Electron Momentum Spectroscopy Investigation of Molecular

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An Electron Momentum Spectroscopy Investigation on Molecular Conformations of Ethanol Considering Vibrational Effects YaGuo Tang, Xu Shan, Shanshan Niu, Zhaohui Liu, Enliang Wang, Noboru Watanabe, Masakazu Yamazaki, Masahiko Takahashi, and Xiangjun Chen J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b10009 • Publication Date (Web): 20 Dec 2016 Downloaded from http://pubs.acs.org on December 23, 2016

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The Journal of Physical Chemistry

An Electron Momentum Spectroscopy Investigation on Molecular Conformations of Ethanol Considering Vibrational Effects Yaguo Tang,† Xu Shan,† Shanshan Niu,† Zhaohui Liu,† Enliang Wang,† Noboru Watanabe,‡ Masakazu Yamazaki,‡ Masahiko Takahashi,‡ and Xiangjun Chen*,†

†

Hefei National Laboratory for Physical Sciences at the Microscale and Department

of Modern Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China ‡

Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan

ABSTRACT The interpretation of experimental electron momentum distributions (EMDs) of ethanol, one of the simplest molecules having conformers, confuses researchers for years. High-level calculations of Dyson orbital EMDs by thermally averaging the gauche and trans conformers as well as molecular dynamical simulations failed to quantitatively reproduce the experiments for some of the outer valence orbitals. In this work, the valence shell electron binding energy spectrum and EMDs of ethanol are revisited by the high-sensitivity electron momentum spectrometer employing symmetric non-coplanar geometry at an incident energy of 1200 eV plus binding energy, together with a detailed analysis of the influence of vibrational motions on the EMDs for the two conformers employing a harmonic analytical quantum mechanical

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(HAQM) approach by taking into account all the vibrational modes. The significant discrepancies between theories and experiments in the previous works have now been interpreted quantitatively, indicating that the vibrational effect plays a significant role in reproducing the experimental results, not only through the low-frequency OH and CH3 torsion modes but also through other high-frequency ones. The rational explanation of experimental momentum profiles provides solid evidence that the trans conformer is slightly more stable than the gauche conformer, in accordance with the thermodynamical predictions and other experiments. The case of ethanol demonstrates the significance of considering vibrational effects when performing conformational study on flexible molecules using electron momentum spectroscopy.

1. INTRODUCTION Conformational phenomena are ubiquitous for polyatomic molecules in nature. The conformational study, including the confirmation of the existence of certain conformers and the determination of the relative stability, has attracted much interest for researchers due to the rather discrepant chemical reactivity of different conformers. Based on the fact that conformers with different geometries generally exhibit quite different electronic wavefunctions for corresponding orbitals, electron momentum spectroscopy (EMS),1-5 a robust technique for exploring the electronic structures of atoms and molecules, has been applied to this field successfully6-24 for years owing to its unique ability of imaging electron momentum distributions (EMDs) for individual molecular orbitals (MOs). The EMS technique is based on the high energy electron


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impact (e, 2e) reaction near the Bethe ridge. Within a series of approximations including Born-Oppenheimer, binary encounter, weak-coupling and plane wave impulse approximations, the triple differential cross section (TDCS) of the (e, 2e) reaction is proportional to the modulus square of the wavefunction of the ionized orbital in momentum space, i.e., electron momentum profile. Many meaningful EMS experiments have been carried out to investigate molecular conformations,6-24 and even to determine the relative abundances of conformers with the aid of theoretical simulations.16 A vital point when employing EMS on conformational study is the precise prediction of momentum profiles for each conformer in theory because conclusions are generally made through comparison between experimental and theoretical ones. Previous studies have proved that several significant factors, including electron correlation,25-27 distorted wave effects,28,29 and nuclear dynamics in the initial and final states,30-42 have to be taken into account when interpreting EMS results due to the possible invalidity of the approximations used in EMS and the complexity of polyatomic molecules. Therefore, careful treatment should be carried out to produce theoretical momentum profiles with high quality in conformational investigation through EMS. Ethanol, one of the most common and important organic molecules, has two conformers, gauche conformer of C1 symmetry and trans conformer of Cs symmetry, corresponding to the two minima of the potential energy surface about the C-C-O-H internal torsional angle.43,44 Confusion still exists for the understanding of the



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experimental momentum profiles of outer valence orbitals of ethanol in the previous EMS works.14,15,19 In the EMS study of Ning et al.,15 momentum profiles of the five bands in the outer-valence region were extracted. The theoretical calculation with 60.7/39.3 gauche/trans abundance ratio reproduced the experimental EMDs well for the second, fourth and fifth bands but failed to reproduce those for the first and third bands to a large extent. The first point one may naturally consider is whether the relative abundances adopted are correct since the EMDs for the first and third bands seem to be well interpreted using abundance ratio of 80/20.18,19 However, various experiments including microwave spectroscopy45,46, far infrared spectroscopy47 and X-ray photoelectron spectroscopy48 as well as theoretical calculations with high accuracy14 exhibit that the trans conformer is slightly more stable than the gauche one and that the relative abundances of the gauche and trans conformers are nearly 61% and 39%, respectively, considering the inherent twofold degeneracy of the gauche conformation. The 80/20 ratio is not appropriate in that it destroys the agreement for other bands dramatically and not in accordance with the thermodynamic prediction and other experimental results. The discrepancies may also be attributed to the distorted wave effect which sometimes results in turn-up in EMD at low momentum. However, the consistent EMS results at incident energies of 1200 eV and 2400 eV proved that the distorted wave effect has little influence on the momentum profiles of ethanol,15 and can be excluded from the possible reasons for the deviation. The next possible reason for the discrepancies can be the inadequate consideration of electron correlation. High-level calculation using one particle Green’s function theory in


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conjunction with the so called third-order Algebraic diagrammatic construction scheme (ADC(3))15 showed that electron correlation can be well described by the B3LYP Kohn-Sham orbitals with suitably large basis sets, and only a very limited improvement for the highest occupied molecular orbital (HOMO) was achieved when using Dyson orbitals from the ADC(3) calculations. Finally, nuclear dynamics in the initial ground and final ionized states may also be responsible for the discrepancies. Nuclear dynamics in the ground state in terms of the OH and CH3 torsions were simulated,19 and gave a feeble improvement for HOMO. Hajgato et al. proposed19 that the structural relaxation induced by the ionization process may be one of the tempting explanations for HOMO. To sum up, by taking all these factors into account, the discrepancies between experiments and theoretical calculations still exist. In this work, we performed a new EMS experiment along with theoretical calculations involving vibrational effects, to check the possible reasons of the disagreement between experimental and theoretical EMDs on both experimental and theoretical aspects. On the experimental side, the inferred momentum profiles from (e, 2e) angular distributions of TDCSs should be checked employing another independent instrument to avoid systematic errors. During the data analysis, the complication of binding energies due to molecular conformation gives rise to the difficulty of extracting accurate momentum profiles. The symmetries of individual orbitals should be checked to make sure whether using one Gaussian peak to represent two or more experimentally unresolved ionization bands in the deconvolution process is suitable. On the theoretical side, nuclear dynamics in the initial ground state, or vibrational



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effects, considering all degrees of freedom have not been examined until now. Recent investigations30-40 have already demonstrated that vibrational motions do make a noticeable influence and play important roles in explaining the substantial unexpected turn-up in the low momentum region of experimental momentum profiles for specific orbitals of polyatomic molecules. Watanabe et al.’s harmonic analytical quantum mechanical (HAQM) approach method33,34,39 provided a simple and practical way to estimate nuclear dynamics in the ground state including all degrees of freedom. It turns out that vibrational modes with extremely high frequency can also influence EMDs greatly, e.g. the effects of the v5 mode (~3000 cm-1) on 1b3g orbital for ethylene33. Our recent work on oxetane40 indicated that both the low-frequency and high-frequency vibrational modes may have a non-negligible influence on EMDs. In this paper, all vibrational modes are taken into account to perform a comprehensive analysis of vibrational effects on the two conformers of ethanol, not just the OH and CH3 torsion modes.

2. EXPERIMENTAL AND THEORETICAL BACKGROUND EMS is a coincidence experiment based on the kinematically complete (e, 2e) reaction, in which a fast incident electron is scattered by a target atom or molecule and meanwhile an electron is knocked out from the target. The conservation of energy and momentum gives the binding energy εf and the momentum p of the target orbital electron as1-5

ε f = E0 − E1 − E 2 ,

(1)


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p = p1 + p2 − p0 ,

(2)

where E0, E1, and E2 are energies, and p0, p1, and p2 are momenta of the incident and two outgoing electrons, respectively. At symmetric non-coplanar geometry, the magnitude of momentum can be expressed as 2

p=

 φ  2 ( p0 − 2 p1 cos θ ) +  2 p1 sin θ sin    ,  2  

(3)

where θ is the polar angle and ϕ is the relative azimuthal angle between the two outgoing electrons. The high-sensitivity EMS apparatus used in this experiment has been described in detail elsewhere49 and only a brief introduction is presented here. The typical energy of the incident electron is 1200 eV plus binding energy. The symmetric non-coplanar kinematics is employed, in which the ejected and scattered electrons with equal polar angles ( θ1 = θ2 = θ = 45o ) and energies ( E1 = E2 ) are analyzed by a 90º sector, 2π spherical electrostatic analyzer. The two electrons are then detected in coincidence by a position sensitive detector placed at the exit plane of the analyzer. With arriving positions of the two outgoing electrons the binding energy and magnitude of the target electron momentum can be deduced. Several modifications have been implemented. The double-half wedge-strip anode of 55 mm in diameter was replaced by a delay line anode (HEX 120 from RoentDek Handels GmbH) to fully utilize the potential of the analyzer. Moreover, the passing energy of the analyzer was decreased from 600 eV to 200 eV using retarding lenses to achieve a better energy resolution. The energy and momentum resolution of the present EMS apparatus are determined to be ~1.3 eV (full width at half maximum (FWHM)) and 7 ACS Paragon Plus Environment


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~0.2 a.u. (∆θ = 0.8º, ∆ϕ = 2.0º), respectively, by measuring Ar 3p orbital. On the theoretical aspect, within the binary encounter and plane wave impulse approximations for randomly oriented atoms or molecules the TDCS for EMS can be expressed as5

σ EMS =

d 3σ pp pp = (2π )4 1 2 f ee Σav pf i = (2π ) 4 1 2 f ee M ( p) , (4) d Ω1d Ω2 dE1 p0 p0

where fee is the e-e collision factor and Σav represents an average over initial i a sum over finial

f

and

degenerate states. M(p) is the relevant structure factor

corresponding to the momentum profile. According to Born-Oppenheimer approximation, the total wavefunction of a molecular system can be separated as a product of electronic, vibrational, and rotational wavefunctions. Ignoring rotational motions and employing the closure relation of the final vibrational eigenstates considering the limited energy resolution of current EMS apparatuses, we can simplify the relevant structure factor as33,34 M ( p ) = ∑ v pv (T ) ∫ χ iv (Q ) ρ f ( p; Q ) dQ , (5) 2

where pv (T ) is the population of the eigenstate v in the ground state at temperature T and χ iv (Q ) is the vibrational wavefunction. ρ f ( p; Q ) is the spherically averaged EMD at a given geometry Q, which reads

ρ f ( p; Q )=

1 2 S f (Q ) ∫ ϕ f ( p; Q ) d Ω p , (6) 4π

where Sf (Q ) is the pole strength or spectroscopic factor and ϕ f ( p; Q ) is the normalized Dyson orbital. If we ignore the change of ρ f ( p; Q ) due to vibrational displacements, in other words, vibrational effects are neglected, the relevant structure factor is no other than the spherically averaged EMD at equilibrium geometry, 8 ACS Paragon Plus Environment

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indicating the capability of EMS probing MOs in momentum space. Watanabe et al.’s HAQM method33,34 makes it available to estimate vibrational effects from every vibrational mode on momentum profiles and to understand which kind of and how vibrational motions influence EMDs. In this method, the rigid-rotator harmonic oscillator (RRHO) approximation is adopted, which can be expressed as

χiv (Q) = ∏ L ξv (QL ) ,

(7)

L

where ξ vL (QL ) is the harmonic function describing molecular vibrations. Then vibrational effects on momentum profiles can be written as a sum of the contribution of each vibrational mode if the cross-terms between vibrational modes are neglected:33,34 M ( p) = ρ f ( p; Q0 ) + ∑ L ∆M L ( p) = ρ f ( p; Q0 ) + ∑ L

(∑

2

vL

pvL (T ) ∫ ξ vL ( QL ) ρf ( p; Q0 + QL qˆL )dQL − ρf ( p; Q0 )

) , (8)

where ∆ M L ( p ) is the contribution to vibrational effects from the L-th normal mode. QL is the displacement from the equilibrium geometry Q0, and qˆ L is the unit vector along the normal coordinate. On the basis of this equation and high-level ab initio calculations, vibrational effects can be evaluated involving all vibrational degrees of freedom. Technically, the structural parameters of the two conformers in the ground state are optimized by density functional theory (DFT) along with the B3LYP functional50,51 and Dunning’s aug-cc-pVTZ basis set52,53 using Gaussian 03 program.54 The B3LYP geometries are good enough compared with experimental data as displayed by Morini et al.14 Then the vibrational frequencies (Table 1 and 2) and



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normal coordinates of each conformer are computed at the B3LYP/aug-cc-pVTZ level of theory, where the computed frequencies are in good agreement with experimental results44 if the scaling factor of 0.968 from ref 55 is employed. In particular, the torsional normal modes from B3LYP/aug-cc-pVTZ appear as the combinations of the two torsional internal coordinates, labeled as v20 and v21 for both conformers. The OH torsion is dominant for the v20 mode, while the v21 mode is mainly the CH3 torsion. The next step is to fit ρ f ( p; Q0 + QL qˆ L ) as a function of QL employing fourth-order polynomial function to compute the contributions of each mode. In order to do this,

ρ f ( p; Q0 + QL qˆ L ) is calculated by B3LYP/aug-cc-pVTZ where the displacement QL 2

is chosen so that ξv (QL ) / ξv (0) L L

2

= 3/4, 1/2, 1/4, 1/8, and 1/16, respectively. Here

the target Kohn-Sham approximation56 is adopted and the pole strengths are assumed to be constant free of vibrational variations for all valence orbitals and to be unity for outer valence orbitals, which is approximately valid in general. In fact, the ADC(3) calculations14 exhibited that Kohn-Sham orbitals are good approximations of Dyson orbitals and the pole strengths of outer-valence orbitals of ethanol are nearly the same (0.90~0.92) for different orbitals and conformers. Finally the theoretical momentum profiles considering vibrational effects for each conformer are calculated according to eq 8 using the Boltzmann distributions of vibrational eigenstates at room temperature (298 K). Actually, the temperature of the sample in the reaction center is hard to be determined since it may cool down through expansion. However, on the one hand, the relative abundance would not change by more than ~2% if the gas was cooled to even 200 K as the two conformers are nearly isoenergetic. On the other hand, the results of


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vibrational effects vary quite a little when a lower temperature, like 270 K, is employed. Noting that the temperature will not decrease too much for a normal diffusive gas beam, the temperature lowering effect is ignored. The relative abundances of 61% and 39% for the gauche and trans conformers are adopted when computing thermally averaged momentum profiles.

3. RESULTS AND DISCUSSION A. Binding energy spectra The B3LYP/aug-cc-pVTZ theory gives the electronic configurations of ethanol as

(core)6 (4a)2 (5a)2 (6a)2 (7a)2 (8a)2 (9a)2 (10a)2 (11a)2 (12a)2 (13a)2 for the gauche conformer and

(core)6 (4a ')2 (5a ')2 (6a ')2 (7a ')2 (1a")2 (8a ')2 (9a ')2 (2a")2 (10a)2 (3a")2 for the trans one, respectively. The two-dimensional electron density map (2D map) of binding energy and relative azimuthal angle of ethanol in our experiment is displayed in Figure 1(a), from which the symmetries of orbitals can be clearly recognized. The total BES obtained by integrating the 2D map over all relative azimuthal angles is shown in Figure 1(b), which is consistent with the previous work15 but with better statistics. The available binding energy region in our measurement mainly covers the whole outer-valence orbitals and two inner-valence ones. Careful analysis must be taken to obtain meaningful momentum profiles as a result of the inherent complication of ionization transitions in the case of the



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conformationally versatile ethanol molecule. The limited energy resolution of 1.3 eV makes it difficult to resolve ionization bands of all orbitals considering also the overlap due to the two conformers. Efforts are made to resolve separate orbital sets from the angle analysis of experimental ionization intensities. Five resolvable bands (A-E) with remarkable different orbital symmetries in the outer valence region and two complete and independent inner valence bands can be clearly recognized from the BES and 2D map. To give a quantitative analysis of those bands, a deconvolution process employing 9 Gaussian peaks is carried out to infer momentum profiles for particular orbital sets with the help of ionization potentials from high resolution photoelectron spectra (PES)57,58 and high-level theoretical calculations15 shown in Table 3. The peak positions and widths of Gaussian functions mainly come from the PES data, with small adjustments for compensating the asymmetric Franck-Condon envelops and considering molecular conformations and the instrumental energy resolution. In order to have an intuitive sight of how MOs of the two conformers are grouped to contribute to the different ionization bands, a diagram is drawn in Figure 2 to show the ionization potentials of different MOs from the ADC(3) calculation.15 In the outer valence region, band A (peak 1) at ~ 10.7 eV corresponds to HOMO {13a, 3a"}, whose momentum distribution can be easily recognized as s-p type character in the 2D map. Band B (peak 2) at ~ 12.1 eV stands for the next orbitals of the two conformers {12a, 10a'}. Since the momentum profiles of 11a+2a" and 10a+9a' have similar shapes with very high intensity at low momentum while that of 8a' orbital


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exhibits typical p type character, we adopt two Gaussian peaks (peak 3 and 4) at 13.5 and 14.4 eV to extract the momentum profile of band C, corresponding to the orbital set {11a, 2a", 10a, 9a', 8a'}, where peak 4 corresponds to the 8a' orbital alone. Analogically, another two Gaussian peaks (peak 5 and 6) at 15.5 and 16.4 eV are used to obtain {9a, 8a, 1a"} momentum profile, referring to band D. Peak 6 is necessary since the shape of momentum profile of the 1a" orbital, whose ionization energy is ~ 0.5 eV larger than that of the 8a orbital, differs from those of the 9a and 8a orbitals. Band E (peak 7), representing {7a, 7a'}, contributes to the shoulder at ~17.5 eV of BES. Band F and G, corresponding to the completely resolved peaks at 20.7 eV and 24.2 eV, characterize {6a, 6a'} and {5a, 5a'}, respectively. Through plotting of the fitted area of the 9 Gaussian peaks in the BES at different azimuthal angles as a function of target electron momentum p (i.e. azimuthal angle), the momentum profiles of the resolvable 7 bands in the valence region can be achieved. Note that momentum distributions for peak 3, 4, 5, or 6 alone is unreliable due to the severe peak overlaps.

B. Momentum profiles Experimental momentum profiles for bands A~G obtained from the deconvolution process described above are presented in Figure 3~7, in which the error bars represents the overall error of deconvolution and statistical uncertainties. The consistency with the previous EMS work15 confirms the reliability of the present experimental outcome. To compare with observed results, the momentum resolution of ∆θ = 0.8º, ∆ϕ = 2.0º is folded in theoretical momentum profiles employing the



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Gaussian weighted planar grid method.59 Experimental data are normalized to theory, in which the global normalization factor comes from the comparison of the sum of momentum profiles of all outer valence orbitals of ethanol assuming that the one-particle picture of ionization is valid and pole strengths are all identical to 1 which is approximately true according to the ADC(3) calculation. The summed momentum profile of all the outer valence orbitals is presented in Figure 3, together with theoretical simulations. A distinct underestimation at low momentum is shown for the associated equilibrium geometry calculation (blue dashed line), which can be accounted for by vibrational effects unambiguously. On one hand, the gauche and trans conformers have similar momentum distributions either considering vibrational effects or using the equilibrium molecular structure. On the other hand, theoretical calculations at equilibrium geometry predict lower intensity at small momentum noticeably for both conformers. Therefore, the fairly good agreement between theory (red solid line) and experiment (solid circle) for total outer valence orbitals has been achieved when vibrational effects are comprehensively taken into account, exhibiting the significance of nuclear dynamics in the ground state. In the following, a detailed analysis on the relevant ionization bands is performed to reveal how vibrational motions affect EMDs and which modes are responsible for the enhancement of the intensity at low momentum. For the HOMO (13a of gauche and 3a" of trans), the experimental momentum profile of band A exhibits much higher intensity than the equilibrium-geometry B3LYP prediction at small momentum taking account of the 61%/39% thermal


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abundances of the gauche and trans conformers, as shown in Figure 4(a), which is in line with the previous EMS works. The large discrepancy at small momentum is obviously decreased with a comprehensive consideration of vibrational effects. It mainly comes from the improvement of intensity at small momentum of the p-type 3a" orbital of trans ethanol. The 3a" orbital, which consists of oxygen 2p lone pair and CH2 bonds, is expected to have zero intensity at zero momentum at equilibrium geometry due to its anti-symmetry character about the CCO plane, keeping in mind that the value of the momentum-space wavefunction at p = 0 reads

ϕ f ( p; Q) p=0 = ( 2π )

−3/2

∫ϕ

f

(r; Q)dr for its Dirac-Fourier transform relation of the

corresponding position space wavefunction. The vibrational modes involving the OH and CH3 torsions (v20, v21), CH2 antisymmetric stretch (v15), and CH2 rock (v18) break the symmetry (Figure 4(d)) and give a positive contribution to the 3a" momentum profile at zero momentum (Figure 4(c)). For the sp-type 13a orbital of gauche ethanol, the contributions of vibrational modes are complicated and nearly smeared out, giving a slight positive contribution on balance (Figure 4(b)). As a result, the deformation of molecular structure by vibrational motions makes a positive modification on the distribution curve with equilibrium geometry at low momentum, which accounts for the discrepancy between experiment and theory principally. The imperfect description of electron correlation for the B3LYP method may be the origin of the remaining deviation since a higher intensity at near zero momentum than that of B3LYP was achieved by the ADC(3) calculation15 which is expected to produce more accurate Dyson orbitals. If we treat the electron correlation and vibrational effects as a first



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order approximation, the total effects can explain the large turn-up of HOMO rationally. Another possible reason is the ultrafast reorganization of the molecular geometry with a sudden removal of an electron as proposed by Hajgato et al.19 It is worthwhile to compare our result with Hajgato et al.’s thermally averaged momentum profile of HOMO over exceedingly large sets of nuclear configurations in terms of different OH and CH3 torsional angles.19 The HAQM result suggests that the torsional vibrations decrease the intensity of momentum profile at zero momentum by 0.0036 for the 13a orbital and increase that by 0.0113 for the 3a" orbital. While the increase of intensity of the 3a" orbital at p ~ 0 through the torsional modes can be easily understood as analyzed above, readers may ask why there is a decrease of intensity for the 13a orbital. Ning et al.15 demonstrated the asymmetric change of intensity at zero momentum along the OH torsional angle for the 13a orbital which reaches a maximum intensity at 90º. It means that the intensity at p ~ 0 will decrease rapidly when the torsional angle moves towards 0 from the equilibrium geometry (~ 62º), while first rises then falls towards 120º. The OH torsional motion will definitely reduce the electron density at p ~ 0 considering the large-amplitude variations. Consequently, the intensity of HOMO at zero momentum will be improved by 0.0022 if the torsional modes are only involved in the HAQM method taking the 61/39 abundance ratio into account. This agrees with Hajgato et al.’s simulations quite well, proving the effectiveness of the HAQM method for the torsional modes which may suffer from anharmonicity due to its large vibrational amplitude when estimating vibrational effects on EMDs.


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Likewise, vibrational motions also have a non-negligible effect on the next orbital of both conformers as displayed in Figure 5(a). Contrary to HOMO, the 12a orbital of the gauche conformer is calculated to show a p-type momentum profile with a maximum at p ~ 0.8 a.u., while the 10a' exhibits an obviously different s-p type momentum distribution. The thermally averaged theoretical momentum distribution at equilibrium geometry underestimates the intensity of band B at p = 0.4~1.0 a.u. noticeably. The discrepancy can be well interpreted by vibrational effects. The intensity in this region is enhanced for both conformers when vibrational motions of all modes are considered. It is interesting that nuclear variations including the OH and CH3 torsions increase the intensity of the momentum profile of the 12a orbital at p < 0.4 a.u. a lot (Figure 5(b)), while decrease that of 10a' of the trans conformer much (Figure 5(c)), and lead to only a small reduction of intensity at low momentum. For bands C and D, the conformation effect on binding energies makes it a little complicated to analyze. Band C is assigned to the orbital sets {11a, 10a, 2a", 9a', 8a'} while band D is assigned to orbital sets {9a, 8a, 1a"}, which are supported by the momentum profiles as shown in Figure 6(a-c). Experimental momentum profile of band C exhibits a much higher intensity at low momentum than the equilibrium geometry calculation. Theoretical calculations considering vibrational effects generally reproduce the experiment well, with a small underestimation and overestimation of intensities at low momentum for bands C and D, respectively. We attribute this small discrepancy to the deconvolution uncertainties due to the overlap of the two bands based on the fact that the HAQM prediction for the sum of bands C



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and D agrees with the measurement perfectly (Figure 6(c)). This indicates that the EMDs of these orbitals are greatly influenced by the vibrational effects to have a higher intensity at low momentum, which accounts for the severe underestimation of the equilibrium geometry simulation on the observed distribution of band C. In Figure 6(d1-i1), we compare the theoretical momentum profiles for individual orbitals corresponding to bands C and D with and without vibrational effects. The contributions of each vibrational mode are also plotted. It should be noted that the 11a and 10a orbitals of gauche ethanol, which have very close ionization potentials, are coupled seriously by the v2, v4, v9, v14 modes. The mixture of momentum profiles makes the fourth order polynomial fitting of ρ f ( p; Q0 + QL qˆ L ) as a function of QL not suitable for separate orbitals, and only a sum of the two orbitals is given here. It is the same case for the 9a and 8a orbitals by the v12 and v20 modes. Generally, calculations with vibrational effects predict higher intensities near zero momentum for all, especially for the 2a" and 1a" orbitals of trans ethanol. The 2a" orbital, consisted of O 2p lone pair and CH bonds and showing an antisymmetric character about the CCO plane at equilibrium geometry (Figure 2), is expected to exhibit typical p type character. The torsional modes (v20, v21) understandably give a positive contribution as they destroy the symmetry seriously. The situation is the same for the 1a" orbital which is composed of CH bonds. The contributions of vibrational modes for other orbitals are complex and cannot be understood intuitively. Nevertheless, their influences are also significant for well reproducing experimental results. For band E (Figure 7(a)), the inferred momentum profile is well interpreted by


Page 18 of 44

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the sum of 7a and 7a' orbitals. The momentum profile of either conformer considering vibrational motions, including the torsional modes and other modes of higher frequency, exhibits higher intensity in the region of less than 1.0 a.u. but a similar shape with that of equilibrium geometry. It should be further noted that significant differences exist in the momentum profiles for every outer valence orbital for the gauche and trans conformers. The wonderful agreement between theory and experiment for the momentum profiles of bands B, C+D, and E, not only indicates the necessity of considering vibrational effects, but also confirms the correction of the 61/39 relative abundance ratio. That is to say, the conclusion that the trans conformer is more stable than the gauche stable is also drawn by the EMS results. In the inner valence region, momentum profiles of the two conformers are predicted to show the same shape and vibrational effects are ignorable for all the relevant orbitals. Theoretical calculations show a good agreement with experiment when pole strengths of 0.87 and 0.76 for the {6a, 6a'} and {5a, 5a'} orbitals respectively are taking into account (Figure 8(a-b)). The pole strength of 0.87 for {6a, 6a'} is in line with the value of 0.90 reported by Ning et al..15 The pole strength of 0.76 for {5a, 5a'} is a higher than Ning et al.’s value of 0.64, while agrees with that of ADC(3) predictions,15 0.70 / 0.91 = 0.77 and 0.67 / 0.91 = 0.74, for the 5a and 5a' orbitals, respectively, considering 0.91 pole strength of HOMO.

4. CONCLUSIONS



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 44

The electron momentum profiles of valence orbitals of ethanol have been revisited by experiment using a newly conducted EMS as well as the theoretical simulations

involving

conformational

and

vibrational

effects.

The

B3LYP/aug-cc-pVTZ calculations taking into account all the vibrational modes through HAQM approach have quantitatively reproduced the experimental results well, except for the HOMO where observable underestimation still remains, although the agreement between the theory and the experiment has sufficiently been improved. The results unambiguously show that the substantial deviations between the theoretical calculations and measurements in the previous works for the ionization bands of the outer valence orbitals, especially HOMO, are attributed to the vibrational effects. The contributions of individual vibrational modes of the gauche and trans conformers are also analyzed comprehensively using the HAQM approach, which shows that besides the torsional modes, various vibrational modes of high or low frequency influence all outer valence orbitals more or less. In particular, the orbitals of the trans conformer with a" symmetry are affected by the torsional and other modes and exhibit a reasonable turn-up on the p-type momentum distributions at low momentum. Meanwhile, the rational explanation of experimental momentum profiles provides solid evidence that the trans conformer is slightly more stable than the gauche conformer, in accordance with thermodynamical predictions and other experiments. The case of ethanol demonstrates the significance of considering vibrational effects when performing conformational study on flexible molecules using EMS. Finally, it is worthwhile to note that by adopting the supersonic molecular beam


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in the future it is possible to perform the experiments at temperature near 0 K. At this temperature, the most stable conformer of ethanol will be dominant. Therefore, one can further confirm the relative stability of the two conformers and can extract the electron momentum profiles for each conformer. The vibrational effects on the individual conformers can then be demonstrated more clearly.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. *Telephone: +86-551-63601170 Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENT This work was supported by the National Natural Science Foundation of China (Grant Nos. 11534011, 11327404). The authors also gratefully acknowledge Professor C. E. Brion from the University of British Columbia (UBC) in Canada for giving us the HEMS programs.

REFERENCE (1) Brion, C. E. Looking at Orbitals in the Laboratory: The Experimental Investigation of Molecular Wavefunctions and Binding Energies by Electron



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90, 1007-1023. (53) Kendall, R. A.; Dunning, T. H.; Harrison, R. J. Electron Affinities of the First-Row Atoms Revisited. Systematic Basis Sets and Wave Functions. J. Chem. Phys. 1992, 96, 6796-6806. (54) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Rob, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A..; Vreven, T.; Kudin, K. N.; Burant, J. C., et al. Gaussian 03. Gaussian, Inc.: Wallingford, CT, 2003. (55) Fábri, C.; Szidarovszky, T.; Magyarfalvi, G.; Tarczay, G. Gas-Phase and Ar-Matrix SQM Scaling Factors for Various DFT Functionals with Basis Sets Including Polarization and Diffuse Functions. J. Phys. Chem. A 2011, 115, 4640−4649. (56) Duffy, P.; Chong, D. P.; Casida, M. E.; Salahub, D. R. Assessment of Kohn-Sham Density-Functional Orbitals as Approximate Dyson Orbitals for the Calculation of Electron-Momentum-Spectroscopy Scattering Cross Sections. Phys. Rev. A 1994, 50, 4707-4728. (57) von Niessen, W.; Bieri, G.; Åsbrink, L. 30.4-nm He (II) Photoelectron Spectra of Organic Molecules. J. Electron Spectrosc. Relat. Phenom. 1980, 21, 175-191. (58) Kimura, K.; Katsumata, S.; Achiba, Y.; Yamazaki, T.; Iwata, S. Handbook of HeI Photoelectron Spectra of Fundamental Organic Molecules. Halsted Press: New York, 1981. (59) Duffy, P.; Casida, M. E.; Brion, C. E.; Chong, D. P. Assessment of Gaussian-Weighted

Angular

Resolution

Functions

in


the

Comparison

of


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Quantum-Mechanically

Calculated

Electron

Momentum

Experiment. Chem. Phys. 1992, 159, 347-363.


Page 30 of 44

Distributions

with

Page 31 of 44

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Tables -1 Table 1. Vibrational frequencies (cm ) for gauche ethanol

a

mode

Main description a

Cal.

Exp.a

1

OH stretch

3812

3662

2

CH3 antisymmetric stretch

3098

2994

3


3084

2987

4


3063

2972

5

CH3 symmetric stretch

3018

2936

6

CH2 symmetric stretch

2988

2912

7

CH2 symmetric deformation

1517

1493

8

CH3 antisymmetric deformation

1493

1465

9

CH3 antisymmetric deformation

1488

1460

10

CH3 symmetric deformation

1415

1394

11

CH2 wag

1403

1373

12

COH bend

1368

1342

13

CH2 twist

1279

1249

14

CH2 rock/CH3 rock

1132

1117

15

CO stretch

1067

1066

16

CH3 rock/COH bend

1057

1058

17

CC stretch

882

879

18

CH3 rock

805

803

19

CCO bend

420

420

20

OH torsion

269

243

21

CH3 torsion

257

274

Reference 44.



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Table 2. Vibrational frequencies (cm-1) for trans ethanol

a

Mode

Main description a

Cal.

Exp.a

1

OH stretch (A')

3828

3676

2

CH3 antisymmetric stretch (A')

3098

2992

3

CH3 symmetric stretch (A')

3032

2922

4

CH2 symmetric stretch (A')

2980

2888

5

CH2 symmetric deformation (A')

1526

1500

6

CH3 antisymmetric deformation (A')

1500

1480

7

CH2 wag (A')

1447

1450

8

CH3 symmetric deformation (A')

1405

1367

9

COH bend (A')

1264

1241

10

CO stretch (A')

1096

1090

11

CC stretch (A')

1028

1027

12

CH3 rock (A')

895

892

13

CCO bend (A')

418

418

14

CH3 antisymmetric stretch (A")

3101

2987

15

CH2 antisymmetric stretch (A")

3004

2901

16

CH3 antisymmetric deformation (A")

1483

1455

17

CH2 twist (A")

1299

1275

18

CH2 rock (A")

1179

1166

19

CH3 rock (A")

822

801

20

OH torsion (A")

276

203

21

CH3 torsion (A")

233

244

Reference 44.


Page 32 of 44

Page 33 of 44

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Table 3. Ionization potentials of ethanol. The values in brackets are pole strengths, which are assumed to be 1 for the outer valence orbitals in EMS MO

He II PES a

He I PES b

EMS c

EMS d

A

13a/3a"

10.7

10.64

10.6(1.0)

B

12a/10a'

12.1

12.18

12.1(1.0)

11a/2a"

13.3

13.21

13.4(1.0)

10a/9a'

13.9

13.86

8a'

(14.5)

14.5

14.4(1.0)

16.0

15.85

15.9(1.0)

Band

C

9a D

8a 1a"

ADC(3)/cc-pVDZ++ c gauche

trans

10.7(1.0)

10.86(0.91)

10.89(0.91)

12.1(1.0)

12.28(0.92)

12.39(0.91)

13.51(0.92)

13.37(0.92)

13.87(0.91)

13.77(0.92)

13.5(1.0) 14.4(1.0) 15.5(1.0)

14.43(0.91) 15.34(0.91) 15.97(0.91)

16.4(1.0)

E

7a/7a'

17.4

F

6a/6a'

20.7

17.35

17.5(1.0)

17.4(1.0)

20.8(0.90)

20.7(0.87)

16.53(0.90) 17.51(0.90)

17.90(0.90)

21.20(0.85)

20.80(0.85)

23.86(0.03) 23.33(0.05) G

5a/5a'

24.2

24.2(0.64)

24.2(0.76)

23.35(0.08)

24.39(0.25)

24.48(0.14)

24.55(0.27)

24.60(0.02)

24.64(0.18)

24.63(0.26) 24.77(0.09) a

Reference 56. Reference 57. Reference 15. Present work. b

c

d



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure Captions Figure1. (a) Two-dimensional energy and relative azimuthal angle spectrum of ethanol. (b) Binding energy spectrum of ethanol. The dotted lines represent the nine Gaussian peaks corresponding to individual molecular orbital sets and the solid line is the sum. Figure 2. Diagram of molecular orbitals of the two conformers of ethanol. The orbital maps are plotted at the contour of 0.05, with different colors representing opposite phases. Ionization potentials are from the ADC(3) calculation.15 The curves above the ionization potential lines are theoretical momentum profiles in the momentum region of 0 ~ 3.5 a.u.by B3LYP/aug-cc-pVTZ. Figure 3. The sum of electron momentum profiles of outer valence orbitals of ethanol. Equilib. stands for the calculation at equilibrium geometry, and vib. means the computation involving vibrational effects. Figure 4. Electron momentum profiles of Band A. (a) Experimental momentum profiles with theoretical ones considering conformational and vibrational effects. (b) Contributions from each vibrational mode to the momentum profile of the 13a orbital of gauche ethanol. (c) Contributions from each vibrational mode to the momentum profile of the 3a" orbital of trans ethanol with a position-space orbital map at equilibrium geometry inside. (d) Nuclear displacement vectors of selected vibrational modes in which the red sphere represents the oxygen atom, and orbital maps of the 3a" orbital of trans ethanol distorted along those modes 2

2

ξv (QL ) / ξv (0) = 1/ 4 . The orbital maps are plotted at a contour of 0.05, with different L

L

colors representing opposite phases. Figure 5. Electron momentum profiles of Band B. (a) Experimental momentum profiles with


Page 34 of 44

Page 35 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


theoretical ones considering conformational and vibrational effects. (b) Contributions from each vibrational mode to the momentum profile of the 12a orbital of gauche ethanol. (c) Contributions from each vibrational mode to the momentum profile of the 10a' orbital of trans ethanol. Figure 6. Experimental momentum profiles with theoretical ones considering conformational and vibrational effects for band (a) C, (b) D and (c) C+D, together with theoretical momentum profiles at equilibrium geometry and considering vibrational effects for (d1) 11a+10a, (e1) 2a", (f1) 9a', (g1) 8a', (h1) 9a+8a and (i1) 1a" orbitals as well as contributions from each vibrational mode to the momentum profiles of these orbital (d2-i2). Note that the momentum resolution is only folded in theoretical momentum profiles in (a-c). Figure 7. Electron momentum profiles of Band E. (a) Experimental momentum profiles with theoretical ones considering conformational and vibrational effects. (b) Contributions from each vibrational mode to the momentum profile of the 7a orbital of gauche ethanol. (c) Contributions from each vibrational mode to the momentum profile of the 7a' orbital of trans ethanol. Figure 8. Experimental momentum profiles with theoretical ones considering conformational and vibrational effects for (a) band F and (b) band G in the inner valence region.


Page 36 of 44

1.000

40

(a)

2.078 4.317

20

8.970 18.64

0

38.72 80.45

-20

167.2 347.3

-40

721.6 1175

10

15

1 20.0k

Relative Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Relative Azimuthal Angle (degree)


3 4 5 6 7

25

8

30

9

Ethanol

C

G

D

15.0k 10.0k

2

(b)

20

B E

A

F

5.0k 0.0 10

15

20

25

Binding Energy (eV)

ACS Paragon Plus Environment

30

Page 37 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Gauche

10

Hf(eV)

Trans

13a

3a"

12a 11a 10a 9a 8a

10a' 2a" 9a' 8a'

15

1a"

7a

7a' 20

6a'

6a

5a

25

5a'



0.6

Band A+B+C+D+E 0.61×gauche+0.39×trans vib. 0.61×gauche vib. 0.39×trans vib. 0.61×gauche+0.39×trans equilib. 0.61×gauche equilib. 0.39×trans equilib.

0.5

Relative Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Page 38 of 44

0.4 0.3 0.2 0.1 0.0 0.0

0.5

1.0

1.5

2.0

2.5

Momentum (a.u.)


3.0

3.5

Page 39 of 44

0.07

0.008

(a)

Band A 0.6113a+0.393a" vib. 0.6113a vib. 0.393a" vib. 0.6113a+0.393a" equilib. 0.6113a equilib. 0.393a" equilib.

Relative Intensity

0.05 0.04 0.03

Contributions of vibrational modes v6 v10

0.004

v12

v14

v19

v20

0.002

v21 sum of other modes total

0.000

0.02

-0.002

0.01 0.00 0.0

13a gauche ethanol

(b)

0.006

Intensity

0.06

0.5

1.0

1.5

2.0

2.5

3.0

3.5

-0.004 0.0

0.5

1.0

Momentum (a.u.) 0.020

(c)

1.5

2.0

2.5

3.0

Momentum (a.u.)

(d)

3a" trans ethanol Contributions of vibrational modes v15

0.015

v18

Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


v20

0.010

v21

v15

sum of other modes total

0.005

v18

0.000 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Momentum (a.u.)


v20

v21

3.5


0.10

(a)

Band B 0.6112a+0.3910a' vib. 0.6112a vib. 0.3910a' vib. 0.6112a+0.3910a' equilib. 0.6112a equilib. 0.3910a' equilib.

Relative Intensity

0.08

0.06

0.04

0.02

0.00 0.0 0.030

0.5

1.0

(b)

0.025

1.5

2.0

3.0

3.5

Contributions of vibrational modes v4 v18 v20

Intensity

2.5

12a gauche ethanol

0.020

v21


0.015 0.010 0.005 0.000 0.0 0.02

0.5

1.0

1.5

2.0

2.5

3.0

3.5

(c)

0.00

Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 44

10a' trans ethanol

-0.02


-0.04


-0.06

-0.08 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Momentum (a.u.)


3.5

Page 41 of 44

0.40 Band C 0.61(11a+10a) +0.39(2a"+9a'+8a') vib. 0.61(11a+10a) vib. 0.39(2a"+9a'+8a') vib. 0.61(11a+10a) +0.39(2a"+9a'+8a') equilib. 0.61(11a+10a) equilib. 0.39(2a"+9a'+8a') equilib.

Relative Intensity

0.16

0.12

0.08

0.16

(b)

Band D 0.61(9a+8a)+0.391a" vib. 0.61(9a+8a) vib. 0.391a" vib. 0.61(9a+8a)+0.391a" equilib. 0.61(9a+8a) equilib. 0.391a" equilib.

0.12

0.08

0.35

0.04

0.04

(c)

Band C+D 0.61×gauche+0.39×trans vib. 0.61×gauche vib. 0.39×trans vib. 0.61×gauche+0.39×trans equilib. 0.61×gauche vib. 0.39×trans vib.

0.30

Relative Intensity

(a)

Relative Intensity

0.20

0.25 0.20 0.15 0.10 0.05

0.00 0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00 0.0

3.5

0.5

1.0


0.09

gauche ethanol 11a+10a vib. 11a+10a equilib. 11a equilib. 10a equilib.

(e1)

2.5

3.0

0.00 0.0

3.5

0.5

1.0

0.10

0.07

1.5

2.0

2.5

3.0

3.5

4.0

Momentum (a.u.)

2a" trans ethanol equilib. vib.

0.08

(f1)

9a' trans ethanol equilib. vib.

0.08

0.06

Intensity

Intensity

0.12

2.0

0.08

Intensity

(d1)

1.5

Momentum (a.u.)

0.10

0.16

0.05 0.04

0.06

0.04

0.03

0.04

0.02

0.02

0.01

(d2)

2.0

2.5

3.0

0.00 0.0

3.5

0.04


0.010

1.0

1.5

2.0

2.5

3.0

0.00 0.0

3.5


0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.01


0.24

0.5

1.0

1.5

(h1)

2.0

2.5

3.0

-0.03 0.0

3.5

v11

v16

0.12

0.5

1.0

1.5

2.0

2.5

3.0

3.5

3.0

3.5

Momentum (a.u.)

0.20

(i1)

gauche ethanol 9a+8a vib. 8a+8a equilib. 9a equilib. 8a equilib.

0.16

0.04

3.5


0.20

Intensity

0.06

3.0


-0.01

v9

Momentum (a.u.)

8a' trans ethanol equilib. vib.

2.5

9a' trans ethanol

-0.02

Momentum (a.u.)

(g1)

2.0

0.00

v21

0.00

0.08

1.5

Momentum (a.u.)

0.01

v20

0.02

-0.01 0.0

1.0

(f2)


0.5

0.02

2a" trans ethanol

v20

0.000

Intensity

(e2)

0.03

v21

0.005

-0.005 0.0

0.5

Momentum (a.u.)

11a+10a gauche ethanol

0.015

Intensity

1.5

Momentum (a.u.)

Intensity

1.0

trans ethanol 1a" vib. 1a" equilib.

0.16

0.12

Intensity

0.020

0.5

Intensity

0.00 0.0

0.08

0.08 0.02 0.04

0.04

0.5

1.0

1.5

2.0

2.5

3.0

0.00 0.0

3.5

0.5

1.0

Momentum (a.u.)

(g2)

8a' trans ethanol

0.02

0.02

0.01

2.0

2.5

3.0

0.00 0.0

3.5

0.5

1.0

v9

v6

v8

v10


0.01

1.5

2.0

2.5

Momentum (a.u.)

9a+8a gauche ethanol Contributions of vibrational modes v7 v14

(h2)

Contributions of vibrational modes v2 v7 Intensity

0.03

1.5

Momentum (a.u.)

v16

v17

v20

v21

0.02

Intensity

0.00 0.0

Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


sum of other modes total 0.00

1a" trans ethanol

(i2)


0.01


0.00

0.00

-0.01 0.0

0.5

1.0

1.5

2.0

Momentum (a.u.)

2.5

3.0

3.5

-0.01 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Momentum (a.u.)


-0.01 0.0

0.5

1.0

1.5

2.0

Momentum (a.u.)

2.5

3.0

3.5


0.12

(a)

Band E 0.617a+0.397a' vib. 0.617a vib. 0.397a' vib. 0.617a+0.397a' equilib. 0.617a equilib. 0.397a' equilib.

Relative Intensity

0.10 0.08 0.06 0.04 0.02 0.00 0.0 0.012 0.010

0.5

1.0

(b)

1.5

v15

0.006

Intensity

2.0

2.5

3.0

3.5

7a gauche confomer Contributions of vibrational modes v6 v7

0.008

v20

v21

0.004


0.002 0.000 -0.002 0.0 0.012

0.5

1.0

(c)

1.5

2.0

2.5

3.0

3.5

7a' trans confomer Contributions of vibrational modes v11 v13

0.008

v15 Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 44

v20

v21

0.004

sum of other modes total 0.000

-0.004 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Momentum (a.u.)


3.5

Page 43 of 44

0.14 0.12

(a)

Band F 0.616a+0.396a' vib. 0.87 0.616a vib. 0.87 0.396a' vib. 0.87 0.616a+0.396a' equilib. 0.87 0.616a equilib. 0.87 0.396a' equilib. 0.87

Relative Intensity

0.10 0.08 0.06 0.04 0.02 0.00 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5


(b)

Band G 0.615a+0.395a' vib. 0.76 0.615a vib. 0.76 0.395a' vib. 0.76 0.615a+0.395a' equilib. 0.76 0.615a equilib. 0.76 0.395a' equilib. 0.76

0.30

Relative Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


0.25 0.20 0.15 0.10 0.05 0.00 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Momentum (a.u.)



0.07

HOMO Equilibrium geometry Vibrational effects

0.06

Relative Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

0.05 0.04 0.03

Gauche 13a 61%

0.02

Trans 3a" 39%

0.01 0.00 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Momentum (a.u.)


3.5

Page 44 of 44

Electron Momentum Spectroscopy Investigation of Molecular

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