Effect of Extreme Variations of Fundamental Constants on the Structure of Atoms and Molecules

The fundamental constants (FCs) of physics are promoted to dynamic quantities in modern theories. So far most of the literature focused on small fractional variations in the values of FCs. In this paper, we investigate the novel regime of extreme but transient variations of FCs. We focus on the speed of light (c) and show that its variation can dramatically change the electronic structure and chemistry of atoms and molecules. These changes are induced by increased relativistic effects when c is reduced from its nominal value. To model these changes, we solve the fully relativistic Dirac equation at different values of c. We show that at extreme variations of c, the periodic table is truncated, the nominal ground states of atoms can change, water fails to serve as a universal solvent, and the ammonia molecule becomes planar.

Analytical nonadiabatic coupling and state-specific energy gradient for the crystal field Hamiltonian describing lanthanide single-ion magnets

Paramagnetic molecules with a metal ion as an electron spin center are promising building blocks for molecular qubits and high-density memory arrays. However, fast spin relaxation and decoherence in these molecules lead to a rapid loss of magnetization and quantum information. Nonadiabatic coupling (NAC), closely related to spin-vibrational coupling, is the main source of spin relaxation and decoherence in paramagnetic molecules at higher temperatures. Predicting these couplings using numerical differentiation requires a large number of computationally intensive ab initio or crystal field electronic structure calculations. To reduce computational cost and improve accuracy, we derive and implement analytical NAC and state-specific energy gradient for the ab initio parametrized crystal field Hamiltonian describing single-ion molecular magnets. Our implementation requires only a single crystal field calculation. In addition, the accurate NACs and state-specific energy gradients can be used to model spin relaxation using sophisticated nonadiabatic molecular dynamics, which avoids the harmonic approximation for molecular vibrations. To test our implementation, we calculate the NAC values for three lanthanide complexes. The predicted values support the relaxation mechanisms reported in previous studies.

Predicting Kinetics and Dynamics of Spin-Dependent Processes

ConspectusPredicting mechanisms and rates of nonadiabatic spin-dependent processes including photoinduced intersystem crossings, thermally activated spin-forbidden reactions, and spin crossovers in metal centers is a very active field of research. These processes play critical roles in transition-metal-based and metalloenzymatic catalysis, molecular magnets, light-harvesting materials, organic light-emitting diodes, photosensitizers for photodynamic therapy, and many other applications. Therefore, accurate modeling of spin-dependent processes in complex systems and on different time scales is important for many problems in chemistry, biochemistry, and materials sciences.Nonadiabatic statistical theory (NAST) and nonadiabatic molecular dynamics (NAMD) are two complementary approaches to modeling the kinetics and dynamics of spin-dependent processes. NAST predicts the probabilities and rate constants of nonradiative transitions between electronic states with different spin multiplicities using molecular properties at only few critical points on the potential energy surfaces (PESs), including the reactant minimum and the minimum energy crossing point (MECP) between two spin states. This makes it possible to obtain molecular properties for NAST calculations using accurate but often computationally expensive electronic structure methods, which is critical for predicting the rate constants of spin-dependent processes. Alternatively, NAST can be used to study spin-dependent processes in very large complex molecular systems using less computationally expensive electronic structure methods. The nuclear quantum effects, such as zero-point vibrational energy, tunneling, and interference between reaction paths can be easily incorporated. However, the statistical and local nature of NAST makes it more suitable for large systems and slow kinetics. In contrast, NAMD explores entire PESs of interacting electronic states, making it ideal for modeling fast barrierless spin-dependent processes. Because the knowledge of large portions of PESs is often needed, the simulations require a very large number of electronic structure calculations, which limits the NAMD applicability to relatively small molecular systems and ultrafast kinetics.In this Account, we discuss our contribution to the development of the NAST and NAMD approaches for predicting the rates and mechanism of spin-dependent processes. First, we briefly describe our NAST and NAMD implementations. The NAST implementation is an extension of the transition state theory to the processes involving two crossing potential energy surfaces of different spin multiplicities. The NAMD approach includes the trajectory surface hopping (TSH) and ab initio multiple spawning (AIMS) methods. Second, we discuss several applications of NAST and NAMD to model spin-dependent processes in different systems. The NAST applicability to large complex systems is demonstrated by the studies of the spin-forbidden isomerization of the active sites of metal-sulfur proteins. Our implementation of the MECP search algorithm within the fully ab initio fragment molecular orbital method allows applying NAST to systems with thousands of atoms, such as the solvated protein rubredoxin. Applications of NAMD to ultrafast spin-dependent processes are represented by the generalized AIMS simulations utilizing the fast GPU-based TeraChem electronic structure program to gain insight into the complex photoexcited state relaxation in 2-cyclopentenone.

Strong Relativistic Effects in Lanthanide-Based Single-Molecule Magnets

Lanthanide-based single-molecule magnets (SMMs) are promising building blocks for quantum memory and spintronic devices. Designing lanthanide-based SMMs with long spin relaxation time requires a detailed understanding of their electronic structure, including the crucial role of the spin-orbit coupling (SOC). While traditional calculations of SOC using the perturbation theory applied to a solution of the nonrelativistic Schrödinger equation are valid for light atoms, this approach is questionable for systems containing heavy elements such as lanthanides. We investigate the accuracy of the perturbation estimates of SOC by variationally solving the Dirac equation for the [DyO]+ molecule, a prototype of a lanthanide-based SMM. We show that the energy splittings between the M J states involved in spin relaxation depend on the interplay between strong SOC and dynamic electron correlation. We demonstrate that this interplay affects the resonances between the spin and vibrational transitions and, therefore, the spin relaxation time.

Palladium(II) Ion Mediated Disulfide/Thiolate Interconversion: Predicting the Disulfide Group State from First Principles

Different reactivity of homologous disulfides toward Pd²⁺ was previously reported: stepwise complexation to Pd²⁺ for l-cystine and cystamine ligands, while for dl-homocystine and 3,3'-dithiodipropionic acid, disulfide's disproportionation toward thiolate and sulfinic acid complexes is observed. The disulfide/thiolate interconversion of four different disulfide ligands in the presence of nonredox metal cation Pd²⁺ in aqueous solution has been computationally investigated. We see this different reactivity in different capacities of considered homologous disulfides to stabilize forming S,S'-binuclear complexes, which are believed to be key intermediates toward interconversion products. We thus devise a theoretical model that rationalizes experimentally observed phenomenon of disulfides different reactivity toward nonredox transition metal cation Pd²⁺.