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.

Tuning symmetry and magnetic blocking of an exchange-coupled lanthanide ion in isomeric, tetrametallic complexes: [LnCl6(TiCp2)3].

The synthesis and magnetic properties of two pairs of isomeric, exchange-coupled complexes, [LnCl6(TiCp2)3] (Ln = Gd, Tb), are reported. In each isomeric pair, the central lanthanide ion adopts either a pseudo-octahedral (O-Ln) or trigonal prismatic geometry (TP-Ln) yielding complexes with C 1 or C 3h molecular symmetry, respectively. Ferromagnetic exchange coupling is observed in TP-Ln as indicated by the increases in χ m T below 30 K. For TP-Gd, a fit to the susceptibility reveals ferromagnetic coupling between the Gd3+ ion and the Ti3+ ions (J = 2.90(1) cm-1). In contrast to O-Tb, which shows no single-molecule magnetic behavior, the TP-Tb complex presents slow magnetic relaxation with a 100s-blocking temperature of 2.3 K and remanent magnetization at zero field up to 3 K. The calculated electronic structures of both compounds imply that trigonal prismatic geometry of TP-Tb is critical to the observed magnetic behavior.

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.

The role of the intermediate triplet state in iron-catalyzed multi-state C-H activation.

Efficient activation and functionalization of the C-H bond under mild conditions are of a great interest in chemical synthesis. We investigate the previously proposed spin-accelerated activation of the C(sp2)-H bond by a Fe(II)-based catalyst to clarify the role of the intermediate triplet state in the reaction mechanism. High-level electronic structure calculations on a small model of a catalytic system utilizing the coupled cluster with the single, double, and perturbative triple excitations [CCSD(T)] are used to select the density functional for the full-size model. Our analysis indicates that the previously proposed two-state quintet-singlet reaction pathway is unlikely to be efficient due to a very weak spin-orbit coupling between these two spin states. We propose a more favorable multi-state quintet-triplet-singlet reaction pathway and discuss the importance of the intermediate triplet state. This triplet state facilitates a spin-accelerated reaction mechanism by strongly coupling to both quintet and singlet states. Our calculations show that the C-H bond activation through the proposed quintet-triplet-singlet reaction pathway is more thermodynamically favorable than the single-state quintet and two-state singlet-quintet mechanisms.

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 MJ 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.

NAST: Nonadiabatic Statistical Theory Package for Predicting Kinetics of Spin-Dependent Processes.

We present a nonadiabatic statistical theory (NAST) package for predicting kinetics of spin-dependent processes, such as intersystem crossings, spin-forbidden unimolecular reactions, and spin crossovers. The NAST package can calculate the probabilities and rates of transitions between the electronic states of different spin multiplicities. Both the microcanonical (energy-dependent) and canonical (temperature-dependent) rate constants can be obtained. Quantum effects, including tunneling, zero-point vibrational energy, and reaction path interference, can be accounted for. In the limit of an adiabatic unimolecular reaction proceeding on a single electronic state, NAST reduces to the traditional transition state theory. Because NAST requires molecular properties at only a few points on potential energy surfaces, it can be applied to large molecular systems, used with accurate high-level electronic structure methods, and employed to study slow nonadiabatic processes. The essential NAST input data include the nuclear Hessian at the reactant minimum, as well as the nuclear Hessians, energy gradients, and spin-orbit coupling at the minimum energy crossing point (MECP) between two states. The additional computational tools included in the NAST package can be used to extract the required input data from the output files of electronic structure packages, calculate the effective Hessian at the MECP, and fit the reaction coordinate for more advanced NAST calculations. We describe the theory, its implementation, and three examples of application to different molecular systems.

Intersystem crossing and internal conversion dynamics with GAIMS-TeraChem: Excited state relaxation in 2-cyclopentenone.

Excited states relaxation in complex molecules often involves two types of nonradiative transitions, internal conversion (IC) and intersystem crossing (ISC). In the situations when the timescales of IC and ISC are comparable, an interplay between these two types of transitions can lead to complex nonadiabatic dynamics on multiple electronic states of different characters and spin multiplicities. We demonstrate that the generalized ab initio multiple spawning (GAIMS) method interfaced with the fast graphics processing unit-based TeraChem electronic structure code can be used to model such nonadiabatic dynamics involving both the IC and ISC transitions in molecules of moderate size. We carried out 1500 fs GAIMS simulations leading to the creation of up to 2500 trajectory basis functions to study the excited states relaxation in 2-cyclopentenone. After a vertical excitation from the ground state to the bright S2 state, the molecule quickly relaxes to the S1 state via conical intersection. The following relaxation proceeds along two competing pathways: one involves IC to the ground state, and the other is dominated by ISC to the low-lying triplet states. The time constants describing the population transfer between the six lowest singlet and triplet states predicted by the GAIMS dynamics are in good agreement with the characteristic times of IC and ISC obtained from the analysis of the time-resolved photoelectron spectrum.

Modeling Spin-Crossover Dynamics.

In this article, we review nonadiabatic molecular dynamics (NAMD) methods for modeling spin-crossover transitions. First, we discuss different representations of electronic states employed in the grid-based and direct NAMD simulations. The nature of interstate couplings in different representations is highlighted, with the main focus on nonadiabatic and spin-orbit couplings. Second, we describe three NAMD methods that have been used to simulate spin-crossover dynamics, including trajectory surface hopping, ab initio multiple spawning, and multiconfiguration time-dependent Hartree. Some aspects of employing different electronic structure methods to obtain information about potential energy surfaces and interstate couplings for NAMD simulations are also discussed. Third, representative applications of NAMD to spin crossovers in molecular systems of different sizes and complexities are highlighted. Finally, we pose several fundamental questions related to spin-dependent processes. These questions should be possible to address with future methodological developments in NAMD.

Full Visible Spectrum and White Light Emission with a Single, Input-Tunable Organic Fluorophore.

The blue emission of M2biQ can be tuned to specific wavelengths throughout the visible region by changing the identity of the cation it interacts with. These optical properties are observed in MeCN solution and the solid state. White light is obtained in MeCN by using either the proper ratio of zinc ions or acid. Thus, M2biQ acts as a nearly universal emitter (λem = 468-690 nm) with large Stokes shifts (116-306 nm, Δν̃ = 7,042-11,823 cm-1). Full spectral profiles as well as quantum yields, lifetimes, and the crystal structures of key RGB and yellow emitters are reported. Emission wavelengths correlate with cationic radius, and TD-DFT calculations show that, for 1:1 complexes, the smaller the ion, the shorter the N-cation bond, and the greater the bathochromic emission shift.

Spin controlled surface chemistry: alkyl desorption from Si(100)-2×1 by nonadiabatic hydrogen elimination.

An understanding of the role that spin states play in semiconductor surface chemical reactions is currently limited. Herein, we provide evidence of a nonadiabatic reaction involving a localized singlet to triplet thermal excitation of the Si(100) surface dimer dangling bond. By comparing the ß-hydrogen elimination kinetics of ethyl adsorbates probed by thermal desorption experiments to electronic structure calculation results, we determined that a coverage-dependent change in mechanism occurs. At low coverage, a nonadiabatic, inter-dimer mechanism is dominant, while adiabatic mechanisms become dominant at higher coverage. Computational results indicate that the spin crossover is rapid near room temperature and the nonadiabatic path is accelerated by a barrier that is 40 kJ mol-1 less than the adiabatic path. Simulated thermal desorption reactions using nonadiabatic transition state theory (NA-TST) for the surface dimer intersystem crossing are in close agreement with experimental observations.

Intersystem crossing in tunneling regime: T1 → S0 relaxation in thiophosgene.

The T1 excited state relaxation in thiophosgene has attracted much attention as a relatively simple model for the intersystem crossing (ISC) transitions in polyatomic molecules. The very short (20-40 ps) T1 lifetime predicted in several theoretical studies strongly disagrees with the experimental values (∼20 ns) indicating that the kinetics of T1 → S0 ISC is not well understood. We use the nonadiabatic transition state theory (NA-TST) with the Zhu-Nakamura transition probability and the multireference perturbation theory (CASPT2) to show that the T1 → S0 ISC occurs in the quantum tunneling regime. We also introduce a new zero-point vibrational energy correction scheme that improves the accuracy of the predicted ISC rate constants at low internal energies. The predicted lifetimes of the T1 vibrational states are between one and two orders of magnitude larger than the experimental values. This overestimation is attributed to the multidimensional nature of quantum tunneling that facilitates ISC transitions along the non-minimum energy path and is not accounted for in the one-dimensional NA-TST.

In Silico Molecular Engineering of Dysprosocenium-Based Complexes to Decouple Spin Energy Levels from Molecular Vibrations.

Molecular nanomagnets hold great promise for spintronics and quantum technologies, provided that their spin memory can be preserved above liquid-nitrogen temperatures. In the past few years, the magnetic hysteresis records observed for two related dysprosocenium-type complexes have highlighted the potential of molecular engineering to decouple vibrational excitations from spin states and thereby enhance magnetic memory. Herein, we study the spin-vibrational coupling in [(CpiPr5)Dy(Cp*)]+ (CpiPr5 = pentaisopropylcyclopentadienyl, Cp* = pentamethylcyclopentadienyl), which currently holds the hysteresis record (80 K), by means of a computationally affordable methodology that combines first-principles electronic structure calculations with a phenomenological ligand field model. Our analysis is in good agreement with the previously reported state-of-the-art ab initio calculations, with the advantage of drastically reducing the computation time. We then apply the proposed methodology to three alternative dysprosocenium-type complexes, extracting physical insights that demonstrate the usefulness of this strategy to efficiently engineer and screen magnetic molecules with the potential of retaining spin information at higher temperatures.

Locating Minimum Energy Crossings of Different Spin States Using the Fragment Molecular Orbital Method.

Spin-dependent processes involving nonadiabatic transitions between electronic states with different spin multiplicities play important roles in the chemistry of complex systems. The rates of these processes can be predicted based on the molecular properties at the minimum energy crossing point (MECP) between electronic states. We present the development of the MECP search technique within the fragment molecular orbital (FMO) method applicable to large complex systems. The accuracy and scalability of the new method is demonstrated on several models of the metal-sulfur protein rubredoxin. The effect of the model size on the MECP geometry and relative energy is discussed. The fragment energy decomposition and spin density delocalization analyses reveal how different protein residues and solvent molecules contribute to stabilization of the spin states. The developed FMO-MECP method can help to clarify the role of nonadiabatic spin-dependent processes in complex systems and can be used for designing mutations aimed at controlling these processes in metalloproteins, including spin-dependent catalysis and electron transfer.

Electronic Transitions Responsible for C60+ Diffuse Interstellar Bands.

Diffuse interstellar bands (DIBs) are puzzling absorption features believed to contain critical information about molecular evolution in space. Despite the fact that C60+ recently became the first confirmed carrier of several DIBs, the nature of the corresponding transitions is not understood. Using electronic structure methods, we show that the two strong C60+ DIBs cannot be explained by electronic transitions to the two different excited 2 E1 g states or the two spin-orbit components of the lowest 2 E1 g state, as suggested before. We argue that the strong DIBs at 9632 and 9577 Å correspond to the cold excitations from the non-Franck-Condon region of the ground electronic state to the two components of the lowest 2 E1 g state split by Jahn-Teller distortion. The weak DIBs at 9428 and 9365 Å are assigned to the first vibronic transitions involving the low-energy vibrational modes and components of the lowest 2 E1 g electronic state.

Predicting Intersystem Crossing Rates with AIMS-DFT Molecular Dynamics.

Accurate prediction of the intersystem crossing rates is important for many different applications in chemistry, physics, and biology. Recently, we implemented the ab initio multiple spawning (AIMS) molecular dynamics method to describe the intersystem crossing processes, where nonradiative transitions between electronic states with different spin multiplicities are mediated by spin-orbit coupling. Our original implementation of the direct AIMS dynamics used the complete active space self-consistent field (CASSCF) method to describe multiple coupled electronic states on which multidimensional Gaussian wave packets were propagated. In this work, we improve the computational efficiency and versatility of the AIMS dynamics by interfacing it with the density functional theory (DFT). The new AIMS-DFT and the earlier AIMS-CASSCF implementations are used to investigate the effects of electronic structure methods on the predicted intersystem crossing rate constants and the lowest triplet state lifetime in the GeH2 molecule. We also compare the rates and lifetimes obtained from the AIMS simulations with those predicted by the statistical nonadiabatic transition state theory (NA-TST). In NA-TST, the probabilities of spin transitions are calculated using the Landau-Zener, weak coupling, and Zhu-Nakamura formulas. Convergence of the AIMS rate constants with respect to the simulation time and the number of initial trajectories (Gaussian wave packets) is analyzed. An excellent agreement between AIMS-DFT and AIMS-CASSCF can be explained by cancelation of two effects: higher energy barriers and a stronger spin-orbit coupling in DFT relative to CASSCF. The rate constants obtained with the AIMS-DFT dynamics are about a factor of 2 larger than those predicted by the statistical NA-TST. This is likely due to the importance of the nonlocal interstate transitions missing from the NA-TST description.

Lactate Racemase Nickel-Pincer Cofactor Operates by a Proton-Coupled Hydride Transfer Mechanism.

Lactate racemase (LarA) of Lactobacillus plantarum contains a novel organometallic cofactor with nickel coordinated to a covalently tethered pincer ligand, pyridinium-3-thioamide-5-thiocarboxylic acid mononucleotide, but its function in the enzyme mechanism has not been elucidated. This study presents direct evidence that the nickel-pincer cofactor facilitates a proton-coupled hydride transfer (PCHT) mechanism during LarA-catalyzed lactate racemization. No signal was detected by electron paramagnetic resonance spectroscopy for LarA in the absence or presence of substrate, consistent with a +2 metal oxidation state and inconsistent with a previously proposed proton-coupled electron transfer mechanism. Pyruvate, the predicted intermediate for a PCHT mechanism, was observed in quenched solutions of LarA. A normal substrate kinetic isotope effect ( kH/ kD of 3.11 ± 0.17) was established using 2-α-2H-lactate, further supporting a PCHT mechanism. UV-visible spectroscopy revealed a lactate-induced perturbation of the cofactor spectrum, notably increasing the absorbance at 340 nm, and demonstrated an interaction of the cofactor with the inhibitor sulfite. A crystal structure of LarA provided greater resolution (2.4 Å) than previously reported and revealed sulfite binding to the pyridinium C4 atom of the reduced pincer cofactor, mimicking hydride reduction during a PCHT catalytic cycle. Finally, computational modeling supports hydride transfer to the cofactor at the C4 position or to the nickel atom, but with formation of a nickel-hydride species requiring dissociation of the His200 metal ligand. In aggregate, these studies provide compelling evidence that the nickel-pincer cofactor acts by a PCHT mechanism.

Ab initio calculations of spectroscopic constants and vibrational state lifetimes of diatomic alkali-alkaline-earth cations.

We investigate the lifetimes of vibrational states of diatomic alkali-alkaline-earth cations to determine their suitability for ultracold experiments where long decoherence time and controllability by an external electric field are desirable. The potential energy and permanent dipole moment curves for the ground electronic states of LiBe+, LiMg+, NaBe+, and NaMg+ are obtained using the coupled cluster with singles doubles and triples and multireference configuration interaction methods in combination with large all-electron cc-pCVQZ and aug-cc-pCV5Z basis sets. The energies and wave functions of all vibrational states are obtained by solving the Schrödinger equation for nuclei with the B-spline basis set method. To predict the lifetimes of vibrational states, the transition dipole moments, as well as the Einstein coefficients describing spontaneous emission, and the stimulated absorption and emission induced by black body radiation are calculated. Surprisingly, in all studied ions, the lifetimes of the highest excited vibrational states are similar to the lifetimes of the ground vibrational states indicating that highly vibrationally excited ions could be useful for the ultracold experiments requiring long decoherence time.

Chiral Peropyrene: Synthesis, Structure, and Properties.

Herein we describe the synthesis, structure, and properties of chiral peropyrenes. Using p-terphenyl-2,2″,6,6″-tetrayne derivatives as precursors, chiral peropyrenes were formed after a 4-fold alkyne cyclization reaction promoted by triflic acid. Due to the repulsion of the two aryl substituents within the same bay region, the chiral peropyrene adopts a twisted backbone with an end-to-end twist angle of 28° that was unambiguously confirmed by X-ray crystallographic analysis. The chiral peropyrene products absorb and emit in the green region of the UV-visible spectrum. Circular dichroism spectroscopy shows strong Cotton effects (Δε = ±100 M-1 cm-1 at 300 nm). The Raman data shows the expected D-band along with a split G-band that is due to longitudinal and transversal G modes. This data corresponds well with the simulated Raman spectra of chiral peropyrenes. The chiral peropyrene products also display circularly polarized luminescence. The cyclization reaction mechanism and the enantiomeric composition of the peropyrene products are explained using DFT calculations. The inversion barrier for racemization was determined experimentally to be 29 kcal/mol and is supported by quantum mechanical calculations.