Isotope Effects and the Temperature Dependences of the Hyperfine Coupling Constants of Muoniated sec-Butyl Radicals in Condensed Phases

Abstract

Reported here is the first μSR study of the muon (A(μ)) and proton (A(p)) β-hyperfine coupling constants (Hfcc) of muoniated sec-butyl radicals, formed by muonium (Mu) addition to 1-butene and to cis- and trans-2-butene. The data are compared with in vacuo spin-unrestricted MP2 and hybrid DFT/B3YLP calculations reported in the previous paper (I), which played an important part in the interpretation of the data. The T-dependences of both the (reduced) muon, A(μ)′(T), and proton, A(p)(T), Hfcc are surprisingly well explained by a simple model, in which the calculated Hfcc from paper I at energy minima of 0 and near ±120° are thermally averaged, assuming an energy dependence given by a basic 2-fold torsional potential. Fitted torsional barriers to A(μ)′(T) from this model are similar (~3 kJ/mol) for all muoniated butyl radicals, suggesting that these are dominated by ZPE effects arising from the C−Mu bond, but for A(p)(T) exhibit wide variations depending on environment. For the cis- and trans-2-butyl radicals formed from 2-butene, A(μ)′(T) exhibits clear discontinuities at bulk butene melting points, evidence for molecular interactions enhancing these muon Hfcc in the environment of the solid state, similar to that found in earlier reports for muoniated tert-butyl. In contrast, for Mu−sec-butyl formed from 1-butene, there is no such discontinuity. The muon hfcc for the trans-2-butyl radical are seemingly very well predicted by B3LYP calculations in the solid phase, but for sec-butyl from 1-butene, showing the absence of further interactions, much better agreement is found with the MP2 calculations across the whole temperature range. Examples of large proton Hfcc near 0 K are also reported, due to eclipsed C−H bonds, in like manner to C−Mu, which then also exhibit clear discontinuities in A(p)(T) at bulk melting points. The data suggest that the good agreement found between theory and experiment from the B3LYP calculations for eclipsed bonds in the solid phase may be fortuitous. For the staggered protons of the sec-butyl radicals formed, no discontinuities are seen at all in A(p)(T), also demonstrating no further effects of molecular interactions on these particular proton Hfcc.

First-principles computational studies of the torsional potential energy surface of the sec-butyl radical

“…A comparison with available experiments has confirmed the existence of the cis-like conformation III by low-temperature HFCC measurements. 9,10 Thus, the WFT methods and several DFT methods in group III (Fig. 1d) outperform other theoretical methods by being more in line with experimental results.…”

“…As verified by a mSR experiment, the cis-like conformation does exist and carries a large value of HFCC on the b-muon. 9,10 In this regard, WFT methods outperform B3LYP-DFT methods decisively.…”

“…If only the static electronic potential energy is considered, muoniated sec-butyl formed from mounium addition to cis-2-butene will not exist or can be easily turned into the gauche conformation II by an extremely small fluctuation (e.g., through vibration) to overcome the tiny barrier TS1, contradicting the experimental observation that the muon HFCC of this structure remained visibly strong over a wide temperature range. 9,10 There is no doubt that other effects stabilizing this molecular species must be taken into consideration.…”

“…The available experimental data were mainly from hyperfine coupling constant (HFCC) study of its muoniated sec-butyl formed from muonium addition to 2butene isomers. 9,10 As a short-lived, light isotope of hydrogen, the muonium, which is composed of a positive muon (antimuon) and an electron, is a good probing atom for the study of various systems. 11 Before any comparison is made, it is important to point out that all sec-butyl isotopomers share the same PES within the Born-Oppenheimer (BO) framework, since the electronic Hamiltonian only parametrically depends on nuclear posi-tions and has nothing to do with nuclear masses.…”

Quantum localization/delocalization of muonium in the glycine–K+ complex

“…In fact, Mu has long been used to understand nuclear quantum effects in chemical reactions including tunneling and quantized vibrations and there have been reported many studies showing very large isotope effects so far [3,4]. In particular, due to its extremely light mass and very large vibrational amplitudes, Mu-containing molecules frequently show a significantly delocalized character in molecular structures compared to hydrogen-and deuteriumcontaining molecules [5][6][7][8][9][10][11][12][13][14][15]. Alternatively, it has been reported that Mu can be localized in a very different region of the potential energy surface compared to hydrogen and deuterium cases due to multi-dimensional effects.…”