How to Read a 3d Molecule Map

Abstruse

Ultrafast light amplification by stimulated emission of radiation pump-probe methods let chemical reactions to be followed in real time, and have provided unprecedented insight into fundamental aspects of chemic reactivity. While evolution of the electronic structure of the system nether study is evident from changes in the observed spectral signatures, information on rearrangement of the nuclear framework is generally obtained indirectly. Disentangling contributions to the signal arising from competing photochemical pathways tin can also be challenging. Here we introduce the new technique of three-dimensional covariance-map Coulomb explosion imaging, which has the potential to provide consummate iii-dimensional information on molecular structure and dynamics as they evolve in real fourth dimension during a gas-stage chemic reaction. We nowadays first proof-of-concept data from contempo measurements on CF_iiiI. Our approach allows the contributions from competing fragmentation pathways to be isolated and characterised unambiguously, and is a promising route to enabling the recording of 'molecular movies' for a wide variety of gas-phase chemical processes.

Introduction

Light amplification by stimulated emission of radiation pump-probe experiments have been used for several decades to probe the dynamics of ultra-fast chemical processes, with the doable time resolution having reached the femtosecond timescale^ane by the mid-1980s. Spectroscopic probing with tens-of-femtosecond time resolution allows the evolving free energy level structure of the chemical organisation nether study to be followed in real time as the reaction proceeds, while velocity-map imaging^2,3 (VMI) allows measurement of the evolving reaction production scattering distribution on the same timescale. In a typical VMI measurement, the pump light amplification by stimulated emission of radiation initiates the chemical procedure of interest, the probe light amplification by stimulated emission of radiation ionises ane or more of the fragments, and the ionised products are then accelerated along a flight tube by an electrical field. At the end of the flight tube their velocities are mapped onto a position-sensitive ion detector, and the optical image generated by the ion detector is recorded with a fast camera. The product scattering distribution recorded in this way provides a detailed fingerprint of the forces acting during the reaction, and therefore of the chemical mechanism. Velocity-map imaging studies over the past ii decades or so have provided unprecedented insight into the dynamics of a wide variety of unimolecular and bimolecular reactions^{iv,five,6,7,8}, even revealing previously unknown reaction mechanisms⁹.

Recently-adult multi-mass velocity-map imaging approaches^10,11,12 have extended the technique to larger chemic systems by enabling detection of all products on each experimental bike, an advance over earlier approaches in which only ane species could exist detected in a given experiment. In addition to substantial gains in data acquisition speed, multi-mass imaging also enables correlations to exist uncovered between the scattering distributions of different reaction products, providing fifty-fifty more than detailed information on the reaction mechanism. Such correlations are revealed by computing the statistical covariance¹³ between the velocity distributions of reaction product pairs. Covariance assay¹⁴ has been exploited previously in applications including time-of-flying mass spectrometry^xv, photoelectron spectroscopy¹⁶, and gamma ray spectroscopy¹⁷ as a powerful tool for uncovering correlations betwixt the velocities of two or more particles. In the context of velocity-map imaging, the information obtained is similar to that revealed in coincidence imaging measurements^{eighteen,19,20,21,22}, which have been used to follow reactions in real fourth dimension²³. A coincidence experiment records the relative position and arrival times of two or more charged particles arising from the same outcome by using the arrival of the first (lightest) particle at the detector to trigger recording of signals for the remaining, heavier particles. An issue is only stored if all (or at to the lowest degree a predefined minimum number) of the expected particles are detected. Coincidence experiments require a depression count rate—typically fewer than one event per experimental wheel—in social club to avert high numbers of fake coincidences which would overwhelm the signal from true coincidences. This necessitates a loftier repetition rate in gild to achieve a sufficiently high data acquisition speed to make the experimental measurements feasible. Covariance imaging, in contrast, can exist used in much higher count-charge per unit regimes, at either depression or high repetition rates, and offers an alternative approach to coincidence imaging, particularly in cases where high repetition rate laser systems are not available. Covariance imaging is likely to prove particularly useful as molecular size increases, since at that place are no intrinsic limitations on the number of ions that tin exist detected on each experimental cycle.

In well-nigh VMI experiments, the probe laser simply ionises the reaction products, and the VMI measurement provides data on product identities and their energy level structure and handful distributions. If instead of ionising the products, a probe laser is employed with sufficiently high intensity to initiate Coulomb explosion¹³, it becomes possible to obtain structural information directly on the femtosecond timescale, providing an culling to diffraction methods such as ultrafast X-ray diffraction^24,25,26 and ultrafast electron-diffraction^27,28. To initiate a Coulomb explosion, an intense probe laser pulse strips multiple valence electrons from the molecule, eliminating one or more than chemical bonds and creating a highly unstable collection of positively charged ions. The nuclei do not have time to motility significantly during this process, and are therefore still located at or very close to their original positions within the structure. Coulomb repulsion between the ions apace leads to a 'Coulomb explosion', during which the initial positions of the ions are mapped onto their final velocities past the repulsive forces acting between the recoiling ions. This mapping is key to the structural measurement. By measuring the ion velocities in the velocity-map imaging step, one can in effect 'work backwards' to the original molecular structure. Under ideal atmospheric condition the probe light amplification by stimulated emission of radiation would strip a sufficient number of electrons from the sample molecule to crusade it to explode into diminutive ions, the and so-called 'pure Coulomb explosion' regime. We have demonstrated this approach in our previous piece of work on substituted methanes, bromines, and biphenyl molecules^{13,29,thirty,31,32}. These before experiments employed traditional 'crushed' velocity-map imaging, and nosotros were therefore limited to recording ii-dimensional projections of the velocity distributions. Using two-body and three-torso covariance approaches, these were analysed to obtain two-dimensional projections of the molecular structures, to distinguish between structural isomers, including enantiomers, and to follow structural change on the femtosecond timescale.

In this piece of work, we extend the approach to iii-dimensions, demonstrating 3D-sliced^33,34 Coulomb-explosion covariance-map imaging for the first time. For this first demonstration nosotros focus on the one-laser photoionization and subsequent fragmentation and Coulomb explosion of CF₃I. Besides every bit demonstrating the potential for structural studies, we as well show that covariance-map imaging offers a powerful tool for disentangling contributions to the overall signal from competing reaction pathways. In particular, it shows definitively which reaction products are (and are not) formed together during a chemical issue, since covariances volition only exist seen between these products. Such tools will become increasingly important as the field of reaction dynamics moves away from studies of modest molecules and towards investigations into larger, more complex chemic systems.

Results

Identification of reaction products

Every bit explained in the Introduction and Methods, post-obit irradiation of gas-phase CF₃I with a loftier intensity, ultra-short 800 nm laser pulse, the imaging detection system records the position and arrival time of each ionised fragment at the position-sensitive detector. Integrating over the spatial coordinates yields the fourth dimension-of-flying spectrum, while plotting the spatial coordinates over the range of arrival times corresponding to a chosen reaction product reveals the handful distribution for that species. The fourth dimension-of-flight mass spectrum for the charged fragments formed post-obit irradiation of neutral CF₃I by a 535 μJ, ∼40 fs pulse from the 800 nm Artemis light amplification by stimulated emission of radiation is shown in Fig. i. We note that the detection sensitivity of the ion detector was attenuated at the inflow times of very intense peaks respective to grand/z = 196 (parent ion), 98 (doubly-charged parent ion), and 18 (H₂O) in lodge to prevent harm to the ion detector. Time-gating of the H₂O groundwork signal in this way unfortunately reduced our ability to detect the nearby F⁺ ion, with m/z = nineteen. Betoken from the atomic ions C⁺, I⁺, F²⁺, C²⁺, I^two+ and I³⁺ is clearly visible in the mass spectrum, as is significant signal from molecular fragment ions, including \({\mathrm{CF}}_3^ +\), \({\mathrm{CF}}_2^ +\), \({\mathrm{CF}}_3^{2 + }\), CF⁺ and \({\mathrm{CF}}_3^{three + }\), indicating that sufficient ionisation was accomplished to initiate Coulomb explosion and generate a variety of diminutive and molecular fragment ions. Note that in that location is some signal (O²⁺, N₂ ⁺, H₂O⁺) from residual air in the chamber, and some (\({\mathrm{CS}}_2^{2 + }\), CS⁺, \({\mathrm{CS}}_2^ +\)) from a previous sample that could not be completely eliminated from the system within the bachelor experimental time. However, these peaks are well separated in time from the CF_iiiI peaks of interest, and with the exception of H₂O⁺ discussed above, exercise not interfere with the signal.

Fig. one: Reaction production identification.

Charged fragments are identified from their arrival times within the time-of-flight spectrum recorded following laser-induced Coulomb explosion of CF₃I. Peaks of interest are labelled in black, with background peaks labelled in gray.

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Observed fragmentation pathways from covariance in ii-dimensions

Fragmentation of doubly-charged CF₃I²⁺ ions following double photoionisation of neutral CF₃I has been studied previously^35,36,37. Four master product channels take been identified, yielding the products \({\mathrm{CF}}_3^ + + {\mathrm{I}}^ +\), \({\mathrm{CF}}_2^ + + {\mathrm{I}}^ + + {\mathrm{F}}\), CF⁺ + I⁺ + 2F and CF₂I²⁺ + F, respectively. The time-of-flight mass spectrum shown in Fig. 1 reveals the presence of nearly of the ionic products from these processes, merely does not in itself allow us to decide whether they are formed via the processes above, or via fragmentation of more than highly charged parent ions. The presence and subsequent fragmentation of parent ions with more than two charges is clear from the presence of multiply charged fragment ions (east.g., C²⁺, Fⁱⁱ⁺, \({\mathrm{CF}}_3^{2 + }\), \({\mathrm{CF}}_3^{3 + }\), I²⁺, I³⁺) in the mass spectrum. Fragmentation of highly charged CF₃I ions has been studied previously past Douglas³⁸. Our intention in this work is not to carry out an exhaustive dynamical report of the photofragmentation dynamics of multiply charged CF₃I, only to use CF_threeI as a test organization to demonstrate the way in which covariance-map imaging can be used to uncrease complex signals arising from multiple competing dissociating pathways. Nosotros volition do this with the aid of a few examples.

We begin past because the dominant and lowest energy Coulomb explosion processes observed under our experimental weather (and previously past others^35,36,37,38), which involve cleavage of the C–I bail post-obit formation of a multiply charged parent ion, i.e.,

$${\mathrm{CF}}_3{\mathrm{I}}^{north + } \to {\mathrm{CF}}_3^{m + } + {\mathrm{I}}^{(n - m) + }$$

(1)

In terms of a strategy for identifying the various possible product pairs from the velocity-map images, we note that each accuse-land pair experiences a characteristic Coulomb repulsion between the recoiling fragments, yielding fragment velocity distributions that are specific to each channel. For example, the measured velocity distribution for \({\mathrm{CF}}_3^ +\) ions contains contributions from channels involving I, I⁺ and I²⁺ partner fragments, which manifest in the \({\mathrm{CF}}_3^ +\) velocity distribution as a series of concentric spheres. These rings are seen clearly in the total 3D-sliced velocity-distribution for \({\mathrm{CF}}_3^ +\) shown on the left-mitt side of Fig. 2, and besides in the central piece through the distribution shown on the top right-manus side of the same effigy.

Fig. 2: 3D and 2d velocity-map and covariance-map images.

a 3D-sliced velocity distribution recorded for \({\mathrm{CF}}_3^ +\) fragments; b central piece of the 3D handful distributions for the \({\mathrm{CF}}_3^ +\), I⁺ and I²⁺ products. Beneath these are shown the covariance-map images for \({\mathrm{CF}}_3^ +\) formed with an I⁺ partner ion and with an Iⁱⁱ⁺ partner ion. The vertical dotted lines show which features of the scattering distributions correspond to the pathways revealed in each of the covariance signals. Notation that the signals in the centres of the distributions correspond to ions formed with a neutral partner, which do non give ascent to a covariance signal since the neutral partners cannot exist detected in our experiment. All images are plotted on a normalised intensity scale.

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Disentangling all of the competing fragmentation pathways that contribute to a particular ion signal in a velocity-map imaging experiment has in the past been a complex process. All the same, covariance assay of the recorded information offers a vast simplification. Since covariances are merely observed between ions that are formed in the aforementioned event, transforming the measured velocity-map images into covariance images for specified ion pairs allows the contribution to the overall ion signals from each pathway to be identified unambiguously. Covariance-map images are shown for the channels \({\mathrm{CF}}_3^ +\) + I⁺ and \({\mathrm{CF}}_3^ +\) + I²⁺ on the right hand side of Fig. 2, reduced to 2D projections for visualisation purposes. The cardinal slices of the total 3D scattering distributions for the \({\mathrm{CF}}_3^ +\), I⁺ and I^two+ fragments are shown in the height panel, with the covariance images between the various ion pairs plotted below. In each covariance image, one of the two products is called equally the reference ion, travelling in the reference management towards the right of the paradigm, indicated by an arrow. The intensity within the image shows the velocity distribution of the partner fragment relative to the reference ion. In each case, a articulate covariance signal is seen, revealing—as expected for a pairwise dissociation—that the 2 fragments recoil in contrary directions with well-defined velocities. Some residual groundwork signal is also present in other regions of the covariance images. This arises from imperfect subtraction of 'simulated covariances' during the conversion from velocity-map images to covariance-map images (see Methods section), and reduces in intensity equally the number of experimental cycles included in the data set is increased. This background indicate tin safely be ignored for the purposes of the present word.

As noted in a higher place, the final velocities of the fragments are determined primarily by the total charge on the dissociating parent ion, which determines the forcefulness of the Coulomb repulsion betwixt the \({\mathrm{CF}}_3^ +\) ion and its I⁺ or I²⁺ partner ion. The repulsion is higher in the instance of more highly charged ions, yielding higher velocities for the \({\mathrm{CF}}_3^ +\) + I²⁺ aqueduct than for the \({\mathrm{CF}}_3^ +\) + I⁺ channel. This is seen clearly in the covariance-map images, with the \({\mathrm{CF}}_3^ +\) velocity peaking further from the centre of the epitome when partnered with I^two+ than when partnered with I⁺. The full kinetic energies of the \({\mathrm{CF}}_3^ +\) and I⁺/I²⁺ ions formed in the two channels are found to be 5.6 eV and 10.55 eV. Based on the 2.144 Å equilibrium bail length of the C–I bail in CF_threeI, these energies are significantly lower than would exist expected if Coulomb repulsion were the merely force acting on the departing ions. In mutual with the findings of other authors^39,40,41,42, we note that all relevant chemical forces must be included in order to construct an accurate model of the potential energy surface over which the dissociation proceeds.

Every bit a second instance, Fig. three shows the key slice of the scattering distribution recorded for \({\mathrm{CF}}_2^{+}\), together with the covariance-map image for \({\mathrm{CF}}_2^ +\) formed together with I⁺. While at that place are various possible routes to forming the \({\mathrm{CF}}_2^ +\) + I⁺ ion pair from multiply-charged CF₃I ions, we believe that the form of the covariance image implies that they arise from dissociation of CF₃I^two+ to form \({\mathrm{CF}}_2^ +\) + I⁺ + F. Eland et al. showed³⁵ that this is the next lowest energy fragmentation pathway for CF_iiiI²⁺ afterward the \({\mathrm{CF}}_3^ +\) + I⁺ pathway considered above. The ion pair is formed in a 2-stride mechanism: the CF_threeIⁱⁱ⁺ parent ion offset loses a neutral F atom, leaving behind CF_iiI²⁺, which subsequently decays into \({\mathrm{CF}}_2^ +\) + I⁺. The detailed form of the covariance image tin can be rationalised past considering the forces acting in each of the two steps. The image is very like to those observed in Fig. 2, which resulted from axial recoil of \({\mathrm{CF}}_3^ +\) from I⁺ or I²⁺. Still, the covariance is non as sharp. Loss of neutral F from CF₃I^two+ results in a modest momentum 'kick' to the resulting CF_iiI²⁺ intermediate. Though the forces involved in this step are much smaller than the Coulomb repulsion acting in the second step, they are sufficient to cause a small blurring in the covariance between the \({\mathrm{CF}}_2^ +\) and I⁺ fragments.

Fig. three: 2D velocity-map and covariance map images for the \({\mathrm{CF}}_2^ +\) + I⁺ + F channel.

a central piece of the 3D scattering distribution for the \({\mathrm{CF}}_2^ +\) product of CF₃Iⁱⁱ⁺ dissociation; b covariance-map image of \({\mathrm{CF}}_2^ +\) formed with an I⁺ partner ion. Both images are plotted on a normalised intensity scale.

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Covariance in three dimensions

Nosotros now movement on to considering the information gear up in iii dimensions in order to demonstrate 3D-sliced covariance-map imaging. As an example, we volition focus our attention on the CF₃I²⁺ →\({\mathrm{CF}}_3^ +\) + I⁺ fragmentation channel. To visualise the covariances in 3 dimensions, the covariance analysis is carried out for each pair of slices inside the 3D-sliced information sets for \({\mathrm{CF}}_3^ +\) and I⁺. A subset of the results of this analysis are shown in Fig. four. In each of the iii panels, \({\mathrm{CF}}_3^ +\) ions within a single slice are used to ascertain the reference direction, and covariances with all slices of the I⁺ data set are plotted. Equally was the case in two-dimensions, the I⁺ ions are seen to recoil in a management opposite to that of the \({\mathrm{CF}}_3^ +\) reference ion. Though the recoil velocity is relatively well divers, equally is the athwart distribution within the plane of any single slice, the distribution is considerably broader than might be expected in the direction defined by the fourth dimension-of-flight axis. Assuming axial recoil of the two fragments, and performing a Gaussian fit to the angular distribution inside the covariance map images, we estimate the full-width-one-half-maximum angular resolution to exist approximately 6 degrees in the azimuthal angle (within the slicing aeroplane) and 25 degrees in the polar angle (measured from the time-of-flight axis). We attribute the observed blurring of the velocity distribution forth the time-of-flying axis to a combination of factors, including the laser pulse length, a small amount of infinite-charge repulsion within the expanding ion cloud arising from ionisation of the He molecular axle carrier gas, the decay lifetime of the phosphor screen that forms part of the ion detection system, and small imperfections in the velocity-mapping field. It will be possible to better on all of these in time to come experiments. The 3D covariance assay can be repeated for all pairs of fragments in lodge to unpick the fragmentation dynamics associated with each fragmentation channel in three dimensions.

Fig. 4: 3D covariance-map images for the \({\mathrm{CF}}_3^ +\) + I⁺ fragmentation aqueduct.

The direction of travel of the \({\mathrm{CF}}_3^ +\) reference ion is shown by the black arrow; the velocity distribution of the I⁺ ion relative to this reference direction is shown by the intensity distribution inside each slice of the 3D covariance-map.

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Discussion

We have introduced the technique of 3D-sliced covariance-map imaging as a new probe of molecular structure and dynamics, and have demonstrated its use for the first time in a prepare of measurements to investigate the laser-induced Coulomb explosion dynamics of CF_threeI. We have shown that the arroyo is able to identify private contributions to a signal comprising contributions from many different competing fragmentation pathways, providing a powerful tool for disentangling complex dynamics within large molecular systems. While this written report illustrates this in the context of dissociative photoionization, the method is equally applicable to studying any photoinitiated process when an appropriate pump-probe laser scheme is employed to initiate reaction and ionise the products to exist detected.

Of equal if non greater interest is the potential to use covariance-map imaging in combination with molecular Coulomb explosions equally a probe of molecular structure in the gas stage. We have shown previously^{xiii,24,xxx,31,32} that significant structural information tin be obtained when employing this arroyo in conventional two-dimensional 'crushed' velocity-map imaging approaches, and in this work we extend the experimental capabilities to 3 dimensions by incorporating slice imaging into the velocity-map imaging detection scheme. This enables us to visualise covariances in three dimensions for the outset time. We note that structural data is obtained on the femtosecond timescale, with no need for preparing spatially aligned or oriented reactants, and no need for image inversion algorithms.

In this work, the light amplification by stimulated emission of radiation pulse energy bachelor at the Artemis ultrafast laser facility was in the range yielding both atomic and molecular fragment ions. With higher light amplification by stimulated emission of radiation pulse energies, such that Coulomb explosion into atomic ions is achieved, the approach is able to provide direct information on 3-dimensional molecular structures via the mapping from atomic positions to fragment ion velocities that occurs during the Coulomb explosion. Achieving this requires that the mapping is well understood. Previously, a diversity of wavepacket and trajectory-based approaches take been applied to the trouble^{24,39,xl,41,42}, in many cases with a high degree of success. Within our ain group, we are currently developing on-the-fly/Built-in-Oppenheimer molecular dynamics trajectory-based methods which take into account all of the chemic forces interim on the separating fragments during a Coulomb explosion. The eventual aim is to implement a 'structure refinement' algorithm to obtain molecular structures from covariance-map images given an 'initial gauge' construction, in an coordinating mode to structure refinement of crystalline solids from X-ray diffraction data.

3D-sliced covariance-map imaging is currently at a relatively early phase of implementation, but with further development will enable recording of 3-dimensional 'molecular movies' in real fourth dimension during a reactive event.

Methods

Coulomb-explosion velocity-map imaging measurements

The experiments were performed at the Artemis ultra-fast light amplification by stimulated emission of radiation facility, office of the Central Light amplification by stimulated emission of radiation Facility in Harwell, Oxfordshire⁴³. The Artemis laser is a customised and modified RedDragon 1 kHz Ti:Sapphire laser from KMLabs, operating at 800 nm.

The velocity-map imaging experiment is independent within a loftier-vacuum system with a base pressure of effectually 10⁻⁷ mbar. Neutral CF_threeI was prepared in a highly diluted seeded molecular beam with He as the buffer gas at a stagnation pressure of 1.2 bar, via supersonic expansion through a Parker Hannifin Series 9 Full general Valve operating at a repetition rate of 20 Hz. After passing through a skimmer into the velocity-map imaging lens, the molecular beam was intersected by a 535 μJ, ∼40 fs pulse from the Artemis laser, initiating multiple ionisation and Coulomb explosion. In addition to employing a very dilute gas mixture, the molecular beam intensity within the vacuum chamber was carefully controlled in gild to minimise space-charge repulsion: a molecular axle intensity that is too high results in considerable distortions to the velocity-map images, with a highly detrimental issue on velocity resolution.

The velocities of the ions generated during the interaction between the laser and molecular axle are measured using 3D-sliced velocity-map imaging. The electric field maintained within the velocity-map imaging lens is used to extract the ions along a time-of-flight tube towards a 75 mm diameter position-sensitive detector (Photonis), separating the ions by inflow time according to their mass-to-charge ratio. The velocity-map imaging lens was based on the 5-lens-element 'DC sliced imaging' design of Townsend et al.³⁴, and the electrical field within the lens is tuned to retain the three-dimensional structure of the scattering (velocity) distribution for each of the ions following the procedure described by the same authors. Typical potentials applied to the v lens elements were 4000 V, 3560 Five, 2400 Five, 1600 V and 0 Five. The terminal lens element is always grounded to maintain field-complimentary conditions within the flying tube. The position along the centrality at which the laser beam crosses the molecular axle inside the VMI lens is non disquisitional; different positions but result in slightly dissimilar optimum slicing potentials.

The detector is comprised of a pair of microchannel plates (MCPs) coupled to a fast phosphor screen. Each ion striking the front confront of the detector generates a pocket-size spot of light on the phosphor, allowing the scattering distribution of each ion to be visualised as the ions strike the detector. The potentials practical to the MCPs were time-gated to reduce the indicate intensities from highly abundant ions (He⁺, H₂O⁺ and Due north_ii ⁺) in gild to avoid harm to the detector. Under typical operating weather, the front end MCP was grounded, and the back MCP was switched between 500 V ("off") and 1850 V ("on"). The phosphor was held at a potential of 4500 V. A PImMS multimass imaging camera^11,12 positioned behind the phosphor screen records the arrival time and position of each ion with a fourth dimension resolution of 12.5 ns. The resulting data set comprises images of the three-dimensional product velocity distribution for each mass-to-charge ratio.

At low laser powers, no Coulomb explosion was observed. As the laser ability was increased up to the optimum value of 535 μJ, the formation of higher charge states of the parent ion could be inferred from the appearance of increasingly high accuse states of atomic iodine in the time-of-flight spectrum, together with the appearance of additional high-velocity rings in the \({\mathrm{CF}}_3^ +\) images. When optimising the experimental conditions, the filibuster between the laser pulse and camera trigger can be tuned to ensure that the centre slice of the velocity distribution is captured by maximising the radius of the observed image for a fragment of involvement. This is useful when comparing the results of 3D slice imaging with conventional 2D piece imaging experiments.

Data processing and assay

Conversion from pixel number to velocity was achieved using a scale based on measurement of Coulomb-explosion images for the well-characterised Coulomb explosion products of N₂ in various charge states⁴⁴, and confirmed using SIMION eight.0 ion trajectory simulations⁴⁵. The raw images were Abel inverted to decide the velocity distribution of each ion species, which is related to the initial position of the ion within the probed molecular structure via the forces experienced during the Coulomb explosion.

Correlated velocity-distributions between pairs of ions were obtained through a covariance analysis of the data. This process has been described in item previously in the context of conventional 'crushed' velocity-map imaging, in which the recorded images represent two-dimensional projections of the full three-dimensional velocity distribution^{thirteen,24,30,31,32}. The covariance between 2 parameters A and B is defined every bit the average of the product of their deviations from their respective hateful values 〈A〉 and 〈B〉.

$${\mathrm{cov}}\left( {{\mathrm{A}},{\mathrm{B}}} \correct) = \langle ({\mathrm{A}} - \langle {\mathrm{A}}\rangle )({\mathrm{B}} - \langle {\mathrm{B}}\rangle )\rangle = \langle {\mathrm{AB}}\rangle - \langle {\mathrm{A}}\rangle \langle {\mathrm{B}}\rangle$$

(2)

When applied to the variation in signal inside each pixel of the velocity-map images for two dissimilar ions, one ionic species is designated every bit the 'reference' ion, and a 2d species is designated every bit the 'point' ion. The covariance is calculated between each pixel in the reference image and each pixel in the signal image, with the averaging carried out over the number of experimental cycles in the acquisition. At the end of this process, each pixel in the reference image has an associated covariance map which shows the covariance between this pixel and all of the pixels in the betoken image. To generate the overall covariance image betwixt the two ions, each individual covariance map is rotated such that the reference pixels lie along a common vector, and the maps for the individual reference pixels are summed.

In this work, the 2nd covariance maps were generated from the central slices of the full iii-dimensional data set for the reference and point ions, while the 3D covariance maps were generated past computing the covariances between all individual pairs of slices of the measured scattering distributions for the two ions.

Data availability

All relevant information are available from the authors on request.

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Acknowledgements

We would like to thank Phil Rice, Alistair Cox and Dave Rose, technical staff at the Artemis facility, the Electronic and Mechanical workshop staff at the University of Oxford's Department of Chemistry, and all members of the PImMS (Pixel Imaging Mass Spectrometry) collaboration (https://pimms.chem.ox.air-conditioning.uk). Nosotros are very grateful for access to the Artemis facility from STFC and for financial support from EPSRC Programme Grant EP/L005913/1.

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Affiliations

1. Section of Chemistry, University of Oxford, Chemistry Research Laboratory, 12 Mansfield Rd, Oxford, OX1 3TA, Britain

   Jason Due west. 50. Lee, Hansjochen Köckert, David Heathcote, Divya Popat & Claire Vallance

2. Primal Laser Facility, Science and Technology Facilities Council, Rutherford Appleton Laboratory, Harwell Campus, Didcot, OX11 0QX, UK

   Richard T. Chapman, Gabriel Karras, Paulina Majchrzak & Emma Springate

Contributions

C.Five. devised the experiments. C.V., J.W.Fifty.L., H.K., D.H., D.P., R.C., E.Due south., K.Thousand. and P.M. performed the experiments. J.W.50.L. and C.V. analysed the data and prepared the paper.

Corresponding author

Correspondence to Claire Vallance.

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Lee, J.Due west.Fifty., Köckert, H., Heathcote, D. et al. Three-dimensional covariance-map imaging of molecular structure and dynamics on the ultrafast timescale. Commun Chem 3, 72 (2020). https://doi.org/ten.1038/s42004-020-0320-3

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• Received: 15 December 2019

• Accustomed: 15 May 2020

• Published: 05 June 2020

• DOI : https://doi.org/10.1038/s42004-020-0320-3

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