##
1Accurate *ab initio* determination of spectroscopic and thermochemical properties of mono- and dichlorocarbenes^{}
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Accurate

*ab initio*determination of spectroscopic and thermochemical properties of mono- and dichlorocarbenes^{}
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The best technically feasible values for the triplet–singlet energy gap and the enthalpies of formation of the HCCl and CCl

_{2}radicals have been determined through the focal-point approach.
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The electronic structure computations were based on high-level coupled cluster (CC) methods, up to quadruple excitations (CCSDTQ), and large-size correlation-consistent basis sets, ranging from aug-cc-pVDZ to aug-cc-pV6Z, followed by extrapolation to the complete basis set limit.

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Small corrections due to core correlation, relativistic effects, diagonal Born–Oppenheimer correction, as well as harmonic and anharmonic zero-point vibrational energy corrections have been taken into account.

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The final estimates for the triplet–singlet energy gap,

*T*_{0}(ã), are 2170 ± 40 cm^{−1}for HCCl and 7045 ± 60 cm^{−1}for CCl_{2}, favoring the singlet states in both cases.
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Complete quartic force fields in internal coordinates have been computed for both the X̃ and ã states of both radicals at the frozen-core CCSD(T)/aug-cc-pVQZ level.

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Using these force fields vibrational energy levels of {HCCl, DCCl, CCl

_{2}} up to {6000, 5000, 7000} cm^{−1}were calculated both by second-order vibrational perturbation theory (VPT2) and variationally.
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These results, especially the variational ones, show excellent agreement with the experimentally determined energy levels.

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The enthalpies of formation of HCCl (X̃

^{1}A^{′}) and CCl_{2}(X̃^{1}A_{1}), at 0 K, are 76.28 ± 0.20 and 54.54 ± 0.20 kcal mol^{−1}, respectively.
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## Introduction

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Carbenes are among the most important of reactive chemical intermediates.

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Moreover their chemistry is particularly fascinating because their lowest singlet and triplet states are expected to be closely spaced in energy but have quite different chemistries.

^{1–5}
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Therefore a precise determination of the singlet/triplet gap, Δ

*E*_{TS}, is important for understanding reaction mechanisms.
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For this reason, the determination of these energy gaps has attracted intense interest from quantum chemists and experimentalists alike.

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This paper will focus upon the study of the singlet/triplet gap of mono- and dichlorocarbene, HCCl and CCl

_{2}, respectively, by state-of-the-art quantum chemistry techniques.
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It will also report related thermodynamic and spectroscopic properties of these molecules.

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17

Nonetheless as the brief discussion below shows, there are still major discrepancies and unanswered questions.

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In this work, we strive to produce calculations of Δ

*E*_{TS}for both HCCl and CCl_{2}of “near-spectroscopic” accuracy.
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Moreover, we give reasonable estimates of the expected errors in these calculations.

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These calculations serve to increase the precision of previous calculations significantly.

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They are also expected to complement experimental work, which ultimately should produce a gold standard of measurement for Δ

*E*_{TS}.
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We believe that our calculations are sufficiently precise to guide in a detailed fashion experimental planning and ultimately to aid the acceptance or rejection of various experimental interpretations of the measured spectra.

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23

The first direct spectroscopic observation of HCCl/DCCl in the gas phase was reported in 1966 by Merer and Travis,

^{6}who have assigned the band system between 550 and 820 nm to the Ã^{1}A″ ← X̃^{1}A′ transition.
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All of these studies revealed strong and complicated perturbations caused by the Renner–Teller effect and spin–orbit coupling with the low-lying ã

^{3}A^{″}state.
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The first data on the X̃ state vibrational levels of HCCl, more specifically the

*ν*_{2}(HCCl bend) and the*ν*_{3}(CCl stretch) fundamentals were provided by matrix isolation infrared (IR) studies.^{7,18}
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These data were notably complemented by Chang

*et al*,^{13,14}who have identified six and 11 vibrational levels in the dispersed fluorescence spectra of HCCl and DCCl, respectively.
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A few years later the same group has re-recorded these spectra and assigned 19/24 vibrational levels of HCCl/DCCl in the X̃ state.

^{17}
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The analysis of these spectra resulted in effective rotational constants, centrifugal distortion constants, nuclear quadrupole interaction constants, and spin-rotation constants for these species.

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31

One of the interesting observations of

^{ref. 20}was that the spin-rotation constants make a significant contribution to the hyperfine structure due to the relatively low-lying Ã state.
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33

Later they revised this number to 4.2 ± 2.5 kcal mol

^{−1}.^{22}
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34

The analysis of the dispersed fluorescence spectra also resulted in triplet–singlet energy splitting values for HCCl and DCCl.

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35

In their first dispersed fluorescence reports Chang

*et al*,^{13,14}due to the lack of perturbations in the observed X̃ state vibrational levels, determined the low limits of the triplet–singlet energy splitting for HCCl/DCCl as ≈8/11 kcal mol^{−1}with an error estimate of ±2 kcal mol^{−1}.
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36

In their recently published paper,

^{17}which presented the analysis of new dispersed fluorescence spectra with much better signal-to-noise ratio, they have not only observed perturbations, but assigned some weak bands to the ã^{3}A^{″}state.
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37

The new, revised Δ

*E*_{TS}values were 6.20 ± 0.05 kcal mol^{−1}for HCCl and 6.25 ± 0.05 kcal mol^{−1}for DCCl.
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At present these values seem to be the most dependable experimental estimates of Δ

*E*_{TS}of HCCl.
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39

The first reliable

*ab initio*study on Δ*E*_{TS}of HCCl was published by Bauschlicher*et al*in .1977^{56}
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Although these calculations were carried out at a relatively low level of electronic structure theory, the singlet and triplet states were treated in a balanced manner,

*i.e.*Hartree–Fock theory was used for the triplet and the generalized valence bond (GVB 1/2) method for the singlet.
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These calculations resulted in Δ

*E*_{TS}= 1.6 kcal mol^{−1}.
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42

After this work the

*ab initio*prediction of the triplet–singlet gap of HCCl has evolved in the following way: 5.4 kcal mol^{−1}(1986),^{57}{5.8, 6.7, 5.6 ± 0.7, 9.3} kcal mol^{−1}(1987),^{58,59}{6.0, 6.4 ± 0.7} kcal mol^{−1}(1990),^{60}6.39 kcal mol^{−1}(1992),^{61}4.8 kcal mol^{−1}(1993),^{62}5.8 kcal mol^{−1}(1996),^{63}6.2 kcal mol^{−1}(1997),^{64}{9.0, 5.7} kcal mol^{−1}(1999),^{65}{0.9–6.6} kcal mol^{−1}(2000),^{66}{6.1, 6.6} kcal mol^{−1}(2000),^{67}{6.1, 6.8, 5.9} kcal mol^{−1}(2001).^{68}
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Considering the most dependable results

^{67,68}among these calculations the computational estimate of Δ*E*_{TS}is 6.4 ± 0.8 kcal mol^{−1}.
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44

The enthalpy of formation, Δ

_{f}*H*_{298}°, of HCCl was obtained experimentally by ion cyclotron resonance (ICR)^{45,46}and collision induced dynamics (CID)^{47}techniques, which resulted in 71 ± 5 kcal mol^{−1}(1985),^{45}75.7 ± 4.8 kcal mol^{−1}(1994),^{46}and 80.4 ± 2.8 kcal mol^{−1}(1997).^{47}
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All the available quantum chemical calculations

^{47,65,77,82}are consistent with these results, scattering between 75.3 and 77.4 kcal mol^{−1}.
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46

Among these predictions for Δ

_{f}*H*_{298}° the most reliable, 76.5 ± 1 kcal mol^{−1}, was obtained by basis set extrapolation of CCSD(T) energies and inclusion of scalar relativistic corrections.^{77}
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47

The first spectroscopic study on CCl

_{2}was carried out in 1967 in an Ar matrix by Milligan and Jacox.^{23}
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48

In this matrix isolation IR study the symmetric and the antisymmetric stretching frequencies, 748 and 721 cm

^{−1}for C^{35}Cl_{2}and 726 and 700 cm^{−1}for C^{35}Cl^{37}Cl, respectively, were obtained, but without an unambiguous assignment of which is which.
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49

A year later Andrews

^{24}performed a similar experiment and assigned the lower of these frequencies to the symmetric stretch (*ν*_{1}).
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51

The Ã

^{1}*B*_{1}← X̃^{1}A_{1}excitation energies have also been obtained,*T*_{0}=17 092 cm^{−1}in Ar, first from matrix isolation experiments.^{23,25–28}
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In 1977 Huie

*et al*^{29}recorded the laser-induced fluorescence (LIF) excitation spectrum of the Ã^{1}B_{1}← X̃^{1}A_{1}transition of CCl_{2}in the gas phase.
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This was followed by several other gas-phase laser

^{30–36,44}and synchrotron^{37,38}fluorescence excitation studies.
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54

Among these probably the most notable are the first rotationally resolved jet-cooled studies of Clouthier and Karolczak,

^{34,35}which yielded structural and vibrational parameters of the two lowest-lying singlet states.
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Since in these works the ground-state vibrational parameters were determined from the observed hot bands of the excitation spectra, these data were substantially refined by the analysis of the recently recorded

^{43,44}dispersed fluorescence spectra.
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These two papers together report 83 and 40 assigned X̃-state vibrational levels for C

^{35}Cl_{2}and C^{35}Cl^{37}Cl, respectively.
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Two microwave studies

^{39,40}on C^{35}Cl_{2}provided not only accurate rotational constants but also centrifugal distortion constants, elements of the complete nuclear quadrupole coupling tensor, and nuclear spin-rotation constants.
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58

Similarly to HCCl, the triplet–singlet energy splitting of CCl

_{2}was first estimated reliably*ab initio*by Bauschlicher*et al*^{56}Including this work the theoretical predictions between 1977 and 1999 started to converge to around 19–23 kcal mol^{−1}as follows: 13.5 kcal mol^{−1}(1977),^{56}19.1 kcal mol^{−1}(1979),^{70}21.9 kcal mol^{−1}(1985),^{71}{21.1, 23.2, 21.6 ± 1.4, 25.9} kcal mol^{−1}(1987),^{58,59}20.5 kcal mol^{−1}(1990),^{60}23.7 kcal mol^{−1}(1991),^{72}20.0 kcal mol^{−1}(1992),^{61}23.7 kcal mol^{−1}(1992),^{73}20.5 ± 1 kcal mol^{−1}(1993),^{62}19.7 kcal mol^{−1}(1996),^{63}21.0 kcal mol^{−1}(1999),^{74}and {23.1, 19.6} kcal mol^{−1}(1999).^{65}
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In this work they have determined the triplet–singlet energy splitting of CCl

_{2}to be 3 ± 3 kcal mol^{−1}.
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61

This has ignited a huge trepidation in the community of theoretically oriented chemists and inspired several groups to perform more accurate theoretical predictions and publish papers on the “surprising difference”

^{75}or on the “remarkable discrepancy between theory and experiment”^{66}including these new estimates for the triplet–singlet splitting: 19.5 ± 2 kcal mol^{−1}(2000),^{75}20.0 ± 1 kcal mol^{−1}(2000),^{76}{19.2, 20.9} kcal mol^{−1}(2000),^{77}{14.7–21.5} kcal mol^{−1}(2000),^{66}{21.0, 21.5, 19.9} kcal mol^{−1}(2001),^{68}19.8 kcal mol^{−1}(2003).^{80}
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62

Ideas have been put forward to reinterpret the “mystery state”

^{75}of the photoelectron spectrum.
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63

Lee

*et al*^{76}suggested that it could be an excited state of the anion or that the discrepancy could come from the errors fitting the Franck–Condon factors.
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64

McKee and Michl assumed,

^{81}and supported it with calculations, that the “mystery” band corresponds to the quartet state of CCl_{2}^{−}.
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65

Efforts to obtain a new experimental value for the triplet–singlet energy gap have also been made by analyzing the laser-induced dispersed fluorescence spectrum of CCl

_{2}.^{43}
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66

Although the spectrum of CCl

_{2}has been recorded up to 8500 cm^{−1}, due to its complexity,*e.g.*, the occurrence of Fermi resonances and an unfavorable signal-to-noise ratio, in the high-energy region it could be fully and unambiguously assigned to X̃-state vibrational levels “only” up to 5000 cm^{−1}.
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67

Hence, only a lower limit of 14 kcal mol

^{−1}could be determined from this experiment.
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68

The enthalpy of formation, Δ

_{f}*H*_{298}°, of CCl_{2}has been obtained experimentally in numerous ways including kinetic studies,^{48}electron impact experiments,^{49,53}ion cyclotron resonance techniques,^{45,50–52}collision induced dynamics studies,^{47,54}and by determination of the ionization potential.^{55}
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All the theoretical results

^{47,65,77–79,82,83}favor the higher value and predict Δ_{f}*H*_{298}° between 51 and 56 kcal mol^{−1}.
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In this study 54.48 ± 0.4 kcal mol

^{−1}was obtained for Δ_{f}*H*_{0}°, which, when combined with other reliable results,^{77}gives 54.8 ± 0.4 kcal mol^{−1}for Δ_{f}*H*_{298}°.
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74

For an even more detailed summary of the experimental and theoretical evaluations of the triplet–singlet energy splittings and enthalpies of formation of HCCl and CCl

_{2}see Tables S1–S4 of the electronic supplementary information (ESI).^{}
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The purpose of this paper is to reduce the uncertainty of the theoretical predictions for the above-discussed spectroscopic and thermochemical properties of the HCCl and CCl

_{2}radicals by using sophisticated theoretical techniques.
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76

Indeed we aim to approach “near-spectroscopic” accuracy,

*i.e.*, ±∼50 cm^{−1}for Δ*E*_{TS}.
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77

After the detailed description of the methodologies applied (Section II), we report in Section III the theoretical determination of the triplet–singlet energy gap [

*T*_{0}(ã)] of HCCl and CCl_{2}by employing the focal-point approach (FPA).^{86,87}
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78

Beyond the apparent accuracy of the FPA method its other advantage is that the uncertainty of its final energy predictions can be estimated reliably due to the systematic build-up of its composite calculations.

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79

In Section IV vibrational energy levels calculated both perturbationally and variationally from an accurate quartic force field representation of the potential energy surfaces (PESs) of HCCl and CCl

_{2}are presented.
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80

It is shown that due to the accuracy of these vibrational calculations they can help the further analysis of the dispersed fluorescence spectra, including the possible identification of the triplet state of CCl

_{2}.
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81

In Section V accurate

*ab initio*determination of the enthalpies of formation, Δ_{f}*H*_{T}°, of HCCl and CCl_{2}is described, utilizing FPA results of this study and related existing high-quality thermochemical data.^{88–92}
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The paper is concluded by a short summary detailing the possible impact of the new theoretical data on subsequent experiments.

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## Computational details

### Electronic structure calculations

83

As it is mentioned in the Introduction the electronic structure calculations have been carried out according to the recipe of the so-called focal-point approach documented well in recent publications.

^{86,87}
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84

Therefore, it is not described here in detail.

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However, the structure of the rest of this section is organized in a way to follow the major steps of FPA and give insight for a reader not familiar with this approach.

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Type: Experiment |
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87

Reference electronic wave functions have been determined by the single-configuration restricted-open-shell Hartree–Fock (ROHF) method.

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88

In the case of CCl

_{2}the computations have been repeated using an unrestricted Hartree–Fock (UHF) reference, as well.
Type: Experiment |
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89

Electron correlation was accounted for by standard methods of electronic structure theory: second-order Møller–Plesset (MP2) perturbation theory,

^{99}and the coupled cluster (CC) series, including single and double (CCSD),^{100}single, double and perturbatively estimated triple [CCSD(T)],^{101}single, double and triple (CCSDT),^{102,103}and single, double, triple and quadruple excitations (CCSDTQ).^{104,105}
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90

In the valence-only correlated-level calculations the 1s orbital of C and the 1s, 2s, and 2p orbitals of Cl were kept doubly occupied.

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91

No virtual molecular orbitals were kept frozen in any of the calculations.

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92

Relativistic electronic energy corrections were determined by the 1-electron mass-velocity–Darwin (MVD1)

^{106,107}and the second-order Douglas–Kroll–Hess [DKH(2)]^{108–112}methods.
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94

Computation of the mass-dependent diagonal Born–Oppenheimer correction (DBOC) was performed by the BORN program operating within the PSI 2 program package at the Hartree–Fock level, using the formalism of Handy, Yamaguchi and Schaefer.

^{115}
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95

The one-particle basis sets chosen for the frozen-core correlation calculations include the correlation-consistent (aug)-cc-pV

*X*Z,*X*= 2(D), 3(T), 4(Q), 5, and 6, basis sets developed by Dunning and co-workers.^{116,117}
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Type: Experiment |
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97

All-electron correlation calculations have been carried out using the (aug)-cc-pCV

*X*Z sets,^{120,121}which are able to describe the core region adequately.
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98

Estimation of the complete basis set (CBS) limits have been performed by well-established extrapolation formulas, namely by an exponential formula,

^{122}*E*^{X}=*E*_{CBS}+*a*exp(−*bX*)in the case of HF and an inverse power formula,^{123}*E*^{X}=*E*_{CBS}+*cX*^{−3}for both the frozen-core and all-electron correlated energy increments.
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99

For DBOC energy correction calculations the Dunning–Huzinaga-type DZP and TZ2P basis sets

^{124}have been used.
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100

Reference geometries of CCl

_{2}and HCCl for the single-point energy calculations within the focal-point approach and for the force field calculations have been obtained by geometry optimization at the all-electron CCSD(T)/aug-cc-pCVTZ level of theory.
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101

The related structural parameters are collected in Table 1.

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102

Quartic (and partial sextic) force fields in (stretch, stretch, bend) internal coordinates have been determined by finite differentiation of frozen-core CCSD(T)/aug-cc-pVQZ energy values.

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ConceptID: Mod6

103

This level of electronic structure theory was chosen because it represents a well-known Pauling-point in the computational armamentarium, and according to our experience it provides an almost as good local PES as the best state-of-the-art

*ab initio*surfaces (*i.e.*CBS extrapolated and augmented by auxiliary corrections)^{125}.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met4

### Vibrational energy level calculations

104

Vibrational energy levels were computed using formulas based on second-order vibrational perturbational theory (VPT2)

^{126–129}and by an approximately variational discrete variable representation (DVR)^{130–132}technique.^{133}
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod7

105

The VPT2 calculations were performed using the ANHARM

^{128}program package.
Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp5

106

Since the geometry optimizations and the force field calculations have been performed at different levels of theory, the force fields included non-zero forces.

Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod8

107

The (stretch, stretch, bend) quartic force fields were first transformed to (SPF, SPF, bend) coordinates, where SPF stands for Simons–Parr–Finlan

^{134}coordinates, where the forces were neglected, then to Cartesian coordinates, the necessary inputs of ANHARM.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod8

108

The variational calculations were performed with the program DOPI3,

^{133}where DOPI stands for DVR (D)—Hamiltonian in orthogonal (O) coordinates—direct product (P) basis—iterative (I) sparse Lanczos eigensolver.
Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp6

109

The PES for the variational calculations was built using force constants in the quartic (SPF, SPF, bend) representation, where the non-zero forces were not neglected in the expansion of the potential.

Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod9

110

The use of the quartic force field in SPF coordinates was chosen because according to previous results

^{133,134}(i) employing an SPF representation instead of the simple stretch representation results in better agreement between the variationally computed and the experimental energy levels; and (ii) the quartic and sextic force fields in SPF coordinates result in highly similar energy levels.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met5

111

All the vibrational energies presented were converged to better than 0.01 cm

^{−1}.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs1

112

In some variational calculations the quintic and sextic diagonal bending internal coordinate force constants have also been included to improve the description of the bending motion.

Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp7

113

All the necessary force field transformations both for the VPT2 and the variational calculations have been carried out with the help of the INTDER

^{135–137}program.
Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp8

## Triplet–singlet energy gap

### HCCl and DCCl

114

The valence-only FPA results for the triplet–singlet energy splitting of HCCl are summarized in Table 2.

Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs2

115

From the data presented the following conclusions, similar to those found for CH

_{2},^{138}can be drawn: (i) Both the extension of the one-particle basis set and the electron correlation treatment systematically lowers the energy of the singlet state with respect to the triplet state.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con5

116

(ii) The HF triplet–singlet energy splitting is fairly independent of the size of the one-particle basis set, it changes only 276 cm

^{−1}between the aug-cc-pVDZ and the CBS limit.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con5

117

Convergence of the higher-order electron correlation contributions, δCCSD(T)

^{139}and above, with the one-particle basis set is even faster.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con5

118

(iii) The δMP2 and δCCSD contributions converge rather slowly, the change of their absolute value from the aug-cc-pCVDZ basis set to the CBS limit is 977 and 522 cm

^{−1}, respectively.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con5

119

(iv) The well-known imbalanced treatment of the two electronic states at the HF level of theory is slowly corrected as the single-reference electron correlation treatment is improved.

Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con5

120

This is well demonstrated by the extremely large δCCSD(T) contribution, 691 cm

^{−1}at the CBS limit.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con5

121

Nevertheless, the δCCSDTQ increment is comfortably small, +47 cm

^{−1}.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res6

122

Our final estimate for the valence-only triplet–singlet energy gap is 2205 ± 35 cm

^{−1}.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res7

123

Furthermore, again similarly to observations for CH

_{2},^{138}inclusion of core correlation is important, it considerably stabilizes the triplet state with respect to the singlet state (see Table 3).
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res8

124

It is also in good correspondence with the observations for CH

_{2}and other previous studies that, due to the opposite signs of the δCCSD and the δCCSD(T) contributions the MP2 level of theory, with a large enough (*e.g.*, cc-pCVQZ) basis set, estimates well the converged core correlation contribution, which is determined in this study to be −146 ± 20 cm^{−1}.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con6

125

Since the contribution of the relativistic effects is expected to be more important in the case of HCCl than in CH

_{2}it was computed in a somewhat more careful manner.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met6

126

First, the one-electron scalar contribution was obtained by the MVD1 perturbation method using the ROHF wave function.

Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met6

127

This was then augmented by the difference of the DKH(2) and the MVD1 results calculated also at the ROHF level.

Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met6

128

Although the two methods approximate the Dirac–Coulomb Hamiltonian by different partitioning schemes, due to the effective treatment of the first- and second-row elements by these relativistic perturbation techniques this difference basically covers the two-electron scalar and spin–orbit relativistic corrections within the Dirac–Coulomb Hamiltonian.

Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac14

129

Finally, the electron correlation contribution to the one-electron scalar terms were obtained as the difference of the ROHF and CCSD(T) MVD1 results.

Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met6

130

As can be seen from Table 4 the relativistic correction calculated by MVD1 perturbation theory and an ROHF wave function estimates the final result well, both the two-electron and the electron-correlation contributions to the total relativistic correction are small.

Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res9

131

Our final estimate of the relativistic corrections to Δ

*E*_{TS}is +54 ± 10 cm^{−1}.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con7

132

As expected, the diagonal Born–Oppenheimer correction (DBOC) to the triplet–singlet energy gap of HCCl/DCCl is smaller (see Table 5) than it was found for CH

_{2}.^{138}
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con8

133

Our best estimate is +10 ± 4 cm

^{−1}and +8 ± 4 cm^{−1}for HCCl and DCCl, respectively.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con8

134

(The isotopologs containing

^{35}Cl and^{37}Cl have the same BODC energy corrections to within 1 cm^{−1}).
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac15

135

The zero-point vibrational energy (ZPE) corrections have been computed both by the VPT2 and the variational methods (see Table 6).

Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met7

136

The total VPT2 ZPE value can be calculated by the following formula:where the three terms are the

*G*_{0}, the harmonic, and the anharmonic contributions, respectively.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod10

137

(A correct analytic formula for the computation of the

*G*_{0}term from quartic force fields for asymmetric tops has been derived by Allen*et al.*^{140})
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod10

138

As can be seen from Table 6, the anharmonic and the

*G*_{0}contributions to the triplet–singlet energy splitting are only on the order of 1–2 cm^{−1}.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs3

139

Furthermore, the total VPT2 ZPE correction agrees with the variational results to about 1 cm

^{−1}.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res10

140

Similarly to findings for CH

_{2},^{138}the ZPE correction is larger for the triplet state, the numerical results for the HCCl and DCCl radicals are 47 and 50 cm^{−1}, respectively.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res11

141

Our error estimate for the ZPE correction is ±5 cm

^{−1}.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res11

142

To obtain the best estimate for

*T*_{0}(ã), one sums the lowest, rightmost numbers in Tables 2–4 and the corresponding bottommost numbers in Tables 5 and 6.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met8

143

The resulting values of HCCl and DCCl are 2170 ± 40 cm

^{−1}(6.204 ± 0.114 kcal mol^{−1}) and 2171 ± 40 cm^{−1}(6.207 ± 0.114 kcal mol^{−1}), respectively.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res12

144

These estimates are in an excellent agreement with the recently revised experimental value, 2167/2187 ± 18 cm

^{−1}for HCCl/DCCl, of Chang*et al*^{17}On the other hand, the experimentally obtained difference of*T*_{0}(ã) of HCCl and DCCl is considerably larger than the theoretically computed difference.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con9

145

A possible source of this apparent discrepancy is the assigned error bar of the experimental observations, which is comparable to the difference of the two

*T*_{0}(ã) values.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con9

146

An alternative explanation is offered if a relatively large spin–vibronic perturbation existed between the singlet and triplet states, and it is different for the two species.

Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con9

147

Although this perturbation is not included in our theoretical treatment, the estimation of the magnitude of this perturbation, based on the comparison of the computed and the experimentally observed vibrational levels, will be discussed in Section V.1.

Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con9

### CCl_{2}

148

Since the technical details and the qualitative observations during determination of the triplet–singlet energy gap of CCl

_{2}by the FPA were similar to those for CH_{2}and HCCl, here we mostly concentrate on the differences and the tendencies in the CH_{2}/HCCl/CCl_{2}substitution series.
Type: Object |
Advantage: None |
Novelty: New |
ConceptID: Obj7

149

Convergence of the valence-only energy difference of the singlet and triplet states of CCl

_{2}with the correlation level is similarly slow (see Table 7) as observed for CH_{2}and HCCl.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res13

150

Consequently, to get accurate valence-only estimates higher-order electron correlation contributions have to be determined in this case, as well.

Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met9

151

At the same time, it is much more demanding to perform higher-order correlation calculations for CCl

_{2}than for the smaller HCCl and CH_{2}systems.
Type: Method |
Advantage: No |
Novelty: New |
ConceptID: Met9

152

Practically we were able to carry out CCSDT calculations only with the aug-cc-pVDZ and the ‘old’ (

*i.e.*one less d orbital on Cl) cc-pVTZ basis set, while CCSDTQ calculations were limited to the ‘old’ cc-pVDZ basis set of Dunning.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs4

153

Although for CH

_{2}and HCCl we found that the post-CCSD(T) electron-correlation contributions are small, and their CBS values can be estimated relatively accurately using small basis sets, it is desirable to check in an independent way whether the same holds for CCl_{2}.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res14

154

A well-established way to do this is the comparison of the correlation series using ROHF and UHF references.

^{141}
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met10

155

It was found in many cases that the convergence with the correlation level is significantly different in the two cases.

Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res15

156

In these situations, since both series converge ultimately to the same valence-only limit, the difference of the restricted and unrestricted methods at the same computational level indicates the uncertainty of the calculations due to the neglect of higher-order correlations.

Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con10

157

In the case of CCl

_{2}the obtained CBS result for {Δ*E*_{TS}(HF), Δ*E*_{TS}(MP2), Δ*E*_{TS}(CCSD), Δ*E*_{TS}[CCSD(T)]} is {–22, 6660, 5896, 6997} cm^{−1}using an ROHF reference (see Table 7), and {–1710, 6922, 5864, 7021} cm^{−1}when an UHF reference is used.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res16

158

This reveals that in spite of the large deviation, 1688 cm

^{−1}, observed at the HF level, the two CBS CCSD(T) values agree within 24 cm^{−1}.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res16

159

From this we expect that the contribution of the post-CCSD(T) electron correlation is on the order of a few tens of cm

^{−1}.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con11

160

Since this contribution is relatively small and the δCCSD(T) contribution converges relatively fast with the basis set size to CBS limit, it is expected that post-CCSD(T) electron correlation contributions are well estimated by CCSDT and CCSDTQ calculations even using small basis sets.

Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con12

161

Consequently, we allocate an 50 cm

^{−1}error bar to the 7050 cm^{−1}valence-only result of the triplet–singlet energy splitting of CCl_{2}.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con12

162

Inclusion of core correlation (Tables 3 and 8) and relativistic effects (Tables 4 and 9) are becoming more and more important as one goes from the lighter to the heavier species.

Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res17

163

Together with this the contribution of their cross term, namely the difference between the correlated and non-correlated one-electron scalar relativistic effects, is also increasing.

Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res18

164

This cross term is three times larger in CCl

_{2}than in HCCl.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs5

165

Our best numerical estimates for the core correlation and the relativistic correction of the triplet–singlet energy gap of CCl

_{2}are −176 ± 25 cm^{−1}and +91 ± 15 cm^{−1}, respectively.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res19

166

As expected, the DBOC contribution (see Table 5) to the triplet–singlet energy gap is decreasing in the CH

_{2}, HCCl (DCCl), and CCl_{2}series.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res20

167

The DBOC contribution, in the case of CCl

_{2}, is only 5 ± 2 cm^{−1}.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res20

168

In contrast to this, the ZPE contribution of the total

*T*_{0}(ã) value, +75 ± 5 cm^{−1}(see Table 6), of CCl_{2}is in between the corresponding values obtained for CH_{2}and HCCl/DCCl.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res21

169

The final estimate of this study for

*T*_{0}(ã) of CCl_{2}is obtained by summing the lowest, rightmost numbers in Tables 5–9.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met11

170

The resulting value is 7045 ± 60 cm

^{−1}(20.13 ± 0.17 kcal mol^{−1}).
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res22

171

This estimate is in good agreement with other recent

*ab initio*predictions, but the assigned error bar of the theoretical prediction is reduced by an order of magnitude.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con13

Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con13

## Vibrational energy levels

173

The VPT2 vibrational parameters of the X̃ and ã states of HC

^{35}Cl, DC^{35}Cl, and C^{35}Cl_{2}are listed in Table 10.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs6

174

The vibrational levels obtained by substituting these parameters into the anharmonic oscillator equation of a triatomic molecule,are given in Tables .11–16

^{142}
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res23

175

These tables also contain the vibrational levels obtained by variational calculations and from experiments.

Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res23

176

Some further converged variational results as well as results for other isotopologs can be found in the ESI.

^{}
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs7

### HCCl and DCCl

177

The vibrational energy levels of singlet HCCl and DCCl computed variationally from the quartic force field (see the Var4 columns of Tables 11 and 13) show excellent agreement with the experimentally observed levels up to 3000 cm

^{−1}.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res24

178

The root-mean-square (rms) errors calculated from the first eight and 12 vibrational levels of HCCl and DCCl are 3.6 and 4.5 cm

^{−1}, respectively.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res25

179

Although the corresponding rms errors of the perturbationally obtained energy levels are somewhat larger, 5.4 and 5.9 cm

^{−1}, this still can be considered as a fine performance for a simple, purely theoretical treatment.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con14

180

Above 3000 cm

^{−1}the situation is, however, quite different.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con15

181

The Var4 results for the vibrational energy levels involving small bending quantum numbers still agree very well with the experimental data, while highly excited bending modes show significant (>15 cm

^{−1}) deviation from the experimental observations.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con15

182

In order to understand the source of this error we have added the pure fifth- and sixth-order bending force constants to the quartic force field and reran the variational calculations using this augmented force field (see the Var4

^{+}columns of Tables 11 and 13).
Type: Goal |
Advantage: None |
Novelty: None |
ConceptID: Goa4

183

As it is expected, the predicted Var4 and Var4

^{+}vibrational energy levels are the same within 1 cm^{−1}for modes with small*n*_{2}vibrational quantum numbers.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res26

184

On the other hand, the Var4 and Var4

^{+}results for highly excited bending modes are rather different, the Var4^{+}energy levels are 15–40% closer to the experimental values than the corresponding Var4 ones.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res27

185

The importance of the inclusion of the higher order bending force constants is connected to the fact that the barrier to linearity of HCCl in its X̃ state is relatively low, 17 766 cm

^{−1}at the all-electron CCSD(T)/aug-cc-pCVTZ level.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con16

186

Somewhat surprisingly the perturbational predictions, which of course utilize the quartic force fields only, are better for the highly excited bending modes than the variational results.

Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con17

187

Nevertheless, this seems to be a consequence of fortuitous cancellation of errors in this region, since the errors of the perturbationally obtained vibrational energy levels of modes with low bending excitation have opposite signs.

Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con17

188

In

^{ref. 17}Chang*et al*discussed the spin–vibronic coupling and the perturbation between certain vibrational levels of the X̃ and ã states.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac16

189

They have estimated the magnitude of these perturbations by the difference between the experimentally determined vibrational levels and the vibrational levels calculated from fitted effective spectroscopic parameters, when only the unperturbed levels were included in the preceding fit.

Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac16

190

In this paper we estimate these spin–vibronic perturbations a similar way, but instead of the fitted expansion we use the Var4

^{+}results.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met12

191

Although the variationally obtained vibrational levels have somewhat larger errors than the levels obtained by the use of the fitted expansion, determination of the perturbations from the variational results has certain advantages.

Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met12

192

First, one does not need to consider prior to the fit which levels are perturbed and which are not and hence all appropriate levels can be considered.

Type: Method |
Advantage: Yes |
Novelty: New |
ConceptID: Met12

193

Second, the variational method, unlike the second-order expansion of the anharmonic oscillator model, treats exactly the resonances between the vibrational levels belonging to the same electronic state.

Type: Method |
Advantage: Yes |
Novelty: New |
ConceptID: Met12

194

Finally, it is noted that larger errors can be by-passed if they are systematic for a given series.

Type: Method |
Advantage: Yes |
Novelty: New |
ConceptID: Met12

195

Chang

*et al*^{17}pointed out large perturbations with given ã-state vibrational levels for the X̃(0,2,0), X̃(0,2,1), and X̃(0,2,2) vibrational levels of HCCl and for the X̃(0,4,0) and the X̃(0,4,1) levels of DCCl.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac17

196

From our calculations the errors of the Var4

^{+}results for the X̃(0,*n*_{2},0) energy levels of HCCl (Table 11) are {+5, −2, +8, +11} cm^{−1}for*n*_{2}={1,2,3,4}.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res28

197

If the trend in the errors is systematic, one would expect a +6 – +7 cm

^{−1}error for the X̃(0,2,0) mode.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res28

198

From this we can deduce an 8–9 cm

^{−1}perturbation between the X̃(0,2,0) level at 2383 cm^{−1}(experimental, Table 11) and the close-lying ã(0,0,0) level at 2167 cm^{−1}(experimental).
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res29

199

This perturbation lowers the energy of ã(0,0,0), in other words the unperturbed

*T*_{0}(ã) of HCCl is larger than the experimentally observed value.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res29

200

Consequently the difference (see Section III.1) between the experimentally determined (20 cm

^{−1}) and the calculated (1 cm^{−1}) difference of the*T*_{0}(ã) of HCCl and DCCl would be slightly smaller if the computed values included spin–vibronic interactions.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con18

201

In a similar way, considering the error series of the calculated X̃(0,

*n*_{2},1) vibrational levels ({0, +3, −4, +4} for*n*_{2}= 0,1,2,3), a smaller, roughly +4 cm^{−1}energy increase would be obtained for the X̃(0,2,1) vibrational level at 3181 cm^{−1}(experimental, Table 11) due to the interaction with the ã(0,1,0) and/or the ã(0,0,1) vibrational levels at 3050 cm^{−1}and 3110 cm^{−1}(experimental*T*_{0}(ã) + Var4^{+}vibrational level), respectively.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con18

202

It is evident that the X̃(0,2,2) level of HCCl at 3976 cm

^{−1}can be perturbed by the close-lying ã(0,2,0) and the ã(0,1,1) vibrational levels at 3915 cm^{−1}and 3983 cm^{−1}(experimental*T*_{0}(ã) + Var4^{+}vibrational level), respectively.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con19

203

Unfortunately, the fourth member of the X̃(0,

*n*_{2},2) series already falls in the region where the accuracy of the variational calculations is not sufficient to be included in the error series.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con19

204

From the fist three members, {−3, −6, −17}, of this error series only a very rough estimate of the perturbation effects can be determined, for X̃(0,2,2), 6–10 cm

^{−1}.
Type: Conclusion |
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205

Similarly to this, both the X̃(0,4,0) and the X̃(0,4,1) levels of DCCl fall in the energy region where the accuracy of the present variational calculations starts to deteriorate, consequently no reliable estimate of the perturbation effects can be determined based on the present data.

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206

There are no experimental data available on the vibrational energy levels of triplet HCCl, and only two vibrationally excited energy levels in the ã state of DCCl were observed experimentally.

^{17}
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207

For these two vibrational levels of DCCl the calculated data and the experimental values agree to within 6–15 cm

^{−1}.
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208

Again, this discrepancy, at least partially, might be caused by spin–vibronic interaction between the singlet and triplet states.

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### CCl_{2}

209

As expected, the variationally calculated vibrational levels of singlet CCl

_{2}show an even better agreement with the experimental observations than it was found for HCCl and DCCl.
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210

Comparing the Var4 energy levels up to 4000 cm

^{−1}to the experimental data of Liu*et al*^{43}results in an rms error of 2.6 cm^{−1}, which is even less than the assigned uncertainty, ±3 cm^{−1}, of the experimental data.
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211

The deviation of the Var4 results from the experimental data set of Kable

*et al*^{44}is somewhat worse, the rms error is 6.9 cm^{−1}for the same region.
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212

The rms error calculated from comparing the Liu

*et al*^{43}data set with the VPT2 results is even larger, it is 9.7 cm^{−1}.
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213

In the former case the larger rms error is probably due to the lower precision of the experimental data set, while in the latter case it is the consequence of the less accurate theoretical treatment,

*i.e.*, perturbational*vs*. variational, of the nuclear motion problem.
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214

As it is expected, no perturbation due to spin–vibronic interaction with the triplet state can be found up to 4000 cm

^{−1}, since the calculated triplet–singlet energy gap is well above this energy region.
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215

Although further converged Var4 results are available in the ESI,

^{}due to the high density of vibrational levels above 4000 cm^{−1}the assignment of these energy states to given vibrational quantum numbers is ambiguous without detailed wave function analysis.
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216

This was omitted in the present study.

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217

The calculated vibrational levels of triplet C

^{35}Cl_{2}are summarized in Table 15.
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218

Considering the excellent performance of the Var4 results for the singlet state, the predictions for the triplet state are expected to be similarly good, which could help the further analysis of the experimental data, including the determination of

*T*_{0}(ã).
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219

Some suggested directions for future experiments utilizing these computed data will be discussed briefly in Section VI.

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## Enthalpies of formation

220

Utilizing the high-quality

*ab initio*results described above, the enthalpies of formation of HCCl(X̃^{1}A′) and CCl_{2}(X̃^{1}A_{1}) at 0 K have been determined by calculating the enthalpy change of the reactionsCH_{2}(ã^{1}A_{1}) + HCl(X̃^{1}Σ^{+}) → HCCl(X̃^{1}A′) + H_{2}(X̃^{1}Σ_{g})andCH_{2}(ã^{1}A_{1}) + 2HCl(X̃^{1}Σ^{+}) → CCl_{2}(X̃^{1}A_{1}) + 2 H_{2}(X̃^{1}Σ_{g})
Type: Model |
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221

For the enthalpies of formation of HCl(X̃

^{1}Σ^{+}), H_{2}(X̃^{1}Σ_{g}), and CH_{2}(ã^{1}A_{1}), required to evaluate Δ_{f}*H*_{0}° (HCCl) and Δ_{f}*H*_{0}° (CCl_{2}), see Table 17.
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222

The advantages of this procedure over calculating the appropriate atomization energies lies in that (i) the contribution of the spin–orbit effect can be neglected since it is much smaller for a non-linear open-shell species than for an atom; and (ii) the errors due to neglecting higher-order correlation effects (

*e.g.*δCCSDTQP) is expected to cancel out in a proper reaction scheme.
Type: Method |
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ConceptID: Met13

### HCCl

Type: Result |
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224

Due to the abovementioned error compensation of the total energy of CH

_{2}(ã^{1}A_{1}) and HCCl(X̃^{1}A′) the enthalpy change of reaction (5) is expected to be estimated to better than ±0.1 kcal mol^{−1}.
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225

A larger part of the uncertainty of the present calculation comes from the uncertainty of Δ

_{f}*H*_{0}° of CH_{2}(ã^{1}A_{1}) and a smaller portion from the uncertainty of Δ_{f}*H*_{0}° of HCl(X̃^{1}Σ^{+}).
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226

Since these uncertainties are ±0.16 and ±0.024 kcal mol

^{−1}, respectively, we allocate a ±0.20 kcal mol^{−1}uncertainty to our final value of Δ_{f}*H*_{0}° (HCCl).
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227

Utilizing the calculated thermal correction, Δ

_{f}*H*_{298}° − Δ_{f}*H*_{0}° = 0.07 kcal mol^{−1}, of^{ref. 77}. results in 76.35 ± 0.20 kcal mol^{−1}for Δ_{f}*H*_{298}° of HCCl(X̃^{1}A′).
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228

The uncertainty of the present result is smaller by a factor of five than the uncertainty of the former highest-level calculation,

^{77}and more than an order of magnitude smaller than the values obtained by experiments^{45–47}or reported in the available thermochemical databases^{143–146}.
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### CCl_{2}

229

The enthalpy of formation of CCl

_{2}(X̃^{1}A_{1}) at 0 K, Δ_{f}*H*_{0}° (CCl_{2}), calculated through Reaction (6), is 54.54 kcal mol^{−1}.
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230

From considerations analogues to those given in Section V.1. the uncertainty of this value is ±0.20 kcal mol

^{−1}.
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231

The thermal correction of the enthalpy of formation of CCl

_{2}(X̃^{1}A_{1}) can be obtained as follows: Δ_{f}*H*_{298}° − Δ_{f}*H*_{0}°[CCl_{2}] (X̃^{1}A_{1})] = {*H*_{298}−*H*_{0}[CCl_{2}(X̃^{1}A_{1})]} − {*H*_{298}−*H*_{0}[C_{graphite}]} − {[Cl_{2}(X̃^{1}Σ_{g})]} = {2.737}^{90}− {2.194}^{90}− {0.251}^{79}kcal mol^{−1}= 0.292 kcal mol^{−1}.
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232

This value is equal to the calculated value of

^{ref. 77}, and it results in 54.83 ± 0.20 kcal mol^{−1}for Δ_{f}*H*_{298}° of CCl_{2}(X̃^{1}A_{1}).
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233

The present result is in excellent agreement with the recent W2 computation of Demaison

*et al*^{79}Furthermore, due to the inclusion of higher-order correlation effects in its computation in this study and utilization of a reaction scheme instead of atomization energies it was possible to reduce the uncertainty of the theoretical predictions by a factor of two.
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234

Note that the present value, as well as recently published theoretical values,

^{78,79}have at least an order of magnitude smaller uncertainty than the values given in the available thermochemical databases^{143–148}.
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## Summary and outlook

235

In this paper the best technically feasible values for the triplet–singlet energy gap of the HCCl/DCCl and CCl

_{2}radicals have been determined through the focal-point approach.
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236

The final estimates for the triplet–singlet energy gap,

*T*_{0}(ã), are 2170 ± 40/2171 ± 40 cm^{−1}for HCCl/DCCl and 7045 ± 60 cm^{−1}for CCl_{2}.
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237

The estimate for HCCl is in very good agreement with the recently revised experimental value, 2167/2187 ± 18 cm

^{−1}for HCCl/DCCl, of Chang*et al*,^{17}while the estimate for CCl_{2}supports alternative reassessments^{76,81}of the photodetachment spectrum of CCl_{2}^{−}over the original assignment,^{42}as well as the experimental lower limit value of*T*_{0}(ã) suggested by Liu*et al*^{43}
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238

Complete quartic force fields in internal coordinates have been computed for both the X̃ and ã states of both radicals at the frozen-core CCSD(T)/aug-cc-pVQZ level.

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239

Using these force fields vibrational energy levels were computed both by second-order vibrational perturbation theory and variationally.

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240

These results, especially the variational ones, show excellent agreement with the experimentally determined energy levels.

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241

The accuracy of these calculations and the systematic behavior of errors of vibrational progressions allowed us to determine the extent of perturbations due to spin–vibronic coupling between singlet and triplet vibrational levels of HCCl.

Type: Conclusion |
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242

In agreement with Chang

*et al*,^{17}significant perturbations, as much as 4–12 cm^{−1}are observed for the X̃(0,2,0), X̃(0,2,1), and X̃(0,2,2) vibrational levels.
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243

From the accurate theoretical values the enthalpies of formation of HCCl(X̃

^{1}A′) and CCl_{2}(X̃^{1}A_{1}) were determined at 0 K, which are 76.28 ± 0.20 and 54.54 ± 0.20 kcal mol^{−1}, respectively.
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244

These results are in good agreement with other recent calculations.

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245

Furthermore, the uncertainties of the present results are smaller by a factor of 2–5 than the uncertainties of even the best of the former theoretical values, and more than an order of magnitude smaller than Δ

_{f}*H*_{0}° given in the available thermochemical databases.
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246

It is worthwhile checking if the available dispersed fluorescence spectrum above 7000 cm

^{−1}(see Fig. 1) is consistent or inconsistent with the computed*T*_{0}(ã) and the ã state vibrational levels of CCl_{2}.
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247

Within the error bar of the theoretically determined

*T*_{0}(ã), three–four peaks can be assigned to the vibrational origin of the triplet state; namely, A: 6954 ± 5 cm^{−1}, B: 7012 ± 5 cm^{−1}, C: 7033 ± 5 cm^{−1}, and D: 7071 ± 10 cm^{−1}.
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248

Marking the calculated triplet state

*n*_{2}vibrational progressions (and the first*n*_{3}level) in the same figure (Fig. 1) it is apparent that progressions starting from peaks A and B match the other peaks of the spectrum best.
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249

Since peak A is slightly out of the error bar of the computed

*T*_{0}(ã), peak B becomes the most probable candidate for the ã(0,0,0) energy level.
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250

Of course, this assignment should be considered only very preliminary and tentative.

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251

It really just demonstrates that there are transitions in this spectral region consistent with the presence of the ã state.

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252

It is unlikely that these transitions are attributable to highly excited X̃ vibrational levels due to the poor Franck–Condon factors involved.

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253

Because of the high density of states in this region, spectra obtained at higher resolution and with better signal-to-noise ratio could notably facilitate arguments about the assignment.

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254

Another problem making the above assignment ambiguous is related to spin–vibronic coupling.

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255

If the coupling is too small, the emissions to triplet state levels might not appear in the dispersed fluorescence spectrum at all.

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256

On the other hand, if the coupling is large, the triplet state vibrational levels computed using the triplet-state PES only could be significantly different from their experimental counterparts.

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257

Hence, it would be advisable to utilize other experiments to determine

*T*_{0}(ã) of CCl_{2}.
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258

Since the bond angles, and consequently the rotational constants are remarkably different in the singlet and triplet states (see Table 1), one possibility would be to record the rotationally resolved stimulated emission pumping (SEP) spectrum of CCl

_{2}.
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259

Another possibility would be to record the absorption spectrum,

*e.g.*, by the cavity ring-down spectroscopy (CRDS) technique.
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260

In this case the high-energy X̃ state vibrational overtones (

*n*_{2}> 20 or*n*_{1}> 10) are not expected to appear in the spectrum, while the intensity of the triplet state levels is determined by the spin–vibronic coupling.
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## Note added in proof

261

After submission of the paper we have received a manuscript from H.-G.

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262

Xu, T. Sears and J. T. Muckerman entitled “Potential energy surfaces and vibrational energy levels of DCCl and HCCl in three low-lying states”.

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263

The MRCI calculations reported in this paper are in good agreement with our results.

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264

The only smaller difference between our and their results is in the numerical value (4

*vs.*22 cm^{−1}, respectively) of the perturbation between the ã(0,1,0) and X̃(0,2,1) levels of HCCl.
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ConceptID: Bac21