701.907^{43} |
ν _{3} + ν_{4}(π_{u}) | 4015.1 | 3878.5(0.5) | 3882.4060^{41} |
ν _{1} + ν_{5}(π_{u}) | 4266.5 | 4098.9(0.5) | 4091.17326^{91} |
ν _{1} + ν_{3}(σ_{u}^{+}) | 6928.7 | 6551.9(2.0) | 6556.46^{40} |
Anharmonic ZPE = 5760.1 |
CCSD(T)/ANO1^{a} | Experimental | ||
---|---|---|---|
ω | ν | ν | |
a Intensities in km mol^{−1} are given in parentheses. | |||
ν _{1}(σ_{g}^{+}) | 3465.8(0) | 3332.5(0) | 3332.15476^{46} |
ν _{2}(σ_{g}^{+}) | 2240.2(0) | 2193.1(0) | 2188.9285^{44} |
ν _{3}(σ_{g}^{+}) | 891.1(0) | 859.2(0) | 871.9582^{44} |
ν _{4}(σ_{u}^{+}) | 3465.9(152.7) | 3333.1(135.5) | 3333.6634^{50} |
ν _{5}(σ_{u}^{+}) | 2054.1(0.2) | 2016.9(0.5) | 2022.2415^{44} |
ν _{6}(π_{g}) | 636.3(0) | 624.2(0) | 625.643507^{29} |
ν _{7}(π_{g}) | 479.8(0) | 476.9(0) | 482.7078^{44} |
ν _{8}(π_{u}) | 636.3(78.7) | 624.1(78.8) | 628.040776^{29} |
ν _{9}(π_{u}) | 220.7(7.3) | 219.6(7.3) | 219.97713^{47} |
2ν_{9}(σ_{g}^{+}) | 441.4 | 438.5(0) | 438.47757^{47} |
ν _{7} + ν_{9}(σ_{u}^{+}) | 700.5 | 696.3(0.8) | 701.8939^{29} |
ν _{6} + ν_{9}(σ_{u}^{+}) | 857.0 | 843.9(0.01) | 845.655513^{29} |
ν _{8} + ν_{9}(σ_{g}^{+}) | 857.0 | 843.9(0) | 848.365918^{29} |
ν _{7} + ν_{8}(π_{u}) | 1116.1 | 1103.1(0.6) | 1111^{45} |
ν _{6} + ν_{8}(σ_{u}^{+}) | 1272.6 | 1244.7(21.8) | 1241.060828^{46} |
2ν_{6} + ν_{8}(π_{u}) | 1909.0 | 1864.6(0.0) | 1863.2512^{44} |
ν _{2} + ν_{9}(π_{u}) | 2460.9 | 2410.0(0.04) | 2406.4251^{44} |
ν _{5} + ν_{7}(π_{u}) | 2533.9 | 2489.0(0.01) | 2500.6458^{44} |
ν _{5} + ν_{6}(π_{u}) | 2690.4 | 2637.0(0.04) | 2643.32323^{46} |
ν _{2} + ν_{8}(π_{u}) | 2876.6 | 2810.9(0.4) | 2805^{45} |
ν _{1} + ν_{9}(π_{u}) | 3686.5 | 3551.6(0.1) | 3551.56158159^{46} |
ν _{1} + ν_{8}(π_{u}) | 4102.1 | 3946.9(0.7) | 3939^{45} |
ν _{4} + ν_{6}(π_{u}) | 4102.3 | 3947.8(0.7) | |
ν _{2} + ν_{5}(σ_{u}^{+}) | 4294.3 | 4194.0(0.1) | |
ν _{4} + ν_{3}(σ_{u}^{+}) | 4357.0 | 4192.3(0.1) | |
ν _{1} + ν_{4}(σ_{u}^{+}) | 6931.7 | 6557.2(3.4) | 6565.472^{49} |
Anharmonic ZPE = 7966.9 |
Based on previous studies of acetylene^{52} and diacetylene,^{53} the use of the ANO2 basis set was evaluated compared to the ANO1 basis set. For some of the vibrational modes, such as the ν_{4} mode of acetylene [612.88 cm^{−1} (observed)],^{42} Martin et al.^{52} showed that CCSD(T)/ANO2 can give a slightly better agreement (o–c value of ∼2 cm^{−1}) compared to the ANO1 basis set (o–c value of ∼12 cm^{−1}). However, the study by Thorwirth et al.^{53} showed that, for diacetylene, the average o–c value with CCSD(T)/ANO2 is comparable to that for the ANO1 basis set (∼6 cm^{−1} and ∼4 cm^{−1}, respectively). Moreover, the time cost of (fc)-CCSD(T)/ANO2 calculations compared to (fc)-CCSD(T)/ANO1 far outweighs the minor frequency differences, and does not justify the higher computational cost of the ANO2 basis set in predicting the fundamental frequencies of longer polyynes.
The (fc)-CCSD(T)/ANO1 anharmonicity constants (x_{ij}, ESI†) also accurately account for the known combination bands of acetylene and diacetylene (Tables 2 and 3, respectively). All the combination bands are within 5 cm^{−1} of their observed values. For both acetylene and diacetylene, the ANO1 basis set is able to most accurately reproduce the C–H asymmetric stretch mode (ν_{3} and ν_{4}, respectively). Significant is the agreement between the experimental and our predicted frequencies of ν_{6} + ν_{8} [1241.060828(38) cm^{−1} (observed)^{46} and 1244.7 cm^{−1} (theoretical)], and 2ν_{6} + ν_{8} [1863.2512(5) cm^{−1} (observed)^{44} and 1864.6 cm^{−1} (theoretical)] of diacetylene; both of which had only previously been calculated with CCSD(T)/cc-pCVQZ, and had o–c values greater than 20 cm^{−1}.^{54} This suggests that the combination band VPT2 frequencies of polyynes determined using (fc)-CCSD(T)/ANO1 are accurate to aid identification of molecules, such as in astronomical surveys.
The vibration–rotation interaction constants (Table 4) are also determined in the course of the VPT2 calculation, and are in good agreement with both previous theoretical studies^{52,54} and experimentally determined values.^{29,44,46,50,51,54} Based on the vibration–rotation interaction constants, the ground state rotational constants (B_{0}) were determined using the AE-CCSD(T)/cc-pCVQZ determined B_{e} values (Table 1). For acetylene, B_{0} = 1.175319 cm^{−1}, which is a 0.1% difference compared to the experimentally determined value of B_{0} = 1.17664632(18) cm^{−1}.^{90} Diacetylene shows a similar 0.2% difference between the theoretical value of B_{0} = 0.146167 cm^{−1}, and the experimentally determined value of B_{0} = 0.1464123(17) cm^{−1}.^{50} The consistent accuracy of these values suggests that the method presented is clearly good enough to be extrapolated to and aid high-resolution infrared spectroscopic searches for the larger polyynes.
Mode | HC_{2}H (×10^{3}) | HC_{4}H (×10^{4}) | HC_{6}H (×10^{5}) | HC_{8}H (×10^{5}) |
---|---|---|---|---|
a Deperturbed. | ||||
α _{1} | 6.853(6.904^{a})^{51} | 2.157(2.153)^{50} | 2.97 | 0.730 |
α _{2} | 6.007(6.181)^{51} | 6.608 | 15.20 | 4.91 |
α _{3} | 5.800(5.882^{a})^{51} | 3.123(3.110^{a})^{54} | 7.44 | 2.55 |
α _{4} | −1.464(−1.354)^{51} | 2.139(2.183)^{50} | 3.82 | 3.76 |
α _{5} | −2.134(−2.232)^{51} | 3.938(3.948)^{44} | 2.99(3.58)^{61} | 0.930 |
α _{6} | 0.730 | −0.700(−0.678)^{29} | 9.91(9.15)^{58} | 0.730 |
α _{7} | 4.06 | −2.703(−2.711)^{46} | 9.91 | 4.06 |
α _{8} | 2.33 | −0.647(−0.636)^{29} | −1.17(−1.071)^{58} | 2.33 |
α _{9} | 2.05 | −4.125(−4.183)^{46} | −5.83 | 2.05 |
α _{10} | −7.42(−7.88)^{58} | −0.295 | ||
α _{11} | −1.06(−1.06)^{57} | −1.95 | ||
α _{12} | −5.07 | −1.69 | ||
α _{13} | −8.47(−8.7207)^{59} | −2.26 | ||
α _{14} | −0.295 | |||
α _{15} | −0.163 | |||
α _{16} | −2.29 | |||
α _{17} | −2.80 |
CCSD(T)/ANO1^{a} | Experimental | ||
---|---|---|---|
ω | ν | ν | |
a Intensities in km mol^{−1} are given in parentheses. | |||
ν _{1}(σ_{g}^{+}) | 3463.1(0) | 3330.4(0) | 3313^{56} |
ν _{2}(σ_{g}^{+}) | 2284.0(0) | 2213.2(0) | 2201^{56} |
ν _{3}(σ_{g}^{+}) | 2061.0(0) | 2023.2(0) | 2019^{56} |
ν _{4}(σ_{g}^{+}) | 616.1(0) | 612.7(0) | 625^{56} |
ν _{5}(σ_{u}^{+}) | 3463.1(126.4) | 3329.5(175.0) | 3329.0533^{61} |
ν _{6}(σ_{u}^{+}) | 2172.2(0.0) | 2130.4(0.1) | 2128.91637^{58} |
ν _{7}(σ_{u}^{+}) | 1169.6(1.7) | 1160.9(0.2) | 1115.0^{59} |
ν _{8}(π_{g}) | 633.0(0) | 620.9(0) | 622.38^{57} |
ν _{9}(π_{g}) | 489.5(0) | 486.2(0) | 491^{56} |
ν _{10}(π_{g}) | 252.0(0) | 251.1(0) | 258^{56} |
ν _{11}(π_{u}) | 632.0(80.5) | 619.9(83.2) | 621.34011^{60} |
ν _{12}(π_{u}) | 444.7(1.0) | 441.8(1.0) | 443.5^{59} |
ν _{13}(π_{u}) | 106.4(4.1) | 105.9(3.5) | 105.038616^{59} |
ν _{9} + ν_{13}(σ_{u}^{+}) | 595.9 | 591.7(0.8) | |
ν _{10} + ν_{12}(σ_{u}^{+}) | 696.7 | 691.8(1.8) | |
ν _{8} + ν_{12}(σ_{u}^{+}) | 1077.7 | 1063.5(0.3) | |
ν _{9} + ν_{11}(σ_{u}^{+}) | 1121.5 | 1107.1(0.7) | |
ν _{8} + ν_{11}(σ_{u}^{+}) | 1265.0 | 1237.4(31.4) | 1232.904295^{58} |
ν _{3} + ν_{7}(σ_{u}^{+}) | 3230.5 | 3182.8(0.1) | |
ν _{2} + ν_{7}(σ_{u}^{+}) | 3453.6 | 3362.2(2.5) | |
3ν_{7}(σ_{u}^{+}) | 3508.7 | 3498.7(0.01) | |
ν _{1} + ν_{13}(π_{u}) | 3569.5 | 3436.1(0.2) | |
ν _{5} + ν_{10}(π_{u}) | 3715.1 | 3583.7(0.1) | |
ν _{4} + ν_{5}(σ_{u}^{+}) | 4079.3 | 3945.8(0.1) | |
ν _{1} + ν_{11}(π_{u}) | 4095.2 | 3940.1(0.8) | |
ν _{5} + ν_{8}(π_{u}) | 4096.2 | 3943.9(0.8) | |
ν _{3} + ν_{6}(σ_{u}^{+}) | 4233.1 | 4141.1(0.1) | |
ν _{2} + ν_{6}(σ_{u}^{+}) | 4456.2 | 4334.7(0.1) | |
ν _{2} + ν_{5}(σ_{u}^{+}) | 5747.2 | 5548.4(0.2) | |
ν _{1} + ν_{5}(σ_{u}^{+}) | 6926.3 | 6555.1(4.6) | |
Anharmonic ZPE = 10095.8 |
For the modes observed in low-resolution studies (e.g., ν_{1} and ν_{12}), the agreement is still good with o–c values less than 20 cm^{−1}. The notable exception is the internal CC asymmetric stretch mode (ν_{7}), which differs by 45 cm^{−1}. Since no rotationally resolved data can be found for this band, it is possible that the band observed at 1115.0 cm^{−1}^{59} was mis-assigned as the ν_{7} fundamental. A more likely assignment for this band is the ν_{9} + ν_{11} combination band, which has a predicted VPT2 frequency of 1107.1 cm^{−1}, a calculated intensity of 0.7 km mol^{−1}, and the same symmetry. Furthermore, the combination band is expected to be 3.5× more intense than the ν_{7} fundamental at 0.2 km mol^{−1}, suggesting that ν_{9} + ν_{11} is more likely of the two to be observed. However, rotationally resolved measurements of this band are clearly needed to confirm this speculation.
We note that, a resonance between the ν_{5} fundamental and the ν_{2} + ν_{7} and 3ν_{7} combination bands must be addressed to achieve the very small (1 cm^{−1}) o–c difference obtained for the C–H asymmetric stretch mode, ν_{5}. The vibrational frequencies as a result of resonant interactions are calculated by a deperturbation-diagonalization technique followed by transformation of the deperturbed transition moments, as discussed in the work of Vázquez and Stanton and Matthews et al.^{85} This combination of Fermi and Darling–Dennison interactions shifts the ν_{5} predicted frequency from 3333.1 to 3329.5 cm^{−1}, which is able to reproduce the experimentally observed frequency [3329.0533(2) cm^{−1}^{61}] with the same accuracy seen for diacetylene (o–c ∼ 0.5 cm^{−1}). The combination bands involved are similarly shifted: ν_{2} + ν_{7} from 3329.5 to 3362.2 cm^{−1}, and 3ν_{7} from 3526.7 to 3498.7 cm^{−1}. Since the shift is most pronounced for the two combination bands, future experimental work to observe either of these bands is required to confirm this prediction.
The vibration–rotation interaction constants for triacetylene are given in Table 4, and are consistent with the previous CCSD(T)/cc-pCVQZ theoretical study^{62} and experimentally determined values.^{57–59,61} Consequently, the calculated ground state rotational constant B_{0} = 0.044092 cm^{−1} is within 0.2% of the experimentally observed B_{0} = 0.0441735(12) cm^{−1}.^{61}
CCSD(T)/ANO1^{a} | Experimental | ||
---|---|---|---|
ω | ν | ν | |
a Intensities in km mol^{−1} are given in parentheses. | |||
ν _{1}(σ_{g}^{+}) | 3462.0(0) | 3330.5(0) | |
ν _{2}(σ_{g}^{+}) | 2263.2(0) | 2208.0(0) | |
ν _{3}(σ_{g}^{+}) | 2134.6(0) | 2094.2(0) | |
ν _{4}(σ_{g}^{+}) | 1296.4(0) | 1285.8(0) | |
ν _{5}(σ_{g}^{+}) | 470.0(0) | 455.3(0) | |
ν _{6}(σ_{u}^{+}) | 3461.6(223.1) | 3328.8(214.2) | 3329.4^{64} |
ν _{7}(σ_{u}^{+}) | 2254.7(1.0) | 2227.6(0.5) | |
ν _{8}(σ_{u}^{+}) | 2064.3(0.3) | 2026.6(0.6) | 2023.3^{64} |
ν _{9}(σ_{u}^{+}) | 911.6(3.2) | 922.4(2.0) | |
ν _{10}(π_{g}) | 632.4(0) | 620.0(0) | |
ν _{11}(π_{g}) | 489.3(0) | 486.0(0) | |
ν _{12}(π_{g}) | 422.3(0) | 419.5(0) | |
ν _{13}(π_{g}) | 158.8(0) | 157.9(0) | |
ν _{14}(π_{u}) | 632.6(79.6) | 619.7(79.9) | 621.5^{64} |
ν _{15}(π_{u}) | 474.2(0.1) | 470.9(0.2) | |
ν _{16}(π_{u}) | 267.7(3.2) | 266.7(3.1) | |
ν _{17}(π_{u}) | 61.0(2.3) | 60.7(2.2) | |
ν _{11} + ν_{17}(σ_{u}^{+}) | 550.3 | 546.5(0.6) | |
ν _{13} + ν_{15}(σ_{u}^{+}) | 633.0 | 628.5(1.7) | |
ν _{12} + ν_{16}(σ_{u}^{+}) | 690.1 | 684.8(3.1) | |
ν _{12} + ν_{15}(σ_{u}^{+}) | 896.5 | 871.9(3.5) | |
ν _{11} + ν_{15}(σ_{u}^{+}) | 963.5 | 970.5(1.3) | |
ν _{10} + ν_{15}(σ_{u}^{+}) | 1106.6 | 1092.2(0.6) | |
ν _{10} + ν_{14}(σ_{u}^{+}) | 1265.1 | 1236.7(37.5) | 1229.7^{64} |
ν _{2} + ν_{9}(σ_{u}^{+}) | 3174.8 | 3130.1(0.5) | |
ν _{4} + ν_{8}(σ_{u}^{+}) | 3360.7 | 3311.4(0.5) | |
ν _{6} + ν_{10}(π_{u}) | 4094.0 | 3939.1(0.8) | |
ν _{1} + ν_{14}(π_{u}) | 4094.6 | 3940.6(0.8) | |
ν _{1} + ν_{6}(σ_{u}^{+}) | 6923.6 | 6550.8(5.7) | |
Anharmonic ZPE = 12218.2 |
Based on the results discussed for the other small polyynes, the theoretical vibration–rotation interaction constants given in Table 4 are sufficient to assist in identification of ro-vibrational bands of tetraacetylene. The α_{i} results in a theoretical ground state rotational constant of B_{0} = 0.018844 cm^{−1} that agrees within errors with the experimentally determined value, B_{0} = 0.020(3) cm^{−1}.^{64} Overall, for polyynes the difference between the experimental and calculated rotational constants (ΔB_{0}) decreases from 0.001 to 0.00008 cm^{−1} as the chain length is increased, which is consistent with the trend seen for other carbon chain molecules (e.g., HC_{n}N, HC_{n}, C_{n}O).^{93} Therefore, if the trend continues as expected then the ΔB_{0} for tetraacetylene is equal to or smaller than that seen for triacetylene, and the determined ground state rotational constant is a good approximation of the true value.
The calculated fundamental frequencies for triacetylene and tetraacetylene give insight as to why tetraacetylene has not yet been observed in space. Observation of centrosymmetric molecules in astronomical environments is mainly through infrared detection of the high intensity bending modes; e.g., ν_{8} [628.040776(36) cm^{−1}]^{29} and ν_{6} + ν_{8} [1241.060828(38) cm^{−1}]^{46} of diacetylene, or ν_{11} [621.34011(42) cm^{−1}]^{60} and ν_{8} + ν_{11} [1232.904295(74) cm^{−1}]^{58} of triacetylene. However, the analogous modes for tetraacetylene are the ν_{14} [621.5(5) cm^{−1}]^{64} and ν_{10} + ν_{14} [1229.7(5) cm^{−1}],^{64} and are predicted to be significantly weaker in intensity due to lower column densities.^{34,35} Consequently, at these frequencies and resolutions of the previous infrared observations where polyynes were detected,^{20–22,24,25} the transitions of tetraacetylene are blended with those of triacetylene. Other bands of tetraacetylene would be more suitable for identification, such as ν_{1} + ν_{6}, ν_{12} + ν_{15}, or ν_{17} that are expected to be equally strong as bands already used to identify di- and triacetylene.
Overall, the resulting computed geometries lead to equilibrium rotational constants (B_{e}), which when corrected for vibrational zero-point effects give ground state equilibrium constants (B_{0}) that agree with experimental values (0.2%). Based on the small o–c values for acetylene, diacetylene, and triacetylene, we are confident that the fundamental frequencies and spectroscopic constants determined here offer an accurate guide for spectroscopic searches focused on detection of ro-vibrational bands of triacetylene and tetraacetylene. Such work is underway in our laboratory.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7cp06131e |
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