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Cyclobutyne: Minimum or Transition State? Zhi Sun, and Henry F. Schaefer J. Org. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.joc.9b00502 • Publication Date (Web): 05 Apr 2019 Downloaded from http://pubs.acs.org on April 7, 2019

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The Journal of Organic Chemistry

Cyclobutyne: Minimum or Transition State?

Zhi Sun and Henry F. Schaefer III*

Center for Computational Quantum Chemistry, University of Georgia Athens, Georgia 30602, USA *E-mail:

[email protected]

1 ACS Paragon Plus Environment

The Journal of Organic Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract A cornucopia of very high-level theoretical methods has been used to study cyclobutyne, a molecule that has been the center of much speculation. We conclude that cyclobutyne is a transition state in its singlet ground state, based on new coupled cluster and multireference computations presented in this research. This is substantially different from other theoretical studies proposing the existence of singlet cyclobutyne as a minimum. The singlet cyclobutyne transition state (C2v) exhibits a ring puckering imaginary vibrational mode leading to two equivalent minima, cyclopropylidenemethylenes in Cs symmetry, with a barrier height of ~23 kcal/mol. In contrast with previous studies, singlet cyclopropylidenemethylene in C2v symmetry was predicted to be a transition state, not a minimum. Triplet cyclobutyne is a genuine minimum and higher-lying than the lowest singlet state by ~15 kcal/mol. New computations give the total ring stain of the singlet cyclobutyne to be 101 kcal/mol, with an in-plane π bond strain of 71 kcal/mol.


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Introduction Small-ring cycloalkynes are highly strained due to the bent -C-C≡C-C- triple bond, and most are thought to be unstable, and existing only as transient intermediates.1-4 The question of “what is the smallest cycloalkyne that can exist” is inevitably raised and of long-standing interest in physical organic chemistry. With only a four-membered ring structure, cyclobutyne (Figure 1) is an extreme case in this context.

Figure 1. Structures of five important C4H4 intermediates noted in the chemical literature.

Although cyclobutyne appears in metal cluster complexes as ligand,5-7 no conclusive experimental evidence for the existence of “free” cyclobutyne has been reported to date. Early



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theoretical studies have proposed the existence of cyclobutyne. The two-configuration selfconsistent-field (TCSCF) method with DZ level basis sets predicts singlet cyclobutyne to be a relative minimum on the C4H4 potential energy surface.8 Using the TCSCF and CCSD(T) methods with DZP basis sets, cyclobutyne was later proposed to be “makeable”. This was due to the high barrier for cyclobutyne isomerization into butatriene (Figure 1), although cyclobutyne lies ~78 kcal/mol above vinylacetylene (Figure 1), the C4H4 global minimum.9 Both MCSCF(4,4)/6-31G(d) and MP2/6-31G(d) predict singlet cyclobutyne as a local minimum,3 which is expected to easily convert to C2v cyclopropylidenemethylene (Figure 1), kinetically and thermodynamically. In addition, triplet cyclobutyne was also described as a minimum with the B3LYP/6-311G(d,p) method.10,11 The above notwithstanding, the idea of singlet cyclobutyne being a minimum has been challenged by relatively recent theoretical studies. It was predicted11 to be a transition state using the B3LYP, CCSD(T), and CASSCF(12,12) methods using 6-311G(d,p) basis sets, with the one imaginary frequency being 580i, 387i, and 442i, respectively. The lowest singlet electronic state of

cyclobutyne

was

also

found12,13

to

easily

rearrange

into

a

“distorted”

cyclopropylidenemethylene (Figure 1), with the tilt of the carbene carbon atom toward one of the 4 ACS Paragon Plus Environment

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ring carbons (in Cs symmetry, compared to its C2v counterpart3) using the B3LYP and CCSD(T) methods. The above conflicting studies are indications that theoretical results for the cyclobutyne could be sensitive to the theoretical level, basis set [for instance,9,11 DZP vs. 6-311G(d,p)], active space [for instance,3,11 (4,4) vs. (12,12)] in multireference treatments, etc. Therefore, finding reliable and accurate theoretical methods is critical to truly understand cyclobutyne. In fact, cyclobutyne also has multireference issues,3,8,9 which increase the uncertainties arising from single-reference methods. Previous multireference treatments of cyclobutyne including TCSCF8,9 and CASSCF3 might lack sufficient dynamic correlation, which could give rise to misleading results. Improved results for cyclobutyne might be achieved using either the coupled cluster theory with high-level excitations or multireference methods with reasonable active spaces and dynamic correlation. This study searches in both directions and aims to answer the title question: what is the nature of cyclobutyne: minimum or transition state?



Theoretical Details In present research, the equilibrium geometries and harmonic vibrational frequencies of cyclobutyne were obtained using the MP2, CCSD(T), CCSDT, and CCSDT(Q) methods implemented in CFOUR 2.0.14,15 Two standard correlation-consistent valence basis sets (cc-pVTZ and cc-pVQZ) were used.16 The restricted (RHF) and restricted open-shell Hartree–Fock (ROHF) references were used for closed-shell and open-shell species, respectively. Core electrons were excluded from the correlation treatment (the “frozen core” approximation). For the very high level CCSDT and CCSDT(Q) methods, numerical gradients and hessians were computed for the geometry optimization and vibrational frequency computations, respectively. For all coupled cluster computations, stringent criteria were set for the SCF densities (10-10), CC amplitudes (1010),

and RMS forces (10-6 Hartree/Bohr). With the CCSD(T)/cc-pVQZ geometries as the starting points, the complete active space

self-consistent field (CASSCF) single-point computations were performed using Molpro 2010.1.17 A relatively large (16o,12e) active space (excluding the 1s and 2s type orbitals of the carbon atoms from the full-valence), that is, CASSCF(16o,12e)/cc-pVQZ, was chosen. For all structures under investigation, only the singlet cyclobutyne (C2v) has a leading configuration percentage lower than 6 ACS Paragon Plus Environment

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90% (C2 = 81%), with a second leading configuration percentage being C2 ≈ 7% (see Table S1 in the Supporting Information). Therefore, C2v singlet cyclobutyne was further treated by a multireference configuration interaction method18,19 with the Davidson correction20 (MRCI+Q, ccpVTZ and cc-pVQZ basis sets16). Within two different ranges of the natural orbital occupation numbers (n) from the CASSCF(16o,12e)/cc-pVQZ computations, 0.04 < n < 1.96 and 0.02 < n < 1.98, two new active spaces (4o,4e) and (8e,7o) were selected for the MRCI+Q optimizations, respectively. The corresponding orbital set selected for the C2v singlet cyclobutyne is shown in Figure 2. For all MRCI+Q computations, the SCF energies and densities were both converged to 10-10, and the RMS forces were converged to 10-6 Hartree/Bohr. For other species showing no apparent multireference issues (Table S1 in the SI), only coupled cluster methods were employed. Following a referee, a set of 16 DFT functionals (Table 2: four GGA, four meta-GGA, four hybrid GGA, and four hybrid meta-GGA functionals) was also tested for the singlet cyclobutyne (C2v). The SCF energies were converged to 10-10, and root mean square (RMS) forces were converged to 10-6 Hartree/Bohr. A fine integration grid (120,974) was used to guarantee the numerical accuracy, and all DFT computations were performed using Q-Chem 5.0.1.21



Figure 2. Orbitals included in the MRCISD+Q computations. Two different active spaces were used: first row: (4o,4e) and first + second row: (7o,8e). C2v singlet cyclobutyne natural orbital occupation numbers (in parentheses) were obtained at the CASSCF(16o,12e)/cc-pVQZ level of theory.

Figure 3. Stationary point geometries of C2v singlet cyclobutyne optimized at seven different theoretical levels.


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Results and Discussion Figure 3 shows optimized geometries of the C2v singlet cyclobutyne at different theoretical levels. The computations with cc-pVQZ basis sets tend to give slightly shorter bond distances than the cc-pVTZ basis sets, for both coupled cluster and MRCI methods. No significant structural changes can be found between our two high level theoretical methods, and the differences in bond distances occur mostly in the third decimal place. However, the vibrational frequency computations show inconsistencies among the different methods, as indicated in Table 1. All MP2 and CASSCF computations incorrectly predict singlet cyclobutyne to be a minimum (see lowest vibrational frequencies in Table 1), generally consistent with previous theoretical studies using MP2,3 TCSCF,8,9 and MCSCF3 methods with various basis sets. On the contrary, both coupled cluster and MRCI methods predict an imaginary vibrational frequency (see Table 1) for C2v singlet cyclobutyne. Despite certain multireference issue mentioned above, high-level coupled cluster [CCSD(T) and CCSDT] and multireference (MRCI+Q) methods agree that the singlet cyclobutyne is a transition state, not a minimum. The above findings generally agree with a previous theoretical study using the B3LYP, CCSD(T), and CASSCF(12,12) methods with 6-311G(d,p) basis sets.11 However, it is worth 9 ACS Paragon Plus Environment


noting that the CASSCF results do not agree. Our CASSCF(4e,4o)/cc-pVTZ and CASSCF(4e,4o)/cc-pVQZ computations (Table 1) predict singlet cyclobutyne to be a minimum, whereas the smaller basis set CASSCF(12,12) computations from reference 11 shows a transition state (442i).11 This is an indication that different active space, orbital set, or basis sets can potentially change the CASSCF results. Such divergence makes it difficult to draw a convincing conclusion on the nature of singlet cyclobutyne from CASSCF computations.

Table 1. Lowest vibrational frequency for C2v singlet cyclobutyne with various ab initio methods. Theorya

a b

Singlet cyclobutyne (C2v)b

MP2/cc-pVTZ

minimum (457)

MP2/cc-pVQZ

minimum (456)

CCSD(T)/cc-pVTZ

transition state (397i)

CCSD(T)/cc-pVQZ


CCSDT/cc-pVTZ


CASSCF(4e,4o)/cc-pVTZ

minimum (290)

CASSCF(4e,4o)/cc-pVQZ

minimum (290)

MRCI+Q(4e,4o)/cc-pVTZ


MRCI+Q(4e,4o)/cc-pVQZ


MRCI+Q(8e,7o)/cc-pVTZ


Both optimization and frequency computations were performed at each level of theory. The lowest vibrational frequencies (in cm-1) are listed in parentheses.


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Therefore, much higher level multireference methods with dynamic correlation (MRCI+Q, Table 1) and different combinations of active space [(4e,4o) or (8e,7o)] and basis sets (cc-pVTZ or cc-pVQZ) were chosen to provide more convincing evidence. For coupled cluster results, current CCSD(T) computations [CCSD(T)/cc-pVTZ and CCSD(T)/cc-pVQZ] agree with one previous result [CCSD(T)/6-311G(d,p)]11 for singlet cyclobutyne. Due to possible multireference issues, however, it is very important to examine the reliability of CCSD(T) results by including higher excitations [CCSDT or CCSDT(Q), Table 1] within the coupled cluster methodology. In this case, the different coupled cluster computations give consistent results. Moreover, when these high-level multireference and coupled cluster methods agree (as shown in Table 1), a confident prediction can then be made. Namely, the lowest C2v singlet electronic state of cyclobutyne is a transition state, not a minimum. The performance of a set of DFT functionals was also evaluated for singlet cyclobutyne, and these results are reported in Table 2. Sixteen functionals including four GGA, four meta-GGA, four hybrid GGA, and four hybrid meta-GGA functionals were tested. In addition to the wellknown functionals (BP86, B3LYP, M06-2X), several newer functionals (B97M-rV, ωB97M-V, MN15) recently recommended in an extensive benchmark study of 200 DFT functionals22 were 11 ACS Paragon Plus Environment


also included to treat this theoretically challenging molecule. In Table 2, half of the functionals give reasonable predictions (transition state) for singlet cyclobutyne, consistent with our coupled cluster and multireference results. However, the other DFT methods incorrectly predict singlet cyclobutyne to be a second order saddle point, and the additional small imaginary vibrational mode consistently corresponds to a ring puckering vibration leading to a nonplanar C4 ring of cyclobutyne. Although Table 2 shows a generally better performance of GGA than the other three types of functionals, no solid conclusion on the DFT functionals should be drawn here for this specific case, because only 16 functionals have been included. However, the point is, without a careful selection of the functionals, even the “best” DFT methods (e.g., the recommended ωB97MV based on large-scale benchmarks22) can give misleading results for theoretically difficult molecular systems. Even if the “right answer” can be achieved by carefully selected DFT functionals, their accuracies should be evaluated if possible, through benchmarks vs. experimental or high-level theoretical results.


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Table 2. Lowest vibrational frequencies for C2v singlet cyclobutyne using 16 well-known DFT functionals with cc-pVTZ basis sets. GGA

meta-GGA

Hybrid GGA

Hybrid meta-GGA

Theory

Singlet cyclobutyne (C2v)a

Reference

BP86


23,24

PBE


25

BLYP


24,26

B97-D3b


27,28

TPSS


29

M06-L

2nd order saddle point (667i, 125i)c

30

B97M-rV


31,32

MN12-L


33

B3LYP


26,34

B3LYP-D3d


26,34,35

BHLYP


36

ωB97X-V


37

M06


38

M06-2X


38

ωB97M-V


39

MN15


40

CCSD(T)


The imaginary vibrational frequencies (in cm-1) are listed in parentheses. The zero-damping formulation of Grimme et al (ref. 28). c The small imaginary vibrational modes consistently correspond to a ring puckering vibration leading to a nonplanar C4 ring of cyclobutyne. d The Becke-Johnson damping formulation (ref. 35).

a

b



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If singlet C2v cyclobutyne is a transition state, two further questions naturally arise: (1) what does this transition state lead to (or what is the true minimum)? All high-level methods (coupled cluster and MRCI+Q) exhibit a ring puckering imaginary vibrational mode leading to two equivalent minima, cyclopropylidenemethylenes in Cs symmetry (left structure in Figure 4). The corresponding energy barrier was computed to be 23-24 kcal/mol at the CCSD(T)/cc-pVTZ and CCSD(T)/cc-pVQZ levels, as indicated by the potential energy surface in Figure 5. (2) What is the relation between the Cs and C2v cyclopropylidenemethylenes (Figure 4), as both structures have been previously predicted as minima?3,12 Our new computations at the CCSD(T)/cc-pVTZ

and

CCSD(T)/cc-pVQZ

levels

indicate

that

the

singlet

C2v

cyclopropylidenemethylene is not a minimum but a transition state (Table 3). Those higher level predictions do not agree with previous results at the MCSCF(4,4)/6-31G(d) and MP2/6-31G(d) levels.3 Our new C2v transition state possesses an imaginary vibrational mode (-C=C: rocking) leading to two equivalent minima, the Cs cyclopropylidenemethylenes (Figures 4 and 5). The barrier for such change of conformation is predicted to be slightly above 2 kcal/mol (Figure 5) at the CCSD(T)/cc-pVTZ and CCSD(T)/cc-pVQZ levels.


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Figure 4. Equilibrium geometries of singlet cyclopropylidenemethylene in Cs and C2v symmetries at the CCSD(T)/cc-pVTZ and CCSD(T)/cc-pVQZ (in parentheses) levels.

Figure 5. Singlet potential energy surface for cyclobutyne and cyclopropylidenemethylene at the CCSD(T)/cc-pVTZ and CCSD(T)/cc-pVQZ (in parentheses) levels of theory.



Finally, we turn to cyclobutyne in its lowest triplet state. Our results show that the C2v triplet cyclobutyne (see structure in Figure 6) is indeed a true minimum at the CCSD(T)/cc-pVTZ and CCSD(T)/cc-pVQZ levels (Table 3). Triplet cyclobutyne is higher-lying than C2v singlet cyclobutyne, and the splitting is 14.8 and 15.6 kcal/mol at the CCSD(T)/cc-pVTZ and CCSD(T)/cc-pVQZ levels, respectively. Moreover, it is of much higher energy than the Cs singlet cyclopropylidenemethylene (minimum, Figure 4) namely about 38-39 kcal/mol at the CCSD(T)/cc-pVTZ and CCSD(T)/cc-pVQZ levels.

Figure 6. Equilibrium geometries of C2v triplet cyclobutyne with the CCSD(T)/cc-pVTZ and CCSD(T)/cc-pVQZ (in parentheses) methods.


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Table 3. Vibrational frequency analyses for cyclopropylidenemethylene and triplet cyclobutyne at various levels of theory.

a

Theorya

Singlet cyclopropylidenemethylene (Cs)

Singlet cyclopropylidenemethylene (C2v)

Triplet cyclobutyne (C2v)

CCSD(T)/cc-pVTZ

minimum

transition state (100i cm-1)

minimum

CCSD(T)/cc-pVQZ

minimum

transition state (110i cm-1)

minimum

The lowest vibrational frequencies (in cm-1) are listed in parentheses.

There is no doubt that cyclic singlet cyclobutyne is highly strained. Although we conclude it to be a transition state, it remains a fundamental and interesting challenge to quantitatively evaluate how strained this species is. It is relatively easy to estimate its total ring strain by the homodesmotic reaction (reaction 1) proposed by Johnson and Daoust.3 The new computations at



the CCSD(T)/cc-pVTZ level in present research give 101 kcal/mol, which is somewhat lower than the 106-107 kcal/mol previously predicted using MP2 and MP4 methods,3 although both of the latter two methods misinterpret singlet cyclobutyne as a minimum. For a closer look, it would be relatively difficult but interesting to estimate the ring strain caused only by the π bonding in the triple bond of cyclobutyne, especially the in-plane π bond. The isodesmic reaction (reaction 2) was designed for this purpose.3 Compared to its double-bonded counterpart, cyclobutene, the extra strain component in the triple-bonded cyclobutyne should mainly come from its in-plane π bond. At the CCSD(T)/cc-pVTZ level, this specific π bond ring strain is estimated to be 71 kcal/mol, close to the 73-75 kcal/mol predicted using the MP2 and MP4 methods,3 with the caveat that the imbalanced σ-π hyperconjugation on two sides of reaction 2 might cause some uncertainty. The strain energies for triplet cyclobutyne can be obtained by simply adding the singlet-triplet energy difference.


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Acknowledgments This research was supported by the U.S. National Science Foundation, Grant No. CHE-1661604.

Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Multireference diagnostics and cartesian coordinates of optimized structures.

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