Supplementary Material for: Enhanced Vibrational Solvatochromism and Spectral Diffusion by Electron Rich Substituents on Small Molecule Silanes Courtney M. Olson,1 Adam Grofe,1 Christopher J. Huber,2 Ivan C. Spector,1 Jiali Gao,1,3 and Aaron M. Massari1,a 1 Department of Chemistry, University of Minnesota – Twin Cities, Minneapolis, Minnesota, 55455, USA 2 Doane University, 1014 Boswell Avenue, Crete, NE, 68333, USA 3 Theoretical Chemistry Institute, Jilin University, Changchun, Jilin Province 130023, PRC a) Author to whom correspondence should be addressed. Electronic mail: [email protected]. This Supplementary Material contains additional details of experimental and computational procedures and analyses. Experimental work is given first, followed by computational studies. 1 S1. Details of 2D-IR and IR pump-probe measurements A regeneratively amplified Ti:Sapphire laser (Spectra-Physics, 800 nm, 40 fs pulse duration, 500 mW, 1 kHz repetition rate) pumped an optical parametric amplifier (OPA, Spectra-Physics), and the near-IR signal and idler beams were difference frequency mixed in a silver gallium sulfide crystal (AgGaS2, 0.5 mm thick) to generate mid-IR pulses (3 µJ /pulse, 90 fs FWHM, ~200 cm-1 bandwidth FWHM). The mid-IR pulses were tuned to the silane (Si-H) stretching frequency (2200 cm-1 for TriMOS and 2130 cm-1 for TriPS), divided into three ~1 µJ p-polarized pulses, and focused at the sample in a BOXCARS geometry.1 The generated vibrational echo signal was heterodyne detected with a liquid N2 cooled MCT linear array detector (Infrared Associates, Inc.) with spectral resolution of ~4 cm-1. The system was continuously purged with dry air (-100 °F dew point) during data collection from the OPA to the detector. The first frequency dimension (x-axis, ωτ) was achieved by scanning the time delay between pulses 1 and 2, τ, in increments of 5 fs and subsequent Fourier transformation.2-4 The second dimension (y-axis, ωm) was obtained by optical Fourier transform of the heterodyne detected vibrational echo signal by dispersing it from the monochromator diffraction grating. Each 2D-IR spectrum was collected while the delay between pulses 2 and 3, Tw, was maintained at a fixed value. The resulting data were processed to obtain the purely absorptive 2D-IR spectrum,5, 6 and phase corrected using the pump-probe projection theorem and the absolute value center as constraints.7, 8 The FTIR spectrum of the sample was used as an absorption correction prior to phasing, since the probe beam passes through the sample while the local oscillator does not in our setup.9 The 2D-IR spectra for TriMOS and TriPS in isopropanol, chloroform and pentane are given, respectively, in Figures S1 through S6, which were analyzed using the centerline slope (CLS) method to obtain the frequency-frequency correlation function (FFCF).8, 10 For the CLS 2 analysis, the maximum intensity for the 0-1 and its central frequency were found for each of the systems. The frequency range for the CLS was +/- 8 cm-1 from the central frequency. Other ranges were chosen, but the CLS did not change significantly, so this range was used for the final analysis. IR pump-probe spectroscopy was carried out with the pump and probe beams polarized at the magic angle to remove contributions from orientational relaxation,11 as described previously.12 The data were fit from 1 to 75 ps to determine the population relaxation times (lifetime, T1) for the v = 0-1 and 1-2 transitions. The vibrational relaxation times for these two transitions consistently showed the same trends, and the 0-1 values were used in data analyses. The vibrational lifetimes (T1) for both molecules in all three solvents are shown in Table SI. -1 Table SI. Experimental Si-H vibrational frequency (cm ), νSi-H, full-width-at-half-maximum -1 (FWHM) widths (cm ), and vibrational lifetimes (ps), T1. Experiment molecule solvent -1 -1 νSiH (cm ) FWHM (cm ) T1 (ps) gas pentane 2203.2 41 9.8 ± 0.2 TriMOS chloroform 2207.2 50 9.9 ± 0.2 isopropanol 2194.6 46 6.0 ± 0.1 gas pentane 2129.2 18 20.0 ± 0.5 TriPS chloroform 2131.1 35 17.2 ± 0.4 isopropanol 2125.7 27 15.3 (±0.3) 3 S2. Analysis of Frequency-Frequency Correlation Functions The FFCF was modeled according to Equation S1. However, only the first two terms were necessary for the molecules in chloroform and pentane. !(!) ! !! ! !! ���� � = + Δ! exp + Δ! exp (S1) !! !! !! The time constants (�! and �!) in this equation were obtained directly from fitting the CLS decays, which has been shown to be highly accurate.8, 10 However, the amplitudes of each exponential contribution (Δ! and Δ!) assume a FFCF normalized to unity and a y-intercept is likewise normalized. The amplitudes from the fits of the CLS decays and the linear FTIR FWHMs were used to calculate approximate values for the amplitudes (Δ!) and T! of the full FFCF by following the procedure by Kwak and co-workers.8, 10 These initial values were then applied to a FFCF, and the first-order response function was used to reproduce the linear FTIR line shape. The line shape was fit by iteratively varying the amplitudes, as well as the central frequencies. The CLS method was developed using the short-time approximation, so the values for Δ! and T! are underestimated due to the method’s inability to distinguish between homogeneous terms and fast spectral diffusion (compared with the FID). Therefore, the floated Δ! and T! were constrained to only increase from the estimated values. 4 Figure S1. 2D-IR spectra of TriMOS in isopropanol. 5 Figure S2. 2D-IR spectra of TriMOS in chloroform. 6 Figure S3. 2D-IR spectra of TriMOS in pentane. 7 Figure S4. 2D-IR spectra of TriPS in isopropanol. 8 Figure S5. 2D-IR spectra of TriPS in chloroform. 9 Figure S6. 2D-IR spectra of TriPS in pentane. 10 S3. Computational Details S3.1. Electronic structure and molecular dynamics simulation Molecular modeling was conducted to provide further insight in to the observations made. A two pronged approach was used: (1) quantum mechanical electronic calculations both in the gas phase and in solutions represented by continuum solvation models to elucidate solvent polarization effects on the vibrational mode, and (2) combined quantum mechanical and molecular mechanical (QM/MM) molecular dynamics simulation to elucidate solvent dynamical effects. First, in the gas-phase and continuum solvation QM calculations, TriMOS and TriPS were treated by the M06-2x density functional theory (DFT) with the 6-31+G(d,p) basis set. Both the SMD and PCM continuum models were examined using the Gaussian software package, with the latter employing the default isoelectron density surface.13 All structures were optimized at each level of theory, and normal mode analysis was performed to obtain the vibrational frequency of the silicon hydride mode. In addition, charge analysis was performed by the CHELPG electrostatic potential fitting procedure,14 and the interaction between molecular orbitals was modeled using natural bonding orbital (NBO).15, 16 The computed vibrational frequencies and partial atomic charges are listed in Table SII. Second, in combined QM/MM molecular dynamics (MD) simulations, the solute molecules were placed in the center of a previously equilibrated solvent box (~50 Å in edge length). All solvent molecules within 3.0 Å of the solute were removed. The solute molecule was represented by the semiempirical Austin Model 1 (AM1) Hamiltonian and the solvent molecules were approximated by the CHARMM force field, and all computations were performed using the CHARMM package.17 The bond lengths of the solvent were held constant using the SHAKE 11 algorithm.18 Possible effects of constraining the bond lengths are considered below. The coordinates were then minimized for 50 steps using the steepest descent algorithm followed by 50 steps using the adopted basis Newton-Raphson algorithm. Long range electrostatic interactions were feathered to zero at 12 Å by a switching function. Next, the simulation box was equilibrated employing the isothermal-isobaric (NPT) ensemble at 25 °C and 1 atm by performing molecular dynamics for 1.0 ns. The production dynamics trajectory was similarly acquired for 2.0 ns during which the atomic configurations were saved every 10 fs. S3.2. Instantaneous vibrational frequency calculations The goal of the MD simulation was to study the vibrational frequency dynamics, and thus to generate a trajectory of frequencies for the solute molecule. This was accomplished by using a recently proposed method—quantum vibrational perturbation theory (QVP)—developed by Xue and coworkers.19 The main purpose of the QVP method was to increase the performance of solving the nuclear wave function on the Born-Oppenheimer potential energy surface to calculate a large number of frequencies (105-107) precisely and quantum mechanically. In that report, 200,000 frequencies were calculated for each MD trajectory. This was accomplished by using two numerical procedures: (1) the nuclear wave function and properties were obtained using a potential-optimized discrete variable representation (PO-DVR), and (2) the effects of solvent dynamic fluctuations were determined using perturbation theory. Overall, this method allows for the efficient computation of vibrational frequencies with systematic improvement by increasing either the number of PO-DVR points or increasing the order of the perturbation. Several improvements from the initial report by Xue and coworkers were made in the present study. First, rather than using the gas-phase wave function and PO-DVR points as the reference for solvent perturbation, an initial (after the equilibration) solvent configuration in the dynamics 12 trajectory was used to define the QVP reference Hamiltonian to further enhance convergence in perturbation calculations. Therefore, the solvent effects in the instantaneous vibrational frequency calculations is reduced to contributions due to solvent fluctuations with respect to the initial solvent configuration.