Spin and Phonon Design in Modular Arrays of Molecular Qubits

Abstract

The transformative applications of quantum information science (QIS) require precise design and integration of networks of qubits, the fundamental units of QIS systems. Chemical synthesis is a powerful approach, offering routes to modular, atomically precise arrangements of identical qubits. Herein, we employed the versatility of framework chemistry to investigate spin and lattice dynamics of the expanded copper(II) porphyrinic framework Zr−Cu−NU-1102 (2) possessing Cu−Cu distances of 18.0 Å. Pulse electron paramagnetic resonance spectroscopy revealed a significant reduction in relaxation processes mediated by qubit−qubit interactions compared with the more spin-dense Cu−PCN-224 (1) framework. With the reduction in the spin−spin relaxation process, phonon-mediated processes emerged as the primary driver of spin−lattice relaxation. We synthesized the isoreticular Hf−Cu−NU-1102 (3) to elucidate the impact of the nodes versus the ligands on the phonon-mediated relaxation process. Measurement of 3 revealed identical spin−lattice relaxation dynamics to 2, thereby excluding involvement of node-centered or bulk framework acoustic modes. Supported by theoretical calculations of the ligand vibrational modes, these results implicated linker-based motions as dominant contributors to phonon-mediated spin−lattice relaxation. These findings provide clear guidelines for synthetic design to control spin and phonon interactions in modular arrays of molecular qubits.

New Modular Organic Platform for Understanding the Effect of Structural Changes on Slow Magnetic Relaxation in Mononuclear Octahedral Copper(ii) Complexes

“…Other excited states correspond to the following configurations: 3rd -with unpaired 3dyz electron and 4th -with unpaired 3dxy electron. The 3rd and 4th excited state are well separated, suggesting that structure 2 is geometrically Please do not adjust margins Please do not adjust margins 72,[86][87][88][89][90] The inclusion of NEVPT2 dynamic corrections for compound 1 shifts the 1 st excited state ~3000 cm -1 up from the ground state, and ~4000 cm -1 for the 2 nd , 3 rd and 4 th exited states. Difference between the 1 st excited state and 2 nd excited state is enlarged from ~700 cm -1 to ~1600 cm -1 .…”

New Modular Organic Platform for Understanding the Effect of Structural Changes on Slow Magnetic Relaxation in Mononuclear Octahedral Copper(ii) Complexes

“…Interestingly, although the monodentate coordination of H2O results in higher deviation from the NNN-OH2 plane in 2 than chemically equivalent NNN-(OH)Me in 1, this effect seems to be more profound than distortions in the planes (B) and (C) associated with coordinating methoxy/ethoxy moieties of the reduced ligand. This can be understood when considering that the spin-active nitrogen atoms have the negative effect on the SIM/qubit behaviour 72,73 , which is however minimized within the square planar coordination environment.…”

“…SHAPE analysis (see Section 2.3) also shows that for 1 the deviations for the plane N2-N9-N17-MeOH from the perfectly square planar disposition are significantly smaller than in compound 2, which is most preferred for QIP systems. 72,73 To gain insight into relaxation processes of the compounds, we performed the pulsed EPR spectra in Q-band down to liquid helium temperatures. The relaxation time T1 determined for both compounds are presented in Figures S23 and S24.…”

“…It was noted that for such systems to exhibit qubit behavior and/or SIM characteristics, the following is preferred: (i) square planar coordination geometry; (ii) coordinating atoms devoid of nuclear spin; (iii) rigidification of the molecular architecture; (iv) minimization of the protons influence above a certain radius from the metal (the concept of spin diffusion barrier. 14,[72][73][74] Although significant information can be extracted from the studies on the related S=½ V(IV) complexes 73,[75][76][77][78][79][80][81] , examples of compounds with experimentally determined field-induced slow magnetic relaxation with single d 9 Cu(II, S = ½) ion are very scarce [82][83][84][85] and their origin is not fully understood. 23,24 Notably, examples of d 9 Cu(II) systems proposed to act as potential spin qubits were phthalocyanines 86,87 , porphyrines 72,[88][89][90] and Scheme 1.…”

“…14,[72][73][74] Although significant information can be extracted from the studies on the related S=½ V(IV) complexes 73,[75][76][77][78][79][80][81] , examples of compounds with experimentally determined field-induced slow magnetic relaxation with single d 9 Cu(II, S = ½) ion are very scarce [82][83][84][85] and their origin is not fully understood. 23,24 Notably, examples of d 9 Cu(II) systems proposed to act as potential spin qubits were phthalocyanines 86,87 , porphyrines 72,[88][89][90] and Scheme 1. Schematic representation of the rationale behind the modular organic platform designed and implemented in the present studies for monometallic magnetostructural correlations.…”