Effects of Solvation and Hydrogen Bond Formation on Singlet and

Article pubs.acs.org/JPCA

Effects of Solvation and Hydrogen Bond Formation on Singlet and Triplet Alkyl or Aryl Carbenes Published as part of The Journal of Physical Chemistry virtual special issue “Mark S. Gordon Festschrift”. Jean M. Standard* Department of Chemistry, Illinois State University, Normal, Illinois 61790-4160, United States S Supporting Information *

ABSTRACT: Formation of hydrogen-bonded complexes involving singlet and triplet alkyl or aryl carbenes and the impacts of solvation and hydrogen bonding upon the carbene singlet−triplet gaps have been investigated using computational methods. Single-point CCSD(T)-F12 and MRCI+Q methodologies have been employed with aug-cc-pVDZ and aug-cc-pVTZ basis sets to determine accurate singlet−triplet gaps of carbenes and hydrogen-bonded complexes involving carbenes, with geometries and vibrational frequencies obtained at the B3LYP-D3/aug-cc-pVTZ level. Using the PCM continuum solvent method and density functional theory (B3LYP/aug-cc-pVTZ), the singlet−triplet gaps of the carbenes are found to exhibit significant solvent effects; due its higher polarity, the singlet carbene is stabilized to a greater degree than the corresponding triplet carbene, impacting the singlet−triplet gap by as much as 4.4 kcal/mol. In addition, water and methanol, acting as hydrogen bond donors, form hydrogen bonds with all the singlet and triplet carbenes studied in this work. Singlet carbenes form relatively strong hydrogen bonds with binding energies in the range 3−9 kcal/mol; triplet carbenes form weaker hydrogen bonds with binding energies in the range 1−4 kcal/mol. NBO analysis demonstrates that the singlet carbene hydrogen bonds are stabilized in typical fashion, through donation of electron density from the lone pair orbital on carbon into the O−H antibonding orbital. This stabilizing interaction also is present in triplet carbene hydrogen bonds; however, a back-donation from the O−H bonding orbital into the carbon lone pair orbitals also is observed, which leads to reduced charge transfer in the triplet carbene hydrogen-bonded complexes. With the exception of methylene, hydrogen bond formation is strong enough to reverse the ordering of the singlet and triplet states for the carbenes possessing triplet ground states. solvent,8 and ab initio calculations at the HF/3-21G level confirmed the possibility of formation of weakly bound ylidelike complexes between the carbenes and fluorinated species such as CH3F and CF4. More recent experimental and computational work has probed reversible complex formation between carbenes and solvent molecules, including carbene− benzene complexes, carbene−ether complexes, carbene− anisole complexes, as well as others.5 The choice of solvent may stabilize one spin state of the carbene relative to the other, leading to a change in the singlet− triplet energy gap. This change may occur due to solvent polarity effects, or it may occur as a result of direct interaction between the carbene and solvent, as in the case of hydrogen bond formation. The specific effects of solvent on carbene singlet−triplet gaps have been probed both experimentally and computationally.9−14 Experimental work in the 1980s and early 1990s demonstrated the effect of solvent on singlet−triplet gaps

1. INTRODUCTION Singlet and triplet carbenes play important roles as intermediates in a variety of chemical reactions and have been extensively studied both experimentally and computationally.1−4 Interestingly, the formation of hydrogen bonds involving carbenes has not been studied in great detail, even though carbenes often are utilized in solvents in which such interactions might commonly occur. Many of the reactions involving carbenes are carried out in the solution phase, and the solvent may mediate the reactivity and selectivity of the carbenes.5 Early work on carbene solvent effects by Tomioka and coworkers demonstrated that the selectivity of phenylcarbene in O−H insertion reactions with alcohols was modified in 1,4dioxane solvent.6 A few years later, Turro et al. established that the reactivity of methylene was impacted by perfluorohexane solvent as a result of intersystem crossing.7 Both of these studies attributed the modified reactivity of the carbene to reversible ylide-like complex formation between the carbene and solvent molecules. Several years later, solvent effects were observed in reactions of carboethoxycarbene in perfluorohexane © XXXX American Chemical Society

Received: November 7, 2016 Revised: December 11, 2016 Published: December 12, 2016 A

DOI: 10.1021/acs.jpca.6b11202 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A of a variety of aromatic carbenes, including diphenylcarbene,9 dimesitylcarbene,10 fluorenylidene,10 and 1,2-diphenyl-1-butylide.11 These carbenes all possess triplet ground states, and the solvent polarity was shown to affect the intersystem crossing rates and reduce the singlet−triplet energy gaps. Computationally, DFT methods along with continuum solvent models have been employed to determine the effects of solvation on the singlet−triplet gaps of various carbenes, including 2-naphthyl(carbomethoxy)carbene12 and methylphenylcarbene,13 as well as methylene and substituted methylenes such as HCF, HCCl, and HCCN.14 These studies found that the singlet state was stabilized more than the triplet state as the solvent polarity increased, leading to a decrease in the singlet−triplet gaps; the observed decrease was typically in the range 1−3 kcal/mol. The first experimental structure of a carbene acting as a hydrogen bond acceptor was the 1995 X-ray crystal structure by Arduengo and co-workers of a C−H---C hydrogen-bonded complex formed in the reaction of 1,3-dimesitylimidazol-2ylidene with a 1,3-dimesitylimidazolium salt.15 The H---C hydrogen bond distance was determined to be 2.03 Å and the C−H−C hydrogen bond angle was close to linear at 172.5°. Recently, a report by Costa and Sander in 2014 employed IR and EPR spectroscopy at low temperature in an argon matrix to demonstrate that hydrogen bonding between methanol and diphenylcarbene switches the spin state of the carbene from triplet (the ground state) to singlet.16 A related study by Sander and co-workers using a water-doped argon matrix also established that singlet diphenylcarbene may act as a strong hydrogen bond acceptor with water.17 In addition, the researchers showed that the hydrogen-bonded complex with water rearranges under the experimental conditions to produce benzhydryl alcohol via an O−H insertion mechanism. A third related study explored the hydrogen-bonding interaction of singlet fluorenylidene with water, which forms a strong hydrogen-bonded complex and then is protonated by water to produce the fluorenyl cation.18 Finally, singlet chloro- and fluorophenylcarbene have been shown to interact via hydrogen bonding with water in argon matrixes at low temperature to form complexes which lead to stabilization of the singlet carbene and switching of the ground state.19 There have been a few other recent attempts to control the spin state of carbenes using methods other than hydrogen bonding.20,21 In one study, light (UV and visible irradiation) was employed, along with heat, to switch the lowest spin state of bis(p-methoxyphenyl)carbene between singlet and triplet in an argon matrix.20 In another study, halogen bonding of CH3I or CH3Br to diphenylcarbene in an argon matrix at low temperature also was found to switch the spin state from triplet to singlet.21 The first computational investigations of carbenes as hydrogen bond acceptors were performed by Pople in the 1980s.22,23 As part of a search for a stable ylide formed between singlet methylene and hydrogen fluoride, HF−CH2, no stable ylidic structure was located. At the Hartree−Fock and MP2 levels of theory with the 6-31G(d) basis set, a hydrogenbonded complex was found in which singlet methylene acted as hydrogen bond acceptor for hydrogen fluoride, with a calculated hydrogen bond strength of about 13 kcal/mol. However, the barrier for rearrangement of the hydrogenbonded complex to methylfluoride was found to be very small, around 1 kcal/mol. A few other computational studies of carbene hydrogen bonding were carried out in the late 1990s.24−26 Using

Hartree−Fock and MP2 levels of theory, Zub and Standard found that the singlet carbenes CH2 and CHCO2Me were able to act as both hydrogen bond acceptors and hydrogen bond donors with H2O and CH3OH.24 Hydrogen bond strengths for singlet carbenes acting as hydrogen bond acceptors ranged from 4 to 6 kcal/mol, whereas those for singlet carbenes acting as hydrogen bond donors were lower, around 2 kcal/mol. A similar computational investigation carried out by Alkorta and Elguero considered the possibility of the singlet carbenes CH2 and CF2 and also silylene SiH2 acting as hydrogen bond acceptors with HF, HCN, H2O, NH3, and CH3+.25 Calculations at the HF, MP2, and MP4 levels of theory found hydrogen bond strengths for H2O−CH2 comparable to those obtained by Zub and Standard.24 Finally, the only early computational study to investigate triplet carbenes as hydrogen bond acceptors was performed by Alkorta and co-workers, who showed that triplet dimethylcarbene forms hydrogen-bonded complexes with HF, HCN, and H2O at the B3LYP and MP2 levels of theory.26 The investigations by Alkorta and co-workers25,26 and Zub and Standard24 appear to be the latest computational work focusing on hydrogen bonding to carbenes until very recently. In 2014, Costa and Sander employed B3LYP and B3LYP-D3/ 6-311++G(d,p) methodologies to corroborate their experimental findings of hydrogen-bond formation between methanol and singlet diphenylcarbene.16 Their calculations indicated that the singlet−triplet gap switches from about 5 kcal/mol (uncomplexed) to −0.4 kcal/mol (complexed). Sander and co-workers followed up that study with another demonstrating hydrogen bond formation between diphenylcarbene and water.17 Calculations at the B3LYP-D3/def2-TZVP level found a singlet−triplet gap of 3.3 kcal/mol for uncomplexed diphenylcarbene and −1.6 kcal/mol complexed with water. A similar investigation of the interaction of fluorenylidene with water demonstrated strong hydrogen bond formation with the singlet, but only a weak interaction with the triplet. 18 Additional studies of chloro- and fluorophenylcarbenes at the B3LYP-D3/6-311++G(2d,2p) level of theory obtained hydrogen-bonded complexes between the singlet carbenes and water with binding energies of around −7 kcal/mol and singlet−triplet gap reversal similar to that found in the previous work.19 Though some specific cases have been studied recently,16−19 the formation of hydrogen bonds involving singlet and triplet carbenes has not received a great deal of attention. The objectives of this study are as follows: first, to determine appropriate computational methods for calculation of reliable geometries and singlet−triplet gaps for the alkyl- and arylcarbenes to be investigated in this work; second, to probe the effects of bulk solvent on the singlet−triplet gaps of alkyland arylcarbenes; third, to investigate the ability of singlet and triplet alkyl- and arylcarbenes to act as hydrogen bond acceptors with the proton donors water and methanol; and fourth, to determine the impact of hydrogen bonding on the singlet−triplet gaps of the alkyl- and arylcarbenes.

2. METHODS The singlet and triplet carbenes studied include methylene (CH2), methylcarbene (MeCH), dimethylcarbene (DiMe), phenylcarbene (PhenCH), methylphenylcarbene (MePhen), and diphenylcarbene (DiPhen). A variety of methods have been employed for calculation of the geometries and energies of the singlet and triplet carbenes to select a computational method that provides good geometries of the carbenes and hydrogenB


Article

The Journal of Physical Chemistry A Table 1. Singlet−Triplet Gaps (kcal/mol) for Alkyl and Aryl Carbenes Computed at Various Levels of Theorya level

CH2

MeCH

DiMe

PhenCH

MePhen

DiPhen

B3LYP/aTZ B3LYP-D3/aTZ ωB97D-X/aTZ M06-2X/aTZ CCSD(T)-F12/aDZ//B3LYP/aTZ CCSD(T)-F12/aTZ//B3LYP/aTZ MRCI+Q/aDZ//B3LYP/aTZ MRCI+Q/aTZ//B3LYP/aTZ experiment

10.92 10.95 11.58 12.97 9.32 9.04 9.73 8.76 9.0b

4.12 4.14 4.74 5.69 3.26 3.02 4.48 3.31

−1.11 −1.30 −0.33 0.31 −2.32 −2.52 −0.62 −1.96

5.72 5.73 6.85 7.97 4.55 4.38 2.37 1.80 2.3c

5.24 5.13 6.28 6.56 3.56 3.36 2.52 1.66 2.0d

5.90 5.36 7.27 6.83 3.61 1.30 1.25

a

Results are corrected for vibrational zero-point energies. Available experimental results also are reported. bReferences 48 and 49. cReferences 50 and 51. dReference 52.

(NPA)42,43 and natural bond orbital analyses44−46 were performed utilizing the NBO 6.0 software package.47 All calculations were performed on Linux workstations at Illinois State University.

bonded complexes as well as accurate determinations of singlet−triplet gaps. Density functional theory (DFT) methods, including B3LYP, B3LYP-D3,27 ωB97D-X,28 and M06-2X,29 along with the MP2(frozen core) methodology were employed for geometry optmizations and vibrational frequency calculations using a variety of basis sets. B3LYP calculations were first performed using 6-31G(d), 6-311++G(d,p), and aug-ccpVTZ basis sets. Additional optimizations were carried out at the B3LYP-D3, ωB97D-X, M06-2X, and MP2 levels with the aug-cc-pVTZ basis set. For methylene, methylcarbene, and dimethylcarbene, geometry optimizations also were carried out using CCSD(T) and MRCI(2,2) levels of theory with aug-ccpVXZ basis sets, with X = D, T, and Q; these basis sets will henceforth be referred to as aDZ, aTZ, and aQZ, respectively. Single-point energy corrections also were determined by using the CCSD(T), CCSD(T)-F12,30 and MRCI(2,2) methods with basis sets up to a5Z for the smaller carbenes and up to aTZ for the arylcarbenes. The internally contracted MRCI(2,2) calculations31,32 were based upon CASSCF(2,2) reference functions employing two electrons in two active orbitals (the lone pair orbitals on the carbene carbon). The Davidson correction33 also was included in the calculations, and results reported with the Davidson correction are denoted as MRCI+Q. To investigate the effects of solvent polarity on the singlet− triplet gaps, geometry optimizations of the alkyl and aryl carbenes were carried out at the B3LYP/aTZ level of theory treating the solvent as a continuum dielectric using the PCM solvation method.34−38 A variety of solvents with dielectric constants ranging from 1.4 (argon) to 78 (water) were utilized. For the hydrogen-bonded complexes, gas phase geometry optimizations using tight convergence criteria were accomplished using the B3LYP-D3 method with the aTZ basis set. Many complexes also were optimized at the B3LYP/6-311+ +G(d,p) level for comparison. Along with the geometry optimizations, vibrational frequency calculations were completed to verify each structure as a minimum on the potential energy surface. Binding energies of the hydrogen-bonded complexes were computed relative to the separated monomers and corrected for vibrational zero-point energies. Single-point energy calculations also were determined using the CCSD(T) and CCSD(T)-F12 methods with aDZ and aTZ basis sets. All DFT and MP2 calculations were performed using the Gaussian 09 software package.39 All CCSD(T), CCSD(T)-F12, and MRCI calculations were carried out using the Molpro 2012 software package.40,41 To study the charge distributions and bonding of the hydrogen-bonded complexes, natural population analyses

3. RESULTS AND DISCUSSION A. Benchmark Calculations of Carbene Singlet− Triplet Gaps. Singlet and triplet carbene energies are of course dependent upon the geometries of the molecules. To benchmark methodologies for calculation of singlet−triplet gaps, we first explored the dependence upon level of theory of key geometrical parameters of the carbenes. Bond distances for bonds involving the carbene center and the bond angle at the carbene center are reported for all the levels of theory at which optimized geometries were obtained; these results may be found in Tables S1−S6 of the Supporting Information. In addition, Cartesian coordinates of all the optimized singlet and triplet carbenes obtained at the B3LYP/aTZ level are included in Appendix S1 of the Supporting Information. The optimized geometries for all the carbenes were obtained at the B3LYP level with 6-31G(d), 6-311++G(d,p), and aTZ basis sets. In addition, optimized geometries were determined for all the carbenes at the B3LYP-D3/aTZ, ωB97X-D/aTZ, M06-2X/ aTZ, and MP2/aTZ levels. Finally, optimized geometries of methylene, methylcarbene, and dimethylcarbene also were calculated at the CCSD(T) and MRCI(2,2) levels of theory with aDZ and aTZ (and aQZ for methylene and methylcarbene) basis sets. In general, there are only small variations in the carbene bond lengths and angles with level of theory. For the smaller carbenes (methylene, methylcarbene, and dimethylcarbene), results from DFT and MP2 levels of theory can be compared with the high-level CCSD(T)/aTZ results. For bond lengths and angles involving the carbene carbon, the DFT and MP2 results for C−H bond lengths are within 0.008 Å, the C−C bond lengths are within 0.021 Å, and the H−C−H or H−C−C bond angles are within 2.7° of the CCSD(T)/aTZ results. Thus, it appears that any of the DFT or MP2 methodologies provide satisfactory geometries for the smaller singlet and triplet carbenes investigated in this work. For the carbenes containing phenyl groups (phenylcarbene, methylphenylcarbene, and diphenylcarbene), geometry optimizations at the CCSD(T) level were not possible due to computational expense. Thus, comparison of results can only be made among the various DFT and MP2 methods. Excluding the B3LYP/6-31G(d) results, the bond lengths and angles at the carbene carbon fall within a range of 0.003 Å for C−H bond lengths, 0.012 Å for C−Me or C−Phen bond lengths, and C


Article

The Journal of Physical Chemistry A

carbene. In part, this is expected because the T1 diagnostic values computed for singlet and triplet methylene, methylcarbene, and dimethylcarbene in this work are below 0.015; a T1 diagnostic of 0.02 or greater is considered significant for multireference character.53 Thus, for calculations involving methylene, methylcarbene, and dimethylcarbene, we surmise that the CCSD(T)-F12/aDZ//B3LYP-D3/aTZ methodology provides accurate values of singlet−triplet gaps. The CCSD(T)-F12/aDZ results for the singlet−triplet gaps of phenylcarbene and methylphenylcarbene are about 1.6−2.3 kcal/mol larger than the corresponding experimental values,50−52 whereas the MRCI+Q/aDZ and MRCI+Q/aTZ results bracket the experimental results. For these carbenes and also diphenylcarbene, the T1 diagnostic for the singlet states is below 0.014 whereas the T1 diagnostic of the triplet state is 0.019−0.021. Thus, multireference character plays a larger role in the arylcarbenes and therefore the MRCI+Q/aDZ (or aTZ)//B3LYP-D3/aTZ methodology will be employed for computation of singlet−triplet gaps in these systems whenever possible. Of the DFT methods, the B3LYP/aTZ and B3LYP-D3/aTZ results are in moderately good agreement with the CCSD(T)F12/aDZ results but tend to overestimate the size of the singlet−triplet gaps by about 0.9−2.3 kcal/mol. The ωB97XD/aTZ and M06-2X/aTZ results are in poorer agreement with the CCSD(T)-F12/aDZ results, overestimating the singlet− triplet gaps by 1.5−3.7 kcal/mol. For all the DFT methods, the errors in the triplet state energies are larger than those of the singlet state energies when compared with CCSD(T)-F12 or MRCI+Q results. On the basis of these findings, the B3LYP/ aTZ and B3LYP-D3/aTZ methods will be utilized throughout the remainder of this work for optimized geometries and singlet−triplet gap estimates, with single-point energies computed at the CCSD(T)-F12 or MRCI+Q levels to obtain improved singlet−triplet gaps. A variety of theoretical methods have been utilized previously to determine singlet−triplet gaps for the carbenes in this study. A fairly recent comprehensive investigation employed the G3MP2 methodology to determine singlet−triplet gaps for a wide range of carbenes.54 For methylene, the G3MP2 result of 9.4 kcal/mol is close to the experimental value of 9.0 kcal/ mol48,49 and the results obtained in this work. For methyl- and dimethylcarbene, the G3MP2 singlet−triplet gaps are +3.0 and −1.0 kcal/mol, respectively, similar to our DFT, CCSD(T)F12, and MRCI+Q results. For phenylcarbene, the G3MP2 result of 2.3 kcal/mol for the singlet−triplet gap is in accord with the experimental estimate of 2.3 kcal/mol50,51 and similar to the MRCI+Q/aTZ result of of 1.8 kcal/mol from this work. The G3MP2 singlet−triplet gap predicted for methylphenylcarbene is 1.0 kcal/mol, low compared with the experimental estimate of 2.0 kcal/mol52 and our MRCI+Q/aTZ result of 1.7 kcal/mol. For the arylcarbenes, previous studies employing DFT methods predict a singlet−triplet gap of 5.455,56 or 5.6 kcal/mol57 for phenylcarbene at the B3LYP/6-311++G(d,p) level, 1.8 kcal/mol13 for methylphenylcarbene at the BPW91/ cc-pVDZ level, and 5.8 kcal/mol57 for diphenylcarbene at the B3LYP/6-311++G(d,p) level. The previous DFT results are in line with the values obtained in this work and are generally expected to overestimate the singlet−triplet gaps by at least 1− 2 kcal/mol. B. Solvent Effects on Carbene Singlet−Triplet Gaps. A continuum solvent approach was utilized to investigate how bulk solvent affects the singlet−triplet gaps of the various

2.4° for H−C−C or C−C−C bond angles when each geometrical parameter is compared across the various levels of theory. Therefore, we conclude that, with the exception of the B3LYP/6-31G(d) level, all the DFT and MP2 levels of theory provide reasonable geometries for the singlet and triplet carbenes studied in this work. The singlet−triplet gap is defined in this work as the electronic energy of the singlet state minus the energy of the triplet state; all the singlet−triplet gaps are corrected for vibrational zero-point energies. Results for singlet−triplet gaps for methylene and alkyl and aryl carbenes at selected levels of theory are presented in Table 1, along with the few available experimental values. There are only three known experimental singlet−triplet gaps.48−52 The methylene singlet−triplet gap is very well-known and has been experimentally determined to be 9.0 kcal/mol.48,49 For phenylcarbene and methylphenylcarbene, estimates of the singlet−triplet gaps from experimental measurements are 2.350,51 and 2.0 kcal/mol,52 respectively. In Table 1, the DFT results for the singlet−triplet gaps were obtained using optimized geometries and vibrational frequencies from the same level of theory. Note that although the MP2 level provides reasonable geometries for the singlet and triplet carbenes studied here, the computed singlet−triplet gaps at the MP2/aTZ level of theory were very poor and are not included in the table. The CCSD(T)-F12 and MRCI+Q results reported in Table 1 were computed as single-point energies using the optimized B3LYP/aTZ geometries. For diphenylcarbene, only the CCSD(T)-F12/aDZ and MRCI+Q/aDZ single-point results are reported; computational cost prohibited calculation of the CCSD(T)-F12 and MRCI+Q singlet−triplet gaps using the aTZ basis set. Results for the singlet−triplet gaps also were obtained at a variety of other levels of theory. All the results obtained for singlet−triplet gaps in which the geometries and vibrational frequencies were determined at the same level of theory are reported in Table S7 of the Supporting Information. Additional single-point energy calculations to determine singlet−triplet gaps were performed for all the carbenes at other levels beyond those reported in Table 1; all the results for singlet−triplet gaps computed using single-point energies can be found in Table S8 of the Supporting Information. Examining the computed singlet−triplet gaps for methylene in Table 1, the CCSD(T)-F12/aDZ results are within 0.3 kcal/ mol of experiment,48,49 whereas the CCSD(T)-F12/aTZ results are within 0.04 kcal/mol. Previous work has shown that results from the CCSD(T)-F12 level are comparable to CCSD(T) results with the next larger basis set.30 Thus, we expect that the CCSD(T)-F12/aDZ results should be comparable to CCSD(T)/aTZ results (reported in Table S8 of the Supporting Information), and they are within 0.4 kcal/ mol for all the carbenes except diphenylcarbene, for which CCSD(T)/aTZ results were not obtained due to computational expense. For methylene, the MRCI+Q/aDZ results are about 0.7 kcal/mol above the experimental value and the MRCI+Q/aTZ results are 0.2 kcal/mol below. For methyl and dimethylcarbene, there are no reported experimental values for comparison. However, the CCSD(T)-F12/aDZ and MRCI+Q/aTZ results agree reasonably well, to within 0.05 kcal/mol for methylcarbene and 0.36 kcal/mol for dimethylcarbene. Even though carbenes are generally expected to possess some multireference character, the single reference CCSD(T)-F12 method appears to perform well for methylene, methylcarbene, and dimethylD


Article


For dimethylcarbene, Figure 1a, the singlet state is lower in energy in the gas phase and remains so as the solvent dielectric constant increases. The dipole moment of the singlet state is 2.04 D in the gas phase, whereas that for the triplet state is only 0.76 D at the B3LYP/aTZ level of theory, primarily as a result of the larger C−C−C angle in the triplet state compared to that of the singlet state, 134° vs 113°, respectively. As a result, as the solvent polarity increases, the energy of the singlet state drops by 0.0066 hartree (about 4.1 kcal/mol) and the energy of the triplet state only drops by 0.0012 hartree (or about 0.8 kcal/ mol) when the solvent dielectric constant is increased to that of water. For systems with a singlet ground state, increasing solvent polarity therefore leads to an increase in the magnitude of the singlet−triplet gap. For phenylcarbene, Figure 1b, the triplet state is lower in energy in the gas phase, and it also remains the ground state as the dielectric constant of the solvent is increased. In this case, the gas phase dipole moment of the singlet state is 4.34 D, compared to only 0.75 D for the triplet state at the B3LYP/aTZ level. As a result of the relatively large dipole moment of the singlet state, the electronic energy drops by 0.0099 hartree (about 6.2 kcal/mol) as the solvent dielectric is increased to that of water, whereas the energy of the triplet state drops by only 0.0029 hartree (about 1.8 kcal/mol). Therefore, for systems like phenylcarbene with a triplet ground state, increasing solvent polarity leads to a decrease in the magnitude of the singlet−triplet gap. Singlet−triplet gaps for all the carbenes in solution phase at the B3LYP/aTZ level are presented in Table 2. Results shown in the table include singlet−triplet gaps computed in a range of nonpolar and polar solvents: argon (dielectric constant ε = 1.43), dichloroethane (ε = 10.1), methanol (ε = 32.4), and water (ε = 78.4); the gas phase values at the same level of theory also are included for comparison. For the carbenes with triplet ground states (all except dimethylcarbene), the singlet−triplet gaps decrease in magnitude as the solvent polarity increases. The decrease in the singlet−triplet gap ranges from 2.6 to 4.4 kcal/mol when the gas phase values are compared to those obtained in water. Note that even though the singlet−triplet gaps decrease for these carbenes, none of the changes are quite enough to lower the singlet state below the triplet at the B3LYP/aTZ level of theory. However, because the B3LYP/aTZ methodology appears to overestimate the singlet−triplet gaps of these carbenes by around 1−2 kcal/mol compared to the values obtained at the CCSD(T)-F12/aDZ level, the solvent effect may in some cases, such as for methylcarbene and phenylcarbene, come very close to switching the ground state from triplet to singlet. The behavior observed in the solution phase for the carbenes investigated in this work is in accord with two previous

carbenes. The polarizable continuum model (PCM) with the B3LYP/aTZ level of theory was employed, and full geometry optimizations were performed in various solvents for the singlet and triplet carbenes. The general behavior of the singlet and triplet carbenes in solution is that the singlet carbene is stabilized more strongly as the solvent polarity increases. Two representative examples are shown in Figure 1 for dimethyl-

Figure 1. PCM results for singlet and triplet states of (a) dimethylcarbene, DiMe and (b) phenylcarbene, PhenCH. The electronic energy (Eel) plus vibrational zero-point energy (EVZP) of each state (in hartrees), optimized at the B3LYP/aTZ level in solution, is shown plotted versus the Onsager function, ε − 1 . ε+2

carbene and phenylcarbene. The electronic plus vibrational zero-point energies of the singlet and triplet carbenes are shown in several solvents; the energies are plotted versus the Onsager function of the dielectric constant ε for the solvent, ε − 1 .58,59 ε+2 Results for the other carbenes are presented in Figure S1 of the Supporting Information.

Table 2. Singlet−Triplet Gaps (kcal/mol) of Carbenes Determined in Solution with Various Solvents Using the PCM Methoda solvent

CH2

MeCH

DiMe

PhenCH

MePhen

DiPhen

gas phase (ε = 1.00) argon (ε = 1.43) dichlorethane (ε = 10.1) methanol (ε = 32.6) water (ε = 78.4)

10.92 10.43 8.75 8.45 8.36

4.12 3.45 1.16 0.76 0.64

−1.11 −1.75 −3.96 −4.36 −4.47

5.72 4.86 1.97 1.46 1.31

5.24 4.72 2.81 2.44 2.33

5.38 4.93 3.22 2.87 2.77

a

Carbene geometries are optimized in solution at the B3LYP/aTZ level of theory and singlet−triplet gaps are corrected for vibrational zero-point energies. E


Article

The Journal of Physical Chemistry A computational studies on the effects of solvent on carbene singlet−triplet gaps.13,14 Cramer et al. showed that the singlet− triplet gap of methylphenylcarbene decreased by 1.8 kcal/mol in a continuum solvent corresponding to acetonitrile (ε = 37.5) using the SM4.5/AM1 solvation model,13 comparable to the 2.9 kcal/mol drop observed in water in this work. Similarly, Gonzalez and co-workers applied the IPCM continuum solvation model to study solvent effects on the singlet−triplet gaps of nitrenium ions and carbenes including methylene.14 A drop in the singlet−triplet gap of a few kcal/mol was found for methylene at the B3LYP/6-311++G(d,p) level of theory, similar to the reduction of 2.6 kcal/mol observed in this work. C. Hydrogen-Bonded Complexes: Geometries and Vibrational Frequencies. The geometries of hydrogenbonded complexes formed between hydrogen-bond donors and the singlet and triplet carbenes are shown in Figure 2 for complexes with water and Figure 3 for complexes with methanol. All geometries were obtained using a dispersioncorrected DFT method, B3LYP-D3, with the aTZ basis set. The only exception is the 1CH2−CH3OH complex, which was unstable to rearrangement to the oxonium ylide at the B3LYPD3/aTZ level. This hydrogen-bonded complex was located as a stable point on the potential energy surface at the B3LYP/6311++G(d,p) level of theory; the structure shown in Figure 3 and results presented in Table 3 are from this calculation. All the hydrogen-bonded complexes involve water or methanol as the hydrogen bond donor and the singlet or triplet carbene as the hydrogen bond acceptor: the hydrogen atom of the OH group of H2O or CH3OH is directed such that it interacts with the central carbene carbon. Table 3 presents key geometrical parameters of the hydrogen-bonded complexes, including the C−H hydrogen bond distance and the C−H−O angle. The Cartesian coordinates of all the hydrogen-bonded complexes obtained at the B3LYP-D3/aTZ level of theory are reported in Appendix S2 of the Supporting Information for complexes involving H2O and Appendix S3 for complexes involving CH3OH. Table 3 also includes the vibrational frequency shifts of the O−H group involved in the hydrogen bond, measured relative to the O−H stretching frequency of the uncomplexed species. Results for the water dimer and for the radical hydrogen-bonded complex CH3O−H2O obtained at the same level of theory are presented for comparison with the H2O complexes, and results for the hydrogen-bonded complexes H2O−CH3OH and CH3O− CH3OH, in which CH3OH acts as the hydrogen bond donor, are included for comparison with the CH3OH complexes. For the singlet carbenes, the C−H hydrogen bond distance ranges from 1.93 to 2.05 Å. For comparison, the O−H hydrogen bond distance is 1.95 Å in H2O−H2O and 1.94 Å in H2O−CH3OH; both these values are comparable to the distances obtained for the singlet carbene hydrogen bonds. The C−H−O angles range from 159 to 173° for the singlet carbene complexes, reasonably close to linearity. Again, for comparison, the O−H−O angle is 172° in H2O−H2O and 176° in H2O− CH3OH. For hydrogen-bonded complexes involving the triplet carbenes, the C−H distances are generally longer than those of their singlet carbene counterparts by about 0.1−0.3 Å, ranging from 2.06 to 2.25 Å. For comparison with radical hydrogen-bonded species, the O−H distance is 1.97 Å in CH3O−H2O and 1.98 Å in CH3O−CH3OH. These values are somewhat shorter by about 0.1−0.2 Å than the results for the triplet carbene hydrogen-bonded complexes; this is likely due in

Figure 2. Optimized geometries at the B3LYP-D3/aTZ level for hydrogen-bonded complexes involving singlet or triplet carbenes and water.

part to the presence of the second unpaired electron in the triplet carbene. The C−H−O angles of the triplet carbene hydrogen-bonded complexes are relatively close to linearity, ranging from 158 to 180°. F


Article


both calculated to be 1.91 Å at the BLYP-D3 level with def2TZVP or 6-311++G(d,p) basis sets, respectively. These values are within a few hundredths of angstroms of those obtained in this work at the B3LYP-D3/aTZ level: 1.95 Å for the H−C distance in the singlet diphenylcarbene−H2O complex and 1.93 Å in the singlet diphenylcarbene−CH3OH complex. For the triplet diphenylcarbene complex with H2O, the H−C distance calculated in this work at the B3LYP-D3/aTZ level, 2.14 Å, is similar to the previous literature report of 2.07 Å obtained at the BLYP-D3/def2-TZVP level.17 In contrast, the H−C distance calculated in this work for the triplet diphenylcarbene−CH3OH complex, 2.09 Å, is quite a bit shorter than reported in the previous study, 2.24 Å at the B3LYP-D3/6311++G(d,p) level and 2.33 Å at the B3LYP/6-311++G(d,p) level.16 Also listed in Table 3 are the O−H vibrational frequency shifts for the O−H group involved in the hydrogen bond, measured relative to the corresponding H2O or CH3OH monomer O−H stretching frequency; note that these are unscaled harmonic frequencies. All the complexes exhibit redshifted O−H stretching frequencies. For the singlet carbene hydrogen-bonded complexes involving H2O, the O−H red shifts are quite large, indicative of strong hydrogen bond formation: the shifts range from −269 to −642 cm−1. For comparison, the O−H shift in H2O−H2O is only −121 cm−1 and that of H2O−CH3OH is −131 cm−1 at the same level of theory. Although the hydrogen-bonded complexes with triplet carbenes exhibit smaller O−H shifts than their singlet carbene counterparts, they do exhibit significant O−H frequency shifts, comparable to those observed in other hydrogen-bonded complexes, and a strong indicator that these are true hydrogenbonded complexes as opposed to weak van der Waals complexes. For the triplet carbene hydrogen-bonded complexes with H2O, the O−H frequency shifts range from −105 to −272 cm−1. Again, for comparison with hydrogen-bonded complexes involving radical species, the O−H frequency shift is −119 cm−1 for CH3O−H2O and −130 cm−1 for CH3O−CH3OH at the same level of theory. The experimental O−H frequency shift for the hydrogenbonded complex formed between singlet diphenylcarbene and methanol was determined to be −864 cm−1 in an argon matrix.16 Other recent experimental studies of diphenylcarbene in water-doped argon matrixes also note formation of a hydrogen-bonded singlet diphenylcarbene−water complex, with IR bands identical to those of the singlet diphenylcarbene−methanol complex.17 The observed experimental frequency shift is even larger than the gas phase value of −617 cm−1 calculated in this work for the singlet diphenylcarbene− methanol complex. We also have carried out calculations of the singlet diphenylcarbene−methanol hydrogen-bonded complex in argon and in methanol using the PCM solvation method and the B3LYP-D3/aTZ level of theory. The results indicate that solvation in argon leads to an even lower O−H stretching frequency for the hydrogen-bonded complex, 3152 cm−1 in argon vs 3853 cm−1 for uncomplexed methanol, a shift of −674 cm−1. This is still not as large as the observed experimental O− H shift of −864 cm−1,16 but it is highly indicative of the strong hydrogen-bonded complex formed between singlet diphenylcarbene and methanol. In the more polar methanol solvent, the calculated O−H frequency shift for the singlet diphenylcarbene−methanol complex is even larger in magnitude at −930 cm−1.

Figure 3. Optimized geometries at the B3LYP-D3/aTZ level for hydrogen-bonded complexes involving singlet or triplet carbenes and methanol.

The geometries obtained in this work for the singlet diphenylcarbene−water and diphenylcarbene−methanol hydrogen-bonded complexes are similar to those recently reported in the literature.16,17 For the singlet diphenylcarbene−H2O and CH3OH complexes, the H−C hydrogen bond distances were G


Article


Table 3. Selected Geometrical Parameters and O−H Frequency Shifts (Δν) for Hydrogen-Bonded Complexes Determined at the B3LYP-D3/aTZ Level of Theory complex

C−H (Å)

∠C−H−O (deg)

CH2−H2O MeCH−H2O DiMe−H2O PhenCH−H2O MePhen−H2O DiPhen−H2O H2O−H2O

2.050 1.991 1.973 1.944 1.936 1.948 1.947

171.2 158.9 163.6 161.8 165.9 168.6 171.5

CH2−H2O MeCH−H2O DiMe−H2O PhenCH−H2O MePhen−H2O DiPhen−H2O CH3O−H2O

2.246 2.171 2.121 2.192 2.118 2.138 1.974

179.9 165.2 174.6 160.8 174.6 170.4 152.7

Δνa (cm−1)

complex

Singlet Carbenes −269.2 CH2−CH3OHc −387.6 MeCH−CH3OH −462.1 DiMe−CH3OH −562.6 PhenCH−CH3OH −602.7d MePhen−CH3OH −574.8 DiPhen−CH3OH −120.9 H2O−CH3OH Triplet Carbenes −104.6 CH2−CH3OH −149.9 MeCH−CH3OH −198.4 DiMe−CH3OH −138.0 PhenCH−CH3OH −180.2 MePhen−CH3OH −166.0 DiPhen−CH3OH −118.5 CH3O−CH3OH

C−H (Å)

∠C−H−O (deg)

Δνb (cm−1)

2.040 1.975 1.953 1.925 1.932 1.929 1.944

173.2 162.9 172.1 163.9 167.5 167.9 176.1

−297.7 −419.1 −509.0 −599.6 −641.5d −616.9 −132.6

2.177 2.129 2.064 2.160 2.110 2.091 1.976

173.4 161.6 173.6 157.8 166.2 163.4 153.0

−172.1 −205.2 −271.9 −190.0 −220.5 −227.9 −129.8

The harmonic frequency of the O−H (symmetric) stretch of water is 3797.7 cm−1 at the B3LYP-D3/aTZ level. bThe harmonic frequency of the O−H stretch of methanol is 3828.6 cm−1 at the B3LYP-D3/aTZ level and 3847.3 cm−1 at the B3LYP/6-311++G(d,p) level. cThe singlet CH2− CH3OH hydrogen-bonded complex is unstable at the B3LYP/aTZ level, rearranging to the corresponding oxonium ylide. Results from the B3LYP/ 6-311++G(d,p) level are reported here instead. dThe O−H stretch is mixed with C−H stretching modes of the phenyl group in this complex. a

D. Hydrogen-Bonded Complexes: Binding Energies and Singlet−Triplet Gaps. Table 4 presents binding energies

donation of electron density from a nonbonding orbital on the carbene carbon into the O−H antibonding orbital of water or methanol. With only one electron occupying each nonbonding orbital in the triplet carbenes, it is no surprise that the binding energies of hydrogen-bonded complexes involving triplet carbenes are lower than those of their singlet carbene counterparts. For the singlet carbenes, binding energies for the hydrogenbonded complexes with water and methanol range from −3.3 to −9.3 kcal/mol at the CCSD(T)-F12 level, whereas the range is −0.6 to −4.5 kcal/mol for the triplet carbene complexes. The magnitudes of the binding energies predicted using the B3LYPD3/aTZ level are higher than the CCSD(T)-F12 results, by about 0.7−1.6 kcal/mol for the singlet carbene complexes and by about 0.3−0.8 kcal/mol for the triplet carbene complexes. The hydrogen-bonded complexes formed with H2O tend to have binding energies slightly lower in magnitude than those for the corresponding complexes formed with CH3OH by roughly 1 kcal/mol. Almost all of the singlet carbene complexes possess hydrogen bonds that are significantly stronger than those of H2O−H2O or H2O−CH3OH. To make some comparisons with the triplet carbene binding energies, we also computed the binding energies for the radical hydrogenbonded complexes CH3O−H2O and CH3O−CH3OH. Most of the binding energies for the triplet carbene hydrogen bonds are comparable to or slightly weaker than the hydrogen bonds involving CH3O. Table 5 presents singlet−triplet gaps for the hydrogenbonded complexes. The singlet−triplet gaps have been determined at the B3LYP-D3/aTZ, CCSD(T)-F12/aDZ// B3LYP-D3/aTZ, and MRCI+Q(2,2)/aTZ//B3LYP-D3/aTZ levels of theory and are corrected for vibrational zero-point energies using the B3LYP-D3/aTZ harmonic frequencies. Note that we have been unable to compute singlet−triplet gaps at the MRCI+Q level for complexes of diphenylcarbene due to computational expense; results from CASSCF(2,2)/aDZ// B3LYP-D3/aTZ calculations are reported for those cases.

Table 4. Binding Energies (ΔEHB, kcal/mol) for HydrogenBonded Complexesa B3LYP-D3/aTZ

CCSD(T)-F12/aDZ// B3LYP-D3/aTZ

complex

ΔEHB, singlet

ΔEHB, triplet

ΔEHB, singlet

ΔEHB, triplet

CH2−H2O MeCH−H2O DiMe−H2O PhenCH−H2O MePhen−H2O DiPhen−H2O CH2−CH3OHb MeCH−CH3OH DiMe−CH3OH PhenCH−CH3OH MePhen−CH3OH DiPhen−CH3OH

−4.11 −6.53 −7.25 −9.09 −8.85 −8.38 −4.94 −7.32 −8.24 −10.09 −10.05 −9.99

−1.02 −2.14 −2.77 −2.31 −2.63 −3.10 −0.88 −2.92 −3.77 −3.56 −3.99 −4.71

−3.33 −5.57 −6.15 −7.69 −7.58 −7.50 −4.03 −6.49 −7.23 −8.88 −9.02 −9.34

−0.56 −1.55 −2.16 −1.76 −2.08 −2.28 −1.09 −2.31 −3.04 −3.19 −3.70 −4.46

a

Results are presented at both the B3LYP-D3/aTZ and CCSD(T)F12/aDZ//B3LYP/aTZ levels of theory, and include vibrational zeropoint energy corrections. bThe singlet CH2−CH3OH complex rearranges to the corresponding oxonium ylide at the B3LYP-D3/ aTZ level, so the optimized geometries and energies from the B3LYP/ 6-311++G(d,p) level were used for this case.

for hydrogen-bonded complexes involving the singlet or triplet carbenes with water and methanol. Binding energies (ΔEHB) have been calculated at the B3LYP-D3/aTZ and CCSD(T)F12/aDZ//B3LYP-D3/aTZ levels of theory and are corrected for vibrational zero-point energies using the B3LYP-D3/aTZ harmonic frequencies. In general, binding energies for hydrogen-bonded complexes involving singlet carbenes are stronger than those involving triplet carbenes. As will be discussed in more detail in the next section, the hydrogen-bonded complexes are stabilized by H


Article

The Journal of Physical Chemistry A Table 5. Singlet−Triplet Gaps (kcal/mol) for Hydrogen-Bonded Complexesa complex

B3LYP-D3/aTZ

CCSD(T)-F12/aDZ//B3LYP-D3/aTZ

MRCI+Q(2,2)/aTZ//B3LYP-D3/aTZ

CH2−H2O MeCH−H2O DiMe−H2O PhenCH−H2O MePhen−H2O DiPhen−H2O CH2−CH3OHc MeCH−CH3OH DiMe−CH3OH PhenCH−CH3OH MePhen−CH3OH DiPhen−CH3OH

7.85 −0.25 −5.78 −1.05 −1.08 0.08 7.69 −0.25 −5.78 −0.88 −0.92 0.08

6.56 −0.74 −6.27 −1.37 −1.90 −1.61 6.38 −0.89 −6.47 −1.14 −1.72 −1.27

5.26 −0.96 −6.33 −4.42 −4.76 −4.35b 5.22 −0.87 −6.36 −4.23 −4.37 −4.68b

a

Results are presented at the B3LYP-D3/aTZ, CCSD(T)-F12/aDZ//B3LYP-D3/aTZ, and MRCI+Q(2,2)/aTZ//B3LYP-D3/aTZ levels of theory, with vibrational zero-point corrections included from the B3LYP-D3/aTZ level. bMRCI+Q(2,2) results were not obtained for the diphenylcarbene complexes due to computational expense. CASSCF(2,2)/aDZ//B3LYP-D3/aTZ results are reported for complexes of diphenylcarbene. cThe singlet CH2−CH3OH complex rearranges to the corresponding oxonium ylide at the B3LYP-D3/aTZ level, so the optimized geometries and energies from the B3LYP/6-311++G(d,p) level were used for this case.

Table 6. Charge Transfer, Second-Order Perturbation Energies for Hydrogen-Bonding Interactions (E(2) in kcal/mol), and Key Changes in Natural Bond Orbital Populations from NBO Deletion Analysis for Complexes Involving Singlet Carbenesa NBO deletionsc complex

charge transfer

CH2−H2O MeCH−H2O DiMe−H2O PhenCH−H2O MePhen−H2O DiPhen−H2O H2O−H2O CH2−CH3OHd MeCH−CH3OH DiMe−CH3OH PhenCH−CH3OH MePhen−CH3OH DiPhen−CH3OH H2O−CH3OH

−0.039 −0.050 −0.052 −0.067 −0.067 −0.057 −0.016 −0.042 −0.058 −0.063 −0.077 −0.074 −0.065 −0.017

b

(2)

E

(kcal/mol), nC → σ*(O−H) 15.60 18.01 21.57 25.97 28.75 27.82 7.29 18.31 21.57 26.33 30.33 31.57 31.56 7.72

ΔPop. nC

ΔPop. σ*(O−H)

0.040 0.044 0.039 0.064 0.049 0.019 0.013 0.047 0.053 0.048 0.076 0.053 0.026 0.013

−0.045 −0.051 −0.054 −0.073 −0.073 −0.064 −0.014 −0.051 −0.058 −0.064 −0.082 −0.078 −0.072 −0.015

a

Results are presented for geometries and NBO analyses obtained at the B3LYP-D3/aTZ level of theory. bCharge transfer is computed as the net charge of H2O or CH3OH as a result of transfer of electron density from the carbene to H2O or CH3OH. cThe changes in population of the carbon lone pair orbital and the O−H antibonding orbital are reported for deletion of the Fock matrix element between the two orbitals. For the H2O−H2O and H2O−CH3OH complexes, the lone pair orbital is on the oxygen atom involved in the hydrogen bond. dThe singlet CH2−CH3OH complex rearranges at the B3LYP-D3/aTZ level, so results from the B3LYP/6-311++G(d,p) level were used in this case.

MRCI+Q singlet−triplet gaps for the hydrogen-bonded arylcarbenes exhibit a large reversal, ranging from −4.2 to −4.8 kcal/mol, about 3 kcal/mol larger in magnitude than the corresponding CCSD(T)-F12 results. For methylcarbene, phenylcarbene, methylphenylcarbene, and diphenylcarbene, the triplet state is the lowest energy state for the uncomplexed carbene, but the singlet−triplet gaps are relatively small, less than 5 kcal/mol. Hydrogen bond complexation in these carbenes is therefore strong enough to lower the singlet state below the triplet in energy, reversing the singlet−triplet gap. Hydrogen bond formation leads to singlet− triplet gaps for these carbenes that range from −0.7 to −1.9 kcal/mol at the CCSD(T)-F12 level and from −0.9 to −4.8 kcal/mol at the MRCI+Q level. The results reported here for the diphenylcarbene−CH3OH hydrogen-bonded complex are similar in some respects to the computational results reported in ref 16. The binding energies reported at the B3LYP/6-311++G(d,p) level for the singlet and

The singlet−triplet gaps for the hydrogen-bonded complexes are impacted significantly by formation of the hydrogen bonds. Due to the greater stabilization of the singlet carbene by hydrogen bond formation, the singlet carbene drops in energy relative to the triplet carbene in the hydrogen-bonded complex. The differences in the singlet−triplet gaps between the uncomplexed and hydrogen-bonded species range from 2.5 to 5.8 kcal/mol at the CCSD(T)-F12 level. The B3LYP-D3 results are qualitatively similar to the CCSD(T)-F12 results but generally predict singlet−triplet gaps for the hydrogen-bonded complexes that are smaller in magnitude. The MRCI+Q results for the singlet−triplet gaps of the hydrogen-bonded complexes are similar to the CCSD(T)-F12 values for the alkylcarbenes, differing by less than 1.3 kcal/mol. For the arylcarbenes, larger differences between the MRCI+Q and CCSD(T)-F12 results are observed due to the higher multireference character of the arylcarbenes. Hence, we expect the MRCI+Q results to predict more accurate singlet−triplet gaps for the arylcarbenes. The I


Article


Table 7. Charge Transfer, Second-Order Perturbation Energies for Hydrogen-Bonding Interactions (E(2) in kcal/mol), and Key Changes in Natural Bond Orbital Populations from NBO Deletion Analysis for Complexes Involving Triplet Carbenesa NBO deletionsd

NBO deletionsf

complex

charge transferb

E(2) (kcal/mol), nC → σ*(O−H)c

ΔPop. nC

ΔPop. σ*(O−H)

E(2) (kcal/mol), σ(O−H) → nCe

ΔPop. σ(O−H)

ΔPop. nC

CH2−H2O MeCH−H2O DiMe−H2O PhenCH−H2O MePhen−H2O DiPhen−H2O CH3O−H2O CH2−CH3OH MeCH−CH3OH DiMe−CH3OH PhenCH−CH3OH MePhen−CH3OH DiPhen−CH3OH CH3O−CH3OH

−0.008 −0.011 −0.013 −0.001 −0.003 −0.003 −0.018 −0.007 −0.008 −0.010 0.002 0.000 0.001 −0.017

4.96 6.20 7.29 5.05 6.70 6.34 6.44 6.39 7.21 9.07 5.91 7.01 7.59 6.39

0.0139 0.0159 0.0168 0.0135 0.0132 0.0081 0.0142 0.0176 0.0178 0.0193 0.0140 0.0135 0.0102 0.0141

−0.0142 −0.0179 −0.0212 −0.0152 −0.0183 −0.0163 −0.0153 −0.0178 −0.0199 −0.0244 −0.0168 −0.0187 −0.0191 −0.0149

1.06 1.31 1.77 1.45 1.94 2.02

0.0051 0.0057 0.0068 0.0069 0.0079 0.0072

−0.0069 −0.0060 −0.0062 −0.0080 −0.0080 −0.0045

1.50 1.72 2.39 1.73 2.24 2.50

0.0083 0.0085 0.0104 0.0092 0.0100 0.0104

−0.0117 −0.0097 −0.0104 −0.0100 −0.0086 −0.0076

a

Results were obtained at the B3LYP-D3/aTZ level of theory. bCharge transfer is computed as the net charge of H2O or CH3OH as a result of transfer of electron density from the carbene to H2O or CH3OH. cThe second-order perturbation energy listed is the sum of energies from interactions of the two singly occupied carbon lone pair orbitals with the O−H antibonding orbital. dThe changes in population of the carbon lone pair orbitals and the O−H antibonding orbital are reported for deletion of the Fock matrix elements between the orbitals. For the CH3O−H2O and CH3O−CH3OH complexes, the lone pair orbital is on the oxygen atom involved in the hydrogen bond. eThe second-order perturbation energy listed is the sum of energies from interactions of the O−H bonding orbital involved in the hydrogen bond with lone pair orbitals of the central carbon atom of the carbene. fThe changes in population of the O−H bonding orbital and the carbon lone pair orbitals are reported for deletion of the Fock matrix elements between the orbitals.

pair orbitals may contribute. The corresponding changes in population that occur as a result of the Fock matrix deletions are reported in Tables 7 and 8. For the hydrogen-bonded complexes of singlet carbenes with water or methanol, the charge transfer listed in Table 7 is substantial, ranging from −0.04 to −0.08; comparable changes in population of the carbon lone pair and O−H antibonding orbitals are generally observed upon deletion of the Fock matrix element for the nC → σ*(O−H) interaction. For comparison, the charge transfer values for H2O−H2O and H2O−CH3OH are much lower. The strong hydrogen bonds formed between water or methanol and singlet carbenes are confirmed by the large stabilization energies for these interactions estimated from second-order perturbation theory, shown in Table 7, which range from 16 to 32 kcal/mol; the corresponding perturbative stabilization energies for H2O−H2O and H2O−CH3OH are much lower at 7−8 kcal/mol. The nC and σ*(O−H) orbital interaction is shown for each complex in the Supporting Information: Figure S2 includes orbital interactions for singlet carbene complexes with water, and Figure S3 includes orbital interactions for singlet carbene complexes with methanol. A reasonably good correlation (R2 = 0.81) between the stabilization energy E(2) and the binding energy of the singlet carbene complexes also can be established, as shown in Figure S4 of the Supporting Information, confirming the key interaction responsible for stabilization in these systems. A similar correlation was observed previously for hydrogenbonded complexes involving the hydroperoxy radical, HO2.60 For the hydrogen-bonded complexes formed between triplet carbenes and water or methanol, the charge transfer listed in Table 7 is significantly lower than that observed for the singlet carbene complexes. For methylene, along with methyl- and dimethylcarbene, the charge transfer is a factor of about 4−7 times smaller than that for complexes involving singlet

triplet complexes of diphenylcarbene with methanol are determined to be −7.7 and −1.8 kcal/mol,16 respectively, whereas we obtain significantly stronger binding, −10.0 and −4.7 kcal/mol, respectively, at the B3LYP-D3/aTZ level. At the same level of theory, we compute the singlet−triplet gap of the diphenylcarbene-methanol complex to be 0.08 kcal/mol, whereas ref 16 reports a small inversion in the singlet−triplet gap of −0.26 kcal/mol (or −0.44 kcal/mol at the B3LYP-D3/6311++G(d,p) level). In contrast, our CCSD(T)-F12/aDZ single points predict a larger reversal of the singlet−triplet gap, − 1.27 kcal/mol, and the CASSCF(2,2) results give an even larger reversal of −4.68 kcal/mol. E. Hydrogen-Bonded Complexes: Charge Transfer and Bonding. Tables 6 and 7 present charge transfer, second-order perturbation theory energies for hydrogenbonding interactions, and key changes in natural bond orbital populations from NBO deletion analysis for hydrogen-bonded complexes of singlet and triplet carbenes, respectively, with water and methanol. The charge transfer corresponds to the excess charge on water or methanol as a result of the hydrogenbonding interaction; electron density is transferred from the carbene to the hydrogen bond donor. The stabilization energy, E(2), calculated from second-order perturbation theory, is listed for the interaction between the carbene carbon lone pair orbital, nC, and the O−H antibonding orbital, σ*(O−H); this is the key stabilizing interaction of the hydrogen-bonded complexes, and is the primary interaction responsible for the red shift of the O−H stretching frequency. To track the electron density removed from the carbene carbon lone pair orbitals and deposited in the O−H antibonding orbital, deletion of Fock matrix elements between the orbitals was carried out by using the NBO 6.0 software package.47 For the singlet carbene complexes, the carbon lone pair orbital is nominally doubly occupied, whereas for the triplet carbene complexes, the two singly occupied carbon lone J


Article


carbenes. For example, for the hydrogen-bonded complex involving triplet dimethylcarbene and water exhibits charge transfer corresponding to −0.013. The population of the O−H antibonding orbital as a result of the nC → σ*(O−H) interaction is determined by NBO deletions to be 0.021, a difference of 0.008 with respect to the magnitude of the computed charge transfer. The σ(O−H) → nC “back-bonding” interaction leads to a deposition of electron density back into the carbon lone pair orbitals corresponding to about 0.006− 0.007, which is in fairly good agreement with the difference between the O−H antibonding population and amount of charge transfer. Thus, the σ(O−H) → nC interaction leads to a reduction in charge transfer for the triplet carbene complexes compared with the expected amount for hydrogen-bonded complexes exhibiting similar O−H red shifts.

carbenes. These values also are smaller than the charge transfer computed for the radical-hydrogen-bonded species CH3O− H2O and CH3O−CH3OH. For the arylcarbenes, the charge transfer is very small and in some cases positive, reflecting the fact that little net electron density is apparently transferred from the carbene to water or methanol; this is counter to what is typically expected for hydrogen-bonded complexes. However, the complexes involving triplet carbenes exhibit other properties that are similar to those of typical hydrogen-bonded complexes, such as appropriate C−H hydrogen bond distances, C−H−O angles close to 180°, red-shifted O−H stretching frequencies, and binding energies in line with other radical-hydrogen bond complexes. Therefore, a more detailed investigation of the charge transfer and bonding for the triplet carbene complexes is warranted. It can be seen in Table 7 that the second-order perturbation energies for the nC → σ*(O−H) interactions, though smaller than those observed for the singlet complexes, are comparable to the stabilization observed in the radical hydrogen-bonded species CH3O−H2O and CH3O−CH3OH. The correlation between the binding energies of the triplet carbene complexes and the second-order perturbation energies for the nC → σ*(O−H) interactions is not nearly as strong as that obtained for the singlet carbene complexes (R2 = 0.35), but there is a rough correlation of increasing binding energy with increasing second-order perturbation energy, as shown in Figure S5 of the Supporting Information. The NBO deletion analysis shown in Table 7 demonstrates that a substantial amount of charge is transferred from the carbon lone pair orbitals into the O−H antibonding orbital. This is the primary reason that there is still a significant red shift in the O−H frequency for these compounds, as a result of the weakening of the O−H bond due to population in the antibonding orbital. The magnitude of the change in population for the O−H antibonding orbital corresponds well with the depletion in the population of the carbon lone pair orbital. The largest discrepancies arise in the complexes involving methylphenylcarbene and diphenylcarbene, in which the depletion of population in the carbon lone pair orbitals is around half to two-thirds of the population of the O−H antibonding orbital; this is a result of further delocalization into the aromatic rings of these systems. The computed charge transfer for the triplet carbene complexes is much lower than expected when compared with the population of the O−H antibonding orbital, with the most significant differences in magnitude observed for the arylcarbenes. Table 7 also provides information related to an additional interaction in the triplet carbene complexes that leads to a reduction in the overall charge transfer. Although the primary stabilizing interaction in all the hydrogen-bonded complexes involves transfer of electron density from the carbon lone pair orbitals into the O−H antibonding orbital, the additional key interaction in the triplet carbene complexes involves essentially a back-bonding type of interaction that corresponds to transfer of electron density from the O−H bonding orbital into the partially filled carbon lone pair orbitals of the triplet carbene, σ(O−H) → nC. This interaction, computed from second-order perturbation theory, ranges from 1.1 to 2.5 kcal/mol. The amount of electron density involved in this “backbonding” interaction is in reasonably good agreement with the reduction in charge transfer that is observed in the triplet

4. CONCLUSIONS Calculations for singlet and triplet alkyl and aryl carbenes have been performed using a variety of theoretical methods to benchmark appropriate levels for accurate determination of geometries and singlet−triplet gaps. We find that DFT methods provide generally reasonable carbene geometries but overestimate the singlet−triplet gaps by at least 1−2 kcal/mol. For methylene, methylcarbene, and dimethylcarbene, the CCSD(T)-F12/aDZ//B3LYP-D3/aTZ methodology provides accurate singlet−triplet gaps, whereas for the arylcarbenes with higher multireference character, the MRCI+Q/aTZ//B3LYPD3/aTZ methodology provides improved singlet−triplet gaps. Solvent effects on the singlet−triplet gaps were studied using the PCM method and the B3LYP/aTZ level of theory. It was demonstrated that the effect of increasing solvent polarity preferentially stabilizes the more polar carbene singlet state relative to the triplet state. This leads to a decrease in the singlet−triplet gap for systems with triplet ground states. Taking into account that the DFT methods overestimate the singlet−triplet gap by at least 1−2 kcal/mol, the effect of solvation may lead to a switch in the ground state from triplet to singlet for some carbenes with small gas phase singlet−triplet gaps, such as methylcarbene and phenylcarbene. In addition to effects due to bulk solvent, hydrogen-bonding interactions of the singlet and triplet carbenes with explicit water and methanol molecules have been investigated. Geometry optimizations and vibrational frequency calculations at the B3LYP-D3/aTZ level of theory demonstrate the formation of strong hydrogen-bonded complexes between the singlet carbenes and water or methanol; in addition, weaker hydrogen-bonded complexes are formed between the triplet carbenes and water or methanol. The hydrogen-bonded complexes involving both singlet and triplet carbenes are characterized by C−H distances ranging from 1.93 to 2.25 Å, near linear O−H−C hydrogen bond angles, and red-shifted O− H stretching frequencies. The singlet−triplet gaps of the carbenes involved in hydrogen-bonded complexes with water or methanol are signficantly affected by the formation of the hydrogen bond. The singlet−triplet gaps of all the carbenes possessing triplet ground states in the gas phase (excluding methylene) exhibit a reversal of the singlet−triplet gap upon hydrogen bond formation, stabilizing the singlet state relative to the triplet state by as much as 5 kcal/mol. Finally, NBO analysis has been employed to investigate the bonding in the hydrogen-bonded complexes of the singlet and triplet carbenes. Interactions between carbon lone pair and O− K


Article


(11) Garcia-Garibay, M. A.; Theroff, C.; Shin, S. H.; Jernelius, J. Solvent Effects on the Singlet − Triplet Equilibrium and Reactivity of a Ground Triplet State Arylalkyl Carbene. Tetrahedron Lett. 1993, 34, 8415−8418. (12) Wang, Y.; Hadad, C. M.; Toscano, J. P. Solvent Dependence of the 2-Naphthyl(carbomethoxy)carbene Singlet-Triplet Energy Gap. J. Am. Chem. Soc. 2002, 124, 1761−1767. (13) Cramer, C. J.; Truhlar, D. G.; Falvey, D. E. Singlet-Triplet Splittings and 1,2-Hydrogen Shift Barriers for Methylphenylborenide, Methylphenylcarbene, and Methylphenylnitrenium in the Gas Phase and Solution. What a Difference a Charge Makes. J. Am. Chem. Soc. 1997, 119, 12338−12342. (14) Gonzalez, C.; Restrepo-Cossio, A.; Marquez, M.; Wiberg, K. B.; De Rosa, M. Ab Initio Study of the Solvent Effects on the SingletTriplet Gap of Nitrenium Ions and Carbenes. J. Phys. Chem. A 1998, 102, 2732−2738. (15) Arduengo, A. J.; Gamper, S. F.; Tamm, M.; Calabrese, J. C.; Davidson, F.; Craig, H. A. A Bis(carbene)-Proton Complex: Structure of a C-H-C Hydrogen Bond. J. Am. Chem. Soc. 1995, 117, 572−573. (16) Costa, P.; Sander, W. Hydrogen Bonding Switches the Spin State of Diphenylcarbene from Triplet to Singlet. Angew. Chem., Int. Ed. 2014, 53, 5122−5125. (17) Costa, P.; Fernandez-Oliva, M.; Sanchez-Garcia, E.; Sander, W. The Highly Reactive Benzhydryl Cation Isolated and Stabilized in Water Ice. J. Am. Chem. Soc. 2014, 136, 15625−15630. (18) Costa, P.; Trosien, I.; Fernandez-Oliva, M.; Sanchez-Garcia, E.; Sander, W. The Fluorenyl Cation. Angew. Chem., Int. Ed. 2015, 54, 2656−2660. (19) Richter, G.; Mendez-Vega, E.; Sander, W. Singlet Halophenylcarbenes as Strong Hydrogen-bond Acceptors. J. Phys. Chem. A 2016, 120, 3524−3532. (20) Costa, P.; Lohmiller, T.; Trosien, I.; Savitsky, A.; Lubitz, W.; Fernandez-Oliva, M.; Sanchez-Garcia, E.; Sander, W. Light and Temperature Control of the Spin State of Bis(p-methoxyphenyl)carbene: A Magnetically Bistable Carbene. J. Am. Chem. Soc. 2016, 138, 1622−1629. (21) Henkel, S.; Costa, P.; Klute, L.; Sokkar, P.; Fernandez-Oliva, M.; Thiel, W.; Sanchez-Garcia, E.; Sander, W. Switching the Spin State of Diphenylcarbene via Halogen Bonding. J. Am. Chem. Soc. 2016, 138, 1689−1697. (22) Pople, J. A. A Theoretical Search for the Methylenefluoronium Ylide. Chem. Phys. Lett. 1986, 132, 144−146. (23) Pople, J. A.; Raghavachari, K.; Frisch, M. J.; Binkley, J. S.; Schleyer, P. v. R. Comprehensive Theoretical Study of Isomers and Rearrangement Barriers of Even-Electron Polyatomic Molecules HmABHn (A, B = C, N, O, and F). J. Am. Chem. Soc. 1983, 105, 6389−6398. (24) Zub, L. L.; Standard, J. M. Theoretical Studies of the Interactions of Singlet Carbenes with Water and Alcohols. J. Mol. Struct.: THEOCHEM 1996, 368, 133−143. (25) Alkorta, I.; Elguero, J. Carbenes and Silylenes as Hydrogen Bond Acceptors. J. Phys. Chem. 1996, 100, 19367−19370. (26) Alkorta, I.; Rosas, I.; Elguero, J. Radicals as Hydrogen Bond Acceptors. Ber. Bunsenges. Phys. Chem. 1998, 102, 429−435. (27) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parameterization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132, 154104. (28) Chai, J.-D.; Head-Gordon, M. Long-range Corrected Hybrid Density Functionals with Damped Atom-atom Dispersion Corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615−6620. (29) Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-class Functionals and 12 Other Functionals. Theor. Chem. Acc. 2008, 120, 215−241. (30) Adler, T. B.; Knizia, G.; Werner, H.-J. A Simple and Efficient CCSD(T)-F12 Implementation. J. Chem. Phys. 2007, 127, 221106.

H antibonding orbitals have been shown to be responsible for stabilization of the hydrogen-bonded complexes involving both singlet and triplet carbenes. In addition, the computed charge transfer from the carbene to the hydrogen-bond donor was found to be much lower than expected in the complexes involving triplet carbenes based upon O−H antibonding orbital populations. It was observed that an additional back-bonding type interaction between the O−H bonding orbital and the carbon lone pairs reduces the expected charge transfer.

■

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b11202. Bond lengths and angles for optimized singlet and triplet carbenes at all levels of theory; singlet−triplet gaps computed at all levels of theory; singlet and triplet energies for methylene, methylcarbene, methylphenylcarbene, and diphenylcarbene in continuum solvent; orbital interactions between the carbon lone orbital and O−H antibonding orbital for hydrogen-bonded complexes of singlet carbenes; correlations between carbene binding energies and second-order perturbation energies; full Gaussian and Molpro citations; Cartesian coordinates of all singlet and triplet carbenes; and Cartesian coordinates of all hydrogen-bonded complexes formed between singlet and triplet carbenes and water or methanol (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail address: [email protected]. ORCID

Jean M. Standard: 0000-0003-1261-9719 Notes

The author declares no competing financial interest.

■

REFERENCES

(1) Kirmse, W. Carbene Chemistry; Academic Press: New York, 1971. (2) Jones, M.; Moss, R. A. Carbenes; Wiley: New York, 1972, Vol. 1; 1975, Vol. 2. (3) Shainyan, B. A.; Kuzmin, A. V.; Moskalik, M. Y. Carbenes and Nitrenes. An Overview. Comput. Theor. Chem. 2013, 1006, 52−61. (4) Gerbig, D.; Lay, D. Computational Methods for Contemporary Carbene Chemistry. WIREs Comput. Mol. Sci. 2013, 3, 242−272. (5) Moss, R. A. Solvation and Complexation of Carbenes − A Perspective. J. Phys. Org. Chem. 2011, 24, 866−875. (6) Tomioka, H.; Ozaki, Y.; Izawa, Y. Modification of Singlet Carbene Reactivities by Solvent. Tetrahedron 1985, 41, 4987−4993. (7) Turro, N. J.; Cha, Y.; Gould, I. R. Reactivity and Intersystem Crossing of Singlet Methylene in Solution. J. Am. Chem. Soc. 1987, 109, 2101−2107. (8) Swanson, J. M.; Dvorak, C. A.; DeLuca, J. P.; Standard, J. M. Complexation of a Singlet Carbene by a Fluoroalkane. Modification of l :CHCO2Et Selectivity in Perfluorohexane Solution and Ab Initio Calculations. J. Org. Chem. 1994, 59, 3026−3032. (9) Langan, J. G.; Sitzmann, E. V.; Eisenthal, K. B. Picosecond Laser Studies on the Effect of Structure and Environment on Intersystem Crossing in Aromatic Carbenes. Chem. Phys. Lett. 1984, 110, 521−527. (10) Sitzmann, E. V.; Langan, J. G.; Griller, D.; Eisenthal, K. B. Effects of Solvent Polarity and Structure on Intersystem Crossing in Diphenylcarbenes. A Picosecond Laser Study on Dimesitylcarbene. Chem. Phys. Lett. 1989, 161, 353−360. L


Article

The Journal of Physical Chemistry A (31) Werner, H.-J.; Knowles, P. J. An Efficient Internally Contracted Multiconfiguration−Reference Configuration Interaction Method. J. Chem. Phys. 1988, 89, 5803−5814. (32) Knowles, P. J.; Werner, H.-J. An Efficient Method for the Evaluation of Coupling Coefficients in Configuration Interaction Calculations. Chem. Phys. Lett. 1988, 145, 514−522. (33) Langhoff, S. R.; Davidson, E. R. Configuration Interaction Calculations on the Nitrogen Molecule. Int. J. Quantum Chem. 1974, 8, 61−72. (34) Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models. Chem. Rev. 2005, 105, 2999−3093. (35) Miertus, S.; Scrocco, E.; Tomasi, J. Electrostatic Interaction of a Solute with a Continuum. A Direct Utilization of Ab Initio Molecular Potentials for the Prevision of Solvent Effects. Chem. Phys. 1981, 55, 117−129. (36) Miertus, S.; Tomasi, J. Approximate Evaluations of the Electrostatic Free Energy and Internal Energy Changes in Solution Processes. Chem. Phys. 1982, 65, 239−245. (37) Pascual-Ahuir, J. L.; Silla, E.; Tunon, I. GEPOL: An Improved Description of Molecular-surfaces. 3. A New Algorithm for the Computation of a Solvent-excluding Surface. J. Comput. Chem. 1994, 15, 1127−1138. (38) Cossi, M.; Barone, V.; Cammi, R.; Tomasi, J. Ab Initio Study of Solvated Molecules: A New Implementation of the Polarizable Continuum Model. Chem. Phys. Lett. 1996, 255, 327−35. (39) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, Revision D.01; Gaussian, Inc.: Wallingford, CT, 2009. (40) Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M. Molpro: A General-purpose Quantum Chemistry Program Package. WIREs Comput. Mol. Sci. 2012, 2, 242−253. (41) Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M.; Celani, P.; Györffy, W.; Kats, D.; Korona, T.; Lindh, R.; et al. MOLPRO, version 2012, a package of ab initio programs. See http:// www.molpro.net (42) Reed, A. E.; Weinhold, F. Natural Bond Orbital Analysis of Near-Hartree-Fock Water Dimer. J. Chem. Phys. 1983, 78, 4066−4073. (43) Reed, A. E.; Weinstock, R. B.; Weinhold, F. Natural Population Analysis. J. Chem. Phys. 1985, 83, 735−746. (44) Foster, J. P.; Weinhold, F. Natural Hybrid Orbitals. J. Am. Chem. Soc. 1980, 102, 7211−7218. (45) Carpenter, J. E.; Weinhold, F. Analysis of the Geometry of the Hydroxymethyl Radical by the ’Different Hybrids for Different Spins’ Natural Bond Orbital Procedure. J. Mol. Struct.: THEOCHEM 1988, 169, 41−62. (46) Weinhold, F.; Landis, C. R.; Glendening, E. D. What is NBO Analysis and How is it Useful? Int. Rev. Phys. Chem. 2016, 35, 399− 440. (47) Glendening, E. D.; Badenhoop, J. K.; Reed, A. E.; Carpenter, J. E.; Bohmann, J. A.; Morales, C. M.; Landis, C. R.; Weinhold, F. NBO 6.0; Theoretical Chemistry Institute, University of Wisconsin: Madison, 2013. (48) McKellar, A. R. W.; Bunker, P. R.; Sears, T. J.; Evenson, K. M.; Saykally, R. J.; Langhoff, S. R. Far Infrared Laser Magnetic Resonance of Singlet Methylene: Singlet-triplet Perturbations, Singlet-triplet Transitions, and the Singlet-triplet Splitting. J. Chem. Phys. 1983, 79, 5251−5264. (49) Leopold, D. G.; Murray, K. K.; Stevens Miller, A. E.; Lineberger, W. C. Methylene: A Study of the X̃ 3B1 and ã 1A1 States by Photoelectron Spectroscopy of CH2− and CD2−. J. Chem. Phys. 1985, 83, 4849−4865. (50) Admasu, A.; Gudmundsdottir, A. D.; Platz, M. S. Laser Flash Photolysis Study of Phenylcarbene and Pentafluorophenylcarbene. J. Phys. Chem. A 1997, 101, 3832−3840. (51) Admasu, A.; Platz, M. S.; Marjcinek, A.; Michalak, J.; Gudmundsdottir, A. D.; Gebicki, J. Laser Flash Photolysis Study of Phenylcarbene, o-Tolylcarbene, and Mesitylcarbene. J. Phys. Org. Chem. 1997, 10, 207−220.

(52) Sugiyama, M. H.; Celebi, S.; Platz, M. S. A Significant Barrier to 1,2-Hydrogen Migration in Singlet 1-Phenylethylidene. A Laser Flash Photolysis Study. J. Am. Chem. Soc. 1992, 114, 966−973. (53) Lee, T. J. Comparison of the T1 and D1 Diagnostics for Electronic Structure Theory: A New Definition for the Open-shell D1 Diagnostic. Chem. Phys. Lett. 2003, 372, 362−367. (54) Gronert, S.; Keeffe, J. R.; O’Ferrall, R. A. M. Stabilities of Carbenes: Independent Measures for Singlets and Triplets. J. Am. Chem. Soc. 2011, 133, 3381−3389. (55) Geise, C. M.; Hadad, C. M. Computational Study of the Electronic Structure of Substituted Phenylcarbene in the Gas Phase. J. Org. Chem. 2000, 65, 8348−8356. (56) Nguyen, T. L.; Kim, G.-S.; Mebel, A. M.; Nguyen, M. T. A Theoretical Re-evaluation of the Heat of Formation of Phenylcarbene. Chem. Phys. Lett. 2001, 349, 571−577. (57) Woodcock, H. L.; Moran, D.; Brooks, B. R.; Schleyer, P. v. R.; Schaefer, H. F. Carbene Stabilization by Aryl Substituents. Is Bigger Better? J. Am. Chem. Soc. 2007, 129, 3763−3770. (58) Wong, M. W.; Frisch, M. J.; Wiberg, K. B. Solvent Effects. 1. The Mediation of Electrostatic Effects by Solvents. J. Am. Chem. Soc. 1991, 113, 4776−4782. (59) Onsager, L. Electric Moments of Molecules in Liquids. J. Am. Chem. Soc. 1936, 58, 1486−1493. (60) Hernandez-Soto, H.; Weinhold, F.; Francisco, J. S. Radical Hydrogen Bonding: Origin of Stability of Radical-Molecule Complexes. J. Chem. Phys. 2007, 127, 164102.

M


Effects of Solvation and Hydrogen Bond Formation on Singlet and

Recommend Documents