Mixed-Valence Molecular Unit for Quantum Cellular Automata: Beyond the Born–Oppenheimer Paradigm through the Symmetry-Assisted Vibronic Approach

Abstract

In this article, we focus on the electron-vibrational problem of the tetrameric mixed-valence (MV) complexes proposed for implementation as four-dot molecular quantum cellular automata (mQCA).1 Although the adiabatic approximation explored in ref 2 is an appropriate tool for the qualitative analysis of the basic characteristics of mQCA, like vibronic trapping of the electrons encoding binary information and cell-cell response, it loses its accuracy providing moderate vibronic coupling and fails in the description of the discrete pattern of the vibronic levels. Therefore, a precise solution of the quantum-mechanical vibronic problem is of primary importance for the evaluation of the shapes of the electron transfer optical absorption bands and quantitative analysis of the main parameters of tetrameric quantum cells. Here, we go beyond the Born-Oppenheimer paradigm and present a solution of the quantum-mechanical pseudo Jahn-Teller (JT) vibronic problem in bielectronic MV species (exemplified by the tetra-ruthenium complexes) based on the recently developed symmetry-assisted approach.3,4 The mathematical approach to the vibronic eigenproblem takes into consideration the point symmetry basis, and therefore, the total matrix of the JT Hamiltonian is blocked to the maximum extent. The submatrices correspond to the irreducible representations (irreps) of the point group. With this tool, we also extend the theory of the mQCA cell beyond the limit of prevailing Coulomb repulsion in the electronic pair (adopted in ref 2), and therefore, the general pseudo-JT problems for spin-singlet ((1)B1g, 2(1)A1g, (1)B2g, (1)Eu) ⊗ (b1g + eu) and spin-triplet states ((3)A2g, (3)B1g, 2(3)Eu) ⊗ (b1g + eu) in a square-planar bielectronic system are solved. The obtained symmetry-adapted electron-vibrational functions are employed for the calculation of the profiles (shape functions) of the charge transfer absorption bands in the tetrameric MV complexes and for the discussion of the magnetic properties.

Quantum Cellular Automata: a Short Overview of Molecular Problem

“…To solve the multidimensional JT problem we have recently suggested [30][31][32] a theoretical tool which has been referred to as "symmetry assisted approach" which takes advantage from the point symmetry of the system. The symmetry assisted approach allows to block the vibronic matrices to full extent in accordance with the point symmetry of the systems and thus to make tractable the complicated dynamic problems for these molecular cells.…”

“…The mathematical details of the approach are described in Refs. [30][31][32]. The main idea is that the evaluation of the vibrational functions can be performed through the action of the symmetry adapted polynomial operators T pnq Γ γ onto the vacuum state: T pnq Γ γ |dn i 0y |n, Γ γy ,…”

“…and spin-triplet states 3 A 2g , 3 B 1g , 2 3 E u¨ pb 1g e u q in a square-planar bi-electronic system has been recently solved [32]. The obtained symmetry adapted electronvibrational functions have been employed for the calculation of the profiles (shape-functions) of the charge transfer absorption bands in the tetrameric MV complexes and for the discussion of the magnetic properties.…”

“…In Ref. [32] we presented also the characteristics of the performance of the evaluation which can be referred to as "index of efficiency" defined as the ratio (CPU time for blocked matrix) / (CPU time for full matrix). In particular, use of the symmetry adapted basis leads to a significant reduction of the CPU time, for example for N 24 (number of the unperturbed vibrational levels) the CPU time with the use of symmetry is only 7.1% of the total time without application of the symmetry assisted approach.…”

VIBPACK: A package to treat multidimensional electron‐vibrational molecular problems with application to magnetic and optical properties

“…However this powerful approach is limited to systems with high (unitary) symmetry, and is restricted also by allowance for the linear vibronic coupling Hamiltonian with definite interrelations between JT parameters (which ensures unitary symmetry). That is why the task of the full exploration of the advantages provided by the point symmetry of the large systems remains a current challenge …”