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[Atsuko Nakayama](https://orcid.org/0009-0002-0016-3750), Naoto Fujii, Koji Hirama, Kentaro Hamada, [Katsuya Shimizu](https://orcid.org/0000-0003-0560-8325), Yuki Nakamoto, [Satoshi Nakano](https://orcid.org/0000-0002-7010-9867), Saori Kawaguchi-Imada, [Yuichi Akahama](https://orcid.org/0000-0003-2736-9855), Ayako Ohmura

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[A High-DensitySupercritical Fluid of H2](https://mdr.nims.go.jp/datasets/11d01077-af9e-493f-a144-49ece70a39dd)

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A High-Density Supercritical Fluid of H2Atsuko Nakayama,* Naoto Fujii, Koji Hirama, Kentaro Hamada, Katsuya Shimizu, Yuki Nakamoto,Satoshi Nakano, Saori Kawaguchi-Imada, Yuichi Akahama, and Ayako OhmuraCite This: J. Phys. Chem. Lett. 2026, 17, 11754−11759 Read OnlineACCESS Metrics & More Article Recommendations *sı Supporting InformationABSTRACT: This study aimed to elucidate the structural evolution of supercritical fluid hydrogen(SCF H2) under high pressure. X-ray diffraction was performed on SCF H2 using synchrotronradiation at room temperature. The structure factor S(Q) was observed in a low-Q region at eachpressure, revealing a crossover at around 0.56 GPa, consistent with our previous Raman spectroscopyresults. The average volume per molecule was calculated at each pressure using the center-to-centerdistance between the nearest neighboring H2 molecules, reflecting van der Waals interactions andcompression of the internuclear distance. The volumes calculated from the face-centered cubic modelwere consistent with those derived from the cited equation of state, with a slight discrepancy thatincreased gradually with the pressure. This finding indicates that further densification following thecrossover occurs primarily by intra-atomic/molecular mechanisms rather than intermolecularshortening of distances, which cannot be adequately explained by the close-packed coordination model alone.Many unresolved issues remain regarding the boundariesof the supercritical fluid (SCF) phase and its intrinsicphysical properties. Numerous studies over the past 20 yearshave suggested that the SCF phase is not a simple single statebut may consist of two states with different physicalproperties.1 Initially, transition in dynamic properties such asthe speed of sound and specific heat were proposed as anexplanation for this.2 However, subsequent research hasreported that the SCF phase cannot be fully explained bythe dualistic concept of static and dynamic properties alone.3In recent years, the concept of the ‘Frenkel line’ has beenintroduced, which classifies the SCF state into ‘nonrigid liquid’and ‘rigid liquid.4,5 Various studies have confirmed that, forseveral pure substances, the Frenkel line acts as a boundary (orregion) where the two states are separated by a smooth andwide-ranging crossover. For example, in SCF N2, theintermolecular distance decreases with increasing pressure upto 150 MPa, resulting in an increase in the coordinationnumber, which stabilizes at a pressure exceeding 150 MPa.6This compression is attributed to a direct reduction in theintermolecular N−N distance. Consequently, at temperaturesand pressures exceeding the Frenkel line, for example, 300 Kand 150 MPa, the aggregation state of N2 molecules changesfrom nonrigid to rigid liquid-like behavior.The SCF phase of H2 has a density equivalent to that ofliquid H2 at 190 MPa and room temperature.7 Furthermore,the transition from the SCF phase to solid phase I occurs at apressure of 5.4 GPa and room temperature.8,9 However, fewstudies have focused on the physical phenomena within anSCF. Until recently, H2 was considered a homogeneous SCFphase at pressures up to 5.4 GPa and room temperature. In ourprevious study, we performed Raman spectroscopy on H2within the pressure range corresponding to the SCF phase atroom temperature and systematically investigated the pressuredependence of the Raman shifts and line widths of therotational and vibrational bands S0(J) and Q1(J), respec-tively.10 As a result, we reported that a crossover occurs at 0.56GPa at room temperature. According to the phase diagram ofH2, which includes the relationship between the temperaturesand pressures at which the speed of sound is minimal,2 welearned that the Frenkel line separating the SCF phase of H2passes through a pressure of approximately 0.56 GPa at roomtemperature.Furthermore, in the postcrossover state of the SCF,pressure-induced changes in the relative intensities of rotonsrevealed that ortho−para conversion occurs at pressures of 1GPa or higher, even in the absence of a catalyst.10 Ortho−paraconversion typically requires several days, even with acatalyst.11 However, under pressure at room temperature,ortho−para conversion occurs within a few hours duringRaman spectroscopy measurements. Elucidating the mecha-nism of ortho−para conversion induced by pressurization atroom temperature without catalysts is crucial; however,research on this mechanism remains in its early stages. Theintermolecular interactions increase with increasing pressure,affecting the nuclear interactions in the postcrossover state. Toverify the mechanism underlying the ortho−para conversionobserved in the higher-pressure SCF phase in the absence ofcatalysis, the collective state of H2 molecules must beReceived: July 21, 2026Revised: September 10, 2026Accepted: September 11, 2026Published: September 29, 2026Letterpubs.acs.org/JPCL© 2026 The Authors. Published byAmerican Chemical Society11754https://doi.org/10.1021/acs.jpclett.6c02439J. Phys. Chem. Lett. 2026, 17, 11754−11759This article is licensed under CC-BY-NC-ND 4.0Downloaded from pubs.​acs.​org/​jpclcd/​article-pdf/​17/​41/​11754/​68705788/​acs.​jpclett.​6c02439.​pdf by NATL INST FOR MATLS SCIENCE (NIMS) user on 16 October 2026https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Atsuko+Nakayama"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Naoto+Fujii"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Koji+Hirama"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kentaro+Hamada"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Katsuya+Shimizu"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Yuki+Nakamoto"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Satoshi+Nakano"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Satoshi+Nakano"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Saori+Kawaguchi-Imada"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Yuichi+Akahama"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Ayako+Ohmura"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.jpclett.6c02439&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?goto=supporting-info&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?fig=tgr1&ref=pdfhttps://pubs.acs.org/toc/jpclcd/17/41?ref=pdfhttps://pubs.acs.org/toc/jpclcd/17/41?ref=pdfhttps://pubs.acs.org/toc/jpclcd/17/41?ref=pdfhttps://pubs.acs.org/toc/jpclcd/17/41?ref=pdfpubs.acs.org/JPCL?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acs.jpclett.6c02439?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://pubs.acs.org/JPCL?ref=pdfhttps://pubs.acs.org/JPCL?ref=pdfhttps://creativecommons.org/licenses/by-nc-nd/4.0/investigated. Information on the structural changes in the SCFphase of H2 could be key to examining the ortho-paraconversion. To this end, H2 must be replaced with D2 to obtainstructural information through neutron diffraction measure-ments. Nevertheless, neutron diffraction experiments on theSCF phase of D2 using a diamond anvil cell (DAC) remaintechnically challenging. As an alternative to neutron diffraction,using X-ray diffraction (XRD) for structural analysis is worthtesting. However, the scattering intensity of H2 is extremelyweak, so it remains to be seen how effective this approach willbe. XRD experiments on the SCF phase of H2 were attemptedusing synchrotron radiation (SR) at SPring-812 and yieldedonly three data points near 0.56 GPa, preventing a detailedcharacterization of the crossover. Furthermore, this analysis didnot quantify the increase in the coordination number of themolecules, which indicates the growth of aggregates uponpressurization. Therefore, in this study, we performed XRD onH2 using SR to obtain detailed data in the pressure range of upto 1.12 GPa at room temperature. We determined thestructure factor at each pressure and investigated how theaggregation state of H2 molecules changes in the SCF state.To prepare the DAC, a phosphor bronze foil with an initialthickness of 300 μm was indented to 230 μm using diamondanvils (DAs) with culets of 800 μm in diameter. A 300 μm holewas drilled at the center of the indentation using an electricaldischarge machine. A gasket was then placed on the lower DA.Ruby balls were placed on the upper DA as pressure markers todetermine the magnitudes of the pressures applied to thesamples. Normal H2 gas with 99.99999% purity was com-pressed to 100 MPa using NIMS gas loading equipment13 andthen filled into the DAC at room temperature. The pressure inthe DAC was determined from the fluorescence of the rubyR1-line using a pressure scale.14The angle-dispersive method was used to obtain thediffraction patterns of the SCF phase using SR on beamlineBL10XU at SPring-8. The X-ray was monochromatized to awavelength λ = 0.4137(1) Å and introduced to the targetthrough a pinhole collimator with a 40 μm diameter. EachXRD image was obtained by exposing the sample to X-rays for120 s per run and averaging the intensity over ten runs. Theaverage measurement temperature during the experiments was299.4 K. All XRD data were collected on an imaging plate (IP)system (Rigaku R-AXIS IV++, readout resolution: 0.1 mm;active area: 300 × 300 mm2). Two-dimensional XRD images,excluding the Kossel lines from the diamond and some spottyreflections that did not form diffraction rings, were integratedalong the rings with a 0.01 degree of 2θ step. Each halo patternwas converted to an intensity vs 2θ profile using anIPanalyzer15,16 and visualized using PDIndexer.17 When usinga DAC, H2 diffraction and Compton scattering from the DAswere obtained simultaneously. Therefore, the XRD pattern ofthe empty DAC was measured and subtracted to remove thebackground diffraction (BG), yielding the diffraction pattern ofH2 at each pressure.Strong Compton scattering from the DAs overlapped withthe weak halo pattern of H2, making it difficult to distinguishthe true intensity of H2 from the raw data. Figure 1a shows theX-ray scattering intensity of H2 against the X-ray scatteringvector Q = 4π sin θ/λ measured at 1.17 GPa through the DAC.The scattering intensity obtained from the empty DAC wasalso plotted on the graph; however, in the regions around Q ≈3 and 4.8 Å−1, unknown diffraction peaks were observed evenfrom the empty DAC. The scattered intensity after subtractingFigure 1. (a) X-ray scattering intensities from H2 sealed within adiamond anvil cell (DAC) at 1.17 GPa and room temperature (H2 +the background diffraction (BG), red dots) and an empty DAC (BG,blue dots). (b) Structure factor S(Q) of H2 at 1.17 GPa. Thescattering intensity of H2 alone was calculated by subtracting the BGintensity from that of H2 + BG, as shown in Figure 1(a), andnormalized using the intensity value at Qmax = 5.8 Å−1 to obtain S(Q).(c) Superimposed image of S(Q) at each pressure. The peakThe Journal of Physical Chemistry Letters pubs.acs.org/JPCL Letterhttps://doi.org/10.1021/acs.jpclett.6c02439J. Phys. Chem. Lett. 2026, 17, 11754−1175911755Downloaded from pubs.​acs.​org/​jpclcd/​article-pdf/​17/​41/​11754/​68705788/​acs.​jpclett.​6c02439.​pdf by NATL INST FOR MATLS SCIENCE (NIMS) user on 16 October 2026https://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?fig=fig1&ref=pdfpubs.acs.org/JPCL?ref=pdfhttps://doi.org/10.1021/acs.jpclett.6c02439?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asthe BG was obtained at each pressure and used to determinethe Qmax value at each pressure. Minimizing the effects of rippleand measurement error required the use of the largest possiblevalue of Q. Consequently, the value of Qmax was set to 5.8 Å−1for all pressures at which the scattering intensities weremeasured. All the scattering intensities were normalized usingthe intensities at Qmax = 5.8 Å−1, resulting in the structurefactors S(Q), as shown in Figure 1b. Complete subtracting theBG from that of H2, including that of the DAC, was unfeasible.Figure 1c shows a superimposed image of S(Q) vs Q plotsobtained at each pressure. Because the unremoved noiseremained unchanged even under pressure, we concluded that itdid not originate from the intrinsic diffraction of H2 in theDAC. At a pressure above 0.41 GPa, a minimal increase in thebaseline appeared at approximately Q = 2 − 3 Å−1. However,when the pressure exceeded 0.56 GPa, a peak shape that isobscured in the BG, represented by asterisks, becomesdetermine the peak shape and grows as a main S(Q) peakwith increasing pressure. At the pressures above 0.56 GPa, themain S(Q) peak shifts continuously and smoothly toward thehigh-Q side with increasing the pressure. The maximumintensity of the main S(Q) peak, observed at Q ≈ 2.3 Å−1,exceeds S(Q) = 1 at pressures of 0.7 GPa. We identified thatthe mountain-shaped reflections and fine peaks, where the Q-values remain constant or jump discontinuously even when thepressure is varied, are not peaks from H2, but rather noise fromstray diamond crystal peaks. The SCF essentially consists of H2molecules arranged randomly, and the diffraction intensitycomprises two contributions: scattering due to H−H bondswithin the molecules and that due to correlations between H2molecules. The main S(Q) peak observed here is locatedaround 2.3−2.5 Å−1, which has been identified as theintermolecular distance. Furthermore, considering from theresults of high-pressure X-ray diffraction study on fluid H2 atroom temperature12 and liquid H2,18 we identified the mainS(Q) peak obtained is the first S(Q) peak for SCF H2.The main S(Q) peak obtained at each pressure was analyzedusing the Lorentzian function. Examples of analyses of S(Q) vsQ plots obtained at pressures of 0.49, 0.56, and 1.17 GPawhere these correspond to the pressure points before, during,and after the crossover, respectively (see Figure S1 inSupporting Information). Although the peak shapes wereslightly broad and weak in the pressure range of 0.28−0.5 GPa,we managed to fit them using Lorentzian functions and obtaineach parameter (see Table S1 in Supporting Information).Figure 2 shows the changes in the position and full width athalf-maximum (FWHM) of the first S(Q) peak with intensityS(Q1st) with increasing pressure (see Table 2S in SupportingInformation). As the pressure increased to 0.56 GPa, the peakposition increases nearly linearly by 1.27 Å−1/GPa. Following atemporary drop in the value of S(Q1st) at 0.56 GPa, the peakposition increases again at a rate of 0.37 Å−1/GPa, which islower than the value obtained below 0.56 GPa. The FWHMdecreases with increasing the pressure, indicating a sharpdecrease within the pressure range of approximately 0.5−0.6GPa. At pressures exceeding 0.56 GPa, the rate of decrease inthe FWHM gradually decreases. The pressure-inducednarrowing of the FWHM for the XRD pattern observed inSCF H2 is explained as follows. In general, the larger the size ofthe ordered region, the narrower the width of the diffractionpeak obtained owing to X-ray interference. As the pressureincreases, the H2 molecules within the fluids come closertogether, and if the size of such larger molecular clustersincreases, the structural units grow. Simultaneously, it issuggested that local molecular orientation correlations mayincrease, leading to a reduction in the disorder of the SCFphase and causing their states to change to more stable andordered structures.We estimated the volume per molecule of SCF H2 toinvestigate the growth of the structural units under pressure.Initially, using a center position Q1st of the S(Q1st) peak, weobtained the average intermolecular distance of H2, dHd2−Hd2≈2π/Q1st, at each pressure, indicating the distance between thenearest hydrogen atoms of neighboring H2 molecules, asillustrated in the inset in Figure 3. To calculate the molarvolume, we needed the distance between the center of adjacentH2 molecules DHd2−Hd2≈ dHd2−Hd2+ rH−H, where rH−H is aninternuclear distance of H2. Therefore, we used our previousRaman spectral data10 to calculate the values of rH−H at eachFigure 1. continuedintensities at approximately 2.5 Å−1, marked by asterisks, increase withincreasing pressure above 0.56 GPa, whereas the line width decreases.Figure 2. Pressure changes in the peak position (top) and full widthat half-maximum (FWHM) (bottom) of the S(Q1st) peak ofsupercritical fluid H2. The errors associated with the values of peakpositions and fwhm’s obtained from the least-squares fit were smallerthan the symbol size. At pressures below 0.56 GPa, the peak shift is1.27 Å−1/GPa; however, it decreases to 0.37 Å−1/GPa above 0.56GPa. The magnitude of the FWHM decreases significantly atapproximately 0.5−0.6 GPa, and a gradual narrowing occurs.The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Letterhttps://doi.org/10.1021/acs.jpclett.6c02439J. Phys. Chem. Lett. 2026, 17, 11754−1175911756Downloaded from pubs.​acs.​org/​jpclcd/​article-pdf/​17/​41/​11754/​68705788/​acs.​jpclett.​6c02439.​pdf by NATL INST FOR MATLS SCIENCE (NIMS) user on 16 October 2026https://pubs.acs.org/doi/suppl/10.1021/acs.jpclett.6c02439/suppl_file/jz6c02439_si_001.docxhttps://pubs.acs.org/doi/suppl/10.1021/acs.jpclett.6c02439/suppl_file/jz6c02439_si_001.docxhttps://pubs.acs.org/doi/suppl/10.1021/acs.jpclett.6c02439/suppl_file/jz6c02439_si_001.docxhttps://pubs.acs.org/doi/suppl/10.1021/acs.jpclett.6c02439/suppl_file/jz6c02439_si_001.docxhttps://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?fig=fig2&ref=pdfpubs.acs.org/JPCL?ref=pdfhttps://doi.org/10.1021/acs.jpclett.6c02439?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-aspressure. If we consider only the normal vibration level (ν = 0),the rotational energy level E(J) can be expressed as follows:19= + + +E J B J J D J J( ) ( 1) ( 1) ...0 02 2(1)where the first term represents the J dependence of therotational energy of a rigid rotor, whereas the coefficientsB0and D0 account for the rotational constants; only the firsttwo terms in eq 1 are considered. The internuclear distancerH−H can be derived using =B rhc0 8 H H202 where h isPlanck’s constant, c is the speed of light, μ is the reduced massof the molecule, and the symbol ⟨···⟩0 denotes averaging overthe zero-point motion of the ν = 0 normal vibration level. Therotational transition energy, S0(J) can be obtained using eq(1), as follows:ikjjj y{zzz ikjjj y{zzz= += + +S J E J E JB D J D J( ) ( 2) ( )(4 6 )3283200 0 03(2)The constants B0 and D0 were obtained using eq (2) via least-squares fitting using the three rotational vibrational levels S0(J)(J 0, 1, 2), as observed in the Raman spectra at each pressure.We then calculated the value of rH−H = ⟨rH − H2⟩1/2, whichrepresents the experimentally derived internuclear distance ofthe H2 molecules.Figure 3 shows the pressure dependence of dHd2−Hd2, rH−H, andDHd2−Hd2. The distance dHd2−Hd2decreased as the pressureincreased up to 0.56 GPa, exhibiting a jump in the data atapproximately 0.56 GPa. When the pressure exceeded 0.56GPa, the value of dHd2−Hd2decreased again; however, thecontraction rate was smaller than that observed at pressuresbelow 0.56 GPa. Conversely, the rH−H distance exhibited anincrease in the contraction rate at pressure exceeding 0.56 GPa,indicating that the space between H2 molecules as well as themolecules themselves were compressed. This finding suggeststhat the intermolecular repulsive forces increased in the postcrossover state in the SCF, resulting in a reduction in the spacebetween the H2 molecules and compression of the H2molecules. The pressure-induced changes in dHd2−Hd2, rH−H,and DHd2−Hd2provided evidence that H2 underwent the crossoverat 0.56 GPa. At this point, the pressure-dependent Raman linewidth exhibited a remarkable shift, indicating changes in therelaxation mechanism of the rotational and vibrationalmodes.10 This finding supports the conclusion that thecollective state of H2 molecules changes, resulting in localhigh-density states.The crossover observed in the SCF phases for neon,4 N2,6 andmethane20 occur along their respective Frenkel lines. It hasbeen observed that, in the pressure range exceeding eachFrenkel line, the coordination number of molecules graduallyincreases with increasing the pressure. The sharp change withincreasing the pressure observed at around 0.56 GPa for H2 isthought to indicate that the crossover has occurred across theFrenkel line. In the pressure range beyond the Frenkel line, H2is also expected to exhibit an increase in the coordinationnumber of its molecule.Subsequently, an average volume per molecule wascalculated using the values of DHd2−Hd2obtained at 0.56 GPaand above to investigate an appropriate model explaining thepressure change in volume following the crossover in SCFphase. In this model, H2 molecules were assumed to be hardspheres, and to take account of the molecules’ coordinationnumber, it was speculated that the molecules are ideally packedin to cubic lattices. When the molecules are arranged in asimple-cubic (SC) coordination model with a lattice parametera = DHd2−Hd2, the average volume per molecule is calculated asVSC = a3 = DHd2−Hd23. In a body-centered cubic (BCC)coordination model, the relationship between DHd2−Hd2and thelattice parameter a is given by =a D23 H H2 2, and the averagev o l ume p e r mo l e c u l e , V B B C , i s o b t a i n e d a s= =V D D( ) 0.7698( )aBCC 243 3 H H3H H332 2 2 2. A coordina-tion model of a face-centered cubic (FCC) lattice has a close-packed structure with a coordination number of 12. Theaverage volume per molecule, VFCC, is calculated as= =V D D( ) 0.7071( )aFCC 424 H H3H H33 32 2 2 2, using therelation a = √2(DHd2−Hd2). Figure 4 shows the pressure changesin the average volumes per H2 molecule, assuming that thepostcrossover state in the SCF phase exhibits a short-rangeorder with SC, BCC, or FCC coordination of H2 molecules.For comparison, we referred to the average volume permolecule calculated at an experimental temperature of 299.4 Kfor XRD using the equation of state (EOS) for the H2 SCFphase, as derived by Mills et al.21 They measured the molarvolume using a piston−cylinder apparatus and defined theEOS for fluid n-H2 based on their detailed experimental results.No abrupt volume changes or transitions were observed at anyFigure 3. Pressure dependence of distances DHd2−Hd2, dHd2−Hd2, and rH−H.The pink solid rhombuses, lavender solid circles, and black solidsquares represent distances DHd2−Hd2, dHd2−Hd2, and rH−H at varyingpressures, respectively. The magnitudes of error bars for data labeledDHd2−Hd2and dHd2−Hd2are smaller than the respective symbols. The insetschematic shows the relative positions of DHd2−Hd2, dHd2−Hd2, and rH−H.The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Letterhttps://doi.org/10.1021/acs.jpclett.6c02439J. Phys. Chem. Lett. 2026, 17, 11754−1175911757Downloaded from pubs.​acs.​org/​jpclcd/​article-pdf/​17/​41/​11754/​68705788/​acs.​jpclett.​6c02439.​pdf by NATL INST FOR MATLS SCIENCE (NIMS) user on 16 October 2026https://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?fig=fig3&ref=pdfpubs.acs.org/JPCL?ref=pdfhttps://doi.org/10.1021/acs.jpclett.6c02439?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asreported pressure. Therefore, we did not refer to the crossoverhere; instead, we compared only the volume per moleculebased on the molecular coordination model with the EOSresults. For instance, the volume at 9.8 kbar (≈ 0.98 GPa) wasapproximately 24.4 Å3 per molecule using EOS. However,using the value of DHd2−Hd2at 0.98 GPa, the volume per moleculecalculated using the SC, BCC, and FCC coordination modelswas 37.84, 29.13, and 26.75 Å3, respectively. The volumederived from the FCC coordination model was closer to thevolume obtained by EOS, with a minimal difference ofapproximately 2.35 Å3. As the center-to-center distancebetween the H2 molecules has been corrected based on theirdumbbell-shaped molecular structure, our data provide micro-scopic insights into the shape of H2 molecules and theintermolecular gaps formed by short-range order. Mills’ datacharacterized the macroscopic result of the number of H2molecules contracted as a whole by deforming their electronclouds under high pressure. The increase in the contraction ofrH−H following the crossover, as shown in Figure 3, suggeststhe acceleration of the compression of the electron cloud of H2molecules in the postcrossover state.It is known that the solid-phase I of H2 exhibits a hexagonalclose-packed (hcp) structure with a coordination number of12.22 Following the SCF phase, the solid phase I also exhibits acoordination number of 12; but, the solid phase I possesses acharacteristic stacking structure, and the hcp structure shouldbe distinguished from the FCC structure. On the other hand,an analysis of the coordination number based on the nearest-neighbor distance and molecular volume does not allow us todistinguish between the FCC and hcp coordination models.Therefore, from here, we refer to it as ″FCC/hcp-likecoordination model″. Although the coordination number canbe 12 following the crossover, the number is fundamentallydependent on the FCC/hcp-like coordination model. On theother hand, this suggests that it may be a general characteristicfor diatomic molecular fluids to change in the FCC/hcp-likecoordination once crossing the Frenkel line. The increase inthe coordination number has been found in SCF N2 reachingthe coordination number of 12 over various ranges of pressureand temperature.23 At pressures of 0.98 GPa and above, thevolume difference increased slightly, indicating that the FCC/hcp-like model could not fully explain this phenomenon. Forinstance, in the Ni−P alloy, the maximum packing fraction forthe random packing of hard spheres was 0.64, whereas for softspheres, the packing fraction exceeded 0.67.24 Therefore, whenpressure was applied from the outside, the particles werecompressed and deformed, increasing the contact area andnumber of contacts between the particles and reducing thegaps between them. For H2, an increase in the ratio of thedecrease in the internuclear distance was observed followingthe crossover. As shown in Figure 4, the packing fraction isexpected to be slightly higher than that of FCC/hcp-likecoordination model. This finding may also demonstrate thepotential limitations of explaining the SCFs of H2 moleculesusing a hard-sphere model.Regarding H2, it was not possible to determine the two-bodydistribution function with sufficient accuracy due to insufficientdiffraction intensity of S(Q). Consequently, reliable coordina-tion numbers25 could not be obtained, and it was not possibleto find the detailed pressure dependence of the coordinationnumbers as reported for N2.6 On the other hand, although theapproach taken in this study differs from conventionalmethods, as estimation of the volume pre H2 molecule basedon the mean intermolecular distances obtained suggests thatthe system forms a state of equal or denser density―equi-valent to or greater than the FCC structure―than thatindicated by the conventional SCF-phase equation of state.In summary, we determined the structure factor of H2 ateach pressure following the crossover in the SCF phase. Theresults revealed that the crossover occurs at 0.56 GPa.Assuming the FCC coordination of H2 model, the averagevolume per molecule and the coordination number followingthe crossover were calculated using the center-to-centerdistance between the nearest-neighbor molecules determinedexperimentally. This model indicates that the rigid fluid formsunder conditions that exceed the Frenkel line.■ ASSOCIATED CONTENT*sı Supporting InformationThe Supporting Information is available free of charge athttps://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439.Additional analysis of the S(Q) versus Q plots, results ofpeak fitting using Lorentzian and Gaussian functions,parameters of peaks 0−6 determined by peak analysisusing Lorentzian and Gaussian functions, and parame-ters of the main and unknown peaks determined by peakanalysis using Lorentzian functions at all the pressurepoints measured. (DOCX)■ AUTHOR INFORMATIONCorresponding AuthorAtsuko Nakayama − Department of Mathematical Science andPhysics, Faculty of Science and Engineering, Iwate University,Morioka, Iwate 020-8551, Japan; orcid.org/0009-0002-0016-3750; Email: atsuko@iwate-u.ac.jpFigure 4. Pressure changes in the average volume per H2 molecule,assuming that the postcrossover state exhibits a short-range order withSC, BCC, or FCC coordination of H2 molecules. The light-blue solidcircles, orange solid squares, and blue solid rhombuses represent thevolumes at pressures obtained by applying DHd2−Hd2data to the SC,BCC, and FCC coordination models, respectively. The green curverepresents the average volume per molecule calculated at anexperimental temperature of 299.4 K for XRD using the EOS forthe H2 SCF phase, as derived by Mills et al.21The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Letterhttps://doi.org/10.1021/acs.jpclett.6c02439J. Phys. Chem. Lett. 2026, 17, 11754−1175911758Downloaded from pubs.​acs.​org/​jpclcd/​article-pdf/​17/​41/​11754/​68705788/​acs.​jpclett.​6c02439.​pdf by NATL INST FOR MATLS SCIENCE (NIMS) user on 16 October 2026https://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?goto=supporting-infohttps://pubs.acs.org/doi/suppl/10.1021/acs.jpclett.6c02439/suppl_file/jz6c02439_si_001.docxhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Atsuko+Nakayama"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0009-0002-0016-3750https://orcid.org/0009-0002-0016-3750mailto:atsuko@iwate-u.ac.jphttps://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.6c02439?fig=fig4&ref=pdfpubs.acs.org/JPCL?ref=pdfhttps://doi.org/10.1021/acs.jpclett.6c02439?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asAuthorsNaoto Fujii − Graduate School of Arts and Science, IwateUniversity, Morioka, Iwate 020-8551, JapanKoji Hirama − Graduate School of Arts and Science, IwateUniversity, Morioka, Iwate 020-8551, JapanKentaro Hamada − Graduate School of Arts and Science,Iwate University, Morioka, Iwate 020-8551, JapanKatsuya Shimizu − KYOKUGEN, Center for Science andTechnology under Extreme Conditions, The University ofOsaka, Toyonaka, Osaka 560-8531, Japan; GeodynamicsResearch Center, Ehime University, Matsuyama, Ehime 790-8577, Japan; orcid.org/0000-0003-0560-8325Yuki Nakamoto − KYOKUGEN, Center for Science andTechnology under Extreme Conditions, The University ofOsaka, Toyonaka, Osaka 560-8531, JapanSatoshi Nakano − National Institute for Materials Science(NIMS), Tsukuba, Ibaraki 305-0044, Japan; orcid.org/0000-0002-7010-9867Saori Kawaguchi-Imada − Diffraction and ScatteringDivision, Japan Synchrotron Radiation Research Institute,Hyogo 679-5198, Japan; Office of Institutional Advancementand Communications, Kyoto University, Hyogo 679-5198,JapanYuichi Akahama − Graduate School of Material Science,University of Hyogo, Hyogo 678-1297, Japan; orcid.org/0000-0003-2736-9855Ayako Ohmura − Faculty of Science, Niigata University,Niigata 950-2181, JapanComplete contact information is available at:https://pubs.acs.org/10.1021/acs.jpclett.6c02439NotesThe authors declare no competing financial interest.■ ACKNOWLEDGMENTSThis study was supported by JSPS KAKENHI (grant numberJP1A24K014270) and partly supported by the NIMSCooperative Research Promotion Program from the NationalInstitute for Materials Science Cooperative Promotion).Synchrotron radiation experiments were performed atBL10XU of SPring-8 with the approval of the JapaneseSynchrotron Radiation Research Institute (Proposal No.[2024B1268]).■ REFERENCES(1) Gorelli, F. 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