### Abstract

- Top of page
- Abstract
- Introduction
- Methodology
- Results and Discussion
- Conclusions
- 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

- Top of page
- Abstract
- Introduction
- Methodology
- Results and Discussion
- Conclusions
- 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 CH_{2}, 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 CF_{2} [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 CF_{2}. Because the early emission and absorption spectroscopic studies of CF_{2} 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] CF_{2,} [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 CF_{2} 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

- Top of page
- Abstract
- Introduction
- Methodology
- Results and Discussion
- Conclusions
- 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, *E*_{CAS} and the dynamical correlation energy (energy difference between MRCI+Q energy and CASSCF energy, *E*_{corr}). In the case of Dunning's correlation-consistent cc-pVXZ basis sets, the zeroth-order energies approaching their CBS limits are expressed as *E*_{CAS} (X) = *E*_{CAS} (CBS) + *a*_{o} exp(−*α*X) 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, Δ*E*_{CORR} (X) = Δ*E*_{CORR} (CBS) + a_{c}X^{−3},[64] and we used the data for X = T,Q to determine the extrapolated value ΔE_{CORR} (CBS). The total energy is the sum of *E*_{CAS} (CBS) and Δ*E*_{CORR} (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 (1–2^{1,3}(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]

### Conclusions

- Top of page
- Abstract
- Introduction
- Methodology
- Results and Discussion
- Conclusions
- 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, CF_{2}, FCCl, FCBr, and FCI. Equilibrium geometries of the X, *S*_{1} and *T*_{1} 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 CF_{2} 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, *S*_{1}, and *T*_{1} 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 *S*_{1}-X adiabatic transition energies (*T*_{00}) and the S-T gaps of all FCX radicals were also calculated in this work at icMRCI/cc-pV5Z level. Both *T*_{00} 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 *T*_{00} 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.