From coherent quasi-irreversible quantum dynamics towards the second law of thermodynamics: The model boron rotor B13+

Abstract

The planar boron cluster B13+ provides a model to investigate the microscopic origin of the second law of thermodynamics in a small system. It is a molecular rotor with an inner wheel that rotates in an outer bearing. The cyclic reaction path of B13+ passes along thirty equivalent global minimum structures (GMi, i = 1, 2, ..., 30). The GMs are embedded in a cyclic thirty-well potential. They are separated by thirty equivalent transition states with potential barrier Vb. If the boron rotor B13+ is prepared initially in one of the thirty GMs, with energy below Vb, then it tunnels sequentially to its nearest, next-nearest etc. neighbors (520 fs per step) such that all the other GMs get populated. As a consequence, the entropy of occupying the GMs takes about 6 ps to increases from zero to a value close to the maximum value for equi-distribution. Perfect recurrences are practically not observable.

Nuclear spin blockade of laser ignition of intramolecular rotation in the model boron rotor B13+11

“…22 They investigate explicitly the example 11 B − 11 using the theory of molecular symmetry (MS) groups 23 and a simple model and extrapolate analogous results for all planar boron rotors. [11][12][13][14][15][16][17][18][19][20] Their model extends that of Refs. 19 and 20 by considering not only the contorsions of the rotors but also the constraints imposed by nuclear spins.…”

“…The contorsion of 11 B + 13 , which means the concerted rotation of the wheel with respect to the bearing combined with the pseudo-rotation of the nuclei of the bearing, is described as motion along the cyclic contorsional angle ξ, 0 ξ 2π. 19,20 The value of the corresponding effective moment of inertia, I eff = 88.5 µÅ 2 , is adapted from Ref. 20.…”

“…19,20 The value of the corresponding effective moment of inertia, I eff = 88.5 µÅ 2 , is adapted from Ref. 20. If the GM shown in Fig.…”

“…The cyclic contorsional thirty-well potential V (ξ) supports the thirty equivalent GM structures of 11 B + 13 , separated by thirty equivalent TSs. It is modeled as 19,20…”

“…., GM N , TS N ,1 , where the total numbers N of the GMs and TSs are rather large: They are equal to the product N = N w × N b of the number N w of atoms that determines the shape of the wheel times the number of atoms N b in the bearing; thus, N = 2 × 9, 3 × 10, 4 × 11, and 5 × 13 for B − 11 , B + 13 , B + 15 , a) Electronic mail: dmjia@email.sxu.edu.cn and B − 19 , respectively. Second, the mobility is supported by pseudo-rotations of the nuclei of the bearings that adapt their shape to the rotating wheel, 19,20 which is analogous to rotating molecules in pseudo-rotating cages. 21 According to the terminology that has been introduced in Ref.…”