BIRADICALS STABILIZED BY INTRAMOLECULAR CHARGE TRANSFER S. Zilberg Institute of Chemistry and the Lise-Meitner-Minerva Center for Computational Quantum Chemistry, The Hebrew University of Jerusalem, Givat Ram, 91904, Jerusalem, Israel Abstract The formally biradicals are theoretically predicted to be stable persistent molecules, as supported by high level quantum chemical calculations. The singlet–triplet energy gaps and the S0-S1 excitation energies of 2,5-di-heterosubstituted-pentalenes and 1,5-diheterosubstituted-cyclooctatetraenes are similar to those of aromatic molecules rather than to standard biradicals. Open form of hetero derivatives of bicyclo[2.1.0]pentane (which is a cyclopentane-1,3-diyl derivative) are the stable bond-stretch isomers. These formal biradicals have a pronounced zwitterion character with a singlet ground state. The marked stabilization of the ground state singlet for these non-Kekule molecules is accompanies by a significant increasing of the HOMO level, leading to a unusual low ionization potential (IP). In the case of diaza-pentalene, the energy of the first electronic excited state is only slightly lower than the ionization potential, making it a candidate for molecular auto-ionization. Introduction Substantial efforts have been made to design and prepare persistent non-classical molecules such as diradicals [1] and triplet [2] or singlet carbenes [3], yet ‘bottleable’ non-Kekule molecules remain a challenge (Scheme 1): Scheme 1. Experimentally observed stable carbenes [2]. 180 Non-Kekule molecules are molecules with a completely conjugated -system, for which no classical Kekule structures can be written [4]. Different kinds of stable biradicals [1, 5, 6] are known. The first stable carbon-based Schlenk’s diradical (a) was prepared in 1915 [7]. (a) (b) cc (c) Scheme 2. Experimentally observed stable singlet diradicals [5]. The most stable localized singlet diradical known to date, (b), has a lifetime of microseconds at room temperature [5]. Lambert quite recently reviewed the designing and synthesizing of relatively stable polycyclic aromatic hydrocarbons (type c), that show pronounced singlet open-shell character [8]. A pair of nonbonding molecular orbitals (NBMO’s) that are occupied by two electrons is the MO portrayal of the diradical‘s electronic origin in non-Kekule hydrocarbons [9]. Tetramethyleneethane (TME) is one of the prototype non-Kekule molecules. Other types of fully -conjugated diradicals are antiaromatic species such as cyclobutadiene (CBD), cyclooctatetraene (COT) or pentalene (PNT). Borden and Davidson predicted the violation of Hund’s rule for diradicals that have disjoint NBMOs [5, 10]. Thus, the ground state of TME is a singlet with a modest singlet-triplet gap ΔEST = ES-ET = -2 kcal/mol, as verified experimentally by negative ion photoelectron spectroscopy [11]. Incorporating the TME fragment in a five-membered ring, as in the case of 3,4-dimethylenecyclopentane-1,3-diyl, Ia, changes the ground state to a triplet [12]. The singlet-triplet gap ΔEST for hydrocarbon disjoint diradicals is usually small, consistent with the high 181 reactivity of these molecules. Qualitative MO arguments suggest that the lowest singlet state can be stabilized by replacing a carbon atom by a heteroatom [13]. Thus, the hetero-derivatives of Ia (Fig. 1) show substantial stabilization of singlet vs. triplet, as has been shown computationally [14, 15] and experimentally [16]. 3 1 6 7 2 X X 2 X 5 4 1 X X 5 8 3 I 4 8 II N NH IV 6 III NH NH 7 NH V N VI Fig. 1. The structures of molecules discussed in the text. (X: a=CH2, b=NH, c=O, d=S). Semiempirical quantum chemical calculations [17] were used to assess the properties of diradicals (I) and (II). The large value of singlettriplet gap (ΔEST) computed for pentalene (II) derivatives led them to discuss criteria for determining whether these systems should be described as biradicals or zwitterions. It was noted that the ratio (C1/C2)2 of the squares of the coefficients of the two leading configurations in the electronic wave function of the ground state singlet is a useful criterion for this purpose. The system has a pronounced zwitterion character if one configuration is dominant (i.e C1>>C2). Thus the ratio was found to be 8.05, 3.28 and 2.46 for IIb, IIc and IId, respectively, showing that IIb is best described as a zwitterion. Cava and coworkers isolated the tetraphenyl substituted derivative of IId, tetraphenylthieno(3,4-c)thiophene (hereafter designated as IIe), leading to the elucidation of its electronic spectrum [18], x-ray structure [19] and photoelectron spectrum [20]. Derivatives of IIb and IIc, as well as of III have not yet been reported to the best of our knowledge. In this work we report high level CASSCF and DFT calculations on these 182 molecules, predicting that all hetero-substituted derivatives (X= NH, O or S) are stable (though possibly reactive) compounds with a singlet ground state. The aza-pentalene derivative IIb is calculated to have an exceptionally low ionization potential, due to a high lying HOMO orbital. Fig. 2 shows the structures of some cyclopentane-1,3-diyl diradicals that were examined as possible stable singlet diradicals. Fig. 2. Open form cyclopentane-1,3-diyl diradicals VIIa-VIIg and closed form heterosubstituted bicyclo[2.1.0]pentane VIIIa-VIIIg (a. X=CH2; b. X=CF2; c. X=C(SiH3)2; d. X=O; e. X=S; f. X=NH; g. X=N(CH3)). Buchwalter and Closs showed in 1975 [21] that triplet diradicals of cyclopentane-1,3-diyl (VIIa) can be prepared and observed by ESR. The triplet-singlet gap (EST) was calculated to be a few kcal/mol, the triplet being more stable. The singlet diradical was taken as the transition state between the two closed forms of the bicyclic compound. Borden et al. [22] proposed that the singlet diradical can be stabilized by substituting the two geminal hydrogen atoms with fluorine ones (VIIb). The idea was that the fluorine atoms will act as electron acceptors and help to delocalize the electronic charge in the singlet state. Indeed, the singlet of 1b was calculated to lie well below the triplet at all geometries but it turned out to be a transition state between the two classical closed structures [22]. Other modes of substitution were proposed theoretically and tested experimentally; Adam et al. [23] presented evidence for the existence of a reactive intermediate Ic, though it could not be observed directly. In an effort to stabilize carbon-based diradicals the Z=SiH3 group was proposed [24] as a potent stabilizer of singlet diradicals with respect to the triplet one; the calculation showed that the singlet is indeed lower than the triplet, but only by about 2 kcal/mol. The singlet open form of VIId was calculated to be 20.8 kcal/mol higher, with a barrier of 9.5 kcal/mol from the open form side. 183 We propose an computational design approach that leads to substantially better stabilization of a singlet state of the open form in comparison to the corresponding triplet and more importantly, to the singlet of the closed isomer in which the two atoms – C1 and C3 - are covalently bonded. In other words, the system is shown to have two stable, iso-energetic bond-stretch singlet isomers, separated by a substantial barrier. Results All computations were carried out using the GAMESS program suite [25], using the cc-pVDZ basis set. GAUSSIAN program suite [26] was used for DFT calculations on the B3LYP/cc-pVDZ level. A complete vibrational analysis was performed at the optimised geometry. Calculations on the parent molecules IIa and IIIa were done only in order to compare with the substituted derivative. Since their singlet states were found to be planar (D2h symmetry), calculations were performed on the X=CH2 molecules at this symmetry also. CASSCF [27] calculations (CAS(8/7)/cc-pVDZ with a full active space) show that the ground state of Ib, Ic and Id is a singlet for all substituents; however only for the aza-derivative (Ib) ΔEST reaches the sizeable value of -10.1 kcal/mol. A more substantial stabilization of singlet ground state and a corresponding increase of the singlet–triplet gap for non-Kekule molecules can be expected for molecules isoelectronic with the dianions of antiaromatic hydrocarbons. Hückel’s (4n+2) rule predicts an aromatic character for dianions of 4n-annulens, but notwithstanding, isolated COT-2 and CBD-2 are known to be unstable with respect to electron loss [28]. Substitution of two carbon atoms by two more electronegative hetero-atoms X adds two electrons to the -system, while keeping the system electrically neutral. The extent of the interaction of these extra electrons with the rest of the -electron system depends on the electronegativity of X and on the overlap of the non-bonding electrons of X with the -electronic structure of the TME fragment in IIb-d or of the two allyl fragments in IIIb-d (Fig. 1). Tables 1 and Tables 2 report the absolute energies and the structure of several 2,5-heterosubstituted pentalenes and 1,5heterosubstituted cyclooctatetraenes. The parent systems IIa and IIIa are 184 typical disjoint diradicals, because the CH2 bridges do not take part in the -delocalization (Table 1, 2). Table 1. Absolute energies (Hartree), bond distances Rij (Å) and the Mulliken charge of X, qx (electronic charge units) for 2,5-di-X-pentalenes IIa-d (CASSCF(10/8)/cc-pVDZ). Δqx(ST) is the excess of charge transferred in the singlet over the triplet. It is a measure of the zwitterion character of the singlet X State Energy CH2 11Ag ( D2h ) -307.55414 1.518 1.391 1.449 +0.05 3 R12 R17 R78 qx CH2 1 B2u ( D2h ) -307.54887 1.516 1.387 1.463 +0.04 NH 11Ag ( D2h ) -339.62983 1.363 1.405 1.443 +0.25 NH 13Au ( C2h ) -339.56190 1.417 1.394 1.456 +0.09 O 11Ag ( D2h ) -379.24513 1.341 1.394 1.445 +0.12 O 13B2u ( D2h ) -379.20886 1.374 1.388 1.454 +0.01 S 11Ag ( D2h ) -1024.61791 1.714 1.403 1.452 +0.43 S 3 1 B2u (D2h) -1024.58510 1.768 1.394 1.461 +0.29 Δqx(ST) +0.01 +0.16 +0.11 +0.14 Table 2. Absolute energies (Hartree), bond distances Rij (angstroms) and the charge of X qx (electronic charge units) for 1,5-di-X-cyclooctatetraenes IIIa-d (CASSCF(10/8)/cc-pVDZ). qx(ST) is the excess of charge transferred in the singlet over the triplet. It is a measure of the zwitterion character of the singlet X CH2 CH2 NH NH O O S S State 11Ag ( D2h ) 13B1u( D2h ) 11Ag ( D2h ) 13Au ( C2h ) 11Ag ( D2h ) 13B1u( D2h ) 11Ag ( D2h ) 13Au ( C2h ) Energy -308.72286 -308.71720 -340.75304 -340.70574 -380.39435 -380.34580 -1025.73221 -1025.59031 R12 1.495 1.502 1.355 1.395 1.319 1.354 1.699 1.763 R23 1.392 1.393 1.389 1.390 1.385 1.386 1.388 1.391 qx +0.06 +0.05 +0.25 +0.10 +0.14 +0.02 +0.43 +0.28 Δqx (ST) +0.01 +0.15 +0.12 +0.15 As seen from Tables 1 and Tables 2, the geometry of the hydrocarbon part does not change much upon substitution. Also, the 185 structures of the singlet and triplet states are very similar, in spite of the different spin state and electric charge distribution. This is a first indication that the two extra electrons find themselves in a non-bonding orbital. Table 3 reports the data obtained for the singlet-triplet gap (ΔEST), the excitation energy of the first electronic excited singlet state (E(S 1)E(S0)) and the first ionization potential (IP). It is seen that the singlettriplet energy gap for the hydrocarbons IIa and IIIa are small: 0.14 and 0.15 eV respectively, very similar to the gap in the prototype TME [7]. Table 3. Singlet-triplet gap, Excitation energy (E(S1)-E(S0)) and the Ionization potential for 2,5-di-X-pentalene and 1,5-di-X-cyclooctatetraenes derivatives (CASSCF(10/8)/cc-pVDZ) (in eV) X CH2 NH O S ΔEST 0.14 1.66 0.99 0.89 PEN derivatives E(S1)-E(S0) 4.30 4.89 5.43 4.47 IP 6.31 4.85 7.16 6.35 ΔEST 0.15 2.16 1.32 1.29 COT derivatives E(S1)-E(S0) 5.25 4.54 5.39 4.65 IP 6.21 5.08 6.02 6.30 In contrast, the oxygen and sulphur derivatives IIc, IIIc and IId, IIId and especially the aza substituted derivatives IIb and IIIb are calculated to have a much larger ΔEST. The large ΔEST computed for the aza-derivatives are in fact typical for aromatic compounds thus confirming the substantial stabilization of the ground singlet state for these non-Kekule molecules. Further evidence for the large stability of these species comes from comparison of the relative stabilization of IIb with its valence isomers IV, V and VI (Figure 1). IV and V have a regular bonding pattern and may be considered as normal Kekule structures, expected therefore to be quite stable. The relative stability of IIb may thus be estimated by comparison with these isomers: a calculation shows that IV (the most stable isomer) is only 10.7 kcal/mol lower in energy than IIb while V – the other ‘normal’ isomer - is more stable by only 6.3 kcal/mol (CASSCF-MP2 results for IIb, IV, V and VI; all structures are optimised on CAS(10/8)/cc-pVDZ level with a full active space). Moreover, the energy of VI – the other non-Kekule isomer - is higher than that of IIb by 20.8 kcal/mol. Thus, the thermodynamic 186 stability of IIb is of the same order as the normal aromatic heterocyclic molecules IV and V, in spite of the loss of one -bond in IIb. The ionization potentials (IPs) of II-type molecules are calculated to be fairly small, especially for IIb. For this compound, IP is of the same order as the energy of the first excited state (CASSCF and also DFT). Even though CAS is known to overestimate the energy of electronic excited states, the very low ionization potential indicates a facile auto-ionization for this molecule. The data are summarized in Table 3. All stable bicyclic compounds VIII considered in this work have Cs symmetry, the symmetry plane being perpendicular to the carbon frame. In contrast, all triplet states were found to have a minimum at C 2 symmetry, due to the release of strain in the small rings. The ground states of open singlet species VII were also found to have a minimum at C2 symmetry, except for X=CH2 and X=CF2 which was a transition state (C2v) between two closed forms (Cs). Table 4 lists the calculated structures and energies of the singlet and triplet forms of all open species, as well as those of the bicyclic compounds. The data show that the X-C1(3) distance is shorter in the open isomer than in the triplet, which is in turn shorter than in the closed bicyclic isomer. The C1 -C3 distances in both the open isomer and the triplet are about 2.3Å. In all calculated species except for the parent cyclopentane-1,3diyl (VII) the singlet form is more stable than the triplet. ΔE ST increases in the sequence X= CH2<CF2<O≈S<NH≈NCH3. The relative stabilities of the open singlet forms vs. the closed ones are drastically changed upon substitution: whereas bicyclo[2.1.0]pentane (VIIIa) is >20kcal/mol more stable than open isomer, the aza-analogs shows preference for the open isomer (-3.2 kcal/mol for X=NH (VIIe) and -6.5 kcal/mol for X=NMe, (VIIf)). The energy difference between the closed form (S0) and the open triplet 1,3-diradical (T1) is much less sensitive to the nature of X: it is 21.9 kcal/mol for the parent hydrocarbon vs. 31.5 kcal/mol for the aza-derivatives. These results hold also upon application of the MP2 correction. Evidently, the open singlet form is more strongly affected by the heteroatom-substituent than the open triplet or closed form singlet. The nitrogen derivatives exhibit exceptional stabilization of their open form isomers. 187 Table 4. Bond lengths and energies in singlet (S0) and triplet (T1) states of some cyclopentane-1,3-diyl species (CASSCF(10/8)/cc-pVDZ); the relative energies of the different structures of a given species are with respect to the closed form. CASMP2 data are also given for of the energy difference (ΔΔE) between the open (VII) and closed (VIII) forms. Structure a R12(23) R13 ΔΔE kcal/mol ( a.u.) Closed (S0) 1.496 1.557 0.0 ( -193.99196 ) CH2 Open -TS (S0) 1.537 2.395 22.7 {31.6}c Open (T1) 1.533 2.386 21.9 Closed (S0) 1.494 1.560 0.0 ( -391.72874 ) CF2 Open –TS (S0) 1.474 2.314 12.3 {16.0}c Open (T1) 1.492 2.371 17.8 Closed (S0) 1.455 1.455 0.0 ( -229.85729 ) Open (S0) 1.365 2.256 18.1 {26.0} c O b TSOC ( S0) 1.396 (1.446) 2.108 47.7 Open (T1) 1.412 2.259 33.8 Closed (S0) 1.864 1.534 0.0 ( -552.50698 ) Open (S0) 1.717 2.443 12.8 {15.1}c S b TSOC ( S0) 1.801 (1.803) 2.452 42.5 Open (T1) 1.801 2.436 27.7 Closed (S0) 1.510 1.511 0.0 ( -210.00437 ) Open (S0) 1.371 2.234 -3.2 {-3.7} c NH b TSOC ( S0) 1.420 (1.457) 2.132 38.5 Open (T1) 1.426 2.235 31.4 Closed (S0) 1.509 1.473 0.0 ( -249.03280 ) NCH3 Open (S0) 1.372 2.309 -6.5 {-8.7} c Open (T1) 1.423 2.283 31.5 a The open form is a transition state for X= CH2 and X= CF2, a minimum for all others. b TS is the transition state for the bond stretch reaction (Fig. 2). In it R12≠R23. c CASMP2 X Table 4 also reports some properties of the transition state for the cyclization reaction between the closed and open singlet isomers (a single imaginary frequency was found in all cases). It is evident that the barrier for the reaction from both sides is substantial (~40 kcal/mol in the case of X=NH) – the open form is consequently predicted to be both thermodynamically and kinetically stable. The singlet transition state 188 between the open and closed (bicyclic) forms for all 2-heterosubstitutedcyclopentanes was found to transform as C1, as expected since the point groups C2 and Cs have no common symmetry element (Fig. 3 shows the structures calculated for the case of IIe). Fig. 3. The calculated structures of the two isomers of the aza analog of 2cyclopentane-1,3-diyl diradical (VIIe) in two projections: left - open form (C2), right - closed (Cs) form and middle - non-symmetric (C1) transition states between them. Further differences between the closed and open forms of the hetero-substituted cyclopentan-1,3-diyls are revealed in Table 5 which reports some electronic properties. Table 5 shows that S0-S1 excitation energies for all open isomers are more or less equal (~5eV, CASSCF level, 3.5-4 eV, CASMP2 level) and similar to the case of ordinary unsaturated molecules. The ΔEST gap strongly depends on the type of heteroatom: for the parent hydrocarbons (X= CH2) the singlet and triplet states are nearly degenerate; X=CF2 leads to the considerable stabilization of singlet state [7] – T1 is a 0.25 eV above the S0. 189 Table 5. The singlet (S0) - triplet (T1) gap, S0-S1 excitation energy, Ionization Potential, energy of HOMO cyclopentane-1,3-diyls (CAS(10/8)/cc-pVDZ) (in eV); the relative energies of the different structures are with respect to the energy of S0 (open form). In each column the left value is calculated using CASSCF(10/8)/cc-pVDZ, the right CASMP2(10/8)/cc-pVDZ. ΔΔE (S0-S1; IP (D1) IP (D1,2) c 11A-11B)b Closed form HOMOd CAS CASMP2 CAS CASMP2 CASSCF CASMP2 CASSCF CASMP2 6.98 (12A) 7.50 (12A) 8.28 9.15 CH2 -0.04 -0.05 5.28 3.41 7.34 (12B) 7.71 (12B) (12A’) (12A’) 7.77 (12B) 8.57 (12B) 9.08 9.99 CF2 0.24 0.44 6.49 4.16 7.76 9.61 (12A) 10.16(12A) (12A”) (12A”) 2 2 6.02 (1 A) 7.20 (1 A) 9.03 9.54 O 0.68 0.76 5.19 3.75 6.25 8.88 (12B) 9.36 (12B) (12A’) (12A’) 6.03 (12A) 6.97 (12A) 7.76 8.41 S 0.65 0.73 4.34 3.29 6.64 8.33 (12B) 8.90 (12B) (12A) (12A) 2 2 5.16 (1 A) 6.34 (1 A) 7.91 8.69 NH 1.50 1.37 5.31 3.99 5.87 8.45 (12B) 9.10 (12B) (12A’) (12A’) 5.02 6.09 7.66 7.66 NCH3 1.65 1.30 5.10 3.70 5.79 8.17 8.81 (12A’) (12A’) X ΔE ST a a) ΔE ST=ΔE (S0-T1) b) Vertical excitation energy. c) IP1,2=E(S0) - E(D1,2) is a difference between energy of neutral molecule and corresponding cation (vertical IP). d) Energy of the HOMO of the open form, by Koopmans theorem, an estimate of the first IP. A modest gap is found for X= O or S (~0.6eV). For the azaderivatives the gap is considerably larger (~1.3eV) a typical value for hetero-substituted conjugated molecules. The trends found for the first ionization potentials (IP) are also informative: the IP of the parent cyclopenta-1,3-diyl and the fluoro-substituted analog are typical to organic radicals ~8 eV (MP2 level). In contrast the IPs of the azacompounds are unusually low compared to stable organic molecules only about 6 eV. The IPs of the closed isomers are 2-3 eV higher than those of the open ones. For the parent molecule (VIIa) the difference between the first two ionization potentials are quite modest, indicating a strong biradical character. In the nitrogen substituted ones (VIIe and VIIf) the difference is much larger – about 2.5-3 eV. This result suggests that the first electron is held much less strongly than the second one. The 190 estimation of the IPs using Koopmans theorem shows reasonable agreement with the more sophisticated CASSCF method in which the energies of the cation and the neutral molecule were compared. Table 6 reports data relating to the electronic structure of the molecules; the second column shows that the principal two configurations account for over 95% of the electronic density population, justifying the use of a two-configuration approximation for further discussion. Column 3 reports the amount of charge transferred from X to rest of the molecule in units of electronic charge and column 4 the charge transferred to each of the two neighboring carbon atoms (in fact, the CH group). Table 6. The contribution of the two leading configurations and the changes in charge distribution in electron charge units (Δq, S0 vs. T1) (CASSCF(10/8)/ccpVDZ) CH2 CF2 O S NH NMe Coefficients of the two Leading Configurations: (CA:CB) 0.70:0.69 0.53:0.83 0.90:0.39 0.91:0.35 0.93:0.31 0.94:0.30 ΔqX ΔqHC1(3) -0.001 -0.054 +0.147 +0.208 +0.207 +0.260 +0.000 +0.020 -0.068 -0.097 -0.092 -0.117 Almost no charge is transferred for X=CH2, in both the singlet and triplet states and ΔEST is negligibly small (~1 kcal/mol). X=CF2 is an electron acceptor, whereas O, S and the nitrogen-based substituents are all donors. A measure for the "diradical-zwitterion"(BR-ZW) vs. the "ylide" (YL) character of the open form may be correlated with the charge transfer. Complete one-electron charge transfer would result in a unit of positive charge on X and 0.5 units each on C1 and C3. However, the charge transfer, even in the case of the aza-derivatives, is limited to only about 0.2e. The fact that even in the case of the most potent donor (NMe) only about a quarter of an electronic charge unit is transferred means that the contribution of the diradicaloid VB structures (BR and ZW) is more significant than that of the polar one (YL). 191 Discussion Pentalene (II) and Cyclooctatetraene (III) [29]. Comparison with experiment A large singlet – triplet splitting for a formal biradical, as displayed in Table 3 for the hetero-substituted molecules, was found in the recently prepared di-tert-butyl derivative of 2,5-diamino-1,4benzoquinonediimine, which exists in a persistent zwitterionic form in the singlet ground state [30, 31]. Apart from tetraphenylthieno(3,4-c)thiophene (IIe) [14, 15, 16] there is no experimental evidence for molecules IIb-d or their derivatives (though Closs et al. reported [32] experimental evidence for II with X=N) nor for IIIb-d, but crystal structures of potassium and ammonium salts of dianion of 1,3,4,6-tetranitro-2,5-diazapentalene have been published [33, 34]. 7,8-diazapentalene, VI, is the least stable diazapentalene isomer, nevertheless its derivatives were obtained and the crystal structures of nitro-substituted-7,8-diazapentalenes were reported [35, 36]. The calculated structure of IId (Table 1) agrees well with the structure of IIe; The calculated ionization potential (6.35 eV, Table 3) is also in good agreement with experiment (6.19 eV [16]). The lowest lying excited singlet of IId is calculated to be about 4.47 eV by CASSCF and 2.82 eV by TDDFT. We propose that the lower experimental value (2.24 eV for IIe) reflects a bathochromic shift due to the interaction between the four phenyl groups and the central bicycle moiety. Electronic structure of II and III and the rationale for the high stability and low IP of S0. The difference between the calculated charge distributions in the singlet and triplet states Δqx(ST) (Table 3) shows that about 0.12÷0.15 electronic charge is transferred from the donor-heteroatom X to the TME fragment in IIb-d or to the two allyl units and IIIb-d. Significantly, IIa and IIIa (X=CH2) do not show any differences in the electronic distribution between the singlet and triplet states, as expected. The same donor groups in 2-heterosubstituted-3,4-dimethylenecyclopentane-1,3diyls, Ib-d, show considerably less tendency for intramolecular charge transfer of this type in the singlet state: Δq= qx(singlet) - qx(triplet) is +0.08 for aza-derivative, Ib; +0.03 for oxa-derivative, Ic, and +0.06 for thia-derivative. Obviously, the degree of donor-acceptor charge transfer 192 and the relative stabilization of the singlet state in IIb-d and IIIb-d are correlated. A simple electrostatic model accounts for the physical origin of the extra-stabilization of singlet state for IIb-d and IIIb-d. Transferring δ units of charge from the donor X to the acceptor TME fragment in I leads to a Coulomb stabilization Ecoul=-δ2/R, where R is a distance between the centers of the positively charged X and the negatively charged accepting group. The same amount of charge transferred from X to TME for II results in a much larger Coulomb stabilization, Ecoul = = -4δ2/R – four times larger (Fig. 4 shows the charge distribution in these molecules). Fig. 4. The intra-molecular charge separation in I vs. II. The electrostatic argument cannot account for the low IP of these molecules. An MO-based model can be proposed to explain both the extra stabilization and the low IP. In ref. 20 an MO diagram for IIe was used to account for the observed photoelectron spectrum. Fig. 5 shows a schematic diagram in which the MOs of the IIb molecule is constructed by the interaction between the MOs of the TME fragment and the two donor groups. As seen from the diagram the only high lying orbitals that can interact are the b2g-type orbitals. The two b2g and au orbitals of the TME biradical fragment are practically degenerate, as are the b2g and b1u orbitals of the two NH groups. In the TME biradical two electrons occupy the two NBOs; the interaction between the two b2g fragment orbitals lifts the degeneracy of both TME and NH-NH orbitals. It turns out that the interaction is very strong – the in-phase combination of the two b2g orbitals is stabilized with respect to the au orbital by about 9 eV! (HF/cc-pVDZ calculation). The other b2g orbital (formed by out-ofphase combination) is strongly destabilized and becomes the LUMO. 193 LUMO (b2g) (au) HOMO (au) (b2g) (b1u) (b2g) (b1u) ( b2g ) Fig. 5. A π-orbital diagram showing the origin of the low ionization potential of 2,5-diheterosubstituted pentalenes IIb-d as well as its high stability as a singlet zwitterion. The left hand π-orbitals are of the carbon skeleton and the right hand ones of the donor X group. The middle ones are the resulting molecular orbitals of II. This strong interaction is the MO manifestation of the stabilization of the singlet state. It is proportional to the orbital overlap and inversely proportional to the energy gap between the NBO and NHNH donor orbitals. The oxo-substitution provides effective overlap, but large energy difference between TME NBO’s level and p-AO of O atom reduce the effectiveness of the interaction. The relatively weak stabilization by S-substitution is due to small overlap between the porbitals of the small carbon atoms with a big S atom. The interaction is especially strong for the aza substituent since only in this case both conditions for strong stabilization are fulfilled. The other TME NBO (au) does not interact with the donor and becomes the HOMO; it is populated by the two electrons which originally occupied the two different, though iso-energetic, au and b2g orbitals. Being now in a single non-bonding orbital, the repulsion interaction between them is stronger, reducing the ionization potential. Moreover, the TME-fragment has also significant additional population on the stabilized b2g MO, as the electrons that occupied the X-X orbital are now partially transferred to the common orbital. These effects lead to 194 the concentration of an electron density on the atoms, but not on the bonds - between atoms. The strong electron-electron repulsion pushes up this HOMO and it results in a very low IP. The electronic structure shown in Fig. 5 is compatible with the data of Table 1 – the similar geometry of all molecules is due to the fact that the two extra electrons find themselves in a non-bonding orbital and thus their effect on bond-lengths is minimal. The dominant ground state electronic configuration of IIb may be written as 1Ag = (b1u)2(au)2(b2g)0(b1u)0. Removal of one electron yields the cation radical with configuration 2Au = (b1u)2(au)1. The first excited electronic state has the configuration 1B2u = (b1u)2(au)1(b2g)1(b1u)0. The transition 1Au →1B2u is allowed, with oscillator strength (TDDFT/B3LYP-cc-pVDZ) of 0.14. As shown in Fig. 6, the system can be readily ionized using UV light. Autoionization 1B 1g 1B 2u M++ e- 2A u h 1A g M Fig. 6. A schematic energy level diagram of IIb showing the S 0-S1 optical transition with a vibronic progression that can lead to autoionization. The high level CASSCF calculations show that the aza-substituted compound has a much more pronounced zwitterion character than the oxo- or thio-substituted ones. The squared ratio of the coefficients of the two principal singlet configurations of the singlet ground state (C1/C2)2 can serve to estimate the nature of these formal biradicals – for a covalent biradical it is near unity, and for a zwitterion it is much larger. 195 Table 6 lists the numerical values for this squared ratio. It is seen that for x=CH2 the singlet ground states of both pentalene (IIa) and cyclooctatetraene (IIIa) are largely biradicals, while for x = NH, they are zwitterions. The oxo and thio compounds are of intermediate nature, but also mostly zwitterions. Comparing with the semi-empirical results, it is seen that the (C1/C2)2 ratio is much larger, by approximately a factor of three. Another quantitative difference is the fact that the (C1/C2)2 ratio is larger by a factor of two for IIb, IIc and IId as compared to the semiempirical result. Table 6. The squared ratio of the coefficients of the two leading configurations of the singlet CI wave function as obtained by the CASSCF calculation. Molecule (C1/C2)2 (C1/C2)2 (ref. 12a) IIa 1.1 IIb 23.9 IIc 9.6 IId 10.3 8.05 3.28 2.46 IIIa 2.2 IIIb 23.9 IIIc 11.3 IIId 13.2 Cyclopentane-1,3-diyl diradicals [37] The open forms of the 1,3-diyls cannot be described by a single Lewis structure. A non-Lewis molecule with two equivalent radical centers is a diradical according to chemical intuition and simple VB description (BR, Fig. 7). However, other VB structures may contribute: the zwitterion (ZW) and the ylide-type structure (YL), see Fig. 7. Fig. 7. VB structures of 2-heterosubstituted-cyclopenta-1,3-diyl: covalent diradical –BR; zwitterion –ZW and ylide – YL. A diradical is defined in the MO approach as a structure with two unpaired electrons populating two degenerate or nearly degenerate MOs [38, 39, 40]. If the molecules under study were predominantly represented by structure BR (Fig. 7), they could be classifies as 196 diradicals. However, it turns out that except for the carbon derivatives (VIIa and VIIb) they exhibit considerable zwitterion character, as expected for structure ZW and ylide-type charge transfer for YL (Fig. 7). This is evident from the large singlet-triplet splitting and the large difference between the first and second IPs. An insight into their nature may be gained by considering a simple two-configuration model. The wave function of the parent 1,3-diyl is usually described in the FMO model by an anti-combination of two configurations distinguished by highest occupied orbitals – non-bonding MOs: A=(φ1-φ3) and B=(φ1+φ3), where φ1 and φ3 are the two atomic orbitals, localized on the C1 and C3 atoms. These two orbitals are degenerate and the corresponding configurations contribute equivalently to the ground state wave function. According to a basic biradical model, the anticombination of degenerate configurations (CA=CB) defines a purely covalent diradical without any ionic contributions: (CA CB 1) BB A A (1 3 )(1 3 ) (1 3 )(1 3 ) (13 ) (13 ) In contrast, when the two configurations are not equivalent a non-zero ionic term appears: (C A CB ) CB BB C A AA CB (1 3 )(1 3 ) C A (1 3 )(1 3 ) (C A CB ){13 13 } (CB C A ){11 33} Thus, the ratio (CB - CA)/(CB + CA) can serve as an index for the relative contributions of an zwitterion form and a diradical one to the electronic wave function at the two-configuration approximation. The computational evidence of the diradical character, based on the ratio of the coefficients of leading configurations in a CI expansion, was discussed by Davidson [41, 42]. Within the two-configuration approximation the square of the ratio will be used as an estimate for the contribution of ZW. Dewar [43] pointed out the importance of weak interaction between the radical centers for the pure diradical character. In the case of the hetero-substituted 1,3-diyls the direct C1-C3 interaction is weak, but the three-centered C1-X-C3 one is quite strong. The interaction of 197 the apical group with the 1,3-diradical moiety leads to the splitting of the degenerate non-bonding pair. Fig. 8 shows two different ways leading to orbital splitting of the two degenerate orbitals (C2 symmetry is used): an acceptor stabilizes the B type orbital, which becomes the HOMO whereas the LUMO is of A symmetry; in contrast, a π-donor inverts this order: the A-type orbital becomes the HOMO, and the B-symmetry one is the LUMO . X 2B X A A X A B X B Donor X=NH X=CH2 1B Ψ= CB{…(B)2} -CA{…(A)2} CB ˜ CA Ψ= CA{…(1B)2 (A)2} –CB{…(1B)2(2B)2} CA > CB Acceptor X=CF2 Ψ= CB{…(B)2} -CA{…(A)2} CB > C A Fig. 8. Orbital interaction diagram between 1,3-diyl unit and donor (left) or acceptor (right) apical group. C2 symmetry is assumed; the HOMO and LUMO orbitals are highlighted by a black solid and a grey dotted circle, respectively. In both of these cases the increased HOMO-LUMO splitting means the increased contribution of one configuration over the other and a larger singlet-triplet splitting, reducing the diradical character. Fig. 8 shows the order of the combined orbitals and, consequently, defines the dominant configuration. Although this is clearly an oversimplified picture in the case of the weak coupling, because the second configuration (of the occupied LUMO, marked by grey color) must also be taken into account, the basic characteristics are explained by the dominant configuration. The relative contribution of these two configurations: (HOMO)2 vs. (LUMO)2 determines the ratio between the 198 covalent diradical contribution (BR) and the zwitterion one (ZW). This reasoning can be compared to Head-Gordon’s suggestion to use the LUMO-occupation numbers as an indication of the extent diradical character [40]. Table 7 summarizes the contribution of the three main VB structures for the different diyls. Table 7. The relative weight (%) of the three main VB structures (Figure 7), the LUMO occupation numbers for and the percentage of charge transferred in electron charge units (Lowdin charges) calculated for the open form of 2-Xcyclopentane-1,3-diyl compounds (CASSCF(10/8)/cc-pVDZ). X BR ZW YL LUMO Occupation Numbers ΔqX CH2 100 0 0 0.947 (0.927) [40] -0.001 CF2 91 4 5 0.562 (0.583) [40] -0.054 O 673 12 15 0.304 +0.147 S 65 14 21 0.245 +0.208 NH 64 15 21 0.192 +0.207 NMe 58 16 26 0.180 +0.260 As a rough approximation, the fraction of charge transferred (Table 6) is used as an estimate for the contribution of the polar form YL; the balance is distributed between the dot-dot form (BR) and the zwitterion one (ZW) using the ratio [(CB - CA)/(CB + + CA)]2: %of ZW = (1- ΔqX)( [(CB - CA)/(CB + CA)]2) %of BR = (1- ΔqX)( [1-(CB - CA)/(CB + CA)]2 where ΔqX is the fraction of charge transferred (Table 7). The last column of Table 7 reports the LUMO occupation numbers [39]; it is evident that the magnitude of charge transfer is closely correlated with these numbers. In the case of the parent singlet cyclopentane-1,3-diylVIIa, which is a well-known perfect diradical [22] the electronic wave function can be described adequately as the anti-combination of two configurations 199 with equivalent weights, which indicates according to Eq. (1) a purely diradical character (BR contributes 100%). Almost no charge is transferred for X=CH2, in both the singlet and triplet states and ΔEST is negligibly small (~1 kcal/mol). In the hetero-substituted molecules the contribution of the two configurations is not equal, leading to two different ionization potentials as found computationally. This difference can be readily verified experimentally by photoelectron spectroscopy. In these molecules the contribution of the polar structure is non-negligible. Borden considered the case of 2,2-difluoro-cyclopentane-1,3-diyl as an acceptor hyperconjugation [22]. An analysis of the Lowdin charge distribution shows that in this case only 0.054 electronic charges is transferred to the CF2 group in the singlet state relative to a perfect diradical triplet. Among the systems considered, this molecule is the only case for which the dominant configuration is B-type (Fig. 8, right); Here CB>CA and the contribution of the covalent configurations is dominant, leading to a relative small ionic contribution: only 4%. All other studied molecules show the domination of the A-type configuration (CA≥0.9), indicating donor substitution (Fig. 8, left). The contribution of the B-type configuration, although small, increases in the sequence CH2<CF2<O<S<NH (Table 6), indicating the decreasing importance of the pure diradical character. The open forms containing X=O and S show 3-4 times larger charge transfer compared to X=CF2. The largest transfer (compared to the triplet) occurs with X=NH(NCH3), wherein about a quarter of an atomic unit charge is transferred. As in the case of the hetero-substituted pentalenes and cyclooctatetraenes, nitrogen proves to be the most efficient atom for stabilizing diradicals. [29] A possible explanation is that although oxygen and sulfur also transfer non-bonding electrons, the effect is smaller in oxygen since it is more electronegative and a weaker donor. Sulfur has a comparable electron affinity to nitrogen; however its larger size leads to a smaller overlap with the orbitals of the neighboring carbon atoms, making it less efficient as an electron donor . The calculated charge transfer indicates the importance of the ylide form YL (Fig. 7). In a previous paper [29] it was proposed that formal diradicals may be stabilized by charge transfer. The systems discussed there (hetero-substituted di-X-pentalenes and di-Xcyclooctatetraenes) were 4n+2 electron systems, so that the stabilization might be assigned to increased aromaticity. The systems studied in this 200 work have four interacting electrons (one each on carbon atoms C1 and C3, two on the heteroatom), yet they are also remarkably stabilized . The upshot of the analysis given above is that these non-Lewis systems are expected to exhibit "normal" properties of a species having partial polar and partial diradical character. Yet, the unusually low IP, especially in the case of aza-derivatives for which it is only ~6eV, is surprising at first sight. It cannot be explained by the contribution of either the biradical structure (BR) or the ylide one (YL). We propose that it is due to the importance of the zwitterion structure ZW in which two electrons occupy a single non- bonding orbital centered on carbon atoms. The simultaneous occupation of an orbital by half electron pair on C1 and C3 increases the electrostatic repulsion, compared to single electron on C1 and C3 in the diradical BR structure. This accumulation of negative charge is equivalent to imparting these species with a quasianion character. Unlike a lone pair on a nitrogen atom, a lone pair on a carbon atom leads to excess charge and strong inter-electron repulsion. An experimental method to probe this prediction is by photoelectron spectroscopy – the open form is predicted to show a much smaller IP than the closed one . Concluding remarks In conclusion, it was shown that formal diradicals - 2,5-diheterosubstituted-pentalenes, 1,5-di-heterosubstituted-cyclooctatetraenes and cyclopentane-1,3-diyl are predicted to be stable persistent nonKekule molecules, due to strong stabilization by intra-molecular charge transfer. The overall stabilization of the singlet is accompanied by a high lying HOMO, resulting in a low ionization potential. The low ionization potential (~5 eV) allows in principle facile auto-ionization in the near UV. 1. 2. 3. 4. 5. 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