Article pubs.acs.org/JPCA
Experimental and Theoretical Investigation on the Outer Valence Electronic Structure of Cyclopropylamine by (e, 2e) Electron Momentum Spectroscopy Yufeng Shi, Xu Shan,* Enliang Wang, Hongjiang Yang, Wei Zhang, and Xiangjun Chen Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China ABSTRACT: The binding energy spectra and electron momentum distributions for the outer-valence molecular orbitals of gaseous cyclopropylamine (CPA) have been measured by (e, 2e) electron momentum spectrometer employing noncoplanar asymmetric geometry at the impact energy of 2500 eV. The experimental results are interpreted on the basis of the quantitative calculations of the ionization energies and the relevant molecular orbitals at benchmark theoretical levels using the outer-valence Green’s function method, the symmetry-adapted cluster configuration interaction method, and the density functional theory with B3LYP hybrid functional. The total energies of the trans and gauche conformers of CPA are also calculated by the second-order Møller−Plesset perturbation theory with large basis sets and the derived enthalpy differences (2.02−2.12 kcal/mol) are consistent with the previous experimental data (2.19 kcal/mol). The theoretical binding energy spectra and electron momentum distributions, in which the relative abundances of trans and gauche are taken into account, are generally in accordance with the experimental results except for the ionization band from the trans 8a′ and gauche 11a orbitals. The discrepancy is explained qualitatively in view of the picture of molecular geometry change at the instant of ionization. basis sets.11−17 Pelissier et al.11 and Mochel et al.12 calculated the torsional potentials of NH2 relative to the carbon ring and predicted that two stable conformers exist in CPA and the more stable is trans conformer, while, in the subsequent calculations,4,13−16 the molecular geometry of the preference conformer (trans) was concentrated on. Recently, Hyla-Kryspin et al.17 calculated the torsional potential at a number of torsional angles and the geometric parameters of trans and gauche conformers using the second-order Møller−Plesset perturbation (MP2) and SCS-MP2 with the TZVPP basis set. As for the energy difference between trans and gauche conformers, the early calculations4,10−12 at the CNDO/2, SCF, and MP2 theoretical levels with small or moderate basis sets determined the values to be somewhat large, from 1539 to 890 cm−1 (4.4−2.54 kcal/mol), which resulted in only 1−3% population of the gauche conformer. The recent calculations17 at the MP2 and SCS-MP2 levels with a large basis set (TZVPP) presented the energy difference of 2.21 and 2.17 kcal/mol suggesting close to 5% gauche population, which was in line with the data from the IR spectra work.7 Relative to the extensive research of molecular geometries and energetic properties, on the other hand, studies of the electronic structure of CPA are very scarce. There is only a report on the ionization spectra measured by He I ultraviolet
I. INTRODUCTION Cyclopropylamine (CPA) is the chemically most reactive cycloalkylamine because of the highly strained bonding in the three-membered ring, and therefore, it is used as an intermediate for agrochemical active substances. There are many experimental and theoretical works devoted to the molecular geometry and energetic properties of CPA. The geometric parameters of CPA were determined by gas-phase microwave spectra (MW)1−4 and electron diffraction (ED),5 as well as the combined analysis of ED and MW spectra.5 The infrared (IR) and Raman spectra of the gaseous, liquid, and solid CPA were recorded by Kalasinsky et al.,6 and an enthalpy difference between the more stable trans and high-energy gauche conformers coexisted in gaseous CPA was derived to be 592 cm−1 (∼1.69 kcal/mol) indicating a ∼10% relative population of gauche conformer at room temperature. Compton et al.7 also observed the IR spectra of gaseous CPA and deduced the enthalpy difference of 766 cm−1 (∼2.19 kcal/ mol) between trans and gauche conformers, which indicated the relative abundance of the gauche conformer is about 5%. Subsequently, the IR spectra work of Hamada et al.8 suggested the population of the gauche conformer should not exceed 5%. However, the IR spectra obtained by Diallo et al.9 at a series of temperatures confirmed only the trans conformer present in CPA, as suggested by the previous MW1−3 and the overtone spectra.10 On the theoretical side, calculations were also performed to describe the molecular geometry and energetic properties of CPA using various methods with different sizes of © 2014 American Chemical Society
Received: March 31, 2014 Revised: June 3, 2014 Published: June 3, 2014 4484
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photoelectron spectroscopy (UPS),18 in which the observed bands were assigned on the basis of calculations at the SCF/431G level. Therefore, it is necessary to carry out the detailed studies on the electronic structure of CPA both experimentally and theoretically. Electron momentum spectroscopy (EMS), also known as binary (e, 2e) spectroscopy, has been proved as a powerful technique for exploring the electronic structures of atoms and molecules due to its unique ability to directly obtain not only the binding energy spectra but also the spherically averaged electron density distributions in momentum space for individual orbitals.19−27 To our best knowledge, no EMS study of CPA has been reported so far. In this work, we report the first EMS measurement on the binding energy spectra and electron momentum distributions for the outer-valence molecular orbitals of gaseous CPA. The experimental results are interpreted on the grounds of quantitative calculations of the ionization energies and the relevant molecular orbitals at benchmark theoretical levels using the outer-valence Green’s function (OVGF),28 the symmetry-adapted cluster configuration interaction (SAC-CI),29 and the density functional theory (DFT) with B3LYP hybrid functional.30 The total energies of trans and gauche conformers of CPA are also calculated by the MP2 method with larger basis sets, and the Boltzmann-weighted thermostatistical abundances of 93.8% for trans and 6.2% for gauche obtained by MP2/aug-cc-pVTZ are taken into account in the comparison of the theoretical and experimental binding energy spectra and electron momentum distributions.
experiment, the energy and momentum resolution of the present EMS spectrometer are determined by measuring Ar 3p ionization to be ∼1.0 eV [full width at half-maximum (fwhm)] and ∼0.1 au, respectively. On the theoretical side, within the binary encounter approximation and the plane wave impulse approximation (PWIA), as well as Born−Oppenheimer approximation and disregarding rotational functions, the triple differential crosssection (σEMS) of (e, 2e) reaction in EMS turns out to be proportional to the squared form factor Fif(p), which is given by19,20 Fif (p) =
(3)
where Xv(Q) and Xv′(Q) are vibrational wave functions for initial and final states, S(f) q (Q) is the overlap integral of the wave functions for the final ion and molecular residue left after the knockout of an electron from one-electron molecular orbital φq(p,Q) in momentum space, and Q is the set of coordinates determining the displacements from equilibrium of N atomic nuclei of the molecule. Equation 3 can further be reduced to20 Fif (p) = gvv ′Sq(f )(Q̅ ) φq(p, Q̅ )
(4)
where = ∫ dQ X*v′ (Q)Xv(Q) is the usual Franck−Condon factor and Q̅ corresponds to some mean values of nuclear coordinates intermediate between the equilibrium coordinates of nuclei Q0 and Q′ in the initial molecule and in the final molecular ion, respectively. Estimations made by Levin et al.20 for light diatomic molecules showed that the value S(q f)(Q) φq(p,Q) slowly varies in the range of Q values between Q0 and Q′0, so the Q̅ value in the calculation for EMS studies is usually chosen as Q0 in the initial molecule. Moreover, since the vibrational states are not resolved by the present EMS spectrometer, σEMS can be expressed as19,20 gvv′
II. EXPERIMENTAL AND THEORETICAL BACKGROUND EMS is based on a kinematically complete (e, 2e) collision experiment in which an electron from target atoms or molecules is cleanly knocked out by a high-energy incident electron and the residual ion acts as a spectrator. In the present EMS spectrometer,31 asymmetric noncoplanar kinematics is employed. In brief, the incident electron beam generated from an electron gun is accelerated by a lens system to the desired energy of 2500 eV plus the binding energy and transferred to the reaction region where the incident electron impacts with the gas-phase target molecule injected by a nozzle. The scattered electron outgoing along polar angle θa = 14° passes through the fast electron analyzer and is detected by a twodimensional position sensitive detector (PSD) over a large range of both energies and azimuthal angles of interest. The ionized electron outgoing along polar angle θb = 76° passes through the slow electron analyzer and is detected by onedimensional PSD. In such experimental condition, considering conservation of energy and momentum, the binding energy ε and magnitude of momentum p of the target electron can be expressed by ε = E0 − Ea − E b (1)
σEMS ∝ |Sq(f )(Q 0)|2
∫ |φq(p, Q 0)|2 dΩ
(5)
The integral in eq 5 is known as the spherically averaged oneelectron momentum distribution or electron momentum profile. |S(q f)(Q0)|2 represents the pole strength and φq(p,Q0) is the Dyson orbital which can be approximated by the oneelectron canonical Hartree−Fock (HF)19 or Kohn−Sham wave function30 in momentum space for the qth orbital from which the electron is ionized.
III. COMPUTATIONAL DETAILS As previously mentioned, the potential energy profiles for the internal rotation of NH2 relative to the cyclopropyl ring were calculated using CNDO/211 and HF12 with small basis sets, MP2 with 6-31G* moderate basis set,10 and MP2 and SCSMP2 with large basis set (TZVPP).17 Three minimum points were found: the one at 0° angle corresponds to the trans conformer, and the other two at ±135° are two equivalent gauche conformers. As for the enthalpy difference between trans and gauche conformers, the calculation using a large basis set17 offered more consistent values (2.02 kcal/mol) with the experimental data (1.69, 2.19 kcal/mol)6,7 than those (4.4− 2.54 kcal/mol) from the calculations with small and moderate basis sets,10−12 indicating the importance of basis set sizes. In the present work, the torsional potentials and geometric parameters are recalculated employing larger basis sets of augcc-pVTZ, cc-pVTZ, and 6-311++G** at the MP2 and B3LYP
p = {p0 2 + pa 2 + pb 2 − 2p0 pa cos θa − 2p0 pb cos θ b + 2pa pb [cos θa cos θ b − sin θa sin θ b cos ϕ]}1/2
∫ dQ Xv*′(Q ) Xv(Q ) Sq(f )(Q ) φq(p, Q )
(2)
where (E0, p0), (Ea, pa) and (Eb, pb) are the energies and momenta of the projectile, scattered, and ejected electrons, respectively. And ϕ is the relative azimuthal angle between the two outgoing electrons. Therefore, by detecting two outgoing electrons in coincidence, the binding energy and momentum of the target electron can be determined. Before normal 4485
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Table 1. Enthalpy Difference (kcal/mol) for Trans and Gauche Conformers of Gaseous CPA at Room Temperature MP2/a ΔH gauche, % a
B3LYP/a
aug-cc-pVTZ
cc-pVTZ
6-311++G**
aug-cc-pVTZ
6-311++G**
SCS-MP2/TZVPP17
IR7
IR6
2.02 6.2
2.08 5.7
2.12 5.3
1.87 7.8
2.03 6.1
2.02 6.2
2.19 4.7
1.69 10
This work.
Table 2. Experimental and Theoretical Ionization Energies for the Outer-Valence Orbitals of CPA SAC−CIa
a
OVGFa
MO no.
trans
gauche
trans
gauche
UPS18
EMSa
MO16 MO15 MO14 MO13 MO12 MO11 MO10 MO9
11a′ 9.02 [0.83] 5a″ 10.20 [0.83] 10a′ 10.72 [0.82] 4a″ 12.89 [0.83] 9a′ 13.59 [0.82] 8a′ 15.47 [0.82] 3a″ 16.38 [0.82] 7a′ 16.92 [0.81]
16a 8.46 [0.83] 15a 10.32 [0.84] 14a 11.44 [0.82] 13a 12.89 [0.84] 12a 13.18 [0.83] 11a 15.50 [0.83] 10a 15.97 [0.83] 9a 16.96 [0.82]
11a′ 9.50 [0.92] 5a″ 10.41 [0.91] 10a′ 11.03 [0.91] 4a″ 13.06 [0.92] 9a′ 13.90 [0.91] 8a′ 15.51 [0.90] 3a″ 16.46 [0.92] 7a′ 17.06 [0.90]
16a 9.01 [0.91] 15a 10.67 [0.91] 14a 11.89 [0.91] 13a 13.24 [0.92] 12a 13.57 [0.91] 11a 15.72 [0.91] 10a 16.15 [0.90] 9a 17.17 [0.90]
11a′ 9.41 5a″ 10.65 10a′ 11.41 4a″ 12.86 9a′ 13.69 8a′ 15.59 7a′ 16.91 3a″
11a′/16a 9.41 5a″/15a 10.65 10a′/14a 11.41 4a″/13a 12.86 9a′/12a 13.69 8a′/11a 15.59 3a″/10a 16.91 7a′/9a 16.91
This work. Pole strengths are listed in square brackets.
IV. RESULTS AND DISCUSSION CPA (C3H5NH2) contains 32 electrons and has 8 outer-valence MOs. Both HF and B3LYP calculations give the ground-state electronic configurations of the trans conformer (CS) as
theoretical levels. The calculated enthalpy differences of trans and gauche conformers, as listed in Table 1, are in agreement with the previous experimental data 6,7 and the recent theoretical results.17 The optimized geometric parameters are also consistent with the previous MW and ED data,1−5 as well as the calculations.17 The theoretical momentum profiles for eight outer-valence molecular orbitals (MOs) of trans and gauche conformers have been calculated, respectively, according to eq 5. Since the DFT method with B3LYP hybrid functional includes the electron exchange and correlation interactions,30 it has been proved to be much better than the HF method in interpreting the experimental momentum profiles in EMS studies.19−27 Therefore, in the present calculations, only the DFT-B3LYP method with different-sized basis sets of 6-311++G, 6-311G**, 6-311+ +G**, cc-pVTZ, and aug-cc-pVTZ are used to calculate the position space Kohn−Sham wave functions of the relevant MOs on the basis of equilibrium geometries of neutral CPA optimized by MP2/aug-cc-pVTZ. The ionization energies for the outer-valence MOs of trans and gauche conformers have been calculated using the OVGF and SAC-CI general-R methods with the 6-311++G** basis set. Note that the OVGF28 and SAC-CI29 methods both include the electron correlation effect and can offer more accurate ionization energies than the HF method. The extra pole strengths can help to know the presence of shakeup states accompanying the ionizations of MOs. In the present SAC-CI calculations, the active space consists of 16 occupied MOs and 121 unoccupied MOs, and only the orbitals of C 1s and N 1s are frozen as cores. The level-three accuracy has been adopted, and R operators are included up to triplicate for taking into account the possible electron correlation effect in the valence range. 250 ionized states are calculated for trans and gauche conformers, respectively, and the ionization energies are up to 26 eV. All of the present calculations are carried out within the Gaussian 03 suite of programs.32
and gauche conformer (C1) as
The vertical ionization potentials (IPs) and pole strengths for eight outer-valence MOs of trans and gauche conformers have been calculated using the OVGF and SAC-CI general-R methods with 6-311++G** basis set. The calculated results are listed in Table 2, together with the experimental IPs deduced from the high-resolution UPS.18 It can be seen that the calculations predicted very close IPs for the relevant MOs except for the outermost one of trans and gauche conformers which could give rise to the same ionization band in the energy spectra. Taking into account a small population of gauche conformer, the experimental IPs values should be from a prominent contribution of trans conformer. Compared with the experiment, the OVGF calculations present more consistent IPs than the SAC-CI for the three outermost MOs. It is noted that no shakeup states accompanying the ionizations of the outervalence MOs have been found in this energy range according to the SAC-CI calculations, which indicates the independent particle picture is still a good approximation for these outervalence MOs. A. Binding Energy Spectra. The outer-valence binding energy spectra (BES) of CPA in the energy range of 7−19 eV have been measured simultaneously in the desired range of azimuthal angles and the summed BES over all of the azimuthal angles ϕ is shown in Figure 1b, together with the previous UPS spectrum in Figure 1a and the simulated spectra in Figure 1c. One can see from Figure 1b that five obvious ionization bands have been observed in BES, encompassing the contributions of eight overlapping ionization lines from the outer-valence MOs. It is preferable to resort to the theoretical simulations for analyzing and assigning the observed structures in the available 4486
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Figure 2. (a) XMP for the first band (p1) of CPA and the thermally averaged TMPs of the corresponding MO16 for trans (93.8%) and gauche (6.2%) conformers calculated using the B3LYP method with various basis sets. (b) Individual TMPs and orbital maps for trans and gauche calculated by B3LYP/aug-cc-pVTZ.
are the combination of the instrumental energy resolution and Franck−Condon widths of ionization bands deduced from the UPS spectrum.18 As shown in Figure 1b, the first band (p1) at 9.4 eV is well resolved and corresponds to the ionization of the highest occupied molecular orbital (HOMO; denoted as MO16:11a′/16a for discussing conveniently), in which the nonbonding lone pair of nitrogen predominates. The second band, including two unresolved p2 at 10.65 eV and p3 at 11.41 eV, are assigned to MO15:5a″/15a and MO14:10a′/14a. The third band seems to appear as two raised structures (p4, p5) at 12.86 and 13.69 eV corresponding to MO13:4a″/13a and MO12:9a′/12a, respectively. In the region of 15−18 eV, although there contain three transitions from MO11:8a′/11a, MO10:3a″/10a and MO9:9a′/9a, only two peaks (p6, p7) at 15.59 and 16.91 eV are observed by EMS, even by UPS, due to the close IPs of these orbitals. According to the OVGF calculations, the band at 15.59 eV should be contributed from the MO11:8a′/11a, and the one at 16.91 eV should be ascribed to the cooperative contribution of MO10:3a″/10a and MO9:9a′/9a. B. Experimental and Theoretical Electron Momentum Profiles. The experimental momentum profiles (XMPs) for each peak (p1−p7) are extracted by deconvoluting a series of angular correlated BES and plotting the area under the corresponding fitted peak as a function of momentum p (i.e., ϕ angle). The theoretical momentum profiles (TMPs) for the outer-valence MOs of trans and gauche conformers have been calculated using the B3LYP method with different-sized basis sets of 6-311++G, 6-311G**, 6-311++G**, cc-pVTZ, and augcc-pVTZ. For the sake of comparison with the XMPs, the TMPs have been folded with the instrumental momentum resolution using the Gaussian-weighted planar grid method.33,34
Figure 1. Binding energy spectra (BES) for the outer-valence orbitals of CPA obtained by (a) UPS, (b) EMS, and (c) the theoretical simulation based on the OVGF/6-311++G** calculations. In b, the dashed lines represent Gaussian peaks fitting the BES. The solid line is the summed fit. The vertical bars indicate the positions of Gaussian peaks. In c, the positions of vertical bars denote the calculated ionization energies. The dashed and dotted curves represent the simulated spectra for the individual trans and gauche, respectively, and the solid curve is the thermally averaged spectra for 93.8% trans and 6.2% gauche conformers.
EMS and UPS spectra. Figure 1c shows the simulated BES constructed by convoluting the calculated results, using the Gaussian function as the convolution function, the width of which is 1.0 eV (fwhm) from the EMS instrumental resolution. The positions of Gaussian functions, as the vertical bars in Figure 1c, are from the IPs calculated by OVGF/6-311++G**, and the intensities from the product of pole strengths and densities of states. Although taking into account the conformational effect on the IPs of MOs for trans and gauche conformers, one can see from Figure 1c the contribution from gauche conformer to the simulated spectra is not striking due to the small relative abundance (6.2% for gauche). In general, the simulated ionization spectra can reproduce the experimental BES well. In order to derive the experimental electron momentum profiles for the outer-valence MOs of CPA, the deconvolution of the BESs for each of a chosen set of angles ϕ has been performed by means of a least-squares-fit technique. Seven Gaussian functions p1−p7 are used to fit the BES as shown by dashed curves in Figure 1b. The positions of Gaussian peaks are referred to the IPs of the high-resolution UPS,18 and the widths 4487
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Figure 3. XMPs for the second band (p2, p3) of CPA and the thermally averaged TMPs of the corresponding molecular orbitals for trans (93.8%) and gauche (6.2%) conformers calculated using the B3LYP method with various basis sets: (a) summed XMP for p2 and p3 and the summed thermally averaged TMPs of MO15 and MO14; (b) XMP for p2 and the thermally averaged TMPs of MO15; (c) XMP for p3 and the thermally averaged TMPs of MO14; (d) individual TMPs and orbital maps of MO 15 for trans and gauche calculated by B3LYP/aug-cc-pVTZ; (e) individual TMPs and orbital maps of MO 14 for trans and gauche calculated by B3LYP/aug-cc-pVTZ.
Furthermore, the XMPs and the TMPs are placed on a common intensity scale using a uniform factor obtained by normalizing the summed XMPs for p1−p5 to the summed TMPs for MO16−MO12 because of their pole strengths close to unity, in which the relative abundances of 6.2% for gauche and 93.8% for trans deduced by MP2/aug-cc-pVTZ calculations are taken into account. Figures 2−5 present the XMPs and the corresponding thermally averaged TMPs for the outer-valence MOs of CPA, together with the individual TMPs and molecular orbital maps for trans and gauche conformers calculated by B3LYP/aug-cc-pVTZ. It is noted that the error bars of experimental data given in the figures represent the overall error of the statistical and deconvolution uncertainties. Figure 2a presents the XMPs for the first ionization band (p1) corresponding to the HOMO (MO16:11a′/16a) in which the lone pair of nitrogen (LPN) predominates. The XMPs shows a p-type character with a maximum at p ≈ 0.75 au, and an extra “turn up” intensity appeared at p < 0.3 au. The TMPs calculated by B3LYP method with various basis sets exhibit a similar shape except for the remarkable intensity at the lowmomentum region. Compared with the XMPs, B3LPY/ccpVTZ calculation gives better agreement with the experiment than others except for the intensity at the origin of the momentum, which suggests that additional diffuse functions in basis sets are not necessary for the HOMO of the CPA
molecule. In addition, the calculations using 6-311++G** and aug-cc-pVTZ almost give the identical TMPs, indicating the basis set approaches to saturation. It is noted that both the TMPs and the XMPs show an obvious intensity at the origin of the momentum. Similar phenomena were observed in the previous study on ethanol35 and ascribed to the hyperconjugative interactions between the oxygen lone pair and σ*C−C or σ*C−H orbitals according to the EMS measurement combined with the natural bond orbitals (NBO) analysis. The NBO analysis transforms the canonical delocalized MOs into localized orbitals, and the hyperconjugative interaction can be treated by E(2) = −nσF2ij/Δε, where Fij is the Fock matrix between the unperturbed occupied (σ) and unoccupied antibonding natural orbitals (σ*), nσ is the σ population, and Δε is the energy difference between σ and σ* orbitals. In this work, the NBO analyses were performed for two CPA conformers using MP2 and B3LYP methods with aug-cc-pVTZ under the NBO program.36 For the trans conformer the hyperconjugative interaction between LPN and σ*C−H (E(2) = 11.97 kcal/mol) is stronger than that of LPN and σ*C−C (E(2) = 1.84 kcal/mol), while for the gauche conformer the interaction between LPN and σ*C−C (E(2) = 13.24 kcal/mol) is stronger than that of LPN and σ*C−H (E(2) = 4.10 kcal/mol). Such interactions lead to an important charge transfer from the local LPN to the delocalized σ*C−H for trans, 4488
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Figure 4. XMPs for the third band (p4, p5) of CPA and the thermally averaged TMPs of the corresponding molecular orbitals for trans (93.8%) and gauche (6.2%) conformers calculated using B3LYP method with various basis sets: (a) summed XMP for p4 and p5 and the summed thermally averaged TMPs of MO13 and MO12; (b) XMP for p4 and the thermally averaged TMPs of MO13; (c) XMP for p5 and the thermally averaged TMPs of MO12; (d) individual TMPs and orbital maps of MO 13 for trans and gauche calculated by B3LYP/aug-cc-pVTZ; (e) individual TMPs and orbital maps of MO 12 for trans and gauche calculated by B3LYP/aug-cc-pVTZ.
and from LPN to σ*C−C for gauche. Consequently, the HOMOs of trans and gauche conformers are composed of the different spatial localized NBOs: ψ(trans) = 0.829LPN + 0.304σC1−H4 + 0.292σC2−C3 and ψ(gauche) = 0.780LPN + 0.458σC1−C3. The introduction of bonding components of the HOMO brings out an obvious intensity of the TMPs and XMPs at the lowmomentum region. Figure 3 compares the XMPs for the second band (p2 and p3) with the TMPs for MO15 (5a″/15a) and MO14 (10a′/ 14a). The MO maps in Figure 3d reveal that MO15 is dominated by a pair of C−C bonds, like a π bonding. As a result, the individual TMPs for trans 5a″ orbital and gauche 15a orbital both show p-type character with a maximum at p ≈ 0.9 au. As shown in Figure 3b, all of the calculations with different basis sets give almost the same TMPs and can reproduce the XMPs well except at the low-momentum region. With regard to MO14, the trans 10a′ orbital is mainly composed of cyclic C−C bonds and a C−N bond, and its TMPs displays an sp-type curve while the TMPs for gauche 15a orbital shows a p-type character which is contributed primarily from a pair of C−C bonds and LPN. Since the gauche conformer has a very small proportion, the thermally averaged TMPs in Figure 3c give a main sp-type curve and well agree with the XMPs except at the low-momentum region. With respect to the discrepancies between the XMPs and the TMPs in Figure 3b,c, the summed XMPs and TMPs for p2 and p3 are presented in Figure 3a and
good agreement has been achieved, indicating that such discrepancies should originate from the deconvolution uncertainties. Figure 4 offers the XMPs for the third band (p4 and p5), together with the TMPs for MO13 (4a″/13a) and MO12 (9a′/ 12a). The MO maps in Figure 4d show that MO13 is dominated by two pairs of C−H bonds, pseudo-π bonding. Consequently, the XMPs and TMPs in Figure 4b both show a p -type character with a maximum at p ≈ 0.8 au and are well in accordance with each other, while, for MO12, composed of the important C−H bonds and C−N bond, the TMPs displays an sp-type curve, and all the TMPs in Figure 4c well agree with the XMPs. For the summed XMPs and TMPs for p4 and p5, as shown in Figure 4a, the good agreement has been achieved naturally. For the last two bands, as mentioned above, the band (p6) at 15.59 eV corresponds to the MO11, and the one (p7) at 16.91 eV is from the cooperative contribution of MO10 and MO9. The MO11 maps in Figure 5d indicate the 8a′ orbital for trans and the 11a for gauche have complex components of C−N, C− C, C−H, and N−H bonds. As shown in Figure 5b, the TMPs for the MO11 present an sp-type character and do not agree with the XMPs for p6. For the MO10, the orbital maps in Figure 5e show the trans 3a″ orbital has a πN−H bonding character and the component of gauche 10a orbital is very complex. As a result, the different orbital components make the 4489
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Figure 5. XMPs for the last two bands (p6, p7) of CPA and the thermally averaged TMPs of the corresponding molecular orbitals for trans (93.8%) and gauche (6.2%) conformers calculated using the B3LYP method with various basis sets: (a) summed XMP for p6 and p7 and the summed thermally averaged TMPs of MO11, MO10, and MO9; (b) XMP for p6 and the thermally averaged TMPs of MO11; (c) XMP for p7 and the summed thermally averaged TMPs of MO10 and MO9; (d) individual TMPs and orbital maps of MO11 for trans and gauche calculated by B3LYP/ aug-cc-pVTZ; (e) individual TMPs and orbital maps of MO10 for trans and gauche calculated by B3LYP/aug-cc-pVTZ; (f) individual TMPs and orbital maps of MO9 for trans and gauche calculated by B3LYP/aug-cc-pVTZ.
TMPs of 3a″ orbital showing a p-type character, while the TMPs of 10a orbital having an sp-type feature. The MO9 maps in Figure 5f indicate that the trans 7a′ orbital and gauche 9a orbital have similar components of C−N, C−H, and N−H bonds, and their TMPs present sp-type character. As shown in Figure 5c, the summed TMPs for MO10 and MO9 are in good agreement with the XMPs for p7. Figure 5a compares the summed XMPs for p6 and p7 with the summed TMPs for the relevant MOs, and one can see that the XMPs put up a high intensity relative to the TMPs at the momentum from 0.4 to 1.2 au. It seems that an extra p-type TMP will be expected to complement the XMPs. We first check one possible cause, the contamination of shakeup states accompanying the ionization of MOs as observed in previous studies.37,38 But according to our SAC-CI calculations, no satellite states appear in this energy region, which indicates this possibility could be excluded. Another possible cause is ultrafast nuclear dynamical processes upon the ionization, such as the molecular geometry distortion (or relaxation) and vibronic coupling interactions in a molecule, which were invoked in order to explain the observed high intensity in recent EMS studies.39,40
It is worthy to note that the cyclic structure of CPA spontaneously undergoes ring opening at the instant of ionization, as reported in the literature.41 Such a process of structural change could be ultrafast, similar to that of cyclopropane molecule reported previously,39 to some extent, comparable to the interaction time of electron impact ionization. We therefore resort to the picture presented in the literature,39 and attempt to qualitatively explain the observed discrepancies in CPA on the basis of the calculations using geometries of the final ion. All attempts to optimize the cyclic structure of ionic CPA failed and led to the open structure. So the geometry of ring-opening ionic CPA, which corresponds to the local minimum point on the potential surface, is employed to calculate the TMPs for neutral nonequilibrium systems according to eq 5 in which ionic Q′ is used instead of neutral Q0, and the results are presented in Figure 6. Compared with the TMPs in Figures 2−5, one can see that the shape of TMPs for MO11 displays a remarkable change as shown in Figure 6f and offers an expected high intensity at the momentum from 0.4 au to 1.2 au, which could qualitatively explain the discrepancy that appeared in Figure 5, to some extent. In addition, with a view to the shape change of 4490
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Figure 6. TMPs of the outer-valence orbitals, (a) MO16, (b) MO15, (c) MO14, (d) MO13, (e) MO12, (f) MO11, (h) MO10, and (h) MO9, calculated using B3LYP/aug-cc-pVTZ within the geometry of the ring-opening ionic structure optimized by MP2/aug-cc-pVTZ.
molecular geometry at the instant of ionization. The stringent calculations involving the original Dyson orbitals and molecular dynamical simulations are desirable. In addition, although taking into account the conformational effect, the contribution of the gauche conformer with small population could not be determined unambiguously from the experiment due to the limit of EMS accuracies (∼10%) in deducing the conformer weight as suggested in previous works.42,43 In the future, the variable-temperature EMS experiments on gaseous CPA with high sensitivity and high energy resolution will be carried out to explore the conformational effect on the shape, topology, and spread of molecular orbitals.
the TMPs for the HOMO in Figure 6a, the difference of the TMPs and XMPs in Figure 2a may be also ascribed to the change of molecular geometry at the instant of ionization. The stringent theoretical descriptions involve the calculation of the overlap integral in eq 4 between neutral and ionic wave functions, as well as molecular dynamical simulations are desirable to further elucidate such phenomena, but this is beyond our ability at present.
V. SUMMARY In this work, we report the first EMS measurement on the outer-valence binding energy spectra and electron momentum profiles for gaseous CPA. The experimental results are interpreted on the basis of quantitative calculations of ionization energies and the relevant Kohn−Sham molecular orbitals at benchmark theoretical levels using the OVGF, SACCI, and B3LYP methods. In general, the experimental and theoretical results are in accordance with each other. But some discrepancies still remained. Such questions could be explained qualitatively in view of the picture about the change of
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AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Notes
The authors declare no competing financial interest. 4491
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(19) (a) McCarthy, I. E.; Weigold, E. Electron Momentum Spectroscopy of Atoms and Molecules. Rep. Prog. Phys. 1991, 54, 789−879. (b) Brion, C. E. Looking at Orbitals in the Laboratory: The Experimental Investigation of Molecular Wavefunctions and Binding Energies by Electron Momentum Spectroscopy. Int. J. Quantum Chem. 1986, 29, 1397−1428. (c) Coplan, M. A.; Moore, J. H.; Doering, J. P. (e, 2e) Spectroscopy. Rev. Mod. Phys. 1994, 66, 985−1014. (20) Levin, V. G.; Neudatchin, V. G.; Pavlitchenkov, A. V.; Smirnov, Y. F. On the Display of Basic Properties of the Molecular Electronic Wavefunctions in the (e, 2e) Quasielastic Knockout Experiments. J. Chem. Phys. 1975, 63, 1541−1546. (21) Mathers, C.; Gover, B.; Ying, J.; Zhu, H.; Leung, K. Experimental Momentum-Space Chemistry of Isobutene: Isomeric Effects on Orbital-Specific Electron Momentum Distributions in Isobutene and Its Cis and Trans Isomers. J. Am. Chem. Soc. 1994, 116, 7250−7257. (22) (a) Zheng, Y.; Neville, J. J.; Brion, C. E. Imaging the Electron Density in the Highest Occupied Molecular Orbital of Glycine. Science 1995, 270, 786−788. (b) Neville, J. J.; Zheng, Y.; Brion, C. E. Glycine Valence Orbital Electron Densities: Comparison of Electron Momentum Spectroscopy Experiments with Hartree−Fock and Density Functional Theories. J. Am. Chem. Soc. 1996, 118, 10533− 10544. (23) (a) Watanabe, N.; Chen, X. J.; Takahashi, M. Interference Effects on (e, 2e) Electron Momentum Profiles of CF4. Phys. Rev. Lett. 2012, 108, 173201. (b) Takahashi, M.; Ogino, R.; Udagawa, Y. Outer Valence Electronic Structure of Pyrrole Studied by Electron Momentum Spectroscopy. Chem. Phys. Lett. 1998, 288, 821−827. (24) Yang, T. C.; Su, G. L.; Ning, C. G.; Deng, J. K.; Wang, F.; Zhang, S. f.; Ren, X. G.; Huang, Y. R. New Diagnostic of the Most Populated Conformer of Tetrahydrofuran in the Gas Phase. J. Phys. Chem. A 2007, 111, 4927−4933. (25) (a) Wang, F.; Downton, M. Inner Valence Shell Bonding Mechanism of N-Butane Studied Using Orbital Momentum Distributions of Its Conformational Isomers. J. Phys. B: At., Mol. Opt. Phys. 2004, 37, 557−569. (b) Wang, F. Assessment of Quantum Mechanical Models Based on Resolved Orbital Momentum Distributions of N-Butane in the Outer Valence Shell. J. Phys. Chem. A 2003, 107, 10199−10207. (26) (a) Deleuze, M. S.; Pang, W. N.; Salam, A.; Shang, R. C. Probing Molecular Conformations with Electron Momentum Spectroscopy: The Case of n-Butane. J. Am. Chem. Soc. 2001, 123, 4049−4061. (b) Deleuze, M.; Knippenberg, S. Study of the Molecular Structure, Ionization Spectrum, and Electronic Wave Function of 1, 3-Butadiene Using Electron Momentum Spectroscopy and Benchmark Dyson Orbital Theories. J. Chem. Phys. 2006, 125, 104309. (27) (a) Zhang, Z.; Shan, X.; Wang, T.; Wang, E. L.; Chen, X. J. Observation of the Interference Effect in Vibrationally Resolved Electron Momentum Spectroscopy of H2. Phys. Rev. Lett. 2014, 112, 023204. (b) Yan, M.; Shan, X.; Wu, F.; Xue, X. X.; Wang, K. D.; Xu, K. Z.; Chen, X. J. Electron Momentum Spectroscopy Study on Valence Electronic Structures of Ethylamine. J. Phys. Chem. A 2008, 113, 507− 512. (c) Chen, X. J.; Zhou, L. X.; Zhang, X. H.; Yin, X. F.; Xu, C. K.; Shan, X.; Wei, Z.; Xu, K. Z. Electron Momentum Spectroscopy of CF2Cl2: Experimental and Theoretical Momentum Profiles for Outer Valence Orbitals. J. Chem. Phys. 2004, 120, 7933−7938. (28) (a) Cederbaum, L. S. One-Body Green’s Function for Atoms and Molecules: Theory and Application. J. Phys. B: At. Mol. Phys. 1975, 8, 290−303. (b) Von Niessen, W.; Schirmer, J.; Cederbaum, L. S. Computational Methods for the One-Particle Green’s Function. Comput. Phys. Rep. 1984, 1, 57−125. (c) Zakrzewski, V. G.; Ortiz, J. V.; Nichols, J. A.; Heryadi, D.; Yeager, D. L.; Golab, J. T. Comparison of Perturbative and Multiconfigurational Electron Propagator Methods. Int. J. Quantum Chem. 1996, 60, 29−36. (29) (a) Nakatsuji, H. Multireference Cluster Expansion Theory: MR-SAC Theory. J. Chem. Phys. 1985, 83, 713−722; Exponentially Generated Wave Functions. J. Chem. Phys. 1985, 83, 5743−5748; Description of Two- and Many-Electron Processes by the SAC-CI Method. Chem. Phys. Lett. 1991, 177, 331−337; Exponentially
ACKNOWLEDGMENTS This work was partially supported by the National Basic Research Program of China (Grant No. 2010CB923301) and the National Natural Science Foundation of China (Grant Nos. 11327404, 20973160, and 10904136). We also gratefully acknowledge Professor C. E. Brion from the University of British Columbia (UBC) in Canada for giving us the HEMS programs.
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REFERENCES
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Experimental and Theoretical Investigation on the Outer Valence Electronic Structure of Cyclopropylamine by (e, 2e) Electron Momentum Spectroscopy Yufeng Shi, Xu Shan,* Enliang Wang, Hongjiang Yang, Wei Zhang, and Xiangjun Chen Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China ABSTRACT: The binding energy spectra and electron momentum distributions for the outer-valence molecular orbitals of gaseous cyclopropylamine (CPA) have been measured by (e, 2e) electron momentum spectrometer employing noncoplanar asymmetric geometry at the impact energy of 2500 eV. The experimental results are interpreted on the basis of the quantitative calculations of the ionization energies and the relevant molecular orbitals at benchmark theoretical levels using the outer-valence Green’s function method, the symmetry-adapted cluster configuration interaction method, and the density functional theory with B3LYP hybrid functional. The total energies of the trans and gauche conformers of CPA are also calculated by the second-order Møller−Plesset perturbation theory with large basis sets and the derived enthalpy differences (2.02−2.12 kcal/mol) are consistent with the previous experimental data (2.19 kcal/mol). The theoretical binding energy spectra and electron momentum distributions, in which the relative abundances of trans and gauche are taken into account, are generally in accordance with the experimental results except for the ionization band from the trans 8a′ and gauche 11a orbitals. The discrepancy is explained qualitatively in view of the picture of molecular geometry change at the instant of ionization. basis sets.11−17 Pelissier et al.11 and Mochel et al.12 calculated the torsional potentials of NH2 relative to the carbon ring and predicted that two stable conformers exist in CPA and the more stable is trans conformer, while, in the subsequent calculations,4,13−16 the molecular geometry of the preference conformer (trans) was concentrated on. Recently, Hyla-Kryspin et al.17 calculated the torsional potential at a number of torsional angles and the geometric parameters of trans and gauche conformers using the second-order Møller−Plesset perturbation (MP2) and SCS-MP2 with the TZVPP basis set. As for the energy difference between trans and gauche conformers, the early calculations4,10−12 at the CNDO/2, SCF, and MP2 theoretical levels with small or moderate basis sets determined the values to be somewhat large, from 1539 to 890 cm−1 (4.4−2.54 kcal/mol), which resulted in only 1−3% population of the gauche conformer. The recent calculations17 at the MP2 and SCS-MP2 levels with a large basis set (TZVPP) presented the energy difference of 2.21 and 2.17 kcal/mol suggesting close to 5% gauche population, which was in line with the data from the IR spectra work.7 Relative to the extensive research of molecular geometries and energetic properties, on the other hand, studies of the electronic structure of CPA are very scarce. There is only a report on the ionization spectra measured by He I ultraviolet
I. INTRODUCTION Cyclopropylamine (CPA) is the chemically most reactive cycloalkylamine because of the highly strained bonding in the three-membered ring, and therefore, it is used as an intermediate for agrochemical active substances. There are many experimental and theoretical works devoted to the molecular geometry and energetic properties of CPA. The geometric parameters of CPA were determined by gas-phase microwave spectra (MW)1−4 and electron diffraction (ED),5 as well as the combined analysis of ED and MW spectra.5 The infrared (IR) and Raman spectra of the gaseous, liquid, and solid CPA were recorded by Kalasinsky et al.,6 and an enthalpy difference between the more stable trans and high-energy gauche conformers coexisted in gaseous CPA was derived to be 592 cm−1 (∼1.69 kcal/mol) indicating a ∼10% relative population of gauche conformer at room temperature. Compton et al.7 also observed the IR spectra of gaseous CPA and deduced the enthalpy difference of 766 cm−1 (∼2.19 kcal/ mol) between trans and gauche conformers, which indicated the relative abundance of the gauche conformer is about 5%. Subsequently, the IR spectra work of Hamada et al.8 suggested the population of the gauche conformer should not exceed 5%. However, the IR spectra obtained by Diallo et al.9 at a series of temperatures confirmed only the trans conformer present in CPA, as suggested by the previous MW1−3 and the overtone spectra.10 On the theoretical side, calculations were also performed to describe the molecular geometry and energetic properties of CPA using various methods with different sizes of © 2014 American Chemical Society
Received: March 31, 2014 Revised: June 3, 2014 Published: June 3, 2014 4484
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photoelectron spectroscopy (UPS),18 in which the observed bands were assigned on the basis of calculations at the SCF/431G level. Therefore, it is necessary to carry out the detailed studies on the electronic structure of CPA both experimentally and theoretically. Electron momentum spectroscopy (EMS), also known as binary (e, 2e) spectroscopy, has been proved as a powerful technique for exploring the electronic structures of atoms and molecules due to its unique ability to directly obtain not only the binding energy spectra but also the spherically averaged electron density distributions in momentum space for individual orbitals.19−27 To our best knowledge, no EMS study of CPA has been reported so far. In this work, we report the first EMS measurement on the binding energy spectra and electron momentum distributions for the outer-valence molecular orbitals of gaseous CPA. The experimental results are interpreted on the grounds of quantitative calculations of the ionization energies and the relevant molecular orbitals at benchmark theoretical levels using the outer-valence Green’s function (OVGF),28 the symmetry-adapted cluster configuration interaction (SAC-CI),29 and the density functional theory (DFT) with B3LYP hybrid functional.30 The total energies of trans and gauche conformers of CPA are also calculated by the MP2 method with larger basis sets, and the Boltzmann-weighted thermostatistical abundances of 93.8% for trans and 6.2% for gauche obtained by MP2/aug-cc-pVTZ are taken into account in the comparison of the theoretical and experimental binding energy spectra and electron momentum distributions.
experiment, the energy and momentum resolution of the present EMS spectrometer are determined by measuring Ar 3p ionization to be ∼1.0 eV [full width at half-maximum (fwhm)] and ∼0.1 au, respectively. On the theoretical side, within the binary encounter approximation and the plane wave impulse approximation (PWIA), as well as Born−Oppenheimer approximation and disregarding rotational functions, the triple differential crosssection (σEMS) of (e, 2e) reaction in EMS turns out to be proportional to the squared form factor Fif(p), which is given by19,20 Fif (p) =
(3)
where Xv(Q) and Xv′(Q) are vibrational wave functions for initial and final states, S(f) q (Q) is the overlap integral of the wave functions for the final ion and molecular residue left after the knockout of an electron from one-electron molecular orbital φq(p,Q) in momentum space, and Q is the set of coordinates determining the displacements from equilibrium of N atomic nuclei of the molecule. Equation 3 can further be reduced to20 Fif (p) = gvv ′Sq(f )(Q̅ ) φq(p, Q̅ )
(4)
where = ∫ dQ X*v′ (Q)Xv(Q) is the usual Franck−Condon factor and Q̅ corresponds to some mean values of nuclear coordinates intermediate between the equilibrium coordinates of nuclei Q0 and Q′ in the initial molecule and in the final molecular ion, respectively. Estimations made by Levin et al.20 for light diatomic molecules showed that the value S(q f)(Q) φq(p,Q) slowly varies in the range of Q values between Q0 and Q′0, so the Q̅ value in the calculation for EMS studies is usually chosen as Q0 in the initial molecule. Moreover, since the vibrational states are not resolved by the present EMS spectrometer, σEMS can be expressed as19,20 gvv′
II. EXPERIMENTAL AND THEORETICAL BACKGROUND EMS is based on a kinematically complete (e, 2e) collision experiment in which an electron from target atoms or molecules is cleanly knocked out by a high-energy incident electron and the residual ion acts as a spectrator. In the present EMS spectrometer,31 asymmetric noncoplanar kinematics is employed. In brief, the incident electron beam generated from an electron gun is accelerated by a lens system to the desired energy of 2500 eV plus the binding energy and transferred to the reaction region where the incident electron impacts with the gas-phase target molecule injected by a nozzle. The scattered electron outgoing along polar angle θa = 14° passes through the fast electron analyzer and is detected by a twodimensional position sensitive detector (PSD) over a large range of both energies and azimuthal angles of interest. The ionized electron outgoing along polar angle θb = 76° passes through the slow electron analyzer and is detected by onedimensional PSD. In such experimental condition, considering conservation of energy and momentum, the binding energy ε and magnitude of momentum p of the target electron can be expressed by ε = E0 − Ea − E b (1)
σEMS ∝ |Sq(f )(Q 0)|2
∫ |φq(p, Q 0)|2 dΩ
(5)
The integral in eq 5 is known as the spherically averaged oneelectron momentum distribution or electron momentum profile. |S(q f)(Q0)|2 represents the pole strength and φq(p,Q0) is the Dyson orbital which can be approximated by the oneelectron canonical Hartree−Fock (HF)19 or Kohn−Sham wave function30 in momentum space for the qth orbital from which the electron is ionized.
III. COMPUTATIONAL DETAILS As previously mentioned, the potential energy profiles for the internal rotation of NH2 relative to the cyclopropyl ring were calculated using CNDO/211 and HF12 with small basis sets, MP2 with 6-31G* moderate basis set,10 and MP2 and SCSMP2 with large basis set (TZVPP).17 Three minimum points were found: the one at 0° angle corresponds to the trans conformer, and the other two at ±135° are two equivalent gauche conformers. As for the enthalpy difference between trans and gauche conformers, the calculation using a large basis set17 offered more consistent values (2.02 kcal/mol) with the experimental data (1.69, 2.19 kcal/mol)6,7 than those (4.4− 2.54 kcal/mol) from the calculations with small and moderate basis sets,10−12 indicating the importance of basis set sizes. In the present work, the torsional potentials and geometric parameters are recalculated employing larger basis sets of augcc-pVTZ, cc-pVTZ, and 6-311++G** at the MP2 and B3LYP
p = {p0 2 + pa 2 + pb 2 − 2p0 pa cos θa − 2p0 pb cos θ b + 2pa pb [cos θa cos θ b − sin θa sin θ b cos ϕ]}1/2
∫ dQ Xv*′(Q ) Xv(Q ) Sq(f )(Q ) φq(p, Q )
(2)
where (E0, p0), (Ea, pa) and (Eb, pb) are the energies and momenta of the projectile, scattered, and ejected electrons, respectively. And ϕ is the relative azimuthal angle between the two outgoing electrons. Therefore, by detecting two outgoing electrons in coincidence, the binding energy and momentum of the target electron can be determined. Before normal 4485
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Table 1. Enthalpy Difference (kcal/mol) for Trans and Gauche Conformers of Gaseous CPA at Room Temperature MP2/a ΔH gauche, % a
B3LYP/a
aug-cc-pVTZ
cc-pVTZ
6-311++G**
aug-cc-pVTZ
6-311++G**
SCS-MP2/TZVPP17
IR7
IR6
2.02 6.2
2.08 5.7
2.12 5.3
1.87 7.8
2.03 6.1
2.02 6.2
2.19 4.7
1.69 10
This work.
Table 2. Experimental and Theoretical Ionization Energies for the Outer-Valence Orbitals of CPA SAC−CIa
a
OVGFa
MO no.
trans
gauche
trans
gauche
UPS18
EMSa
MO16 MO15 MO14 MO13 MO12 MO11 MO10 MO9
11a′ 9.02 [0.83] 5a″ 10.20 [0.83] 10a′ 10.72 [0.82] 4a″ 12.89 [0.83] 9a′ 13.59 [0.82] 8a′ 15.47 [0.82] 3a″ 16.38 [0.82] 7a′ 16.92 [0.81]
16a 8.46 [0.83] 15a 10.32 [0.84] 14a 11.44 [0.82] 13a 12.89 [0.84] 12a 13.18 [0.83] 11a 15.50 [0.83] 10a 15.97 [0.83] 9a 16.96 [0.82]
11a′ 9.50 [0.92] 5a″ 10.41 [0.91] 10a′ 11.03 [0.91] 4a″ 13.06 [0.92] 9a′ 13.90 [0.91] 8a′ 15.51 [0.90] 3a″ 16.46 [0.92] 7a′ 17.06 [0.90]
16a 9.01 [0.91] 15a 10.67 [0.91] 14a 11.89 [0.91] 13a 13.24 [0.92] 12a 13.57 [0.91] 11a 15.72 [0.91] 10a 16.15 [0.90] 9a 17.17 [0.90]
11a′ 9.41 5a″ 10.65 10a′ 11.41 4a″ 12.86 9a′ 13.69 8a′ 15.59 7a′ 16.91 3a″
11a′/16a 9.41 5a″/15a 10.65 10a′/14a 11.41 4a″/13a 12.86 9a′/12a 13.69 8a′/11a 15.59 3a″/10a 16.91 7a′/9a 16.91
This work. Pole strengths are listed in square brackets.
IV. RESULTS AND DISCUSSION CPA (C3H5NH2) contains 32 electrons and has 8 outer-valence MOs. Both HF and B3LYP calculations give the ground-state electronic configurations of the trans conformer (CS) as
theoretical levels. The calculated enthalpy differences of trans and gauche conformers, as listed in Table 1, are in agreement with the previous experimental data 6,7 and the recent theoretical results.17 The optimized geometric parameters are also consistent with the previous MW and ED data,1−5 as well as the calculations.17 The theoretical momentum profiles for eight outer-valence molecular orbitals (MOs) of trans and gauche conformers have been calculated, respectively, according to eq 5. Since the DFT method with B3LYP hybrid functional includes the electron exchange and correlation interactions,30 it has been proved to be much better than the HF method in interpreting the experimental momentum profiles in EMS studies.19−27 Therefore, in the present calculations, only the DFT-B3LYP method with different-sized basis sets of 6-311++G, 6-311G**, 6-311+ +G**, cc-pVTZ, and aug-cc-pVTZ are used to calculate the position space Kohn−Sham wave functions of the relevant MOs on the basis of equilibrium geometries of neutral CPA optimized by MP2/aug-cc-pVTZ. The ionization energies for the outer-valence MOs of trans and gauche conformers have been calculated using the OVGF and SAC-CI general-R methods with the 6-311++G** basis set. Note that the OVGF28 and SAC-CI29 methods both include the electron correlation effect and can offer more accurate ionization energies than the HF method. The extra pole strengths can help to know the presence of shakeup states accompanying the ionizations of MOs. In the present SAC-CI calculations, the active space consists of 16 occupied MOs and 121 unoccupied MOs, and only the orbitals of C 1s and N 1s are frozen as cores. The level-three accuracy has been adopted, and R operators are included up to triplicate for taking into account the possible electron correlation effect in the valence range. 250 ionized states are calculated for trans and gauche conformers, respectively, and the ionization energies are up to 26 eV. All of the present calculations are carried out within the Gaussian 03 suite of programs.32
and gauche conformer (C1) as
The vertical ionization potentials (IPs) and pole strengths for eight outer-valence MOs of trans and gauche conformers have been calculated using the OVGF and SAC-CI general-R methods with 6-311++G** basis set. The calculated results are listed in Table 2, together with the experimental IPs deduced from the high-resolution UPS.18 It can be seen that the calculations predicted very close IPs for the relevant MOs except for the outermost one of trans and gauche conformers which could give rise to the same ionization band in the energy spectra. Taking into account a small population of gauche conformer, the experimental IPs values should be from a prominent contribution of trans conformer. Compared with the experiment, the OVGF calculations present more consistent IPs than the SAC-CI for the three outermost MOs. It is noted that no shakeup states accompanying the ionizations of the outervalence MOs have been found in this energy range according to the SAC-CI calculations, which indicates the independent particle picture is still a good approximation for these outervalence MOs. A. Binding Energy Spectra. The outer-valence binding energy spectra (BES) of CPA in the energy range of 7−19 eV have been measured simultaneously in the desired range of azimuthal angles and the summed BES over all of the azimuthal angles ϕ is shown in Figure 1b, together with the previous UPS spectrum in Figure 1a and the simulated spectra in Figure 1c. One can see from Figure 1b that five obvious ionization bands have been observed in BES, encompassing the contributions of eight overlapping ionization lines from the outer-valence MOs. It is preferable to resort to the theoretical simulations for analyzing and assigning the observed structures in the available 4486
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Figure 2. (a) XMP for the first band (p1) of CPA and the thermally averaged TMPs of the corresponding MO16 for trans (93.8%) and gauche (6.2%) conformers calculated using the B3LYP method with various basis sets. (b) Individual TMPs and orbital maps for trans and gauche calculated by B3LYP/aug-cc-pVTZ.
are the combination of the instrumental energy resolution and Franck−Condon widths of ionization bands deduced from the UPS spectrum.18 As shown in Figure 1b, the first band (p1) at 9.4 eV is well resolved and corresponds to the ionization of the highest occupied molecular orbital (HOMO; denoted as MO16:11a′/16a for discussing conveniently), in which the nonbonding lone pair of nitrogen predominates. The second band, including two unresolved p2 at 10.65 eV and p3 at 11.41 eV, are assigned to MO15:5a″/15a and MO14:10a′/14a. The third band seems to appear as two raised structures (p4, p5) at 12.86 and 13.69 eV corresponding to MO13:4a″/13a and MO12:9a′/12a, respectively. In the region of 15−18 eV, although there contain three transitions from MO11:8a′/11a, MO10:3a″/10a and MO9:9a′/9a, only two peaks (p6, p7) at 15.59 and 16.91 eV are observed by EMS, even by UPS, due to the close IPs of these orbitals. According to the OVGF calculations, the band at 15.59 eV should be contributed from the MO11:8a′/11a, and the one at 16.91 eV should be ascribed to the cooperative contribution of MO10:3a″/10a and MO9:9a′/9a. B. Experimental and Theoretical Electron Momentum Profiles. The experimental momentum profiles (XMPs) for each peak (p1−p7) are extracted by deconvoluting a series of angular correlated BES and plotting the area under the corresponding fitted peak as a function of momentum p (i.e., ϕ angle). The theoretical momentum profiles (TMPs) for the outer-valence MOs of trans and gauche conformers have been calculated using the B3LYP method with different-sized basis sets of 6-311++G, 6-311G**, 6-311++G**, cc-pVTZ, and augcc-pVTZ. For the sake of comparison with the XMPs, the TMPs have been folded with the instrumental momentum resolution using the Gaussian-weighted planar grid method.33,34
Figure 1. Binding energy spectra (BES) for the outer-valence orbitals of CPA obtained by (a) UPS, (b) EMS, and (c) the theoretical simulation based on the OVGF/6-311++G** calculations. In b, the dashed lines represent Gaussian peaks fitting the BES. The solid line is the summed fit. The vertical bars indicate the positions of Gaussian peaks. In c, the positions of vertical bars denote the calculated ionization energies. The dashed and dotted curves represent the simulated spectra for the individual trans and gauche, respectively, and the solid curve is the thermally averaged spectra for 93.8% trans and 6.2% gauche conformers.
EMS and UPS spectra. Figure 1c shows the simulated BES constructed by convoluting the calculated results, using the Gaussian function as the convolution function, the width of which is 1.0 eV (fwhm) from the EMS instrumental resolution. The positions of Gaussian functions, as the vertical bars in Figure 1c, are from the IPs calculated by OVGF/6-311++G**, and the intensities from the product of pole strengths and densities of states. Although taking into account the conformational effect on the IPs of MOs for trans and gauche conformers, one can see from Figure 1c the contribution from gauche conformer to the simulated spectra is not striking due to the small relative abundance (6.2% for gauche). In general, the simulated ionization spectra can reproduce the experimental BES well. In order to derive the experimental electron momentum profiles for the outer-valence MOs of CPA, the deconvolution of the BESs for each of a chosen set of angles ϕ has been performed by means of a least-squares-fit technique. Seven Gaussian functions p1−p7 are used to fit the BES as shown by dashed curves in Figure 1b. The positions of Gaussian peaks are referred to the IPs of the high-resolution UPS,18 and the widths 4487
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Figure 3. XMPs for the second band (p2, p3) of CPA and the thermally averaged TMPs of the corresponding molecular orbitals for trans (93.8%) and gauche (6.2%) conformers calculated using the B3LYP method with various basis sets: (a) summed XMP for p2 and p3 and the summed thermally averaged TMPs of MO15 and MO14; (b) XMP for p2 and the thermally averaged TMPs of MO15; (c) XMP for p3 and the thermally averaged TMPs of MO14; (d) individual TMPs and orbital maps of MO 15 for trans and gauche calculated by B3LYP/aug-cc-pVTZ; (e) individual TMPs and orbital maps of MO 14 for trans and gauche calculated by B3LYP/aug-cc-pVTZ.
Furthermore, the XMPs and the TMPs are placed on a common intensity scale using a uniform factor obtained by normalizing the summed XMPs for p1−p5 to the summed TMPs for MO16−MO12 because of their pole strengths close to unity, in which the relative abundances of 6.2% for gauche and 93.8% for trans deduced by MP2/aug-cc-pVTZ calculations are taken into account. Figures 2−5 present the XMPs and the corresponding thermally averaged TMPs for the outer-valence MOs of CPA, together with the individual TMPs and molecular orbital maps for trans and gauche conformers calculated by B3LYP/aug-cc-pVTZ. It is noted that the error bars of experimental data given in the figures represent the overall error of the statistical and deconvolution uncertainties. Figure 2a presents the XMPs for the first ionization band (p1) corresponding to the HOMO (MO16:11a′/16a) in which the lone pair of nitrogen (LPN) predominates. The XMPs shows a p-type character with a maximum at p ≈ 0.75 au, and an extra “turn up” intensity appeared at p < 0.3 au. The TMPs calculated by B3LYP method with various basis sets exhibit a similar shape except for the remarkable intensity at the lowmomentum region. Compared with the XMPs, B3LPY/ccpVTZ calculation gives better agreement with the experiment than others except for the intensity at the origin of the momentum, which suggests that additional diffuse functions in basis sets are not necessary for the HOMO of the CPA
molecule. In addition, the calculations using 6-311++G** and aug-cc-pVTZ almost give the identical TMPs, indicating the basis set approaches to saturation. It is noted that both the TMPs and the XMPs show an obvious intensity at the origin of the momentum. Similar phenomena were observed in the previous study on ethanol35 and ascribed to the hyperconjugative interactions between the oxygen lone pair and σ*C−C or σ*C−H orbitals according to the EMS measurement combined with the natural bond orbitals (NBO) analysis. The NBO analysis transforms the canonical delocalized MOs into localized orbitals, and the hyperconjugative interaction can be treated by E(2) = −nσF2ij/Δε, where Fij is the Fock matrix between the unperturbed occupied (σ) and unoccupied antibonding natural orbitals (σ*), nσ is the σ population, and Δε is the energy difference between σ and σ* orbitals. In this work, the NBO analyses were performed for two CPA conformers using MP2 and B3LYP methods with aug-cc-pVTZ under the NBO program.36 For the trans conformer the hyperconjugative interaction between LPN and σ*C−H (E(2) = 11.97 kcal/mol) is stronger than that of LPN and σ*C−C (E(2) = 1.84 kcal/mol), while for the gauche conformer the interaction between LPN and σ*C−C (E(2) = 13.24 kcal/mol) is stronger than that of LPN and σ*C−H (E(2) = 4.10 kcal/mol). Such interactions lead to an important charge transfer from the local LPN to the delocalized σ*C−H for trans, 4488
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Figure 4. XMPs for the third band (p4, p5) of CPA and the thermally averaged TMPs of the corresponding molecular orbitals for trans (93.8%) and gauche (6.2%) conformers calculated using B3LYP method with various basis sets: (a) summed XMP for p4 and p5 and the summed thermally averaged TMPs of MO13 and MO12; (b) XMP for p4 and the thermally averaged TMPs of MO13; (c) XMP for p5 and the thermally averaged TMPs of MO12; (d) individual TMPs and orbital maps of MO 13 for trans and gauche calculated by B3LYP/aug-cc-pVTZ; (e) individual TMPs and orbital maps of MO 12 for trans and gauche calculated by B3LYP/aug-cc-pVTZ.
and from LPN to σ*C−C for gauche. Consequently, the HOMOs of trans and gauche conformers are composed of the different spatial localized NBOs: ψ(trans) = 0.829LPN + 0.304σC1−H4 + 0.292σC2−C3 and ψ(gauche) = 0.780LPN + 0.458σC1−C3. The introduction of bonding components of the HOMO brings out an obvious intensity of the TMPs and XMPs at the lowmomentum region. Figure 3 compares the XMPs for the second band (p2 and p3) with the TMPs for MO15 (5a″/15a) and MO14 (10a′/ 14a). The MO maps in Figure 3d reveal that MO15 is dominated by a pair of C−C bonds, like a π bonding. As a result, the individual TMPs for trans 5a″ orbital and gauche 15a orbital both show p-type character with a maximum at p ≈ 0.9 au. As shown in Figure 3b, all of the calculations with different basis sets give almost the same TMPs and can reproduce the XMPs well except at the low-momentum region. With regard to MO14, the trans 10a′ orbital is mainly composed of cyclic C−C bonds and a C−N bond, and its TMPs displays an sp-type curve while the TMPs for gauche 15a orbital shows a p-type character which is contributed primarily from a pair of C−C bonds and LPN. Since the gauche conformer has a very small proportion, the thermally averaged TMPs in Figure 3c give a main sp-type curve and well agree with the XMPs except at the low-momentum region. With respect to the discrepancies between the XMPs and the TMPs in Figure 3b,c, the summed XMPs and TMPs for p2 and p3 are presented in Figure 3a and
good agreement has been achieved, indicating that such discrepancies should originate from the deconvolution uncertainties. Figure 4 offers the XMPs for the third band (p4 and p5), together with the TMPs for MO13 (4a″/13a) and MO12 (9a′/ 12a). The MO maps in Figure 4d show that MO13 is dominated by two pairs of C−H bonds, pseudo-π bonding. Consequently, the XMPs and TMPs in Figure 4b both show a p -type character with a maximum at p ≈ 0.8 au and are well in accordance with each other, while, for MO12, composed of the important C−H bonds and C−N bond, the TMPs displays an sp-type curve, and all the TMPs in Figure 4c well agree with the XMPs. For the summed XMPs and TMPs for p4 and p5, as shown in Figure 4a, the good agreement has been achieved naturally. For the last two bands, as mentioned above, the band (p6) at 15.59 eV corresponds to the MO11, and the one (p7) at 16.91 eV is from the cooperative contribution of MO10 and MO9. The MO11 maps in Figure 5d indicate the 8a′ orbital for trans and the 11a for gauche have complex components of C−N, C− C, C−H, and N−H bonds. As shown in Figure 5b, the TMPs for the MO11 present an sp-type character and do not agree with the XMPs for p6. For the MO10, the orbital maps in Figure 5e show the trans 3a″ orbital has a πN−H bonding character and the component of gauche 10a orbital is very complex. As a result, the different orbital components make the 4489
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Figure 5. XMPs for the last two bands (p6, p7) of CPA and the thermally averaged TMPs of the corresponding molecular orbitals for trans (93.8%) and gauche (6.2%) conformers calculated using the B3LYP method with various basis sets: (a) summed XMP for p6 and p7 and the summed thermally averaged TMPs of MO11, MO10, and MO9; (b) XMP for p6 and the thermally averaged TMPs of MO11; (c) XMP for p7 and the summed thermally averaged TMPs of MO10 and MO9; (d) individual TMPs and orbital maps of MO11 for trans and gauche calculated by B3LYP/ aug-cc-pVTZ; (e) individual TMPs and orbital maps of MO10 for trans and gauche calculated by B3LYP/aug-cc-pVTZ; (f) individual TMPs and orbital maps of MO9 for trans and gauche calculated by B3LYP/aug-cc-pVTZ.
TMPs of 3a″ orbital showing a p-type character, while the TMPs of 10a orbital having an sp-type feature. The MO9 maps in Figure 5f indicate that the trans 7a′ orbital and gauche 9a orbital have similar components of C−N, C−H, and N−H bonds, and their TMPs present sp-type character. As shown in Figure 5c, the summed TMPs for MO10 and MO9 are in good agreement with the XMPs for p7. Figure 5a compares the summed XMPs for p6 and p7 with the summed TMPs for the relevant MOs, and one can see that the XMPs put up a high intensity relative to the TMPs at the momentum from 0.4 to 1.2 au. It seems that an extra p-type TMP will be expected to complement the XMPs. We first check one possible cause, the contamination of shakeup states accompanying the ionization of MOs as observed in previous studies.37,38 But according to our SAC-CI calculations, no satellite states appear in this energy region, which indicates this possibility could be excluded. Another possible cause is ultrafast nuclear dynamical processes upon the ionization, such as the molecular geometry distortion (or relaxation) and vibronic coupling interactions in a molecule, which were invoked in order to explain the observed high intensity in recent EMS studies.39,40
It is worthy to note that the cyclic structure of CPA spontaneously undergoes ring opening at the instant of ionization, as reported in the literature.41 Such a process of structural change could be ultrafast, similar to that of cyclopropane molecule reported previously,39 to some extent, comparable to the interaction time of electron impact ionization. We therefore resort to the picture presented in the literature,39 and attempt to qualitatively explain the observed discrepancies in CPA on the basis of the calculations using geometries of the final ion. All attempts to optimize the cyclic structure of ionic CPA failed and led to the open structure. So the geometry of ring-opening ionic CPA, which corresponds to the local minimum point on the potential surface, is employed to calculate the TMPs for neutral nonequilibrium systems according to eq 5 in which ionic Q′ is used instead of neutral Q0, and the results are presented in Figure 6. Compared with the TMPs in Figures 2−5, one can see that the shape of TMPs for MO11 displays a remarkable change as shown in Figure 6f and offers an expected high intensity at the momentum from 0.4 au to 1.2 au, which could qualitatively explain the discrepancy that appeared in Figure 5, to some extent. In addition, with a view to the shape change of 4490
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Figure 6. TMPs of the outer-valence orbitals, (a) MO16, (b) MO15, (c) MO14, (d) MO13, (e) MO12, (f) MO11, (h) MO10, and (h) MO9, calculated using B3LYP/aug-cc-pVTZ within the geometry of the ring-opening ionic structure optimized by MP2/aug-cc-pVTZ.
molecular geometry at the instant of ionization. The stringent calculations involving the original Dyson orbitals and molecular dynamical simulations are desirable. In addition, although taking into account the conformational effect, the contribution of the gauche conformer with small population could not be determined unambiguously from the experiment due to the limit of EMS accuracies (∼10%) in deducing the conformer weight as suggested in previous works.42,43 In the future, the variable-temperature EMS experiments on gaseous CPA with high sensitivity and high energy resolution will be carried out to explore the conformational effect on the shape, topology, and spread of molecular orbitals.
the TMPs for the HOMO in Figure 6a, the difference of the TMPs and XMPs in Figure 2a may be also ascribed to the change of molecular geometry at the instant of ionization. The stringent theoretical descriptions involve the calculation of the overlap integral in eq 4 between neutral and ionic wave functions, as well as molecular dynamical simulations are desirable to further elucidate such phenomena, but this is beyond our ability at present.
V. SUMMARY In this work, we report the first EMS measurement on the outer-valence binding energy spectra and electron momentum profiles for gaseous CPA. The experimental results are interpreted on the basis of quantitative calculations of ionization energies and the relevant Kohn−Sham molecular orbitals at benchmark theoretical levels using the OVGF, SACCI, and B3LYP methods. In general, the experimental and theoretical results are in accordance with each other. But some discrepancies still remained. Such questions could be explained qualitatively in view of the picture about the change of
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Corresponding Author
*E-mail: [email protected]. Notes
The authors declare no competing financial interest. 4491
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ACKNOWLEDGMENTS This work was partially supported by the National Basic Research Program of China (Grant No. 2010CB923301) and the National Natural Science Foundation of China (Grant Nos. 11327404, 20973160, and 10904136). We also gratefully acknowledge Professor C. E. Brion from the University of British Columbia (UBC) in Canada for giving us the HEMS programs.
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