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Probing Molecular Electronic Structure Using High Harmonic Generation Tomography

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Probing Molecular Electronic Structure Using High Harmonic Generation Tomography

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The structure of valence electronic orbitals of a molecule determines the majority of chemical properties. Generation of high-order harmonic frequencies from atomic sources has been directly related to the electronic structure of the atom, (1) and extended as far as tomographic reconstruction of linearly symmetric polyatomic molecular systems with some success. (2,3,4)

However, because of the increased resolution of these reconstructions, discrimination of fine details of the orbital reconstructions reveals some inconsistencies in the orbital shapes when compared with past models & theoretical calculations. (2) There are several proposed corrections to the Strong Field Approximation (SFA) that currently underlies tomographic reconstruction as well as all other experiments that use high harmonic generation (HHG) to probe molecular systems. (5,6,7)
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1. Lewenstein et al. Phys Rev A 49 (3) 1994.
2. Salieres, Maquet, Haessler, Caillat, Taieb. Rep. Prog. Phys. 75 (2012) 062401.
3. Li, Liu, Yang, Song, Zhao, Lu, Li, Xu. Opt. Ex. 21 (6) 2013. 7599.
4. Torres et al. Phys Rev. Lett. 98 (2007) 203007.
5. Diveki et. al. J. Chem Phys. 414 (2013) 121.
6. Yip, Palacios, Rescigno, McCurdy, Martin. J. Chem Phys 414 (2013) 112.
7. Spanner, Patchkovskii. J. Chem. Phys. 414 (2013) 10.

The structure of valence electronic orbitals of a molecule determines the majority of chemical properties. Generation of high-order harmonic frequencies from atomic sources has been directly related to the electronic structure of the atom, (1) and extended as far as tomographic reconstruction of linearly symmetric polyatomic molecular systems with some success. (2,3,4)

However, because of the increased resolution of these reconstructions, discrimination of fine details of the orbital reconstructions reveals some inconsistencies in the orbital shapes when compared with past models & theoretical calculations. (2) There are several proposed corrections to the Strong Field Approximation (SFA) that currently underlies tomographic reconstruction as well as all other experiments that use high harmonic generation (HHG) to probe molecular systems. (5,6,7)
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1. Lewenstein et al. Phys Rev A 49 (3) 1994.
2. Salieres, Maquet, Haessler, Caillat, Taieb. Rep. Prog. Phys. 75 (2012) 062401.
3. Li, Liu, Yang, Song, Zhao, Lu, Li, Xu. Opt. Ex. 21 (6) 2013. 7599.
4. Torres et al. Phys Rev. Lett. 98 (2007) 203007.
5. Diveki et. al. J. Chem Phys. 414 (2013) 121.
6. Yip, Palacios, Rescigno, McCurdy, Martin. J. Chem Phys 414 (2013) 112.
7. Spanner, Patchkovskii. J. Chem. Phys. 414 (2013) 10.

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Probing Molecular Electronic Structure Using High Harmonic Generation Tomography

  1. 1. PROBING MOLECULAR ELECTRONIC STRUCTURE USING HIGH HARMONIC GENERATION TOMOGRAPHY CHELSEY CROSSE LEVINGER GROUP | COLORADO STATE UNIVERSITY LITERATURE SEMINAR | OCTOBER 23, 2013
  2. 2. MOLECULAR ELECTRONIC STRUCTURE Geometry Chang. Chemistry, 8th ed.; McGraw-Hill:New York, 2005. Benzene Reactions, Tutorvista. chemistry.tutorvista.com/ (accessed 11 Oct. 2013). Han, Choi, Kumar & Stanley. Nature Physics. 2010, 6, 633. Phase Behavior 1 Bonding
  3. 3. Hydrogenic Orbitals Molecular Orbitals Siriwardane. CHEM 281, LA Tech. www.chem.latech.edu (accessed 11 Oct. 2013). N2 HOMO Highest Occupied Molecular Orbital 2 MOLECULAR ORBITALS OF NITROGEN
  4. 4. EXPERIMENTAL METHODS OF MEASURING MOLECULAR STRUCTURE de Oteyza et al. Science. 2013, 340, 1434. 3 3Å
  5. 5. MEASUREMENT REQUIREMENTS FOR ORBITAL TOMOGRAPHY 1. Observable • High Harmonic Generation (HHG) radiation 2. Selective Tunneling probability • Molecular alignment 4 •
  6. 6. OVERVIEW OF HIGH HARMONIC GENERATION TOMOGRAPHY Diveki et al. Chemical Physics, 2013, 414, 121. ”High Harmonic Generation” Wikipedia. en.wikipedia.org (accessed 18 Oct. 2013). 5 “A MOLECULE BEING PROBED BY ONE OF ITS OWN ELECTRONS”
  7. 7. HARMONIC GENERATION IN A GAS JET • • • Odd order harmonics Linear trend Multi-photon Ionization followed by electron relaxation. Low Intensity (I ≤1013 W/cm2) Number of photons • Classical Harmonic Generation: Harmonic order (n) • Plateau followed by linear decrease DIFFERENT PHYSICAL MECHANISM New & Ward. Physical Review Letters. 1967, 19, 556. Hecht, J. “Photonic Frontiers: High Harmonic Generation,” LaserFocusWorld 2012. Harmonic order (n) 6 • Number of photons • High Harmonic Generation (HHG) High Intensity ( I ≥1014 W/cm2)
  8. 8. Probe Torres et. al. Physical Review Letters. 2007, 98, 203007. Alignment: ~100 fs Ti:Sapph @ 808 nm, I ≤ 1013 W/cm2 Probe: ~15 fs Ti:Sapph, I ~1014 W/cm2 Alignment 7 EXPERIMENTAL SETUP
  9. 9. SEMI-CLASSICAL THREE STEP MODEL 1. Tunneling (Quantum Mechanical) 2. Acceleration of Electron in Laser Field (Classical) 3. Recombination (Quantum Mechanical) 0t =0 Elaser = 0 0t ~ /2 Elaser Lewenstein et al. Physical Review A. 1994, 49, 2117. Mahieu Seminar at UNG 2009. 3. 2. 0t = Elaser = 0 0t ~ 3 /2 Elaser 0t =2 Elaser = 0 8 1.
  10. 10. SEMI-CLASSICAL THREE STEP MODEL 0t =0 Elaser = 0 Energy Ground state (SCHEMATIC) EI 0 Distance from Molecular Center of Mass Mahieu Seminar at UNG 2009. 9 e-
  11. 11. SEMI-CLASSICAL THREE STEP MODEL 0t ~ /2 Elaser 0t = Elaser =0 Energy 1. Tunneling (Quantum Mechanical) 0 Distance from Molecular Center of Mass Mahieu Seminar at UNG 2009. 10 e-
  12. 12. 1. Observable • HHG radiation Energy MEASUREMENT REQUIREMENTS FOR ORBITAL TOMOGRAPHY 2. Selective Tunneling probability • Molecular alignment e- 0 Distance from Molecular Center of Mass 11 
  13. 13. SEMI-CLASSICAL THREE STEP MODEL 0t ~ /2 Elaser 0t ~ 3 /2 Elaser 2. Acceleration of Free Electron in Laser Field (Classical) 0 Distance from Molecular Center of Mass Mahieu Seminar at UNG 2009. 12 Energy e-
  14. 14. SEMI-CLASSICAL THREE STEP MODEL 0t =0 Elaser = 0 3. Recombination (Quantum Mechanical) 0 Distance from Molecular Center of Mass Mahieu Seminar at UNG 2009. 13 Energy e-
  15. 15. 1. Observable  HHG radiation Energy MEASUREMENT REQUIREMENTS FOR ORBITAL TOMOGRAPHY 2. Selective Tunneling probability • Molecular alignment e- 0 Distance from Molecular Center of Mass 14 
  16. 16. THREE STEP MODEL RELATES TO RADIATION   f  I HHG µ g (k, I L , q )a(k, I L )d (k, q ) q IL  k 1. Tunneling (Quantum Mechanical)  g (k, I L ,q ) • Tunneling probability 2. Acceleration of Electron in Laser Field (Classical)  • a(k, I L ) 3. Recombination (Quantum Mechanical) •   f ˆ d (k,q ) = <y0 (q ) | d | yc (k)> f Acceleration Transition dipole Diveki et al. Chemical Physics, 2013, 414, 121. 15 matrix
  17. 17. CALIBRATION OF MEASUREMENTS • •   f  I HHG µ g (k, I L , q )a(k, I L )d (k, q )  Function of laser characteristics a(k, I L )  g (k, I L ,q ) Function of ionization potential Given observation of a reference system:  f  1 I(w, I L , q )  f  ˆ <y0 (q ) | d | yc (k)> = d (k, q ) µ dref (k ) R(q ) I ref (w, I L ) f Diveki et al. Chemical Physics, 2013, 414, 121. 16 ANGULAR DEPENDENCE
  18. 18. Smith. The Scientist & Engineer's Guide to Digital Signal Processing. California Technical Publishing 1997. www.dspguide.com (accessed 16 Oct. 2013). 17 TOMOGRAPHY INTERLUDE: COMPUTED TOMOGRAPHY
  19. 19. Smith. The Scientist & Engineer's Guide to Digital Signal Processing. California Technical Publishing 1997. www.dspguide.com (accessed 16 Oct. 2013). 18 TOMOGRAPHY INTERLUDE: COMPUTED TOMOGRAPHY
  20. 20. ab initio HOMO res et. al. Chemical Physics. 2013, 414, 121. N2 HOMO HHG Tomography HOMO 19 MOLECULAR TOMOGRAPHY
  21. 21. MOLECULAR ALIGNMENT • Molecular Sample • T ~ 100 K • Initial alignment: • • • • ~100 fs pulse I ~ 1013 W/cm2 Induces rotational wave packet NON-ADIABATIC • Rotational Revival • ~70% rotational realignment Distinguishable within 5° at 100K Lock et al. Physical Review Letters. 2012, 108, 133901. 20 •
  22. 22. MEASUREMENT REQUIREMENTS FOR ORBITAL TOMOGRAPHY 1. Observable  HHG radiation 2. Selective Tunneling probability  Molecular alignment 21 
  23. 23. N2 HOMO Itatani et. al. Nature. 2004, 432, 867. 22 THEORETICAL EXPERIMENTAL HHG TOMOGRAPHY DATA: N2
  24. 24. THE STRONG FIELD APPROXIMATION Assumptions:  • Born-Oppenheimer approximation  • Hartree-Fock approximation  • Koopman’s approximation • Free electron is a plane wave • Single active electron • Neglect the Stark effect • Neglect relativity Diveki et al. Chemical Physics, 2013, 414, 121. Spanner, Patchkovskii. Chemical Physics 2013, 414 10. 23 • Neglect Coulombic interaction
  25. 25. CONTINUUM WAVEFUNCTIONS N2 HOMO Dyson Orbital for N2 Ionization: ydj = n < I j | N > Spanner, Patchkovskii. Chemical Physics 2013, 414 10. 24 Modeled < yc |
  26. 26. CONTINUUM WAVEFUNCTIONS Dyson Orbital for CO2 Ionization Spanner, Patchkovskii. Chemical Physics 2013, 414 10. 25 Modeled < yc |
  27. 27. THE STRONG FIELD APPROXIMATION Assumptions:  Born-Oppenheimer approximation  Hartree-Fock approximation  Koopman’s approximation o Free electron is a plane wave • Single active electron • Neglect the Stark effect • Neglect relativity Diveki et al. Chemical Physics, 2013, 414, 121. Spanner, Patchkovskii. Chemical Physics 2013, 414 10. 26 • Neglect Coulombic interaction
  28. 28. MULTIPLE ACTIVE ELECTRONS THEORETICAL SINGLE ACTIVE ELECTRON Itatani et. al. Nature. 2004, 432, 867. Patchkovskii, Zhao, Brabec, Villeneuve. Physical Review Letters. 2006, 97, 12003. 27 MULTIPLE ACTIVE ELECTRONS
  29. 29. THE STRONG FIELD APPROXIMATION Assumptions:  Born-Oppenheimer approximation  Hartree-Fock approximation  Koopman’s approximation o Free electron is a plane wave o Single active electron • Neglect the Stark effect • Neglect relativity Diveki et al. Chemical Physics, 2013, 414, 121. Spanner, Patchkovskii. Chemical Physics 2013, 414 10. 28 • Neglect Coulombic interaction
  30. 30. N2 HOMO Patchkovskii, Zhao, Brabec, Villeneuve. Physical Review Letters. 2006, 97, 12003. 29 THEORETICAL MULTI ACTIVE ELECTRONS REMAINING DISTORTIONS
  31. 31. FUTURE GOAL: POLYATOMIC MOLECULES CHALLENGES: • Closer energy spacing • Complex free electron wavefunctions Siriwardane. CHEM 281, LA Tech. www.chem.latech.edu (accessed 11 Oct. 2013). 30 • Smaller molecular dipoles
  32. 32. FUTURE GOAL: POLYATOMIC MOLECULES CHALLENGES: • Closer energy spacing • Complex free electron wavefunctions Dyson Orbital for Modeled < yc | Corenene Ionization for Corenene Spanner, Patchkovskii. Chemical Physics 2013, 414 10. 31 • Smaller molecular dipoles
  33. 33. FUTURE GOAL: POLYATOMIC MOLECULES CHALLENGES: • Closer energy spacing • Complex free electron wavefunctions Acetylene Allene Torres et. al. Physical Review Letters. 2007, 98, 203007. 32 • Possibility of smaller torque
  34. 34. •  Physical mechanism •  Some agreement EXPERIMENTAL MULTI ACTIVE ELECTRONS SUMMARY •  Polyatomic systems Spanner, al. Nature. 2004, 432, 867. Itatani et. Patchkovskii. Chemical Physics 2013, 414 10. ”High Harmonic Generation” Wikipedia. en.wikipedia.org (accessed 18 Oct. 2013). Patchkovskii, Zhao, Brabec, Villeneuve. Physical Review Letters. 2006, 97, 12003. Modeled < yc | for Corenene 33 Remaining Distortions THEORETICAL THEORETICAL •  Revisions &
  35. 35. ACKNOWLEDGEMENTS Levinger Group: • Dr. Nancy Levinger • Ben Wiebenga-Sanford CSU Department of Chemistry PEERS Chemistry: Faculty: • Dr. Elliot Bernstein • Dr. Mario Marconi • Dr. Carmen Menoni Laura Tvedte, Jenée Cyran, Jake Nite, Kathryn Tracy Electrical & Computer Engineering: • Dr. Randy Bartels Reed Hollinger, Clayton Bargsten, Drew Schiltz Communication: Post-Doctorates & Staff Scientists: Vicky Webber Materials Science: • Dr. Amber Krummel • Dr. Brad Luther Katherine Sebeck 34 • Dr. Christopher Rich
  36. 36. MULTIPLE ACTIVE ELECTRONS N2 HOMO HOMO res et. al. Chemical Physics. 2013, 414, 121. HOMO-1 B-1 THEORETICAL – Hartree-Fock
  37. 37. THEORETICAL H-F HOMO res et. al. Chemical Physics. 2013, 414, 121. N2 HOMO EXPERIMENTAL Harmonics 17-31 B-3 MULTIPLE ACTIVE ELECTRONS
  38. 38. THEORETICAL H-F HOMO-1 res et. al. Chemical Physics. 2013, 414, 121. N2 HOMO EXPERIMENTAL Harmonics 17-31 B-3 MULTIPLE ACTIVE ELECTRONS
  39. 39. MULTI-ACTIVE ELECTRONS res et al Chemical Physics 414 (2013) 121–129 IL = 1.0x1014 W/cm2 B-4 IL = 1.2x1014 W/cm2
  40. 40. RECONSTRUCTION Inverse Fourier transform of the recombination dipole moment yields: res et al Chemical Physics 414 (2013) 121–129 C u = x ', z'   1 D(w, I L , q )  f  ˆ r du (k ) =< y 0 | u | k >= dref (k ) R(q ) Dref (w, I L )  rˆ Á ® r '[du (kx ', kz ' )] u y0 (x ', z') = k u
  41. 41. HHG TOMOGRAPHY DATA: N2 0° Itatani et. al. Nature. 2004, 432, 867. D HHG Tomography HOMO
  42. 42. ELECTRON TRAJECTORY Electron position x x(ti)=0 v(ti)=0 1 0 21 19 17 15 0 Mairesse et al. Science 302, 1540 (2003) Kazamias and Balcou, PRA 69, 063416 (2004) Short traj. Chirp > 0 Long traj. Chirp < 0 Emission time (te) E Harmonic order Time (TL)

Notas do Editor

  • Thank you for coming to my talk. Today I will cover:Physical background of the high harmonic generation tomography techniqueOverview of recent benchmark measurements of molecular electronic structureFuture directions
  • Electronic structure determines ALLchemical properties: Bonding (Hydrogen) chemical structure (benzene) phase transitions much more
  • energy levels of the valence electrons of the nitrogen atomhydrogen is the only atomic system that can be solved exactlyenergy levels that are shown here are the hydrogenic orbitalsA molecule is formed of two atomsCombining their orbitalsNew energy levels are found using geometry optimization techniquesThe electrons are then redistributedThe geometries (occupied in blue/green, unoccupied in red/yellow)Surfaces of highest probability position of the electronsIn N2, 3sg is the highest occupied, or HOMOI will talk about n2 a lot today, when we are discussing this N2 HOMO I will put this symbol in the top right corner
  • Recently this de Oteyza paper was published showing these beautiful images of molecular structuresSTM is difficult to resolve the molecular structureAFM measurements with high resolution allow distinguishing between single &amp; triple bondsThis resolution is still not great enough to distinguish orbital shapes, but HHG tomography permits 0.5 A resolution!
  • Any good measurement technique needs to be observable &amp; selective:This technique will observe HHG radiationThe system observed will be selected by:The tunneling probability of the HOMO electronThe alignment of the molecule
  • Described by Diveki et al. as: “ “Basic premise:Tunneling of electron away from the moleculeAcceleration of the free electron in space under laser field (away from and back towards molecule)Recombination back to ground state of the molecule, releasing excess energy as a photon
  • To start with, HHG is not SFG, like I have in this laser pointer. This pointer is a YAG laser which emits at 1064nm, but you can see the radiationdoubling crystal in the pointer which converts the light to the visible regionLinear decrease in intensity of harmonic ordersThis is the type of harmonic generation that most of us are familiar with, in theSOLID STATELOW INTENSITIESHHG tomography uses a GAS JETLOW INTENSITIES (analogous to laser pointer)odd order harmonicsstill has the linear trend in intensitiesMechanism:MULTI photon ionizationfollowed by electron relaxation to the ground stateHHG radiationHIGH intensitiesHIGH HARMONIC PLATEAUDifferent physical mechanismProvides more information about the generating medium
  • Example of a typical HHG tomography experiment:Ti:Sapph light comes in, split into probe &amp; alignment beamsProbe:compressed to shorter pulses &amp; intensities &gt;=10^14 W/cm^2 required for HHGArrives after the alignment beamAlignmentVariable delay controls arrival timePolarization controls the alignment of the moleculesIntensities must be low enough that there is no HHGProbe beam is focused at front edge of the gas jet to minimize distribution of intensities in beamVacuum must be used to propagate HHG, prevent interaction of radiation with other substances before observationAny detection system will work as long as it has the correct frequency range and intensity detectionsCommonly a phosphorescent screen will be used before the CCD to detect UV/XUV
  • Commonly described using QM &amp; classical in three steps.Diagrams indicatelaser pulse (red, solid is field &amp; dotted is the wave packet) relative to the molecule (black line)Each step can occur at a range of times, as indicated by these boxes
  • Schematic of the ground state of an electron in one dimension:X axis: the position of the electron relative to the center of mass of the moleculeY axis: the corresponding potential energyGap from the highest possible potential energy to the lowest potential energy is referred to as the IONIZATION ENERGYTIME: before the field interacts with the molecule
  • When a field is applied across the molecule:potential energy of the electron outside of the molecule becomes equal to that in the moleculePotential energy barriertunneling
  • Tunneling is exponentially dependent on the energy of the electronstrongly selective of highest energy electron (HOMO)If the frequency of the radiation is too high, electron may just overcome barrier instead of tunneling
  • As the field is applied to this free electron, it accelerates away from &amp; back towards the molecule, gaining kinetic energy.
  • Once the field is removed, the electron recombines to the ground state, releasing the energy in the form of a photon.
  • This photon is the observable.
  • The intensity &amp; frequency of light describes the interaction of the electron with the electron density remaining in the molecule, much like STM.To extend the use of this, Itatani et al. proposed that the molecular orbital can be reconstructued using prior knowledge of the tunneling probability, laser field &amp;
  • Angular is faster, only need to measure 90 degrees.
  • As anyone who has had a CT scan knows, to get accurate measurements you have to hold very, very still. I’m sure no one here would expect molecules to hold their breath, so to get this structure it will be necessary to align the molecules.
  • Short, intense laser pump pulse creates rotational coherence  Induces nonadiabatic alignment with anisotropic polarizability of the moleculeRotational wave packet manifests periodic quantum “revivals” &amp; fractional revivals of alighment distribution that create transient alignment and anti-alignment of molecular sample at certain times after pump pulseCheck:T. Seideman and E. Hamilton, Adv. At. Mol. Opt. Phys. 52, 289 (2006).H. Stapelfeldt and T. Seideman, Rev. Mod. Phys. 75, 543 (2003).T. Seideman, Phys. Rev. Lett. 83, 4971 (1999).UCLA?
  • Laser does not induce multi-electron effects (single active electron approximation SAE)—&lt;Seen studies now, but not molecular yet&gt;.Hartree-Fock ApproximationAssumes a set of single-electron wavefunctionsKoopman’s approximationNeglect correct antisymmeterization between continuum electrons &amp; remaining bound electrons&lt;ionized electron does not distort the bound electrons. May be valid if electron is removed so rapidly that the electrons do not have force exerted on them?&gt;Neglect relativity &lt;what is the limit of this approximation?&gt;Born-Oppenheimer, also constant during laser pulse &lt;what are the time-scales for nucleus motion and the laser pulses? Pulses ~40fs usually?&gt;Limited number of neutral &amp; cation field-free eigenstates.
  • ----- Meeting Notes (10/23/13 10:08) -----Model!
  • Laser does not induce multi-electron effects (single active electron approximation SAE)—&lt;Seen studies now, but not molecular yet&gt;.Hartree-Fock ApproximationAssumes a set of single-electron wavefunctionsKoopman’s approximationNeglect correct antisymmeterization between continuum electrons &amp; remaining bound electrons&lt;ionized electron does not distort the bound electrons. May be valid if electron is removed so rapidly that the electrons do not have force exerted on them?&gt;Neglect relativity &lt;what is the limit of this approximation?&gt;Born-Oppenheimer, also constant during laser pulse &lt;what are the time-scales for nucleus motion and the laser pulses? Pulses ~40fs usually?&gt;Limited number of neutral &amp; cation field-free eigenstates.
  • Laser does not induce multi-electron effects (single active electron approximation SAE)—&lt;Seen studies now, but not molecular yet&gt;.Hartree-Fock ApproximationAssumes a set of single-electron wavefunctionsKoopman’s approximationNeglect correct antisymmeterization between continuum electrons &amp; remaining bound electrons&lt;ionized electron does not distort the bound electrons. May be valid if electron is removed so rapidly that the electrons do not have force exerted on them?&gt;Neglect relativity &lt;what is the limit of this approximation?&gt;Born-Oppenheimer, also constant during laser pulse &lt;what are the time-scales for nucleus motion and the laser pulses? Pulses ~40fs usually?&gt;Limited number of neutral &amp; cation field-free eigenstates.
  • CHALLENGES:Closer energy spacingMore tunneling character from non-HOMO electronsComplex free electron wavefunctionsMore complicated function for continuum wavefunction, . Smaller molecular dipolesLess precise alignment
  • CHALLENGES:Closer energy spacingMore tunneling character from non-HOMO electronsComplex free electron wavefunctionsMore complicated function for continuum wavefunction, . Smaller molecular dipolesLess precise alignment
  • CHALLENGES:Closer energy spacingMore tunneling character from non-HOMO electronsComplex free electron wavefunctionsMore complicated function for continuum wavefunction, . Smaller molecular dipolesLess precise alignment
  • 1 a.u. = 0.529177249 angstrom
  • 1 a.u. = 0.529177249 angstrom
  • 1 a.u. = 0.529177249 angstrom
  • 1 a.u. = 0.529177249 angstrom
  • 1 a.u. = 0.529177249 angstrom
  • Measured at 19 angles between 0-90 degrees (some are omitted for clarity of the image).Ar is the reference atom for this measurement.

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