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Keywords:

  • fluorine-substituted carbenes;
  • excited states;
  • icMRCI+Q

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methodology
  5. Results and Discussion
  6. Conclusions
  7. Acknowledgment

High-level calculations using internally contracted multireference configuration interaction including Davidson correction (icMRCI+Q) method have been carried out for the ground singlet states, the first excited states, and the lowest triplet states of a series of fluorine-substituted carbenes FCX (X = H, F, Cl, Br, and I). Equilibrium geometries and vibrational frequencies of the three electronic states, adiabatic transition energy of the first excited singlet state, as well as the ground singlet—lowest triplet energy gap (S-T gap) of each of FCX carbenes have been obtained. Effects of the basis set of icMRCI+Q calculation on the geometries and energies have been investigated. In addition, various corrections, including the scalar relativistic effect, spin-orbit coupling, and core-valence correlation, have been studied in calculating the transition energies and the S-T gaps, especially for heavy-atom carbenes. This results have been compared with previous calculations using a variety of methods. Our icMRCI+Q results are in very good agreement with the high-resolution laser-based spectroscopic results where available. Some structure and spectroscopic constants of the fluorine-substituted carbenes which are void in the literature have been provided with consistent high-level calculations. © 2013 Wiley Periodicals, Inc.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methodology
  5. Results and Discussion
  6. Conclusions
  7. Acknowledgment

Carbenes are important free radicals in a wide variety of chemical reactions such as combustion chemistry, stratosphere, interstellar chemistry, organic reaction, and so on. It is well-known that the low-lying singlet and triplet states of carbenes exhibit different chemical activities. Intense research interest has been received during the past several decades regarding the electronic structure and photochemistry of carbenes which continues to be an active research area. Unlike the smallest carbene CH2, which has a triplet ground state, all halogenated carbenes studied to date have a singlet ground state. As pointed out by Kable et al. in their recent review,[1] halogenated carbenes are set forth as model systems for understanding the spectroscopy, dynamics, and chemistry of carbenes, and benchmarks for comparison between theoretical and experimental investigations. Indeed, halogenated carbenes have been the subject of the myriad of studies reported in the literature, using various spectroscopic techniques and computational methods, to reveal the nature of the low-lying electronic states of carbenes (for reference, see [1] and references therein).

Here, we focus on a series of fluorine-substituted carbenes, FCX (X = H, F, Cl, Br and I), which are believed to be products or intermediates of reactions of fluorocarbons and halons in the upper atmosphere. The history of study of fluorine-substituted carbenes has dated back to more than 50 years ago when Venkateswarlu reported the first observation of the emission band of CF2 [2] With rapid development of high-resolution spectroscopic techniques along with high-level calculation methods, our understanding of fluorine-substituted carbenes is now blossoming. To date, most experimental studies concerned the small fluorine-substituted carbenes, FCH, and CF2. Because the early emission and absorption spectroscopic studies of CF2 were carried out several decades ago,[2-6] many experimental efforts have been made to determine the structure and spectroscopic constants of the ground and first excited singlet states of FCH (and/or FCD(isotope of FCH)),[7-22] CF2, [23-29] FCCl,[30-33] as well as FCBr, [32],[34-37] using a variety of laser-based spectroscopic techniques. For some carbenes, experimental studies for the spectrum and dynamics of the states beyond the A state were carried out recently, for example, the B state of FCH [38] and dissociation dynamics of FCCl and FCBr at 193 nm.[32] For the triplet states, as well as the ground singlet-lowest triplet energy gap (S-T gap), experimental studies are sparse, mostly by negative ion photoelectron spectroscopy. [39-42] On the other hand, a number of ab initio theoretical studies were performed on the fluorine-substituted carbenes with different calculation methods.[28, 35, 43-54] For example, Gaussian-2 and Quadratic Configuration Interaction (QCI) theory with basis sets up to 6–311+G(3df,2p) were employed to obtain geometries and vibrational frequencies of the singlet and triplet states, as well as the S-T gaps of all halocarbenes.[45] Ground and excited state properties of a series bromine- and iodine-containing singlet carbenes was investigated at the CASSCF, CASPT2 and CISD levels of theory.[44] CASPT2 method was employed to investigate the ground and first excited singlet state of FCI,[48] and recently the excited states of FCBr.[52] The S-T gaps of FCX were also calculated by several groups.[45-47, 49, 51, 55] MRCI calculation was reported for CF2 with an aug-cc-pVQZ or complete basis set (CBS) level [26] and FCBr with a cc-pVTZ basis set.[49, 52]

Despite that many experimental and theoretical studies have been carried out in the literature, the structure or dynamics of the low-lying states of FCX is not completely known. From the experimental point of view, clean production of carbenes in situ is difficult and there is only one stable isotope for fluorine thus impossible for studies of isotopic species. From the theoretical point of view, highly electronegative character of the fluorine atom requires a reliable ab initio calculation of FCX to be performed at large basis sets and highly correlated methods, especially for heavier FCX (X = Cl, Br, I). In addition, due to the complicated interactions between different degrees of freedom (rotational, vibrational, and electronic), to retrieve accurate structure and spectral parameters of carbenes is generally a challenge work, which could not be accomplished without a combination of high-resolution spectroscopic experiments and high-level calculations. Regarding the structure of the triplet states and the S-T gap of halogenated carbenes, ab initio calculations in most cases lead experimental investigations. A reliable theoretical prediction is no doubt but necessary and important to understand the structure, spectrum, and dynamics of halogenated carbenes.

In this work, high-level internally contracted multireference configuration interaction including Davidson correction (icMRCI+Q) studies were carried out for all of FCX, X = H, F, Cl, Br, and I. Equilibrium geometries, vibrational frequencies, and excitation energies of the low-lying electronic states of each carbene were obtained, and the results were compared with previous available theoretical and experimental studies. The effect of basis set on icMRCI+Q calculations was studied, and various corrections, including the scalar relativistic effect, spin-orbit coupling (SOC), and Core-Valence correlation, were investigated in calculating the transition energies and the S-T gaps, especially for heavy-atom carbenes.

Methodology

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methodology
  5. Results and Discussion
  6. Conclusions
  7. Acknowledgment

In our work, fluorine-substituted carbenes, FCX (X = H, F, Cl, Br and I) were investigated using full-valence complete active space multiconfiguration self-consistent field [56] and icMRCI [57, 58]method. Davidson correction (+Q) [59] was used to account for higher-order excitation configurations. The active space consists of 18 valence electrons and 12 valence orbitals (18e, 12o) corresponding to n = 2 atomic orbitals of C and F atoms and outer valence orbital of X atom for FCX molecule (X = F, Cl, Br, and I), 12 valence electrons and nine valence orbitals (12e,9o) for FCH. The correlation consistent basis sets cc-pVXZ (X = T, Q, 5) [60-62] were used in ab initio calculations.

We performed the geometry optimizations of the ground and first excited singlet states and the lowest triplet states of all of the fluorine-substituted carbenes using standard all-electron correlation-consistent basis sets of 5-ζ quality with polarization functions, cc-pV5Z, for hydrogen, carbon, fluorine, and bromine. A similar basis set including tight-d functions, cc-pV(5+d)Z, was employed for chlorine. For iodine, a relativistic effective core potential ECP28MDF [63] along with the corresponding cc-pV5Z basis set was employed.

For FCBr radical, we also performed cc-pVXZ(X = T, Q, 5) calculations and TQ extrapolation to CBS limit. The extrapolation to the CBS limit was performed for the energies (not directly for geometries), including the zeroth-order reference energy (CASSCF energy, ECAS and the dynamical correlation energy (energy difference between MRCI+Q energy and CASSCF energy, Ecorr). In the case of Dunning's correlation-consistent cc-pVXZ basis sets, the zeroth-order energies approaching their CBS limits are expressed as ECAS (X) = ECAS (CBS) + ao exp(−αX) and we used the values for X = T,Q,5 to determine the three unknowns, ECAS(CBS), ao, and α. The dynamical correlation energies approach their CBS limits according to the inverse power law, ΔECORR (X) = ΔECORR (CBS) + acX−3,[64] and we used the data for X = T,Q to determine the extrapolated value ΔECORR (CBS). The total energy is the sum of ECAS (CBS) and ΔECORR (CBS). We then used numerical optimization to get the CBS geometries of FCBr. The energy convergence threshold is 10−8 hartree or better, the gradient convergence threshold in geometry optimization is 10−4 a.u. The harmonic vibrational frequencies were determined by employing the methods described above at icMRCI+Q/cc-pVTZ level. The S-T gaps and adiabatic transition energies were computed at the icMRCI+Q/cc-pV5Z level using the geometries optimized at the same level. In addition, adiabatic transition energies and S-T gap of FCBr as a function of basis set were given and scalar relativistic effect, SOC, and core-valence (CV) correlations were considered.

The scalar relativistic effect was estimated with icMRCI+Q method in combination with appropriate basis sets for FCBr systems using second-order Douglas–Kroll–Hess Hamiltonian.[65, 66] The SOC was determined with state-interacting approach using the Breit–Pauli Hamiltonian for FCBr. Eight spin-free states (1–21,3(A′/A″)) were coupled in SOC calculations, and the icMRCI+Q/cc-pVTZ energies were used to replace the diagonal spin-orbit matrix elements. In the CV calculations, the core and core-valence correlations of 3s3p3d orbitals of Br in FCBr were estimated using icMRCI+Q method with appropriate triple-zeta basis sets (cc-pwCVTZ for C, F, and Br).[67, 68] All calculations were carried out using the MOLPRO software package.[69, 70]

Results and Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methodology
  5. Results and Discussion
  6. Conclusions
  7. Acknowledgment

icMRCI+Q calculations of FCX radicals

Except for CF2, which has a C2V symmetry, all other fluorine-substituted carbenes are in a lower Cs symmetry group. The ground electronic states of all FCX are singlet (1A1 for CF2 or 1A′ for the others). The first excited singlet state is the 1B1 state of CF2 or the 1A″ state of the others, whereas the lowest triplet state is the 3B1 state of CF2 or the 3A″ state of the others. For simplification, we use X, S1, and T1 to indicate the ground state, the first excited singlet state and the lowest triplet state of FCX throughout the article. In this section, we present our icMRCI+Q calculation results, including the equilibrium geometries and the harmonic vibrational frequencies of the X, S1, and T1 states, the adiabatic transition energies of the S1 states, and the S-T energy gaps, of all of the FCX radicals, and compare our results with available experimental and calculation values reported in the literature.

Equilibrium geometries of the X, S1 and T1 states of FCX radicals

The equilibrium bond lengths and bond angles of the X, S1, and T1 states of FCX are listed in Table 1, which were calculated at icMRCI+Q/cc-pV5Z level. Our calculated C[BOND]F bond lengths of different fluorine-substituted carbenes were similar, ranging from 1.294 to 1.316 Å for all the electronic states studied. The C[BOND]X (X = H, F, Cl, Br, I) bond length, however, increases from ∼1.1 Å for FCH to ∼2.1 Å for FCI, which can be understood as the substituted atom size increases from hydrogen to iodine. The bond lengths of different electronic states are almost identical for each fluorine-substituted carbene. The calculated X[BOND]C[BOND]F bond angle, on the other hand, is different for different electronic states. The bond angle of the ground state is the smallest, in range of 102.2–108.2° for different fluorine-substituted carbenes, which can be attributed to the in-plane sp2-like orbital of the two nonbonded electrons of carbon in the ground state. The bond angles of the S1 and T1 states are close, but about 20° larger than those of the ground states, due to transition of at least one nonbonding electron to an out-of-plane p type orbital of carbon.

Table 1. Equilibrium geometries of fluorine-substituted carbenes calculated at icMRCI+Q/cc-pV5Z level.
CarbeneRC[BOND]F (Å)RC[BOND]X(Å)∠F[BOND]C[BOND]X(°)
  1. [a]Ref. [ [19].

  2. [b]Ref. [28].

  3. [c]Ref. [ [33].

  4. [d]Ref. [ [22].

  5. [e] Ref. [ [23].

  6. [f]Ref. [ [6].

  7. The values in the brackets are available experimental results.

Ground singlet state
FCH1.309(1.305[a])1.120(1.130[a])102.2(103.0[a])
CF21.299(1.2975[b])1.299(1.2975[b])104.8(104.8[b])
FCCl1.294(1.32[c])1.739(1.714[c])106.6(107.6[c])
FCBr1.2951.923107.3
FCI1.2982.155108.2
Excited singlet state
FCH1.298(1.308[d])1.100(1.063[d])124.4(123.8[d])
CF21.316(1.316[e])1.316(1.316[e])122.0(122.3[e])
FCCl1.308(1.33[c])1.667(1.652[c])126.5(126.9[c])
FCBr1.3061.865125.9
FCI1.2982.154124.9
Triplet state
FCH1.3131.084121.5
CF21.312(1.298[f])1.312(1.298[f])119.1(118.1[f])
FCCl1.3161.681123.2
FCBr1.3131.850123.9
FCI1.3092.065125.2

Also listed in Table 1 are experimentally measured geometries reported in the literature, which are only available for light-atom fluorine-substituted carbenes, FCH, CF2, and FCCl.[19, 22, 23, 28, 33]. For the singlet states, our calculated geometries are in fairly good agreement with those experimental results, with differences as large as 0.037 Å for the bond lengths and 1.0° for bond angles. The only experimental results for the triplet states are those of CF2 from early absorption spectrum,[6] which are 0.014 Å and 1.0° different from our calculated results, for C[BOND]F bond length and bond angle, respectively. However, it is usually difficult to estimate the accuracy of experimentally determined geometries due to the uncertain of various factors of the methods (anharmonic resonance, magnetic correction, Coriolis resonance, state perturbation, etc). On the other hand, the calculated geometries of the X, S1, and T1 states of FCH and CF2 using a variety of theoretical methods (including the results presented in this work) are well-consistent with each other, with discrepancy mostly less than 0.01 Å for bond lengths and 0.5° for bond angles. Regarding the heavy-atom fluorine-substituted carbenes (FCBr and FCI), no available experimental geometries are reported in the literature for either of the electronic states. In addition, less theoretical studies were carried out previously [35, 44, 48, 49, 52] in comparison with light-atom carbenes FCH and CF2, and the discrepancy of the results of different calculation methods are relatively larger. Taking FCBr as an example, the discrepancy of the calculated bond lengths is as large as 0.1 Å (in the C[BOND]Br bond length of the X state, 2.001 [44] vs. 1.898 Å[35]), and that of the bond angle is as large as 1.2° (in the bond angle of the S1 state, 126.5[35] vs. 125.3° [49]). On the contrast, our high-level icMRCI+Q/cc-pV5Z results presented here are in good agreement with the most recent results calculated at CASPT2/cc-pV5Z[52] and MRCI/cc-pVTZ level.[49]

Vibrational frequencies of the X, S1 and T1 states of FCX radicals

The calculated harmonic vibrational frequencies at icMRCI+Q/cc-pVTZ level are listed in Table 2. The frequencies ω1, ω2, and ω3 in the table refer to the frequencies of low-frequency stretch modes, bending modes, and high-frequency stretch modes of fluorine-substituted carbenes, respectively. Recent experimental results reported in the literature are also included in the table. As shown in the table, our calculated frequencies are generally larger than those obtained from experimental studies, as anharmonic effects were included in some reported experimental frequencies while the calculated frequencies are harmonic ones.

Table 2. Harmonic vibrational frequencies of fluorine-substituted carbenes calculated at icMRCI+Q/cc-pVTZ level.
Carbeneω1ω2ω3
  1. [a]Ref. [ [11].

  2. [b]Ref. [ [15].

  3. [c]Ref. [ [28].

  4. [d]Ref. [ [31].

  5. [e]Ref. [ [35].

  6. [f]Ref. [ [37].

  7. [g]Ref. [ [41].

  8. [h]Ref. [ [18].

  9. [i]Ref. [ [16].

  10. [j]Ref. [ [42].

  11. [k]Ref. [ [39].

  12. The values in the brackets are available experimental results. All values are in cm−1.

Ground singlet state
FCH1434.0(1461[a]/1445.1[b])1201.0(1213[a]/1211.2[b])2771.0(2710[a]/2785.2[b])
CF21171.1(1114.4[c])673.6(666.3[c])1254.1(1225.1[c])
FCCl767.5(763.5[d])454.6(454.1[d])1206.8(1185.5[d])
FCBr679.0(671.2[e]/665.38[f])357.2(348.7[e]/349.5[f])1225.8(1198[e]/1165.9[f])
FCI588.4(573[g])290.31217.5(1133[g])
Excited singlet state
FCH1285.0(1260[h])1045.9(1035.6[h])2971.3(2852[h]/2799.7[i])
CF21061.0(1012.1[c])497.2(496.7[c])1280.0(1180.2[c])
FCCl701.7(748.0[d])391.2(399.2[d])1253.1(1229[d])
FCBr496.7(649[e]/493.8[f])301.3(336[e]/303.7[f])1233.6(1134[e])
FCI339.2183.11223.0
Triplet state
FCH1261.7(1248 (25) [g])1127.4(1054 (25)[g])3128.3
CF21161.8(1020[j])517.8(520[j]/517[k])1347.1
FCCl810.9393.61278.4
FCBr672.0321.81261.2
FCI568.2275.51249.2

For the singlet X and S1 states, experimental values of the vibrational frequencies are available in the literature for all the FCX radicals except FCI. Our calculated harmonic frequencies of the bending modes (ω2), of which the anharmonic effect is expected to be low, are in very good agreement with the experimental results, with difference in the range of 0.5–25 cm−1 for all the X and S1 states of the FCX radicals. Our calculated ω1 and ω3 values, however, are much larger than the experimental values. The largest differences between our calculated results and the most recent experimental results are 56.7 cm−1 for ω1 (in the X state of CF2, 1171.1 vs. 1114.4 cm−1) and 171.6 cm−1 for ω3 (in the S1 state of FCH, 2971.3 vs. 2799.7 cm−1), which still correspond to 4.8% for ω1 and 5.7% for ω3, respectively. Experimentally, accurate determination of the vibrational frequencies relies heavily on the resolution of spectroscopic measurements. There exists quite large discrepancy in available experimental vibrational frequencies of FCX radicals. For instance, the ω3 frequency of the S1 state of FCH was recently reassigned to be 2799.7 cm−1,[16] instead of 2852 cm−1 measured by the same group using laser-induced fluorescence (LIF) spectroscopy [18]; the ω1 frequency of the S1 state of FCBr was 155.2 cm−1 difference between early LIF experiment,[35] and the recent one [37] (649 vs. 493.8 cm−1). On the other hand, the discrepancy of the calculated harmonic frequencies of the FCX radicals can reach as large as 120 cm−1, using different theoretical methods. To show the accuracy of our icMRCI+Q calculation, we compare in Table 3 the present calculated frequencies of FCBr with the recent experimental results, along with the most recent theoretical results. It is apparent that our high-level icMRCI+Q calculated frequencies are more consistent with the newest high-resolution experimental results.

Table 3. Comparison of the present calculated frequencies of FCBr with recent theoretical and experimental results.
 ω1ω2ω3
  1. [a]This work.

  2. [b]Ref. [ [45]

  3. [c]Ref. [ [49]

  4. [d]Ref. [ [52]

  5. [e]Ref. [ [35]

  6. [f]Ref. [ [37].

  7. All values are in cm−1.

Ground singlet state
icMRCI+Q/cc-pVTZ[a]679.0357.21225.8
QCISD/6–311G(d,p)[b]6353321155
MRCI/cc-pVTZ[c]7733611252
CASPT2/cc-pV5Z[d]640.7335.21164.1
CASSCF/cc-pVTZ[e]662.2360.31274.7
CASPT2/cc-pVTZ[e]641.7345.21258.0
Experiment671.2[e]/665.4[f]348.7[e]/349.5[f]1198[e]/1165.9[f]
First excited singlet state
icMRCI+Q /cc-pVTZ[a]496.7301.31233.6
MRCI/cc-pVTZ 2011[c]5793011267
CASPT2/cc-pV5Z[d]559.5315.91212.5
CASSCF/cc-pVTZ[e]553327.91270.2
MRCI/cc-pVTZ[e]577.1326.11260.3
Experiment649.5[e]/493.8[f]336.9[e]/303.7[f]1134[e]
Lowest triplet state
icMRCI+Q /cc-pVTZ[a]672.0321.81261.2
QCISD/6–311G(d,p)[b]6473101203
MRCI/cc-pVTZ[c]7343561291
CASSCF/cc-pVTZ[e]662.6320.71262.7

Regarding the triplet T1 states, the experimental frequencies were reported only for ω1 and ω3 of FCH [41] and CF2 [42], both using negative ion photoelectron spectroscopy. Our calculated results are in very good agreement with the experimental ones. No spectroscopic studies and only a few theoretical studies [44, 45, 48] were performed for FCI in the literature. Our high-level icMRCI+Q results would provide valuable references for further investigation the spectrum of the heavy-atom fluorine-substituted carbenes.

Transition energies of the S1 states and S-T gaps of FCX radicals

Table 4 lists the S1-X adiabatic transition energies (T00) of all FCX radicals calculated in this work at icMRCI+Q/cc-pV5Z level, along with recent calculated results and experimentally measured values. The T00 values of FCX covers a wide range from 17715 cm−1 for FCH to 37677 cm−1 for CF2. Previous Gaussian-2 and QCI calculation on a series of carbenes [45] and recent MRCI calculation on bromocarbenes [49] suggested that the T00 values of halogenated carbenes increases monotonically with increasing electronegativity of the substituted atoms. Our results on FCX show the same tendency, that is, T00 (FCH) < T00 (FCI) < T00 (FCBr) < T00 (FCCl) < T00 (CF2) as the electronegativity of substituted atoms H < I < Br < Cl < F.

Table 4. Adiabatic transition energies of fluorine-substituted carbenes.
 Adiabatic transition energy
CarbeneThis workCalculationPreviousExperiment
  1. [a]Ref. [ [51]

  2. [b]Ref. [ [54]

  3. [c]Ref. [ [9]

  4. [d]Ref. [ [11]

  5. [e]Ref. [ [28]

  6. [f]Ref. [ [29]

  7. [g]Ref. [ [30]

  8. [h]Ref. [ [47]

  9. [i]Ref. [ [31]

  10. [j]Ref. [ [49]

  11. [k]Ref. [ [35]

  12. [l]Ref. [ [52]

  13. [m]Ref. [ [37]

  14. [n]Ref. [ [48]

  15. [o]Ref. [ [44].

  16. [p]Ref. [ [33].

  17. All values are in cm−1.

FCH17,71516,763[a]/17,015[a]/16,434[a]/17,018.7[b]17,282[c]/17,277[d]
CF237,67735,282[e]/39,972[e]/38,060[e]37,216[f]/37,226[g]
FCCl24,68226,141[h]/25,278[h]/28,859[h]/20,692[h]25,284[i]/25,287[g]/25,278[p]
FCBr22,63423,437[j]/18,490[k]/23,328[l]23,271[m]/20,906[k]
FCI18,76916,237[n]/17,508[n]/16,959[o]

Experimental T00 values are available except for FCI. The results of different experimental studies on FCH,[9, 11] CF2,[29, 30] or FCCl [30, 31, 33] are consistent, giving almost identical T00 value of each radical with discrepancy less than 10 cm−1. On the contrary, previous calculation studies resulted in large deviations of T00 values with different calculation methods and/or different basis sets (see Table4). Our high-level icMRCI+Q/cc-pV5Z calculations are in good agreement with the experimental results, with discrepancy less than 600 cm−1 for T00 values of FCH, CF2, and FCCl. In regarding to FCBr, two LIF experiments concerning S1-X transition were reported in the literature with different T00 values. Early study by Knepp et al.[35] concluded the origin at 20,906 cm−1, which is 2416 cm−1 higher than their CASPT2/cc-PVTZ result. The origin was later reassigned to be 23271 cm−1 by LIF spectroscopy with sub-Doppler resolution,[37], which is consistent with the results of recent CASPT2/cc-pV5Z [52] and MRCI/cc-pVTZ [49] calculations. Our calculated T00 of FCBr at icMRCI+Q/cc-pV5Z level is 22,634 cm−1, which is 1728 cm−1 higher than that in ref. [35] but is 637 cm−1 lower than that in Ref. [37]. As discussed in the following section, our calculated T00 value of FCBr is in better agreement with the most recent experimental result if various correlation effects are included in the calculation. For heaviest FCI, the experimental T00 value is not available in the literature, and the difference between our calculation result and several previous theoretical results is large (ranged from 1200 to 2700 cm−1).

Our calculated S-T gaps of all FCX carbenes at icMRCI+Q/cc-pV5Z level are listed in Table 5. The result of FCH exhibits the smallest S-T gap (5276 cm−1) in all FCX carbenes, whereas that of CF2 gave the largest S-T gap (19957 cm−1). Same as the calculated T00 values shown in Table 4, the S-T gaps of FCX also increase monotonically with increasing electronegativity of the substituted atoms. This indicates stabilization of the singlet ground electronic states of FCX carbenes by the electronegative X atom, which may be explained by enhancement of the s character of the singlet's nonbonding orbital (σ-electron-withdrawing capacity of the halogen atoms), or inductive singlet stabilization by electron donation to the empty p orbital (π-electron-donating capacity of the halogen atoms).[45]

Table 5. S-T gaps of fluorine-substituted carbenes.
 S-T gap
CarbeneThis workCalculationPreviousExperiment
  1. [a]Ref. [ [51]

  2. [b]Ref. [ [55]

  3. [c]Ref. [ [54]

  4. [d]Ref. [ [41]

  5. [e]Ref. [ [28].

  6. [f]Ref. [ [42].

  7. [g]Ref. [ [47].

  8. [h]Ref. [ [53].

  9. [i]Ref. [ [49].

  10. [j]Ref. [ [45].

  11. [k]Ref. [ [40].

  12. All values are in cm−1.

FCH52764622[a]/5290[a]/4725[a]/3252[b]/3795[b]/4371.6[c]5210[d]/5140[k]
CF219,95719,753[b]/19,202[b]/17,332[e]/19,510[e]19828[f]
FCCl11,94212,339[b]/12,581[b]/12,769[g]/12,167[g]/12,972[h]
FCBr10,75910,090[b]/10,391[b]/11,418[i]
FCI87778744[b]/9129[b]/9480[b]/9153[j]/10240.3[j]

Also listed in Table 5 are available previous calculated and experimental results for comparison. Experimental values of the S-T gaps of FCX were determined by negative ion photoelectron spectroscopy for FCH [40, 41] and CF2. [42] Our calculated results are in relatively good agreement with experimental values, with discrepancy of ∼130 cm−1 for CF2 and less than 70 cm−1 for FCH. On the other hand, theoretical studies by different methods were employed for the S-T gaps of all FCX carbenes. Although the results are comparable, the deviation of the S-T gaps between different calculations could be as large as 10%, particularly for heavy-X carbenes.

Effects of basis sets and corrections on the icMRCI+Q calculations

For fluorine-substituted carbenes, especially heavy-atom ones, the choice of basis sets as well as various correlation effects are necessary to be considered in the calculation. In this section, we present additional icMRCI+Q calculations on FCBr with different basis sets and including scalar relativistic effect, CV correlation, and SOC effect, to show the effects on the calculated geometries, frequencies, and energies.

Effect of basis sets on the calculated geometries of FCBr

Table 6 shows the calculated equilibrium geometries of FCBr with cc-pVTZ, cc-pVQZ, and cc-pV5Z basis sets. The CBS geometries of FCBr, which were obtained from numerical optimization, are also included in the table. The starting geometries for CBS calculations were chosen as those from MRCI+Q/cc-pV5Z results. Comparing with recent MRCI/cc-pVTZ geometries of FCBr,[49] it is found that the effect of Davidson correction is not very significant for the ground state, with difference of 0.005 Å for the C[BOND]F bond length, 0.01 Å for the C[BOND]Br bond length, and 0.3° for the bond angle. The effect of Davidson correction is similar for the excited singlet state as for the ground state. For the triplet state, the effect of Davidson correction is even smaller.

Table 6. Calculated equilibrium geometry of FCBr at icMRCI+Q/cc-pVnZ (n = T, Q, 5, CBS) level.
 RC[BOND]F(Å)RC[BOND]Br(Å)∠F[BOND]C[BOND]X (°)
Ground singlet state
cc-pVTZ1.2961.939107.3
cc-pVQZ1.2951.929107.3
cc-pV5Z1.2951.923107.3
CBS1.2951.921107.2
Excited singlet state
cc-pVTZ1.3101.889125.5
cc-pVQZ1.3071.871125.8
cc-pV5Z1.3061.865125.9
CBS1.3051.862125.9
Triplet state
cc-pVTZ1.3161.861124.1
cc-pVQZ1.3141.853124.0
cc-pV5Z1.3131.850123.9
CBS1.3121.849123.9

Except for the calculated bond angle of the S1 state, the result of which increases as the basis set is increased, the calculated values of the bond length and the bond angle decrease as the basis sets change from cc-pVTZ to cc-pV5Z. The convergence behaviors for each geometrical parameter can be found as increasing of basis sets. Generally, the deviation between cc-pVQZ and cc-pV5Z level is less than that between cc-pVTZ and cc-pVQZ level, indicating that the accuracy is systemically improved by using larger basis set. By comparing results of cc-pV5Z and those of CBS, we found the bond distances and the bond angles converge in the magnitude order of 10−3 angstroms and 10−1 degrees. For the C[BOND]F bond length of each state, the difference between the cc-pVTZ result and the CBS result is less than 0.005 Å. On the other hand, the difference of the C[BOND]Br bond length or the bond angle calculated at cc-pVTZ level and CBS level is several times larger comparing to that of the C[BOND]F bond; the largest difference is 0.027 Å for the C[BOND]Br bond length, 0.4° for the bond angle in the S1 state. It seems that large basis set could be necessary for accurate determination of geometries of FCBr radical, which contains highly electronegative fluorine atom and high-Z bromine atom.

Effect of basis sets and corrections on the calculated energies of FCBr

To present the effect of basis sets as well as additional corrections on the calculated energies of the excited singlet state and the triplet state, we list in Table 7 the results of T00 and the S-T gap of FCBr calculated at icMRCI+Q/cc-pVTZ, icMRCI+Q/cc-pVQZ, icMRCI+Q/cc-pV5Z, and icMRCI+Q/CBS levels. Single-point energy calculations were based on the icMRCI+Q/CBS geometries. Corrections for scalar relativistic effect, CV correlation, and SOC effect are also included in the table. Those factors could be significant in calculated energies of heavy-atom halogenated carbenes.[55] It seems that a basis set of cc-pV5Z is large enough for energy calculation as the difference between cc-pV5Z and CBS results is only ∼20 cm−1 (∼0.09%) for T00 and ∼50 cm−1 (∼0.4%) for S-T gap.

Table 7. Adiabatic transition energy and S-T Gap of FCBr as a function of basis set.
FCBrT00S-T gap
  1. [a]MRCI+Q/cc-pVQZ-DK.

  2. [b]MRCI+Q/uncontracted cc-pVQZ.

  3. [c]Ref. [ [37].

  4. [d]Ref. [ [35].

  5. All values are in cm−1.

cc-pVTZ23,533.111,351.7
cc-pVQZ23,478.711,479.2
cc-pV5Z23,448.211,514.4
CBS23,428.911,566.6
+DK810.0[a]/162.7[b]3495.8[a]/200.2[b]
+CV−330. 3−564.1
+SOC8.77−39.56
Total23,917.4/23,270.114,458.7/11,163.1
Exp23,270[c]/20,906[d]

As shown in Table 7, the scalar relativistic effects for T00 and S-T gap of FCBr, calculated by icMRCI+Q method with cc-pVQZ-DK basis set, are quite large (810.0 and 3495.8 cm−1). We examined the scalar relativistic corrections using MRCI+Q/uncontracted cc-pVQZ method, and the corrections are 162.7 cm−1 for T00 and 200.2 cm−1 for S-T gap, which are close to the results for HCBr reported by Bacskay.[71] The CV correlations give additional corrections of −330.3 and −564.1 cm−1, for T00 and S-T gap, respectively. SOC effect gives a very minor correction, which was 8.77 and −39.56 cm−1, for T00 and S-T gap, respectively. The total T00 of FCBr (CBS+DK+CV+SOC) is improved to be 23,917.4 cm−1 if the scalar relativistic correction was calculated with cc-pVQZ-DK basis set, and 23,270.1 cm−1 if the scalar relativistic correction was calculated with uncontracted cc-pVQZ basis set. The latter is only 0.1 cm−1 difference from the newest experimental result.[37] Further insight study is necessary to investigate the dependence of the scalar relativistic corrections on basis sets.

Conclusions

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methodology
  5. Results and Discussion
  6. Conclusions
  7. Acknowledgment

In this work, we carried out a high-level icMRCI+Q study on the ground and the first excited singlet states as well as the lowest triplet state for a series of fluorine-substituted carbenes FCH, CF2, FCCl, FCBr, and FCI. Equilibrium geometries of the X, S1 and T1 states of all fluorine-substituted carbenes were determined at icMRCI+Q/cc-pV5Z level. The calculated geometries of our study and previous calculations using various methods are well consistent for FCH and CF2 radicals and in relative good agreement with available experimental results. The basis set effect on the calculated geometries of FCBr is examined; the results indicate that large basis set may be necessary for calculations of carbenes containing high-Z elements. Harmonic vibrational frequencies of the X, S1, and T1 states of all fluorine-substituted carbenes were calculated at icMRCI+Q/cc-pVTZ level, and compared with previous available experimental and theoretical results. Our high-level icMRCI+Q results are more consistent with the most recent measured vibrational frequencies by high-resolution experimental studies. The S1-X adiabatic transition energies (T00) and the S-T gaps of all FCX radicals were also calculated in this work at icMRCI/cc-pV5Z level. Both T00 and S-T gaps of FCX carbenes increase monotonically with increasing electronegativity of the substituted atoms. The effect of basis sets as well as the SOC effect, the scalar relativistic effect, and the CV correlation on the calculated T00 and S-T gaps of FCBr were investigated. The results indicate that while the basis sets and the SOC effect have a very minor correction on the calculated energies, the effects of scalar relativistic effect and CV correlation are quite significant for heavy FCX. In conclusion, our MRCI calculations provide comprehensive results at a consistent high level of calculation thus will add some understanding and shed more light on the electronic states for all of the fluorine-substituted carbenes.

Acknowledgment

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methodology
  5. Results and Discussion
  6. Conclusions
  7. Acknowledgment

The authors acknowledge the High Performance Computing Center (HPCC) of Jilin University for supercomputer time.