Article pubs.acs.org/JPCA
Formylmethylene: The Triplet Ground State and the Lowest Singlet State Jun Guan,*,† Katherine R. Randall,*,‡,§ Henry F. Schaefer, III,*,‡ and Huidong Li∥ †
School of Chinese Materia Medica, Beijing University of Chinese Medicine, Beijing, P. R. China 100029 Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602 United States § Research Focus Area for Chemical Resource Beneficiation, North-West University, Hoffman Street, Potchefstroom, South Africa 2520 ∥ School of Physics and Chemistry, Research Center for Advanced Computations, Xihua University, Chengdu, P. R. China 610065 ‡
ABSTRACT: The ground triplet state and lowest singlet state of formylmethylene have been proposed as important intermediates in the Wolff rearrangement of α-diazo ketones into ketenes. The ground triplet state of formylmethylene has been examined experimentally, but the lowest singlet state has yet to be observed. We predict equilibrium geometries, energies, bonding, dipole moments, and harmonic vibrational frequencies for these two lowest states of formylmethylene at the cc-pVQZ CCSD(T) level of theory. The singlet− triplet energy difference [ΔE(S-T)] is quite sensitive to the level of theory. The highly accurate cc-pVQZ CCSD(T) level of theory yields the most reliable result of only 2.0 kcal mol−1. An estimate based on the experimentally characterized CH2 molecule yields ΔE(S-T) = 1.27 kcal mol−1. In addition, accurate quartic force fields have been determined at the cc-pVTZ CCSD(T) level of theory. Fundamental vibrational frequencies, anharmonic constants, and vibration−rotation coupling constants were determined using vibrational second-order perturbation theory (VPT2). Our results should aid in experimental detection and characterization of the lowest singlet state of formylmethylene, which is highly desirable for better understanding the mechanism of the Wolff rearrangement.
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calculations indicated a moderately large (25 kcal mol−1) singlet−triplet gap.18 Inclusion of electron correlation reduces the singlet−triplet gap substantially, to 3.4 kcal mol−1 at the CCSD(T)/cc-pVTZ level of theory.17 This raises the obvious question: might the singlet state actually be the electronic ground state? Since the singlet−triplet separation is critical to understanding the energetic features of formylmethylene, further examination of this gap is important. The lowest singlet electronic state of formylmethylene (Figure 1, structure 2, R1R2H) may undergo a 1,2-H atom shift to directly form ketene (Figure 1, structure 5, R1 R2H).1,8 The barrier for this process is 5.7 kcal mol−1 at the HF DZ level of theory. However, the energy barrier disappears at higher levels of theory with small basis sets (MP210 and CISD9). Applying high-level ab initio methods with larger basis sets, a more significant barrier of 6.0 kcal mol−1 was found at the cc-pVTZ CCSD(T) level of theory.11 Oxirene (Figure 1, structure 3, R1R2H) has also been proposed as an intermediate in the Wolff rearrangement.9,11−13,24,27 The most complete theoretical study of oxirene is that of Vacek and co-workers.28,29 At the cc-pVTZ CCSD(T) level of theory, the oxirene structure lies only 0.6 kcal mol−1 above formylmethylene.11 There is little or no
INTRODUCTION The conversion of α-diazo ketones into ketenes, activated by heat or light, was first documented1 in 1902 and is now known as the Wolff rearrangement (WR). This reaction has important applications in several diverse fields, such as photochemistry, synthetic chemistry, and photolithography.2 Two different mechanistic pathways have been proposed for the Wolff rearrangement; see Figure 1. The first is called the concerted Wolff rearrangement (concerted WR), in which the formation of ketene and extrusion of molecular nitrogen proceed simultaneously. The other is the stepwise Wolff rearrangement (stepwise WR). In the latter mechanism, the α-diazo ketone loses molecular nitrogen to form a ketocarbene intermediate, which then isomerizes into ketene. In 1966, Kaplan and Meloy proposed that syn-α-diazo ketones favor the concerted WR, whereas anti isomers promote the stepwise WR.3 Experiments indicate that stepwise and concerted mechanisms often operate competitively.2,4−7 Formylmethylene (see Figure 1, structures 2 and 4, R1 R2H) is the simplest possible ketocarbene intermediate for the WR. Thus, it is an attractive subject for mechanistic studies.1−3,8−26 The lowest singlet state of formylmethylene is predicted to be nonplanar, with the carbene−H bond nearly perpendicular to the plane of the formyl group.9,11,14,15 However, the ground triplet state of formylmethylene has a planar trans geometry (Figure 1, structure 4, R1R2H) at various levels of theory.15,16 Early ab initio molecular orbital © 2013 American Chemical Society
Received: November 27, 2012 Revised: February 13, 2013 Published: February 13, 2013 2152
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Figure 1. General mechanism of Wolff rearrangement.
observation of singlet formylmethylene.26 Why has singlet formylmethylene so far escaped unambiguous detection? One possibility is that the singlet undergoes a barrierless rearrangement to ketene.9,10 Another possibility is that the singlet formylmethylene-oxrirene PES is so flat that minima and transition states can no longer be clearly distinguished.11 In the present investigation, we perform vibrational analyses on singlet and triplet formylmethylene. It is hoped that our results will aid in the spectroscopic identification of elusive singlet formylmethylene, and provide further insight into the mechanism of the Wolff rearrangement.
energy barrier separating formylmethylene and oxirene; the potential energy surface linking these two species is extremely flat.11 The Wolff rearrangement is usually considered to occur on the singlet surface.4,5,9,14,29,30 Nevertheless, the possibility of a singlet−triplet crossing cannot be disregarded.15,16 Ketocarbenes with triplet ground states may undergo intersystem crossing (ISC) from singlet excited states.6,7 The singlet PES which links formylmethylene to oxirene crosses the triplet PES. Along this path, ISC is likely and yields triplet formylmethylene.17 Recently, spectroscopic results showed that triplet trans-formylmethylene undergoes WR into ketene in 180 s.19 Thus, WR may occur by singlet formylmethylene undergoing ISC to its ground triplet state and then rearranging to ketene. Although formylmethylene may be an important intermediate in the WR, it is still a challenge to observe this short-lived species. The triplet ground electronic state has been observed experimentally. In reactions of oxygen atoms [O(3P)] with acetylene,20,21 formylmethylene was one of the initial products. The lifetime of formylmethylene is on the order of 1 ns at room temperature.24,25 In 2004, Misochko and co-workers19 observed triplet trans-formylmethylene. The electron affinity of ground state formylmethylene (43.1 kcal mol−1) has also been determined, but there has not been an unambiguous
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METHODS Geometry optimizations and total energy computations were carried out using a number of ab initio methods, including restricted Hartree−Fock (RHF),31restricted open-shell HF (ROHF),32 coupled cluster with single and double excitations (CCSD),33−35 and CCSD with perturbative triple excitations [CCSD(T)].36 The coupled cluster wave functions for the closed-shell singlet formylmethylene used an RHF reference, while those for triplet formylmethylene used an ROHF reference. The Dunning correlation-consistent polarizedvalence basis sets [cc-pVXZ (X = T and Q)]37,38 and the core−valence extensions to these basis sets [cc-pCVXZ (X = 2153
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Table 1. Computed Total Energies (in hartree), ZPVEs (in kcal mol−1), and Singlet-Triplet Gaps (in kcal mol−1) for the Triplet and Singlet States of Formylmethylene singlet (1A)
triplet (3A″)
method
total energy
ZPVE
total energy
ZPVE
singlet−triplet gap
cc-pVTZ HF cc-pCVTZ HF cc-pVQZ HF cc-pVTZ CCSD cc-pCVTZ CCSD cc-pVQZ CCSD cc-pVTZ CCSD(T) cc-pCVTZ CCSD(T) cc-pVQZ CCSD(T)
−151.668815 −151.668583 −151.680298 −152.203316 −152.360422 −152.246177 −152.234214 −152.393118 −152.279650
80.20 80.13 80.32 78.21 78.42 78.28 77.48 77.63 77.41
−151.703498 −151.704208 −151.714626 −152.219780 −152.377079 −152.261366 −152.242444 −152.401214 −152.286339
85.71 85.68 85.73 80.54 80.70 80.64 79.52 79.65 79.58
16.3 16.8 16.1 8.0 8.2 7.2 3.1 3.1 2.0
Figure 2. Predicted equilibrium geometry for the triplet ground state of formylmethylene (planar, Cs, 3A″). Distances are in Å, and angles are in degrees.
T)]37−39 were employed. The 1s core orbitals of the carbon and oxygen atoms were frozen in the correlation treatments using the cc-pVXZ basis sets; no orbitals were frozen when using the cc-pCVXZ basis sets. Computations were performed using the MOLPRO 2010.140 and CFour41,42 program packages. Second-order perturbation theory (VPT2)43−48 was applied to the force field in order to obtain fundamental vibrational frequencies and vibrationally averaged rotational constants. To gain a qualitative understanding of formylmethylene, Wiberg bond indices49 (WBIs) and molecular orbitals (MOs) were computed at the B3LYP50,51 6-311+G*52 level of theory using Gaussian 03.53
triplet ground state; this is indeed a very small singlet−triplet gap. Compared with previous results,9,17,18 the singlet−triplet gap is expected to become smaller as higher levels of theory and larger basis sets are used. Specifically, for the parent CH2 molecule, our cc-pVQZ CCSD(T) method yields ΔE(S-T) = 9.79 kcal mol−1,54 whereas the experimental value is 9.03 kcal mol−1.55 Should this offset of 0.76 kcal mol−1 apply to formylmethylene, our estimated formylmethylene ΔE(S-T) would be 1.27 kcal mol−1 . B. Electronic Structure Considerations. The triplet ground state of formylmethylene has the following electron configuration:
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[core]4a′2 5a′2 6a′2 7a′2 8a′2 1a″2 9a′2 10a′2a″
RESULTS AND DISCUSSION A. Energies. The total energies, zero-point vibrational energies (ZPVEs), and relative energies (singlet−triplet gaps) for the ground state triplet and lowest singlet state of formylmethylene at various levels of theory are listed in Table 1. At the cc-pVQZ CCSD(T) level of theory with ZPVE, the lowest singlet state is only 2.03 kcal mol−1 higher than the
where [core] = 1a′22a′23a′2 denotes the three lowest-lying core (C:1s-like and O:1s-like) orbitals. The lowest singlet state of formylmethylene arises from the electron configuration [core]4a 25a 26a 27a 28a 29a 210a 211a 2 2154
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Figure 3. Predicted equilibrium geometry for the lowest singlet electronic state of formylmethylene (C1, 1A). Distances are in Å, and angles are in degrees.
where [core] = 1a22a23a2 denotes the three lowest-lying core (C:1s-like and O:1s-like) orbitals. C. Structure and Bonding. Geometries for the triplet ground state and lowest singlet state of formylmethylene molecules are depicted in Figures 2 and 3, respectively. They were optimized at the HF, CCSD, and CCSD(T) levels of theory, with cc-pVTZ, cc-pCVTZ, and cc-pVQZ basis sets. At a given level of theory, geometries obtained using the cc-pVTZ and cc-pVQZ basis sets are very similar to those from the ccpCVTZ basis set. This indicates that core−electron correlation is not very important for these two states of formylmethylene. Based on comparison with experimental data on a series of small molecules, cc-pVQZ CCSD(T) results should be highly accurate for species where core−electron correlation is not important.56 Furthermore, our results show that valenceelectron correlation has a greater influence on the singlet state than on the triplet ground state of formylmethylene. For example, improved descriptions of correlation decrease the C1− C2 bond length, decrease the C1−C2−O3 bond angle, increase the C1−C2−H5 bond angle, and so on. More complete treatments of electron correlation have a smaller effect on the triplet ground state; the RHF geometry is very similar to the CCSD(T) geometry. Bonding analyses for the triplet ground state and lowest singlet state are depicted in Figures 4 and 5, respectively. Ground state triplet formylmethylene is a planar molecule;15,16 see Figure 2. At the cc-pVQZ CCSD(T) level of theory, the bond length of C1−C2 is 1.427 Å, which is between the typical CC double bond length (1.34 Å) and typical C− C single bond length (1.54 Å).57 The WBI for this bond is 1.26. Similarly, the C2−O3 distance is 1.231 Å; slightly longer than a typical CO double bond (1.20 Å), but much shorter than a C−O single bond (1.43 Å).57 Again, the WBI supports this interpretation; it is 1.64. The C2−O3 and C1−C2 bond lengths provide evidence for electron delocalization in the C1−C2−O3
Figure 4. Bonding diagram for the ground triplet formylmethylene.
Figure 5. Bonding diagram for the lowest singlet state of formylmethylene.
plane. The C1−C2−H5 and H5−C2−O3 angles are close to 120°, indicating an sp2 hybridized C2 atom. In addition, the C2−C1−H4 angle is 129°, so atom C1 also has sp2 hybridization. The sp 2 hybridized carbon atoms (C 1 , C 2 ) and the unhybridized O3 atom each provide a parallel singly occupied p orbital. 2155
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Figure 6. Molecular orbitals of singlet formylmethylene, showing delocalization from the lone pair of O3 into the unoccupied p-orbital of C1 (LP → p, HOMO−4) and from the C1 lone pair into the carbonyl π antibonding orbital (LP → π*, HOMO).
average percent difference is slightly larger (3.2%) using the significantly more complete cc-pVQZ CCSD(T) basis set. These differences are mainly due to anharmonicity. The anharmonic effects on the vibrational frequencies of formylmethylene will be addressed in the following section. F. Anharmonic Vibrational Analysis. Fundamental vibrational frequencies (νr) are related to the harmonic frequencies (ωr) by the anharmonic vibrational constants χrs according to the following equation:43,44,58−60
In contrast, the lowest singlet state of formylmethylene is nonplanar (Figure 3). This is in accord with previous theoretical work.9,11,14,15 At the cc-pVQZ CCSD(T) level of theory, the bond length C1−C2 is 1.350 Å, which is very slightly longer than a typical CC double bond (1.34 Å), but much shorter than a typical C−C single bond (1.54 Å).57 The WBI is 1.19. In addition, the C2−O3 bond length is 1.278 Å. This is longer than a ketone CO bond (1.23 Å57) but much shorter than a single C−O bond (1.43 Å).57 Here, the WBI of 1.79 indicates a near-double bond. Thus, the C1−C2 and C2−O3 bond lengths indicate some electronic delocalization in the C1− C2−O3 plane. There are two types of delocalization, depicted in Figure 5. (1) The carbonyl oxygen donates its lone pair (LP) electrons into the vacant p orbital of the carbene carbon C1. This LP→p interaction is possible because the carbene-H bond (H4−C1) is nearly perpendicular to the plane of C1−C2−O3 and the C1−C2−O3 angle is 92.0°. Furthermore, C1 is only 1.891 Å from O3. The LP → p interaction is apparent in the orbital four below the highest occupied molecular orbital (HOMO−4), shown in Figure 6. (2) The lone pair orbital of C1 overlaps with the π antibonding orbital of the carbonyl group CO. This is called an LP → π* interaction; the HOMO is the relevant molecular orbital (Figure 6). These delocalizations elongate the C2O3 bond and shorten the C1− C2 bond. D. Dipole Moment. The computed dipole moments of triplet and singlet formylmethylene are 1.948 and 2.382 D respectively, at the cc-pVQZ CCSD(T) level of theory. The substantial dipole moments are encouraging, as they may enable experimental observation of these species by microwave spectroscopy. E. Harmonic Vibrational Frequencies and Infrared (IR) Intensities. Harmonic vibrational frequencies for the triplet ground state and lowest singlet state of formylmethylene are presented in Tables 2 and 3, respectively. The IR intensities, computed within the double harmonic approximation, are given in units of km mol−1 in parentheses. The strongest feature in the IR spectrum of singlet formylmethylene will be ν2, and the second strongest feature will be ν3. The other bands have much weaker intensities, and should be more difficult to observe experimentally. In Table 3, harmonic vibrational frequencies for triplet formylmethylene are compared with the experimentally observed fundamental vibrational frequencies.19 Six fundamental frequencies of triplet formylmethylene have been observed by IR spectroscopy;19 the experiments were performed in solid argon matrices. The average percent difference between the ccpVTZ CCSD(T) computed harmonic frequencies and the experimental fundamental vibrational frequencies is 3.1%. The
vr = ωr + 2χrr +
1 2
∑ χrs s≠r
(1)
The diagonal χrr constants may be derived from the modified Nielsen perturbation theory:43,44,60 χrr =
1 1 ϕ − 16 rrrr 16
∑
ϕrrs 2(8ωr 2 − 3ωs 2) ωs(4ωr 2 − ωs 2)
s
(2)
Similarly, the off-diagonal elements are χrs =
1 1 ϕrrss − 4 4 −
1 2
∑ t
∑ t
ϕrrtϕsst ωt ϕrst 2ωt(ωt 2 − ωr 2 − ωs 2)
[(ωr + ωs)2 − ωt 2][(ωr − ωs)2 − ωt 2]
⎛ ω⎞ (a) 2 (b) 2 (c) 2 ωr + [Ae(ζr,s + s⎟ ) + Be (ζr,s ) + Ce(ζr,s ) ]⎜ ωr ⎠ ⎝ ωs (3)
Here the ϕrrss terms are the quartic force constants in normal coordinates and the ζ(b) r,s terms are the Coriolis interaction constants. Fermi resonances occur when 2ωr ≈ ωs and ϕrrs ≠ 0, or ωr + ωs ≈ ωt and ϕrst ≠ 0. This means that the terms χrr (eq 2) and/ or χrs (eq 3) become large and the perturbative treatment can break down. In this research, there were Fermi resonances in both singlet and triplet formylmethylene. For the former, 2ω2 ≈ ω4, ω2 + ω3 ≈ ω5 and ω1 + ω5 ≈ ω7. In the latter, ω1 + ω3 ≈ ω6, ω2 + ω4 ≈ ω7, and ω6 + ω7 ≈ ω8. The anharmonic vibrational corrections for the triplet ground state of formylmethylene are reasonable. The largest anharmonic corrections are for the C1−H4 out-of-plane bend [ω2 (A″)] and the C2−H5 stretch [ω8, (A′)]. These corrections are only slightly larger than 5% of the corresponding harmonic vibrational frequencies. Our computed fundamental frequencies are compared to the six observed fundamental frequencies in Table 3. The average percent difference between the computed anharmonic frequencies and experimental values is 1.6%. The largest 2156
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(231.6) (233.5) (202.9) (−28.7)
2(A) 470.6 460.6 444.0 −26.6
Fermi resonance between ω2 and ω3. See text.
(16.9) (31.9) (5.2) (−11.7)
1(A)
321.6 303.8 292.9 −28.7
(90.0) (79.4) (72.9) (−17.1)
3(A) 699.3 685.5 697.8 −1.5
(5.5) (6.1) (5.9) (0.4)
4(A) 986.3 977.0 941.9 −44.4
5(A) 1167.8 (27.4) 1163.8 (31.8) 828.2a −339.6a
(32.6) (36.9) (29.5) (−3.1)
6(A) 1428.4 1415.5 1382.8 −45.6
(17.3) (16.3) (15.8) (−1.5)
7(A) 1510.0 1526.1 1464.3 −45.7
(12.9) (8.7) (12.5) (−0.4)
8(A) 3157.8 3168.8 3022.6 −135.2
(5.8) (8.8) (15.9) (10.1)
9(A) 3215.6 3234.2 3070.2 −145.4
2157
experiment19 (νexpt) cc-pVTZ (ω) ω−νexpt difference cc-pVQZ (ω) ω−νexpt difference cc-pVTZ (ν) cc-pVTZ ν−ω ν−νexpt difference
mode
438.2 (42.5) −8.6 (−4.0)
447.4 (47.5)
446.8 (46.5)
1(A′) 583 596.0 (28.3) 13.0 2.2% 598.3 (27.5) 15.3 2.6% 566.1 (27.6) −29.9 (−0.7) −16.9 2.9%
2(A″) 899 937.6 (10.9) 38.6 4.2% 938.8 (9.8) 39.8 4.3% 895.5 (11.1) −42.1 (0.2) −3.5 0.4%
3(A′)
954.6 (0.6) −19.9 (0.4)
972.3 (1.2)
974.5 (1.0)
4(A′) 1120 1132.4 (44.4) 12.4 1.1% 1137.0 (45.4) 17.0 1.5% 1090.8 (41.3) −41.6 (−3.1) −29.2 2.6%
5(A′)
1374 1413.5 (9.2) 39.5 2.8% 1409.7 (9.2) 35.7 2.6% 1382.1 (8.4) −31.4 (−0.8) 8.1 0.6%
6(A′)
1496 1575.6 (43.1) 79.6 5.2% 1575.6 (48.2) 79.6 5.2% 1507.8 (2288.5) −67.8 (2245.4) 11.8 0.8%
7(A′)
2934 3023.7 (57.9) 89.7 3.0% 3028.0 (51.0) 94.0 3.2% 2867.9 (60.2) −155.8 (2.3) −66.1 2.3%
8(A′)
3085.8 (2.2) −128.8 (−0.3)
3217.9 (2.9)
3214.6 (2.5)
9(A′)
Table 3. Theoretical Harmonic Vibrational Frequencies (ω, in cm−1), Anharmonic (Fundamental) Vibrational Frequencies (ν, in cm−1), and Infrared Intensities (in km mol−1, in Parentheses) for the Triplet State of Formylmethylene at the CCSD(T) Level of Theory
a
cc-pVTZ (ω) cc-pVQZ (ω) cc-pVTZ (ν) cc-pVTZ (ν−ω)
mode
Table 2. Theoretical Harmonic Vibrational Frequencies (ω, in cm−1), Anharmonic (Fundamental) Vibrational Frequencies (ν, in cm−1), and Infrared Intensities (in km mol−1, in Parentheses) for the Lowest Singlet State of Formylmethylene at the CCSD(T) Level of Theory
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discrepancies are −29.2 cm−1 for the C1−C2 stretching mode and −66.1 cm−1 for the C2−H5 stretching mode. These discrepancies are possibly due to higher anharmonicity in these modes, causing VPT2 to break down, or due to matrix effects. However, the anharmonic correction for ω5 (A) of singlet formylmethylene is quite large. This is due to strong Fermi resonance between modes ω2 and ω3. Since the intensity of ω5 is so low, this does not affect the usefulness of our results for spectroscopists. As discussed above, the most prominent features in the singlet formylmethylene IR spectrum will be ν2 and ν3. The anharmonic corrections for these important modes are reasonably small (less than 6% of the corresponding harmonic frequency), indicating that they are not adversely affected by Fermi resonance.
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CONCLUSIONS In the current research, equilibrium geometries, total energies, and harmonic frequencies for the triplet ground state and lowest singlet state of formylmethylene are reported at the CCSD(T) level of theory with the cc-pVTZ, cc-pCVTZ, and cc-pVQZ basis sets. We also report values for the singlet− triplet gap at the same levels of theory. Since we determined that core−electron correlation was not important for formylmethylene, the cc-pVQZ CCSD(T) computations should yield the most accurate information about formylmethylene to date.56 Accurate quartic force fields were predicted for the two states of formylmethylene at the cc-pVTZ CCSD(T) level of theory. The force fields have been analyzed using vibrational second-order perturbation theory (VPT2), in order to determine fundamental (anharmonic) frequencies. The mean absolute difference between computed and experimental fundamental frequencies for triplet formylmethylene is 1.6%. We hope that the present research will guide experimental detection of the lowest singlet state of formylmethylene, and aid in understanding the Wolff rearrangement.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected];
[email protected]; qc@ uga.edu. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research was funded by the U.S. Department of Energy (DOE) Grant No. DEFG02-97-ER14748 and the China Scholarship Council (CSC, 2011) Grant No. 3006. We thank Dr. Yaoming Xie, Dr. Yukio Yamaguchi, and Jowa Wu for many good suggestions and helpful discussions.
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