Effects of Cyano Substituents on Cyclobutadiene and Its Isomers

May 13, 2010 - Department of Chemistry, Truman State UniVersity, 100 Normal AVenue, ... compound.20 The electronic states of cyclobutadiene have been...
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J. Phys. Chem. A 2010, 114, 6431–6437

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Effects of Cyano Substituents on Cyclobutadiene and Its Isomers Jessica L. Menke,† Eric V. Patterson,‡ and Robert J. McMahon†,* Department of Chemistry, UniVersity of Wisconsin, 1101 UniVersity AVenue, Madison, Wisconsin, 53706-1322, Department of Chemistry, Truman State UniVersity, 100 Normal AVenue, KirksVille, Missouri, 63501-4200 ReceiVed: March 4, 2010; ReVised Manuscript ReceiVed: April 17, 2010

The effects of cyano substitution on cyclobutadiene are explored using density functional, coupled-cluster, CASSCF, and CASPT2 calculations. An isodesmic reaction is employed to gauge the relative stabilization (∆H°rxn) of cyclobutadienes with varying numbers of cyano groups. Although density functional theory predicts a relatively large stabilization for the addition of four cyano substituents to cyclobutadiene (18.5 kcal/mol), coupled-cluster theory predicts a smaller stabilization (9.3 kcal/mol). The effect of the number of cyano groups on the singlet-triplet gaps is also investigated. NBO calculations lend insight into the structural trends of the triplets, and the comparison of coupled-cluster and CASSCF calculations sheds light on the multireference electronic character in these systems. The effect of tetracyano substitution on tetrahedrane and other C4H4 isomers is also explored. Introduction A variety of organic compounds bearing cyano (-C≡N), as well as iso-cyano (-NdC), substituents have been identified in the interstellar medium (ISM)1-5 and in the atmosphere of Titan, Saturn’s largest moon.6-9 Cyano- and dicyanoacetylene have been observed on Titan, while larger cyanopolyynes, up to H-(C≡C)5-C≡N, have been observed in dense clouds of the interstellar medium. The detection of these species relies upon the combination of observational astronomy and laboratory spectroscopysoften with the assistance of theoretical/computational studies. The intrinsic polarity of the cyano substituent may give rise to strong infrared and rotational absorptions, which renders cyano-containing compounds as important probes in astrochemistry. Cyano-containing molecules show interesting reactivity due to the strong electron-withdrawing capability of the cyano group.10 In the context of astrochemistry, cyano compounds are hypothesized to be intermediates in the formation of biologically relevant molecules.11,12 The chemistry of cyanoacetylene is of particular interest to us. Cyanoacetylene trimerizes to form tricyanobenzenes under both thermal13 and photochemical14,15 conditions. In these reactions, dicyanocyclobutadienes are predicted intermediates. Cyclobutadiene (1) has been a molecule of great interest for over a century due to recurring questions of its antiaromatic character, geometry, electronic structure, and reactivity.16-18 In the gas phase or in solution, cyclobutadiene undergoes rapid [4 + 2] dimerization.16,17,19 It has been generated and spectroscopically characterized only when isolated in a rare gas matrix16,17 or within the cavity of a supramolecular container compound.20 The electronic states of cyclobutadiene have been explored using a wide variety of computational methods, and the general features are depicted in Figure 1.21,22 The singlet ground state exhibits a rectangular structure (11Ag). The first excited statesa triplet with a square geometry (13A2g)sis lowlying in energy. * To whom correspondence should be addressed. Telephone: (608) 2620660. Fax: (608) 263-5549. E-mail: [email protected]. † University of Wisconsin. ‡ Truman State University.

Figure 1. Lowest electronic states of cyclobutadiene.21,22

Baird argued in 1972 that the 4n + 2 and 4n π-electron rules for ground-state aromaticity are reversed for cyclic hydrocarbons in their lowest triplet states.23 Recent computational studies support this interpretation by predicting characteristic features of aromaticity (planarity, equalization of bond lengths, diatropic ring current, large shielding of 1H NMR chemical shift; negative values of nucleus-independent chemical shift (NICS), magnetic susceptibility, and magnetic susceptibility exaltation) for a number of 4n π-electron triplet annulenes, including triplet cyclobutadiene.24-26 Judicious choice of substituents affords cyclobutadiene derivatives that are amenable to preparation and isolation under normal laboratory conditions. Bulky groups block dimerization, enabling the isolation of a number of substituted cyclobutadiene derivatives,17,18,27 including the symmetrically tetra-substituted

10.1021/jp101963p  2010 American Chemical Society Published on Web 05/13/2010

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CHART 1: Structures of Singlet Cyclobutadiene (1) and Its Mono- (2), Di- (3a,b,c), Tri- (4), and Tetracyano (5) Derivatives

Menke et al. TABLE 1: Computed Rotational Constants and Dipole Moments for Singlet Cyanocyclobutadienesa,b Ae Be Ce µ a

2

3b

4

14762 2450 2101 4.4

2942 1844 1134 5.1

2134 952 658 3.4

B3LYP/6-31G*.

b

Rotational constant (MHz), dipole moment

(D).

species tetra-tert-butylcyclobutadiene and tetrakis(trimethylsilyl)cyclobutadiene.16,28 In addition to simple steric effects, electronic characteristics of the substituents may also play a role in determining the structure and stability of substituted cyclobutadiene derivatives. The highly electronegative fluorine substituents in tetrafluorocyclobutadiene cause a subtle pyramidalization of the ring carbons, resulting in a nonplanar structure.29 With respect to cyano-substituted cyclobutadienes (Chart 1), little is known, experimentally. Dicyanocyclobutadienes have been invoked as intermediates in the trimerization of cyanoacetylene.13,14,30,31 The aromatic dianion of tetracyanocyclobutadiene represents an intriguing target,27 but neither the dianion nor the neutral precursor have been isolated.32 EckertMaksic´ et al. recently reported a computational study on several cyanocyclobutadiene derivatives, focusing on the effect of the cyano substituent on the barrier to degenerate bond-shifting (automerization).33 In this report, we describe computational studies that probe the structural, spectroscopic, and energetic consequences of cyano substitution of cyclobutadiene, tetrahedrane, and other members of the C4H4 family of isomers. Computational Methods Initial optimized structures and energies were computed using the B3LYP density functional34-36 with the 6-31G* or the 6-311+G* basis sets.37 Further calculations were done using coupled-cluster singles and doubles (CCSD)38 with unrestricted Hartree-Fock references and Dunning’s correlation consistent double-ζ basis set (cc-pVDZ).39 Single point calculations on the CCSD/cc-pVDZ geometries were completed at the CCSD(T)/ cc-pVDZ level (includes triple excitations noniteratively).40 Additional single point calculations were performed using the complete-active-space multiconfigurational SCF methods (CASSCF41 and CASPT242) with the ANO-L-VTZP43 basis set. All values, unless otherwise noted, have been corrected for zero point vibrational energies (ZPVE) computed at the B3LYP/6311+G* level. For the multireference calculations, the active spaces were chosen to include the pz π/π* orbitals in each system, resulting in a CAS(4,4) active space for 1; a CAS(6,6) active space for 2; a CAS(8,8) active space for 3a, 3b, and 3c; a CAS(10,10)

active space for 4; and a CAS(12,12) active space for 5. We use the designation CAS(x,x) when referring to this series of calculations. To probe whether or not the size of the active space was sufficient, calculations were performed in which the active space was expanded to include the py π/π* orbitals on the cyano substituent(s): CAS(8,8) for 2; CAS(12,12) for 3a, 3b, and 3c. In each case, the smaller active space provided a value for the singlet-triplet energy gap within (0.3 kcal/mol of the value predicted by the larger active space. Therefore, we focus our discussion on data obtained using the smaller active space, while the remaining data may be found in Supporting Information. The Gaussian 03 package was used for DFT and CCSD(T) calculations,44 the ACES II MAB program was used for CCSD calculations,45 and the MOLCAS program was used for CAS and CASPT2 calculations.46 Harmonic vibrational frequencies were computed for the DFT structures to verify all geometries were minima (no imaginary frequencies) and to obtain zeropoint vibrational energies (ZPVE). Natural bond orbital (NBO) calculations were done at the HF level of theory on the B3LYP geometries using the NBO 5.0 program.47,48 As a test of this protocol, NBO calculations on 2 were performed at HF/6-31G*// B3LYP/6-31G* and HF/6-31G*//CCSD/cc-pVDZ levels. Little difference was found between the two levels of theory. Results and Discussion Structure and Spectroscopy. Optimized structures obtained using B3LYP or CCSD methods reveal no significant differences (see Supporting Information). This finding supports the validity of using either structure as the basis for subsequent single-point electronic structure calculations. The singlet cyclobutadienes exhibit rectangular structures with bond-length alternation (1.34 and 1.56 Å), whereas the triplet states are square, or very nearly so (1.45 Å). Neither the structure of the singlet nor the triplet state exhibits a notable dependence on the number or position of the cyano substituents. The observed bond-length equalization in the triplet structures is consistent with the aromatic character of these states.23-26 Additional evidence in support of aromaticity of the triplet states is provided by NICS values and computed 1 H NMR chemical shifts (see Supporting Information). Several of the cyano-substituted cyclobutadienes (2, 3b, 4) are quite polar, which will give rise to strong rotational transitions and infrared absorptions. In support of future efforts to detect and characterize these species by rotational spectroscopy, computed rotational constants and dipole moments are summarized in Table 1. In support of future efforts to detect and characterize these species using matrix-isolation spectroscopy, computed harmonic vibrational frequencies and infrared intensities are included in the Supporting Information section. Stabilization/Electronic Structure/Singlet-Triplet Gap. The following isodesmic reaction has been employed to examine

Effects of Cyano Substituents on Cyclobutadiene

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CHART 2: Stabilization Enthalpies (∆H°rxn kcal/mol, without ZPVE) for Cyclobutadiene Derivativesa,b,c

TABLE 2: Stabilization Enthalpies (∆H°rxn kcal/mol, with ZPVE) for Cyano Substitution of the Closed-Shell Singlet Ground State of Cyclobutadienea

1 2 3a 3b 3c 4 5

n

symmetry

B3LYP/ 6-31G*

B3LYP/ 6-311+G*

0 1 2 2 2 3 4

D2h Cs C2h C2V C2V Cs C2h

0.0 -9.4 -15.3 -14.5 -15.3 -17.8 -18.5

0.0 -7.7 -12.0 -11.1 -11.8 -12.7 -11.5

CCSD

CCSD(T)b

0.0 -5.2 -7.9

0.0 -4.7 -9.4 -6.0d -10.0 -8.3 -9.3

c

-7.3 -7.0 -4.5

a Evaluated using an isodesmic reaction (eq 1). b Single-point calculation on the CCSD/cc-pVDZ structure. c Structure optimized to that of 3c. d Single point calculation on the B3LYP/6-311+G* structure.

TABLE 3: Stabilization Enthalpies (∆H°rxn kcal/mol, with ZPVE) for Cyano Substitution of the Lowest Triplet State of Cyclobutadienea n symmetry 3

a

Evaluated using an isodesmic reaction (eq 1). b B3LYP/6-31G* structures. c Values for molecules 6-9 from refs 28 and 49.

the enthalpic effect of substituents on cyclobutadiene and tetrahedrane28,49

1 2 3 3a 3 3b/33c 3 4 3 5 3

a

C4H4 + nCH3R f C4H(4-n)Rn + nCH4

(1)

where R is the substituent of interest, and n is the number of substituents. By computing ∆H°rxn for various substituents and values of n, one can determine if the substituents have a stabilizing effect (∆H°rxn < 0) or a destabilizing effect (∆H°rxn > 0) on the ring. Maier et al.28 and Balci et al.49 computed ∆H°rxn for R ) H, CH3, C(CH3)3, SiH3, and Si(CH3)3 (with n ) 4). For comparison to their work, we computed ∆H°rxn for R ) CN (n ) 4) at a comparable level of theory (B3LYP/6-31G*, without ZPVE correction), as shown in Chart 2. At this level of theory, four cyano substituents are predicted to confer a modest stabilization (-14.8 kcal/mol) to singlet cyclobutadiene. Although a family of techniques has been developed to evaluate reaction thermochemistry (isogyric, isodesmic, homodesmotic reactions, etc.),50 we chose to utilize eq 1 in order to facilitate comparison with closely related studies in the literature.28,49 The full series of cyano-substituted cyclobutadienes was explored, in greater detail, using data obtained at higher levels of theory. Table 2 gives the stabilization enthalpies (∆H°rxn) determined from eq 1 for the singlet ground state of cyclobutadiene for R ) CN and n ) 1-4 using values derived from DFT or coupled-cluster methods. There is a significant variation between the methods. As a point of comparison, the stabilization enthalpies for tetracyanocyclobutadiene (5) vary from -18.5 kcal/mol (B3LYP/6-31G*) to -4.5 kcal/mol (CCSD/cc-pVDZ), with a value of -9.3 kcal/mol for CCSD(T)/cc-pVDZ//CCSD/ cc-pVDZ. Since the overall electronic delocalization increases as more cyano groups are added, and since DFT has a known tendency to artificially favor delocalized systems,51-54 we feel that the results obtained using coupled-cluster calculations are more reliable. The earlier DFT calculations for compounds 6-9 are less likely to suffer from the same problem, since the substituents in those systems do not introduce additional π-conjugation. Indeed, calculation of the stabilization enthalpy for tetramethylcyclobutadiene (6) using either CCSD/cc-pVDZ

0 1 2 2 3 4

D4h C2V D2h C2V C2V D4h

B3LYP/ B3LYP/ 6-31G* 6-311+G* CCSD CCSD(T)b 0.0 -11.0 -17.1 -18.2 -21.5 -22.7

0.0 -9.3 -13.8 -14.8 -16.5 -15.8

0.0 -6.7 -10.0 -10.3 -10.4 -9.1

Evaluated using an isodesmic reaction (eq 1). calculation on the CCSD/cc-pVDZ structure.

b

0.0 -7.1 -11.1 -11.3 -12.0 -12.1 Single-point

or B3LPY/6-31G* values affords comparable results (∆H°rxn ) -32.3 vs -35.3 kcal/mol, respectively, with ZPVE) (Table 2). The sequential introduction of cyano substituents in singlet cyclobutadiene yields a nonmonotonic trend in the stabilization enthalpy predicted by the isodesmic reaction, eq 1 (Table 2). Although we were initially misled by the predictions of the DFT calculations, it appears clear from the coupled-cluster data that the first and second cyano substituents each confer a modest enthalpic stabilization to the system, but the third and fourth cyano substituents do not. Stabilization enthalpies (∆H°rxn) were also determined from eq 1 for the lowest triplet state of cyclobutadiene for R ) CN and n ) 1 - 4 (Table 3). In these calculations, the triplet state energies of cyclobutadiene and the corresponding cyanosubstituted cyclobutadiene derivatives were used, along with singlet state energies of acetonitrile and methane. The trends for the triplets closely follow those of the singlets. There is an increase in stabilization upon introduction of the first two cyano substituents, but little additional stabilization upon introduction of the third and fourth cyano groups. Adiabatic singlet-triplet (S-T) energy gaps for the series of cyano-substituted cyclobutadienes, computed at various levels of theory, are presented in Table 4. (A negative S-T gap indicates a singlet ground state.) Although we were initially captivated by the DFT prediction of very small S-T gaps in this seriessincluding the prediction of a triplet ground state for tetracyanocyclobutadiene (5)sit became apparent that these predictions are inaccurate. Further investigation using both coupled-cluster and multireference calculations (see below) reveals very little dependence of the S-T gap with increasing cyano substitution. Actually, the DFT prediction for this trend is qualitatively correct, but the calculation is fundamentally crippled by the fact that the singlet-triplet gap for cyclobutadiene itself (1) is underestimated by ca. 10 kcal/mol (Table 4).

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Menke et al.

TABLE 4: Computed S-T Gap (kcal/mol with ZPVE) for Cyano-Substituted Cyclobutadienesa 1 2 3a 3b 3c 4 5

B3LYP/6-31G*

B3LYP/6-311+G*

CCSD

CCSD(T)b

CAS(x,x)b,c

CAS(x,x)PT2b,c

CAS(4,4)PT2b,d

MR-AQCCd,e

-4.1 -2.5 -2.2 -0.4 -1.2 -0.3 +0.2

-4.9 -3.4 -3.0 -1.2 -1.9 -1.1 -0.6

-9.5 -8.1 -7.4

-11.2 -8.8 -10.0 -6.2g -9.6 -7.5 -8.4

-16.0 -12.9 -14.3 -16.1g -13.7 -14.9 -12.3

-10.3 -7.1 -8.6 -7.3g -7.6 -8.0 -7.0

-10.3 -12.6 -9.4 -8.1g -8.7 -9.2 -8.3

-14.9 -13.5 -12.8 -11.1 -10.5

f

-6.6 -6.1 -5.0

a S-T gap < 0 indicates singlet ground state. b Single-point calculation on the CCSD structures. c Active space contains all pz π/π* orbitals (see computational methods). d Active space contains only pz π/π* orbitals of cyclobutadiene ring (4,4). e S-T gap determined using the electronic energies (MR-AQCC(4,4)/6-311G(2d,p)//CASSCF/6-31G*) from ref 33. f Not computed because the singlet structure optimized to that of 3c. g Energy of singlet state determined by single-point calculation on the B3LYP/6-311+G* structure.

TABLE 5: Weight of the Reference Configuration for Cyclobutadienes (1-5) CAS(x,x)PT2/ANO-L-VTZP// CCSD/cc-pVDZa 1 2 3a 3b 3c 4 5

CHART 3: Computed Natural Charges for Triplet Cyclobutadienesa

CAS(4,4)PT2/ANO-L-VTZP// CCSD/cc-pVDZb

singlet

triplet

singlet

triplet

0.88 0.84 0.80 0.81 0.80 0.77 0.73

0.92 0.88 0.84 0.84 0.84 0.76 0.76

0.88 0.87 0.87 0.88 0.87 0.87 0.87

0.92 0.96 0.92 0.93 0.92 1.00 0.91

a

Active space contains all pz π/π* orbitals (see computational methods). b Active space contains only pz π/π* orbitals of cyclobutadiene ring (4,4).

By including the perturbative triples correction, the CCSD(T) results should be an improvement over the CCSD data. Even in cases where multireference character is expected, CCSD(T) performs remarkably well for a single-reference method.55 At first glance, it is not obvious that there should be much multireference character for either singlet or triplet state in these cyclobutadiene derivatives. In the majority of species studied, however, our results reveal that the reference configuration contributes less than 85% in the CI expansion for the CAS(x,x)PT2 calculation (Table 5).56 Only 31 appears to be welldescribed by a single-reference configuration (>90% contribution from the reference configuration). Moreover, there is a clear trend of increasing multireference character as the number of cyano groups increases. Thus, we expect the S-T gaps predicted by the CAS(x,x)PT2 calculations to be the most accurate. Eckert-Maksic´ et al. recently reported calculations on 1-3 at the MR-AQCC level of theory.33 The S-T gaps that they report are determined at the square geometry (i.e., the energy difference between the transition state on the singlet surface and the energy minimum on the triplet surface). Using the total electronic energies reported in their study, the adiabatic S-T gap at the MR-AQCC level can be ascertained (Table 4). It is important to note that the MR-AQCC calculations were based on a CAS(4,4) reference for all species, whereas our CAS(x,x)PT2 calculations are based on the full pz π/π* active spaces, as described above. If we decrease the active space of our reference wave function to CAS(4,4), in order to more closely replicate the methodology employed by Eckert-Maksic´ et al., the S-T gaps obtained at CAS(4,4)PT2 are slightly larger in magnitude (ca. 1 kcal/mol) than the CAS(x,x)PT2 values (Table 4). Although the energy differences are not large, the multireference character of each wave function is substantially reduced, particularly for the triplet states (Table 5). We therefore

a Natural charges on H omitted for clarity. Total natural charge on ring carbons in parentheses.

conclude that it is important to include the full pz π/π* space in the reference wave function for any post-CASSCF correlation method. Insight into the trend in the S-T gap can be found by considering the stabilization enthalpies in Tables 2 and 3. In each individual case, the cyano substituent(s) stabilize the triplet to a greater degree than the singlet, resulting in a decrease in the S-T gap. The nonmonotonic stabilization of the singlet state, upon increasing cyano substitution, leads to a nonmonotonic trend in the S-T gap. The net effect of cyano substitution on the magnitude of the S-T gap, however, is quite modest (ca. 2-4 kcal/mol). NBO Analysis of the Triplet State. The preceding analyses establish that cyano substituentssespecially the third and fourth substituentssdo not confer much stabilization to either singlet or triplet state of cyclobutadiene. These findings were puzzling to us, especially in the case of the triplets, for which extended delocalization of the unpaired electrons might be envisioned to be a stabilizing factor. To better understand the electronic structure of these triplets, we performed a series of NBO calculations on the B3LYP/6-31G* structures. Computed NBO natural charges for triplet cyanocyclobutadienes 1-5 are depicted in Chart 3. These data reveal the substantial perturbation of charge density that accompanies the introduction of cyano substituents. The total natural charge on the ring carbons is -0.88 in cyclobutadiene (1), but only -0.12 in tetracyanocy-

Effects of Cyano Substituents on Cyclobutadiene CHART 4: Computed Spin Densities for Triplet Cyclobutadienesa

J. Phys. Chem. A, Vol. 114, No. 22, 2010 6435 CHART 5: Resonance Structures for Triplet Cyclobutadiene Derivatives

a Spin densities on H are omitted for clarity. Total spin density on ring carbons in parentheses.

clobutadiene (5). The molecules display increasing electrical polarity (dipole, quadrupole, octupole moments) across the series. Thus, the cyano substituents indeed provide a substantial perturbation to the electronic structure of cyclobutadiene. To the degree that Baird’s analysis of triplet 4π-electron systems as aromatic provides qualitative insight,23 one recognizes that the cyanocyclobutadienes represent a conundrum. The cyano substituents serve to withdraw electron density from the aromatic systemsan effect that operates in opposition to stabilization that may be conferred by delocalization of charge density or unpaired spins. The cyano substituents confer a fascinating perturbation of spin density in triplet cyclobutadienes. Computed NBO spin densities are depicted in Chart 4. The cyano substituents effectively delocalize spin density, with spin densities at nitrogen ranging from 0.6 to 0.8. The effect of spin polarization, however, results in the accrual of substantial negative spin density at the carbon atom of the cyano group, rendering the net spin density on the ring carbons only slightly diminished (Chart 4). It is also worth noting that, throughout this analysis, we were unable to discern an obvious correlation between the patterns of spin density and natural charge. Remarkably, cyanocyclobutadiene (32) exhibits nearly zero spin density at the ring carbon opposite the cyano group, while tricyanocyclobutadiene (34) exhibits negative spin density at the equivalent position. Spin densities and bond lengths are rationalized by contributions from the allylic resonance structures depicted in Chart 5. These structures account for the very small spin densities at the central carbon of the allylic moiety, as expected on the basis of qualitative concepts in bonding theory. The topology of the substitution pattern for 1,2-dicyanocyclobutadiene (33b) does not support an analysis in terms of the same type of allylic resonance structure. In this case, the tendency of the cyano substituents to pull spin density to the ipso carbon appears to cause localization of the CdC bond at C3-C4. The resonance structures shown in Chart 5 help rationalize spin densities and bond lengths. The structures of the triplet cyanocyclobutadienes are reminiscent of the cyclobutane-1,3-diyls and related structures that received considerable attention from both a fundamental perspective of high-spin organic molecules and a

TABLE 6: Computed Energies (kcal/mol) of Cyclobutadienes and Tetrahedranesa C4R4

R ) H R ) CH3 R ) C(CH3)3 R ) Si(CH3)3 R ) CNd

tetrahedrane cyclobutadiene

0.0 0.0

Stabilization Enthalpyb,c -23.5 -17.1 -30.6 +8.5

-76.7 -43.6

-0.1 -14.8

tetrahedrane cyclobutadiene

24.3 0.0

Relative Energyb 31.4 -1.2 0.0 0.0

-8.8 0.0

39.0 0.0

a Reference 28. b B3LYP/6-31G*, ZPVE not included. c From eq 1. d This work.

technological perspective as organic ferromagnets.57 Dougherty and co-workers concluded that the 2,4-dimethylene-1,3-cyclobutanediyl structure (B) represents a more important contributor to the resonance hybrid than the 1,3-dimethylenecyclobuta-1,3-diene structure (A) (Chart 5).58 It is also interesting to note that the triplet state of this hydrocarbon is the ground electronic state, whereas the ground state of the analogous diketone is a singlet.58-60 C4(CN)4 Isomers. Along with the general interest in cyclobutadiene comes experimental and computational interest in tetrahedrane. Insightful use of substituents enabled the synthesis and isolation of a number of tetrahedrane derivatives.16,28,61-64 In both tetra-t-butyl-tetrahedrane and tetrakis(trimethylsilyl)tetrahedrane, bulky substituents buttress the system toward the closed, polycyclic structure, and they destabilize the transition states leading to ring-opening. Thermodynamically, the t-butyl and trimethylsilyl derivatives of tetrahedrane are actually computed to be lower in energy than the corresponding cyclobutadiene derivatives (Table 6).28 By contrast, tetracyano

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TABLE 7: Computed Relative Energies (kcal/mol) for Ground States of C4(CN)4 Isomersa

Menke et al. to enter the potential energy surface. Comparison of the relative energies with those of the parent hydrocarbons66,67 reveals a qualitatively similar trend. In other words, the energy differences between hydrocarbon isomers are sufficiently large that cyano substitution does not alter the energy ordering. Summary Cyano substitution confers a modest enthalpic stabilization to the cyclobutadiene ring, as evaluated using isodesmic reactions. Subtle offsetting factors result, however, in little effect on the adiabatic S-T energy gap. The S-T gaps and the triplet states, themselves, were analyzed in some detail. These systems are best treated by inclusion of all of the pz π/π* orbitals in the active space of a multireference calculation. For the triplet states, NBO natural charges reveal that increasing cyano substitution leads to a significant withdrawal of charge density from the ring. The pronounced effects of spin polarization and negative spin densities, however, render the influence of cyano substituents on the spin density of the cyclobutadiene ring to be modest. Computed rotational constants and infrared spectra may be of value in the future experimental efforts to detect and characterize these species. Acknowledgment. We gratefully acknowledge the National Science Foundation for support of this project (CHE-0715305) and the computational resources provided to the UW Chemistry Parallel Computing Center (CHE-0091916). Partial support for computing facilities at Truman State University was provided by the National Science Foundation (CHE-0746096) and the Research Corporation for Science Advancement (CC7789).

a

Singlet ground state unless specified. b B3LYP/6-31G* with ZPVE. c ∆∆H°298, CCSD(T)/cc-pVTZP, ref 66.

substitution (σ-acceptor, π-acceptor) serves to increase the energy difference between the tetrahedrane and cyclobutadiene derivatives from 24.3 to 39.0 kcal/mol, relative to the unsubstituted compounds (Table 6). The origin of this effect is intriguing. The calculations predict that the effect does not arise as a result of the destabilization of tetrahedrane upon cyano substitution. The isodesmic reaction (eq 1) predicts essentially no influence of the cyano group (Table 6). Rather, the effect arises as a consequence of the stabilization of cyclobutadiene upon cyano substitution. NBO analyses of tetrahedrane and tetracyanotetrahedrane reveal only subtle effects: although the natural charge on the carbon atoms of the tetrahedron decreases from -0.26 to -0.03 upon substitution, the computed C-C bond lengths (1.479 Å vs 1.492 Å) and orbital occupancies (1.96 vs 1.92) change only slightly (see the Supporting Information). These effects are less pronounced than those predicted for tetranitrotetrahedrane (natural charge on carbons of the tetrahedron +0.17).65 To provide some context for experimental studies of isomers in the tetracyano series, we computed geometries, relative energies, dipole moments, rotational constants, harmonic vibrational frequencies, and infrared intensities for selected C4(CN)4 isomers. Structures and relative energies are depicted in Table 7. Although tricyano-2,3-pyridyne is a C8N4 isomer, it is not, technically, a C4(CN)4 isomer. We chose to include it in our analysis because it represents a feasible experimental target

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