High-Level ab Initio Predictions for the Ionization Energy, Electron

Article pubs.acs.org/JPCA

High-Level ab Initio Predictions for the Ionization Energy, Electron Affinity, and Heats of Formation of Cyclopentadienyl Radical, Cation, and Anion, C5H5/C5H5+/C5H5− Po-Kam Lo and Kai-Chung Lau* Department of Biology and Chemistry, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong S Supporting Information *

ABSTRACT: The ionization energy (IE), electron affinity (EA), and heats of formation (ΔH°f0/ΔH°f298) for cyclopentadienyl radical, cation, and anion, C5H5/C5H5+/C5H5−, have been calculated by wave function-based ab initio CCSDT/CBS approach, which involves approximation to complete basis set (CBS) limit at coupled-cluster level with up to full triple excitations (CCSDT). The zero-point vibrational energy correction, core− valence electronic correction, scalar relativistic effect, and higher-order corrections beyond the CCSD(T) wave function are included in these calculations. The allylic [C5H5(2A2)] and dienylic [C5H5(2B1)] forms of cyclopentadienyl radical are considered: the ground state structure exists in the dienyl form and it is about 30 meV more stable than the allylic structure. Both structures are lying closely and are interconvertible along the normal mode of b 2 in-plane vibration. The CCSDT/CBS predictions (in eV) for IE[C5H5+(3A1′)←C5H5(2B1)] = 8.443, IE[C5H5+(1A1)←C5H5(2B1)] = 8.634 and EA[C5H5−(1A1′)←C5H5(2B1)] = 1.785 are consistent with the respective experimental values of 8.4268 ± 0.0005, 8.6170 ± 0.0005, and 1.808 ± 0.006, obtained from photoelectron spectroscopic measurements. The ΔH°f0/ΔH°f298’s (in kJ/mol) for C5H5/C5H5+/C5H5− have also been predicted by the CCSDT/CBS method: ΔH°f0/ ΔH°f298[C5H5(2B1)] = 283.6/272.0, ΔH°f0/ΔH°f298[C5H5+(3A1′)] = 1098.2/1086.9, ΔH°f0/ΔH°f298[C5H5+(1A1)] = 1116.6/ 1106.0, and ΔH°f0/ΔH°f298[C5H5−(1A1′)] = 111.4/100.0. The comparisons between the CCSDT/CBS predictions and the experimental values suggest that the CCSDT/CBS procedure is capable of predicting reliable IE(C5H5)’s and EA(C5H5) with uncertainties of ±17 and ±23 meV, respectively.

I. INTRODUCTION Cyclopentadienyl anion (C5H5−), having six π electrons, is known to be aromatic according to the Hückel’s rule.1 It is an important ligand in many inorganic and organometallic complexes such as metallocene and cyclopentadienyl-containing metalate.2 The cyclopentadienyl cation (C5H5+) with four π electrons exhibits antiaromatic character.3 This species is involved in various chemical reactions and processes. For example, the solvolysis of cyclopentadienyl trifluoroacetates has been found to proceed via a C5H5+ intermediate,3 which is shown responsible for the formation of soot in fuel combustion. The cyclopropenyl cation first reacts with acetylene and forms C5H5+;4 which further reacts with acetylene in a chain of ion− molecule reactions leading to polycyclic aromatic hydrocarbons and eventually soot. Due to importance of cyclopentadienyl neutral and ions in organometallic and combustion chemistry, the thermochemical properties of five-membered cyclopentadienyl radical (C5H5) and its ions have attracted considerable attention in chemistry. The Jahn−Teller distortion in C5H5 radical and singlet C5H5+ have been studied experimentally and theoretically.5−9 The C5H5(2E1″) undergoes Jahn−Teller distortion to a lower C2v symmetry along a degenerate e2′-type vibration, splitting into two nearly isoenergetic states: C5H5(2B1) [dienylic form] and C5H5(2A2) [allylic form].5,7,8 Due to vibronic coupling and © 2014 American Chemical Society

Jahn−Teller effect, the ground state structures of C5H5 and singlet C5H5+ have not been determined and still remain controversial.10−13 Zilberg and Haas8 employed the Longuet− Higgins loops method to study the Jahn−Teller degeneracy of C5H5(2E1″) and found that the C5H5(2A2) form is a saddle point connecting two equivalent C5H5(2B1) structures. The C5H5(2A2) structure is stabilized by allyl-type resonance;14 the energy difference between C5H5(2A2) and C5H5(2B1) is negligibly small and results in two nearly isoenergetic structures. On the theoretical end, Applegate et al.5 found that the C5H5(2A2) structure is a stable minimum and the C5H5(2B1) structure is a first-order saddle point using the CASSCF method with an active space of five π electrons in five π orbitals, [CASSCF(5,5)/6-31G(d)]. However, the reverse was reported by Kiefer et al.7 and Bearpark et al.13 at the CASSCF(5,5)/ccpVDZ level. Similar to the C5H5 radical, two possible structures (dienylic and allylic forms) are found for singlet C5H5+ and the ground state structure is still undetermined. Glukhovstev et al.10 concluded that the two singlet C5H5+ structures are almost isoenergetic at HF/6-31G(d), MP2/6-31G(d), and Received: December 17, 2013 Revised: March 12, 2014 Published: March 12, 2014 2498

dx.doi.org/10.1021/jp412323j | J. Phys. Chem. A 2014, 118, 2498−2507

The Journal of Physical Chemistry A

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cules (C4H4X/C4H4X+, where X = S, O, NH, CH2 and BH),36 we have found the coupled cluster based method could give accurate IE predictions to within ±13 meV. Encouraged by the good agreement between the ab initio predictions and experimental IE values,36−39 we now extend the theoretical predictions to C5H5/C5H5+/C5H5−.

MP4SDTQ(fc)/6-31G(2d,p)//MP2/6-31G(d) levels. From the vibrational frequency calculations, the allylic form is a minimum at the HF/6-31G(d) level whereas it turns out to be a saddle point at MP2/6-31G(d) level. Lee et al.11 found that the allylic structure is a minimum at the CASSCF(4,5)/631G(d,p) level but it becomes a saddle point at the MP2/6311G(2d,p) level. Reindl and Schleyer15 suggested both forms are minima, but a slight energetic preference (0.8 kJ/mol) for the dienylic form over the allylic form is suggested using the force-field-parameterized ab initio method. To the best of our knowledge, there is no systematic theoretical study on the ionization processes of C5H5(2E1″) and the electron detachment process of C5H5−(1A1′). The thermodynamic properties such as ionization energy (IE), electron affinity (EA), and heats of formation (ΔH°f0/ΔH°f298) of C5H5/C5H5+/C5H5− have not been well-established; the previous experimental measurements and theoretical values always have a large discrepancy.16−21 The measured EA(C5H5) values fall into a wide range of 1.786−1.84 eV,19,20 and the calculated value of 1.947 eV at the G2M(RCC,MP2) level21 is considerably larger than any of the experimental measurements. Wörner et al.9 measured the IE(C5H5) value to be 8.4268 ± 0.0005 eV from a pulsed-field-ionization zero-kinetic-energy (PFI-ZEKE) photoelectron spectroscopic measurement. The G2 value of 8.41 eV22 is very close to this experimental IE whereas the G2M(RCC,MP2) value (a variant of G2 method) of 8.46 eV21 is significantly larger. In addition to the EA(C5H5) and IE(C5H5) values, the experimentally measured ΔH°f298(C5H5) values also span a wide range from 242 ± 616 to 293 ± 2117,18 kJ/mol. When different isodesmic reactions (at different levels of theory) are employed, the ΔH°f298(C5H5) has been reported from 258.4 to 281.0 kJ/mol.23,24 Janoschek et al.25 have determined the ΔH°f0/ΔH°f298(C5H5) = 269.64/258.79 kJ/mol25 at the G3MP2B3 level and ΔH°f298 = 287.0 kJ/mol26 at G2 level using the atomization scheme. When the enthalpy of reaction is computed for the isodesmic reaction, C5H5 + 5CH4 → C2H5 + 2C2H6 + 2C2H4, the ΔH°f298(C5H5) is calculated to be 258.423 (CBS-Q), 259.723 (CBS-QB3), 268.623 [CCSD(T)], and 259.412 [G2(B3LYP/MP2,SVP)] kJ/mol. Employing another isodesmic reaction of C5H6 + C6H5 → C5H5 + C6H6, Moskaleva and Lin24 have calculated the ΔH°f0/ΔH°f298 to be 271.1/260.0, 276.6/265.5, 285.4/274.3, and 292.2/281.0 kJ/ mol at G2(MP2), CASPT2(7,6)/6-31G(d,p), ROHF-CCSD(T)/6-311G(d,p), and G2M(RCC,MP2) levels, respectively. Tokmakov et al.27 have calculated the ΔH°f0 to be 274.8 kJ/ mol at the UCCSD(T)/6-311G(d,p) level from the reaction enthalpy of C5H6 + C3H6 → C5H6 + C3H5. Nguyen et al.21 have reported the G2M(RCC,MP2) ΔH°f298’s and obtained an average value of 265.7 kJ/mol for ΔH°f298(C5H5) from six different isodesmic schemes. In view of inconsistency between experimental values and theoretical predictions, we carry out high-level theoretical predictions on the IE(C5H5), EA(C5H5) and ΔH°f0/ΔH°f298’s for C5H5/C5H5+/C5H5−. The theoretical predictions have been performed using the ab initio CCSDT/CBS extrapolation approach,28−34 which approximates the CCSDT energy at the complete basis set (CBS) limit. The method includes the zeropoint vibrational energy (ZPVE), core−valence (CV), scalarrelativistic (SR), and higher-order corrections (HOC) beyond the CCSD(T)35 wave function. On the basis of the comparison between previous CCSD(T)/CBS IE predictions and the experimental IE values of five-membered heterocyclic mole-

II. COMPUTATIONAL METHODS The IE(C5H5), EA(C5H5), and ΔH°f0/ΔH°f298(C5H5/C5H5+/ C5H5−) predictions are performed at an “effective” CCSDT/ CBS level. The CCSDT/CBS procedure involves approximation to the CBS limit at the CCSD(T) level of theory with full triple electronic correlations (estimated with a smaller basis set). The current CCSDT/CBS procedure is slightly different from the CCSD(T)/CBS method36−39 in which the full triple electronic excitations are not included. We choose to use the partially unrestricted implementation, conventionally labeled as ROHF-CCSD(T) for the treatment of open-shell molecules. This implementation is based on restricted open-shell Hartree− Fock (ROHF) orbitals and it relaxes the spin restriction throughout the coupled cluster calculation.40,41 A. Geometry Optimization and Extrapolated Valence Correlation Energy. The structures of C5H5/C5H5+/C5H5− have been optimized at the CCSD(T)/aug-cc-pVTZ level of theory. On the basis of the optimized structures, single-point energy calculations are then carried out at the CCSD(T) level using Dunning’s augmented correlation consistent polarization basis sets (aug-cc-pVXZ) where X = T, Q, and 5.42 The inner shell 1s electrons on carbon are kept frozen and uncorrelated. The total valence CCSD(T) energies are used to estimate the CBS limit (ΔEextrapolated CBS) by two different extrapolation schemes: (i) A three-point extrapolation scheme28 using the mixed exponential/Gaussian function of the form: E(X ) = Eextrapolated CBS + B exp[−(X − 1)] +C exp[−(X − 1)2 ]

(1)

where X is 3, 4, and 5 for aug-cc-pVTZ, aug-cc-pVQZ, and aug-cc-pV5Z, respectively. Here we denote the CBS energies extrapolated by eq 1 with successive aug-ccpV[T-5]Z basis sets as CBSTQ5. (ii) A two-point extrapolation scheme43−46 using the simple power function involving the reciprocal of X: B (2) X3 where X is 4 and 5 for aug-cc-pVQZ and aug-cc-pV5Z, respectively. We denote the CBS energies extrapolated by eq 2 with basis sets of aug-cc-pV[Q,5]Z as CBSQ5. B. Zero-Point Vibrational Energy Correction. The ZPVE corrections (ΔEZPVE) are computed using the vibrational frequencies at the CCSD(T) and MRCI levels with aug-ccpVTZ basis sets. The MRCI method is based on the complete active space self-consistent field (CASSCF) reference configuration47,48 and the CASSCF space of C5H5+/C5H5/C5H5− consists of five π orbitals and four/five/six π electrons. C. Core−Valence Electronic Correction. The CV energy (ECV) takes into account the electronic correlation contributions between the core and valence electrons and those within core electrons. The ECV is taken as the difference between the energy with only valence electrons correlated and the energy E(X ) = Eextrapolated CBS +

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Figure 1. Schematic plot of relative energy levels of C5H5(2B1 and 2A2), C5H5+(1A1 and 3A1′), and C5H5−(1A1′) at the CCSDT/CBS level. All optimized bond lengths (Å) are at the CCSD(T)/aug-cc-pVTZ level.

ΔH°f298(C) = 716.68 kJ/mol. The atomic spin−orbit coupling (ESO) is directly taken from the experimental excitation energies tabulated by Moore.58

with both core and valence electrons correlated at the CCSD(T)/aug-cc-pwCVQZ49 level. In all molecular species, the core electrons to be correlated are the 1s electrons on carbon atoms. D. Scalar Relativistic Effect. The SR energy (ESR) is computed using the second-order spin-free, one-electron Douglas−Kroll−Hess (DKH) Hamiltonian.50,51 The calculations are done with the DKH-contracted aug-cc-pVQZ-DK basis sets52,53 at the CCSD(T) level. The SR energetic contributions are taken as the difference between electronic energies at the CCSD(T)/aug-cc-pVQZ level without using the DKH Hamiltonian and at the CCSD(T)/aug-cc-pVQZ-DK level with the DKH Hamiltonian. E. Higher-Order Correlation. The higher-order correction (EHOC) incorporates higher-order full triple excitation, where the full triple excitation effect is estimated by the difference between CCSDT and CCSD(T) energies using the aug-ccpVTZ basis set for C and the aug-cc-pVDZ basis set for H. The EHOC for C5H5/C5H5+/C5H5− is represented by the following:

III. RESULTS AND DISCUSSION A. Electronic Ground States, Molecular Structures and Orbitals of C5H5−, C5H5 and C5H5+. The closed-shell cyclopentadienyl anion (C5H5−) has six π electrons on a fivemember aromatic ring. It has a D5h symmetry and an electronic configuration of [...(a2″)2(e1″)2(e1″)2]. The five equivalent CC bond lengths are 1.418 Å at the CCSD(T) level (depicted in Figure 1). In terms of molecular structure, the cyclopentadienyl radical (C5H5) is more complicated and has been subjected to extensive experimental and theoretical studies.5,6,8,13 The C5H5(2E1″, D5h) normally undergoes Jahn−Teller distortion along the degenerate e2′-type vibration and its electronic configuration [...(a2″)2(e1″)2(e1″)1] is splitted into two nearly degenerate electronic states: 2B1 [...(b1)2(a2)2(b1)1] (dienylic form) and 2A2 [...(b1)2(b1)2(a2)1] (allylic form), where the doubly degenerate e1″ orbitals (in D5h symmetry) corresponding to a2 and b1 orbitals (C2v symmetry). The highest (doubly) occupied molecular orbital (HOMO) in the dienylic form [C5H5(2B1)] possesses a2 symmetry and the singly occupied molecular orbital (SOMO) is in b1 symmetry. The order of HOMO and SOMO are swapped in the allylic form [C5H5(2A2)]. The SOMOs in C5H5(2A2) and C5H5(2B1) have identical orbital energies of −0.199 au, which lie above the HOMOs by ∼0.035 au (Table 1). The energy difference between the C 5 H 5 ( 2 B 1 ) and C5H5(2A2) forms are very small. At the CCSD(T) level and CBS limit, the C5H5(2B1) form is isoenergetic to the C5H5(2A2) form. When the ΔEZPVE, ΔECV, ΔESR, and ΔEHOC contributions

E HOC = ECCSDT/aug‐cc‐pVTZ(C),aug‐cc‐pVDZ(H) − ECCSD(T)/aug‐cc‐pVTZ(C),aug‐cc‐pVDZ(H)

(3)

In the present work, all CCSD(T) single-point energy calculations, vibrational frequency calculations, and correlation contributions were performed using the MOLPRO 2010.154 suite of program, and the CCSDT calculations were done with the string-based many-body MRCC program55 interfaced with MOLPRO. The CCSDT/CBS values for the ΔH°f0 and ΔH°f298 of the C5H5/C5H5+/C5H5− were calculated using atomization scheme56 and the following experimental values:57 ΔH°f0(H) = 216.02, ΔH°f0(C) = 711.20, ΔH°f298(H) = 218.00, 2500



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Table 1. Leading Atomic Orbitals of π Orbitals in C5H5(2B1) and C5H5(2A2) Structures at the CASSCF/aug-cc-pVTZ Level MO

orbital energy (au)

b 1 -orbital in dienylic C 5 H 5 ( 2 B 1 ); (ii) an allyl form, C5H5+(1A1,allyl), by ionizing an electron from the a2-orbital in allylic C5H5(2A2). The allyl form of C5H5+ is a saddle point at the CCSD(T) [ω(b2) = 245i cm−1] and MRCI [ω(b2) = 312i cm−1] levels (Supporting Information, Table S1), which is slightly higher in energy than the dienyl form by 12 meV at the CCSDT/CBS level (including the ΔEZPVE, ΔECV, ΔESR, and ΔEHOC corrections). The dienyl form of singlet C5H5+ lies above the triplet ground state by ∼0.28 eV at the CCSD(T) level and CBS limit, agrees excellently with previous calculation (∼0.28 eV) at the RCCSD(T)/cc-pVTZ//QCISD/6-31G(d,p) level.11 This energy difference decreases to ∼0.19 eV when the ΔEZPVE, ΔECV, ΔESR, and ΔEHOC corrections are taken into account, which is in line with the singlet−triplet interval of 0.1902 ± 0.0007 eV, taken as the difference between experimental IE[C5H5+(1A1)←C5H5] = 8.6170 ± 0.0005 eV and IE[C5H5+(3A1′)←C5H5] = 8.4268 ± 0.0005 eV.9 The main atomic contribution to SOMO in C5H5(2B1) is the π orbitals on C1, C4, and C5, removal of a π electron from the SOMO greatly elongates the C4C5 bond by 0.07−0.08 Å whereas the C1C2 and C2C4 bonds are unaltered (Table 1); these changes are reflected in the structural differences between the C5H5(2B1) and C5H5+(1A1,dienyl). B. Electron Affinity of C5H5. The individual energy corrections (ΔEextrapolated CBS, ΔEZPVE, ΔECV, ΔESR, and ΔEHOC) for the EA[C5H5−(1A1′)←C5H5(2B1)] and EA[C5H5−(1A1′)←C5H5(2A2)] predictions using the CCSDT/ CBS method are summarized in Table 2. The valence electronic contribution (ΔEextrapolated CBS) to EA[C5H5(2B1)] is 1.831 eV and the CCSD(T)-based ΔEZPVE is −25 meV. Upon including the CV (4 meV), SR (−2 meV), and HOC (−23 meV) contributions, we arrive at a CCSDT/CBS value of 1.785 eV for EA[C5H5(2B1)] value. The EA[C5H5(2A2)] = 1.816 eV is a bit higher than EA[C5H5(2B1)] by ≈30 meV, pinpointing the electronic ground state of C5H5 is 2B1. Both EA values are in line with an experimental EA of 1.808 ± 0.006 eV61 obtained from negative ion photoelectron spectroscopic measurement. Two slightly lower EA values observed from the threshold of photodetachment electron spectra: 1.786 ± 0.02019 and 1.789 ± 0.047 eV,62 both agree excellently with the predicted EA[C5H5(2B1)] of 1.785 eV. Compared with these three EA values, together with the upper limit reported by Richardson to be ≤1.84 ± 0.03,20 our prediction for adiabatic EA for electron attachment process of C5H5−(1A1′)←C5H5(2B1) lies within the experimental range. The equilibrium structure of C5H5(2B1) lies in the vicinity of that of C5H5(2A2); both structures perform pseudorotation almost barrierlessly along the normal mode of b2 in-plane vibration (Figure S1, Supporting Information). It is logical to expect that the potential energy surface between C5H5(2B1) and C5H5(2A2) is very flat along this normal mode; thus the theoretical determination of vibrational frequency for the b2 inplane vibration could be difficult (or erroneous). As mentioned previously, the C5H5(2B1) structure has all positive vibrational frequencies at the MRCI level and one imaginary vibrational frequency at the CCSD(T) whereas the C5H5(2A2) structure has all positive vibrational frequencies at the CCSD(T) level but one imaginary vibrational frequency at the MRCI level. The above theoretical results imply that the potential energy surface along the b2 in-plane vibration between C5H5(2B1) and C5H5(2A2) structure is very shallow and both structures, sitting ≈17000 cm−1 below the zero-point level, are thermally interconvertible. In view of this floppy in-plane vibration, we

atomic contribution 2

b1

−0.474

a2 (HOMO)

−0.234

b1 (SOMO)

−0.199

b1

−0.474

b1 (HOMO)

−0.234

a2 (SOMO)

−0.199

C5H5( B1) 0.34C1(2px) + 0.36C2(2px) + 0.36C3(2px) + 0.35C4(2px) + 0.35C5(2px) 0.52C2(2px) − 0.52C3(2px) + 0.35C4(2px) − 0.35C5(2px) 0.58C1(2px) + 0.15C2(2px) + 0.15C3(2px) − 0.44C4(2px) − 0.44C5(2px) C5H5(2A2) 0.36C1(2px) + 0.35C2(2px) + 0.35C3(2px) + 0.36C4(2px) + 0.36C5(2px) 0.53C1(2px) + 0.19C2(2px) + 0.19C3(2px) − 0.46C4(2px) − 0.46C5(2px) 0.54C2(2px) − 0.54C3(2px) + 0.30C4(2px) − 0.30C5(2px)

are included, the C5H5(2B1) structure becomes slightly stable by ∼30 meV. In previous CASSCF calculations, the energy gap was also found to be on the order of a few wavenumbers.5,7,13 A somewhat larger energy difference (48 meV) was obtained at the CISD/cc-pVDZ level.8 The C5H5(2B1) and C5H5(2A2) structures are interconvertible without barrier on the potential energy surface of C5H5 radical. The near-degeneracy of C5H5(2B1) and C5H5(2A2) structures may complicate the theoretical calculations of vibrational frequencies of C5H5 radical and its ZPVE and thus the ambiguous determinations of EA(C5H5) and IE(C5H5) values. Experimentally, the C5H5(2B1) and C5H5(2A2) forms are found interconvertible at 25 K via the b2-type vibration in an electron paramagnetic resonance (EPR) study of C5H5 radical;59 this suggests that reorganization of electron distribution happens rapidly even at a very low temperature. Compared with the C5H5(2B1) form, the C5H5(2A1) form has a longer C2C4/C3C5 bond (differ by ∼0.10 Å) and a shorter C4C5 bond (differ by ∼0.12 Å) at CCSD(T) and MRCI levels. The CCSD(T) structures in the present work are in reasonable agreement with previous calculations at the CASSCF5,8,13 and CISD8 levels. However, the agreement is less satisfactory when the experimental bond lengths derived from vibronic analysis are compared, which used the distortion vector to adjust the atomic positions from D5h geometry.6 From the vibrational frequency calculations, the C5H5(2B1) form is a minimum at the MRCI level whereas it becomes a saddle point at the CCSD(T) level [ω(b2) = 191i cm−1]. The reverse behavior is observed for C5H5(2A2): it is a saddle point at the MRCI level [ω(b2) = 50i cm−1] and becomes a minimum at the CCSD(T) level (detailed vibrational frequencies are listed in Table S1 in Supporting Information). Removal of an electron from the a2-orbital [b1-orbital] in C5H5(2B1) [C5H5(2A2)] structure would yield a triplet C5H5+(X 3A1′) cation and its electronic configuration is [... (a2″)2(e1″)1(e1″)1]. The triplet state is the ground state of C5H5+, supported by ab initio calculations10,22 and EPR spectroscopic observation. 60 The CC bond lengths in C5H5+(3A1′) are 1.426 Å at the CCSD(T) level. The π electrons in the HOMO of C5H5+ are delocalized, very little changes in the CC bond distances (≤0.06 Å) are found in the ionization process of C5H5+(3A1′) ← C5H5(2B1/2A2). Two structures of singlet C5H5+ cation (1A1) can be formed: (i) a dienyl form, C5H5+(1A1,dienyl), by ionizing an electron from the 2501



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Table 2. Individual Energy Corrections to the EA(C5H5) and IE(C5H5) Predictions Using the CCSDT/CBS Method (All Values in eV)a ΔEextrapolated CBS

a

ΔEZPVEb ΔECVc ΔESRd ΔEHOCe CCSDT/CBS EAf exptl value

ΔEextrapolated CBSa

ΔEZPVEb ΔECVc ΔESRd ΔEHOCe CCSDT/CBS IEf exptl value

ΔEextrapolated CBSa

ΔEZPVEb ΔECVc ΔESRd ΔEHOCe CCSDT/CBS IEf exptl value

EA[C5H5−(1A1′)←C5H5(2B1)]

EA[C5H5−(1A1′)←C5H5(2A2)]

1.829 1.833 1.831 −0.025 0.004 −0.002 −0.023 1.785

1.831 1.834 1.833 0.001 0.004 −0.002 −0.020 1.816

CBSTQ5 CBSQ5 average CCSD(T)

1.786 ± 0.020g 1.789 ± 0.047h 1.808 ± 0.006i ≤1.84 ± 0.03j IE[C5H5+(3A1′)←C5H5(2B1)]

IE[C5H5+(3A1′)←C5H5(2A2)]

8.337 8.342 8.340 0.090 0.017 −0.002 −0.002 8.443

8.335 8.341 8.338 0.064 0.017 −0.002 −0.005 8.412

CBSTQ5 CBSQ5 average CCSD(T)

8.40 ± 0.05k 8.41l 8.4268 ± 0.0005m 8.44 ± 0.05n 2 + 1 IE[C5H5 ( A1,dienyl)←C5H5( B1)] IE[C5H5+(1A1,allyl)←C5H5(2B1)] CBSTQ5 CBSQ5 average CCSD(T)

8.617 8.621 8.619 0.016 0.020 −0.003 −0.018 8.634

8.630 8.634 8.632 0.016 0.020 −0.002 −0.020 8.646 8.6170 ± 0.0005m ≤8.626o

a Extrapolated from the frozen-core energies with the aug-cc-pV[T-5]Z and aug-cc-pV[Q-5]Z basis sets, respectively. bBased on the harmonic vibrational frequencies at the CCSD(T)/aug-cc-pVTZ level. cCore−valence electron correlation obtained as the difference of all-electron and frozencore energies at the CCSD(T)/aug-cc-pwCVQZ level. dScalar relativistic effect calculated at the CCSD(T)/aug-cc-pVQZ-DK level. eHigher-order effect calculated at the CCSDT level using the aug-cc-pVTZ basis set for C and the aug-cc-pVDZ basis set for H. fEA (or IE) = ΔEextrapolated CBS + ΔEZPVE + ΔECV + ΔESR + ΔEHOC gFrom ref 19. hFrom ref 62. iFrom ref 61. jFrom ref 20. kFrom ref 64. lFrom ref 65. mFrom ref 9. nFrom ref 63. o From ref 75.

scopic measurement.9 This confirms that the ground state of cyclopentadienyl cation is 3A1′. Besides the laser-based PFIphotoionization measurement, the IE(C5H 5 ) has been measured by synchrotron-based photoionization mass spectrometry of fuel flame by Qi and Li63 and Hansen et al.64 Two IE(C5H5) values, 8.44 ± 0.0563 and 8.40 ± 0.05 eV,64 were reported from the signal threshold of C5H5 radical in photoionization efficiency spectrum. Another IE(C5H5) of 8.41 eV65 has been reported by Traeger and Lossing in an electron monochromator-mass spectrometer combination experiment of C5H5 radicals produced in pyrolytic reaction. Although the latter three experimental IE(C5H5) values bear a larger uncertainty, the deviation of the predicted adiabatic IE(C5H5) from these experimental IEs is no more than 43 meV. Using MRCI-based ΔEZPVE corrections do not alter the

have not included its vibrational frequency in the ZPVE correction of C5H5(2B1) and C5H5(2A2). When the MRCIbased ΔEZPVE corrections are used in the CCSDT/CBS EA predictions, it gives a lower EA value of 1.775 eV for C5H5(2B1) and a significantly smaller EA of 1.779 eV for C5H5(2A2) (Table S2, Supporting Information). Nevertheless, the C5H5(2B1) and C5H5(2A2) structures are almost isoenergetic, their adiabatic EAs are of similar magnitude. C. Ionization Energy of C5H5. Taking the C5H5(2B1) structure as the ground state of the cyclopentadienyl radical, the CCSDT/CBS IE for the adiabatic ionization transition yielding C5H5+(3A1′) is 8.443 eV. Obviously, the respective IE for ionization transition of C5H5+(3A1′) ← C5H5(2A2) is 8.412 eV. The CCSDT/CBS IE of 8.443 eV for C5H5+(3A1′) ← C5H5(2B1) is just 16 meV above the adiabatic IE of 8.4268 ± 0.0005 eV obtained in a PFI-ZEKE photoelectron spectro2502



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Table 3. Comparisons of CCSDT/CBS EA(C5H5) and IE(C5H5) Predictions with the G2, G3, and G4 Methods (All Values in eV) recommended exptl value

G2

G3

G4

CCSDT/CBS

± ± ± ±

1.93 8.41 8.51 10.34

1.84 8.41 8.63 10.25

1.82 8.52 8.76 10.34

1.785 8.443 8.634 10.228

EA[C5H5−(1A1′)←C5H5(2B1)] IE[C5H5+(3A1′)←C5H5(2B1)] IE[C5H5+(1A1,dienyl)←C5H5(2B1)] EA[C5H5−(1A1′)←C5H5(2B1)] + IE[C5H5+(3A1′)←C5H5(2B1)] a

1.808 8.4268 8.6170 10.235

0.006a 0.0005b 0.0005b 0.006

From ref 61. bFrom ref 9.

Table 4. Comparisons of the CCSDT/CBS (in Bold Font) ΔH°f0 and ΔH°f298 Values (kJ/mol) for C5H5/C5H5+/C5H5− with Available Experimental Data (in Normal Font) C5H5(2B1) ΔH°f0

a

ΔH°f298a

283.6 290.3 ± 289.7 ± 279.2 ± 276.3 ± 266.4 ±

7.1b 8.4c 5.4d 4.2e 5.3f

272.0 278.7 ± 278.1 ± 267.6 ± 264.7 ± 254.8 ±

7.1b 8.4c 5.4d 4.2e 5.3f

C5H5+(3A1′)

C5H5+(1A1,dienyl)

1098.2 1103.4 ± 7.1b 1102.8 ± 8.4c 1092.3 ± 5.4d 1089.4 ± 4.2e 1079.5 ± 5.3f 1063g 1086h ≤1153 ± 17i 1086.9 1092.1 ± 7.1b 1091.5 ± 8.4c 1081.0 ± 5.4d 1078.1 ± 4.2e 1068.2 ± 5.3f 1052g 1075h ≤1142 ± 17i

1116.6 1121.7 ± 1121.1 ± 1110.6 ± 1107.7 ± 1097.8 ±

7.1b 8.4c 5.4d 4.2e 5.3f

1106.0 1111.1 ± 1110.5 ± 1100.0 ± 1097.1 ± 1087.2 ±

7.1b 8.4c 5.4d 4.2e 5.3f

C5H5− 111.4 115.9 ± 7.1b 115.3 ± 8.4c 104.8 ± 5.4d 101.9 ± 4.2e 92.0 ± 5.3f 90 ± 8i 100.5j 100.0 104.5 ± 7.1b 103.9 ± 8.4c 93.4 ± 5.4d 90.5 ± 4.2e 80.6 ± 5.3f 79 ± 8i 89.1j

The ΔH°f0 of neutrals and ΔH°f0/ΔH°f298 of ions are converted from the vibrational frequencies obtained in this study and the experimental IE[C5H5+(3A1′)←C5H5] = 8.4268 ± 0.0005 eV,9 IE[C5H5+(1A1)←C5H5] = 8.6170 ± 0.0005 eV,9 or EA(C5H5) = 1.808 ± 0.006 eV.61 bDerived from 298 K C−H bond dissociation energy taken from ref 23. cDerived from D0(C5H5−H) taken from ref 72. dDerived from D0(C5H5−H) taken from ref 61. eDerived from D0(C5H5−H) taken from ref 71. fThe ΔH°f298(C5H5) is from ref 70. gThe ΔH°f298(C5H5+) is from ref 57. hThe ΔH°f298(C5H5+) is from ref 73. iThe ΔH°f298(C5H5+) and ΔH°f298(C5H5−) are from ref 18. jThe ΔH°f298(C5H5−) is from ref 74. a

IE(C5H5) predictions significantly, the IE[C5H5(2B1)] is 8.449 eV (Table S2, Supporting Information). The CCSDT/CBS prediction gives the IE[C 5 H 5 + ( 1 A 1,dienyl )←C 5 H 5 ( 2 B 1 )] = 8.634 eV and IE[C5H5+(1A1,allyl)←C5H5(2B1)] = 8.646 eV, in which the former come closer to the experimental value of 8.6170 ± 0.0005 eV in a PFI-ZEKE photoelectron spectroscopic measurement.9 The current theoretical calculations suggest that the allyl form of singlet cyclopentadienyl cation is slightly higher than the dienyl form by ∼12 meV. D. IE(C5H5) and EA(C5H5) Predictions by Gaussian-n Methods. The Gaussian-n (n = 2−4) method by Pople et al. is a series of composite model for thermochemistry prediction.66−68 It is less accurate and less computationally demanding than the CCSDT/CBS method. We find that the G3 method gives the best IE(C5H5) and EA(C5H5) predictions (Table S3, Supporting Information). Exceptions are the G4 IE[C 5 H 5 + ( 3 A 1 ′)←C 5 H 5 ( 2 B 1 )] and IE[C 5 H 5 + ( 1 A 1,dienyl )← C5H5(2B1)] values, being overestimated by ∼0.1 and ∼0.14 eV, respectively (Table 3). Both the G2 and G3 methods (in fact, the underlying MP2 method) incorrectly predict that the C5H5(2A2) is the ground state structure of cyclopentadienyl radical. To avoid ambiguity in the ground state structure of C5H5 radical, one may examine the sum of EA[C5H5−(1A1′)← C5H5] and IE[C5H5+(3A1′)←C5H5], which represents the

energy difference of cyclopentadienyl anion and cation. As expected, the G3[EA(C5H5)+IE(C5H5)] prediction of 10.25 eV is superior to the G2 and G4 results and comes very close to the experimental value (10.235 ± 0.006 eV) and the CCSDT/ CBS prediction (10.228 eV). The G4 method performs less satisfactorily than G3 method in this regard. E. CCSDT/CBS Predictions of the ΔH°f0/ΔH°f298’s of C5H5/C5H5+/C5H5−. The CCSDT/CBS ΔH°f0/ΔH°f298 values are listed in Table 4, together with the available experimental data for comparison. Unless specified, the experimental ΔH°f0/ ΔH°f298 for ions and ΔH°f0 of neutral are obtained by converting the available ΔH° f298 of neutral with the experimental IE/EA and the thermal corrections using the CCSD(T) vibrational frequencies of C5H5+/C5H5/C5H5−. In previous study on CCSD(T)/CBS calculations on C4H4X (X = S, O, NH, CH2 and BH),36 we have benchmarked the ΔH°f0/ ΔH°f298 of cyclopentadiene (C4H4CH2) with available experimental ΔH°f0/ΔH°f298 values;69 we recommended the ΔH°f0/ ΔH°f298 = 154.2/138.9 kJ/mol to be used as the experimental values in the following discussion. By studying the kinetics for iodination reaction of cyclopentadiene, C5H6 + I ⇌ HI + C5H5, Furuyama et al.70 have obtained an activation energy of 44.6 ± 1.8 kJ/mol at 498 K for forward reaction and deduced the enthalpy change (ΔH°298 = 40.6 ± 5.3 kJ/mol) of iodination reaction by assuming the 2503



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ΔH°298 of backward reaction is 4.2 ± 4.2 kJ/mol. When the ΔH°298 = 40.6 ± 5.3 kJ/mol in the iodination is combined with the known ΔH°f298(I) = 106.7, ΔH°f298(HI) = 26.4, and ΔH°f298(C5H6) = 133.5 kJ/mol, a ΔH°f298(C5H5) value of 254.8 ± 5.3 kJ/mol is determined and a ΔH°f0 = 266.4 ± 5.3 kJ/mol value is obtained by thermal correction using the CCSD(T) vibrational frequencies of C5H5. The ΔH°f(C5H5) may also be determined by the energy conservation in the bond dissociation process of C5H6 → C5H5 + H, using the known values for ΔH°f0/ΔH°f298(H) = 216.02/ 218.0057 and ΔH°f0/ΔH°f298(C5H6) = 154.2/138.9 kJ/mol69 and the 0 K C−H bond energy of C5H6, D0(C5H5−H), from experiments. Roy et al.71 have measured forward and backward rate coefficients for C−H bond cleavage of C5H6 by atomic resonance absorption spectroscope and obtained a D0(C5H5− H) of 338.1 ± 4.2 kJ/mol. On the basis of energy conservation in the negative ion thermochemical cycle in C5H6 → C5H5− + H+ and in the bond dissociation process of C5H6 → C5H5 + H, Ichino et al.61 have derived a slightly higher value of 341.0 ± 5.4 kJ/mol for D0(C5H5−H), using the EA(C5H5) = 1.808 ± 0.006 eV,61 IE(H) = 13.59844 eV, and the gas-phase acidity (1478.6 ± 5.4 kJ/mol) of C5H6. Kern et al.72 have observed the pyrolysis of cyclopentadiene with time-of-flight mass spectrometry and laser-schlieren densitometry techniques; they have reported a value for D0(C5H5−H) of 351.5 ± 8.4 kJ/mol. On the basis of solution-phase 298 K C−H bond dissociation energy of C5H6 (362.8 ± 7 kJ/mol) obtained in a time-resolved photoacoustic calorimetry experiment, Nunes et al.23 have determined a 298 K gas-phase De(C5H5−H) = 357.8 ± 7.1 kJ/ mol by assuming the solvation enthalpy of a hydrogen atom is 5 ± 1 kJ/mol and the difference in solvation enthalpy between C5H6 and C5H5 is negligible. From the aforementioned experiments,23,61,71,72 four D0(C5H5−H) (or De) values are obtained: 338.1 ± 4.2, 341.0 ± 5.4, 351.5 ± 8.4, and 357.8 ± 7.1 kJ/mol. The D0(C5H5−H)’s can be combined with known values of ΔH°f0/ΔH°f298(H)57 and ΔH°f0/ΔH°f298(C5H6),69 and this gives four sets of ΔH°f0/ΔH°f298(C5H5): 276.3 ± 4.2/ 264.7 ± 4.2, 279.2 ± 5.4/267.6 ± 5.4, 289.7 ± 8.4/278.1 ± 8.4, and 290.3 ± 7.1/278.7 ± 7.1 kJ/mol. The CCSDT/CBS ΔH°f0/ΔH°f298[C5H5(2B1)] values of 283.6/272.0 kJ/mol fall between the experimental values of 279.2 ± 5.4/267.6 ± 5.4 and 289.7 ± 8.4/278.1 ± 8.4 kJ/mol. If the uncertainty is taken into account, the CCSDT/CBS predictions are within ±3 kJ/ mol from these four sets of deduced values. The experimental values of ΔH°f0/ΔH°f298 = 266.4 ± 5.3/254.8 ± 5.3 kJ/mol determined by Furuyama et al.70 are likely too low. There are a number of previous ΔH°f0/ΔH°f298(C5H5) calculations; in general, most values are probably underestimations. Janoschek et al.25 have determined the ΔH°f0/ ΔH°f298(C5H5) = 269.64/258.79 kJ/mol25 at the G3MP2B3 level using atomization scheme. When the enthalpy of reaction is computed for the isodesmic reaction, C5H5 + 5CH4 → C2H5 + 2C2H6 + 2C2H4, the ΔH°f298(C5H5) is calculated to be 258.423 (CBS-Q), 259.723 (CBS-QB3), and 259.412 [G2(B3LYP/MP2,SVP)] kJ/mol. On the other hand, the G2 ΔH°f298 of 287.0 kJ/mol26 is larger than most of the experimental ΔH°f’s. Our CCSDT/CBS prediction is in better agreement with Moskaleva and Lin’s calculation24 (ΔH°f0/ ΔH°f298 = 285.4/274.3 kJ/mol), which are determined from the isodesmic reaction of C5H6 + C6H5 → C5H5 + C6H6 at the ROHF-CCSD(T)/6-311G(d,p) level. The CCSDT/CBS ΔH°f0/ΔH°f298 values of C5H5+(3A1′) and C5H5+(1A1,dienyl) are 1098.2/1086.9 and 1116.6/1106.0 kJ/

mol, respectively. Using the experimental IE[C5H5+(3A1′)← C5H5] = 8.4268 ± 0.0005 eV9 and IE[C5H5+(1A1)←C5H5] = 8.6170 ± 0.0005 eV,9 the ΔH°f0/ΔH°f298(C5H5) values and the experimental ΔH°f0/ΔH°f298 values of C5H5+ are deduced and listed in Table 4. The ΔH°f298(C5H5+) values of 105257 and 1075 73 kJ/mol, taken from two thermochemical data compilations, are less than our CCSDT/CBS prediction (1086.9 kJ/mol) by ≥35 and ≥12 kJ/mol, respectively. Domenico et al.18 have measured the appearance energy (1225 ± 10 kJ/mol) of C5H5+ ion formed in an electron bombardment ionization of cyclopentadiene, C5H6 + e− → C5H5+ + H + 2e−. Using the appearance energy with the known ΔH°f298(C5H6) = 133.9 kJ/mol and ΔH°f298(H) values, an upper limit of ≤1142 ± 17 kJ/mol for ΔH°f298(C5H5+) is obtained. Our CCSDT/CBS predictions of 1098.2/1086.9 kJ/ mol for ΔH°f0/ΔH°f298[C5H5+(3A1′)] are in very good agreement with the ΔH°f0/ΔH°f298 values, 1092.3 ± 5.4/ 1081.0 ± 5.4, 1102.8 ± 8.4/1091.5 ± 8.4, and 1103.4 ± 7.1/ 1092.1 ± 7.1 kJ/mol, determined from the deduced ΔH°f0/ ΔH°f298(C5H5)’s above and IE[C5H5+(3A1′)←C5H5] = 8.4268 ± 0.0005 eV.9 There are only a few theoretical calculations on ΔH°f0/ΔH°f298(C5H5+). The ΔH°f298[C5H5+(3A1′)] is 1090.6 kJ/mol22 at the G2 level and 1087.8 kJ/mol21 at the G2M(RCC,MP2) level. Reindl and Schleyer15 have developed a force-field-parameterized ab initio method to determine ΔH° f298 for a series of carbocations, the reported ΔH°f298[C5H5+(1A1,dienyl)] of 1056.9 kJ/mol is considerably less than the experimental and CCSDT/CBS values by more than 30 kJ/mol. By measuring the appearance energy (164 ± 10 kJ/mol) for the reaction of C5H6 + e− → C5H5− + H, Domenico et al.18 have obtained ΔH°f298(C5H5−) = 79 ± 8 kJ/mol with the known ΔH°f298(C5H6) and ΔH°f298(H). Bartmess et al.74 have measured gas-phase acidity of C5H6 (1489.9 ± 8.4 kJ/mol at 298 K) by pulsed ion cyclotron resonance spectrometry. Using this value in conjunction with ΔH°f298(C5H6) = 133.5 kJ/mol and ΔH°f298(H+) = 1536.3 kJ/mol, they have obtained ΔH°f298(C5H5−) = 89.1 kJ/mol. At the G2M(RCC,MP2) level, Nguyen et al.21 have obtained a ΔH°f298(C5H5−) of 78.7 kJ/mol. These experimental values and the G2 predictions are obviously too small compared with the CCSDT/CBS ΔH°f0/ ΔH°f298(C5H5−) values of 111.4/100.0 kJ/mol. The CCSDT/ CBS predictions are consistent with the deduced ΔH°f0/ ΔH°f298(C5H5) values of 104.8 ± 5.4/93.4 ± 5.4, 115.3 ± 8.4/ 103.9 ± 8.4, and 115.9 ± 7.1/104.5 ± 7.1 kJ/mol. In view of good agreement between the theoretical predictions and experimental values, the CCSDT/CBS ΔH°f0/ΔH°f298 values together with IE(C5H5) and EA(C5H5) should constitute a consistent set of thermochemical data for C5H5/C5H5+/C5H5−.

IV. CONCLUSION We have predicted the IE(C5H5), EA(C5H5), and ΔH°f0/ ΔH°f298(C5H5/C5H5+/C5H5−) values by wave function based ab initio CCSDT/CBS approach, which involves approximation to CBS limit at coupled cluster level with single, double, and full triple excitations (CCSDT). The ZPVE correction, CV electronic correlation, and SR and HOC contributions beyond the CCSD(T) wave function are included. The ground state of cyclopentadienyl radical is found to be the C5H5(2B1) form, and it is about 30 meV more stable than the C5H5(2A2) structure. Both structures lie very closely on the potential energy surface and they are interconvertible via the normal mode of b2 inplane vibration. Thus, the vibrational frequency of this b2 in2504



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(8) Zilberg, S.; Haas, Y. A Valence Bond Analysis of Electronic Degeneracies in Jahn-Teller Systems: Low-Lying States of the Cyclopentadienyl Radical and Cation. J. Am. Chem. Soc. 2002, 124, 10683−10691. (9) Wörner, H. J.; Merkt, F. Diradicals, Antiaromaticity, and the Pseudo-Jahn-Teller Effect: Electronic and Rovibronic Structures of the Cyclopentadienyl Cation. J. Chem. Phys. 2007, 127, 34303. (10) Glukhovtsev, M. N.; Reindl, B.; Schleyer, P. V. What is the Preferred Structure of the Singlet Cyclopentadienyl Cation. Mendeleev Commun. 1993, 3, 100−102. (11) Lee, E. P. F.; Wright, T. G. A Study of the Lowest-Lying Triplet and Singlet States of the Cyclopentadienyl Cation (c-C5H5+). Phys. Chem. Chem. Phys. 1999, 1, 219−225. (12) Wang, H.; Brezinsky, K. Computational Study on the Thermochemistry of Cyclopentadiene Derivatives and Kinetics of Cyclopentadienone Thermal Decomposition. J. Phys. Chem. A 1998, 102, 1530−1541. (13) Bearpark, M. J.; Robb, M. A.; Yamamoto, N. A CASSCF Study of the Cyclopentadienyl Radical: Conical Intersections and the JahnTeller Effect. Spectrochim. Acta A Mol. Biomol. Spectrosc. 1999, 55, 639−646. (14) Levin, G.; Goddard, W. A., III. The Generalized Valence Bond Description of Allyl Radical. J. Am. Chem. Soc. 1975, 97, 1649−1656. (15) Reindl, B.; Schleyer, P. V. Molecular Mechanics and Ab Initio Calculations on Cyclopentadienyl Cations. J. Comput. Chem. 1998, 19, 1402−1420. (16) McMillen, D. F.; Golden, D. M. Hydrocabon Bond Dissociation Energies. Annu. Rev. Phys. Chem. 1982, 33, 493−532. (17) Bischof, P. Forbidden Radical Rearrangements - Comparison with Potential Surfaces of Jahn-Teller Radicals. J. Am. Chem. Soc. 1977, 99, 8145−8149. (18) Domenico, A. D.; Franklin, J. L.; Harland, P. W. Negative Ion Formation and Negative Ion-Molecular Reactions in Cyclopentadiene. J. Chem. Phys. 1972, 56, 5299−5307. (19) Engelking, P. C.; Lineberger, W. C. Laser Photoelectron Spectrometry of C5H5−: A Determination of the Electron Affinity and Jahn-Teller Coupling in Cyclopentadienyl. J. Chem. Phys. 1977, 67, 1412−1417. (20) Richardson, J. H.; Stephenson, L. M.; Brauman, J. I. Photodetachment of Electrons from Large Molecular Systems: Cyclopentadienide and Methylcyclopentadienide Ions. An Upper Limit to the Electron Affinitiesof C5H5 and CH3C5H4. J. Chem. Phys. 1973, 59, 5068−5076. (21) Nguyen, T. L.; Le, T. N.; Mebel, A. M. Thermochemistry of Cyclopentadienylidene (c-C5H4, C2v, 3B1), Cyclopentadienyl Radical (c-C5H5•, C2v, 2B1) and 1,3-cyclopentadiene (c-C5H6, C2v, 1A1): a Theoretical Study by the G2M(RCC,MP2) Method. J. Phys. Org. Chem. 2001, 14, 131−138. (22) Glukhovtsev, M. N.; Bach, R. D.; Laiter, S. Computational Study of the Thermochemistry of C5H5+ Isomers: Which C5H5+ Isomer Is the Most Stable? J. Phys. Chem. 1996, 100, 10952−10955. (23) Nunes, P. M.; Agapito, F.; Cabral, B. J. C.; dos Santos, R. M. B.; Simoes, J. A. M. Enthalpy of Formation of the Cyclopentadienyl Radical: Photoacoustic Calorimetry and Ab Initio Studies. J. Phys. Chem. A 2006, 110, 5130−5134. (24) Moskaleva, L. V.; Lin, M. C. Unimolecular Isomerization/ Decomposition of Cyclopentadienyl and Related Bimolecular Reverse Process: Ab Initio MO/Statistical Theory Study. J. Comput. Chem. 2000, 21, 415−425. (25) Janoschek, R.; Rossi, M. J. Thermochemical Properties from G3MP2B3 Calculations, Set-2: Free Radicals with Special Consideration of CH2CH-C•CH2, cyclo-•C5H5, •CH2OOH, HO-•CO, and HC(O)O• degrees. Int. J. Chem. Kinet. 2004, 36, 661−686. (26) Catoire, L.; Swihart, M. T.; Gail, S.; Dagaut, P. Anharmonic Thermochemistry of Cyclopentadiene Derivatives. Int. J. Chem. Kinet. 2003, 35, 453−463. (27) Tokmakov, I. V.; Moskaleva, L. V.; Lin, M. C. Quantum Chemical/vRRKM Study on the Thermal Decomposition of Cyclopentadiene. Int. J. Chem. Kinet. 2004, 36, 139−151.

plane mode has been excluded from ZPVE correction. Our CCSDT/CBS predictions of IE[C5H5+(3A1′)←C5H5(2B1)] = 8.443 eV, IE[C5H5+(1A1)←C5H5(2B1)] = 8.634 eV, and EA[C5H5−(1A1′)←C5H5(2B1)] = 1.785 eV are in good agreement with the experimental values. The respective CCSDT/CBS ΔH° f0 /ΔH° f298 values for C 5 H 5 ( 2 B 1 ), C5H5+(3A1′), C5H5+(1A1), and C5H5−(1A1′) are 283.6/272.0, 1098.2/1086.9, 1116.6/1106.0, and 111.4/100.0 kJ/mol, which are within the uncertainty of available experimental values. The comparisons between the CCSDT/CBS predictions and the available experimental data suggest that the CCSDT/CBS procedure is capable of providing accurate and reliable IE(C5H5)’s and EA(C5H5) with uncertainties of ±17 and ±23 meV, respectively.

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ASSOCIATED CONTENT

* Supporting Information S

Vibrational frequencies calculated at CCSD(T) and MRCI levels together with the available experimental data are in Table S1. Comparison between CCSD(T)- and MRCI-based ΔEZPVE corrections to the IE(C5H5) and EA(C5H5) is in Table S2. Electronic and ZPVE energy contributions to the EA(C5H5) and IE(C5H5) predictions using the G2, G3, and G4 methods are in Table S3. Potential energy surface for pseudorotation between C5H5(2A2) and C5H5(2B1) structures along the normal mode of b2 in-plane vibration is in Figure S1. This information is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*K.-C. Lau: e-mail, [email protected]; phone, (852) 34426849. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work described in this article was fully supported by a Strategic Research Grant from City University of Hong Kong (Project No. 7004019).

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REFERENCES

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High-Level ab Initio Predictions for the Ionization Energy, Electron

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