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K. H. Kim et al., Nature 518, 385 (2015)�

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scattering curves, qDS(q, t), where q is the momentum transfer betweenthe incident and the elastically scattered X-ray waves andDS is the dif-ference between scattering intensities measured before the laser excita-tion (that is, at a negative time delay) and after the laser excitation (thatis, at a positive time delay). The experimental difference scattering curves

measured at various time delays from –800 fs to 300 ns are shown inFig. 2a. The difference scattering curves show distinct oscillatory featuresalong the q axis, which indicate large structural changes in [Au(CN)2

–]3

during the formation of covalent Au–Au bonds. Considering that theoscillatory features appear distinct even after the shortest time delay

2 4 6 81 2 3 4 5 6

Diff

eren

ce s

catt

erin

g in

tens

ity, qΔS

(q) (

a.u.

)

a

F2 = 4.81

F2 = 1.70

b

Linear

Bent

Rad

ial i

nten

sity

, r2 S

(r) (a

.u.)

ExperimentTheory

ResidualsAu–Au pairs

ExperimentTheoryResiduals

Linear

Bent

q (Å–1) r (Å)

Figure 3 | Structure determination of the S1 state using the experimentalscattering curve at 200 fs time delay in momentum space and real space.a, Theoretical difference scattering curves (red) for linear (upper) and bent(lower) structures shown together with the experimental difference scatteringcurve at 200 fs (black). The residuals (blue) between the theoretical and theexperimental curves are shown together. The linear structure gives a much

better fit than the bent structure, which has the same Au–Au–Au bond angle asthe S0 state, thereby indicating that the bent-to-linear transition is completed at200 fs time delay. b, Corresponding experimental (black) and theoretical(red) RDFs, rS(r). It can be seen that in the bent structure R13 is too small to fitthe experimental RDF at 200 fs.

Species R12 R23 R13 R34

S0 3.87 ± 0.04 Å 3.30 ± 0.06 Å 5.56 ± 0.11 Å —

S1 2.82 ± 0.04 Å 2.81 ± 0.03 Å 5.63 ± 0.09 Å —

T1 2.71 ± 0.03 Å 2.70 ± 0.05 Å 5.41 ± 0.11 Å —

Tetramer 2.89 ± 0.06 Å 2.62 ± 0.06 Å — 2.88 ± 0.04 Å

1 2 3 4

1 2 3

Linear staggered structure(shorter distance)

Tetramer

1 2 3

Bent structure

1

2326

7 nm

Linear staggered structure (longer distance)

S1

S0

T1

Ener

gy

Further Au–Au bond shortening (1.6 ps)

Tetramer formation (3 ns)

Bent-to-linear relaxation and Au–Au bond shortening (<500 fs)

Reaction progress

Structural parameters

a

b

Figure 4 | Mechanism of photoinduced bond formation in [Au(CN)2–]3.

a, Femtosecond TRXSS reveals the dynamics and the atomic movementsassociated with the Au–Au bond formation in real time with sub-angstromspatial resolution. The S0 state with weakly bound Au atoms in a bent geometrytransforms to the S1 state with tightly bound Au atoms in a linear geometry.

Subsequently, the S1 state transforms first to the T1 state, with furthercontraction of Au–Au bonds, and then to a tetramer through formation ofanother Au–Au bond. b, Structural parameters of each state and their standarderrors determined from 50 independent measurements.

LETTER RESEARCH

1 9 F E B R U A R Y 2 0 1 5 | V O L 5 1 8 | N A T U R E | 3 8 7

Macmillan Publishers Limited. All rights reserved©2015

the TRXSS experiment at an XFEL facility7 (SACLA), we were able tostudy the ultrafast structural dynamics of bond formation in [Au(CN)2

–]3

in solution with subpicosecond time resolution and sub-angstrom spa-tial resolution.

The femtosecond TRXSS experiment performed in this study is shownschematically in Fig. 1, and the details of the experimental procedureand the analysis are described in Methods and Extended Data Table 1.

For the sample, we used an aqueous solution of Au(CN)2– at a concen-

tration of 300 mM, because in a solution of this concentration the[Au(CN)2

–]3 trimer has much higher absorbance at 267 nm than doesa monomer or a dimer of Au(CN)2

– (Supplementary Information). Asa result, the laser excitation at 267 nm used in our TRXSS experimentpredominantly excites the [Au(CN)2

–]3 trimer while exciting the otherspecies negligibly. From the TRXSS experiment, we obtained difference

2 4 6q (Å–1)

FT

qΔS

(q) (

a.u.

)[Au(CN)2–]3 in water

200 fs

10 ps

10 ns

–5 ps

~100 fs, 267 nm laser pulses

X-ray arrival, 0 s

<100 fs, 15 keVX-ray pulses

CCD detector

200 fs10 ps10 ns

2 4 6 8 10r (Å)

200 fs10 ps10 ns

r2 S(r)

(a.u

.)

Time

200 fs

10 ps

10 ns

–5 ps

Time-dependentstructural changes

a b

Figure 1 | Femtosecond time-resolved X-ray solution scattering at the XFELfacility and the data analysis. a, The photochemical reaction of solutessupplied by a liquid-flowing system is triggered by a femtosecond optical laserpulse. Subsequently, a time-delayed X-ray pulse synchronized with the laserpulse probes the structural dynamics of the reaction. The scattering pattern isdetected by a fast two-dimensional charge-coupled device (CCD) detector asshown at the bottom. We measure time-resolved scattering patterns whilevarying the time delay between the laser and X-ray pulses. b, By integrating the

two-dimensional scattering pattern azimuthally, subtracting solventcontributions, performing a Fourier transform (FT) and compensating for thedepletion of the initial solute contribution due to photochemical reaction,we obtain one-dimensional RDFs in real space as shown in the plot at thetop left. These display the interatomic distances of transient species andproducts. In this way, Au–Au bond lengths of the [Au(CN)2

2]3 complex can beidentified with sub-angstrom accuracy, and the time-dependent structuralchanges of the metal complex can be determined in real time.

2 4 6 2 4 6 8 10

a

– 800 fs

200 fs

700 fs

1.7 ps

3.2 ps

Rad

ial i

nten

sity

, r2 S

(r) (a

.u.)

10 ps

30 ps

100 ps

300 ps

1 ns

3 ns

10 ns

30 ns

100 ns

300 ns

Diff

eren

ce s

catt

erin

g in

tens

ity, qΔS

(q) (

a.u.

)

– 800 fs

200 fs

700 fs

1.7 ps

3.2 ps

10 ps

30 ps

100 ps

300 ps

1 ns

3 ns

10 ns

30 ns

100 ns

300 ns

b

r (Å)q (Å–1)

p1 p2 p3

2 4 6 8 10 12

10–1 100 101 102 103 104 105

S1

T1Tetramer

S0

1.6 ps 3 ns 100 ns c

Con

cent

ratio

n

Time (ps)

dS0

S1

T1

Tetramer

Experiment Theory Au–Au pairs

r (Å)

Rad

ial i

nten

sity

, r2 S

(r) (a

.u.)

R12: 3.30 ± 0.06 ÅR23: 3.87 ± 0.04 ÅR13: 5.56 ± 0.11 Å

R12: 2.81 ± 0.03 ÅR23: 2.82 ± 0.04 ÅR13: 5.63 ± 0.09 Å

R12: 2.70 ± 0.05 ÅR23: 2.71 ± 0.03 ÅR13: 5.41 ± 0.11 Å

R12: 2.88 ± 0.04 ÅR23: 2.62 ± 0.06 ÅR34: 2.89 ± 0.06 Å

Figure 2 | Time-dependent structural changes of [Au(CN)2–]3.

a, Experimental difference scattering curves, qDS(q), measured at various timedelays from –800 fs to 300 ns (black). For clarity, only data at selected timedelays are shown. a.u., arbitrary units. b, RDFs, r2S(r), obtained by Fourier sinetransformation of qDS(q) after subtracting solvent contributions. The RDF ofthe S0 state was added to the RDFs at all time delays to emphasize only thecontributions of the transient solute species associated with bond formation.The blue dashed arrows indicate the time-dependent changes in the locations ofthe p1 and p2 peaks. The red dashed line represents the position of the p3

peak, corresponding to the signature of the tetramer. c, Time-dependentconcentrations of the four states and their transition kinetics. The notation foreach species is indicated above each trace. The error bar at each data point

indicates the standard error determined from 50 independent measurements(that is, 50 scattering images). The vertical black dotted lines indicate thetemporal positions corresponding to the time constants of the three kineticcomponents. d, Species-associated RDFs of the four structures obtained fromthe singular value decomposition and principal-component analyses (black)and their fits (red) obtained by using model structures containing multipleAu–Au pairs. The blue arrows indicate the changes in R12, R23 and R13 astransitions occur between states. As fitting parameters, we considered threeAu–Au pairs for the S0, S1 and T1 states and six Au–Au pairs for the tetramer.For each state, the structural parameters obtained from the fits are shown alongwith their standard errors determined from 50 independent measurements.

RESEARCH LETTER

3 8 6 | N A T U R E | V O L 5 1 8 | 1 9 F E B R U A R Y 2 0 1 5

Macmillan Publishers Limited. All rights reserved©2015

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