T ransition metal complexes (TMCs) are a major research focus of inorganic chemistry and have garnered significant attention from both theoretical and experimental chemists in recent decades, driven by their exceptional excited state properties, which offer extensive potential applications in areas including luminescent materials, optoelectronic conversion, and photocatalysis. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] Au(I) complexes represent a class of pivotal TMCs renowned for their remarkable optoelectronic properties. 19,20 Among these, Au(CN) 2 -stands out as the simplest Au(I) gold atomic complex. A notable character of Au(CN) 2

-is aggregation under ultraviolet irradiation as experimental evidence has shown the excited state bond formation between gold atoms in solvent. [21][22][23][24] Theoretical investigations on the photochemical Au(I)-Au(I) bond formation have focused on the stationary points and excitation energies of ground and excited states. 25 However, a detailed examination of the excited-state dynamics pertaining to this ultrafast process remains absent in the literature. Although most photophysical and photochemical processes can be studied experimentally using time-resolved absorption spectroscopy on femtosecond or picosecond time scales, such methodologies are often unable to provide detailed insights into the nonradiative transitions that occur during excitation dynamics. These nonradiative transitions are crucial as they govern structural changes in the complex on excited state potential energy surfaces, providing valuable information for elucidating photochemical reaction pathways. 12,17,[26][27][28][29][30] Photochemical pathways in TMCs are predominantly governed by internal conversion (IC) and intersystem crossing (ISC). Internal conversion, a spin-conserving process, is driven by nonadiabatic coupling (NAC), while intersystem crossing involves a change in spin angular momentum facilitated by spin-orbit coupling. Both processes are nonradiative and occur on ultrafast time scales ranging from femtoseconds to picoseconds, and the complex interplay between spinconserving and spin-changing transitions drives the bond formation process. In this study, we investigate the ultrafast Au-Au bonding process in the [Au(CN) 2 ] 2 2-dimer by performing nonadiabatic dynamics simulations that account for both the IC and ISC pathways.

Using density functional theory calculations described in Computational Details, the calculated Au-Au equilibrium bond distance in the ground S 0 state is 3.51 Å, and the dihedral angle between the dicyanoaurate units is 74.1°, in agreement with experimental measurements. 22 The photochemical reaction is initiated by optical excitation from the ground state using a 270 nm pulse. Linear response time-dependent density functional theory (TDDFT) calculations reveal that the S 1 state is an optically bright state with an oscillator strength of f = 0.4675, corresponding to a σ* → σ transition. This state has an excitation wavelength of 243 nm, which aligns closely with the experimental excitation conditions. 23 To explore the photochemical reaction pathways associated with Au-Au bond shortening, a potential energy surface (PES) scan in the spin-diabatic representation (e.g., singlet and triplet) in the absence of the spin-orbit coupling was conducted. A set of 200 geometries was generated uniformly over a displacement range of -4.0 to +2.0 Å from the Au-Au ground state equilibrium bond length of the [Au(CN) 2 ] 2 2complex. For each geometry, we computed the spin-diabatic excited state energies and potential energy surfaces for seven excited states, including S 1-2 and T 1-5 , as plotted in Figure 1a. These states were selected due to their close energetic proximity to the S 1 state within the Franck-Condon region. Spin-diabatic states in a same manifold are ordered based on their energetics. Spin-orbit couplings between singlet and triplet states were computed using the perturbative TDDFT-SO approach. 31 Nonadiabatic couplings within a same spindiabatic manifold (e.g., singlet) were also evaluated using the method illustrated in the Computational Details section.

The computed PESs reveal local minima at 2.7 ∼ 2.8 Å for the T 1-2 and S 1-2 states. For the T 1 minimum, the Au-Au bond distance shortens to 2.76 Å, and the dihedral angle between the dicyanoaurates increases to 89.9°. This observation suggests that the [Au(CN) 2 ] 2 2-complex may undergo a bond-shortening photochemical reaction. However, it remains unclear which specific excited state drives the observed photochemical reaction and the pathways involved in its progression. To further elucidate the bond-forming mechanism, nonadiabatic dynamics simulations are necessary.

Starting from the Franck-Condon region, two singlet states (S 1 -S 2 ) and five triplet states (T 1 -T 5 ) are considered according to the energy profile in Figure 1a. The ground state S 0 is not considered in Figure 1 because it is energetically well-separated from excited states under investigation. State-tostate spin-orbit and nonadiabatic coupling matrix elements (SOC and NAC) were obtained for 200 geometry points. We are able to fit an effective Hamiltonian along the Au-Au bond by the piecewise cubic Hermite interpolating polynomial method. 32 The fitted NAC and SOC curves along the reaction coordinate can be found in Figure 1b and Figure 1c.

A total of 10,000 of initial conditions, including coordinate and velocity, were sampled from the Wigner distribution using the effective mass of bond-forming vibration mode, and nonadiabatic dynamics trajectories were carried out along this degree of freedom. The initial coordinate is sampled in the range of 3.25 Å to 3.77 Å for the Au-Au bond length near the S 0 minimum. The range of simulation is set to be within 1.45 Å to 4.55 Å for the Au-Au bond length. A trajectory is abandoned if it reaches outside the simulation range. Among the 10,000 trajectories, only 95 trajectories were discarded due to the restriction of the simulation range.

The results of the nonadiabatic dynamics simulations are presented in Figure 2 and Figure 3. Figure 2 shows the timedependent populations of the electronic states, while Figure 3 depicts the trajectory progression as a function of the Au-Au distance and the potential energy surface. In Figure 3, only 2% of the trajectories are displayed for clarity, with the color of each trajectory indicating the excited state at the corresponding simulation time. The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Letter https://doi.org/10.1021/acs.jpclett.5c00310 J. Phys. Chem. Lett. 2025, 16, 3816-3821

The photochemical dynamics starts on the S 1 potential energy surface in the Franck-Condon region. Figure 2 shows a rapid decrease in the S 1 population within the first 100 fs, driven by intersystem crossing events into T 2 -T 5 . Notably, the most significant population drop occurs within the initial 10 fs, primarily due to the S 1 → T 2 intersystem crossing rather than the transition to the energetically proximate T 5 . This behavior is due to the S 1 -T 2 spin-orbit coupling being the strongest among all intersystem crossing pathways at the Franck-Condon point (see Figure 1a). As the reaction progresses, a considerable portion of the population recrosses back to S 1 , which subsequently triggers the S 1 -T 5 intersystem crossing. Although T 2 and T 4 also have noticeable populations, the dynamics in the first 100 fs are largely characterized by a rapid exchange of population among S 1 , T 2 , and T 5 , driven by strong spin-orbit coupling, which gives rise to the seemingly coherent oscillatory behavior.

Starting from 100 fs, rapid population exchange stabilizes into several distinct channels. The most prominent reaction channel follows the reaction pathway on either the S 1 state or the T 2 state, with population exchange between these states characterized by an out-of-phase oscillation pattern. Oscillations on the T 3 PES also occur at times up to 100 fs, as makes sense given that T 3 and T 2 cross near 3.6 Å, which is close to the Franck-Condon region. The dynamics for T 1 , T 2 , T 3 , T 4 , and T 5 can be considered adiabatic between 150 and 300 fs, as there is no significant population exchange or decay observed during this period. In contrast, the population growth of the S 2 state is associated with the initial population decay of T 4 and T 5 between 100 and 150 fs, facilitated by the ISC mechanism. Once the reaction on the S 2 state stabilizes into an adiabatic process, the continued population decay of T 4 and T 5 beyond 150 fs is correlated with the population growth of T 1 via the internal conversion pathway.

To understand how the population dynamics on different reaction surfaces can lead to the Au-Au bond formation, we track 2% of the trajectories and plot them in Figure 3 to illustrate the evolution of the Au-Au bond length over time. Figure 3 shows that within the first 100 fs, the wavepacket splits into two distinct branches: a dominant branch moving along the bond-forming pathway (ΔR < 0) and a weaker branch following the dissociation pathway (ΔR > 0). The color variation along the trajectory reflects changes in the potential energy surface during the reaction dynamics.

The bond elongation pathway is primarily governed by reactions occurring on T 2 -T 5 , with minimal population exchange between the states. Around 100 fs, trajectories on T 4 and T 5 reach turning points and begin to shift toward bond shortening, whereas those on T 2 and T 3 continue along the elongation pathway, driven by a relatively flatter potential energy surface. In the region where the Au-Au bond length exceeds 4.2 Å, T 2 and T 3 states exhibit crossings with T 1 , leading to significant nonadiabatic couplings. As a result, many trajectories in this minor branch undergo internal conversion to the attractive T 1 surface in 200-250 fs, as indicated by the color change in Figure 3 in the >4.2 Å regime.

The reaction pathways in the bond shortening branch are considerably more complex than those in the bond elongation branch due to rapid population exchange among excited states, as indicated by the fast color changes in Figure 3 along each trajectory. Starting from 150 fs, most trajectories stabilize on either the S 1 or T 2 potential energy surface, exhibiting a strong bond shortening effect. As the reaction progresses, more pronounced bond shortening reactions occur on the T 1 surface. This observation agrees with the experimental hypothesis that intersystem crossing occurs within 200 fs. 23 This analysis indicates that the intersystem crossing mechanism plays a crucial role in modulating the early excited-state reaction dynamics. As the singlet-to-triplet branching stabilizes, internal conversion subsequently drives the reaction toward the lowest triplet state.

In this study, we performed nonadiabatic dynamic simulations of the ultrafast photochemical Au-Au bonding process in the [Au(CN) 2 ] 2 2-dimer. Both intersystem crossing and internal conversion pathways, driven by spin-orbit and nonadiabatic couplings, respectively, were thoroughly examined.

The photochemical behavior of the [Au(CN) 2 ] 2 2-dimer reveals a complex reaction landscape, involving transitions through multiple singlet and triplet states. Analysis indicates that the initial stage of the reaction is dominated by spin-orbit coupling, with rapid intersystem crossings and recrossings between singlet and triplet states occurring within the first 100 fs. This fast population exchange stabilizes into adiabatic branches favoring bond shortening. Subsequently, the internal conversion mechanism gradually transfers population from higher-energy triplet states to the lowest T 1 state, intensifying the bond shortening process.

The S 1 decay process revealed in our study is consistent with findings from other gold-containing systems. 33 In ref 33, onthe-fly nonadiabatic dynamics simulations of representative Au(I)-naphthalene complexes demonstrate a similar trend, characterized by rapid intersystem crossing dominating early dynamics and weak internal conversion. These dynamics ultimately culminate in a trapped T 2 state population with a prolonged lifetime. Despite differences in bonding environments, the shared feature is the significantly enlarged energy gap between S 1 -T 1 and T 2 -T 1 , which underpins the observed behavior.

This study provides critical insights into the competing photophysical mechanisms driving Au-Au bond formation, highlighting the interplay between intersystem crossing and internal conversion. Understanding these pathways can inform the design of light-driven transition-metal-based materials with tailored photochemical properties. The Journal of Physical Chemistry Letters ■ COMPUTATIONAL DETAILS All electronic structure calculations were performed using the development version of the Gaussian quantum chemistry software package. 34 The [Au(CN) 2 ] 2 2-S 0 geometry is optimized with Kohn-Sham DFT using the B3LYP functional with GD3 dispersion correction. 35 Au atoms were described using the LANL2TZ(f) effective core potential along with its complementary basis set. The Pople 6-31G(d) basis set was used for C and N. For both ground-and excited-state calculations, the polarizable continuum model (PCM) 36 is used to simulate the aqueous environment.

Excited-state properties were computed from the optimized ground-state minimum structure using linear response TDDFT. The all-electron Sapporo-DKH3-2012-DZP basis set with diffuse functions was applied for Au, while the 6-31G(d) basis set was used for C and N. Scalar relativistic effects are included. The 10 lowest singlet and 10 lowest triplet excited states were considered for the nonadiabatic molecular dynamics (NAMD) calculations. The total simulation time for NAMD was set to 300 fs, with a time step of 0.1 fs.

The fewest-switches surface hopping (FSSH) method 37,38 was employed to investigate ultrafast excited-state reaction dynamics, incorporating both intersystem crossing and internal conversion mechanisms. In the spin-diabatic framework, intersystem crossing is driven by spin-orbit coupling, 39 while nonadiabatic couplings lead to internal conversion. In the nonadiabatic dynamics, we employed an energy-gap-based decoherence procedure throughout the simulation to mitigate overcoherence. 40 This approach has been demonstrated to effectively describe the electronic decoherence process.

Spin-orbit coupling strengths between singlet and triplet excited states were calculated using the TDDFT-SO module 31 in the Gaussian development version. The two-electron spinorbit correction was approximated via the screened-nuclear spin-orbit approach, 41 parametrized with Dirac-Coulomb-Breit calculations. 42 Effective spin-orbit strengths were averaged over triplet microstates. 31,43 Nonadiabatic coupling (NAC) strengths between states of identical spin symmetry were determined using a finitedifference numerical approach, using TDDFT-derived state vectors. [44][45][46] To reduce computational cost during the numerical evaluation of NAC, only the 50 highest occupied and 50 lowest virtual molecular orbitals were included. A finite difference step of 1.0 × 10 -5 Å was applied along the bondforming coordinate.