ARTICLE pubs.acs.org/JPCA
High-Level ab Initio Predictions for the Ionization Energies and Heats of Formation of Five-Membered-Ring Molecules: Thiophene, Furan, Pyrrole, 1,3-Cyclopentadiene, and Borole, C4H4X/C4H4Xþ (X = S, O, NH, CH2, and BH) Po-Kam Lo and Kai-Chung Lau* Department of Biology and Chemistry, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
bS Supporting Information ABSTRACT: The ionization energies (IEs) and heats of formation (ΔH°f0/ΔH°f298) for thiophene (C4H4S), furan (C4H4O), pyrrole (C4H4NH), 1,3-cyclopentadiene (C4H4CH2), and borole (C4H4BH) have been calculated by the wave function-based ab initio CCSD(T)/ CBS approach, which involves the approximation to the complete basis set (CBS) limit at the coupled-cluster level with single and double excitations plus a quasi-perturbative triple excitation [CCSD(T)]. Where appropriate, the zero-point vibrational energy correction (ZPVE), the core-valence electronic correction (CV), and the scalar relativistic effect (SR) are included in these calculations. The respective CCSD(T)/CBS predictions for C4H4S, C4H4O, C4H4NH, and C4H4CH2, being 8.888, 8.897, 8.222, and 8.582 eV, are in excellent agreement with the experimental values obtained from previous photoelectron and photoion measurements. The ΔH°f0/ΔH°f298 values for the aforementioned molecules and their corresponding cations have also been predicted by the CCSD(T)/CBS method, and the results are compared with the available experimental data. The comparisons between the CCSD(T)/CBS predictions and the experimental values for C4H4S, C4H4O, C4H4NH, and C4H4CH2 suggest that the CCSD(T)/CBS procedure is capable of predicting reliable IE values for five-membered-ring molecules with an uncertainty of (13 meV. In view of the excellent agreements between the CCSD(T)/CBS predictions and the experimental values for C4H4S, C4H4O, C4H4NH, and C4H4CH2, the similar CCSD(T)/CBS IE and ΔH°f0/ΔH°f298 predictions for C4H4BH, whose thermochemical data are not readily available due to its reactive nature, should constitute a reliable data set. The CCSD(T)/CBS IE(C4H4BH) value is 8.868 eV, and ΔH°f0/ΔH°f298 values for C4H4BH and C4H4BHþ are 269.5/258.6 and 1125.1/1114.6 kJ/mol, respectively. The highest occupied molecular orbitals (HOMO) of C4H4S, C4H4O, C4H4NH, C4H4CH2, and C4H4BH have also been studied by the natural bond orbital (NBO) method, and the extent of π-electron delocalization in these five-membered rings are discussed in correlation with their molecular structures and orbitals.
I. INTRODUCTION Three five-membered heterocyclic molecules, thiophene, furan, and pyrrole, all play a significant role in biological activities and synthetic processes.1-5 For example, the furan functional group in deoxyribonucleic acid (DNA) is responsible for efficient DNA cross-linking. Thiophene-containing compounds serve as the starting materials in many polymerization processes. Due to the unusual electrical and optical properties, five-membered heterocyclic oligomers and polymers have received considerable attention on the synthesis and characterization of novel polymers.6,7 Thus the thermochemical properties of these heterocyclic molecules attract attention from both experimental and computational chemists.8-15 In spite of this, there have been no high-level theoretical predictions on the thermodynamic properties such as ionization energy (IE) and heat of formation (ΔH°f) for these five-membered heterocyclic compounds. r 2011 American Chemical Society
Over the past decade, owing to the continuous improvements in computer hardware and theoretical algorithm, tremendous progress in terms of accuracy and reliability has been made in theoretical predictions on thermochemical properties. Composite methods such as the Gaussian-n (Gn, n = 1 - 4) by Pople et al.,16-20 the Weizmann-n (Wn, n = 1 - 4) by Martin et al.,21-24 and the complete basis set extrapolation (CBS) by Petersson et al.25-29 have been proposed and developed for thermochemistry predictions. In particular, the W4 and high-accuracy extrapolated ab initio thermochemistry (HEAT)30-32 methods have been shown to be capable of providing thermochemical predictions at an accuracy of (1 kJ/mol (or ≈10 meV) for some rather Received: November 3, 2010 Revised: December 14, 2010 Published: January 6, 2011 932
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II. COMPUTATIONAL METHODS We have used the CCSD(T)/CBS method to perform the IE and ΔH°f predictions. This method involves the approximation to the CBS limit at the CCSD(T) level. The auxiliary high-level corrections, including those of ZPVE, CV, and SR effects, will be described individually as follow. In the CCSD(T)/CBS approach, we choose to use the partially unrestricted implementation, conventionally labeled as ROHF-UCCSD(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.47,48 A. Extrapolated Valence Correlation Energy. The structures of furan, thiophene, pyrrole, borole, and 1,3-cyclopentadiene molecules and their corresponding cations have been optimized at the CCSD(T)/6-311G(2df,p) level of theory. Based on the optimized structures, single-point energy calculations are then carried out at the CCSD(T) level using Dunning’s correlation consistent polarization basis sets (cc-pVXZ) where X = Q, 5, and 6.49 The basis sets augmented with inner core polarization function [cc-pV(Xþd)Z]50 are used for thiophene and its cation. The inner shell 1s electrons on carbon, oxygen, and nitrogen, as well as the 1s/2s/2p electrons on sulfur are kept frozen and uncorrelated. The total valence CCSD(T) energies (sum of HF and correlation energies) are used to estimate the CBS limit (ΔEextrapolated CBS) by two extrapolation schemes:
small species. One of the key steps in the development and refinement of these computational methodologies is to benchmark and test the proposed methods against a known set of experimental data, thus allowing the assignment of a targeted error range for predictions. With this task in mind, we have benchmarked the theoretical IE predictions for a series of hydrocarbon radicals, including CH2, CH3, C2H, C2H3, C2H5, C3H2, C3H3, C3H5, C3H7, C4H7, C6H5, and C6H5CH2.33-36 The theoretical predictions have been performed using the ab initio CCSD(T)/CBS extrapolation approach,37-43 which takes into account the zero-point vibrational energy (ZPVE), core-valence (CV), scalar-relativistic (SR), and higher-order corrections beyond the CCSD(T)44 wave function. On the basis of the comparison between the CCSD(T)/CBS IE predictions and the experimental IE values of the hydrocarbon radicals, we have concluded that the CCSD(T)/CBS method could give accurate IE predictions to within (10 meV for C1-C3 radicals33 and up to (22 meV for C4 radicals. 36 Furthermore, the comparison between the highly precise experimental IE(C6H5CH2) value and the theoretical CCSD(T)/CBS prediction has allowed us to assign the upper error limit of (35 meV for the CCSD(T)/CBS approach for the IE predictions of C7 hydrocarbon radicals.34 Encouraged by the good agreement observed between the ab initio predictions and experimental IE values for these hydrocarbon radicals, we are now extending the theoretical IE calculations to a series of five-membered heterocyclic compounds. There have been several theoretical calculations on the IEs and ΔH°f’s of these five-membered-ring molecules. A series of DFT methods have been employed to predict IE(C4H4CH2) by Jursic,12 IE(C4H4O) and IE(C4H4S) by Ciofini et al.,15 incorporating the average density self-interaction correction formalism in the process. The DFT based IE values always fall into a wide range. The deviations between different DFT estimations could be up to 4.75 eV. Jursic’s14 evaluations on the ΔH°f298 of C4H4O and C4H4S with 24 DFT methods also showed that the ΔH°f298 values strongly depended on the DFT methods. The variations among the 24 DFT calculations on the ΔH°f298 could be as large as 60 kJ/mol. The G3 predictions on the ΔH°f’s and IEs of furan, thiophene, and pyrrole, included in the G2-2 molecules set of Gn theory, are found to deviate from experimental data by 2.1-5.4 kJ/mol.19 We now carry out systematic high-level CCSD(T)/CBS predictions to the IEs, ΔH°f0 and ΔH°f298 of five cyclic C4H4X/C4H4Xþ (X = S, O, NH, CH2, and BH) molecules. In the present work, we will compare the CCSD(T)/CBS predictions on the IE values of the furan, pyrrole, thiophene, 1,3-cyclopentadiene, and borole with the available experimental data. The IEs for the first four molecules have been measured experimentally with uncertainties ranging from 0.2 to 10 meV.45,46 These highly precise experimental data will serve as an excellent test set for benchmarking the accuracy of the theoretical models such as the CCSD(T)/CBS method employed here. We benchmark the calculated thermochemical properties for these cyclic molecules with existing experimental data to establish a reliable thermochemical data for reactive molecule such as C4H4BH and C4H4BHþ, where the IE and ΔH°f’s may not be easily obtained from experiments. The natural bond orbital (NBO) formalism will be used to analyze the highest-occupied molecular orbitals (HOMOs) of C4H4X (X = S, O, NH, CH2, and BH) and the nature (or extent) of π-electron delocalization on each five-membered ring is examined in relations with the molecule’s structures, orbital occupancies and energy levels.
(i) A three-point extrapolation scheme37 using the mixed exponential/Gaussian function of the form EðX Þ ¼ E extrapolated CBS þ B exp½ - ðX - 1Þ þ C exp½ - ðX - 1Þ2
ð1Þ
where X is 4, 5, and 6 for cc-pVQZ, cc-pV5Z, and ccpV6Z, respectively. Here we denote the CBS energies extrapolated by eq 1 with successive cc-pV[Q-6]Z basis sets as CBSQ56 (ii) A two-point extrapolation scheme51-54 using the simple power function involving the reciprocal of X: EðX Þ ¼ Eextrapolated CBS þ
B X3
ð2Þ
where X is 5 and 6 for cc-pV5Z and cc-pV6Z, respectively. We denote the extrapolated CBS energies extrapolated by eq 2 with basis sets of cc-pV[5,6]Z as CBS56. B. Zero-Point Vibrational Energy Correction. To account for the ZPVE corrections (ΔEZPVE), we have computed the harmonic vibrational frequencies and anharmonicities using second-order perturbative (MP2) vibrational treatment implemented in the Gaussian 03 package of programs.55 Under this scheme, it has been shown56-59 that the ZPVE can be approximated as the average between ZPVE obtained from harmonic frequencies (ZPVEharm) and ZPVE obtained from anharmonic frequencies (ZPVEanharm): 1 ZPVE ¼ ðZPVEharm þ ZPVEanharm Þ ð3Þ 2 It assumes that the zero-order vibrational term is negligibly small and has not been included in the above approximation. 933
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The ZPVEharm is essentially taken as the half-sum 1/2 Σ3N-6 i=1 ωi, where N is the number of atoms and ωi is the harmonic vibrational frequency calculated at the CCSD(T) level. The ZPVEanharm is taken to be the half-sum 1/2 Σ3N-6 i=1 υi of the anharmonic vibrational frequencies (υi) calculated effectively at the CCSD(T) level. To obtain the anharmonic vibrational frequencies, we first calculated the harmonic vibrational frequencies at the CCSD(T) level, together with the harmonic frequencies and anharmonic effects at the MP2 and B3LYP levels. The CCSD(T) harmonic vibrational frequencies are then corrected with the anharmonicities obtained at the MP2 and the density-functional B3LYP levels to yield anharmonic vibrational frequencies effectively at the CCSD(T) level of theory. This approximation for anharmonic vibrational frequencies at the CCSD(T) level has been used to predict the ZPVE contributions to the IE and ΔH°f calculations for a number of molecular systems.33-36 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 with both core and valence electrons correlated at the CCSD(T)/ccpwCVQZ60 level. The 1s/2p electrons for carbon, oxygen and nitrogen, and the 2s/2p/3s/3p electrons for sulfur are correlated. D. Scalar Relativistic Effect. The SR energy (ESR) is computed using the spin-free, one-electron Douglas-Kroll-Hess (DKH) Hamiltonian.61,62 The calculations are done with the DKHcontracted cc-pVQZ-DK basis sets63,64 at the CCSD(T) level. The SR energetic contributions are taken as the differences between electronic energies at the CCSD(T)/cc-pVQZ level without using the DKH Hamiltonian and at the CCSD(T)/cc-pVQZ-DK level with the DKH Hamiltonian. In this work, all CCSD(T) single-point energy calculations, vibrational frequency calculations, and correlation contributions were performed using the MOLPRO 2009.1 suite of program.65 The harmonic and anharmonic vibrational frequencies at the MP2 and B3LYP levels were calculated using the GAUSSIAN03 package. The CCSD(T)/CBS values for the ΔH°f0 and ΔH°f298 of the five-membered-ring molecules and cations were calculated using the atomization scheme66 and the following experimental values:67 ΔH°f0(H) = 216.02, ΔH°f0(B) = 559.819, ΔH°f0(C) = 711.20, ΔH°f0(N) = 470.83, ΔH°f0(O) = 246.81, ΔH°f0(S) = 274.72, ΔH°f298(H) = 218.00, ΔH°f298(B) = 565, ΔH°f298(C) = 716.68, ΔH°f298(N) = 472.68, ΔH°f298(O) = 249.18 and ΔH°f298(S) = 276.98 kJ/mol. The atomic spin-orbit coupling (ESO) is directly taken from the experimental excitation energies tabulated by Moore.68
Table 1. NBO Occupancies and Energies (hartrees) of the CdC π-Orbitals and the Nonbonding p Orbitals on X in the Leading Resonance Structures of C4H4X Molecules, Where X = S, O, NH, CH2, and BH, at the B3LYP/6-311G(2df,p) Level C C π-orbitalsa
1 2
X occupancy energy
out-of-plane p orbitalsb on-the-plane p orbitals occupancy
energy
occupancy
energy
c
S
1.88
-0.27529
1.61
-0.24258
1.99
-0.61987
O
1.88
-0.27226
1.70
-0.33170
1.97
-0.57507
1.59
-0.25316
0.13
0.00074
NH
1.85
-0.24459
CH2
1.91
-0.25782
BH
1.91
-0.27075
The two degenerate π-orbitals are of a2 (X = CH2, NH, O, and S) or a00 (X = BH) symmetry. b The out-of-plane p orbital is of b1 (X = CH2, NH, O, and S) or a0 (X = BH) symmetry. c The NBO analysis found that the out-of-plane p orbital is the HOMO instead of the π orbitals, which is opposite to the results by Mulliken population analysis. a
p orbitals (on heterocyclic atom X) in the leading resonance structures of each C4H4X molecules are shown in the Table 1. The occupancy of the two π orbitals for all five C4H4X molecules is about 1.9. In C4H4BH, a tiny amount of electronic charge is found to delocalize in the low-lying out-of-plane 2p orbital of heterocyclic boron (with an occupancy of 0.13). In C4H4CH2, as there is neither vacant p orbital nor nonbonding p electron on methylene carbon, the π-electron delocalization is confined on the remaining four methine carbons. With six π delocalized electrons in pyrrole, it is regarded as aromatic. In its leading resonance structure, the NBO occupancy in the out-of-plane p orbital on nitrogen is about 1.60 with some electronic charge delocalized onto the cyclic ring. In furan (and thiophene), there are two pairs of nonbonding p electrons on oxygen (and sulfur), with one pair each occupying in the out-of-plane and on-the-plane p orbitals. As expected, the out-of-plane p orbital is involved in the π-electron delocalization within the furan and thiophene rings; this is confirmed by the NBO occupancies of ∼1.6 to 1.7. The occupancy of the on-the-plane p orbitals remains close to 2 because they are not involved in the π-electron delocalization. All five neutral C4H4X molecules, where X = BH, CH2, NH, O, and S, have ground electronic state of 1A1 (in C2v symmetry). Due to the π-electron delocalization in C4H4X, the CC bond lengths are somewhere between the distances of typical carboncarbon single and double bonds. As given in the Supporting Information (Table SI-1), the 1C2C bond lengths for C4H4S/ C4H4O/C4H4NH molecules at the CCSD(T)/6-311G(2df,p) level are around 1.36-1.38 Å, while the 2C2C bond lengths are 1.42-1.44 Å. For the C4H4CH2 and C4H4BH with only four π delocalized electrons, the 1C2C bond lengths are found to be ≈1.35 Å but the 2C2C bond lengths are significantly elongated to 1.473 and 1.517 Å, respectively. The longer 2C2C bonds found in C4H4CH2 and C4H4BH agree with NBO analysis that the πelectron delocalizations are mainly confined on the methine carbons. Removal of an electron from the HOMO (π orbitals of a2 symmetry) yields a C4H4Xþ cation in its ground electronic state of 2A2 (X = CH2, NH, O, and S, with C2v symmetry) or 2A00 (X = BH, with Cs symmetry). As the electrons in the HOMO are delocalized in the π-electron framework, the changes in the bonding parameters accompanied by the ionization processes are substantial. For example, the 1C2C bond distances in C4H4X increases by 0.04-0.06 Å upon ionization while the 2C2C bond lengths decrease by 0.05-0.07 Å. The XC bond distance and
III. RESULTS AND DISCUSSION A. π-Electron Delocalization in C4H4X/C4H4Xþ. The five-
membered-ring C4H4X molecules studied here, where X = BH, CH2, NH, O, and S, have very similar bonding natures. In the C4H4NH, C4H4O, and C4H4S, there are six delocalized π electrons (four 2p electrons from the carbons and two electrons from the out-of-plane p orbitals of the heterocyclic atom). On the other hand, there are only four π electrons in C4H4BH and C4H4CH2. The HOMOs for all five molecules is the two degenerate π orbitals delocalized among the homocyclic carbons on the ring. On the basis of the NBO analysis at the B3LYP/6-311G(2df,p) level, the nature of the π-electron delocalization is confirmed. The NBO occupancies and energies of the π orbitals and the out-of-plane 934
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Table 2. Individual Energy Corrections to the Adiabatic IE Predictions for C4H4X, Where X = S, O, NH, CH2, and BH, Using the CCSD(T)/CBS Methoda C4H4S ΔEextrapolated CBSb
ΔEZPVEc
C4H4O
C4H4NH
C4H4CH2
C4H4BH
CBSQ56
8.905
8.894
8.217
8.560
8.846
CBS56 av
8.914 8.910
8.903 8.898
8.227 8.222
8.566 8.563
8.852 8.849
0.006
0.003
-0.035
-0.021
-0.015
0.002
0.001
0.004
0.002
-0.019
MP2 B3LYP
-0.020
av ΔECVd
0.020
0.022
0.018
0.017
0.019
ΔESRe
-0.007
-0.003
-0.002
-0.002
-0.002 8.868
CCSD(T,Full)/CBS IEf
8.888
8.897
8.222
8.582
exptl value
8.8742 ( 0.0002g 8.87 ( 0.01h
8.8863 ( 0.0002g
8.2099 ( 0.0002g
8.57 ( 0.01i 8.58 ( 0.02j
a
All energy differences (ΔEs) and IEs are in eV. b Extrapolated from the frozen-core energies using eqs 1 and 2 with the cc-pV[Q-6]Z and cc-pV [5-6]Z basis sets, respectively. c The ΔEZPVE contributions to IE values are obtained through B3LYP and MP2 anharmonicity corrections to the CCSD(T)/6-311G(2df,p) harmonic vibrational frequencies using eq 3. d Core-valence electron correlation obtained as the difference of allelectron and frozen-core energies at the CCSD(T)/cc-pwCVQZ level. e Scalar relativistic effect calculated at the CCSD(T)/cc-pVQZ-DK level. f IE = ΔEextrapolated CBS þ ΔEZPVE þ ΔECV þ ΔESR. g From ref 45. h From ref 72. i From ref 46. j From ref 80.
SC, 1C2C, and 2C2C bond lengths in C4H4S are predicted to be 1.725, 1.369, and 1.428 Å, which are very close to the corresponding experimental values70 of 1.714, 1.369, and 1.423 Å. Similar agreement is also found between the predicted CCSD(T) bonding parameters of furan and the experimental data.71 As shown in Table 2, the average of the ΔEextrapolated CBS contribution to the IE(C4H4S), based on the two- and three-point extrapolation methods, is 8.910 eV. The ΔEZPVE from the B3LYP anharmonicity corrections is -0.035 eV. After including the CV (0.020 eV) and SR (-0.007 eV) effects, we have arrived at a CCSD(T)/CBS IE value of 8.888 eV. This result is in excellent agreement with the IE value of 8.8742 ( 0.0002 eV obtained from a pulsed-field-ionization photoelectron spectroscopic measurement by Yang et al.45 and an earlier value of 8.87 ( 0.01 eV by photoion-photoelectron coincidence measurement.72 Our CCSD(T)/CBS prediction on the IE(C4H4S) differs from both experimental values by only 14 meV. At the PW86-PW91/augcc-pV5Z level, Shapley et al.13 reported the vertical IE for thiophene to be 8.87 eV. Although this value agrees nicely with the experimental IE values,45,72 the vertical IE value for thiophene is expected to be much larger than the adiabatic IE as the ground state structure of C4H4Sþ is very different from that of neutral C4H4S (see Table SI-1, Supporting Information). Compared with our CCSD(T)/ CBS prediction for IE(C4H4S), a lower value of 8.71 eV was obtained by Rennie et al.73 at the B3LYP/6-311þG(3df,3pd) level. On the basis of the average-density self-interaction correction approach, Ciofini et al. intended to remove the selfinteraction error in density functional theory method and arrived at a much higher IE value of 9.75 eV. 15 The IE(C 4H4S) values obtained with the DFT calculations are likely less reliable. As Table 2 shows, the CCSD(T)/CBS IE(C4H4O) of 8.897 eV is 10 meV above the experimental value of 8.8863 ( 0.0002 eV, measured in previous PFI-PE spectroscopic experiment.45 There are a few other theoretical results for IE(C4H4O): Shapley et al.13 calculated a value of 8.87 eV at the PW86-PW91/aug-cc-pV5Z level, which is in excellent agreement with the PFI-PE measurement by Yang et al.45 On the other hand, using CISD method and MIDI-4-type basis set, Takeshita and Yamamoto74 predicted a value of 8.53 eV, which is too low. The current CCSD(T)/CBS
other interatomic angles in C4H4X are almost unaffected by the ionization process. According to the Koopmans’ theorem,69 the negative of the HOMO or frontier orbital energy is equal to the energy required to ionize an occupied electron in the orbital, i.e., vertical ionization energy. By examining the energies of the π orbitals in Table 1, one may find that the adiabatic IEs, corresponding to form the C4H4X cations in the 2A2 (X = CH2, NH, O, and S) or 2A00 (X = BH) state, follow the order of IE(C4H4S) ≈ IE(C4H4O) > IE(C4H4BH) > IE(C4H4CH2) > IE(C4H4NH). In fact, the trend of IE values for the five species dictated by the Koopmans theory is in total accord with the trend predicted by the CCSD(T)/CBS results. The energy level of π orbital of each species is in a linear relationship with its adiabatic IE at the CCSD(T)/CBS level. For C4H4X (X = NH, O, and S), ionization of an electron from the out-of-plane p orbital (b1) results in an electronically excited 2B1 cation. As shown by the NBO energies in the Table 1, the out-ofplane p orbital is lying below the π orbitals by 0.23 and 1.61 eV for C4H4NH and C4H4O, respectively. For C4H4S, NBO analysis surprisingly indicates that the out-of-plane p orbital sits above the π orbitals by 0.89 eV, which is in reverse order predicted by simple Mulliken population analysis. However, further CCSD(T)/CBS calculations on the C4H4Sþ cation confirm that the 2B1 cationic state is indeed an excited state while the ground electronic state of C4H4Sþ is 2A2. The individual energy corrections (ΔEextrapolated CBS, ΔEZPVE, ΔECV, and ΔESR) for IE(C4H4BH), IE(C4H4CH2), IE(C4H4NH), IE(C4H4O), and IE(C4H4S) calculations are shown in Table 2. The ΔEextrapolated CBS obtained from the respective two-point and threepoint extrapolation schemes according to eqs 1 and 2 can differ up to 10 meV. Thus, an average of the two extrapolated values is adapted. The ΔEZPVE values based on the two anharmonicity corrections at the MP2 and B3LYP levels of theory are very similar. Except for the C4H4Sþ and C4H4NHþ species where the MP2 anharmonic frequencies are unavailable, the average of MP2 and B3LYP ΔEZPVE values is used for the IE and ΔH°f predictions of all other species. B. Ionization Energies of C4H4S and C4H4O. Isoelectronic thiophene and furan have similar chemical properties. The ground state structures of thiophene/furan and their cations have C2v symmetry. At the CCSD(T)/6-311G(2df,p) level, the respective 935
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delocalized π electrons in the 1,3-cyclopentadiene and borole molecules. The C4H4CH2 molecule has neither vacant p orbital nor nonbonding p electrons and the π-electron delocalization is only contributed from the methylenic carbons. The π-electron delocalization framework in 1,3-cyclopentadiene is very similar to that found in cis-butadiene. At the CCSD(T)/6-311G(2df,p) level, the 1C2C and 2C2C bonding distances in C4H4CH2 are 1.350 and 1.473 Å, respectively, which are essentially identical to the corresponding CdC and C;C bond lengths of 1.340 and 1.473 Å in the cis-butadiene. Together with the H2C-1C bond length of 1.506 Å, the predicted C4H4CH2 structure at the CCSD(T)/6-311G(2df,p) level is very comparable with the experimental data.79 The CCSD(T)/CBS prediction for IE(C4H4CH2) value is 8.582 eV. Unlike furan, thiophene, and pyrrole, there has been no PFI-PE measurement on C4H4CH2 yet. However, an IE(C4H4CH2) value of 8.57 ( 0.01 eV has been determined from the photoelectron spectrum measurement by Derrick et al.46 and a very similar value of 8.58 ( 0.02 eV has also been reported by Bieri et al.80 Although the uncertainty of this experimental IE value is relatively large (compared with the PFI-PE measured values of C4H4S, C4H4O, and C4H4NH), our CCSD(T)/CBS predicted value of 8.582 eV is still in excellent agreement with the experimental values.46,80 In terms of accuracy, the CCSD(T)/ CBS IE(C4H4CH2) value is also superior to previous theoretical predictions. Delaere et al.76 reported an IE(C4H4CH2) of 8.4 eV, which is crudely estimated from the HOMO energy of neutral C4H4CH2 at the HF/SV(P) level. Using the G2M(RCC, MP2) method, Nguyen et al. obtained an IE(C4H4CH2) of 8.67 eV,81 which is larger than the experimental value by 0.09 eV. Borole is a unique molecule: it has four π electrons delocalized among five p orbitals. According to the NBO results, a tiny amount of electronic charge (an occupancy of 0.13) is found to be delocalized on the out-of-plane p orbital of boron. The p orbital of boron is virtually vacant and nonbonding (as indicated by its NBO energy level). Thus, borole is regarded as a good Lewis acid or electron acceptor. Chemically, borole is reactive and unstable in ambient conditions. The pentaphenylborole analog is a highly reactive green solid; it readily undergoes oxidation, partial protolysis, and the Diels-Alder reaction with dienophiles.82 Borole, even in perarylated form, is still very labile.83 Due to its reactive nature, the structural parameters and thermochemical data of borole are not known. In the CCSD(T)/6-311G(2df,p) optimized structure of borole, the BC, 1C2C, and 2C2C bond lengths are 1.582, 1.349, and 1.517 Å, respectively, and those in its cation are 1.583, 1.392, and 1.448 Å, respectively. The CCSD(T)/CBS IE(C4H4BH) value is 8.868 eV. In view of the excellent agreements between the CCSD(T)/CBS predictions and the experimental IE values for four aforementioned five-membered-ring species, the predicted IE value for borole molecule should be reliable. Due to the reactive nature of borole, the preparation of borole for experimental measurements could be a challenging task. E. CCSD(T)/CBS Predictions to the ΔH°f0/ΔH°f298’s of Neutral C4H4X Molecules and Cations. The CCSD(T)/CBS ΔH°f0/ΔH°f298 values are listed in Table 3, together with the available experimental data for comparison. The experimental ΔH°f’s of C4H4S/C4H4O/C4H4NH have been determined by calorimetric methods.8-11 Unless specified, the experimental ΔH°f0 and ΔH°f298 for cations and ΔH°f0 of neutral are obtained by converting the available ΔH°f’s of neutral with the experimental
IE(C 4 H 4 O) prediction is in par with the W1 value of 8.878 eV.22 As mentioned previously, ionization of an out-of-plane p electron on C4H4O/C4H4S would generate the first electronically excited state (2B1) of the cations, the structure of C4H4Oþ/ C4H4Sþ in the 2B1 state is expected to be similar to that of neutral C4H4O/C4H4S: the respective SC, 1C2C and 2C2C bond lengths in the C4H4Sþ (2B1) are 1.724, 1.362, and 1.490 Å, which are very close to the lengths of 1.725, 1.369, and 1.428 Å in the neutral C4H4S, whereas the structure of C4H4Sþ in the 2A2 state, with SC, 1C2C, and 2C2C bond lengths of 1.716, 1.427, and 1.375 Å, are farther away from the bond lengths of the neutral C4H4S. As a result, the Franck-Condon factor (FCF) for ionization process C4H4Sþ (2B1) r C4H4S (X 1A1) should be more favorable than that for the ionization process of C4H4Sþ (X 2A2) r C4H4S (X 1A1). Nevertheless, the adiabatic ionizations of C4H4O/C4H4S have been observed by Mo and co-workers using the PFI-PE spectroscopic method.45 C. Ionization Energy of C4H4NH. At the CCSD(T)/6-311G(2df,p) level, the respective HN-C, 1C2C, and 2C2C bond distances of pyrrole are 1.373, 1.377, and 1.426 Å, which are in good accord with the experimental values75 of 1.370, 1.382, and 1.417 Å. The valence electronic contributions, ΔEextrapolated CBS, to IE(C4H4NH) is 8.222 eV. At the MP2/6-311G(2df,p) level, the anharmonicities calculations of the C4H4NHþ cation give physically unreasonable results; thus only the B3LYP based anharmonic correction (-0.015 eV) is used for the ZPVE correction. At the CCSD(T)/6-311G(2df,p) level, the 2B1 excited state is lying 0.8 eV above the ground state for the C4H4NHþ cation. Upon including the ZPVE, CV, and SR contributions, we arrive at a CCSD(T)/CBS IE value of 8.222 eV, which is slightly higher than the experimental value (8.2099 ( 0.0002 eV) by 12 meV.45 Estimated from the negative HOMO energy at the HF/SV(P) level, Delaere et al.76 obtained a vertical IE(C4H4NH) value of 8.1 eV, which is much lower than the experimental value by 0.11 eV. Wang et al.77 employed the neural-networks-based and multiple-linear-regression-based correction approaches at the B3LYP/6-311þG(3df,2p) level to predict the IE(C4H4NH) values of 8.44 and 8.37 eV, respectively. These values are larger than the experimental value by at least 0.15 eV, suggesting that the previous DFT predictions are too high. At the CCSD(T)/6-311G(2df,p) level, the 2B1 excited states of C4H4Xþ (X = O, S, and NH) are found to be lying above the respective ground states (2A2) by about 1.4, 0.4, and 0.8 eV, respectively. For the latter two cations, the MP2 anharmonicity corrections are physically unreasonable to be used for ZPVE corrections and have not been included in Table 2. The unreasonable MP2 anharmonic corrections are likely due to the perturbations to the potential energy surfaces of the ground state cations (2A2) by the low-lying excited state (2B1). These perturbations may arise from the vibronic interactions of the 2A2 and 2 B1 states via the b2 vibrational modes of furan, thiophene, and pyrrole cations.78 Trofimov et al. found that the vibronic interactions are strongest in C4H4NHþ and C4H4Sþ, where the conical interaction between the two adiabatic surfaces occurs above the upper 2B1 state by 0.04 and 0.01 eV, respectively. The vibronic perturbation on C4H4Oþ is likely minimal as the corresponding conical interaction is lying 0.5 eV above the upper 2B1 state. This also agrees with our calculations that no anharmonic irregularity is found for the C4H4Oþ cation. D. Ionization Energies of C4H4CH2 and C4H4BH. Unlike the three C4H4X (X = S, O, and NH) species, there are only four 936
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IE45,46 and the thermal corrections using the CCSD(T)/ 6-311G(2df,p) vibrational frequencies. The ΔH°f298 of C4H4S has been determined by bomb calorimetric methods8,9 over five decades ago. By measuring the 298 K heat of combustion reaction of C4H4S(l) þ 13/2 O2(g) þ xH2O(l) f 4CO2(g) þ [H2SO4 3 (x þ 1)H2O](l), Waddington et al. determined ΔH°f298(C4H4S(l)) to be 81.67 kJ/mol, using the known ΔH°f298 values of water, carbon dioxide, and aqueous sulfuric acid. This ΔH°f298(C4H4S(l)) = 81.67 kJ/mol can then be converted to ΔH°f298(C4H4S(g)) = 116.40 kJ/mol, using the 298 K heat of vaporization (ΔH°vap) of thiophene obtained in the same study.8 Later on, Hubbard et al. remeasured the ΔH°vap value of thiophene using the rotating-bomb calorimetric method, which is supposed to be more reliable for sulfur-containing compounds than the previous bomb calorimetric method, and revised the ΔH°f298(C4H4S) value to 115.0 ( 1.0 kJ/mol.9 In any event, the CCSD(T)/CBS ΔH°f298(C4H4S) of 116.0 kJ/mol is in excellent agreement with both experimental values of 116.40 and 115.0 ( 1.0 kJ/mol.8,9 Our prediction is also in line with the recommended values for ΔH°f298(C4H4S) of 115.1 and 115.7 kJ/mol, taken from two thermochemical data compilations.67,84 In summary, the CCSD(T)/CBS ΔH°f0/ΔH°f298 values of C4H4S and C4H4Sþ are 126.4/116.0 and 983.9/974.4 kJ/mol, these results deviate from experimental data by 1.0/1.0 and 2.3/ 2.3 kJ/mol, respectively. From the measurement of 298 K heat of combustion of liquid furan in a bomb calorimeter experiment, Guthrie et al.10 obtained the ΔH°f298(C4H4O(l)) value of -62.3 kJ/mol using the known values for ΔH°f298(CO2) and ΔH°f298(H2O). Combining the ΔH°f298(C4H4O(l)) value with the ΔH°vap(C4H4O), they arrived at the ΔH°f298(C4H4O(g)) = -34.7 kJ/mol. In the same study, using the heat of combustion data as well as the thermodynamic functions of furan, graphite, hydrogen, and oxygen,85 Guthrie et al. derived a value of -21.6 kJ/mol for ΔH°f0(C4H4O).10 Our CCSD(T)/CBS ΔH°f0 and ΔH°f298 values of furan are -20.0 and -31.2 kJ/mol, respectively, which are just 1.6 and 3.5 kJ/mol off the experimental data. Using the ΔH°f298(C4H4O(l)) values of -55.4 and -57.5 kJ/mol reported by Zaheeruddin et al.86 and Landrieu et al.,87 respectively, two experimental values of -27.7 and -29.8 kJ/mol for ΔH°f298(C4H4O(g)) are obtained.88 The latter value of ΔH°f298(C4H4O(g)) = -29.8 kJ/mol, derived from the ΔH°f298(C4H4O(l)) by Landrieu et al.,87 is in very good agreement with our CCSD(T)/CBS prediction of -31.2 kJ/mol, while the former ΔH°f298(C4H4O(g)) = -27.7 kJ/mol, derived from the ΔH°f298(C4H4O(l)) by Zaheeruddin et al.,86 is likely to be too high. Comparing with available experimental ΔH°f0/ΔH°f298’s of C4H4O and C4H4Oþ, our CCSD(T)/CBS predictions of -20.0/-31.2 and 838.4/827.5 kJ/mol deviate from experimental data by 1.6/3.5 and -0.4/-0.4 kJ/mol, respectively. Likewise, the experimental ΔH°f0/ΔH°f298 values of 125.0 ( 0.50/108.3 ( 0.50 kJ/mol for C4H4NH have been determined from the heat of combustion of pyrrole in conjunction with the known ΔH°f values of CO2 and H2O by Waddington and coworkers in a bomb calorimetric measurement.11 Our CCSD(T)/ CBS predictions of ΔH°f0/ΔH°f298 = 126.0/110.9 kJ/mol are less than 2 kJ/mol off the experimental values. Willams and Whitehead89 employed the isolobal reaction scheme to estimate the ΔH°f298(C4H4NH) at semiempirical and Hartree-Fock levels. Their best estimation for ΔH°f298(C4H4NH), obtained at the HF/6-31G(d,p) level, is 111.3 kJ/mol. Although this estimate agrees well with the experimental value of 108.3 ( 0.50 kJ/mol
Table 3. Comparisons of the CCSD(T)/CBS (Bold Font) ΔH°f0 and ΔH°f298 Values (kJ/mol) for C4H4X and C4H4Xþ where X = S, O, NH, CH2, and BH, with Available Experimental Data (Normal Font) C4H4S ΔH°f0
a
C4H4O
C4H4CH2
126.4
-20.0
126.0
152.1
126.8b
-21.6 f
125.0 ( 0.50i
149.6 ( 1.7k
125.4 ( 1.0c
-16.5g
123.9 j
148.8l
d
-18.6
125.5
126.13
h
269.5
154.2m
-31.2
110.9
136.8
116.4b 115.0 ( 1.0c
-34.7 f -27.7g
108.3 ( 0.50i 108.8 j
134.3 ( 1.7k 133.5l
115.1d
-29.8h
115.73
C4H4BH
e
ΔH°f298 116.0
258.6
138.9m
e
C4H4Sþ ΔH°f0a
C4H4NH
C4H4Oþ
C4H4NHþ
C4H4CH2þ C4H4BHþ
983.9
838.4
919.3
983.0b
835.8 f
917.1 ( 0.50i 977.4 ( 2.6k
981.6 ( 1.0c
840.9g
916.0 j
d
h
981.7 982.36e
980.1 976.6l 982.0m
838.8
ΔH°f298a 974.4
827.5
904.2
973.5b
824.9 f
902.0 ( 0.50i 962.5 ( 2.6k
972.1 ( 1.0c
830.0g
900.9 j
d
h
972.2
827.9
1125.1
965.2
1114.6
961.7l 967.1m
e
972.86
The ΔH°f0 of neutrals and ΔH°f0 and ΔH°f298 of cations are converted from the vibrational frequencies obtained in this study and the experimental IE from ref 45 or 46. b ΔH°f298(C4H4S) is from ref 8. c ΔH°f298(C4H4S) is from ref 9. d ΔH°f298(C4H4S) is from ref 67. e ΔH°f298(C4H4S) is from ref 84. f ΔH°f0(C4H4O)/ΔH°f298(C4H4O) is from ref 10. g ΔH°f298(C4H4O) is from ref 86. h ΔH°f298(C4H4O) is from ref 87. i ΔH°f0(C4H4NH)/ΔH°f298(C4H4NH) is from ref 11. j ΔH°f298(C4H4NH) is from ref 90. k ΔH°f298(C4H4CH2) is from ref 91. l ΔH°f298(C4H4CH2) is from ref 90. m ΔH°f298(C4H4CH2) is from ref 92. a
by Waddington and co-worker, we believe that the agreement is likely fortuitous because the correlation effect in the “designed” products and reactants may not completely cancel each other out in the isolobal reaction scheme. The CCSD(T)/CBS predicted ΔH°f0/ΔH°f298 values for C4H4NH and C4H4NHþ are 126.0/110.9 and 919.3/904.2 kJ/mol; our predictions deviate from experimental data by 1.0/1.0 and 2.3/2.3 kJ/mol, respectively. The respective CCSD(T)/CBS ΔH°f0/ΔH°f298 of C4H4CH2 and C4H4CH2þ are 152.1/136.8 and 980.1/965.2 kJ/mol. There have been several experimental determinations for the ΔH°f298 value of neutral C4 H4CH2 (133.5,90 134.3 ( 1.7,91 and 138.992 kJ/mol), which are consistent with our calculations. Using the CCSD(T) anharmonic vibrational frequencies of 1,3cyclopentadiene and the experimental IE value of 8.58 ( 0.02 eV,46 we have converted the three available values of ΔH°f298(C4H4CH2) into the corresponding ΔH°f0(C4H4CH2)/ ΔH°f0(C4H4CH2þ)/ΔH°f298(C4H4CH2þ) values and listed in Table 3. Our CCSD(T)/CBS ΔH°f0/ΔH°f298 predictions on C4H4CH2 and C4H4CH2þ are 2.5/2.5 and 2.7/2.7 kJ/mol off these experimental data. Besides the current theoretical CCSD(T)/CBS values, the ΔH°f298(C4H4CH2) and ΔH°f298(C4H4CH2þ) have 937
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The Journal of Physical Chemistry A been calculated to be 134.3 and 968.6 kJ/mol, respectively, at the G2M(RCC,MP2) level by Nguyen et al.81 The former is on par with the CCSD(T)/CBS prediction, while the latter deviates from the available experimental value of 962.5 ( 2.6 kJ/mol91 by over 6 kJ/mol. In addition to this, a slightly higher ΔH°f298 value of 137.6 kJ/mol for C4H4CH2 at the G3 level has been reported.93 The experimental value for ΔHof’s of C4H4BH and C4H4BHþ is not known. In view of the excellent agreement between our theoretical predictions and experimental measurements on the thiophene, furan, pyrrole, and 1,3-cyclopentadiene molecules, the respective ΔHof0/ΔHof298 of 269.5/258.6 and 1125.1/ 1114.6 kJ/mol for the chemically reactive borole and its cation, predicted at the CCSD(T)/CBS level, should constitute a reliable set of thermochemical data. The individual energetic contributions to the total atomization energies for all five heterocyclic compounds and their cations are compiled in Supporting Information (Table SI-2). In addition to the valence electronic CBS energies, both the ZPVE and CV corrections make significant contributions to the total atomization energies. The CV electronic correlations, ranged from 18.2 to 23.7 kJ/mol, always lead to larger total atomization energies and bring the theoretical predictions closer to the experimental values.
IV. CONCLUSION We have predicted the IEs and ΔH°f0/ΔH°f298 values for thiophene, furan, pyrrole, 1,3-cyclopentadiene, and borole by the wave function based ab initio CCSD(T)/CBS approach, which involves the approximation to the CBS limit at the coupled cluster level with single and double excitations plus quasiperturbative triple excitation effect [CCSD(T)]. The anharmonic ZPVE correction, the CV electronic correlation, and the SR corrections have also been included in these calculations. Our CCSD(T)/ CBS predictions of 8.888, 8.897, and 8.222 eV for thiophene, furan, and pyrrole are in excellent agreement with the highly precise IE values of 8.8742 ( 0.0002, 8.8863 ( 0.0002, and 8.2099 ( 0.0002 eV, all determined from previous PFI-PE measurements.45 For 1,3-cyclopentadiene, the CCSD(T)/CBS predicted IE value of 8.582 eV is also in good accord with the experimental IEs of 8.57 ( 0.01 and 8.58 ( 0.02 eV, determined from photoelectron and photoion spectroscopic measurements.46,80 The CCSD(T)/ CBS ΔH°f0/ΔH°f298 predictions for C4H4S/C4H4Sþ, C4H4O/ C4H4Oþ, C4H4NH/C4H4NHþ, and C4H4CH2/C4H4CH2þ are also in good agreement with the available experimental data, with deviations well within the so-called chemical accuracy (
