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Chirality and Relativistic Effects in Os3(CO)12.

ABSTRACT: The energy and structural parameters were obtained for all forms of the carbonyl complex of osmium Os3(CO)12 with D3h and D3 symmetries using density functional theory (DFT) methods. The calculations took into account various levels of relativistic effects, including those associated with nonconservation of spatial parity. It was shown that the ground state of Os3(CO)12 corresponds to the D3 symmetry and thus may be characterized either as left-twisted (D3S) or right-twisted (D3R). The D3S↔D3R transitions occur through the D3h transition state with an activation barrier of ~10-14 kJ/mol. Parity violation energy difference (PVED) between D3S and D3R states equals to ~5 × 10-10 kJ/mol. An unusual three-center exchange interaction was found inside the {Os3} fragment. It was found that the cooperative effects of the mutual influence of osmium atoms suppress the chirality of the electron system in the cluster.

SUBMITTER: Ryzhikov MR

PROVIDER: S-EPMC8199560 | biostudies-literature | 2021 Jun

REPOSITORIES: biostudies-literature

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Chirality and Relativistic Effects in Os3(CO)12.

Ryzhikov Maxim R MR Mirzaeva Irina V IV Kozlova Svetlana G SG Mironov Yuri V YV

Molecules (Basel, Switzerland) 20210601 11

The energy and structural parameters were obtained for all forms of the carbonyl complex of osmium Os3(CO)12 with D3h and D3 symmetries using density functional theory (DFT) methods. The calculations took into account various levels of relativistic effects, including those associated with nonconservation of spatial parity. It was shown that the ground state of Os3(CO)12 corresponds to the D3 symmetry and thus may be cha ...[more]

PMID: 34206080

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Project description:Periodic space crystals are well established and widely used in physical sciences. Time crystals have been increasingly explored more recently, where time is disconnected from space. Periodic relativistic spacetime crystals on the other hand need to account for the mixing of space and time in special relativity through Lorentz transformation, and have been listed only in 2D. This work shows that there exists a transformation between the conventional Minkowski spacetime (MS) and what is referred to here as renormalized blended spacetime (RBS); they are shown to be equivalent descriptions of relativistic physics in flat spacetime. There are two elements to this reformulation of MS, namely, blending and renormalization. When observers in two inertial frames adopt each other's clocks as their own, while retaining their original space coordinates, the observers become blended. This process reformulates the Lorentz boosts into Euclidean rotations while retaining the original spacetime hyperbola describing worldlines of constant spacetime length from the origin. By renormalizing the blended coordinates with an appropriate factor that is a function of the relative velocities between the various frames, the hyperbola is transformed into a Euclidean circle. With these two steps, one obtains the RBS coordinates complete with new light lines, but now with a Euclidean construction. One can now enumerate the RBS point and space groups in various dimensions with their mapping to the well known space crystal groups. The RBS point group for flat isotropic RBS spacetime is identified to be that of cylinders in various dimensions: mm2 which is that of a rectangle in 2D, (∞/m)m which is that of a cylinder in 3D, and that of a hypercylinder in 4D. An antisymmetry operation is introduced that can swap between space-like and time-like directions, leading to color spacetime groups. The formalism reveals RBS symmetries that are not readily apparent in the conventional MS formulation. Mathematica script is provided for plotting the MS and RBS geometries discussed in the work.

Dataset Information

Chirality and Relativistic Effects in Os3(CO)12.

Publications

Chirality and Relativistic Effects in Os<sub>3</sub>(CO)<sub>12</sub>.

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