Ring-Puckering Effects on Electron Momentum Distributions of

Article pubs.acs.org/JPCA

Ring-Puckering Effects on Electron Momentum Distributions of Valence Orbitals of Oxetane Jing Yang,† Xu Shan,†,‡ Zhe Zhang,† Yaguo Tang,† Minfu Zhao,† and XiangJun Chen*,†,‡ †

Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui 230026, China ‡ 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 oxetane have been measured utilizing (e, 2e) electron momentum spectrometer with non-coplanar asymmetric geometry at the impact energy of 2500 eV. The experimental momentum distributions were compared with the density functional theory calculations employing B3LYP hybrid functional with aug-cc-pVTZ basis set. It was found that the calculation at planar geometry (C2v) completely fails to interpret the large “turn-up” at low momentum region in electron momentum distribution of the highest occupied molecular orbital (HOMO) 3b1, while the calculations considering the thermal abundances of planar (C2v) and bent (Cs) conformers or the thermally populated vibrational states of ring-puckering motion have significantly improved the agreement. The results indicate that the ring-puckering motion of oxetane has a strong effect on the electron density distribution of HOMO.

simulations employing the classical MM3 force field and largescale quantum mechanical simulations employing Born− Oppenheimer molecular dynamics. It was demonstrated that the thermal deviations from the lowest energy path for pseudorotation, in the form of considerable variations of the ring-puckering amplitude, have a significant influence on the outer-valence EMDs. For a four-membered ring molecule like oxetane (or trimethylene oxide), as sketched in Figure 1, the ring-puckering motion becomes much simpler. There is no pseudorotation anymore. In the ground electronic state the molecule oscillates between two equivalent bent conformers (Cs) in a ring-

I. INTRODUCTION It is well-known that the closed ring in many cyclic compound molecules is often not planar but puckered. The molecule undergoes an internal motion corresponding to an out-of-plane ring-puckering vibration. This particular kind of vibrational motion was originally postulated for cyclopentane,1 where the displacement of carbon atom perpendicular to an invariant mean plane could be expressed as a function of puckering amplitude and a phase angle describing various kinds of puckering. Motion involving a change in phase angle at constant puckering amplitude was referred to as pseudorotation. The pseudorotational path connects different conformers corresponding to local energy minima through transition states without passing through a higher energy planar structure saddle point on the potential energy surface.1−5 It is well-established4,6−16 that, for the structurally versatile molecules, conformational rearrangements may have strong effects on the electron momentum distributions (EMDs) for the inner- and outer-valence molecular orbitals (MOs) that can be experimentally obtained for specific orbitals by means of electron momentum spectroscopy (EMS).17−21 The response of the EMDs of MOs to pseudorotation was first investigated by EMS studies on five-membered ring molecule tetrahydrofuran (THF).2−5 The envelope (Cs) and twisted (C2) conformers, as well as the C1 transition states, were taken into account to interpret the measured EMD for the highest occupied molecular orbital (HOMO) of THF.2−4 In these works, however, the variations of the ring-puckering amplitude due to the thermally induced vibrational effects were not considered. In a recent work by Shojaei et al.,5 the measured EMDs were reinterpreted on the basis of molecular dynamical © 2014 American Chemical Society

Figure 1. Structure of oxetane. Received: September 20, 2014 Revised: November 14, 2014 Published: November 25, 2014 11780

dx.doi.org/10.1021/jp509526a | J. Phys. Chem. A 2014, 118, 11780−11786

The Journal of Physical Chemistry A

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coplanar kinematics, the magnitude of momentum of the ionized electron prior to being knocked out can be expressed as

puckering vibration of small amplitude, which can be described as one dimension vibration.22−28 The calculated potential function showed two minima (Cs) and a small barrier in the planar configuration (C2v). It is quite unusual for the oxetane molecule that the lowest vibrational level lies 11.86 ± 0.05 cm−1 above the top of the barrier.29 Therefore, the ring of the molecule can essentially be regarded as planar.30−33 Meanwhile, the frequency of the ring-puckering vibration is sufficiently low so that many excited vibrational levels in this mode are appreciably populated at room temperature.24,27,28 Recent EMS studies by Miao et al.34 and Watanabe et al.35 showed that the EMDs of the valence orbitals can be affected noticeably by the vibrational motions. In line with this idea, it is possible to investigate the ring-puckering effect on the EMDs for oxetane by taking into account the thermally populated vibrational states of the ring-puckering. In this paper, we report the first EMS measurement on this four-membered ring molecule oxetane. The experiments were performed utilizing (e, 2e) electron momentum spectrometer with non-coplanar asymmetric geometry at the impact energy of 2500 eV. The binding energy spectra as well as the electron momentum distributions for the outer-valence MOs were obtained. The experimental momentum distributions were compared with the density functional theory (DFT) calculations employing B3LYP hybrid functional with aug-cc-pVTZ basis set at planar geometry (C2v), as well as considering the thermal abundances of planar (C2v) and bent (Cs) conformers. Furthermore, the experimental results were also interpreted by the calculation which takes into account the thermally populated vibrational states of ring-puckering motion of oxetane molecule.

p = {p02 + p12 + p12 − 2p0 p1 cos θ1 − 2p0 p2 cos θ2 + 2p1 p2 [cos θ1 cos θ2 − sin θ1 sin θ2 cos φ]}1/2

where φ is the relative azimuthal angle between the two outgoing electrons. Before formal experiments, the energy and momentum resolutions of the apparatus were determined to be ∼1.0 eV [full width at half-maximum (fwhm)] and ∼0.1 au by measuring the ionization of the Ar 3p orbital. The liquid sample of oxetane was purchased from Alfa Aesar with about 96% stated purity. It was water-bathed at 350 K during the experiments to keep the vapor pressure stable. The triple differential cross section for (e, 2e) ionization is19 σEMS =

(1)

p = p1 + p2 − p0

(2)

pp d3σ = (2π )4 1 2 d Ω1d Ω 2dE2 p0

∑ |⟨p1p2I |T |G p0⟩|2 av

(4)

where the operator T governs the transition from the entrance channel defined by the projectile momentum p0 and the initial target state |G⟩, to the exit channel defined by the momenta p1, p2 of the two outgoing electrons and the state |I⟩ of the residual ion. ∑av denotes a sum for final states and average for initial states that cannot be resolved in the experiments and are regarded as degenerate. For a molecular target we describe the initial state |G⟩ and the observed ionic state |I⟩ in terms of the Born−Oppenheimer approximation as a product of separate electronic, vibrational, and rotational functions19

II. EXPERIMENTAL AND THEORETICAL BACKGROUND The EMS is a coincidence experiment which is based on the (e, 2e) reaction. In this reaction, a fast incident electron is scattered by a target atom or molecule, while an electron is knocked out from the target. From the conservations of energy and momentum the binding energy εf and momentum p of the target orbital electron can be obtained as εf = E0‐E1‐E2

(3)

|G⟩ =|0VμDν ⟩ |I ⟩ =|iV μ′ ′Dν′ ′⟩

(5)

Here, we assume that the initial electronic state is ground state represented by the notation 0, and i represents the final electronic state of ion. Vμ and Dν are the vibrational and rotational functions for the initial state. The indices μ and v represent the sets of quantum numbers that specify the vibrational and rotational states, respectively. Final vibrational and rotational quantities are denoted by primes. Ignoring rotational motion and using the closure relation of the final vibrational eigenstates, the differential cross section then reduces to19 pp σEMS = (2π )4 1 2 ∑ Q p0 av (6)

where E0, E1, and E2 are energies and p0, p1, and p2 are momenta of the incident and two outgoing electrons, respectively. By detecting the two outgoing electrons in coincidence, the binding energy and the momentum of the target electron can be determined. The details and operation of the present (e, 2e) spectrometer employing asymmetric noncoplanar kinematic arrangement have been described elsewhere,36,37 and thus, only a brief description will be given here. The incident electron beam generated from an electron gun is accelerated to energy of 2500 eV plus the binding energy before reaching the reaction region where it impacts with the gas-phase target molecules injected from a nozzle. The scattered electron outgoing along polar angle θ1 = 14° passes through the fast electron analyzer and is detected by a two-dimensional position sensitive detector (PSD) over a large range of both energies and azimuthal angles of interest. The ionized electron outgoing along polar angle θ2 = 76° enters into the slow electron analyzer and is detected by a one-dimensional PSD. In the employed asymmetric non-

where ∑av denotes average for initial vibrational states and Q = (4π )−1

∫ dΩ⟨Vμ||⟨p1p2i|T|0p0⟩|2 |Vμ⟩

(7)

−1

The integral (4π) ∫ dΩ represents the spherical averaging due to the random orientation of gaseous molecular targets. Within the plane wave impulse approximation (PWIA) and the weak-coupling approximation, we get Q = (4π )−1fee

∫ dΩ⟨Vμ||⟨pi|0⟩|2 |Vμ⟩

= (4π )−1fee Siα 11781

∫ dΩ⟨Vμ||ϕα(p)|2 |Vμ⟩

(8)



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where ϕα(p) is the momentum space representation of the normalized Dyson orbital, fee is the e−e collision factor, and Sαi is the spectroscopic factor. By further using the target Kohn−Sham (KS) approximation, we then have Q = (4π )−1fee Siα

∫ dΩ⟨Vμ||ϕKS(p)|2 |Vμ⟩

(9)

where ϕ (p) is the momentum space representation of the neutral state KS one-electron wave function of the orbital from which the electron is ejected. The differential cross section can thus be simplified to KS

σEMS ∝

∑ ∫ dΩ⟨Vμ||ϕKS(p)|2 |Vμ⟩

(10)

av

For one dimension vibration along z axis, we have σEMS ∝

35

∑ ∫ dz |Vμ(z)|2 ∫ dΩ |ϕKS(p, z)|2 av

=

∑ ∫ dz |Vμ(z)|2 ρ(p, z) av

Figure 2. Potential curves (solid line represents Chan’s potential curve and the dashed line represents the present potential curve). The first 14 vibrational wave functions based on the present potential curve are also shown in the figure as dashed-dotted lines.

(11)

where ρ(p, z) is the spherically averaged electron momentum distribution or electron momentum profile at a given z coordinate. We consider Boltzmann distribution of vibrational levels of the target and let Mμ represent the normalized weight factor for the μth vibrational state, which satisfies

Different from Chan et al., a constrained geometry optimization was performed at each ring-puckering displacement coordinate z, in which the C−C, C−O, and C−H bonds as well as the methylene angles are set free. The corresponding potential curve is shown as dashed line in Figure 2. With these potential functions, we were able to calculate the wave functions of the ring-puckering vibration by numerically solving the Schrödinger equations. The first 14 vibrational wave functions based on the present potential function are shown as dashed-dotted lines in Figure 2. Therefore, the differential cross section can be calculated using eq 13 by discretizing along z-axis34

∑ Mμ = 1 (12)

μ

We then have σEMS ∝

∑ Mμ ∫ dz |Vμ(z)|2 ρ(p, z) (13)

μ

As we have mentioned, the ring-puckering vibration of oxetane can be described as one dimension vibration. Chan et al.22−24 defined the out-of-plane displacement of the ring atoms as the displacement relative to the average plane defined by a hypothetical planar ring. This average plane is located so that, at any instant, the magnitude of the displacements of the oxygen atom and all three carbons from this plane are equal. This outof-plane displacement of the ring atoms was designated as z. They further assumed that during the out-of-plane bending motion, there is no stretching of the C−C and C−O bonds and each of the methylene angles remain constantly bisected by the plane defined at any instant by its carbon atom and the two adjacent atoms in the ring. They also assumed there is no stretching of the carbon−hydrogen bonds and no deformation of the methylene angles. In terms of this ring-puckering displacement coordinate z, the potential function for the ringpuckering vibration in oxetane was approximated as24 (shown by solid line in Figure 2) U (cm ‐1) = 7.422 × 105z4 − 6.738 × 103z 2

14

σEMS ∝

∑

e−Eμ / kBT

14 −Eμ / kBT μ = 0 ∑μ = 0 e

∑ ρ(p, zn) ∫ n

zn + ε /2

zn − ε /2

|Vμ(z)|2 dz (15)

where Eμ is the eigenenergy of the μth vibrational state, kB is the Boltzmann constant, and T is the sample temperature (T = 350 K in the present work). The entire range of z is divided into n bins. The electron momentum profile ρ(p, z) is calculated by DFT method employing B3LYP hybrid functional with aug-cc-pVTZ basis set. All the calculations are carried out using the Gaussian03 package of program.38

III. RESULTS AND DISCUSSION With the assumption of C2v symmetry,30−33 the ground state electronic configuration of oxetane by Hartree−Fock calculation is

(z in Å) (14)

In the present work we also calculated the potential function for the ring-puckering using MP2/aug-cc-pVTZ method.

core: (1a1)2 (2a1)2 (1b2 )2 (3a1)2

valence: (4a1)2 (5a1)2 (2b2 )2 (6a1)2 (1b1)2 (7a1)2 (3b2 )2 (1a 2)2 (2b1)2 (4b2 )2 (8a1)2 (3b1)2

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peaks (9.76 eV for 3b1, 11.44 eV for 8a1,12.22 eV for 4b2, 13.36 eV for 2b1, 14.20 eV for 1a2, and 15.20 eV for 3b2) are referred to the VIPs measured by high resolution PES32 with small adjustments due to the asymmetric Franck−Condon profiles of the ionization bands. Also, the widths of the Gaussian peaks are the Franck−Condon widths folded with the instrumental energy resolution (1.0 eV in fwhm). The solid line in Figure 3b indicates the summed fit. The experimental momentum profiles (XMPs) have been obtained for each of the six peaks, by deconvoluting the corresponding ionization peaks from the BES at different azimuthal angle φ and plotting the area under the fitted Gaussian peaks as a function of momentum p (i.e., φ). The XMP for 3b2 is not convincible, because part of the peak is out of the range of the BES. Therefore, only the XMPs for the five outermost MOs are extracted and shown in Figures 4 and 5 as

The binding energy spectra (BES) of oxetane summed over all the azimuthal angles in the simultaneous measurement range is shown in Figure 3b. Oxetane has been studied by high

Figure 3. Measured binding energy spectra for the outer valence orbitals of oxetane by (a) PES and (b) EMS. In part b, the dashed lines represent the Gaussian peaks corresponding to individual transitions, and the solid line indicates the summed fit. Vertical bars denote the positions of the Gaussian peaks.

resolution photoelectron spectroscopy (PES) utilizing He I ultraviolet30−32 and synchrotron radiations.33 The most recent He I PES result32 is shown in Figure 3a for comparison. Furthermore, in order to assign the observed bands conveniently, the ionization energies for the outer valence orbitals of oxetane for the planar conformer (C2v) and the bent conformer (Cs) are calculated by the partial third-order electron propagator (P3) and B3LYP methods with the aug-cc-pVTZ basis set. As a comparison, the experimental and calculated ionization energies are listed in Table 1. As shown in Figure 1b, in our experiment, the observed binding energy range is from 7.5 to 15.6 eV, showing three spectral envelopes. The first envelope corresponds to the ionization from HOMO 3b1. The second one belongs to the next two MOs 8a1 and 4b2, and the third one belongs to MOs 2b1, 1a2, and 3b2. The energy scale is calibrated with reference to the vertical ionization potential (VIP) of 3b1 as measured by He I PES.32 Six Gaussian functions are used to fit the peaks corresponding to the individual ionization transitions, as shown by dashed lines in Figure 3b. The positions of the Gaussian

Figure 4. Experimental and theoretical momentum profiles for HOMO 3b1 of oxetane.

solid circles with error bars which include both the statistical uncertainties and the uncertainties introduced during the deconvolution procedure. The theoretical momentum profiles (TMPs) are also plotted in the figures for comparison. 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.39 In order to place the XMPs and TMPs on a common intensity scale, a normalization factor common for all the states is needed. In this work, this normalization factor has been obtained by normalizing the XMP for the outmost 3b1 orbital to its TMP calculated by B3LYP/aug-cc-pVTZ. The XMPs for all the other transitions are then to be placed on the common intensity scale by multiplying the normalization factor.

Table 1. Ionization Potentials (eV) for the Outer Valence Molecular Orbitals of Oxetane shifted B3LYPe

P3/aug-cc-pVTZf

MO

EMSa

PESb

PESc

PESd

C2v

Cs

C2v

Cs

3b1 8a1 4b2 2b1 1a2 3b2

9.76 11.44 12.22 13.36 14.20 15.20

9.63 11.32 11.98 13.4 14.0 14.8

9.65 11.35 12.18 13.33 14.00 15.2g

9.68 11.50 12.17 13.58 13.98 15.05

9.76 11.37 11.98 13.18 13.96 14.88

9.76 11.43 11.96 13.16 13.89 14.84

9.89(0.91) 11.46(0.9) 12.03(0.91) 13.43(0.91) 14.36(0.91) 15.03(0.9)

9.91(0.91) 11.56(0.9) 12.04(0.91) 13.44(0.91) 14.29(0.91) 15.08(0.9)

a

Present work. bFrom ref 31. cFrom ref 32. dFrom ref 33. eThe absolute values of the orbital energies calculated by B3LYP/aug-cc-pVTZ are shifted to align the ionization potential of 3b1 orbital with the first experimental peak. fPole strengths are listed in brackets. gThis value is obtained by fitting the PES from ref 32. 11783



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character, giving the first maximum at about 0.4 au, and the second maximum at about 1.1 au, as shown in Figure 5b. The next two MOs are both π-type: 2b1 composed from oxygen and carbon atom on the opposite site of the ring, while 1a2 composed from two carbon atoms adjacent to oxygen. As shown in Figure 5c,d, the XMPs of these two orbitals both exhibit p-type character with maximum at about 0.75 au. As we have mentioned that for the oxetane molecule the lowest vibrational level of ring-puckering lies 11.86 cm−1 above the top of the barrier.29 Therefore, the ring of the molecule can essentially be regarded as planar (C2v).30−33 The TMPs calculated at planar geometry (solid curves) generally reproduce the XMPs except HOMO where the TMP at C2v geometry completely fails to interpret the large “turn-up” at low momentum region (see Figure 4). In fact, the ring of the oxetane molecule is actually puckered. The potential function of ring-puckering motion shows two minima (Cs) and a small barrier (C2v). As we have known, for the structurally versatile molecules, conformational rearrangements may have strong effects on the EMDs for the valence MOs.5−16 The Boltzmann weighted TMPs for different conformers are usually sufficient to interpret the conformational influence. The experimentally reported value of the barrier height is 15.52 ± 0.05 cm−1.29 Hence the calculated abundances at T = 350 K for planar (C2v) and bent (Cs) conformers are 32% and 68%, respectively. The Boltzmann weighted TMPs are drawn as dashed-dotted lines in Figures 4 and 5. It is quite obvious as indicated in Figure 4 that the synthesized TMP for HOMO has significantly improved the agreement with the experiment in the low momentum region, while for other MOs no distinct influences can be found. More precisely, the variations of the ring-puckering amplitude due to the thermally induced vibrational effects should also be considered. This can be achieved by employing eq 15 where the thermally populated vibrational states of the ring-puckering are taken into account. In practical calculations, the range of z ∈ [−0.3 Å, 0.3 Å] is divided into n = 120 bins

Figure 5. Experimental and theoretical momentum profiles for (a) 8a1, (b) 4b2, (c) 2b1, and (d) 1a2 of oxetane.

In Figure 6 we plot the orbital maps of all the five orbitals involved in this work. As revealed by the orbital map, HOMO 3b1 is a π-type nonbonding orbital predominated by oxygen 2p lone pair. As shown in Figure 4, its XMP exhibits a p-type character with a maximum at p ≈ 1 au, but substantially high intensity has been observed in the low momentum region. The next 8a1 orbital is a σ-type orbital which is also predominated by oxygen 2p lone pair. The XMP of 8a1 exhibits a double ptype character with the first maximum at about 0.35 au and the second one at about 1.35 au, as shown in Figure 5a. The 4b2 orbital is also a σ-type orbital of the oxetane ring excluding oxygen, the XMP of which also exhibits a double p-type

Figure 6. Molecular orbital maps for oxetane at planar geometry (C2v). 11784



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with the width of ε being about 0.005 Å. Only the first 14 vibrational states are taken into account in the calculations because the population is less than 0.1% as μ > 14. When calculating vibrational wave functions, two kinds of potential functions have been employed. One is Chan’s potential function, and the other is the present calculated one, the details of which have been described in the last section. The results are shown as dotted lines (Chan’s potential function) and dashed lines (present potential function) in Figures 4 and 5. As can be seen in Figure 4, although the discrepancy still exists in the low momentum region, the new calculations further improve the agreement with the experiment especially the calculation using the present newly calculated potential curve. Interestingly, for other MOs, there are still no distinct influences. It is reasonable because the ring-puckering motion can be regarded as the movement of the oxygen atom relative to other three carbon atoms. As can be seen in orbital maps in Figure 6, only the HOMO can significantly be influenced by the ring-puckering. The bending of the oxygen atom relative to the other three carbon atoms effectively influences the intramolecular hyperconjugative interactions between oxygen lone pair (nO) and the nearby C−H bonds, introducing symmetric component in the electron momentum profile. This can be demonstrated by the natural bond orbital (NBO) analysis. The NBO analysis transforms the canonical delocalized MOs into localized orbitals, and the hyperconjugative interaction can be evaluated by second order perturbation energy 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. The NBO analyses were performed for both planar (z = 0) and bent (z = 0.165 Å) geometries by B3LYP/ aug-cc-pVTZ employing NBO program.40 For the planar conformer the predominant hyperconjugative interactions are four equivalent nO → σ*CH interactions (E(2) = 5.54 kcal/ mol), while for the bent conformer the energies for these four predominant hyperconjugative interactions change to 6.98 kcal/mol for nO → σ*C3H8, nO → σ*C4H10, and 2.07 kcal/mol for nO → σ*C3H7, nO → σ*C4H9. The significant changes in hyperconjugative interactions will lead to different charge transfer from nO to the nearby C−H bonds, resulting in the observed influence on the electron momentum distribution of HOMO.

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grants 11327404, 20973160, 10904136) and the National Basic Research Program of China (Grant 2010CB923301). The authors 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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IV. SUMMARY In this work, the binding energy spectra and electron momentum distributions for the outer-valence molecular orbitals of oxetane have been measured for the first time by utilizing (e, 2e) electron momentum spectrometer with noncoplanar asymmetric geometry at the impact energy of 2500 eV plus binding energy. A large “turn-up” has been observed at low momentum region in the XMP for HOMO 3b1, which cannot be reproduced by the B3LYP/aug-cc-pVTZ calculation employing planar ring geometry. The ring-puckering effect has been investigated by comparing the XMP for HOMO with the calculations considering the thermal abundances of planar (C2v) and bent (Cs) conformers as well as the thermally populated vibrational states of the ring-puckering motion. Significant improvements in agreement with the experiments have been achieved indicating that the ring-puckering motion has a strong effect on the electron density distribution of the HOMO for oxetane molecule. The conclusion has further been supported by the NBO analysis. 11785



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