2020
DOI: 10.1063/5.0021831
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Instanton theory of tunneling in molecules with asymmetric isotopic substitutions

Abstract: We consider quantum tunnelling in asymmetric double-well systems for which the local minima in the two wells have the same energy, but the frequencies differ slightly. In a molecular context, this situation can arise if the symmetry is broken by isotopic substitutions. We derive a generalization of instanton theory for these asymmetric systems, leading to an semiclassical expression for the tunnelling matrix element and hence the energy-level splitting. We benchmark the method using a set of one-and two-dimens… Show more

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Cited by 18 publications
(45 citation statements)
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“…Symmetric parents for other well investigated structural families with respect to (partial) localization by chemical or isotopic symmetry breaking include porphycen (tunneling splitting of 4.4 cm ) [ 37 , 38 , 39 , 40 , 41 ], malonaldehyde (21.6 cm ) [ 4 , 7 , 14 ] and 9-hydroxyphenalenone (69 cm ) [ 3 , 42 , 43 , 44 , 45 ].…”
Section: Introductionmentioning
confidence: 99%
“…Symmetric parents for other well investigated structural families with respect to (partial) localization by chemical or isotopic symmetry breaking include porphycen (tunneling splitting of 4.4 cm ) [ 37 , 38 , 39 , 40 , 41 ], malonaldehyde (21.6 cm ) [ 4 , 7 , 14 ] and 9-hydroxyphenalenone (69 cm ) [ 3 , 42 , 43 , 44 , 45 ].…”
Section: Introductionmentioning
confidence: 99%
“…For a molecular cluster, in general, different configurations are distinguishable and acquire different energies. In asymmetric environments, the delocalization of the protons by tunneling usually competes with the localization of the protons by the environment, and the latter usually wins, with only a few exceptions reported so far [20] . As a result, it is rare to observe proton tunneling in molecular complexes.…”
Section: Figurementioning
confidence: 99%
“…The description of tunneling in such slightly asymmetric double-minimum potentials continues to draw interest from the theoretical side. [6][7][8][9][10][11][12][13][14] Known experimental splittings for hydrogen atom tunneling span a range of more than eight orders of magnitudes, with most of them being (far) smaller than 1 cm −1 hc ( ≈ 0.01 kJ mol −1 ) [15]. For this reason, localization is the typical, but not the strict, outcome from symmetry breaking by chemical [3,[16][17][18][19] or isotopic [4,5,[20][21][22][23][24][25][26][27][28] substitution, internal rotation of molecular groups [6,16,20,24,29], or from environmental influences such as solvation [16,30], matrix embedding [3,31,32] or crystallization [33].…”
Section: Introductionmentioning
confidence: 99%
“…Symmetric parents for other well investigated structural families in respect to (partial) localization by chemical or isotopic symmetry breaking include porphycen (tunneling splitting of 4.4 cm −1 hc) [37][38][39][40][41], malonaldehyde (21.6 cm −1 hc) [4,7,14] and 9-hydroxyphenalenone (69 cm −1 hc) [3,[42][43][44][45].…”
Section: Introductionmentioning
confidence: 99%