Cyanoform and Its Isomers. Relative Stabilities, Spectroscopic

Article pubs.acs.org/JPCA

Cyanoform and Its Isomers. Relative Stabilities, Spectroscopic Features, and Rearrangements by Coupled Cluster and MCSCF-Based Methods Published as part of The Journal of Physical Chemistry virtual special issue “Mark S. Gordon Festschrift”. Marek Szczepaniak and Jerzy Moc* Faculty of Chemistry, Wroclaw University, F. Joliot-Curie 14, 50-383 Wroclaw, Poland W Web-Enhanced Feature * S Supporting Information *

ABSTRACT: Although an isolation of elusive tricyanomethane HC(CN)3 was recently reported, the existence of other HC4N3 species has yet to be confirmed. In this work, the relative stabilities, spectroscopic features, and rearrangements of tricyanomethane and its four isomers are examined using single- (CCSD(T), CCSD(T)-F12) and multireference (MCSCF, MRPT2) methods. Tricyanomethane and dicyanoketenimine (NC)2CCNH, which are found to be the two most stable HC4N3 isomers lying within 9 kcal/mol, can be discriminated by their spectroscopic parameters. The predicted stepwise interconversion path relating HC(CN)3 and (NC)2CCNH features the HC4N3 species comprising the C− C−N ring moiety, with the largest barrier being associated with the initial H migration to one of the CN carbons. Adding a water molecule reduces the H migration barrier strongly and makes it possible to interconvert tricyanomethane to dicyanoketenimine in a “concerted” way.

1. INTRODUCTION The existence and spectroscopic characterization of tricyanomethane (cyanoform) HC(CN)3 (Scheme 1a) was recently

were obtained in the gas phase as a byproduct in two different chemical procedures.3 In the latter study, cyanoform was identified at very low pressure by microwave (MW) spectroscopy.3 In addition to cyanoform, other HC4N3 structures are conceivable. These include dicyanoketenimine (NC)2CCNH (Scheme 1b) (its unsuccessful isolation attempts were reported ref 2) and closely related dicyanoisonitrile (NC)2CNCH (Scheme 1d). The other plausible HC4N3 structures comprise a three-membered C−C−N ring moiety that involves either a C−H or N−H bond (Scheme 1c,e). Except for tricyanomethane,1,3 no other HC4N3 species have been observed experimentally. The HC4N3 structures shown in Scheme 1 feature three or two cyano functional groups (CN). The small molecules containing a single CN group, like HCN and methyl cyanide (CH3CN), are of astrochemical interest due to their occurrence in interstellar media and implicated significance in prebiotic chemistry.4,5 The multiple CN containing organic compounds, for example, tetracyanoethylene (TCNE) and its derivatives, have found application in the design of magnetic materials.6 To the best of our knowledge, theoretical studies on HC4N3 involved only tricyanomethane HC(CN)31,2 and dicyanokete-

Scheme 1. HC4N3 Isomers Examined

reported by Soltner et al.1 Tricyanomethane was prepared by the reaction of calcium tricyanomethanide Ca(C(CN)3)2 with hydrogen fluoride at low temperature. The obtained microcrystalline product involving HC(CN)3 appeared to be stable only below −40 °C.1 It should be added that the successful preparation of HC(CN)3 was preceded by many unsuccessful attempts undertaken over the last 100 years to isolate this compound.2 Prior to the confirmation of HC(CN)3 existence in the condensed phase, small amounts of unstable cyanoform © XXXX American Chemical Society

Received: October 31, 2016 Revised: January 13, 2017 Published: January 17, 2017 A

DOI: 10.1021/acs.jpca.6b10951 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

Figure 1. Geometrical structures of HC4N3 isomers 1−5 optimized at the CCSD(T)/cc-pVQZ level. Bond distances are in Å, and bond angles are in degrees. Note that the atom numbering of the C−C−N ring moiety in 3 and 5 is consistent with that used in TS3-4, TS3-5, and TS5-2 in Figure 2.

methods are employed in the first place to locate interconversion transition states (TSs), to determine associated minimum-energy pathways, and to estimate energy barriers involved (the details concerning the coupled cluster and multiconfigurational calculations are given in the next section).

nimine (NC)2CCNH,2 and they were at relatively low theoretical levels. Although these studies agree on the energetic preference of the former isomer over the latter, their relative energies have been the subject of some controversy because the reported ab initio (MP2/6-311++G(2d,2p)) and DFT (B3LYP/aug-cc-pVTZ) evaluations differ vastly in this respect.2 To assign the observed Raman spectra, Soltner et al.1 computed harmonic vibrational frequencies and Raman activities for HC(CN)3 and its deuterated form DC(CN)3 at the PBE0/6311G(3df,3dp) level. In this work, five HC4N3 isomers (whose schematic structures are shown in Scheme 1) are systematically investigated using coupled cluster methods with the aim to determine the relative stabilities and various spectroscopic features that can facilitate their future observation. For the recent example demonstrating an accuracy of the coupled cluster methods for predicting spectroscopic (IR, Raman, and NMR) properties of systems including nitrogen atoms, see ref 7. To gain an understanding of the ability of interconversion of the HC4N3 isomers, especially the most stable ones, we examine the relevant rearrangement pathways. As can be envisaged from Scheme 1, the latter reactions can entail π bond breaking or ring opening. Therefore, multiconfigurational

2. METHODS The coupled cluster singles and doubles with perturbative triples correction (CCSD(T))8 method with the cc-pVnZ (n = D,T,Q) basis sets9 was used to optimize molecular geometries on the lowest-energy singlet potential energy surface of HC4N3. The CCSD(T) vibrational frequencies were first calculated within the harmonic approximation, followed by accounting for the anharmonic corrections (the method of estimation of the latter is detailed in section 3.2). Relative energies were further improved by single-point calculations with the explicitly correlated coupled cluster theory CCSD(T)-F12.10,11 Both CCSD(T)-F12a and CCSD(T)-F12b variants were utilized along with the 3C(FIX) ansatz,10,11 employing the cc-pVnZF12 (n = T,Q) basis sets12 and the associated auxiliary basis sets.13−15 All of the coupled cluster calculations were performed with the MOLPRO2012.116 and CFOUR17 programs. B


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D,T,Q), CCSD(T)-F12/cc-pVnZ-F12 (n = T,Q), MCSCF(12e/11o)/cc-pVTZ, and MRPT2/cc-pVTZ levels of theory. One clear observation to be drawn from Table 1 is that tricyanomethane (1) is found to be the most stable of the HC4N3 isomers. Figure 1 shows that (1) has C3v symmetry, in agreement with the PBE0/6-311++G(3df,3pd)1 and MP2/6311++G(2d,2p)2 results. This HC4N3 isomer features three CN groups with the C−N triple bond of 1.157 Å (the same C−N bond length is calculated here by the CCSD(T)/cc-pVQZ method for the HCN molecule), and these CN moieties make a nearly linear CCN arrangement with the central carbon (which was also mentioned in ref 1). The presence of the three CN moieties in HC(CN)3 adds up to its thermodynamic stability. On the basis of Table 1, dicyanoketenimine (2) is predicted to be the second most stable HC4N3 isomer. With the CCSD(T)-F12/cc-pVQZ-F12 calculations expected to be most accurate in this table, dicyanoketenimine lies 9.0 kcal/mol higher in energy than tricyanomethane. Our CCSD(T)-F12/ccpVQZ-F12 energy difference between tricyanomethane and dicyanoketenimine can be compared with the literature MP2/6311++G(2d,2p) and B3LYP/aug-cc-pVTZ results of 12.7 and 1.8 kcal/mol, respectively.2 As can be seen from Table 1, the dicyanoketenimine structure features two equivalent CN groups that are bonded to the planar carbon along with the CNH moiety. Consequently, (NC)2CCNH (2) contains two kinds of C−N and C−C bonds. Those with the respective distances of 1.161 and 1.431 Å refer to both terminal CN groups making the linear CCN arrangement, as in HC(CN)3, and the other C−C and C−N linkages involve the CNH moiety. The CCSD(T)/cc-pVQZ determined C−C separation in (NC)2CCNH of 1.338 Å corresponds to the C−C double bond; it agrees well with the C−C bond length computed by us at this level for the ethylene molecule of 1.334 Å (the experimental C−C bond distance for C2H4 was reported to be 1.3305 Å).22 The predicted C−N(H) distance in (2) of 1.207 Å can be viewed as a relatively short C−N double bond; a comparison might be to a cyanomethyl cation (H2C−C−N+) with a CCSD(T)/cc-pVQZ C−N separation of 1.182 Å, where the corresponding bond was viewed “essentially triple”,23 and to the C−N double bond in methanimine (H 2CNH) with a B3LYP/6-311++G(d,p) reported distance of 1.267 Å.24 Note also that the C−C− N(H) bond angle in (2) of 173.1° deviates more from linearity than that made by the CN moieties. At the CCSD(T)-F12/cc-pVQZ-F12 level, dicyanoisonitrile isomer (4) is calculated to be 35.5 kcal/mol less stable than tricyanomethane (Table 1). The structure of dicyanoisonitrile differs from that of dicyanoketenimine mainly by containing the NCH moiety instead of the CNH one (Figure 1), and because of this similarity, we discuss (4) before (3). The CCSD(T)F12/cc-pVQZ-F12 computed energy difference between (NC)2CCNH and (NC)2CNCH of 26.5 kcal/mol, with the former being more stable, contrasts with the energy difference between the HNC and HCN isomers of 15.2 kcal/mol (MP4/ 6-311++G(3df,3pd)),25 with the latter molecule being energetically preferred. The N−C(H) separation in (NC)2CNCH of 1.190 Å (Figure 1) might be compared with the CCSD(T)/cc-pVQZ (cc-pV5Z) determined N−C distance in the isocyanomethyl cation (H2C−N−C+, involving the terminal C) of 1.228 (1.221) Å, where the respective linkage was described as “a long carbon−nitrogen triple bond”.23 In turn, the other (involving the NCH moiety) C−N separation in (NC)2CNCH of 1.313 Å

All of the multiconfigurational calculations were carried out using the GAMESS program.18 TSs were located employing multiconfigurational self-consistent field (MCSCF) wave functions19 with the cc-pVnZ (n = D,T) basis sets.9 The active space consisted of 12 electrons in 11 orbitals, denoted (12e/ 11o), yielding 60984 configuration state functions (CSFs). After being confirmed to be a first-order saddle point by the Hessian calculation, a minimum-energy path was determined at the MCSCF/cc-pVTZ level using the intrinsic reaction coordinate (IRC)20 to find a pair of HC4N3 isomers connected by this path. This was followed by MCSCF/cc-pVnZ (n = D,T) geometry optimization of the resulting structures (the local minima were confirmed by the Hessian calculation as well). The energies of all of the MCSCF stationary points were next refined by including the effects of dynamic correlation via second-order multireference perturbation theory (MRPT2)21 with the cc-pVTZ basis set. In addition, the TSs for rearrangement of the HC4N3 isomers were located using the coupled cluster CCSD(T) method and the cc-pVnZ (n = D,T) basis sets to comply with the levels of theory used for geometry optimization of the minima structures and to be able to make a direct comparison with the TS geometries and barrier heights calculated with the multiconfigurational methods.

3. RESULTS AND DISCUSSION 3.1. Structures and Stabilities. Geometries of the five HC4N3 isomers optimized by the CCSD(T) method with the cc-pVQZ basis set are shown in Figure 1 (the corresponding CCSD(T) and MCSCF(12e/11o) optimized geometries using the cc-pVDZ and cc-pVTZ basis sets are included in Figures S1 and S2 of the Supporting Information (SI)). These isomers are tricyanomethane (1), dicyanoketenimine (2), the isomer comprising the C−C−N ring moiety with a C−H bond (3), dicyanoisonitrile (4), and the isomer comprising the ring moiety with a N−H bond (5). Table 1 tabulates the relative energies of 1−5 calculated at the CCSD(T)/cc-pVnZ (n = Table 1. Relative Energies (kcal/mol) of HC4N3 Isomers 1− 5 at the MCSCF(12e/11o)/cc-pVTZ, MRPT2/cc-pVTZ, CCSD(T)/cc-pVnZ (n = D,T,Q), and CCSD(T)-F12/ccpVnZ-F12 (n = T,Q) Levelsa HC4N3 isomer

1

2

3

4

5

MCSCF(12e/11o)/cc-pVTZb MRPT2/cc-pVTZc CCSD(T)/cc-pVDZb CCSD(T)/cc-pVTZb CCSD(T)/cc-pVQZb CCSD(T)-F12a/cc-pVTZ-F12d CCSD(T)-F12b/cc-pVTZ-F12d CCSD(T)-F12a/cc-pVQZ-F12d CCSD(T)-F12b/cc-pVQZ-F12d

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

15.6 9.3 13.5 10.1 9.4 9.2 9.1 9.1 9.0

39.3 30.0 31.8 30.1 29.6 29.1 29.2 29.2 29.2

41.0 34.8 38.8 36.4 35.7 35.7 35.6 35.5 35.5

67.9 60.8 60.0 58.4 57.9 57.6 57.6 57.6 57.6

a

Energies are relative to 1 and include ZPE correction from the CCSD(T)/cc-pVTZ calculations, except for the CCSD(T)/cc-pVDZ energies including the CCSD(T)/cc-pVDZ ZPE correction and MCSCF(12e/11o)/cc-pVTZ and MRPT2/cc-pVTZ energies including the MCSCF(12e/11o)/cc-pVTZ ZPE correction. bAt the geometry optimized at this computational level (the CCSD(T)/ccpVnZ (n = D,T) and MCSCF(12e/11o)/cc-pVTZ optimized geometries of 1−5 are included in Figures S1 and S2, respectively). c At the geometry optimized at the MCSCF(12e/11o)/cc-pVTZ level. d At the geometry optimized at the CCSD(T)/cc-pVQZ level. C


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Table 2. Equilibrium Rotational Constants (in MHz) and Dipole Moments (in D) of HC4N3 Isomers 1−5 Calculated at the CCSD(T)/cc-pVQZ Levela rotational constants (MHz)

dipole moment (D)

1

2

3

4

5

1501.84 2851.67 2851.67 (2865.08)b 2.76

1407.85 2798.50 2812.46 5.28

1744.59 2690.13 3984.23 4.46

1461.51 2779.72 3063.02 5.63

1743.97 2668.94 4025.12 4.69

a

Calculated at the CCSD(T)/cc-pVQZ optimized geometries. bThe experimental value of the rotational constant Bo of tricyanomethane (1) is taken from the MW study (ref 3).

Table 3. CCSD(T)/cc-pVTZ Calculated Harmonic Vibrational Frequencies (ωi) of HC4N3 Isomers 1−5 (in cm−1)a exp.b

1 mode

ωi

sym

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

3065 2302 2301 1296 1029 832 564 563 336 334 161 128

A1 A1 E E E A1 E A1 A2 E A1 E

(9) (1) (7) (3) (16) (7) (0) (0) (0) (0) (22) (7)

[80] [71] [18] [2] [1] [7] [1] [4] [0] [2] [2] [4]

2885 2287 2259 1253 1022 825 575 567 347

2 ωi

sym

3532 2280 2279 2111 1320 1214 875 745 644 616 580 571 434 393 367 169 131 130

A′ A′ A″ A′ A′ A″ A′ A″ A′ A″ A′ A′ A′ A″ A″ A′ A′ A″

3 (107) (7) (6) (486) (5) (2) (469) (77) (0) (3) (11) (1) (30) (6) (0) (7) (8) (0)

ωi

sym

3255 2288 2282 1695 1244 1170 1049 781 770 637 584 555 508 488 259 220 201 130

A′ A″ A′ A′ A′ A″ A′ A″ A′ A′ A′ A′ A″ A″ A″ A″ A′ A′

4 (8) (4) (0) (13) (13) (32) (17) (26) (5) (5) (0) (3) (5) (1) (9) (1) (8) (7)

ωi

sym

3246 2266 2260 2045 1330 1244 784 671 649 585 578 556 431 401 343 161 133 129

A′ A′ A″ A′ A′ A″ A″ A′ A′ A″ A′ A′ A′ A″ A″ A′ A″ A′

5 (16) (7) (4) (363) (2) (12) (22) (757) (24) (11) (0) (3) (17) (3) (4) (3) (0) (5)

ωi

sym

3564 2285 2278 1580 1211 1181 1049 767 635 583 561 525 522 450 257 213 196 128

A′ A″ A′ A′ A′ A″ A′ A′ A′ A′ A″ A′ A″ A″ A″ A″ A′ A′

(106) (1) (2) (39) (6) (28) (12) (11) (19) (0) (96) (1) (3) (23) (12) (0) (12) (7)

a The values in parentheses are infrared intensities (in km/mol). The values in brackets are Raman activities (in Å4/amu) calculated at the MP2/ccpVTZ level with the GAMESS electronic structure suite18 (the corresponding MP2/cc-pVTZ frequencies are included for completeness in the SI). The infrared intensities for 3, 4, and 5 were calculated at the CCSD(T)/cc-pVDZ level (the vibrational frequencies obtained at the CCSD(T)/ccpVDZ level are included for completeness in the SI). bObserved Raman frequencies (in cm−1) for tricyanomethane (1) were taken from Table 1 of ref 1.

1.426 Å, respectively, point to both the elongated C4−N3 double bond and noticeable elongation of the C2−C4 bond, that is, by about 0.2 Å from (3). In summary, the CCSD(T)/ cc-pVQZ calculated geometrical parameters of (3) and (5) are consistent with the structures shown in Scheme 1c,e, respectively, with the former species found to be appreciably more stable. Upon basis set enlargement from cc-pVTZ (Figure S1) to ccpVQZ (Figure 1), the changes in the calculated bond lengths (bond angles) do not exceed 0.004 Å (one degree) for the HC4N3 structures not containing the C−C−N ring moiety and 0.006 Å for those including the ring. 3.2. Spectroscopic Features. The equilibrium rotational constants and dipole moments of isomers 1−5 based on the CCSD(T)/cc-pVQZ calculations are given in Table 2. It is seen from this table that the calculated rotational constants are distinct enough to serve as the structures’ “fingerprints”. For tricyanomethane (1), the theoretical constant of 2851.67 MHz agrees well (to within 13.5 MHz) with the rotational constant Bo of 2865.08 MHz available from the MW study.3 It is therefore reasonable to expect a similar degree of accuracy of the theoretical rotational constants provided for the other HC4N3 species.

appears to be the elongated double C−N bond; by invoking again ref 23, the CCSD(T)/cc-pVQZ (cc-pV5Z) computed C− N distance in H2C−N−C+ (involving the methylene C) of 1.279 (1.284) Å was referred to as an “essentially double bond”. One can infer from the above data that the predicted structure of (NC)2CNCH (4) conforms to the one in Scheme 1d. Although HC4N3 isomers (3) and (5) share the structural motif of the C−C−N ring moiety bonded to the two CN groups at the carbon C2 (Figure 1), they differ greatly in stability. Structure (3), which involves the C4−H bond, is found to be the third most stable HC4N3 isomer, lying 29.2 kcal/mol higher in energy than tricyanomethane (Table 1). In other words, the ring-comprising isomer (3) turns out to be more stable than dicyanoisonitrile (4) by 6.3 kcal/mol at the CCSD(T)-F12/cc-pVQZ-F12 level. For the C−C−N ring moiety in (3), the C2−C4, C4−N3, and C2−N3 distances of 1.462, 1.253, and 1.556 Å are indicative of the C2−C4 single and C4−N3 double bonds. Hydrogen transfer from the carbon C4 in (3) to the nitrogen N3 gives rise to isomer (5) with the N3−H bond (Figure 1). Structure (5) is predicted to be the least stable of the HC4N3 isomers considered, lying 57.6 kcal/ mol higher in energy than tricyanomethane at the CCSD(T)F12/cc-pVQZ-F12 level (Table 1). The C2−C4, C4−N3, and C2−N3 ring moiety distances of (5) being 1.635, 1.280, and D


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Figure 2. Geometrical structures of TSs for rearrangement of HC4N3 isomers 1−5 optimized at the MCSCF(12e/11o)/cc-pVTZ and CCSD(T)/ccpVTZ levels; the geometrical parameters shown for TS1-3 in parentheses were optimized at the CCSD(T)/cc-pVQZ level. Bond distances are in Å, and bond and dihedral angles are in degrees.

at the CCSD(T)/cc-pVTZ level. Also included in this table are the observed1 Raman frequencies of tricyanomethane (1) along with the predicted (at the MP2/cc-pVTZ level) Raman activities28 of this isomer. Table 3 shows an overestimation of the harmonic frequencies of (1) compared to experiment of 180 cm−1 for the C−H stretch (mode 1), of 15−42 cm−1 for the CN stretches (modes 2 and 3), and of 43 cm−1 for the C−C−H bend (mode 4). For the C−H stretch mode of the “related” HCN molecule, the reported29 CCSD(T)/aug-ccpVTZ harmonic vibrational frequency was greater than the experimental (anharmonic) value by 121 cm−1. In the case of the remaining lower-frequency modes of (1), for which experimental data are available (Table 3), the CCSD(T)/ccpVTZ harmonic frequencies are overestimated by 7 cm−1 (modes 5 and 6), and underestimated by 4−13 cm−1 (modes 7, 8, and 10).

Judging by the magnitude of the CCSD(T)/cc-pVQZ calculated dipole moments (Table 2), ranging from 2.76 to 5.63 D, it is evident that all of the HC4N3 isomers are highly polar; for comparison, the dipole moment of an isolated water monomer is 1.855 D.26 Because the dipole moment of dicyanoketenimine (2) (5.28 D) is found to be almost twice that of tricyanomethane (1) (2.76 D), distinguishing between the two lowest-energy HC4N3 structures (in the gas phase) should be feasible. The reliability of the calculated dipole moments in Table 2 is supported by the results of the systematic coupled cluster study27 of this quantity, which demonstrated that with augmentation of the cc-pVQZ basis set to the aug-cc-pVQZ level the mean absolute change in the equilibrium CCSD(T) dipole moments was 0.025 D. Table 3 summarizes harmonic vibrational frequencies (ωi) and infrared intensities of the HC4N3 isomers (1−5) calculated E


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Table 4. Relative Energies (kcal/mol) of TSs for Rearrangement of HC4N3 Isomers at the MCSCF(12e/11o)/cc-pVTZ, MRPT2/cc-pVTZ and CCSD(T)/cc-pVnZ (n = D,T) Levels of Theorya MCSCF(12e/11o)/cc-pVTZ MRPT2/cc-pVTZc CCSD(T)/cc-pVDZb CCSD(T)/cc-pVTZb

b

TS1-3

TS3-4

TS3-5

TS5-2

80.3 63.3 70.0 70.1 (70.1)d

91.2 71.7 80.7e 79.7e

109.1 95.8 95.5 94.4

106.0 86.6 92.7 91.7

a Energies are relative to 1. The CCSD(T)/cc-pVTZ energies include the ZPE correction from the CCSD(T)/cc-pVTZ calculations, the CCSD(T)/ cc-pVDZ energies include the CCSD(T)/cc-pVDZ ZPE correction, and the MCSCF(12e/11o)/cc-pVTZ and MRPT2/cc-pVTZ energies include the MCSCF(12e/11o)/cc-pVTZ ZPE correction. bAt the geometries optimized at this computational level (the CCSD(T)/cc-pVDZ optimized geometries of the TSs are included in Figure S3). cAt the geometries optimized at the MCSCF(12e/11o)/cc-pVTZ level. dThe barrier in parentheses was calculated at the CCSD(T)/cc-pVQZ level using the CCSD(T)/cc-pVQZ optimized geometries and CCSD(T)/cc-pVTZ ZPE correction. eRefers to the broken-symmetry structure (cf. Figure 2 and see the text).

Next, anharmonic vibrational frequencies (νi) of the HC4N3 isomers (1−5) have been calculated by adding anharmonic corrections from second-order vibrational perturbation theory (VPT2)30 (based on the MP2/cc-pVTZ calculations) to the CCSD(T)/cc-pVTZ harmonic frequencies. The anharmonic results are shown in Table S3 (for the results of the test calculations carried out with this approach for HCN, see Table S4). For the tricyanomethane (1) modes (1−4), adding anharmonic corrections decreases the absolute deviation from experiment to 44 cm−1 for the C−H stretch (mode 1), to 2−27 cm−1 for the CN stretches (modes 2 and 3), and to 13 cm−1 for the C−C−H bend (mode 4). The magnitude of the anharmonic corrections for the CN stretching modes of (1) of about 40 cm−1 (Tables 3 and S3) is consistent with the recent systematic DFT study of CN stretchings, which found an average anharmonic correction of about 35 cm−1.6 Comparison of Tables 3 and S3 indicates that for the isomers 2−5, anharmonic corrections of similar size as those for (1) have been predicted for the higher-frequency modes (1−4). It is suggested that the CCSD(T)/cc-pVTZ harmonic infrared intensities (Table 3) (along with the anharmonic frequencies in Table S3) can assist in identification/characterization of the HC4N3 species, in particular, in differentiating between (1) and (2). This notion is justified based on the recent analytic calculations of anharmonic vibrational spectra,31 which found that considering anharmonic effects is more important in the prediction of the vibrational frequencies than in the calculation of infrared and Raman intensities. 3.3. Rearrangement Pathways. It follows from the previous considerations that tricyanomethane (1) and dicyanoketenimine (2) are the two most stable HC4N3 isomers, with the latter lying 9 kcal/mol higher in energy than the former (Table 1). Using the MCSCF(12e/11o)/cc-pVTZ method, we have found that the mechanism behind the interconversion of the two species is a multistep one that involves other HC4N3 isomers; for the associated MCSCF minimum-energy paths, see Figures S4−S7 of Supporting Information. This way we have also revealed energy barriers separating the local minimum-energy structures on the lowest potential energy surface of HC4N3. In this section, we report on the predicted rearrangement steps in some detail. In addition, we compare the results obtained by the single- and multireference methods. Figure 2 shows the TSs involved in various rearrangements of the HC4N3 structures, located on both the MCSCF(12e/ 11o)/cc-pVTZ and CCSD(T)/cc-pVTZ PES, with the relevant energies in Table 4. Let us assume that an interconversion between (1) and (2) starts with the experimentally observed1,3

tricyanomethane. The MCSCF calculations indicate that the initial isomerization step that proceeds via the TS TS1-3 entails the H migration to one of the CN carbons, which is accompanied by the C−C(H)−N bending, ending up with the formation of the ring to yield (3) (IRC movies32 1, 2, 3, and 4 of this and other HC4N3 rearrangements discussed in this section are available). The MCSCF calculated geometry of TS1-3 contains the partially formed C−H bond with a distance of 1.176 Å (the original C−H bond of (1) is essentially broken with the C−H distance of 1.790 Å) and a C−C(H)−N bond angle of 161.9°. It is instructive to compare the MCSCF optimized structure of TS1-3 with that found at the CCSD(T) level (Figure 2). First, the two TSs look qualitatively similar (this is not always the case, as discussed below). Furthermore, the MCSCF and CCSD(T) geometrical parameters describing the “active” site of TS1-3 agree reasonably well. For instance, the newly formed C−H bond distance and C−C(H)−N bond angle computed by the two schemes are within 0.015 Å and 3.5°, respectively. The additional TS1-3 geometry optimization using the CCSD(T)/ cc-pVQZ method (the geometrical parameters in parentheses in Figure 2) has afforded the structure that varies insignificantly relative to the CCSD(T)/cc-pVTZ one. The relative energy profiles for a stepwise interconversion of tricyanomethane to dicyanoketenimine by the MRPT2/ccpVTZ and CCSD(T)/cc-pVTZ methods are summarized in Figure 3. The latter figure shows that there is a large energy barrier for (1) rearranging to (3) of 63.3 kcal/mol at the

Figure 3. MRPT2/cc-pVTZ and CCSD(T)/cc-pVTZ energy profiles for stepwise interconversion of tricyanomethane (1) into dicyanoketenimine (2) calculated at the MCSCF(12e/11o)/cc-pVTZ and CCSD(T)/cc-pVTZ geometries, respectively, with ZPE corrections obtained at the respective geometry optimization levels. F


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(2), the initial step entailing H migration to one of the CN carbons and subsequent formation of the HC4N3 “intermediate” comprising the C−C(H)−N ring moiety is kinetically most demanding, with the associated energy barrier amounting to 70.1 kcal/mol at the CCSD(T)/cc-pVTZ (cc-pVQZ) level. In this section, we report on the effect of microhydration (by a single water molecule) on this reaction. Figure 4 depicts the CCSD(T)/cc-pVTZ optimized TS TS12_H2O for water-assisted rearrangement of tricyanomethane

MRPT2/cc-pVTZ level, reflecting the tricyanomethane C−H bond breaking involved. At the CCSD(T)/cc-pVTZ level, the barrier is about 7 kcal/mol higher (70.1 kcal/mol), and the same barrier is found from the CCSD(T)/cc-pVQZ calculations. Also note that allowing for dynamic correlation via MRPT2 stabilizes the TS1-3 structure by as much as 20 kcal/ mol relative to the MCSCF energy, bringing the barrier estimate by the former approach to much better agreement with the CCSD(T) results (Table 4). Though a rearrangement of (3) to (4), which we deal with next, is not directly related to the conversion of tricyanomethane to dicyanoketenimine, it affords dicyanoisonitrile of comparable stability to (3) (Table 1); we also think it is methodologically instructive. The former rearrangement occurs by opening of the C−C−N ring moiety through TS TS3-4 (cf. Figure 2). The MCSCF calculated TS3-4 has Cs symmetry with an essentially broken C2−C4 bond (the C2−C4 distance is 2.164 Å) and an overall structure resembling that of isomer (3) (the C1−C2−N3−C4 dihedral angle = −91.9°). For comparison, the CCSD(T)/cc-pVTZ optimized TS3-4 exhibits a significantly shorter C2−C4 distance of 2.052 Å, and by contrast with the corresponding MCSCF structure, it breaks heavily Cs symmetry, as evident from the nonequivalent terminal CN groups that it contains and the C1−C2−N3− C4 dihedral angle of 141.9°. Analysis of the MCSCF electronic configurations for TS3-4 reveals significant muliconfigurational character, with the coefficients of two dominant configurations being 0.76 and −0.58. For this reason, CCSD(T) breaks down for TS3-4. At the MRPT2/cc-pVTZ level, TS TS3-4 lies 41.7 kcal/mol above isomer 3 (although the corresponding CCSD(T)/cc-pVTZ relative energy is not reliable, it is also included in Table 4 to report the case). Now, being back to the (1) → (2) multistep conversion mechanism, we examine hydrogen transfer leading from (3) to (5) that happens with involvement of the TS TS3-5. Figure 3 shows that this is an endothermic step. The TS3-5 structure features a nonclassical C4−H−N3 bridge motif (Figure 2), and it is of predominant single-configurational character. The latter is also reflected to be in good agreement with the geometrical parameters obtained (for the “active site”) by the single- and multireference methods. On the basis of the MRPT2/cc-pVTZ (CCSD(T)/cc-pVTZ) calculations, the energy barrier separating (3) from (5) is estimated to be 65.8 (64.3) kcal/mol, and its magnitude is related to the nonclassical TS structure mentioned above. The final step along the interconversion route in question involves ring opening in (5) to deliver dicyanoketenimine (2). This strongly exothermic rearrangement (Figure 3) occurs through the TS TS5-2 whose MCSCF geometry comprises C2−N3 breaking bond with a C2−N3 distance of 2.021 Å and a C2−C4−N3 bond angle close to 90° (Figure 2). In the CCSD(T) geometry of TS5-2, the breaking bond separation appears to be 0.050 Å shorter than the MCSCF separation, with the other distances (angles) describing the C−C−N ring moiety opening differing up to 0.054 Å (1.4°). Significantly, the calculated energy barrier separating (5) from (2) is the lowest along the multistep interconversion path, amounting to 25.8 (MRPT2/cc-pVTZ) and 33.5 (CCSD(T)/cc-pVTZ) kcal/mol (Figure 3). 3.4. Water-Mediated Rearrangement of Tricyanomethane to Dicyanoketenimine. The results of the previous section have indicated that, in the stepwise interconversion of tricyanomethane (1) to dicyanoketenimine

Figure 4. Geometrical structure of TS TS1-2_H2O for water-assisted rearrangement of tricyanomethane (1) to dicyanoketenimine (2) optimized at the CCSD(T)/cc-pVTZ level (the imaginary frequency for TS1-2_H2O is 300i cm−1 based on the CCSD(T)/cc-pVDZ Hessian calculation; see Figure S8).

Figure 5. CCSD(T)/cc-pVTZ energy profile for water-mediated rearrangement of tricyanomethane (1) to dicyanoketenimine (2), occurring with formation of prereaction complex 1···H2O and postreaction complex 2···H2O, calculated at the CCSD(T)/cc-pVTZ geometries with ZPE corrections obtained at the CCSD(T)/cc-pVDZ level (CCSD(T)/cc-pVDZ energy profile is shown for comparison).

(1) to dicyanoketenimine (2), with the energy profile of the associated reaction pathway given in Figure 5. The latter figure shows that the water-mediated conversion proceeds with formation of the prereaction complex 1···H2O, stabilized by 6.4 kcal/mol relative to separated 1 and H2O (Table 5); for the structure of 1···H2O, including the C−H···O hydrogen bond, see Figure S8 (for a recent example of the nonconventional C− H···O hydrogen bond, see ref 33). Formation of the complex 1···H2O with the C−H···O hydrogen bond gives access to concerted migration of two H G


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Table 5. Relative Energies of Species Involved in Water-Assisted Rearrangement of Tricyanomethane (1) to Dicyanoketenimine (2)a b

CCSD(T)/cc-pVDZ CCSD(T)/cc-pVTZc

1 + H2O

1···H2O

TS1-2_H2O

2···H2O

2 + H2O

0.0 0.0

−7.6 −6.4

28.0 28.1

3.4 1.6

13.5 10.1

a

Energies are relative to 1 + H2O and include ZPE correction from the CCSD(T)/cc-pVDZ calculations. bAt the geometries optimized at the CCSD(T)/cc-pVDZ level (the CCSD(T)/cc-pVDZ optimized geometries of 1···H2O, TS1-2_H2O, and 2···H2O are shown in Figure S8). cAt the geometries optimized at the CCSD(T)/cc-pVTZ level (the CCSD(T)/cc-pVTZ optimized geometries of 1···H2O and 2···H2O are shown in Figure S8).

atoms taking place via TS1-2_H2O wherein the tricyanomethane C−H bond is already broken (with a C−H distance of 1.950 Å), and the partial O−H bond is formed (with an O−H distance of 1.025 Å); at the same time, one of the water molecule’s innate hydrogens is transferred to the N atom (Figure 4) to eventually make a N−H bond. Compared to the H migration barrier of the nonhydrated interconversion via TS1-3 (Figure 3), adding a water molecule reduces the barrier strongly. Indeed, at the CCSD(T)/cc-pVTZ level, the water-mediated H migration barrier through TS12_H2O amounts to 28.1 (34.5) kcal/mol relative to separated 1 + H2O (1···H2O complex) (Figure 5, Table 5), meaning a barrier reduction by as much as 42.0 (36.5) kcal/mol. Figure 5 further shows that H migration results in postreaction complex 2···H2O, bound by 8.5 kcal/mol with respect to separated 2 and H2O; for the structure of 2···H2O featuring a N−H···O hydrogen bond, see Figure S8. The final water detachment from 2···H2O yields the dicyanoketenimine isomer (2).

Full citation for refs 16−18, CCSD(T)/cc-pVnZ (n = D,T) optimized geometries of 1−5 (Figure S1), MCSCF/cc-pVnZ (n = D,T) optimized geometries of 1−5 (Figure S2), MCSCF/cc-pVDZ and CCSD(T)/ccpVDZ optimized geometries of the TSs for rearrangements of the HC4N3 isomers (Figure S3), MCSCF/ccpVTZ minimum-energy paths for rearrangements of the HC4N3 isomers (Figures S4−S7), CCSD(T)/cc-pVDZ optimized geometry of the TS TS1-2_H2O and CCSD(T)/cc-pVnZ (n = D,T) optimized geometries of 1···H2O and 2···H2O (Figure S8), MP2/cc-pVTZ harmonic vibrational frequencies of 1 (Table S1), CCSD(T)/cc-pVDZ harmonic vibrational frequencies of 3−5 (Table S2), calculated anharmonic vibrational frequencies of 1−5 (Table S3), and calculated and experimental harmonic and anharmonic vibrational frequencies of HCN (Table S4) (PDF) W Web-Enhanced Features *

IRC movies of the 1 → 3, 3 → 4, 3 → 5, and 5 → 2 rearrangements, based on the MCSCF/cc-pVTZ calculations, are available in avi format in the online version of the paper.

4. SUMMARY We have examined the relative stabilities, spectroscopic features, and rearrangements of tricyanomethane and its four isomers using single- (CCSD(T), CCSD(T)-F12) and multireference (MCSCF, MRPT2) methods. The results show that tricyanomethane HC(CN) 3 and dicyanoketenimine (NC)2CCNH are the two most stable HC4N3 isomers, with the latter lying 9 kcal/mol higher in energy with our most accurate CCSD(T)-F12/cc-pVQZ-F12 calculations. The other HC4N3 isomers studied, including those comprising the C−C− N ring moiety, turned out to be less stable than tricyanomethane by at least 29 kcal/mol at this level of theory. Tricyanomethane HC(CN) 3 and dicyanoketenimine (NC)2CCNH can be discriminated by their spectroscopic parameters. The MCSCF calculations suggest that there is a pathway from HC(CN)3 to (NC)2CCNH interrelating also the two HC4N3 local minimum-energy structures comprising the C−C−N ring moiety, which is formed or opened along this pathway. Starting from tricyanomethane, the energy barriers separating any HC4N3 isomer from a nearby structure are calculated to be in the range of 25.8−63.3 kcal/mol (at the MRPT2/cc-pVTZ level) and 33.5−70.1 kcal/mol (at the CCSD(T)/cc-pVTZ level), with the largest barrier being associated with initial H migration to one of the CN carbons. It is found that adding a water molecule reduces the H migration barrier strongly and makes it possible to interconvert tricyanomethane to dicyanoketenimine in a concerted way.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel. (48)(71) 375-7267. ORCID

Jerzy Moc: 0000-0002-8221-1914 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge computational resources provided by the Wroclaw Centre for Networking and Supercomputing, WCSS.

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REFERENCES

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b10951. H


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Cyanoform and Its Isomers. Relative Stabilities, Spectroscopic

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