Photoelectron and Electron Momentum Spectroscopy of

Article pubs.acs.org/JPCA

Photoelectron and Electron Momentum Spectroscopy of Tetrahydrofuran from a Molecular Dynamical Perspective S. H. Reza Shojaei, Filippo Morini, and Michael S. Deleuze* Research Group of Theoretical Chemistry and Molecular Modelling, Hasselt University, Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium ABSTRACT: The results of experimental studies of the valence electronic structure of tetrahydrofuran employing He I photoelectron spectroscopy as well as Electron Momentum Spectroscopy (EMS) have been reinterpreted on the basis of Molecular Dynamical simulations employing the classical MM3 force field and large-scale quantum mechanical simulations employing Born− Oppenheimer Molecular Dynamics in conjunction with the dispersion corrected ωB97XD exchange-correlation functional. Analysis of the produced atomic trajectories demonstrates the importance of thermal deviations from the lowest energy path for pseudorotation, in the form of considerable variations of the ringpuckering amplitude. These deviations are found to have a significant influence on several outer-valence electron momentum distributions, as well as on the He I photoelectron spectrum.

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INTRODUCTION Tetrahydrofuran (THF), C4H8O, is the simplest model for the deoxyribose building block of DNA. The backbone of DNA may be seen as a series of THF molecules held together by phosphate bonds to which the bases are attached. THF has therefore been widely studied experimentally and theoretically as a means of understanding electron interactions with the DNA backbone.1,2 Like other molecules with a five-membered ring, THF is not planar but puckered. This molecule is subject to an internal motion known as pseudorotation,3 corresponding to an out-of-plane ring-puckering vibration, with the ring atoms moving in such a way as to cause the phase of the puckering to move around the ring.4 This particular kind of vibrational motion was originally postulated for cyclopentane,5 in order to account for abnormally high entropy values. Pseudorotation in cyclopentane and THF arises from near cancellation of angular strains due to nontetrahedral bond angles and torsional forces due to repulsion forces between hydrogen atoms.3 Assuming an invariant mean plane xy, pseudorotation in five-membered rings can be conveniently described 6−8 by means of polar coordinates (q, ϕ), where q is the ring puckering amplitude, and ϕ is the phase of the ring puckering, which describes the ring conformation: zj =

⎛ 4π (j − 1) ⎞ 2 + ϕ⎟ q cos⎜ ⎝ ⎠ 5 5

∑ zj 2 = q 2 The pseudorotational path characterizing THF connects different conformers of Cs and C2 symmetry, corresponding to local energy minima referred to as the envelope (ϕ = 0° or ϕ = 180°) and twisted (ϕ = ± 90°) structures, respectively, through (first-order) transition states of C1 symmetry (ϕ = ±∼55° or ϕ = ±∼125°), without passing through a higher energy planar structure (C2v) corresponding (Figure 1) to a second-order saddle point at q = 0 on the potential energy surface.9,10 Conformational analysis along this path appeared to be extremely difficult and controversial, in view of extremely small energy differences among the conformations of THF, which go beyond the known accuracy of standard quantum mechanical models: the energy order of conformers largely depends upon the employed theoretical models11−15 and experimental methods.16 To our knowledge, the most precise ab initio studies upon THF are the coupled cluster calculations with single, double, and perturbative triple excitations [CCSD(T)] by Rayón and Sordo,11 supplemented with extrapolations to the limit of an asymptotically complete (cc-pV∞Z) basis set, and incorporating zero-point energy and anharmonicity corrections, which indicate that the envelope (Cs) conformer is the most stable one. According to these calculations, the Cs conformer is located at 56 cm−1 (0.16 kcal/mol) and 76 cm−1 (0.22 kcal/mol) below the twisted C2 structure and C1 first-

(1)

where ϕ ∈ [0, 2π]. In the above equation, the zj coordinate of the jth atom of the ring measures its displacement along the z-axis, out of the mean plane xy. The zj displacements are normalized so that © 2013 American Chemical Society

(2)

j=1

Received: October 30, 2012 Revised: February 5, 2013 Published: February 7, 2013 1918

dx.doi.org/10.1021/jp310722a | J. Phys. Chem. A 2013, 117, 1918−1929

The Journal of Physical Chemistry A

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Figure 1. Conformational energy map of THF, a function of the ring puckering phase (ϕ = 0° to 360°) and amplitude (q = 0 to 5 Å).

order transition state. The second-order C2v saddle-point at q = 0 is located correspondingly at 1348 cm−1 (3.85 kcal/mol) relative to the Cs global energy minimum. In view of so low conformational energy differences and energy barriers, and of the topology of its conformational energy map V(q,ϕ) (Figure 1), THF can be essentially regarded as a free pseudorotor, for which the phase ϕ of the ring puckering may take all possible values in between 0° and 360°, whereas the amplitude q oscillates around ∼0.40 Å, according to a potential energy curve which is merely harmonic at small Δq displacements. Since a first exhaustive study on n-butane,17 the archetype of structurally versatile molecules, it is now well-established18−24 that conformational rearrangements may leave strong fingerprints, throughout the inner- and outer-valence regions, in the electron momentum distributions that can be experimentally obtained for specific orbitals, or sets of orbitals, by means of Electron Momentum Spectroscopy (EMS).25−29 With this spectroscopic approach, spherically averaged orbital momentum distributions are inferred from an angular analysis of ionization intensities obtained in coincidence at specific electron binding energies (εb) from (e, 2e) electron impact ionization experiments (M + e−[E0 + εb] → M+ + 2e−[E0/2]) at high kinetic energies (typically, with E0 in the range 1.2−2.4 keV). A noncoplanar symmetric kinematic setup is usually employed in order to maximize the momentum transfer and ensure a clean “knock-out” (e, 2e) process. The influence of the molecular conformation upon momentum distributions is often strong enough to justify the idea of using Electron Momentum Spectroscopy (EMS) for evaluating conformational abundances and conformer energy differences. In line with this idea, previous EMS studies of THF9,10 have concentrated on the characteristics of the isolated envelope (Cs) and twisted (C2) conformers, as well as of the C1 transition states, and upon their influence upon the recorded momentum distributions. These studies have exploited in particular the extreme sensitivity of the electron momentum profile character-

izing the highest occupied molecular orbital (HOMO) to the molecular conformation to changes induced in the molecular structure by pseudorotational motions.20 However, because of the very low energy barriers between the Cs and C2 conformers, molecular structures neighboring the transition states produced by pseudorotation can also acquire a significant weight at room temperature. As a result, the experimental results have been more appropriately simulated by considering a thermal (Boltzmann) distribution of 24 structures located on the minimal energy path for pseudorotation in THF.20 A weakness of this depiction is that it neglects the couplings between the large amplitude and low frequency vibrational motions associated to ring puckering with more localized distortions, such as angle bendings and bond stretchings, which may result in substantial deviations from the pseudorotational pathway, i.e., the lowest energy path connecting the Cs and C2 structures via the C1 transition states, through the valley of the ring potential surface (Figure 1). More specifically, if they accounted for variations of the phase of the ring puckering from 0° to 360°, Ning et al. did not consider likely variations of the ring puckering amplitude, q, due to thermally induced vibrational effects. In line with a recent study upon group 6 metal hexacarbonyl compounds,30 the main purpose of the present work is to provide a more realistic and more complete description of these effects, and of their influence on the electronic structure and the spherically averaged and resolution folded electron momentum distributions of THF, by resorting to the principles of simulations employing Molecular Dynamics (MD),31 in conjunction with classical and quantum force fields. A main advantage of this approach is that, by virtue of the ergodic principle, it enables a complete exploration of phase space, which is equivalent to an ensemble average over all internal degrees of freedom of the system of interest, such as is computed in Monte Carlo simulations. 1919



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THEORY AND COMPUTATIONAL DETAILS A first series of MD calculations presented in this work have been performed with the 4.2 version of the TINKER package of programs32 together with the classical MM3 force field.33−35 In contrast with other classical force fields such as AMBER,36 CHARMM,37 and MACROMODEL,38 which have been especially designed for treating solvated systems like proteins, the MM3 force field has been parametrized for the purpose of accurate evaluations of conformational energies and rotational barriers in small organic molecules, in particular cyclic and cage compounds.39−41 Compared with the results of temperaturedependent nuclear magnetic resonance (NMR) measurements, this force field was found to afford highly consistent insights into particularly complex molecular motions, such as the circumrotations of benzylic amide catenanes.42 The quantitative agreement between the theoretically predicted and experimentally inferred energy barriers for such motions indicates that the MM3 force field implicitly accounts for the major structural effects of electron correlation, by virtue of its parametrization. The accuracy of the MM3 force field also has been verified in a study of the torsional characteristics of trans-stilbene and comparison with highly accurate quantum mechanical data.43 A temperature of 298 K has been imposed in the MD//MM3 simulations through coupling of the system with an external bath, using the Groningen method.44 The atom trajectories have been calculated by using the modified Beeman algorithm,45 along with the following inputs for the MD computations: an integration time step of 1 fs along with a dumping of nuclear coordinates at every 0.1 ps, for a total run time of 0.2 ns, resulting in the generation of 2000 essentially independent and properly thermalized structures. The initial structure used in these simulations was inferred from neutron powder diffraction data.46 A second series of MD simulations presented in this work employs the principles of Born−Oppenheimer Molecular Dynamics (BOMD),47−49 in conjunction with Density Functional Theory (DFT),50 the dispersion corrected ωB97XD exchange-correlation functional,51 and Dunning’s augmented correlation consistent polarized valence basis set of double-ζ quality (aug-cc-pVDZ).52,53 Born−Oppenheimer Molecular Dynamics is formally the most convenient approach for a realistic description of the intrinsically chaotic nature of nuclear motions in large molecules, taking into account nonharmonic effects (anharmonicities in the vibrational potentials, couplings between vibrations and rotations, couplings between internal and external rotations due to Coriolis forces, ...) in the classical approximation. The interested reader is referred in particular to studies of nonharmonic effects in infrared vibrational spectra, obtained by Fourier transforming to the energy domain dipole time-dependent autocorrelation functions inferred from BOMD simulations.54−57 In the BOMD simulations, the Bulirsch−Stoer method was used for the integration scheme,58,59 along with an integration step size of 0.2 fs, and using a fifth-order polynomial fit in the integration-correction scheme. The trajectory step size was set to 0.250 au (amu1/2 bohr), and atomic coordinates were dumped at time intervals of approximately 1 fs. Thermalization of the BOMD trajectories to standard room temperature (298 K) was enforced by setting the initial rotational energy from a thermal distribution assuming a symmetric top. The BOMD simulations were performed for a microcanonical (NVE) ensemble and the equilibration time was set to 0.1 ps. Thermalization was

checked by monitoring the time-dependence of the kinetic energies and potential energies obtained at each point of the computed trajectories. The total runtime was 1.526 ps, resulting again in the generation of 2000 thermally distorted structures. The results of these classical MD and BOMD simulations were analyzed by using the RING puckering program,60,61 in order to evaluate for each dumped molecular structure the corresponding phase ϕ and amplitude q of the ring puckering, according to a fitting of atomic coordinates to eqs 1 and 2. In a subsequent step, all molecular structures produced by the MD//MM3 and BOMD//ωB97XD/aug-cc-pVDZ simulations were used as input geometries in single-point DFT calculations employing the Becke-3-parameters-Lee−Yang− Parr (B3LYP) functional62,63 and Dunning’s aug-cc-pVTZ basis set. Homemade C-shell scripts have been developed to automatically convert the molecular coordinates output of the MD//MM3 and BOMD//ωB97XD/aug-cc-pVDZ runs into input for further B3LYP/aug-cc-pVTZ calculations of the electronic structure and related properties, using the GAUSSIAN09 package of programs,64 and to combine results for further analysis. Specifically, the results of these B3LYP/ aug-cc-pVTZ calculations were in turn used to compute thermally averaged model ionization spectra and (e, 2e) electron momentum distributions. For a consistent analysis of electron momentum distributions of structurally versatile molecules inferred from the angular dependence of (e, 2e) ionization cross sections at specific ionization energies, it is essential17,19 to account for the influence of the molecular conformation on the energy order and relative distribution of ionization lines, and assess in particular to which ionization band each ionization line contributes. Therefore, accurate estimates of one-electron ionization energies of OVGF65,66 (Outer Valence Green’s Function) quality were computed for all retained structures by rescaling Kohn−Sham B3LYP/aug-cc-pVTZ occupied orbital energies according to a sixth order polynominal function of the form: y = (3.0757 × 10−4)x 6 − 0.0158x 5 + 0.3185x 4 − 3.0866x 3 + 13.9246x 2 − 17.7250x − 24.0772

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This correlation is the result of a comparison (Figure 2) of B3LYP/aug-cc-pVTZ occupied orbital energies with valence one-electron ionization energies obtained from OVGF/aug-ccpVTZ calculations that were performed on 10 randomly chosen

Figure 2. Correlation between OVGF/aug-cc-pVTZ ionization energies and B3LYP/aug-cc-pVTZ occupied orbital energies. All energy values are in eV. 1920



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Table 1. Comparison of Conformer Energies, in kcal/mol, Relative to the Cs Global Energy Minimum, Using Different Methods and Basis Sets structure

MM3a

ωB97XD/aug-ccpVDZa

ωB97XD/aug-ccpVTZa

MP2/aug-ccpVDZa

MP2/aug-ccpVTZa

MP2/CBS (TQ5)b

CCSD(T)/ CBS(MP2)c

Cs C2 C1 C2v

0.000 0.190 0.200 4.210

0.000 0.038 0.130 3.170

0.000 −0.009 0.122 3.111

0.000 −0.101 0.024 4.317

0.000 0.031 0.171 4.306

0.000 0.077 0.206 4.251

0.000 0.177 0.217 3.834

a

This work. bWork by Rayón and Sordo.11 MP2/cc-pVXZ relative energies (X = T, Q, 5) extrapolated to the limit of an asymptotically complete ccpV∞Z basis set. cWork by Rayón and Sordo.11 CCSD(T)/cc-pVXZ//MP2/cc-pVTZ relative energies (X = T, Q, 5) extrapolated to the limit of an asymptotically complete cc-pV∞Z basis set and incorporating zero-point vibrational and anharmonic corrections.

momentum distributions approaching the results of benchmark Dyson orbital calculations.74,75 To enable physically meaningful comparisons with the latest experimental momentum profiles by Ning et al.,20 the theoretical spherically averaged momentum distributions have been convoluted with the experimental momentum resolution, using Monte Carlo methods,76 and according to an experimental angular resolution of 0.84° and 0.57° on azimuthal and polar angles, respectively. The theoretical electron momentum distributions have been recast onto the relative intensity scales defined by the (e, 2e) experimental electron counts measured by Ning et al. in their latest high-resolution EMS study of THF,20 using a global rescaling factor obtained from a least-squares fit between the experimental and theoretical (e, 2e) ionization intensities for all valence ionization lines, up to electron binding energies of 18 eV. Lacking the original numerical data, experimental (e, 2e) ionization cross sections were obtained by digitizing the experimental momentum distributions presented in ref 20, as a function of the target electron momentum, by means of the so-called “GetData Graph Digitizer” package.77

structures produced in the course of the MD//MM3 simulations. Virtually the same regression between OVGF ionization energies and B3LYP orbital energies has been obtained when considering structures generated by the BOMD//ωB97XD/aug-cc-pVDZ simulations. OVGF pole strengths were found to be larger than 0.862 at binding energies ranging from 9 to 18 eV, indicating67−69 that in the investigated energy range, the one-electron picture of ionization70 prevails. According to CCSD(T)/aug-cc-pVTZ results, the vertical double ionization energy thresholds of the C2 and Cs conformers of THF are located at ∼27.16 and 27.53 eV, respectively. Shake-off bands are therefore unlikely to play any role in the investigated binding energy range. The polynominal expression given in eq 3 is introduced before all for the purpose of replacing computationally highly demanding OVGF calculations on an exceedingly large number of structures without any particular symmetry by much simpler DFT calculations. Although a standard view expressed in the literature50 is that Kohn−Sham orbital energies are merely auxiliary quantities which in general have no definite physical meaning, an extension of Koopmans’s theorem to DFT indicates that these energies represent approximations to relaxed ionization energies.71 The very strong dominance (Figure 2) of the linear component in our sixth-order regression in between B3LYP/aug-cc-pVTZ Kohn−Sham orbitals energies and OVGF/aug-cc-pVDZ ionization energies confirms further the view72 that there exist simple scaling relationships in between Kohn−Sham orbital energies and oneelectron ionization energies. Theoretical ionization spectra have been constructed by convoluting the rescaled B3LYP/aug-cc-pVTZ occupied orbital energies, assuming that all ionization lines have the same spectroscopic strength (Γ = 1), and using as convolution function a Voigt profile combining a Gaussian and a Lorentzian function with equal weight and a constant full width at halfmaximum (FWHM) parameter of 0.2 or 0.8 eV. These parameters have been chosen to enable meaningful comparisons with available ultraviolet He I photoelectron spectroscopic (UPS) or EMS measurements, respectively, taking into account the corresponding experimental resolution as well as the average natural line width. We note that the vibrational contribution to band broadening is accounted for by virtue of the MD//MM3 or BOMD//ωB97XD/aug-cc-pVDZ simulations. Spherically averaged orbital momentum distributions have been generated for each resolved ionization band from the results of the single-point B3LYP/aug-cc-pVTZ calculations, using the MOMAP program by Brion and co-workers,73 and homemade interfaces. The B3LYP exchange-correlation functional was selected because it is known to yield electron

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RESULTS AND DISCUSSION Prior to deciphering the ionization spectra and electron momentum distributions of THF, it is useful to compare first results of MM3 and ωB97XD calculations of the conformational energy surface of this compound with the results of MP2 (second-order Møller−Plesset) and higher-order CCSD(T) (coupled cluster theory with single, double, and perturbative triple excitations) calculations, in conjunction with the aug-ccpVDZ and aug-cc-pVTZ basis sets, as well as the asymptotically complete cc-pV∞Z basis sets (CBS). From Table 1, it is immediately apparent that both the MM3 and ωB97XD approaches enable consistent insights into the conformational energy differences and energy barriers of THF. Both approaches describe the C2 and Cs structures as being essentially isoenergetic and separated by an energy barrier of the order of 0.1 to 0.2 kcal/mol, in line with the benchmark CCSD(T) calculations by Rayón and Sordo.11 Also in line with these calculations, the C2v second-order saddle point (q = 0) is located with the MM3 and ωB97XD approaches at 3 or 4 kcal/ mol above the Cs and C2 structures. From this latter observation, one may conclude therefore that both approaches are suited for molecular dynamical simulations of the interplay of pseudorotational motions, as described by the phase angle ϕ, with further vibrational motions (bond stretchings, angle bendings, ...) that will affect the amplitude, q, of the ring puckering. It is worth noticing that, compared with benchmark CCSD(T) results, the MM3 force field enables better insights into the conformational energy differences and barriers of THF 1921



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Figure 3. Analysis of (a) MD//MM3 and (b) BOMD//ωb97XD/aug-cc-pVDZ molecular dynamical simulations for tetrahydrofuran in terms of the phase (ϕ) and amplitude (q) of ring puckering, using polar coordinates.

than DFT calculations employing the dispersion corrected ωB97XD exchange-correlation functional. Compared with these results, the MM3 force field enables us to reproduce the relative energies of stationary points on the potential energy surface of tetrahydrofuran within 0.2 to 0.4 kcal/mol accuracy, which is amply sufficient for the purpose of generating accurate enough conformer distributions from molecular dynamical simulations. The reader is referred to Figure 3 for a plot using polar coordinates of the distribution of all molecular structures dumped from the MD//MM3 and BOMD//ωB97XD/aug-ccpVDZ simulations as a function of the corresponding ring puckering phase (ϕ) and amplitude (q). From this figure, it is immediately apparent that the phase may take all possible values in between 0° and 360°, as is to be expected for an

almost free pseudorotor, whereas the amplitude of the ring puckering varies considerably, from 0.16 to 0.54 Å in the MD// MM3 simulation (Figure 3a), and from 0.26 to 0.51 Å in the BOMD//ωB97XD/aug-cc-pVDZ simulation (Figure 3b). Quite clearly therefore, thermal deviations from the lowest energy path for pseudorotational motions in THF need to be taken into account for a qualitatively correct discussion of the influence of the temperature on the ionization spectra and electron momentum distributions of this compound. With Figure 4 and Table 2, we compare the He I ultraviolet photoelectron spectrum of THF recorded by Kimura et al. (Figure 4a)78 with the results (Figure 4b) of calculations based on MD//MM3 simulations, and thermal averaging therefore upon 2000 structures, using B3LYP/aug-cc-pVTZ orbital energies which were rescaled according to eq 3, as well as 1922



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Table 2. Comparison of Theoretical OVGF Ionization Spectra with Experimental Data levels 1 2 3 4 5 6 7 8 9 a

theoretical UPSa

He I (21 eV)b

theoretical EMSa

exptl EMS (1200 eV)c

I (10.14) II + III (11.60)

I (9.74) II (11.52) III (12.07) IV (12.52) V (12.97) VI (14.10) VII (14.50) VIII (15.40) IX (16.80)

A (10.19)

A (9.76)

B (12.04)

B (12.14)

C (14.45)

C (14.53)

D (16.60)

D (16.74)

IV (12.27) V (12.56) VI (14.04) VII (14.58) VIII (15.34) IX (16.52)

This work. bKimura, ref 78. cNing et al., ref 20.

which is in line with the standard expectation for an OVGF calculation. Essentially the same results are obtained when considering the outcome of BOMD//ωB97XD/aug-cc-pVDZ simulations. The momentum−energy (M−E) density map which has been experimentally inferred for THF by Ning et al.20 is compared in Figure 5 with the results of molecular dynamical simulations employing the MM3 force field, in conjunction with B3LYP/aug-cc-pVTZ single-point calculations of electron momentum distributions and rescaled orbital energies (eq 3). We correspondingly display in Figure 6 the experimentally inferred (Figure 6a) and theoretically predicted (Figure 6b) (e, 2e) ionization spectra of THF, obtained after integrating the M−E density map on the azimuthal angle used in the (e, 2e) setup, starting from 0° to 30° in steps of 2°. The experimental (e, 2e) ionization spectrum is displayed along with (Figure 6a) the four Gaussian bands used by Ning et al. for deconvolving their EMS measurements. Comparison is made with the distribution of ionization lines obtained from the MD//MM3 computations, which are displayed in the form of a spike spectrum (Figure 6c). In the latter simulation, line intensities were scaled according to the computed (e, 2e) ionization cross sections. From Figures 5 and 6, it is clear that our MD//MM3 simulations enable all in all highly consistent insights into experimentan observation that calls for a more detailed analysis. These figures (Figure 6b in particular) confirm that the latest EMS measurements by Ning et al.20 can be interpreted in terms of four resolved ionization bands (A, B, C, D), corresponding to ionization lines in the following energy ranges: 9.00 to 10.80 eV, 10.80 to 13.36 eV, 13.36 to 15.92 eV, and 15.92 to 18.00 eV, respectively. The experimental momentum profiles inferred for bands A, B, C, and D from the latest EMS study of THF by Ning et al.20 are analyzed in Figures 7−10, respectively, according to singlepoint B3LYP/aug-cc-pVTZ calculations of the electronic wave function and resolution folding of the correspondingly obtained momentum distributions at impact energies of 1.2 or 2.4 keV. Both theoretically and experimentally, the electron impact energy strongly influences the electron momentum distributions at small electron momenta, mainly due to resolution folding. Thermalized B3LYP momentum distributions obtained with the aug-cc-pVDZ and aug-cc-pVTZ basis sets were found to be quasi-identical, which demonstrates the convergence of these results with regards to further improvements of the basis set. In these figures, results of our MD//MM3 and BOMD// ωB97XD/aug-cc-pVDZ simulations are superposed to the theoretical momentum profiles obtained by Ning et al.,20 also

Figure 4. Comparison of the (a) He I photoelectron spectrum of tetrahydrofuran by Kimura et al.78 with (b) thermally averaged MD// MM3 simulations of OVGF/aug-cc-pVTZ quality (see text for explanation, FWHM = 0.2 eV), and individual OVGF/aug-cc-pVTZ simulations for the (c) Cs conformer and (d) C2 conformer, using a FWHM parameter of 0.6 eV. See Table 2 for a quantitative assignment of bands.

with the results of OVGF/aug-cc-pVTZ calculations on the Cs and C2 conformers (Figure 4c,d). Whereas none of the individual conformer structures enables consistent insights into the He I spectrum of THF, it is clear that the latter can be almost perfectly reproduced when taking molecular dynamics into accountwith the exception of bands II and III, which theory fails to sufficiently resolve. Except for these two bands, the location of all bands seen in the He I spectrum is reproduced by our model within ∼0.3 eV accuracy (Table 2), 1923



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Figure 5. (a) Experimental20 and (b) simulated (this work) outer valence momentum−energy density maps of tetrahydrofuran, at an electron impact energy of 1200 eV plus binding energy.

In view of these contrasted results, it is useful to remember that all models so far consider a vertical depiction for the (e, 2e) ionization processes, and neglect therefore the outcome of structural relaxation in the final ionized state. At this stage, it is also worth remembering that Ning et al.20 used the same B3LYP/aug-cc-PVTZ model of the electronic structure as the one we use in the present work for computing electron momentum distributions from Kohn−Sham orbitals. The better match of the theoretical results by Ning et al. for band A is therefore most probably the result of a cancellation of errors due to the neglect of nuclear dynamics in the final state, of distorted wave and postcollision effects, and of thermal alterations of the ring puckering amplitude in the initial ground state. Considering the extreme structural versatility of THF, ionization of its Highest Occupied Molecular Orbital (HOMO) is indeed very likely to result in ultrafast nuclear dynamical processes of large amplitude in the final state, since this orbital merely corresponds to a strongly localized oxygen lone pair, with some admixture of σ and σ* contributions from the neighboring C−H and C−C bonds, respectively, due to anomeric interactions with the oxygen lone pair (Figure 11). The situation is very much reminiscent of that observed for the HOMO of ethanol,79 corresponding also essentially to a strongly localized oxygen lone pair, the ionization of which results in an ultrafast stretching of the neighboring C−C bond, by 0.55 Å within 55 fs, which leads in turn to a significant

according to single-point B3LYP/aug-cc-pVTZ calculations of the electronic wave function, but assuming a Boltzmann thermostatistical distribution of conformer abundances along the pseudorotational minimal energy path calculated by Rayón and Sordo.11 Whatever the level of theory employed, band A (Figure 7) is characterized by a momentum profile of mixed s-p type, with two maxima in electron densities at p = 0.00 au and p ≈ 1.00 au (1 au = 1 bohr−1), and one minimum at p ≈ 0.45 au, whereas band B (Figure 8) possesses a double-p type momentum distribution, with two maxima at p of ∼0.35 and ∼1.05 au, and two minima at p = 0.0 and ∼0.7 au. Band C yields a p-type momentum profile (Figure 9) with a single maximum at p ≈ 0.70 au, whereas the momentum profile inferred for band D (Figure 10) is dominantly of the s-type, with a shoulder contribution at an electron momentum around 0.8 au. It is immediately apparent that a thermal averaging of the molecular structure accounting for oscillations of the ring puckering amplitude around the minimal energy path for pseudorotation yields significantly different results for bands A, B, and C (Figures 7−9), whereas no obvious difference is observed for band D (Figure 10). An improvement of the fit between theory and experiment is observed for bands B and C (Figures 8 and 9) when fully accounting for molecular dynamics, whereas the theoretical predictions for band A by Ning et al.20 are apparently in better match with experiment (Figure 8). 1924



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momenta for the electron momentum profile inferred experimentally for band A, compared with the results of our MD//MM3 and BOMD//ωB97XD/aug-cc-pVDZ simulations of molecular motions in the electronic ground state. In support of this suggestion, we note that the first ionization band in the He I photoelectron spectrum (Figure 4a) is strongly asymmetric and shows evidence of a vibronic progression. Further BOMD simulations coping both with the structural versatility of THF in its neutral electronic ground state and final ionized state are needed to quantitatively assess the influence of ionization-induced structural relaxation effects on the frontier electron momentum profile of this compound. Figure 6a indicates that overlap effects are likely to slightly complicate the analysis of the electron momentum profiles inferred for bands B, C, and D. To verify the consistency of our analysis, in spite of these effects, we compare in Figure 12 the total experimental momentum profiles inferred for these three bands with the results of MD//MM3 and BOMD//ωB97XD/ aug-cc-pVDZ simulations. Compared with the results of Ning et al., a significant improvement is all in all noticed with our dynamical simulations, especially at electron momenta comprised between 0.5 and 1.2 au, which demonstrates again that alterations of the ring puckering amplitude and deviations from the pseudorotational minimal energy path need to be taken into account for disentangling in a proper way the electron momentum profiles inferred from EMS experiments on THF.

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CONCLUSIONS The present contribution emphasizes the extreme structural versatility of tetrahydrofuran (THF), through a reinterpretation of experiments employing He I photoelectron spectroscopy as well as Electron Momentum Spectroscopy (EMS), on the basis of Molecular Dynamical simulations employing the classical MM3 force field and large-scale quantum mechanical simulations based on Born−Oppenheimer Molecular Dynamics in conjunction with the dispersion corrected ωB97XD exchange-correlation functional and the aug-cc-pVDZ basis set. The present work is, to our knowledge, the first study exploiting the principles underlying molecular dynamical simulations for the purpose of unraveling the influence of thermally induced nuclear motions onto the ionization bands and (e, 2e) electron momentum distributions of a conforma-

Figure 6. (a) Experimental20 and simulated (this work) binary (e, 2e) ionization spectra of tetrahydrofuran, in (b) their convolved form (FWHM = 0.8 eV) and (c) in the form of the underlying spike spectrum. In the latter spectrum, lines are scaled according to the computed (e, 2e) ionization cross sections, i.e., according to integrated momentum densities.

enhancement of the electron densities inferred for the HOMO at low electron momenta. By analogy with ethanol, we expect therefore that nuclear dynamics in the final ionized state of THF will explain the apparent turn-up observed at low electron

Figure 7. Comparison between experimental20 and theoretical electron momentum distributions inferred at an electron impact energy of 1.2 and 2.4 keV (+binding energy) for ionization lines at binding energies comprised between 9.00 and 10.80 eV (ionization band A). 1925



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Figure 8. Comparison between experimental20 and theoretical electron momentum distributions inferred at an electron impact energy of 1.2 and 2.4 keV (+binding energy) for ionization lines at binding energies comprised between 10.80 and 13.36 eV (ionization band B).

Figure 9. Comparison between experimental20 and theoretical electron momentum distributions inferred at an electron impact energy of 1.2 and 2.4 keV (+binding energy) for ionization lines at binding energies comprised between 13.36 and 15.92 eV (ionization band C).

Figure 10. Comparison between experimental20 and theoretical electron momentum distributions inferred at an electron impact energy of 1.2 and 2.4 keV (+binding energy) for ionization lines at binding energies comprised between 15.92 and 18.00 eV (ionization band D).

tionally versatile molecule, THF. If our results certainly confirm that THF can be merely regarded as an almost free pseudorotor, an analysis of the produced atomic trajectories demonstrates the importance of thermal deviations from the lowest energy path for pseudorotation, in the form of

considerable variations of the ring puckering amplitude. Compared with the latest interpretation of high-resolution EMS measurements by Ning et al. upon this compound,20 according to a thermostatistical distribution of conformers located on the lowest energy path for pseudorotation, these 1926



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Figure 11. Contour plot of the HOMO of THF in its (a) envelope (Cs) and (b) twisted (C2) conformations, using a contour value of 0.05.

Figure 12. Comparison between experimental20 and theoretical electron momentum distributions inferred at an electron impact energy of 1.2 and 2.4 keV (+binding energy) for ionization lines at binding energies comprised between 10.80 and 18.00 eV (ionization bands B + C + D).

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ACKNOWLEDGMENTS This work has been supported by the FWO_Vlaanderen, the Flemish branch of the Belgian National Science Foundation, and by the “Bijzonder OnderzoeksFonds” of Hasselt University. F.M. is a postdoctoral fellow from the FWO at Hasselt University. The authors especially acknowledge financial support within the framework of a Research Program of the Research Foundation-Flanders (FWO_Vlaanderen; project no. G.0350.09N, entitled “From orbital imaging to quantum similarity in momentum space”).

deviations were found to have a significant influence on the computed outer-valence electron momentum distributions. Comparison of individual conformer contributions with thermally averaged simulations demonstrates also the influence of molecular dynamics in the electronic ground state on the He I photoelectron spectrum of THF. Taking molecular dynamics into account enables us to more faithfully reproduce the experimentally inferred momentum distributions, with the exception of the momentum profile corresponding to the HOMO, for which nuclear dynamics in the final ionized state is likely to have a significant influence. The computed momentum profiles appear to be quite sensitive to details of the potential energy surface underlying the molecular dynamical simulations which we have performed. The greatest care is required therefore when interpreting EMS experiments on a compound with such high structural versatility as tetrahydrofuran. Further complications, such as nuclear dynamics in the final ionized state, or a breakdown of the Plane Wave Impulse Approximation (PWIA) in the form of distorted wave and postcollision effects, will have to be considered in future works for a definite interpretation of EMS experiments on this compound.

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REFERENCES

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