Three-dimensional view of (a) cyclopentyldienyl manganese tricarbonyl (CMT) and (b) β-cyclodextrin CMT (cdCMT) complex where the cyclopentyldienyl ring of CMT is centered in the hydrophobic cavity (see the supplementary material 29 for discussion of the model inclusion complex geometry).
To facilitate the use of the dipole orientation, φ k,τ , in computing the microenvironment, the dipole orientation is represented as discrete steps. Although realistic solvent molecules do not have finite orientations, due to computational time constraints and the need to enumerate all possible solvent configurations, we limit the dipole orientation to range from −10 to 10.
The microenvironment distribution function, D(m; t), plotted against time. All simulations begin with the same microenvironment but diffuse away from it through the course of the simulation. We use R(t), Eq. (7) , to measure extent of the microenvironment diffusion.
Area-normalized experimentally measured FTIR spectrum of CMT in various solvents (a) and (b).
2DIR spectra of CMT's asymmetric peak in methanol at t2 time steps of (a) 0.25 ps and (b) 5 ps. Each spectrum consists of 2 peaks, a positive valued fundamental peak at 1947 cm−1 and the anharmonic peak at 1928 cm−1. At early times, the nodal line (NL) in red is slanted due to inhomogeneous broadening. At later times, the NL has no slope due to a loss of memory of the original vibrational frequency.
(a) The asymmetric peak volumes of the rephasing and non-rephasing spectra measured by integrating the signal absolute value over ω 1 and ω 3 between 1910 cm−1 and 1960 cm−1, which are used in Eq. (1) to calculate (b) the inhomogeneous index at each t2 time step. The inhomogeneous index of HeOH decays noticeably slower than that of MeOH and is offset for ease of viewing.
The spectral diffusion time scales of CMT in a series of alcohol solvents plotted against viscosity of the solvent with the corresponding linear fit (red). The standard error tends to increase as the spectral diffusion time constant increases.
The FTIR of CMT (black) has only minimal differences when complexed with β-cyclodextrin (red), demonstrating the insensitivity of the linear IR spectrum of the carbonyl modes to the presence of the inclusion complex.
The spectral diffusion time constant of cdCMT in a series of alcohol solvents plotted against viscosity of the solvent with its corresponding linear fit (red). The fit constant of ethanol is plotted for both the fresh (immediate after mixing) and aged (∼3 h) samples.
The spectral diffusion time constants of cdCMT, CMT, and DMDC in methanol and their standard errors. Because of the fast spectral diffusion, the three time constants are significantly distinct. Due to the vibrational lifetime, as time constants increase the standard errors correspondingly increase creating overlap in the measurements. See the supplementary material for a full analysis of the errors. 29
A probe with a small IR active surface area (a) has fewer dipoles participating in the microenvironment than does a probe with a larger IR active surface area (b).
We measure the simulation's diffusion of microenvironments using R(t), Eq. (7) , for both (a) arrangement independent (AI) and (b) arrangement dependent (AD) with varying number of dipoles, N. AI is analogous to “Stark spectroscopy” and AD is analogous to a probe whose frequency to microenvironment map is complex. Due to the carbonyl triple bond and multiple carbonyls, we presume both DMDC and CMT are AD. (c) The R(t) half-life values, analogous to spectral diffusion time constant, of AI (red) and AD (black). The increase in half-life for the AD case indicates manganese carbonyls are effectively arrangement dependent.
Parameters of linear fits to the alcohol solvent dependent spectral diffusion time scales, with the corresponding solute solvent accessible surface area. 29
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