Global reaction route mapping of isomerization pathways of exotic C6H molecular species Vikas and Gurpreet Kaur Citation: The Journal of Chemical Physics 139, 224311 (2013); doi: 10.1063/1.4840755 View online: http://dx.doi.org/10.1063/1.4840755 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/139/22?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Erratum: “Global reaction route mapping of isomerization pathways of exotic C6H molecular species” [J. Chem. Phys.139, 224311 (2013)] J. Chem. Phys. 141, 039901 (2014); 10.1063/1.4890076 Synthesis of interstellar 1,3,5-heptatriynylidyne, C 7 H ( X Π 2 ) , via the neutral-neutral reaction of ground state carbon atom, C ( P 3 ) , with triacetylene, HC 6 H ( X Σ 1 g + ) J. Chem. Phys. 131, 104305 (2009); 10.1063/1.3212625 Coupling properties of imidazole dimer radical cation assisted by embedded water molecule: Toward understanding of interaction character of hydrogen-bonded histidine residue side-chains J. Chem. Phys. 122, 184324 (2005); 10.1063/1.1895671 Vibrational spectra of the methanol tetramer in the OH stretch region. Two cyclic isomers and concerted proton tunneling J. Chem. Phys. 114, 2623 (2001); 10.1063/1.1319647 Chlorine atom addition reaction to isoprene: A theoretical study J. Chem. Phys. 113, 153 (2000); 10.1063/1.481782

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THE JOURNAL OF CHEMICAL PHYSICS 139, 224311 (2013)

Global reaction route mapping of isomerization pathways of exotic C6 H molecular species Vikasa) and Gurpreet Kaur Quantum Chemistry Group, Department of Chemistry and Centre of Advanced Studies in Chemistry, Panjab University, Chandigarh 160 014, India

(Received 16 August 2013; accepted 14 November 2013; published online 13 December 2013) C6 H radical is known to exist in the astrophysical environment in linear form; however, it may originate from nonlinear isomeric forms. Potential energy surface of C6 H is explored to search isomers of C6 H and transition states connecting them. This work reports first-ever identification of reaction pathways for isomerization of C6 H. The reaction route search is performed through global reaction route mapping method, which utilizes an uphill walking technique based on an anharmonic downward distortion following approach to search intermediates and transition states. The computations performed at the CASSCF/aug-cc-pVTZ, CCSD(T)/6-311++G(d,p)//DFT/B3LYP/6-311++G(d,p), and DFT/B3LYP/aug-cc-pVTZ levels of the theory identified 14 isomers (including 8 new isomeric forms of C6 H) and 28 transition states. Most of the identified isomers are found to have significant multireference character. The kinetic stability and natural bond orbital analysis of the identified isomers is also investigated. The isomeric forms are further characterized using spectral analysis involving rotational constants, vibrational frequencies, and Raman scattering activities as well as analyzing the effect of isotopic substitution of hydrogen on the spectral features. This study proposes that the linear-C6 H can readily isomerize to a six-member ring isomer. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4840755] I. INTRODUCTION

Astrophysical observation of linear carbon-chain radical species,1–4 namely, Cn H (n = 2–8) in the interstellar medium (ISM) and molecular clouds, has attracted considerable attention of the experimentalists and theoreticians in the last few years.5 The catenating property of carbon is known to have sustained all forms of life on the earth. The carbon-chain radicals, in fact, are also active intermediates in the astrophysical molecular processes4, 6 where they are found to be very dynamic in the rapid transformations occurring in the ISM and molecular clouds. In fact, these transitory, short lived, reactive radical species had played an important role in the evolution of different molecular species. Moreover, the block building behavior of such fundamental radical species has tempted computational chemists to re-investigate the root radical concept.7 One such radical, in which we are interested in this work, is the hydrogen doped carbon chain C6 H, which is known to have high electron affinity and hence, an active precursor in the synthesis of functional molecular materials and chain lengthening process. The linear isomer of C6 H has been reported to be present in a molecular cloud, TMC-1,1 and in a carbon star, IRC + 10216.2, 3 The spectroscopic properties as well as theoretical studies of linear-C6 H had already been well investigated.5, 8–12 However, in the astrophysical environment such as that exists in the ISM and molecular clouds, there is every possibility that the nonlinear branched and cyclic isomeric forms of C6 H a) Author to whom correspondence should be addressed. Electronic

addresses: [email protected] +91-172-2534408.

and

[email protected].

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may exist which can readily transform to linear-C6 H. Therefore, from a theoretical as well as experimental perspective, it would be interesting to investigate the isomerization pathways of C6 H. Recently, Wu,13 employing density functional theory (DFT),14, 15 had investigated the structure, relative stability, electron affinity, and spectral analysis of eight isomers in the ground state of neutral and anionic species of C6 H. The nonlinear isomers of C6 H that were identified include 3–6 membered cyclic rings. Moreover, the radical species, such as C4 H and C6 H, are known to have significant multireference character with nearly degenerate lower lying states. For example, in case of C4 H, the ground state 2  + and excited state 2 , are only 0.035 eV apart.16 In C6 H, the ground state is 2  whereas the lowest-lying excited state is 2  + that lay only 0.068 eV above the ground state.9–12 Therefore, to describe these radical species appropriately, a multi-configurational self consistent field (MC-SCF) approach is required which is though quite expensive. However, a relatively inexpensive method based on complete active space (CAS) SCF and unrestricted Hartree-Fock (UHF) natural orbital (NO) subspace, known as (UNO-CAS)17 had been successfully applied for correct qualitative description of C6 H radical.12 In the present work, the isomers identified for C6 H at the level of DFT are further treated at the single-reference level of coupled-cluster (CC) theory18 and at the multireference level of CASSCF.19 To the best of our knowledge, there have been no studies on the exploration of isomerization pathways of C6 H, which can be of immense assistance in the future identification of new astrochemical species and their mechanism of formation. To achieve this, we employ a global reaction route mapping (GRRM) method20–32 to search different isomeric

139, 224311-1

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forms, equilibrium states (EQs) and transition states (TSs) connecting them on the potential energy surface (PES) of C6 H. GRRM is an automated reaction-route following technique to explore reaction pathways by locating possible EQs, TSs, and dissociation channels (DCs) on a PES. The GRRM method, through anharmonic downward distortions following (ADDF),20–22 uses a scaled hypersphere search (SHS) technique20, 22 as an uphill walking method. In fact, mapping of reaction routes from an EQ to TS and DC by uphill walking has remained a major challenge, whereas reaction route from a TS to EQ or DC by downhill walking along the minimum energy path or intrinsic reaction coordinates (IRC) can be easily followed using the steepest descent method.33–37 ADDF, in fact, is an effective technique to search TSs starting form EQs. Therefore, the GRRM method, through ADDF and IRC, can be used to perform an automated and systematic search of reaction pathways starting from a known equilibrium structure. The GRRM has been successfully applied to explore the PES of CH3 CN,23 cyanoacetylene (HCCCN),24 formaldehyde, CH3 CHO,25 propyne,20 C3 H6 O,26 C2 H7 + , C3 H9 + ,27 to name a few. Besides this, GRRM has also been employed to study conical intersections.28 Moreover, GRRM method in combination of artificial-force induced reaction (AFIR) method has been developed to search reaction pathways from given reactants without requiring a guess of TS.29, 30 In this paper, our primary aim is to explore the PES of C6 H for isomers (EQs) and TSs connecting them in order to predict the isomerization pathways. The multireference character of a few lowest-lying isomers is further explored at the CASSCF level. The kinetic stability and spectral properties of isomers as well as isotopic substitution effect on the rotational constants, vibrational frequency and Raman scattering activity of the identified isomers, are also addressed through computations performed at the level of the DFT. The paper is organized as follows: Sec. II outlines the computational details for exploring EQs and TSs on the PES of C6 H using GRRM method. This is followed by Sec. III where the isomerization pathways are explored with detailed analysis of geometrical parameters, kinetic stability and spectral properties of the identified EQs and TSs connecting them. Finally, a few concluding remarks are presented in the last section. II. COMPUTATIONAL

The GRRM program20–32 requires the knowledge of normal coordinates of a known equilibrium structure (EQ), which can be obtained by geometry optimization and harmonic vibrational analysis through any quantum mechanical software package. In the present work, all the required computations for the GRRM program are performed in assistance with GAUSSIAN 0338 quantum mechanical software package. The GRRM program, using SHS method based on the ADDF, searches the TSs or DCs along the possible reaction pathways around the EQ, and connectivity of the obtained EQs is then verified using IRC computations through the quantum mechanical software. Further, in the present work, all the computations involving geometry optimization and frequency analysis in the GRRM search, were first performed

J. Chem. Phys. 139, 224311 (2013)

at DFT/B3LYP/6-31G level of the theory for identification of all minima, stationary and saddle points. The obtained EQs and TSs were then refined at DFT/B3LYP/6-311++G(d,p) level of the theory taking into account the zero-point energy (ZPE) correction through frequency analysis. This was also followed by IRC calculations at the same DFT/B3LYP/6311++G(d,p) level of the theory to confirm reaction pathways connecting right EQs through the TSs. All the isomers that have been searched had all frequencies real, whereas all the interconnecting transition states had one imaginary frequency. The relative energies of obtained EQs at DFT/B3LYP/ 6-311++G(d,p) level were further refined using coupledcluster (CC) theory18 at CCSD(T)/6-311++G(d,p)//DFT/ B3LYP/6-311++G(d,p) level taking ZPE correction into account and also compared at DFT/B3LYP/aug-cc-pVTZ//DFT/ B3LYP/6-311++G(d,p) level using aug-cc-pVTZ correlation consistent basis set.39–41 However, since these isomers are expected to exhibit multireference character, T1 diagnostics42 at the CCSD/6-311++G(d,p)// DFT/B3LYP/6-311++G(d,p) level, were performed. The isomers with T1 diagnostic value >0.02 are generally considered as having significant multireference character. The five-lowest lying isomers of C6 H were further treated at the multireference CASSCF(11,11)/aug-ccpVTZ level. The active space in CASSCF (11,11) computations was build considering the fact12 that the ground state of C6 H radical at UHF/6-31G** level has occupancy in range of 1.98−0.02 for 11 UHF natural orbitals which also corresponds to valence π orbitals occupied by 11 electrons. All the CASSCF computations were carried out using ORCA43 quantum mechanical software package, employing an improved resolution of identity (RIJCOSX) approximation.44, 45 Further, natural bond orbital (NBO) analysis46 of the relevant EQs obtained at DFT/B3LYP/6-311++G(d,p) level was performed to identify the possible resonating structures. The optimal Lewis structure obtained from the alpha spin orbitals in free NBO search is compared with the structure resulted in NBO search performed on a chosen resonating structure. Besides this, the potential isomers identified were also characterized through spectral analysis involving rotational constants, vibrational frequencies, IR intensities, and Raman scattering activities at DFT/B3LYP/aug-cc-pVTZ level of the theory. The effect of isotopic substitution of 1 H by 2 H on the vibrational frequencies, rotational constants, and Raman scattering activities of the potential EQs were also explored at the DFT/B3LYP/aug-cc-pVTZ level of the theory. It should be further noted that since in this work we are mainly interested in the feasible isomerisation routes, therefore, the reported EQs and TSs are obtained using an option of 7 random structures (considering 7 atoms of C6 H), with position of all atoms being randomized, as starting points in the GRRM program. Further, only 5 lowest barrier pathways (largest ADDs) are followed from each EQ, and the ADDF is applied only to the 7 lowest EQs. However, with this choice, only one direct dissociation pathway was observed, and the other dissociation pathways are predicted mainly considering the EQs and TSs obtained, and through the corresponding NBO analysis. Furthermore, on increasing the number of random structures from an initial 7 to an arbitrary 24 as

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starting points in the GRRM computations at DFT/B3LYP/631G+ level (which also increased the computational time enormously), we were able to locate other possible dissociation pathway which could have also been traced through fullADD-following for searching all the pathways, and also using fragments for generation of random structure. With the above specified options for C6 H, GRRM program explored 14 isomers with different interconversion transition states as discussed in Sec. III.

III. RESULTS AND DISCUSSION

The computations using GRRM program, on the doublet PES of C6 H, resulted in 14 isomers (EQs) (listed in Table I) and 28 interconversion transition states, TSm/n(k), where k denotes the kth transition state connecting mth isomer with nth isomer. The optimized geometries, obtained at DFT/B3LYP/6-311++G(d,p) level of the theory, for EQs and TSs, and mapped reaction routes of isomerization of C6 H are depicted in Figures 1 and 2. A schematic doublet potential energy profile of C6 H is further illustrated in Figure 3, whereas the ZPE corrected energies of EQs and TSs relative to lowest-lying isomer, EQ0, obtained at CCSD(T)/6-311++G(d,p)//DFT/B3LYP/6-311++G(d,p), are listed in Table II. However, as evident from values of T1 diagnostics in Table II, most of the identified isomers have multireference character with value >0.02 at CCSD/6-311++G(d,p)//DFT/B3LYP/6-311++G(d,p) level. Therefore, five-lowest lying isomers were also optimized at the multireference level of CASSCF(11,11)/aug-cc-pVTZ, and the optimized geometries are depicted in Figure 4. Further, the harmonic vibrational frequencies, IR intensities, Raman activities, rotational constants and their relative shift upon isotopic substitution by 2 H of potential isomers, at DFT/B3LYP/aug-cc-pVTZ level, are collected in Table III and Tables S1–S7 of the supplementary material.47 An analysis of EQs, TSs, and isomerization pathways show interesting features which are described below:

A. Isomers

The 14 isomers (EQs depicted in Figures 1 and 4) that were detected on the doublet potential energy surface of C6 H, can be sorted into six categories: linear EQ0, acyclic EQ7 and EQ7 , three-member ring isomers EQ3, EQ4, EQ11, and EQ12, four-member ring isomers EQ2, EQ8, and EQ9,

• C1

C2

C3

C4

C5

C6

H7

where | denotes a lone pair of electrons and • represents a single electron. It should be noted that the structure on the left hand side corresponds to an optimal Lewis structure obtained from the alpha spin orbitals in free NBO search, and that on the right corresponds to structure obtained from NBO search on a chosen resonating structure. With the structure on left

five-member ring isomers EQ10, six-member ring isomers EQ1 and EQ5, and bicyclic three-member ring isomer EQ6. The geometrical parameters of these isomers are listed and compared with known literature values13 in Table I. Six of the isomers (EQ0, EQ1, EQ2, EQ6, EQ7, and EQ9) have also been previously reported,13 whereas remaining eight isomers are reported for the first time. The lowest energy isomer, EQ0, is found to be linear, which has also been perceived in the outer space as well as synthesized in the laboratory. The order of thermodynamic stability of isomers of C6 H relative to linear EQ0 at CCSD(T)/6-311++G(d,p)//DFT/B3LYP/6311++G(d,p) level, in kcal/mol, is: EQ0 (0) > EQ1 (9.79) > EQ2 (20.9) > EQ3 (29.81) > EQ4 (32.38) > EQ5 (33.70) > EQ6 (38.97) > EQ7 (45.06) > EQ7 (52.65) > EQ8 (62.12) > EQ9 (66.27) > EQ10 (69.47) > EQ11 (77.12) > EQ12 (77.75), where the value in the parenthesis represents the ZPE corrected energy of the isomers relative to EQ0, which are further listed in Table II. EQ0, the linear isomer possessing 2  ground state with C∞v symmetry, is an H-terminated linear carbon chain with mixed double- and triple-bond character of C–C bond due to resonance. It should be noted that EQ0 is found to be having multireference character as evident from T1 diagnostics value of 0.056, however, computations at CASSCF(11,11)/aug-ccpVTZ, also revealed EQ0 to be the lowest-lying isomer at multireference level of the theory. EQ0 is further characterized on the basis of spectral features (listed in Table III), which are observed to be in good agreement with the previous studies.13 For example, the computed value of linear rotor rotational constant is 1.3962 GHz as compared to the experimental value of 1.3912 GHz. Moreover, the highest IR intensities are found to be associated with the C≡C stretching modes, namely, at 1897 and 2131.7 cm−1 . The linear structure of EQ0 was also confirmed by the corresponding Raman scattering activity which was found to be maximum for the relatively inactive IR mode at 2099.7 cm−1 . The terminal-H was additionally characterized by analyzing the corresponding spectral shift in C–H stretch, at 3451.2 cm−1 , upon isotopic substitution by 2 H. Further, from the natural bond order (NBO) analysis,46 the testification of its covalent structure was carried out. The spin density distribution in EQ0 at C(1), C(2), C(3), C(4), C(5), C(6), and H(7) is found to be 0.108, −0.301, 0.100, 0.051, −0.112, −0.019 and 0.227e, respectively. The bond lengths of C1 –C2 (1.29 Å), C3 –C4 (1.24 Å), and C5 –C6 (1.21 Å) bonds are closer to that of C≡C(1.21 Å) bond suggesting the structure resonating between triacetylene and cumulin structures which can be viewed as

| C1

C2

C3

•

C4

C5

C6

H7

found to contribute significantly, EQ0 can be considered to form by the combination of C4 + C2 H fragments. EQ1, having 2 A1 electronic ground state, is cyclic six-member ring isomer with C2v symmetry, and resembles benzene in structure. EQ1 lay only 9.79 kcal above EQ0 as indicated at CCSD(T)/

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TABLE I. Geometrical parameters (with bond lengths in Å, and angles in degrees) of 14 identified isomers (EQs) of C6 H optimized at the DFT/B3LYP/6311++G(d,p) level of the theory. The values compared in the parenthesis are from Ref. 9 computed at DFT/B3LYP/aug-cc-pVTZ level of the theory. The CASSCF(11,11)/aug-cc-pVTZ optimized parameters for five lowest-lying isomers are represented in bold. H r1 r2 C r1

H

r2

r3

C

r4

C

r5

C

r3

r6

C

C

C C

C

r7

C

θ1 θ2

r4

r6 C

θ2 r7

C

θ1

r6

C

C

r4

C

r5

r2

C

C

r1

C

H

θ2 r2 C r3 r1 C r 5 r4 C r6 H C θ1

C

r5

r7

C EQ3

EQ2

EQ1

EQ0

r3

H θ2

C r5

r6

r7

r3

C r C 4

C

θ1

C

r2

r3

C

r1

C

r3

H r1 r4

C

θ1

C

r5

θ2

C

r2 r6

H θ1

C

r1

C

r3

r2

C

C

θ2 r4

C

r6

C

r7

r7

C

C

θ 2 r6

C r 2

C r5

θ1

C r7

H

r3

r2

C

C

r4 r5

C

θ1

C

C

r3

C r1

r6

EQ7

C

r5

r9

θ2

C

r4 r3

C r8

H

r1 r2

r3

C

C

θ1

r2 r1 C

c

θ1

r4

θ2 r7

C C

r5 r6

C

EQ 10

C r5

C

θ 2 r6

r4

H

EQ9

EQ8

r4

θ1 r 4 C

r1

r2

C

r5

EQ 7′

r1

C

EQ6

r6

C C

C

θ2

C

r1

C

θ1 r3

r3

r5

C

EQ5

C

C

r6

C

C

EQ4

r2

r7

θ2 C

r4

H

H C

θ1

C

H

H

r1

r2 C

C r7 C

C EQ 11

EQ 12

Geometrical parameters Isomer EQ0

EQ1

EQ2

EQ3 EQ4 EQ5 EQ6 EQ7 EQ7 EQ8 EQ9 EQ10 EQ11 EQ12

r1

r2

r3

r4

r5

r6

r7

1.064 (1.062) 1.059 1.076 (1.074) 1.064 1.065 (1.063) 1.058 1.079 1.066 1.064 1.056 1.080 1.079 (1.077) 1.092 (1.089) 1.094 1.087 1.101 (1.073) 1.074 1.095 1.100

1.218 (1.215) 1.172 1.384 (1.380) 1.369 1.225 (1.203) 1.177 1.351 1.385 1.206 1.171 1.411 1.397 (1.390) 1.373 (1.370) 1.337 1.463 1.329 (1.285) 1.336 1.315 1.312

1.334 (1.333) 1.373 1.329 (1.325) 1.284 1.361 (1.385) 1.375 1.500 1.411 1.382 1.391 1.321 1.340 (1.336) 1.279 (1.275) 1.289 1.373 2.503 (1.459) 1.399 1.428 1.427

1.243 (1.240) 1.176 1.332 (1.329) 1.316 1.437 (1.412) 1.392 1.387 1.309 1.431 1.376 1.337 1.449 (1.444) 1.349 (1.346) 1.417 1.455 1.393 (1.538) 1.296 1.353 1.351

1.313 (1.311) 1.321 1.332 (1.329) 1.288 1.482 (1.454) 1.473 1.306 1.368 1.355 1.326

1.285 (1.282) 1.155 1.329 (1.325) 1.293 1.483 (1.454) 1.340 1.278 1.207 1.490 1.432

1.384 (1.380) 1.364 1.437 (1.412) 1.379 1.298 1.306 1.322 1.333

1.389 (1.386) 1.268 (1.265) 1.262 1.450 1.406 (1.457) 1.469 1.495 1.509

1.394 (1.388) 1.300 (1.296) 1.327 1.321 1.452 (1.415) 1.306 1.422 1.416

r8

r9

1.342 (1.336)

1.274 1.435 (1.415) 1.533 1.322 1.321

1.411 (1.457)

1.512 (1.517)

θ1

θ2

100.76 (100.42) 98.47 66.43 (79.18) 64.16 139.88 147.27 139.60 143.93 107.93 59.96 (59.87) 119.27 (119.25) 122.98 72.10 64.92 (62.70) 81.95 115.75 108.43

93.27 (92.93) 99.91 64.15 (76.45) 65.44 152.14 148.72 161.16 152.36 78.65 57.54 (57.48)

174.84 70.21 22.60 (50.68) 95.22 140.57 139.70

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Vikas and G. Kaur

J. Chem. Phys. 139, 224311 (2013)

FIG. 1. Isomerization and dissociation pathways on the doublet PES of C6 H connecting different isomers (EQs) with the TSs. The geometries (with bond lengths in Å and angles in degrees) of EQs depicted are optimized at the DFT/B3LYP/6-311++G(d,p) level of the theory. The values in parenthesis refer to ZPE corrected relative energies (in kcal/mol) with respect to linear-C6 H (EQ0) obtained at the CCSD(T)/6-311++G(d,p)//B3LYP/6-311++G(d,p) level.

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Vikas and G. Kaur

J. Chem. Phys. 139, 224311 (2013)

FIG. 2. Same as Figure 1, but for transition states (TSs) connecting EQs in Figure 1. TSs are designated as TSm/n(k), wherever mentioned k denotes the kth transition state connecting mth EQ with nth EQ.

6-311++G(d,p)//DFT/B3LYP/6-311++G(d,p) level of the theory, however, at CASSCF(11,11)/aug-cc-pVTZ level of the theory, EQ0 is observed to be lying 43.93 kcal below EQ1. In case of EQ1, highest IR intensity, at 1729.3 cm−1 ,

is found to be associated with asymmetric C–C stretch, whereas highest Raman activity was associated with C–H stretch at 3275.3 cm−1 with an isotopic shift of 844.4 cm−1 as evident in Table S1 of the supplementary material.47

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J. Chem. Phys. 139, 224311 (2013)

FIG. 2. (Continued.)

The computed value of rotational constants are found to be 7.751, 7.516, and 3.816 GHz as compared to the previously reported13 values of 7.754, 7.518, and 3.817 GHz, respectively. In EQ1, C1 –C2 (1.38 Å) bond-distance lies between C=C(1.35 Å) and C–C (1.47 Å), whereas C2 –C3

(1.33 Å) and C3 –C4 (1.32 Å) bonds are slightly longer than C=C bond. Moreover, the spin density distribution in EQ1 is found to be −0.403, 0.193, −0.212, 0.180, and 0.260e, respectively, at C(1), C(2)/C(6), C(3)/C(5), C(4), and H(7).The NBO analysis indicates the structure of EQ1 by two

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J. Chem. Phys. 139, 224311 (2013)

as also indicated by relatively lower T1 diagnostic value of 0.028 for the multireference character: • • C C1

| C2

1

C4

C5

C6

H7

| C2

FIG. 3. Potential energy profile (in kcal/mol), at CCSD(T)/6311++G(d,p)//B3LYP/6-311++G(d,p) level of the theory, for isomerization pathways of C6 H depicted in Figure 1 connecting isomers EQ0-12 through TSs depicted in Figure 2. The higher transition states TSm/n(k), with k > 1 are not included in the energy profile.

resonating geometries with triradical structure on the left contributing significantly with multireference character indicated by T1 diagnostics value of 0.040: H7 C1 C6

• C5

C4

•

C2

C6

C3 •

C5

C1

C4

•

C5

C6

EQ3, the newly reported isomer, is a three-member ring with Cs symmetry having exocyclic C–C–C fragment. Another three-member ring isomer (EQ4) reported by previous studies,13 however, is relatively less stable (see below). Further, the C–C stretching vibrational mode at 2017.5 cm−1 in EQ3 was observed with highest intensity, while highest Raman activity was found to be associated with C–H stretch at 3260.5 cm−1 having an isotopic frequency shift of 816.2 cm−1 as evident in Table S3 of the supplementary material.47 Further, C(1), C(2), C(3), C(4), C(5), C(6), and H(7) in EQ3 is found to have spin density distribution of 0.020, 0.204, −0.015, 0.161, −0.378, 0.181, and 0.246e, respectively, and bonds C1 –C2 (1.35 Å), C3 –C4 (1.31 Å), C4 –C5 (1.29 Å), and C5 –C6 (1.30 Å) are comparable to the C=C bond. NBO analysis supported the structure by two resonating forms; however, EQ3 is having low multireference character: • | C1 C1 C2

C2

C3 C4

C3

C5

•

C4

H7

C5 C6|

C6 |

C2 C3

•

EQ2, is a four-member ring isomer, which possesses a C–C cross bond suggesting that the structure has two three-member rings fused via transannular bond. EQ1 and EQ2, at the CCSD(T)/6-311++G(d,p)//DFT/B3LYP/6311++G(d,p) level lay 9.79 and 20.90 kcal/mol, respectively, above EQ0 indicating that they have considerable thermodynamic stability. However, at CASSCF/aug-cc-pVTZ and DFT/B3LYP/6-311++G(d,p) level of the theory, EQ2 is observed to by lying above EQ3 (as evident in Table II) indicating considerable amount of electron correlation involved. Further, as evident in Table S2 of the supplementary material47 for isomer EQ2, highest IR intensity at 3454 cm−1 corresponds to C–H stretch with an observed isotopic shift of 796.4 cm−1 . For C–C stretching vibrational mode, highest Raman activity was observed at 2092.9 cm−1 . The computed value of rotational constants are 37.069, 2.318, and 2.182 GHz as compared to the previously reported values13 of 20.168, 2.619, and 2.445 GHz, respectively. In EQ2, the calculated bonddistances: C1 –C2 (1.48 Å), C2 –C3 (1.48 Å), C3 –C4 (1.44 Å), and C1 –C4 (1.44 Å) are closer to C–C bond, whereas C5 –C6 (1.23 Å) bond resembles C≡C bond. The isomer is observed to have strongly delocalized structure with spin density distribution of 0.105, −0.150, 0.105, −0.145, −0.069, −0.085, and 0.240e, respectively, at C(1), C(2), C(3), C(4), C(5), C(6), and H(7). NBO analysis supported the structure by two resonating forms with the structure on the left contributing significantly

H7

•

H7

H7

C4 C3

C3

EQ4, a C3 ring isomer, reported for the first time, is Cs symmetrized having exocyclic C–C–H fragment at one arm, and C-atom at other arm. In EQ4, highest IR intensity at 1711.6 cm−1 was found to be associated with C–C stretch whereas highest Raman activity was observed for C–C stretching vibrational mode at 2192.1 cm−1 as evident from Table S4 of the supplementary material.47 Further, the spin density distribution is found to be 0.214, −0.344, 0.090, −0.061, −0.077, −0.064, and 0.243e, respectively, at C(1), C(2), C(3), C(4), C(5), C(6), and H(7). In EQ4, C5 –C6 (1.21 Å) bond has bond order of C≡C bond, and the bonddistances: C3 –C4 (1.36 Å), C2 –C4 (1.43 Å) lies between that of C=C(1.35 Å) and C–C (1.47 Å). NBO calculations justify structure of EQ4, with lower multireference character, through two resonating forms: • C3 | C3 C2

| C1

C4

C2

C5 C6 H7

| C1 •

C4 C5 C6 H7

From these structures, EQ4 may be considered to be formed from C2 H +cyc-CCC-C fragments. EQ5, is a newly reported six-member ring isomer which can also be seen as a stretching form of EQ1, but it is 23.91 kcal/mol less stable than EQ1. In case of EQ5, as evident from Table S5 of the supplementary material,47 highest IR intensity was found at 1795.5 cm−1 which is associated with asymmetric C–C stretch whereas high Raman activity was found to be associated with C–H stretch at 3221 cm−1 showing an

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224311-9

Vikas and G. Kaur

J. Chem. Phys. 139, 224311 (2013)

TABLE II. Relative energies (in kcal/mol) of identified isomers (EQ0-12) of C6 H, transition states, TSs (depicted in Figures 1 and 2) and dissociation fragments, with respect to energy of EQ0a , at the ZPE corrected (A) DFT/B3LYP/6-311++G(d,p), (B) CCSD(T)/6-311++G(d,p)//B3LYP/6-311++G(d,p), and (C) DFT/B3LYP/aug-cc-pVTZ//B3LYP/6-311++G(d,p), level of the theory. T1 diagnostics performed for isomers, at CCSD/6-311++G(d,p)//DFT/B3LYP/6311++G(d,p) level, are indicated in italics, and relative energies of five-lowest lying isomers, at CASSCF(11,11)/aug-cc-pVTZ level of the theory, are represented in bold.

Species EQ0 EQ1 EQ2 EQ3 EQ4 EQ5 EQ6 EQ7 EQ7 EQ8 EQ9 EQ10 EQ11 EQ12 TS0/1 TS0/3 TS0/3(2) TS0/4 TS0/4(2) TS0/7 TS1/5 TS1/5(2) TS1/7 TS1/10b TS1/11 TS2/7b TS3/4 TS3/6 TS3/8 TS3/9 TS3/9(2) TS4/11 TS4/12 TS8/12 TS9/11 TS9/12 TS11/12 TS0/0 TS1/1 TS6/6 TS7/7 TS7 / C3 +C3 H C +C5 H(2 ) C3 (1  g + )+C3 H(2 )c C4 (3  g − )+C2 H(2  + )c C2 (1  g + )+C4 H(2 )c C6 (3  g − )+H(2 A1g )d

Symmetry

ZPE (A)

DFT/ B3LYP /6-311++G(d,p) + ZPE (A)

C∞v C2v C2v Cs Cs C2v Cs Cs Cs C1 Cs Cs Cs Cs C1 Cs Cs Cs Cs Cs Cs Cs C1 Cs Cs Cs C1 C1 Cs Cs Cs Cs Cs C1 Cs Cs C1 Cs C1 Cs C2v Cs

0.00 − 1.13 1.57 0.94 1.07 − 1.57 1.32 1.07 1.19 0.88 2.64 0.69 2.38 2.51 0.82 1.82 2.38 1.88 2.01 4.39 0.19 0.94 0.94 1.07 2.13 1.38 3.01 1.69 2.13 3.07 3.33 3.95 4.39 3.01 2.57 2.70 2.89 3.77 2.76 0.82 4.02 4.89 3.70 5.33 5.02 4.14 7.3

0.00 24.03 37.53 34.83 44.93 44.36 52.59 50.64 71.22 75.11 85.53 85.22 92.31 92.56 63.00 54.41 52.52 57.35 68.65 85.84 57.73 90.42 79.69 86.78 92.93 48.26 97.70 60.87 81.26 99.21 99.33 92.68 92.56 111.95 94.82 95.26 96.51 87.98 89.11 59.11 73.29 126.82 188.63 127.82 161.96 173.82 119.04

CCSD(T) /6-311++G(d,p) //DFT/B3LYP/6311++G(d,p)+ ZPE (A) (T1 diagnostics)

ZPE (C)

0.00 (0.056) 09.79 (0.040) 20.90 (0.028) 29.81 (0.027) 32.38 (0.031) 33.70 (0.056) 38.97 (0.016) 45.06 (0.046) 52.65 (0.057) 62.12 (0.037) 66.27 (0.025) 69.47 (0.069) 77.12 (0.030) 77.75 (0.029) 55.35 43.80 46.50 42.67 55.53 89.36 44.99 72.85 66.89 69.40 77.18 33.89 83.52 50.39 69.65 82.77 83.02 78.12 78.06 95.70 78.50 78.88 80.38 80.89 75.18 76.18 72.35 112.89 150.10 90.11 119.73 111.51 108.37

0.00 − 1.44 1.19 0.56 0.69 − 1.88 1.13 0.63 1.07 0.50 2.26 0.38 1.95 2.07 0.44 1.19 1.95 1.07 1.57 4.02 − 0.19 0.56 0.56 1.00 1.76 1.00 2.70 1.26 1.82 2.70 2.95 3.58 3.95 2.57 2.20 2.38 2.51 3.45 2.45 0.56 3.58 4.45 3.77 4.96 5.02 3.83 6.9

DFT/B3LYP/aug-ccpVTZ //DFT/ B3LYP/6-311++ G(d,p) + ZPE (C) (CASSCF(11,11)/augcc-pVTZ+ZPE (C) 0.00 (0.00) 23.91 (43.93) 37.84 (49.45) 35.27 (44.30) 45.37 (46.37) 44.30 52.77 51.58 72.04 76.05 86.16 85.66 93.12 93.44 63.32 55.10 53.28 58.30 69.40 85.97 57.73 93.37 80.32 87.22 93.75 48.76 98.46 61.81 81.95 101.03 102.85 93.25 93.12 113.52 95.96 96.20 97.77 88.23 89.17 59.43 73.54 128.58 192.52 130.02 164.93 175.01 119.98

a

The total energy including (ZPE) of EQ0 at DFT/B3LYP/6-311++G(d,p), CCSD(T)/6-311++G(d,p)//B3LYP/6-311++G(d,p), and DFT/B3LYP/aug-cc-pVTZ//B3LYP/6311++G(d,p) level of the theory is −228.9655 (0.0351), −228.3213 (0.0351), and −228.9892 (0.0345) a.u., respectively. b TS obtained from double ended version of SHS method. c Proposed dissociation fragments. d DC observed in GRRM computation with 24 random structures as starting points.

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224311-10

Vikas and G. Kaur

J. Chem. Phys. 139, 224311 (2013)

FIG. 4. CASSCF(11,11)/aug-cc-pVTZ optimized geometries of five-lowest lying isomers of C6 H, with bond lengths depicted in Å and angles in degrees. The value in parenthesis represents total energy (in a.u.).

isotopic shift of 937.1 cm−1 . The spin density distribution at C(1), C(2),C(3), C(4), C(5), C(6), and H(7) is observed to be 0.277, −0.010, 0.081, −0.083, 0.081, −0.010, and 0.218e, respectively. In EQ5, computed C1 –C2 (1.41 Å) bond-length lays between C=C(1.35 Å) and C–C(1.47 Å) bond-lengths, whereas that of C3 –C4 (1.34 Å) lays between C≡C(1.21 Å) and C=C(1.35 Å) bond-lengths. NBO analysis supported the structure by two resonating forms: H7

• C6

C1

• C5

H7 C1

C2•

• C6 C5

C3

C2 • C3

C4

C4

•

It should be noted that EQ5 is having significant multireference character as evident from T1 diagnostics value of 0.056, and it can originate by ring closure of EQ7 (see below); however, the transition state governing this conversion has not been located. EQ6 is Cs symmetrized and can be described as bicyclic three-member ring isomer having butterfly like geometry in which the two rings are in different planes. EQ6 does not have multireference character as indicated by T1 diagnostics value of 0.016 whereas most of the isomers of C6 H have significant multireference character. The C–C unsymmetric stretching vibrational mode at 348.109 cm−1 in EQ6 was observed with highest intensity, while highest Raman activity was found to be associated with C–C symmetric stretch at 1764.35 cm−1

TABLE III. Unscaled harmonic vibrational frequencies (in cm−1 ), IR intensities (in km/mol), Raman scattering activities (in Å/a.m.u.), rotational constants (in GHz), and corresponding isotopic (2 H) shifts calculated for isomer, EQ0, at DFT/B3LYP/aug-cc-pVTZ level. 2 H-substituted

EQ0 Rotational constants

Mode ν1 ν2 ν3 ν4 ν5 ν6 ν7 ν8 ν9 ν 10 ν 11 ν 12 ν 13 ν 14 ν 15 ν 16

Be = 1.3962

EQ0

Be = 1.3325

Frequency

IR Intensity

Raman scattering activity

Frequency shift

IR intensity change

Raman activity change

3451.7 2131.7 2099.7 1897.0 1225.5 699.8 651.0 572.1 544.5 502.3 461.2 388.8 241.8 189.7 105.9 88.8

131.1 223.2 31.4 257.4 5.3 27.9 1.1 50.6 3.5 2.8 0.6 0.1 6.3 20.1 0.4 7.9

43.0 64.6 1878.4 105.6 21.9 7.8 53.0 6.3 11.3 6.2 3.0 88.7 0.2 65.5 0.0 18.9

− 799.3 − 5.1 − 79.2 − 24.2 − 11.7 − 56.9 − 81.1 − 41.3 − 42.1 − 31.3 − 31.8 − 12.7 − 4.3 − 5.7 − 3.5 − 1.9

− 96.2 − 65.8 203.9 − 113.9 1.2 − 27.0 3.2 − 39.7 − 2.2 3.2 18.6 − 0.1 0.9 0.1 0.0 − 0.3

54.4 382.6 − 783.2 210.2 − 5.9 46.3 − 50.3 24.2 − 6.4 3.2 − 0.6 − 12.5 − 0.2 3.6 0.2 − 3.7

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224311-11

Vikas and G. Kaur

J. Chem. Phys. 139, 224311 (2013)

having an isotopic frequency shift of 17.3 cm−1 as evident in Table S6 of the supplementary material.47 The spin density distribution at C(1), C(2), C(3), C(4), C(5), C(6), and H(7) is observed to be −0.005, −0.005, −0.023, −0.075, −0.006, −0.123, and 0.236e, respectively. NBO calculations justify structure of EQ6 through two resonating forms: H7

| C1

C6

C3

•

C4

C2

C5 |

H7

•

C1

C6

C3

C4

| C2

C5 |

EQ7, an acyclic isomer, is inverted Y-shaped possessing Cs symmetry and 2 A ground state. Further, as evident from Table S7 of the supplementary material,47 the C–C stretching vibrational mode at 2074.4 cm−1 is observed with highest IR intensity, and C–H stretch at 3091.3 cm−1 is observed with highest Raman activity. The computed values of rotational constants are 19.290, 1.823, and 1.666 GHz which are in good agreement with the previously calculated values of 19.298, 1.823, and 1.665 GHz, respectively. The spin density distribution at C(1), C(2), C(3), C(4), C(5), C(6), and H(5) in EQ6 is computed to be 0.289, −0.444, 0.364, −0.282, −0.262, 0.075, and 0.260e, respectively. In EQ6, the calculated bonddistances, C2 –C3 (1.31 Å), C1 –C5 (1.29 Å) lay between that of C=C(1.35 Å) and C≡C (1.21 Å), whereas that of C1 –C2 (1.30 Å), C3 –C4 (1.35 Å), and C4 –C5 (1.37 Å) are closer to C=C bond-length. NBO analysis supports the structural description of isomer through two resonating forms: H7

•

C6

C5

C4

H7 C3

C2

C1 |

| C6

C5

C4

C3

C2 • C1 |

Based on the above structures, it can be seen that delocalization can occurs on the two fork ends of carbon chain. EQ7 has significant multireference character and it can be considered to be a combination of C + C5 H on the basis of donoracceptor interactions predicted by NBO analysis. EQ7 resembles EQ7, but it is 7.59 kcal/mol less stable than EQ7. It mainly differs from EQ7 in having a bent C–C bond in C–C–C fragment. The remaining isomers EQ8-12 have relatively higher energy and low kinetic stability (as discussed in Sec. III B), therefore, for the sake of brevity, the structural details of these isomers are not discussed. Besides the linear isomer EQ0, five other isomers, namely, EQ1, EQ2, EQ6, EQ7, and EQ9 have been reproduced out of the eight previously theoretically reported13 isomers. The geometries of the isomers reported by previous studies, and the relative energies are in good agreement with previously reported isomers as evident in Tables I and II. The remaining two isomers, which the present work is unable to reproduce, are of quite high energy and hence, are less significant. B. Isomerization routes and kinetic stability

The linear EQ0 is the lowest lying isomer and can be considered to be the global minima on the doublet PES. Since greater kinetic stability makes it difficult for an isomer to

convert further to other isomers, therefore, by observing the conversion barriers, the kinetic stability of the isomers can be analyzed. Isomer EQ0 is kinetically most stable as evident in Table II and Figure 3, and the lowest activation energy for its isomerisation is to EQ3 and EQ4, which is computed to be 43.80 and 42.67 kcal/mol, respectively, via TS0/3 and TS0/4, at CCSD(T)/6-311++G(d,p)//DFT/B3LYP/6-311++G(d,p) level of the theory. It should be noted that EQ3 is being reported for the first-time. The isomerisations: EQ0 ↔ EQ3 and EQ0 ↔ EQ4, can also proceed via higher lying transition states TS0/3(2) and TS0/4(2), respectively. Further, the isomerisation of EQ0 to EQ1, however, requires higher activation energy of 55.35 kcal/mol via TS0/1. In fact, EQ0 and EQ1 are observed to be well separated at CASSCF(11,11)/aug-cc-pVTZ level. The interconversion between EQ1 and EQ2 is found to be hindered but can crop up indirectly through the route EQ1 ↔ EQ7 ↔ EQ2. Moreover, since the conversion barriers from EQ1 and EQ2 to EQ7 are relatively high, the kinetic stability of EQ1 and EQ2 is reasonable which enhances the chance of their experimental observation. The activation energy for isomerisation of EQ0 to EQ1 is though higher than that required for EQ1 to relatively less stable EQ5 but the latter can be considered as a metastable intermediate since the kinetic barrier for its conversion to low lying EQ1 is only 11.29 kcal/mol. The highest activation energy, however, is observed for the isomerisation route EQ0 → EQ7, which involves proton-hopping that bypasses a carbon atom from C(1) to C(3). Further, cyclic EQ1 can be converted to acyclic EQ7 by C–C bond cleavage due to destabilization caused by strong stretching motion of C–C bond via acyclic transition state TS1/6. Similarly, cyclic EQ2 can isomerize to acyclic EQ7 via TS2/7, however, reverse isomerisation is more feasible in this case since the conversion barrier for EQ7 → EQ2 is negative. Furthermore, EQ1 can exist in another potential equilibrium state EQ5 which can result from EQ1 via low-lying TS1/5 and high lying TS1/5(2), with former requiring only 35.20 kcal/mol which is even less than that required for the isomerisation of EQ0 to EQ1. The six-member EQ1 can also isomerise to five-member EQ10, and to the three-member EQ11 via TS1/10 and TS1/11, respectively, with activation energy of 59.61 and 67.39 kcal/mol. The ring reduction occurs via C–C bond cleavage and formation. Further, the interconversion between three-member ring isomers EQ3, EQ4, and EQ11, occurs directly through proton-hopping route: EQ3 → EQ4 → EQ11/EQ12 with the respective transition states TS3/4, TS4/11, or TS4/12 at 83.52, 78.12, and 78.06 kcal/mol, respectively. The reverse rearrangement route, however, is comparatively less energetic. It is creditable to note that TS4/11 lays only 0.06 kcal/mol above TS4/12 indicating that the respective conversion routes are challenging each other. Furthermore, the C3 ring isomer EQ3 is excited to bicyclic TS3/6 to form EQ6 having two three-member rings separated by C–C bond, with the reverse conversion being relatively much less energetic. However, higher activation energy is required for ring extension in EQ3 to isomerise to four-member EQ8 and to bicyclic ring isomer EQ9 via TS3/8 and TS3/9, respectively, with the latter having another closely

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224311-12

Vikas and G. Kaur

lying transition state TS3/9(2). Moreover, the high energy doublet isomers EQ8, EQ9, EQ10, EQ11, and EQ12 have lower kinetic stability since they reside in much shallow potential wells, and can easily isomerise to each other and to the other low energy isomers. The least conversion barriers observed with the isomerisations involving high lying EQs are: 0.60 kcal/mol for EQ11 → EQ1, −0.07 kcal/mol for EQ10 → EQ1, 7.53 kcal/mol for EQ8 → EQ3, 16.50 kcal/mol for EQ9 → EQ3, 17.95 kcal/mol for EQ12 → EQ8, 1.38 kcal/mol for EQ11 → EQ9, 1.13 kcal/mol for EQ12 → EQ9, and 2.63 kcal/mol for EQ12 → EQ11. For the sake of brevity, structural description of their transition states is not presented here. Besides above isomerisation pathways, global reaction route mapping also traced out four potential automerisation pathways, namely, EQ0 ↔ EQ0, EQ1 ↔ EQ1, EQ6 ↔ EQ6, and EQ7 ↔ EQ7, which can crop up through the conversion barriers of 80.89, 75.18, 76.18, and 72.35 kcal/mol, respectively. The automerisation, EQ0 ↔ EQ0, proceeds via TS0/0 that involves proton-hopping at the two opposite ends of linear C6 carbon chain in a seven-member ring formation. Similar proton-hopping, but at neighbouring carbon atoms, is responsible for other automerisation pathways that occur via TS1/1 and TS7/7. C. Dissociation channels

Finally, along the identified dissociation pathways, only one direct dissociation fragment, C + C5 H(2 ), has been traced out by GRRM program with the default option of 7 random structures as starting points as described in the Sec. II on computational details. Besides this, a second fragment, C3 (1  g + ) + C3 H(2 ), was revealed from the transition state TS7 /C3 + C3 H. In fact, as evident from Table II, this fragment is the least endothermic pair observed at CCSD(T)/6-311++G(d,p)//DFT/B3LYP/6-311++G(d,p) level of the theory. However, on increasing the number of random structures from an initial 7 to an arbitrary 24 as starting points in the GRRM computations at DFT/B3LYP/6-31G+ level, we were able to locate the most likely C6 (3  g − ) + H(2 A1g )fragment. However, as evident in Table II, this fragment is the least endothermic pair only at DFT/B3LYP/6-311++G(d,p) level of the theory, but surprisingly it is not the least endothermic pair at CCSD(T)/6311++G(d,p)//DFT/B3LYP/6-311++G(d,p) level of the theory. It should be noted that the carbon chain radical species are known to have large density of electronic states closer to the ground electronic state, and there is a very high probability of spin contamination and vibronic interaction between the states. Further, the other expected dissociation fragments proposed based on NBO analysis of EQs are: C4 (3  g − ) + C2 H(2  + ), and C2 (1  g + ) + C4 H, with the C4 H found in an unexpected 2  electronic state at DFT/B3LYP/6311++G(d,p) level, however, C4 H is known16 to have nearly degenerate 2  + and 2  states with the latter lying only 0.035 eV above the 2  + which has been predicted using multireference configuration interaction method. Furthermore, only isomer EQ7 can dissociate via a transition state, namely, TS7 /C3 + C3 H lying at 112.89 kcal/mol,

J. Chem. Phys. 139, 224311 (2013)

whereas, other isomers can directly decompose without any dissociation barrier indicating that they might freely recombine from the respective fragments. Further, the dissociation energy of EQ0 to C6 + H, C4 + C2 H, and C2 + C4 H is computed to be 108.37, 119.73, and 111.51 kcal/mol, respectively, at CCSD(T)/6-311++G(d,p)//DFT/B3LYP/6-311++G(d,p) level of the theory, which shows that the recombination may occur easily in the exothermic process. Furthermore, since no dissociation state, except TS7 /C3 + C3 H, was located along the dissociation pathways, we speculate that all the isomers decompose without any dissociation barrier indicating that the isomers can freely recombine from the respective fragments. Since the energies of dissociation fragments lay significantly higher above all the isomers and transition states, therefore, isomerisation seems to dominate the dissociation processes, in particular, the isomerisation of linear isomer EQ0 to sixmember ring isomer EQ1 is highly feasible. IV. CONCLUSIONS

The present work, while exploring the PES of C6 H through GRRM uphill walking method, reported eight new isomeric forms of C6 H, three of which are found to be potential isomers on the isomerization pathways of C6 H. The relevant isomers identified were further characterized on the basis of the spectral features involving harmonic vibrational frequencies, IR intensities, Raman scattering activities, and their relative shift upon isotopic substitution by 2 H. The observed geometrical parameters and spectral features are found to be in good agreement with the previously reported studies for the similar isomers identified in the present work. However, the present study first-time reported the isomerization pathways along with the transition states connecting the identified isomers. Besides this, GRRM also mapped a few dissociation channels for the decomposition of C6 H. However, the present computation with GRRM has been performed with program options such that computational cost and time remain low. The results may differ, in particular, regarding prediction of dissociation channels, if options at high level of the theory are chosen for the GRRM computations. Finally, since most of the isomers of C6 H have significant multireference character, therefore, multireference level of the theory is required for correct qualitative description of the identified isomers of C6 H radical. However, automated exploration of PES at the DFT level is sufficient for C6 H since isomers are observed to be well separated at the single-reference level as well as at the multireference level. The GRRM search performed at multireference level may be more appropriate which is though computationally highly expensive. Nonetheless, GRRM as a compass has been proved to be of immense guidance in the systematic and automated search for the isomerization pathways for the exotic C6 H, which may be quite helpful in the future investigation of this species and other molecular species evolving from it in the outer space. ACKNOWLEDGMENTS

The authors are grateful to Professor Koichi Ohno for providing GRRM program, and to Dr. Neetu Goel and De-

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224311-13

Vikas and G. Kaur

partment of Chemistry, Panjab University, Chandigarh for providing other computational software and resources. One of the authors, G.K., thanks University Grants Commission (UGC), India for providing financial support in the form of UGC-JRF(NET) fellowship. The authors are also obliged to the anonymous referees for their helpful suggestions in improvement of the paper. 1 H.

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