Chinese Journal of Chemical Physics  2019, Vol. 32 Issue (4): 423-430

The article information

Yi-chun Wang, Shan-shan Niu, Ya-guo Tang, Yu Zhang, Xu Shan, Chun-kai Xu, Xiang-jun Chen
王忆纯, 牛珊珊, 唐亚国, 张钰, 单旭, 徐春凯, 陈向军
Electron Momentum Spectroscopy Investigation on Electronic Structure of Iso-dichloroethylene Valence Shell
异二氯乙烯价壳层轨道电子结构的电子动量谱研究
Chinese Journal of Chemical Physics, 2019, 32(4): 423-430
化学物理学报, 2019, 32(4): 423-430
http://dx.doi.org/10.1063/1674-0068/cjcp1903059

Article history

Received on: March 22, 2019
Accepted on: April 29, 2019
Electron Momentum Spectroscopy Investigation on Electronic Structure of Iso-dichloroethylene Valence Shell
Yi-chun Wang , Shan-shan Niu , Ya-guo Tang , Yu Zhang , Xu Shan , Chun-kai Xu , Xiang-jun Chen     
Dated: Received on March 22, 2019; Accepted on April 29, 2019
Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
Abstract: Here an electron momentum spectroscopy study on the electronic structure of valence shell of iso-dichloroethylene molecule is reported. The experiment is carried out with a binary (e, 2e) spectrometer at incident electron energy of 1200 eV, employing noncoplanar symmetric arrangement. The binding energy spectra and electron momentum distributions (EMDs) of iso-dichloroethylene valence shell have been obtained. Theoretical EMDs are predicted with both Hartree-Fock and density functional theory methods, generally indicating good agreements with the measurement results. The interference effect is observed to significantly influence the EMDs of 2a$ _2 $ and 5b$ _2 $ Cl lone-pair orbitals.
Key words: Electron momentum spectroscopy    Valence orbital    Lone-pair orbital    Interference effect    
Ⅰ. INTRODUCTION

Electron momentum spectroscopy (EMS), or binary (e, 2e) spectroscopy, is based on kinematically complete ionization experiments initiated by high energy electrons. In the past decades, it has been proven as a powerful technique for investigating both the binding energy spectra (BES) and the electron momentum distributions (EMDs) for individual atomic and molecular orbitals [1-7]. Such information helps us to evaluate the quality of different theoretical models for calculating electronic wave functions of atoms and molecules [1], as well as understand the relation between electron density distribution and chemical reactivity [8]. Iso-dichloroethylene (iso-C$ _2 $H$ _2 $Cl$ _2 $) is one of the three isomers of dichloroethylene, in which the two chlorine atoms are bound to the same carbon atom. Since it plays an important role as a common chlorine source for processing and treatment of silicon wafers in semiconductor material industry [9, 10], its electronic structure has been investigated extensively by electron energy loss spectra [9, 11], photoelectron spectra (including resonant Auger spectra) [12-18], X-ray absorption spectra [16-18], Penning ionization electron spectra [19], etc. The EMS study on iso-C$ _2 $H$ _2 $Cl$ _2 $ has also been performed by Chuaqui et al. [20]. However, only the EMDs for part of 12 valence orbitals were presented, including 3 outer-valence orbitals (3b$ _1 $, 10a$ _1 $ and 6b$ _2 $) and 4 inner-valence orbitals (9a$ _1 $, 8a$ _1 $, 5b$ _2 $ and 7a$ _1 $). There remained an obvious discrepancy between the experiment and calculations.

In this work, we report an EMS study on the electronic structure of all the iso-C$ _2 $H$ _2 $Cl$ _2 $ valence orbitals. The experiment is performed by a high-sensitivity angle and energy dispersive multichannel electron momentum spectrometer at incident energy of 1200 eV plus the binding energy. Two-dimensional energy and azimuthal angle density map in the valence region have been measured, from which the BES as well as the EMDs of the iso-C$ _2 $H$ _2 $Cl$ _2 $ valence shell are obtained. Theoretical calculations are carried out using Hartree-Fock (HF) and density functional theory (DFT) methods within the framework of plane wave impulse approximation (PWIA). The interference effect is observed to significantly influence the EMDs of 2a$ _2 $ and 5b$ _2 $ orbitals, which consist of mainly Cl lone-pair electrons.

Ⅱ. EXPERIMENTS

EMS experiment is based on the (e, 2e) process, in which a fast incident electron impacts with a target atom or molecule and knocks an electron out. By measuring the two outgoing electrons in coincidence, the kinematics of this process can be fully determined. The conservation of energy and momentum gives the binding energy $ \varepsilon_f $ and the momentum p of the electron in target orbital as

$ \begin{eqnarray} \varepsilon _f & = & E_0 - E_a - E_b \end{eqnarray} $ (1)
$ \begin{eqnarray} \textbf{p}& = &\textbf{p}_a + \textbf{p}_b - \textbf{p}_0 \end{eqnarray} $ (2)

where $ E_0 $, $ E_a $, and $ E_b $ are kinetic energies and $ \textbf{p}_0 $, $ \textbf{p}_a $ and $ \textbf{p}_b $ are momenta of the incident and two outgoing electrons respectively. In the present work, the experiment on iso-C$ _2 $H$ _2 $Cl$ _2 $ is performed using a high-sensitivity EMS spectrometer with a symmetric non-coplanar geometry, the details of which can be found elsewhere [21, 22]. During the experiment, the incident electron beam with the energy of 1200 eV plus binding energy collides with the target gas beam in the reaction region. The scattered and ejected electrons having equal polar angles ($ \theta_a $ = $ \theta_b $ = $ \theta $ = 45$ ^{\circ} $) and energies ($ E_a $ = $ E_b $) are detected in coincidence by a 90$ ^{\circ} $ sector spherical electrostatic analyzer with 2$ \pi $ azimuthal range followed by a position-sensitive detector, to obtain their energies and azimuthal angles simultaneously. The magnitude of the target orbital electron momentum $ \textbf{p} $ is then expressed as

$ \begin{eqnarray} \textbf{p} = \left\{\left( {\sqrt 2 \textbf{p}_a - \textbf{p}_0 } \right)^2 + \left[ {\sqrt 2 \textbf{p}_a \sin \left( {{\varphi }/2}\right)}\right]^2\right\}^{1/2} \end{eqnarray} $ (3)

where $ \varphi $ is the relative azimuthal angle between the two outgoing electrons. From Eq.(1) and Eq.(3), the binding energy and momentum of the target electron can be determined. The energy and momentum resolution of the present EMS instrument are determined to be $ \sim $1.1 eV (full width at half maximum (FWHM)) and $ \sim $0.2 a.u. respectively, by measuring the ionization spectra and electron momentum distribution of Ar 3p orbital.

On the theoretical aspect, within the binary encounter approximation and plane wave impulse approximation (PWIA), the triple differential cross-section (TDCS) of (e, 2e) reaction for a molecule oriented randomly is given by [3]

$ \begin{eqnarray} \sigma _{ \rm{EMS}} & = & \frac{{ \rm{d}^3 \sigma }}{{ \rm{d}\Omega _1 \rm{d}\Omega _2 \rm{d} E_1 }} \\ & = & \left( {2\pi } \right)^4 \frac{{\textbf{p}_a \textbf{p}_b }}{{\textbf{p}_0 }}f_{ \rm{ee}} \sum\limits_{ \rm{av}} {\left| {\left\langle {{\bf{p}}\left. {\psi _f } \right|\psi _i } \right\rangle } \right|} ^2 \end{eqnarray} $ (4)

where $ f_{ \rm{ee}} $ is the electron-electron Mott scattering cross-section, and $ {\sum\limits_{ \rm{av}}} $ represents an average over initial neutral $ \psi_i $ and a sum over final ion $ \psi_f $ states. Under the weak-coupling approximation [1] and the target HF [1, 23-25] or Kohn-Sham (KS) approximation [26-28], the Eq.(4) can be simplified to

$ \begin{eqnarray} \sigma _{ \rm{EMS}} \propto S_i^f \frac{1}{{4\pi }}\int {\left| {\phi _i \left( {\bf{p}} \right)} \right|^2 \rm{d}\Omega _p } \end{eqnarray} $ (5)

Here $ S^f_i $ is called spectroscopic factor or pole strength (PS) which is the possibility of finding a one-hole configuration in the final ion state, and $ \phi_i $($ \textbf{p} $) is the one-electron momentum space canonical HF or KS orbital wave function in the neutral initial state for the $ i $th electron corresponding to the orbital from which the target electron is ionized. The integral in Eq.(5) is referred to as the electron momentum profile (EMP).

In the present work, the EMPs for the valence shell of iso-C$ _2 $H$ _2 $Cl$ _2 $ have been calculated by the GAUSSIAN 09 program [29]. HF as well as DFT along with B3LYP functional methods is employed, with 6-31++G$ ^{**} $ and aug-cc-pVTZ basis sets. To be compared with the experiment, the calculations have been convoluted with the finite acceptance angles of the (e, 2e) spectrometer in both $ \theta $ and $ \varphi $ ($ \Delta \theta $ = 0.8$ ^{\circ} $, $ \Delta \varphi $ = 2.0$ ^{\circ} $), using the Gaussian-weighted planar grid method [30]. The symmetry-adapted-cluster configuration-interaction (SAC-CI) general-$ R $ methods [31, 32] employing aug-cc-pVTZ basis set are also used to calculate the binding energy spectra of iso-C$ _2 $H$ _2 $Cl$ _2 $ for all the valence orbitals.

Ⅲ. RESULTS AND DISCUSSION A. Binding energy spectrum

For iso-C$ _2 $H$ _2 $Cl$ _2 $ molecule, there are 12 valence orbitals, which are classified into 4 inner-valence and 8 outer-valence orbitals. B3LYP calculation gives the electric configuration of iso-C$ _2 $H$ _2 $Cl$ _2 $ as

$ \begin{eqnarray} &&\left( {{\rm{core}}} \right)^{14} \underbrace {\left( {7 \rm{a}_1 } \right)^2 \left( {5 \rm{b}_2 } \right)^2 \left( {8 \rm{a}_1 } \right)^2 \left( {9 \rm{a}_1 } \right)^2 }_{{\rm{inner \rm{-}valance }}}\\ &&\underbrace {\left( {6 \rm{b}_2 } \right)^2 \left( {10 \rm{a}_1 } \right)^2 \left( {2 \rm{b}_1 } \right)^2 \left( {7 \rm{b}_2 } \right)^2 \left( {11 \rm{a}_1 } \right)^2 \left( {2 \rm{a}_2 } \right)^2 \left( {8 \rm{b}_2 } \right)^2 \left( {3 \rm{b}_1 } \right)^2 }_{{\rm{ outer \rm{-}valence}}} \end{eqnarray} $

The two-dimensional density map (2D map) of binding energy (in the range of 7-29.8 eV) and relative azimuthal angle (in the range from -50$ ^{\circ} $ to 50$ ^{\circ} $) measured in the experiment are shown in FIG. 1(a), from which the momentum distributions and symmetries of Iso-C$ _2 $H$ _2 $Cl$ _2 $ valence orbitals can be clearly recognized. Integrating the 2D map over the complete azimuthal range, we obtain the total BES, which is shown in FIG. 1(b). Twelve Gaussian peaks (denoted as p1 to p12), corresponding to the ionization bands of the twelve valence orbitals, are employed to deconvolute the total BES. The position and width of each peak are determined with the help of the corresponding valence ionization energy and Franck-Condon width from high-resolution synchrotron radiation photoelectron spectra (SR PES) [14], with small adjustments to compensate the asymmetries of Franck-Condon profiles and the instrumental energy resolution. The fitted Gaussian peaks are drawn as blue dashed lines in FIG. 1(b), while the overall fitted spectra are plotted as red solid line. It is illustrated that the first peak in BES at 10.0 eV (band p1) is well resolved, which is contributed from the ionization of the highest occupied molecular orbital (HOMO) 3b$ _1 $. The next seven bands at 11.6, 12.1, 12.5, 13.8, 14.3, 15.7, and 16.5 eV (p2 to p8) are assigned to the orbitals of 8b$ _2 $, 2a$ _2 $, 11a$ _1 $, 7b$ _2 $, 2b$ _1 $, 10a$ _1 $, and 6b$ _2 $, respectively, all of which are outer-valence orbitals. The rest four bands in BES belong to the inner-valence shell, which are denoted as p9 (18.7 eV), p10 (23.4 eV), p11 (25.5 eV), and p12 (27.7 eV), corresponding to the ionizations from 9a$ _1 $, 8a$ _1 $, 5b$ _2 $, and 7a$ _1 $ orbitals respectively. The ionization potentials (IPs) for the valence shells of iso-C$ _2 $H$ _2 $Cl$ _2 $ obtained in the present experiment are presented in Table Ⅰ, as well as those from He I [13], SR PES [14] and previous EMS experiments [20].

FIG. 1 (a) Two-dimensional electron density maps (2D maps) and (b) total binding energy spectra (BES) of iso-C$ _2 $H$ _2 $Cl$ _2 $. (c) Simulated BES by SAC-CI general-$ R $. The vertical bars represent ionization transitions and their heights are pole strengths. The height of the vertical bars above 22 eV is multiplied by a factor of 2
Table Ⅰ Ionization potential (IP), assignment and pole strength (PS) for the ionization bands of iso-dichloroethylene valence shells

For the sake of comparison, SAC-CI general-R calculations employing aug-cc-pVTZ basis set have been performed to calculate the IP and PS for each ionization transitions, which are also compiled in Table Ⅰ. FIG. 1(c) shows the simulated BES by employing the calculated IPs convoluting with the instrumental function of 1.1 eV. The vertical bars represent ionization transitions and their heights are pole strengths. The height of the vertical bars above 22 eV is multiplied by a factor of 2. It can be seen that in the outer valence region, the SAC-CI general-$ R $ simulation reproduces the measured BES pretty well, while it fails to describe both the positions and intensities of the ionization bands from the three innermost valence orbitals.

B. Electron momentum profiles

Momentum-dispersed BES are converted from the 2D map according to Eq.(3), which are then deconvoluted with Gaussian function to obtain the experimental momentum profiles (XMPs) for the valence orbitals of iso-C$ _2 $H$ _2 $Cl$ _2 $. The deconvolution parameters are from the total BES and the XMPs are presented by the area under the fitted Gaussian peaks as a function of momentum p. Statistical uncertainty as well as deconvolution error is taken into account to determine the error bar of each XMP datum. For comparison, theoretical momentum profiles (TMPs) are calculated by HF and DFT-B3LYP methods with 6-31++G$ ^{**} $ and aug-cc-pVTZ basis sets, using the Gaussian 09 program [29]. The spectrometer acceptance angles of $ \Delta \theta $ = 0.8$ ^{\circ} $ and $ \Delta \phi $ = 2.0$ ^{\circ} $ are folded into the TMPs using the Gaussian-weighted planar grid method [30]. A global normalization factor, which is determined from the comparison of the maximum in the momentum profile of HOMO (3b$ _1 $) obtained by experiment and B3LYP/aug-cc-pVTZ calculation, is employed to normalize the XMPs to the TMPs. The results are illustrated in FIGs. 2-4, where the XMPs are plotted as solid circles with error bars, and the TMPs are drawn as olive dot line for HF/6-31++G$ ^{**} $, blue dash line for HF/aug-cc-pVTZ and red solid line for B3LYP/aug-cc-pVTZ respectively.

FIG. 2 Experimental and theoretical electron momentum profiles for the ionization bands from p1 to p4, which are corresponding to the iso-C$ _2 $H$ _2 $Cl$ _2 $ outer-valence orbitals of 3b$ _1 $ (a), 8b$ _2 $ (b), 2a$ _2 $ (c) and 11a$ _1 $ (d) respectively. The incident energy is 1200 eV plus binding energy. The calculated electron density distributions of these orbitals are shown as the inserts

The first band p1 in BES is contributed from the ionization of 3b$ _1 $ orbital (HOMO), the XMP and TMPs of which are given in FIG. 2(a). It should be noted that from the SAC-CI general-$ R $ calculation, the PS with respect to the ionization of HOMO is assumed to be 0.83. Therefore the global normalization factor is actually determined by normalizing the maximum of the XMP to that of the relevant TMP which is calculated by B3LYP/aug-cc-pVTZ and multiplied by a factor of 0.83, for the 3b$ _1 $ orbital (HOMO). For the ionizations of other iso-C$ _2 $H$ _2 $Cl$ _2 $ valence orbitals, the PS is determined experimentally by comparing XMPs with TMPs (calculated by B3LYP/aug-cc-pVTZ) multiplied by the corresponding factors, which are listed in Table Ⅰ. From FIG. 2(a), we can observe that all of the XMPs and TMPs show a typical p-type character with a maximum at about 0.75 a.u. The theoretical calculations reproduce the experimental data very well in large momentum region, but underestimate the XMPs in low momentum region. Such turn-up effects, which have been frequently reported in EMS studies on molecular $ \pi^* $ orbitals or atomic d orbitals, are usually ascribed to the distorted wave effects [33-36]. According to Ref.[20], the 3b$ _1 $ orbital of iso-C$ _2 $H$ _2 $Cl$ _2 $ consists primarily of out-of-plane $ \pi $ bonding, but contains weak $ \pi^* $ overlaps as well. Therefore the observed turn-up effect in FIG. 2(a) may stem from the $ \pi^* $ component of this orbital, consequently being attributed to the distorted wave effects. As for the theoretical calculations, all the calculated curves show almost no difference from each other. This indicates that for the TMP calculations of this orbital, 6-31++G$ ^{**} $ basis set is large enough, and the selection of methods (HF or B3LYP) has little influence.

The XMPs and TMPs of the p2 (8b$ _2 $), p3 (2a$ _2 $), and p4 (11a$ _1 $) ionization bands are shown in FIG. 2 (b), (c), and (d) respectively, which have not been reported before. It is observed that both the experimental and calculated momentum profiles of these orbitals display mainly p-type characters, with the maximums at about 0.90, 0.75, and 0.45 a.u., corresponding to 8b$ _2 $, 2a$ _2 $ and 11a$ _1 $ orbitals respectively. All the calculations for each of these three orbitals are shown to be consistent with each other and fit the experimental data very well. The PS values for these three ionization bands are determined experimentally, all of which are 0.83, being equal to that for HOMO (3b$ _1 $).

The next four ionization bands p5-p8 are assigned to the outer-valence orbitals of 7b$ _2 $, 2b$ _1 $, 10a$ _1 $ and 6b$ _2 $ respectively. The XMPs and TMPs of 7b$ _2 $ and 2b$ _1 $ orbitals have not been reported before, while those of 10a$ _1 $ and 6b$ _2 $ orbitals were investigated by Chuaqui et al. [20]. However, only the combined momentum profile is given in Ref.[20], and significant discrepancy between the experiment and calculations was observed. In the present work, the measured momentum profiles of 7b$ _2 $, 2b$ _1 $, 10a$ _1 $ and 6b$ _2 $ orbitals are shown in FIG. 3 (a)-(d) respectively, together with the theoretical calculations. In FIG. 3(a), both the XMPs and TMPs of 7b$ _2 $ orbital exhibit a double p-type distribution with the first maximum at about 0.40 a.u. and the second maximum at about 1.15 a.u. It is observed that the calculations employing whether HF or B3LYP methods with aug-cc-pVTZ basis set resemble the XMP pretty well, but the one calculated with 6-31++G$ ^{**} $ basis set obviously underestimates the XMP in the region below 1.15 a.u. This indicates that adequately large basis set is of most importance in the calculations for 7b$ _2 $ orbital. The PS for this ionization band is also determined to be 0.83. The momentum distributions of 2b$ _1 $ orbital are illustrated in FIG. 3(b), which shows a p-type character with a maximum at about 0.50 a.u. All theoretical calculations exhibit almost no difference from each other, and reproduce the XMP well. The PS for this band is determined experimentally to be 0.78. The last two outer-valence orbitals are 10a$ _1 $ and 6b$ _2 $, the XMP and TMPs of which are shown in FIG. 3 (c) and (d) respectively. It is observed that for both orbitals, B3LYP and HF calculations with aug-cc-pVTZ basis sets show no difference. However, the discrepancy between the calculations with large basis set (aug-cc-pVTZ) and relatively small basis set (6-31++G$ ^{**} $) are obvious for 10a$ _1 $ but slight for 6b$ _2 $ orbitals. The general agreement between the XMP and TMPs are fairly well for both orbitals, and the discrepancy may be due to the electron correlation effect, distorted wave effect or the uncertainty in the deconvolution procedure. The PSs for these two bands are determined to be 0.83 and 0.79 respectively.

FIG. 3 Experimental and theoretical electron momentum profiles for the ionization bands from p5 to p8, which are corresponding to the iso-C$ _2 $H$ _2 $Cl$ _2 $ outer-valence orbitals of 7b$ _2 $ (a), 2b$ _1 $ (b), 10a$ _1 $ (c) and 6b$ _2 $ (d) respectively. The incident energy is 1200 eV plus binding energy. The calculated electron density distributions of these orbitals are shown as the inserts

There are four inner-valence orbitals of iso-C$ _2 $H$ _2 $Cl$ _2 $, which are 9a$ _1 $, 8a$ _1 $, 5b$ _2 $ and 7a$ _1 $. In the present work, the BES range covers the ionization energies of all the inner-valence orbitals. Therefore the XMPs of these orbitals are obtained and displayed in FIG. 4 (a)-(d) respectively, together with the calculated TMPs. In general, for each of the four orbitals, all the TMPs show almost no difference from each other, indicating the independence of the calculations on the method as well as the basis set larger than 6-31++G$ ^{**} $. For 9a$ _1 $ orbital, the TMPs fit the XMP pretty well, demonstrating an sp-type character with the second maximum at about 0.80 a.u., as shown in FIG. 4(a). The momentum distributions of 8a$ _1 $ orbital are shown in FIG. 4(b), showing a p-type character with the maximum at about 0.55 a.u. The TMPs reproduce the XMP well only in the peak region from 0.4 a.u. to 1.2 a.u., but underestimate it in the else region. As for 5b$ _2 $ orbital in FIG. 4(c), the calculations are observed to well resemble the experimental data below 1.5 a.u., which also show a p-type distribution with the maximum at about 0.55 a.u. How- ever, deviations between the theoretical curve and the experimental data can be found in the higher momentum region (above 1.5 a.u.). The XMP and TMPs of the last inner-valance orbital 7a$ _1 $ are shown in FIG. 4(d). Although all the momentum profiles exhibit s-type character, the TMPs fit the XMP not so well. The discrepancies between the calculation and experiment for 8a$ _1 $, 5b$ _2 $ and 7a$ _1 $ orbitals are probably due to the breakdown of the PWIA, since in the inner-valence shell the distorted wave effect becomes more and more important. Besides, from the SAC-CI general-$ R $ simulated BES shown in FIG. 1(c), we can observe several satellites overlapping in the energy range covering the ionization bands p10-p12, corresponding to these three most-inner valance orbitals. This may be another reason why the calculated EMDs do not agree with the experimental data very well for 8a$ _1 $, 5b$ _2 $ and 7a$ _1 $ orbitals. The PSs for the ionization of all the inner-valence orbitals are determined experimentally, which are 0.68 (9a$ _1 $), 0.83 (8a$ _1 $), 0.19 (5b$ _2 $) and 0.28 (7a$ _1 $) respectively.

It is worth noting that from the electron density distributions displayed in the inserts of FIG. 2(c) and FIG. 4(c), the orbitals 2a$ _2 $ and 5b$ _2 $ of iso-C$ _2 $H$ _2 $Cl$ _2 $ are mainly Cl 3p and 3s lone-pair electrons respectively. Recent researches have revealed that due to the multiple atomic centers participating in the bonding or antibonding interaction, the EMPs of lone-pair orbitals in molecules such as CF$ _4 $ [37], SF$ _6 $ [6, 38], CCl$ _4 $ [39], C$ _3 $H$ _8 $ [40] etc. will be influenced significantly by the interfe- rence effects (also referred as bond oscillations). Under the linear combination of atomic orbitals approximation, the TDCS of EMS for lone-pair orbital can be written as

FIG. 4 Experimental and theoretical electron momentum profiles for the ionization bands from p9 to p12, which are corresponding to the iso-C$ _2 $H$ _2 $Cl$ _2 $ inner-valence orbitals of 9a$ _1 $ (a), 8a$ _1 $ (b), 5b$ _2 $ (c) and 7a$ _1 $ (d) respectively. The incident energy is 1200 eV plus binding energy. The calculated electron density distributions of these orbitals are shown as the inserts
$ \begin{eqnarray} \sigma _{ \rm{EMS}} \left( {p} \right) \propto \sigma _{ \rm{AO}} \left( {p} \right)I\left( {p} \right) \end{eqnarray} $ (6)

Here $ \sigma _{ \rm{AO}} \left({p}\right) $ is the TDCS for the atomic orbital (AO) of an isolated atom corresponding to the lone-pair electrons, and $ I\left(p\right) $ is referred to as the interference factor (IF). For 2a$ _2 $ and 5b$ _2 $ orbitals of iso-C$ _2 $H$ _2 $Cl$ _2 $, the IF can be deduced as [37, 38]

$ \begin{eqnarray} \rm{IF}& = &1 + a_0 \frac{{\sin \left( {pR} \right)}}{{pR}} + \\ &&a_2 \frac{{3\left[ {\sin \left( {pR} \right) - pR\cos \left( {pR} \right)} \right] - \left( {pR} \right)^2 \sin \left( {pR} \right)}}{{\left( {pR} \right)^2 }} \end{eqnarray} $ (7)

where $ a_0 $ and $ a_2 $ are the coefficients of the spherical Bessel functions of order 0 and 2 respectively, and $ R $ is the distance between two Cl nuclei. According to B3LYP/aug-cc-pVTZ calculation, these three parameters are determined to be -1 for both of a$ _0 $ and a$ _2 $, and 5.51 a.u. for $ R $ respectively. In FIG. 5 (a) and (b), the EMPs of 2a$ _2 $ and 5b$ _2 $ orbitals are compared with those of the corresponding AOs respectively. In each figure, the XMP and TMP of iso-C$ _2 $H$ _2 $Cl$ _2 $ lone-pair orbital are shown as black solid circle and red solid line respectively, the IF is denoted as olive dot dash line, and the TMP of respective Cl AO and that multiplied by IF are plotted as black dot line and blue dash line respectively. The TMPs of the Cl 3p and 3s AOs are calculated by B3LYP method employing aug-cc-pVTZ basis set, into which the present instrumental momentum resolution is folded for comparison. In FIG. 5(a), it is shown that both of the EMPs for 2a$ _2 $ orbital and Cl 3p AO exhibit p-type character, but the peak maximum in EMP for Cl 3p AO shifts to lower momentum compared with that for 2a$ _2 $ orbital. Multiplied by IF, the EMP of Cl 3p AO fits that of 2a$ _2 $ orbital very well. In FIG. 5(b), we can observe that the EMP of 5b$ _2 $ orbital exhibits p-type character, whereas that of Cl 3s AO shows s-type distribution. Being modulated by IF, which is illustrated to drop to zero as the momentum decreases to the origin in the momentum region below 1.0 a.u., the EMP of Cl 3s AO then displays p-type character, reproducing that of 5b$ _2 $ orbital in shape pretty well but underestimating it in intensity. From the electron density distributions shown in the inserts of FIG. 5, we can observe that the 2a$ _2 $ orbital is a relatively pure Cl lone-pair orbital, whereas the 5b$ _2 $ orbital is slightly contributed from the C-Cl bonding electrons. This may explain the discrepancy of EMP between the Cl 3s AO multiplied with IF and the 5b$ _2 $ orbital in FIG. 5(b). These results indicate that the interference effects will greatly influence the momentum distributions of Cl lone-pair orbitals in iso-C$ _2 $H$ _2 $Cl$ _2 $ valence shell.

FIG. 5 Comparison of the EMPs for (a) 2a$ _2 $ lone-pair orbital with Cl 3p AO and (b) 5b$ _2 $ lone-pair orbital with Cl 3s AO. The XMPs and TMPs of iso-C$ _2 $H$ _2 $Cl$ _2 $ lone-pair orbitals are shown as black solid circle and red solid line respectively, the IF is denoted as olive dot dash line, and the TMPs of Cl AOs and that multiplied by IF are plotted as black dot line and blue dash line respectively
Ⅳ. CONCLUSION

We report the EMS studies on all of the iso-C$ _2 $H$ _2 $Cl$ _2 $ valence orbitals at incident energy 1.2 keV plus binding energy. The two-dimensional electron density map with respect to binding energy and azimuthal angle is measured, and the XMP of each valence orbital is obtained through deconvolution process. The TMPs are calculated by both HF and DFT-B3LYP methods, employing 6-31++G$ ^{**} $ and aug-cc-pVTZ basis sets. The comparison of TMPs indicates that the calculations employing B3LYP method and HF method with aug-cc-pVTZ basis set show almost no difference from each other. For most of the iso-C$ _2 $H$ _2 $Cl$ _2 $ valence orbitals, 6-31++G$ ^{**} $ basis set is proven to be large enough for the calculations, which fits the XMP as well as the calculations with aug-cc-pVTZ. However, for 11a$ _1 $, 7b$ _2 $ and 10a$ _1 $ orbitals, the TMPs calculated with 6-31++G$ ^{**} $ show obvious discrepancies with the XMPs, while those calculated with aug-cc-pVTZ still fit the experimental data very well. It is observed that the momentum profiles of 2a$ _2 $ and 5b$ _2 $ orbitals which belong to Cl 3p and 3s lone-pair orbitals respectively, are significantly influenced by interference effects.

Ⅴ. ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (No.11534011) and the National Key Research and Development Program of China (No.2017YFA0402300). The authors also gratefully acknowledge Professor C. E. Brion at the University of British Columbia (UBC) in Canada for giving us the HEMS programs.

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异二氯乙烯价壳层轨道电子结构的电子动量谱研究
王忆纯 , 牛珊珊 , 唐亚国 , 张钰 , 单旭 , 徐春凯 , 陈向军     
中国科学技术大学近代物理系,合肥微尺度物质科学国家研究中心,合肥 230026
摘要: 本文报道了异二氯乙烯分子价壳层轨道电子结构的电子动量谱研究.实验由一台(e,2e)电子动量谱仪在非共面对称的几何条件下开展,入射电子能量为1200 eV.实验获得了异二氯乙烯价壳层各个轨道的电离能谱和电子动量分布.采用Hartree-Fock方法和密度泛函方法结果与实验数据基本一致.研究发现,干涉效应会对2a2和5b2这两个Cl孤对电子轨道的电子动量分布产生显著影响.
关键词: 电子动量谱    价壳层轨道    孤对电子轨道    干涉效应