## 2 Materials and Methods  
The experiment was carried out at the atomic, molecular and optical physics (AMO) end station at the LCLS free electron laser facility (SLAC National Laboratory, Menlo Park, CA, USA). The photon energy used was 1619 eV which dominantly ionizes the M1 subshell of iodine. The pulse duration for both pump and probe was 50 fs and the pulse energy measured upstream the focusing mirrors and the XRSD was 1.3 mJ. Considering an X-ray transportation loss of 85%, the actual total pulse energy at the interaction region is estimated to be \(\sim\)0.2 mJ, corresponding to an intensity of 4 \(\times\) 10\({}^{16}\) W/cm\({}^{2}\) with a focal size of \(\sim\)10 \(\upmu\)m\({}^{2}\). Gas phase CH\({}_{3}\)I was delivered using a pulsed valve jet. Ion Time of flight (TOF) signal was detected and recorded at different pump-probe delay times. The details of the experimental setup are described in [8].  
The XRSD apparatus (see [8] for details) consists of two plane mirrors, is designed for soft X-ray photon energy range (250 eV-1800 eV) and is located downstream of the X-ray focusing mirrors of the AMO hutch. The positions (angles and height) of the two mirrors are adjusted by actuators to achieve the desired pump-probe delay time with a minimum time-resolution of 100 as and the maximum delay time of about 400 fs. The high position reproducibility of the actuators using position sensors make possible reliable pre-experiment calibration of the actuator settings for any particular pump-probe delay-time with optimal spatial overlap.  
To extract the KE distribution of the ions, we first obtained with SIMION (v5, SIS Inc., Ringoes, NJ, USA) simulation the peak shapes B (\(E_{j}\), \(t_{i}\)) of the TOF response for a sequence of discrete energy release, \(E_{j}\) (\(j\) = 1, 2,..., \(n\)). These peak profiles are regarded as a set of base functions. The experimental TOF was fitted by the following function:  
\[TOF(t_{i})=\sum_{j=1}^{n}I_{j}B\big{(}E_{j},t_{i}\big{)}\Delta E_{j}\]  
where \(\Delta E_{j}\) is the energy interval and \(I_{j}\) are the fitting coefficients.  
We also used a point-charge Coulomb explosion model to calculate the time evolution for the various ionic charges. The model is described in detail in [11], where it was applied to a single-pulse scenario. The model is designed to represent, in average, the time evolution into any given set of final atomic fragment charges, including charge build-up, redistribution, and the concurrent Coulomb explosion. The sequence starts by single-photon absorption by the M1 subshell of iodine, with subsequent positive charge created by Auger cascades and possibly by additional photoabsorption. Due to large disparity in photoionization cross-sections in iodine and in the methyl group at this photon energy, only iodine is assumed to absorb the photons and charge build-up in the methyl group that occurs via electron dynamics, such as Auger cascades involving molecular orbitals. The statistical nature of the molecule is reflected in the smooth charge build-up function (instead of stepwise increase at random intervals for each single event)  
\[Q_{tot}(t)=Q_{tot,\ final}\bigg{(}1-\exp{(-\frac{t}{\tau})}\bigg{)},\]  
where \(\tau\) is the empirical, adjustable charge build-up constant.