Switching of carbene spin states: effect of hydrogen bond donors

Abstract:

Quantum chemical calculations predict that the spin states of simple carbenes can be switched over from triplet to singlet via hydrogen bonding, and thus the spin specificity of their reactions can be tuned. The stability of the singlet state of simple carbenes like: CH₂ increases due to hydrogen bond formation with a single molecule of water or methanol, although the triplet state is found to be the ground state. However, the most dramatic effect of spin switch is found for diphenylcarbene (Ph₂C), which becomes a ground state singlet due to formation of a hydrogen bond with the hydrogen atom of water or methanol. The present calculations reveal that the effect of hydrogen bonds on switching the spin state of carbenes is only applicable to Ph₂C, as it has a very small singlet–triplet gap in its free form, ie, when it is not hydrogen bonded with water or methanol. Further, the presence of such hydrogen-bonding interaction has been verified within the realm of atoms-in-molecules analysis of the electron density.

Keywords::

• carbenes
• spin states
• quantum chemical calculations
• hydrogen bonding
• atoms in molecules

Introduction

Carbenes (R₂C:) are divalent carbon species having two nonbonding electrons. These nonbonding electrons may have antiparallel spins (singlet state) or parallel spins (triplet state).^1–6 The parent carbene CH₂ has a triplet ground state with an experimental singlet–triplet (S–T) energy gap of 9.05±0.06 kcal/mol.^7–9 The small difference between the S₀ and T₁ may be easily overcome by tuning the substituents attached to the carbene center.¹⁰ Various factors dictate the ground state multiplicity or the S–T separation of carbenes.¹¹ Apart from the effect of substituents, solvents are found to stabilize the singlet state more than the triplet state.^12–16

Products of carbene reactions are solely determined by the carbene’s spin state. For example, the singlet carbene inserts in to the O-H bonds of alcohol,¹⁷ whereas the triplet carbene undergoes insertion into C-H bonds¹⁸ (Figure 1).¹⁹ This reactivity difference of carbenes with alcohol has been extensively studied, and spin selectivity of carbene chemistry has been developed.^19–22

Figure 1 Proposed reactions of singlet and triplet carbenes with an alcohol.

Note: Methanol was the alcohol used in this figure.

Recently, Costa and Sander¹⁹ investigated the reaction of diphenylcarbene (DPC), Ph₂C, an archetypical ground state triplet carbene, with methanol and isolated a singlet metastable complex (the complex was found to be electron spin resonance silent) in low-temperature matrices. The formation of the metastable methanol complex has been monitored and characterized by infrared spectroscopy. They also characterized the O−H insertion product, a typical product expected for singlet state carbene. Based on a different spectroscopic technique and theoretical calculations, they predicted that the singlet state of DPC can become more stable by hydrogen bonding interactions with solvents. Their results showed an interesting chemistry of switching the ground state multiplicity of carbenes by solvent interactions, and there by providing a hint toward a unique way to control the carbene’s chemical reactivity. In another report, Costa et al²⁰ observed that the reaction of DPC with a single molecule of water switches its spin state. This prompted us to investigate the effect of hydrogen bond donors such as H₂O and CH₃OH on the spin states of simple alkyl and aryl carbenes, R₂C: (R=H, Me, Et, Ph). Here, we present quantum chemical calculations,^23–37 which reveal that the spin states of alkyl or aryl carbenes can be tuned by interaction with a hydrogen bond donor solvent or reactant. The goal of controlling the spin state of a carbene is to change the reaction path so as to achieve the good desired reaction selectivity. In order to react with an alcohol, the hydrogen bond between carbene and the solvent molecules should be broken first. Then, the carbene carbon atom can get close to and react with the alcohol. In this case, the hydrogen-bond-induced spin state change may have no effect on the real reactions. However, this hydrogen bonded interaction may prevent the dimerization of triplet carbenes by providing stability to the singlet state.

Computational details

Geometry optimization of all the molecules without any symmetry constraint were performed at B3LYP,^23,24 BNL,^25–27 B3LYP-D,²⁸ LC-BLYP,²⁹ and M06-2X³⁰ functional using the 6-311++G(d, p) basis set frequency calculations have been performed at these levels of theory to characterize the nature of stationary points. Single point energy calculations at CCSD(T)/6-311++G(d, p)³¹ level of theory has been performed using the ORCA³² suite of program. However, the performance of B3LYP functional is found to better (Figure S1, supporting information) and hence, the discussion in the text is based on B3LYP level of theory. We have also calculated the S–T gap of the parent carbenes at B3LYP/Aug-cc-pVDZ. All geometry optimizations and frequency calculations have been performed using NWChem 6.1 program in gas phase.³³ Quantum theory of atoms in molecules (QTAIM)³⁴ and electron localization function (ELF)^35,36 have been performed using Multiwfn 3.1 suite of program.³⁷

Results and discussions

Table 1 lists the S–T energy separations, ΔE_ST, calculated at B3LYP level using the 6-311++G(d, p) and Aug-cc-pVDZ basis sets in the gas phase for four carbenes. The B3LYP/6-311++G(d, p) method gave the least absolute error in the S–T energy gaps when compared with the values computed at CCSD(T)/6-311++G(d, p) level of theory (Figure S1). The calculated values of ΔE_ST at B3LYP/6-311++G(d, p) level are very close to those obtained in the previous studies^38,39 and are very close to the values calculated at CCSD(T)/6-311++G(d, p) level of theory. Similar results are obtained using the larger basis set (Aug-cc-pVDZ). However, the S–T gaps are slightly smaller with the Aug-cc-pVDZ basis set than with the 6-311+G(d, p) basis set. Thus, the discussion in this text is based on the B3LYP/6-311(d, p) results. The simplest carbene, methylene, has a triplet ground state with ΔE_ST of 11.73 kcal/mol calculated at B3LYP/6-311++G(d, p) level of theory. The experimental value of S–T separation of CH₂ is 9.05 kcal/mol,⁷ which is 2.68 kcal/mol less than our B3LYP/6-311++G(d, p) calculated value. Increase in the basis set size to Aug-cc-pVDZ leads to a ΔE_ST value of 11.13 kcal/mol, which is 2.08 kcal/mol less than the reference value.

Table 1 B3LYP calculated gas phase singlet–triplet energy separations (kcal/mol) for carbenes

Entry	Calculated, ΔΕSΤ at 6-311 ++G(d, p)		ΔΕST at Aug-cc-pVDZ without ZPE
	With ZPE	Without ZPE
H2C	11.73	12.15 (12.06)	11.13
Me2C	−0.75	−0.36 (−0.38)	−1.02
Et2C	−3.18	−2.45	−3.05
Ph2C	5.64	5.92	4.82

Notes: Values in parentheses were calculated at CCSD(T)/6-311++G(d, p) level without ZPE correction. Basis set used are 6-311++G(d, p) and Aug-cc-pVDZ.

Abbreviations: ΔE_ST, singlet–triplet energy separation; ZPE, zero-point energy.

The S–T gap of dimethylcarbene, Me₂C, is found to be −0.75 kcal/mol at B3LYP level of theory. This implies that the ground state of Me₂C is singlet. The stability of the singlet state of Me₂C can be explained by hyperconjugation. Since, singlet carbenes are isoelectronic with carbocations, hyperconjugation stabilizes the singlet state more than the triplet radical species.¹¹ The effect of hyperconjugation is more pronounced in case of Et₂C. Similarly, the conjugation of aryl groups, as in Ph₂C, reduces the S–T gap of aryl carbenes.¹¹ However, the effect of conjugation is somewhat less compared to the stabilization provided by the hyperconjugation of methyl and ethyl groups in Me₂C and Et₂C, respectively.

Previous studies reveal that polar solvents reduce the S–T gap of carbenes by increasing the dipole moment of the singlet state.^11–16 The reduction of the S–T gap for carbenes in polar solvents has been computationally verified.¹² The plot of experimentally determined S–T gaps as a function of solvent polarity was found to be linear,¹¹ which led to the conclusion that specific carbene–solvent interaction does not play a significant role.¹¹ However, the recent report by Costa and Sander¹⁹ and Costa et al²⁰ clearly establishes that the spin states of carbenes can be tuned by interaction with hydrogen bond donor solvents and that the carbene–solvent interaction has a vital role to play in the ground state multiplicity of carbenes. Although the effect of solvent polarity on the S–T gap of carbenes has been theoretically explored, the explicit interaction of solvent molecules with carbenes needs to be understood.

Table 2 collects the S–T gap of carbene–solvent complexes. Interaction of H₂O with CH₂ reduces the S–T gap by 3.81 kcal/mol (triplet state is more stable). The most dramatic effect of solvent interaction is found in the case of Me₂C…solvent complexes (the … signifies a weak interaction between atoms). The S–T gap is dramatically reduced, thus making the singlet state more stable. The effect of solvent interaction in reducing the S–T gap is also observed in the case of Ph₂C. The singlet state of Ph₂C…solvent complexes are found to be slightly more stable. This is in agreement with recent observation of Costa and Sander¹⁹ and Costa et al.²⁰

Table 2 Gas-phase B3LYP/6-311++G(d, p) calculated singlet–triplet energy separations (in kcal/mol) and dipole moments (in debye) for carbene–solvent complexes^a,b

Entry	∆EST		∆(∆EST)	μ
	With ZPE	Without ZPE		S	T
H2C…H–OH	7.95	7.04 (7.74)	3.78	3.95	2.50
H2C…H–OCH3	7.74	7.10 (7.76)	3.99	3.70	2.06
Me2C…H–OH	−5.73	−6.03 (−4.15)	4.98	4.26	2.66
Me2C…H–OCH3	−5.82	−5.97	5.07	4.22	2.40
Et2C…H–OH	−3.75	−4.18	0.57	4.36	2.74
Et2C…H–OCH3	−3.91	−4.28	0.73	4.37	2.67
Ph2C…H–OH	−0.45	−0.62	6.09	4.47	2.72
Ph2C…H–OCH3	−0.18	−0.42	5.92	4.36	2.53

Notes: Values in parentheses refer to CCSD(T)/6-311++G(d, p) energies without ZPE correction. ^aΔ(ΔE_ST) = ΔE_ST (free carbene) – ΔE_ST (carbene…solvent complex); ^bsinglet states are more stable. The … signifies a weak interaction between atoms.

Abbreviations: ΔE_ST, singlet–triplet energy separation; ZPE, zero-point energy; μ, dipole moment; S, singlet; T, triplet.

The interaction of hydrogen bond donors (H₂O and CH₃OH) increases the dipole moment of the singlet more than that of the triplet. This increase in dipole moment indicates a higher stability of the more polar singlet state over the triplet state. This is in agreement with previous theoretical studies on the preferential stabilization of the singlet state in a polar solvent due to an increase in dipole moment.^11–16

Figure 2 shows the optimized geometries of the carbene…solvent complexes at the B3LYP/6-311++G(d, p) level of theory. The C…HO distances are found to be close to 2 Å, which are ~30% shorter than the sum of the van der Waals radii of carbon and hydrogen (2.85 Å).⁴⁰

Figure 2 B3LYP/6-311++G(d, p) optimized singlet state geometries of carbene–solvent complexes.

The spin cross-over of Ph₂C complexed with CH₃OH were explored by a relaxed potential energy scan, keeping the C…HO distance fixed and optimizing all other coordinates at B3LYP/6-311++G(d, p) level. Figure 3 is a plot of the energies (kcal/mol) of the respective singlet and triplet states of the Ph₂C…H-OCH₃ complex. It is evident from Figure 3 that the spin cross-over from triplet to singlet takes place at C…HO distance of ~2.30 Å, which is longer than the C…HO equilibrium distance of 1.971 Å.

Figure 3 Spin cross-over for Ph₂C…H−OCH₃ complex calculated at the B3LYP/6-311++G(d, p) level without zero-point energy correction.

Note: The … signifies a weak interaction between atoms.
Abbreviation: E_el, electronic energy.

The formation of hydrogen bonds has been confirmed by applying the QTAIM³⁴ and the ELF^35,36 analysis (Figure 4 and Table 3). These topological analyses reveal a bond path and a (3, −1) bond critical point between the carbenic carbon and the hydrogen atom of the H−O bond of H₂O or CH₃OH (Figure 4). The Laplacian of the electron density, ∇²ρ, is positive and the local electronic energy density, H(r), is negative, which is a characteristic feature of a polar covalent bond.³⁴ The ELF^35,36 values at the bond critical points of these complexes are also significant. All these topological features confirm the presence of such interaction.

Figure 4 Molecular graph of the Me₂C…H−OCH₃ complex showing the topological parameters at the C…HO bond critical point. All values are in atomic units.

Note: The … signifies a weak interaction between atoms.
Abbreviations: ρ, electron density; ∇²ρ, laplacian of electron density; H(r), local energy density; ELF, electron localization function.

Table 3 Topological analysis of the C…H−O bond for the complexes

Entry		ρ (rho)	▽^2ρ	H(r)	ELF
H2C…H–OH		0.029	0.051	−0.003	0.181
H2C…H–OCH3		0.031	0.050	−0.004	0.194
Me2C…H–OH		0.033	0.049	−0.005	0.197
Et2C…H–OH		0.042	0.048	−0.006	0.215
Et2C…H–OCH3		0.046	0.052	−0.007	0.221
Me2C…H–OCH3		0.034	0.048	−0.006	0.254
Ph2C…H–OH		0.034	0.062	−0.003	0.232
Ph2C…H–OCH3		0.035	0.066	−0.004	0.241

Notes: All values are in atomic units. The … signifies a weak interaction between atoms.

Abbreviations: ELF, electron localization function; ρ, electron density; ∇²ρ, laplacian of electron density; H(r), local energy density.

Conclusion

In conclusion, quantum chemical calculations showed that the interaction of hydrogen bond donor molecules can modify the S–T gap of alkyl or aryl carbenes. This interaction may lead to a higher stability of the singlet state over the triplet state by increasing the dipole moment of the former. This increase in dipole moment results in more charge reorganization in the singlet state, rendering them more stable. A simple carbene like CH₂ shows a decrease in S–T gap of ~4.0 kcal/mol due to formation of hydrogen bonds with water or methanol, although the triplet state is still the ground state. The most dramatic effect of hydrogen bond formation on the spin state of carbenes is observed for DPC, for which the singlet state becomes the ground state. Thus, it appears that hydrogen bond-induced spins witch over is applicable to DPCs among the four carbenes considered in this study. This might be due to the fact that the S–T gap of the parent Ph₂C is very small (~5 kcal/mol) and may get reduced upon hydrogen bond formation to such an extent that the hydrogen bonded singlet Ph₂C becomes the ground state. This observation is in line with the recent experimental finding of Costa and Sander¹⁹ and Costa et al.²⁰ The existence of this hydrogen-bonded interactions has been verified by our topological studies of the electron density. The outcome of this study is encouraging in the sense that a single hydrogen bond donor molecule may switch the ground state spin multiplicity of those carbenes with a smaller S–T gap, and thus may prevent their dimerization in solutions of polar solvents.

Disclosure

The authors report no conflicts of interest in this work.

Supplementary material

Cartesian coordinates of all the molecules calculated at B3LYP/6-311++G(d, p) level.

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