Rotating molecules trapped in pseudorotating cages

Vibrational band-structures caused by internal rotations of the boron Wankel rotor B11. RSC Adv 2021;11:3613-3621. [PMID: 35424268 PMCID: PMC8694174 DOI: 10.1039/d0ra08821h]

Nuclear quantum effects are often neglected for systems without hydrogen atoms. However some planar boron rotors turn out to exhibit remarkable nuclear quantum effects. Recent experiment on infrared spectroscopy of B₁₃⁺ shows unexpected spectral broadening which still awaits physical explanation. Here we present quantitative investigations of the vibrational energy levels of B₁₁⁻ up to full dimension. A harmonic-bath averaged Hamiltonian suitable for planar boron rotors is constructed and used to predict typical types of vibrational states of B₁₁⁻. Band structures caused by internal rotations are found for all the investigated vibrational states. The experimental phenomenon of spectral broadening is thus due to the band structures of the corresponding vibrational levels. The detailed information of the relevant vibrational states reported in the present work may provide valuable references for future investigations of high resolution spectroscopy of B₁₁⁻.

The band structures of the vibrational energy levels of B₁₁⁻ lead to corresponding spectral broadening. The vibrational band-structures of planar boron rotors are caused by internal rotations.

Nuclear spin blockade of laser ignition of intramolecular rotation in the model boron rotor B 13 + 11

The boron rotor B 13 + 11 consists of a tri-atomic inner "wheel" that may rotate in its pseudo-rotating ten-atomic outer "bearing"-this concerted motion is called "contorsion." B 13 + 11 in its ground state has zero contorsional angular momentum. Starting from this initial state, it is a challenge to ignite contorsion by a laser pulse. We discover, however, that this is impossible, i.e., one cannot design any laser pulse that induces a transition from the ground to excited states with non-zero contorsional angular momentum. The reason is that the ground state is characterized by a specific combination of irreducible representations (IRREPs) of its contorsional and nuclear spin wavefunctions. Laser pulses conserve these IRREPs because hypothetical changes of the IRREPs would require nuclear spin flips that cannot be realized during the interaction with the laser pulse. We show that all excited target states of B 13 + 11 with non-zero contorsional angular momentum have different IRREPs that are inaccessible by laser pulses. Conservation of nuclear spins thus prohibits laser-induced transitions from the non-rotating ground to rotating target states. We discover various additional constraints imposed by conservation of nuclear spins, e.g., laser pulses can change clockwise to counter-clockwise contorsions or vice versa, but they cannot stop them. The results are derived in the frame of a simple model.

Temperature dependence of the intensity of the vibration-rotational absorption band ν2 of H2O trapped in an argon matrix

Using two sets of effective rotational constants for the ground (000) and the excited bending (010) vibrational states the calculation of frequencies and intensities of vibration-rotational transitions for J^″=0-2; and J^'=0-3; was carried out in frame of the model of a rigid asymmetric top for temperatures from 0 to 40K. The calculation of the intensities of vibration-rotational absorption bands of H₂O in an Ar matrix was carried out both for thermodynamic equilibrium and for the case of non-equilibrium population of para- and ortho-states. For the analysis of possible interaction of vibration-rotational and translational motions of a water molecule in an Ar matrix by 3D Schrödinger equation solving using discrete variable representation (DVR) method, calculations of translational frequencies of Н₂О in a cage formed after one argon atom deleting were carried out. The results of theoretical calculations were compared to experimental data taken from literature.

A universal mechanism of the planar boron rotors B11-, B13+, B15+, and B19-: inner wheels rotating in pseudo-rotating outer bearings

Planar boron clusters B₁₁^-, B₁₃⁺, B₁₅⁺, and B₁₉^- have been introduced recently as molecular Wankel motors or tank treads. Here we present a universal mechanism for these dynamically fluxional clusters; that is, they are molecular rotors with inner wheels that rotate almost freely in pseudo-rotating outer bearings, analogous to rotating molecules trapped in pseudo-rotating cages. This mechanism has significant quantum mechanical consequences: the global-minimum structures of the clusters have C_2v symmetry, whereas the wheels rotating in pseudo-rotating bearings generate rosette-type shapes with D_9h, D_10h, D_11h, and D_13h symmetries. The related rotational/pseudo-rotational energies appear with characteristic band structures, effecting the dynamics.

Isotope effects of reactions in quantum solids initiated by IR + UV lasers: quantum model simulations for Cl((2)P(3/2)) + X(2)(ν) → XCl + X in X(2) matrices (X = H, D)

Six isotope effects (i)-(vi) are discovered for the reactions Cl + H(2)(ν) → HCl + H in solid para-H(2) ( 1 ) versus Cl + D(2)(ν) → DCl + D in ortho-D(2) ( 2 ), by means of quantum reaction dynamics simulations, within the frame of our simple model ( J. Phys. Chem. A 2009 , 113 , 7630 . ). Experimentally, the reactions may be initiated for ν = 0 and ν ≥ 1, by means of "UV only" photodissociation of the matrix-isolated precursor, Cl(2), or by "IR + UV" coirradiation ( Kettwich , S. C. , Raston , P. L. , and Anderson , D. T. J. Phys. Chem. A 2009 , 113 , 7621 . ), respectively. Specifically, (i) various shape and Feshbach reaction resonances correlate with vibrational thresholds of reactants and products, due to the near-thermoneutrality and low barrier of the system. The energetic density of resonances increases as the square root of mass, from M(X) = M(H) to M(D). (ii) The state selective reaction ( 1 ), ν = 1, is supported by a shape resonance, whereas this type of resonance is absent in ( 2 ), ν = 1. As a consequence, time-resolved measurements should monitor different three-step versus direct error-function type evolutions of the formation of the products. (iii) The effective barrier is lower for reaction 1 , ν = 0, enhancing the tunneling rate, as compared to that for reaction 2 , ν = 0. (iv) For reference, the reaction probabilities P versus total energy E(tot) in the gas exhibit sharp resonance peaks or zigzag behaviors of the reaction probability P versus total energy, near the levels of resonances ( Persky , A. and Baer , M. J. Chem. Phys . 1974 , 60 , 133 . ). These features tend to be washed out and broadened for reaction 1 , and even more so for reaction 2 . For comparison, they disappear for reactions in classical solids. (v) The slopes of P versus E(tot) below the potential barrier increase more steeply for reaction 1 , ν = 0, than for reaction 2 , ν = 0. This enhances the tunneling rate of the heavier isotopomer, reaction 2 , ν = 0, compared to that for reaction 1 . (vi) For a given value of the UV frequency, the translational energy E(trans) increases with mass M(X). Again, this effect supports tunneling of the heavier isotopomer. The isotope effects (i)-(iii), (iv)-(v), and (vi) may be classified as energetic, translational amplitude, and kinematic, respectively. Specifically, the effects (iv)-(v) are due to a systematic decrease of the amplitudes of translational motions of the reactant molecules, from quasi infinite in the gas via still rather large values of para-H(2)(ν) and smaller values for ortho-D(2)(ν) to very small values in classical solids. These isotope effects are special phenomena in quantum solids, which do not occur, neither in the gas phase nor in classical solids. Quantitative predictions, e.g., for the effects of increasing UV frequency on the ratio of reactions probabilities for the UV only versus IR + UV experiments, must account for the interplay of various isotope effects, e.g., (vi) combined with the antagonistic effects (iii) versus (iv) and (v).

Rotation of methyl radicals in a solid krypton matrix

Electron spin resonance (ESR) measurements were carried out to study the rotation of methyl radicals (CH(3)) in a solid krypton matrix at 17-31 K temperature range. The radicals were produced by dissociating methane by plasma bursts generated by a focused 193 nm excimer laser radiation during the krypton gas condensation on the substrate. The ESR spectrum exhibits only isotropic features at the temperature range examined, and the intensity ratio between the symmetric (A) and antisymmetric (E) spin state lines exhibits weaker temperature dependence than in a solid argon matrix. However, the general appearance of the methyl radical spectrum depends strongly on temperature due to the pronounced temperature dependency of the E state linewidths. The rotational energy level populations are analyzed based on the static crystal field model, pseudorotating cage model, and quantum chemical calculations for an axially symmetric, planar rotor. Crystal field strength parameter values of -140 cm(-1) in Ar and -240 cm(-1) in Kr match most closely the experimentally observed rotational energy level shifts from the gas phase value. In the alternative model, considering the lattice atom movement in a pseudorotating cage, the effective lowering of the rotational constants B and C to 80%-90% leads to similar effects.

Rotation of methyl radicals in a solid argon matrix

Electron spin resonance (ESR) measurements were carried out to study the rotation of methyl radicals (CH3) in a solid argon matrix at 14-35 K temperatures. The radicals were produced by dissociating methane by plasma bursts generated either by a focused 193 nm laser radiation or a radio frequency discharge device during the gas condensation on the substrate. The ESR spectrum exhibits axial symmetry at the lowest temperature and is ascribed to ground state molecules with symmetric total nuclear spin function I=3/2. The hyperfine anisotropy (Aparallel)-Aperpendicular) was found to be -0.01 mT, whereas that of the g value was 2.5x10(-5). The anisotropy is observed for the first time in Ar and is manifested by the splitting of the low-field transition. Elevation of temperature leads reversibly to the appearance of excited state contribution having antisymmetric I=1/2. As a function of the sample temperature, the relative intensities of symmetric and antisymmetric spin states corresponding to ground and excited rotor states, respectively, proton hyperfine and electron g-tensor components, and spin-lattice relaxation rates were determined by a numerical fitting procedure. The experimental observations were interpreted in terms of a free rotation about the C3 axis and a thermal activation of the C2-type rotations above 15 K. The ground and excited rotational state energy levels were found to be separated by 11.2 cm-1 and to exhibit significantly different spin-lattice coupling. A crystal field model has been applied to evaluate the energy levels of the hindered rotor in the matrix, and crystal field parameter varepsilon4=-200 cm-1, corresponding to a 60 cm-1 effective potential barrier for rotation of the C3 axis, was obtained.

Unidirectional Electronic Ring Current Driven by a Few Cycle Circularly Polarized Laser Pulse: Quantum Model Simulations for Mg−Porphyrin

A circularly polarized ultraviolet (UV) laser pulse may excite a unidirectional valence-type electronic ring current in an oriented molecule, within the pulse duration of a few femtoseconds (e.g., tau = 3.5 fs). The mechanism is demonstrated by quantum model simulation for |X = |1(1)A(1g) --> |E(+) = |4 (1)E(u+) population transfer in the model system, Mg-porphyrin. The net ring current generated by the laser pulse (I = 84.5 microA) is at least 100 times stronger than any ring current, which could be induced by means of permanent magnetic fields, with present technology.