Photoelectron Spectroscopy of the Hydroxymethoxide Anion, H 2 C(OH)O

Transcription

1 Supplementary Material for: Photoelectron Spectroscopy of the Hydroxymethoxide Anion, H 2 C(OH)O Allan M. Oliveira, Julia H. Lehman, Anne B. McCoy 2 and W. Carl Lineberger JILA and Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado Department of Chemistry, University of Washington, Seattle, Washington 9895 Table of Contents A. Calculated Torsional Potential Energy Curves and Wavefunctions... S B. Calculated Torsional Wavefunctions... S3 C. H 2 C(OH)O X 2 A Relaxed Torsional Potential... S4 D. Separability of the Torsional Coordinate... S6 E. Calculated Photoelectron Spectra... S8 F. Rotational Band Shift... S0 G. Experimentally determined peak center positions and vibrational assignments... S2 H. References... S3 A. Calculated Torsional Potential Energy Curves and Wavefunctions The calculated H-OCO torsional potential energy curves are shown in Fig. S (which is similar to Fig. of the main text). In this figure, the anion potential energy surface was calculated by varying the φ HOCO dihedral angle while allowing the remaining coordinates to be optimized (referred to as a relaxed scan). The neutral surfaces were constructed by calculating the energy of the neutral molecule (X 2 A and A 2 A states) at the optimized anion geometries, referred to as the vertical potential energy curves, which represent the region of the potential energy surfaces important to photodetachment. The calculated points and fitting parameters (see Equation ) are shown in Tables S and S2, respectively. S

2 Table S: Calculated torsional potential energy surface scan (CCSD(T)/aug-cc-pVTZ for H 2 C(OH)O X Aʹ and H 2 C(OH)O X 2 A, and EOM-CCSD/aug-cc-pVTZ for H 2 C(OH)O A 2 A). The offset refers to the relative position of the calculated point to the energy of the anion φ HOCO = 0 structure, i.e. summing the offset value to each column will result in the energy of these points relative to the anion minimum energy, which is plotted in Fig. of the main text and Fig. S. φ HOCO (degrees) E anion Relaxed (cm - ) E neutral (X 2 A) Relaxed (cm - ) E neutral (X 2 A) Vertical (cm - ) E neutral (A 2 A) Vertical (cm - ) Offset S2

3 Table S2: Fit parameters of Equation for each of the potentials. The A parameter defines the absolute energy of the V(φ HOCO = 0) point. All parameters have units of cm -. Also included are the expansion coefficients for the G φhoco,φ HOCO term in Eq. 2 of the main text, which is an expansion in cos(nφ HOCO ), analogous to the equation listed in the table below. Fit Parameter A (relative to anion min.) A (relative to potential min.) Anion (X Aʹ) Neutral (X 2 A) Neutral (X 2 A) Neutral (A 2 A) G φhoco,φ HOCO Relaxed Relaxed Vertical Vertical V V V V V V(φ HOCO ) = A + V n ( cos(nφ HOCO )) n= B. Calculated Torsional Wavefunctions As discussed in the main text, the calculated torsional ground state wavefunction has significant amplitude over both wells of the neutral potential. This is also true for the lowest excited state of the neutral. The calculated D wavefunctions are shown below, in Fig. S. The parity of the wavefunctions further clarifies the selection rules observed in the experiment. S3

4 Figure S: Calculated D potential energy curves as functions of the torsional coordinate for the H 2 C(OH)O X Aʹ (blue), H 2 C(OH)O X 2 A (red), and H 2 C(OH)O A 2 A (purple) states. The vibrational wave functions are plotted in black (even functions) and green (odd functions). All potentials are the calculated at the optimized anion geometries and cover the same energy range. These potentials are the same as in Fig. of the main text, but with different angle and energy ranges in order to better view the wavefunctions. C. H 2 C(OH)O X 2 A Torsional Potential The surface used to calculate the reported torsional FCFs is referred to as the vertical detachment surface (shown in Fig. of the main text and Fig. S). The neutral ground state surface was also calculated as a relaxed scan, meaning that the energy of H 2 C(OH)O was calculated at each φ HOCO S4

5 dihedral angle (stepped between 0 and 80 ) while allowing the remaining coordinates to be optimized. In order to provide a comparison between the neutral vertical and relaxed potentials energy curves (ROCCSD(T)/aug-cc-pVTZ), these potentials are shown in Fig. S2. As Fig. S2 shows, the main difference between these surfaces are the location of the minima and the barrier heights, along with an energy offset relative to the anion minimum. The vertical surface is located ca cm - (0.27 ev) above the relaxed potential. Figure S2: H 2 C(OH)O X 2 A H-OCO calculated (ROCCSD(T)/aug-cc-pVTZ) torsional potential comparison. The green circles and trace represent the relaxed potential energy surface, where all coordinates were optimized for each value of φ HOCO. The red triangles represent the vertical detachment surface, where the neutral surface was calculated at the optimized anion geometries for each value of φ HOCO. ΔE barrier represents the D barrier height with respect to the potential minima. S5

6 D. Separability of the Torsional Coordinate The calculated FCFs of the H-OCO torsional mode were treated separately from the other normal modes, as discussed in the main text. This separate D treatment is an approximation that is justified by comparing the structural parameters and vibrational frequencies of the minimum energy structure (C symmetry) and the transition state (C s symmetry, φ HOCO = 0 ). The corresponding calculated results are shown below in Tables S3 and S4, which show that there is a 2±2% change in the structural parameters and vibrational frequencies between the equilibrium and transition state (φ HOCO = 0 ) of H 2 C(OH)O X 2 A. This implies that the torsional coordinate is indeed a coordinate which is separable from the remaining normal modes and hence it is well treated by the model discussed in the main text. Similar small changes are calculated between the H 2 C(OH)O A 2 A equilibrium and transition state structures. The H 2 C(OH)O A 2 A and H 2 C(OH)O X A vibrational frequencies are listed in Tables S5 and S6, respectively. Table S3: Calculated (ROCCSD(T)/aug-cc-pVTZ) optimized geometries of H 2 C(OH)O X 2 A at its equilibrium (φ HOCO = ±48 ) and transition state (φ HOCO = 0 ) structures. Bond distances (r) are given in Angstroms while bond angles ( ) and dihedral angles (φ) are given in degrees. The atom numbering is based on Fig. in the main text and is repeated here for convenience. Parameter Equilibrium Transition Δ (TS-Eq) State (%) r CO r CO r CH r CH r OH OCO HCO H2CO H3O2C φ HCOO φ H2COO φ H3O2CO ( φ HOCO ) S6

7 Table S4: Calculated (ROCCSD(T)/aug-cc-pVTZ) harmonic vibrational frequencies of H 2 C(OH)O X 2 A, for both the equilibrium structure (φ HOCO = ±48 ) and transition state (φ HOCO = 0 ), together with the approximate mode description. All values are reported in cm -. X 2 A Equilibrium X 2 A Transition Δ (TS-Eq) ω i Mode description Structure State (%) 2 O H torsion i - OCO bend In plane HCH rock OCO Sym. Stretch OCO Asym. Stretch Out of plane HCH rock In phase HOC bending/ch 2 wagging Out of phase HOC bending/ch 2 wagging HCH bend HCH Sym. Stretch HCH Asym. Stretch OH Stretch Table S5: Calculated (CIS/aug-cc-pVTZ) harmonic vibrational frequencies of H 2 C(OH)O A 2 A for both the equilibrium structure (φ HOCO = ±70.9 ) and transition state (φ HOCO = 0 ), together with the approximate mode description. All values are reported in cm -. A 2 A Equilibrium A 2 A Transition Δ (TS-Eq) ω i Mode description Structure State (%) 2 O H torsion i - OCO bend OCO Sym. Stretch OCO Asym. Stretch In plane HCH rock In phase HOC bending/ch 2 wagging Out of plane HCH rock Out of phase HOC bending/ch 2 wagging HCH bend HCH Sym. Stretch HCH Asym. Stretch OH Stretch S7

8 Table S6: Calculated (CCSD(T)/aug-cc-pVTZ) harmonic vibrational frequencies of H 2 C(OH)O X A. Note the difference in mode descriptions between the anion and neutral structures. The convention used in this paper is to refer to modes based on the neutral H 2 C(OH)O X 2 A mode numbering/descriptor. All values are reported in cm -. ω i Mode description H 2 C(OH)O X A 2 O H torsion 273 OCO bend OCO Sym. Stretch 77 9 OCO Asym. Stretch 2 8 In plane HCH rock 3 7 Out of plane HCH rock In phase HOC bending/ch 2 wagging 30 5 HCH bend Out of phase HOC bending/ch 2 wagging HCH Asym. Stretch HCH Sym. Stretch 2722 OH Stretch 3757 E. Calculated Photoelectron Spectra The calculated photoelectron spectrum for detachment to H 2 C(OH)O X 2 A for the experimentally observed ebe range corresponding to h = 3.49 ev is shown below in Fig. S3. The calculation shows overall good agreement with the experimental data and provides confidence in the assignments and interpretation. The calculation also shows a large degree of spectral congestion, which, coupled to the experimental resolution, contributes to the difficulty in assigning transitions for ebes higher than 2.4 ev. The calculated photoelectron spectrum for detachment to H 2 C(OH)O A 2 A is shown in Fig. S4 (including the cutoff for the photon energy used and threshold effects, as discussed in the main text). The full Franck-Condon simulation shows a very long (over 2 ev) progression, a symptom of unphysical behavior. This likely arises from the harmonic treatment inherent in the simulation to model the vibrational modes associated with the large geometry change in the r CO bond lengths and H3O2C. However, the lower binding energy range (near the origin) is what is accessed in the experiment and qualitatively matches the results quite well. S8

9 Figure S3: Photoelectron spectrum of H 2 C(OH)O taken with 355 nm photons (3.49 ev) in comparison with the full calculated spectrum for detachment to H 2 C(OH)O X 2 A. The FCFs were calculated assuming a vibrational temperature of 20K, based on the observed hot-band (Fig. 4 of the main text). The calculated transitions (green sticks) were convoluted with Gaussian functions of varying fwhm in order to match the experimental resolution (blue trace) and provide a direct comparison between calculated and experimental data. S9

10 Figure S4: Calculated photoelectron spectrum for detachment to H 2 C(OH)O A 2 A compared to the experimental photoelectron spectrum taken with 3.49 ev photon energy (black). The FCFs were calculated assuming a vibrational temperature of 20K and include threshold effects of photoelectron detachment using 3.49 ev photons, as discussed in the main text. The calculated transitions (green sticks) were convoluted with Gaussian functions of varying fwhm (blue trace) in order to match the experimental resolution and provide a direct comparison between calculated and experimental data. F. Rotational Band Shift The observed peak maxima in the spectrum shown in Fig. 4 of the main text may not represent the band origin of the transition due to unresolved rotational structure. With the experimental resolution, the shape of the rotational band contour underlying the observed peak could result in an asymmetric intensity profile with respect to the band origin, resulting in a shift of the observed peak maxima compared to the transition origin. To address this, the procedure described by Engelking was employed S0

11 to obtain the displacement of the band origin from the observed peak center. This model accounts for the fact that rigid-rotor rotational selection rules appropriate for a bound-free transition are more complicated than for a bound-bound transition; however, the analysis is limited to a selection rule of no change in the J, K populations (ΔJ = ΔK = 0). In the ev photoelectron spectrum, the detachment shows an essentially isotropic angular distribution (s-wave, β = 0). Since the additional electron in the H 2 C(OH)O anion is primarily located at the O atom, the anion HOMO is essentially a p-orbital. 2 The observed anisotropy implies that the photon angular momentum is largely accounted for by the ejected photoelectron. This observation further strengthens the validity of the approximation that ΔJ = ΔK = 0 in the Engelking model. The offset between the peak center and the band-origin, ΔE rot, as a function of rotational temperature is given by: 3 E rot k B T [ A B 2A + + C 3 ] + B B 2B 2C 2 3 () where A, B and C are the rotational constants of H 2 C(OH)O. The primed quantities refer to the upper state (neutral) and the double-primed quantities refer to the lower state (anion). Since there is no experimental measurement of the H 2 C(OH)O /H 2 C(OH)O molecules rotational constants, calculated (CCSD(T)/augcc-pVTZ) ones were used (Table S7). Assuming a rotational temperature of 20 ± 50 K, based on the vibrational temperature and in accord with previous experiments done with this ion source, 4-6 this leads to a shift of the origin (EA) peak of (3) ev. Table S7: Calculated rotational constants (CCSD(T)/aug-cc-pVTZ, RO for neutral) for H 2 C(OH)O and H 2 C(OH)O. All values are given in cm -. Rotational Constants (cm - ) Anion Neutral (TS) A B C S

12 G. Experimentally determined peak center positions, vibrational assignments and associated uncertainties Table S8: Vibrational transition assignments for the peaks labeled a e (Fig. 4) and B (Fig. 3) in the photoelectron spectra reported in the main text. Both the absolute peak position (ebe, reported in ev) and the energy relative to the EA (reported in cm - ) are given. The H 2 C(OH)O (X 2 A) (ν ν 2 ) H 2 C(OH)O (X A ) (ν ν 2 ) transitions are labeled using the standard shorthand notation ( ν ν ν 2 2ν2 for vibrational transitions. The assignments are based on the results of the calculated photoelectron spectrum. The question marks indicate the peaks in this region where the assignment is ambiguous (see Figs. 3 and 4) due to spectral congestion. Peak Label (Fig. 4) Absolute Peak Center Position (ev) Peak Position Relative to EA (cm - ) Assignment a' a b c ? 0 2 d e and /or B (Fig. 3) ? ? 5 0 ) Although the largest contribution to the uncertainties reported in the main text come from the energy scale calibration, they can be separated into the following contributors: i) statistical error in finding the peak center, ii) error in locating the calibration image center, iii) error in the rotational contour shift, and iv) error in locating the data image center. (i.) The statistical error in finding the peak center arises from the ability of the peaks to be fit to a Gaussian function. Here, for the EA peak, this uncertainty is approximately ev. (ii.) The error in locating the center of the calibration image is the largest contributor to the overall uncertainty. Since the photoelectron images in our experiment are not perfectly circular, there is an error in finding the center of the image, which is necessary for the image reconstruction. This affects the energy scale in two ways, both in defining the absolute zero S2

13 of the energy scale (linear offset) and the magnification factor (slope) when transforming image pixels to kinetic energy. Here, the uncertainty on the linear offset is ev and the slope has an uncertainty around % of the eke. (iii.) The error in the shift of the peak center due to an underlying rotational contour arises from the uncertainty in the rotational temperature, in combination with the uncertainty of the calculation of the rotational constants of the anion and neutral molecules. Here, this uncertainty is ~ ev. (iv.) Similar to (ii), locating the center of the data image has an uncertainty associated to it and is usually limited to ± pixel. Depending on the electron kinetic energy, this ± pixel can result in different energy shifts. Here this uncertainty is at most ev. These uncertainties were considered to be independent of one another and therefore were added in quadrature, resulting in the values reported in the main text. The exceptions are the 2 sequence band, where the peak fwhm/2 was used for its uncertainty due to its very large peak width and non-gaussian peak shape. H. References P. C. Engelking, J. Phys. Chem. 90, 4544 (986). 2 W. Eisfeld, and J. S. Francisco, J. Chem. Phys. 3, 3433 (2009). 3 M. J. Travers, D. C. Cowles, E. P. Clifford, G. B. Ellison, and P. C. Engelking, J. Chem. Phys., 5349 (999). 4 Y. J. Lu, J. H. Lehman, and W. C. Lineberger, J. Chem. Phys. 42, (205). 5 A. M. Oliveira, Y. J. Lu, J. H. Lehman, P. B. Changala, J. H. Baraban, J. F. Stanton, and W. C. Lineberger, J. Am. Chem. Soc. 37, 2939 (205). 6 A. M. Oliveira, J. H. Lehman, A. B. McCoy, and W. C. Lineberger, J. Phys. Chem. A 20, 652 (206). S3