Electronic spin separation induced by nuclear motion near conical intersections

Infrared-driven dynamics and scattering mechanisms of NO radicals with propane and butane: impacts of pseudo Jahn-Teller effects

The topology of multidimensional potential energy surfaces defines the bimolecular collision outcomes of open-shell radicals with molecular partners. Understanding these surfaces is crucial for predicting the inelastic scattering and chemical transformations of increasingly complex radical-molecule collisions. To characterize the inelastic scattering mechanisms of nitric oxide (NO) radicals with large alkanes, we generated the collision complexes comprised of NO with propane or n-butane. The infrared action spectroscopy and infrared-driven dynamics of NO-propane and NO-(n-butane) collision complexes in the CH stretch region were recorded, while also comparing the results to the analogous experiments carried out for NO-CH4 and NO-ethane. The infrared spectroscopy is analyzed using rovibrational simulations to characterize the transition bands and to determine the vibrational predissociation lifetimes of NO-propane and NO-(n-butane). Due to pseudo Jahn-Teller dynamics, the NO-propane and NO-(n-butane) decay mechanisms from IR activation appear similar to those for NO-ethane previously reported from this laboratory (J. P. Davis et al. Faraday Discuss., 2024, 251, 262-278). Furthermore, the NO (X2Π, v'' = 0, J'', Fn, Λ) product state distributions from NO-alkane fragmentation reveal a strong electron-spin polarization and a propensity for NO products to rotate in the plane of the π* molecular orbital, yielding mechanistic insights into the inelastic scattering outcomes. We hypothesize that a geometric phase may be present, impacting the relative population distributions, in addition to the accessible pathway timescales.

Spin-Charge Conversion in Chiral Polymers with Hopping Conduction

Organic and biological materials are often chiral. Chiral polymers, as recent experiments indicate, facilitate spin-charge conversion: a charge current results in a spin polarization and vice versa, dubbed chirality-induced spin selectivity (CISS) and inverse CISS (ICISS). While CISS/ICISS in crystalline chiral systems such as tellurium can be understood in terms of their chirality- and spin-dependent band structure, such a picture becomes inapplicable to disordered chiral polymers, where carrier transport is via hopping rather than band conduction. Here, we develop a microscopic theory to describe CISS and ICISS in disordered chiral organics, in which chirality-induced geometric spin-orbit coupling leads to a purely geometric spin-dependent Berry phase in electron hops involving triads, whose orientations are dictated by the material's chirality. Our theory reveals a central role of spin-flip hopping, which suppresses CISS but enables ICISS.

Insights into the Mechanism of Chiral-Induced Spin Selectivity: The Effect of Magnetic Field Direction and Temperature

Chiral oligopeptide monolayers are adsorbed on a ferromagnetic surface and their magnetoresistance is measured as a function of the angle between the magnetization of the ferromagnet and the surface normal. These measurements are conducted as a function of temperature for both enantiomers. The angle dependence is found to follow a changing trend with a period of 360°. Quantum simulations reveal that the angular distribution can be obtained only if the monolayer has significant effective spin orbit coupling (SOC), that includes contribution from the vibrations. The model shows that SOC only in the leads cannot reproduce the observed angular dependence. The simulation can reproduce the experiments if it included electron-phonon interactions and dissipation.

Persistent Chirality-Induced Spin-Selectivity Effect in Circular Helix Molecules

The spin-orbit coupling (SOC), the dynamics of the nonequilibrium transport process, and the breaking of time-reversal and space-inversion symmetries have been regarded as key factors for the emergence of chirality-induced spin selectivity (CISS) and chirality-dependent spin currents in helix molecules. In this work, we demonstrated the generation of persistent CISS currents in various circular single-stranded DNAs and 310-helix proteins for the first time, regardless of whether an external magnetic flux is applied or not. This new CISS effect presents only in equilibrium transport processes, distinct from the traditional CISS observed in nonequilibrium transport processes and linear helix molecules; we term it as the PCISS effect. Notably, PCISS manifests irrespective of whether the SOC is chirality-driven or stems from heavy-metal substrates, making it an efficient way to generate chirality-locked pure spin currents. Our research establishes a novel paradigm for examining the underlying physics of the CISS effect.

Chiral Induced Spin Selectivity

Since the initial landmark study on the chiral induced spin selectivity (CISS) effect in 1999, considerable experimental and theoretical efforts have been made to understand the physical underpinnings and mechanistic features of this interesting phenomenon. As first formulated, the CISS effect refers to the innate ability of chiral materials to act as spin filters for electron transport; however, more recent experiments demonstrate that displacement currents arising from charge polarization of chiral molecules lead to spin polarization without the need for net charge flow. With its identification of a fundamental connection between chiral symmetry and electron spin in molecules and materials, CISS promises profound and ubiquitous implications for existing technologies and new approaches to answering age old questions, such as the homochiral nature of life. This review begins with a discussion of the different methods for measuring CISS and then provides a comprehensive overview of molecules and materials known to exhibit CISS-based phenomena before proceeding to identify structure-property relations and to delineate the leading theoretical models for the CISS effect. Next, it identifies some implications of CISS in physics, chemistry, and biology. The discussion ends with a critical assessment of the CISS field and some comments on its future outlook.

Linear and angular momentum conservation in surface hopping methods

We demonstrate that, for systems with spin-orbit coupling and an odd number of electrons, the standard fewest switches surface hopping algorithm does not conserve the total linear or angular momentum. This lack of conservation arises not so much from the hopping direction (which is easily adjusted) but more generally from propagating adiabatic dynamics along surfaces that are not time reversible. We show that one solution to this problem is to run along eigenvalues of phase-space electronic Hamiltonians H(R, P) (i.e., electronic Hamiltonians that depend on both nuclear position and momentum) with an electronic-nuclear coupling Γ · P [see Eq. (25)], and we delineate the conditions that must be satisfied by the operator Γ. The present results should be extremely useful as far as developing new semiclassical approaches that can treat systems where the nuclear, electronic orbital, and electronic spin degrees of freedom altogether are all coupled together, hopefully including systems displaying the chiral-induced spin selectivity effect.

Phonon-assisted nearly pure spin current in DNA molecular chains: a multifractal analysis

Motivated by the development of molecular spintronics, we studied the phonon-assisted spin transport along a DNA chain in the presence of environmental-induced dephasing using multifractal analysis. The results demonstrate that a nearly pure spin current is generated in the presence of the voltage gate. The pure spin current is enhanced by increasing thermal effects. The vibration modes due to the thermal phonon bath assist in generating the spin current, so the spin state is more delocalized in strong electron-phonon coupling. The phonon chirality can translate to the electron spin to create a nontrivial spin texture, including spin currents. The spin states become more extended by increasing the phonon temperature. On the other hand, the spin states are less localized in longer chains as the spin selectivity is higher in longer chains than in short ones. Therefore, we can engineer a molecular spintronic device by controlling phonon effects on the storage and transport of binary digits.

On the circularly polarized luminescence of individual triplet sublevels

We discuss the possibility of using circularly polarized luminescence (CPL) as a tool to probe individual triplet spin sublevels that are populated nonadiabatically following photoexcitation. This study is motivated by a mechanism proposed for chirality-induced spin selectivity in which coupled electronic-nuclear dynamics may lead to a non-statistical population of the three triplet sublevels in chiral systems. We find that low-temperature CPL should aid in quantifying the exact spin state/s populated through coupled electronic-nuclear motion in chiral molecules.

Interplay of structural chirality, electron spin and topological orbital in chiral molecular spin valves

Chirality has been a property of central importance in physics, chemistry and biology for more than a century. Recently, electrons were found to become spin polarized after transmitting through chiral molecules, crystals, and their hybrids. This phenomenon, called chirality-induced spin selectivity (CISS), presents broad application potentials and far-reaching fundamental implications involving intricate interplays among structural chirality, topological states, and electronic spin and orbitals. However, the microscopic picture of how chiral geometry influences electronic spin remains elusive, given the negligible spin-orbit coupling (SOC) in organic molecules. In this work, we address this issue via a direct comparison of magnetoconductance (MC) measurements on magnetic semiconductor-based chiral molecular spin valves with normal metal electrodes of contrasting SOC strengths. The experiment reveals that a heavy-metal electrode provides SOC to convert the orbital polarization induced by the chiral molecular structure to spin polarization. Our results illustrate the essential role of SOC in the metal electrode for the CISS spin valve effect. A tunneling model with a magnetochiral modulation of the potential barrier is shown to quantitatively account for the unusual transport behavior.

Spin-Based Chiral Separations and the Importance of Molecule-Solvent Interactions

This work uses magneto-electrochemical quartz crystal microbalance methods to study the enantiospecific adsorption of chiral molecules onto a ferromagnetic substrate. The effects of solution conditions, pH, and solvent isotope composition indicate that the kinetics of the enantiomeric adsorption depend strongly on the charge state and geometry of the adsorbate, whereas no thermodynamic contributions to enantiospecificity are found. Density functional theory calculations reveal that an interplay between the adsorbate and solvent molecules is important for defining the observed enantiospecific preference with an applied magnetic field; however, it remains unclear if intermolecular vibrational couplings contribute to the phenomenon.

Infrared Activated Signatures and Jahn-Teller Dynamics of NO-CH4 Collision Complexes

Bimolecular collision outcomes sensitively depend on the chemical functionality and relative orientations of the colliding partners that define the accessible reactive and nonreactive pathways. Accurate predictions from multidimensional potential energy surfaces demand a full characterization of the available mechanisms. Therefore, there is a need for experimental benchmarks to control and characterize the collision conditions with spectroscopic accuracy to accelerate the predictive modeling of chemical reactivity. To this end, the bimolecular collision outcomes can be investigated systematically by preparing reactants in the entrance channel prior to reaction. Herein, we investigate the vibrational spectroscopy and infrared-driven dynamics of the bimolecular collision complex between nitric oxide and methane (NO-CH₄). We recorded the vibrational spectroscopy of NO-CH₄ in the CH₄ asymmetric stretching region using resonant ion-depletion infrared spectroscopy and infrared action spectroscopy, thus revealing a significantly broad spectrum centered at 3030 cm^-1 that extends over 50 cm^-1. The asymmetric CH stretch feature of NO-CH₄ is explained by CH₄ internal rotation and attributed to transitions involving three different nuclear spin isomers of CH₄. The vibrational spectra also show extensive homogeneous broadening due to the ultrafast vibrational predissociation of NO-CH₄. Additionally, we combine infrared activation of NO-CH₄ with velocity map imaging of NO (X²Π, ν″ = 0, J″, F_n, Λ) products to develop a molecular-level understanding of the nonreactive collisions of NO with CH₄. The anisotropy of the ion image features is largely determined by the probed rotational quantum number of NO (J″) products. For a subset of NO fragments, the ion images and total kinetic energy release (TKER) distributions show an anisotropic component at low relative translation (∼225 cm^-1) indicating a prompt dissociation mechanism. However, for other detected NO products, the ion images and TKER distributions are bimodal, in which the anisotropic component is accompanied by an isotropic feature at high relative translation (∼1400 cm^-1) signifying a slow dissociation pathway. In addition to the predissociation dynamics following vibrational excitation, the Jahn-Teller dynamics prior to infrared activation need to be considered to fully describe the product spin-orbit distributions. Therefore, we correlate the Jahn-Teller mechanisms of NO-CH₄ to the symmetry-restricted NO (X²Π, ν″ = 0, J″, F_n, Λ) + CH₄ (ν″) product outcomes.

Representation and conservation of angular momentum in the Born-Oppenheimer theory of polyatomic molecules

This paper concerns the representation of angular momentum operators in the Born-Oppenheimer theory of polyatomic molecules and the various forms of the associated conservation laws. Topics addressed include the question of whether these conservation laws are exactly equivalent or only to some order of the Born-Oppenheimer parameter κ = (m/M)^1/4 and what the correlation is between angular momentum quantum numbers in the various representations. These questions are addressed in both problems involving a single potential energy surface and those with multiple, strongly coupled surfaces and in both the electrostatic model and those for which fine structure and electron spin are important. The analysis leads to an examination of the transformation laws under rotations of the electronic Hamiltonian; of the basis states, both adiabatic and diabatic, along with their phase conventions; of the potential energy matrix; and of the derivative couplings. These transformation laws are placed in the geometrical context of the structures in the nuclear configuration space that are induced by rotations, which include the rotational orbits or fibers, the surfaces upon which the orientation of the molecule changes but not its shape, and the section, an initial value surface that cuts transversally through the fibers. Finally, it is suggested that the usual Born-Oppenheimer approximation can be replaced by a dressing transformation, that is, a sequence of unitary transformations that block-diagonalize the Hamiltonian. When the dressing transformation is carried out, we find that the angular momentum operator does not change. This is a part of a system of exact equivalences among various representations of angular momentum operators in Born-Oppenheimer theory. Our analysis accommodates large-amplitude motions and is not dependent on small-amplitude expansions about an equilibrium position. Our analysis applies to noncollinear configurations of a polyatomic molecule; this covers all but a subset of measure zero (the collinear configurations) in the nuclear configuration space.

Symmetric Post-Transition State Bifurcation Reactions with Berry Pseudomagnetic Fields

We investigate how the Berry force (i.e., the pseudomagnetic force operating on nuclei as induced by electronic degeneracy and spin-orbit coupling (SOC)) might modify a post-transition state bifurcation (PTSB) reaction path and affect product selectivity for situations when multiple products share the same transition state. To estimate the magnitude of this effect, Langevin dynamics are performed on a model system with a valley-ridge inflection (VRI) point in the presence of a magnetic field (that mimics the Berry curvature). We also develop an analytic model for such selectivity that depends on key parameters such as the surface topology, the magnitude of the Berry force, and the nuclear friction. Within this dynamical model, static electronic structure calculations (at the level of generalized Hartree-Fock with spin-orbit coupling (GHF+SOC) theory) suggest that electronic spin induced Berry force effects may indeed lead to noticeable changes in methoxy radical isomerization.

Chiral-Induced Spin Selectivity and Non-equilibrium Spin Accumulation in Molecules and Interfaces: A First-Principles Study

Electrons moving through chiral molecules are selected according to their spin orientation and the helicity of the molecule, an effect known as chiral-induced spin selectivity (CISS). The underlying physical mechanism is not yet completely understood. To help elucidate this mechanism, a non-equilibrium Green's function method, combined with a Landauer approach and density functional theory, is applied to carbon helices contacted by gold electrodes, resulting in spin polarization of transmitted electrons. Spin polarization is also observed in the non-equilibrium electronic structure of the junctions. While this spin polarization is small, its sign changes with the direction of the current and with the handedness of the molecule. While these calculations were performed with a pure exchange-correlation functional, previous studies suggest that computationally more expensive hybrid functionals may lead to considerably larger spin polarization in the electronic structure. Thus, non-equilibrium spin polarization could be a key component in understanding the CISS mechanism.

Modeling Spin-Dependent Nonadiabatic Dynamics with Electronic Degeneracy: A Phase-Space Surface-Hopping Method

Nuclear Berry curvature effects emerge from electronic spin degeneracy and can lead to nontrivial spin-dependent (nonadiabatic) nuclear dynamics. However, such effects are not captured fully by any current mixed quantum-classical method such as fewest-switches surface hopping. In this work, we present a phase-space surface-hopping (PSSH) approach to simulate singlet-triplet intersystem crossing dynamics. We show that with a simple pseudodiabatic ansatz, a PSSH algorithm can capture the relevant Berry curvature effects and make predictions in agreement with exact quantum dynamics for a simple singlet-triplet model Hamiltonian. Thus, this approach represents an important step toward simulating photochemical and spin processes concomitantly, as relevant to intersystem crossing and spin-lattice relaxation dynamics.

On the meaning of Berry force for unrestricted systems treated with mean-field electronic structure

We show that the Berry force as computed by an approximate, mean-field electronic structure can be meaningful if properly interpreted. In particular, for a model Hamiltonian representing a molecular system with an even number of electrons interacting via a two-body (Hubbard) interaction and a spin-orbit coupling, we show that a meaningful nonzero Berry force emerges whenever there is spin unrestriction-even though the Hamiltonian is real-valued and formally the on-diagonal single-surface Berry force must be zero. Moreover, if properly applied, this mean-field Berry force yields roughly the correct asymptotic motion for scattering through an avoided crossing. That being said, within the context of a ground-state calculation, several nuances do arise as far interpreting the Berry force correctly, and as a practical matter, the Berry force diverges near the Coulson-Fischer point (which can lead to numerical instabilities). We do not address magnetic fields here.

Electron transfer and spin-orbit coupling: Can nuclear motion lead to spin selective rates?

We investigate a spin-boson inspired model of electron transfer, where the diabatic coupling is given by a position-dependent phase, e^iWx. We consider both equilibrium and nonequilibrium initial conditions. We show that, for this model, all equilibrium results are completely invariant to the sign of W (to infinite order). However, the nonequilibrium results do depend on the sign of W, suggesting that photo-induced electron transfer dynamics with spin-orbit coupling can exhibit electronic spin polarization (at least for some time).

Theory of Chirality Induced Spin Selectivity: Progress and Challenges

A critical overview of the theory of the chirality-induced spin selectivity (CISS) effect, that is, phenomena in which the chirality of molecular species imparts significant spin selectivity to various electron processes, is provided. Based on discussions in a recently held workshop, and further work published since, the status of CISS effects-in electron transmission, electron transport, and chemical reactions-is reviewed. For each, a detailed discussion of the state-of-the-art in theoretical understanding is provided and remaining challenges and research opportunities are identified.

Incorporating Berry Force Effects into the Fewest Switches Surface-Hopping Algorithm: Intersystem Crossing and the Case of Electronic Degeneracy

We present a preliminary surface-hopping approach for modeling intersystem crossing (ISC) dynamics between four electronic states: one singlet and one (triply degenerate) triplet. In order to incorporate all Berry force effects, the algorithm requires that, when moving along an adiabatic surface associated with the triplet manifold, one must also keep track of a quasi-diabatic index (akin to a "m_s" quantum number) for each trajectory. For a simple model problem, we find that a great deal of new physics can be captured by our algorithm, setting the stage for larger, more realistic (or perhaps even ab initio) simulations in the future.

Spin Fano Resonances in Chiral Molecules: An Alternative Mechanism for the CISS Effect and Experimental Implications

Experiments on spin transport through a chiral molecule demonstrated the attainment of significant spin polarization, demanding a theoretical explanation. We report the emergence of spin Fano resonances as a mechanism in the chiral-induced spin-selectivity (CISS) effect associated with transport through a chiral polyacetylene molecule. Initializing electrons through optical excitation, we derive the Fano resonance formula for the spin polarization. Computations reveal that quasidegeneracy is common in this complex molecular system. A remarkable phenomenon is the generation of pronounced spin Fano resonances due to the contributions of two near-degeneracy states. We also find that the Fano resonance width increases linearly with the coupling strength between the molecule and the lead. Our findings provide another mechanism to explain the experimental observations and lead to new insights into the role of the CISS effect in complex molecules from the perspective of transport and spin polarization resonance, paving the way for chiral molecule-based spintronics applications.

Semiclassical description of nuclear dynamics moving through complex-valued single avoided crossings of two electronic states

The standard fewest-switches surface hopping (FSSH) approach fails to model nonadiabatic dynamics when the electronic Hamiltonian is complex-valued and there are multiple nuclear dimensions; FSSH does not include geometric magnetic effects and does not have access to a gauge independent direction for momentum rescaling. In this paper, for the case of a Hamiltonian with two electronic states, we propose an extension of Tully's FSSH algorithm, which includes geometric magnetic forces and, through diabatization, establishes a well-defined rescaling direction. When combined with a decoherence correction, our new algorithm shows satisfying results for a model set of two-dimensional single avoided crossings.

Electronic spin separation induced by nuclear motion near conical intersections

Though the concept of Berry force was proposed thirty years ago, little is known about the practical consequences of this force as far as chemical dynamics are concerned. Here, we report that when molecular dynamics pass near a conical intersection, a massive Berry force can appear as a result of even a small amount of spin-orbit coupling (<10⁻³ eV), and this Berry force can in turn dramatically change pathway selection. In particular, for a simple radical reaction with two outgoing reaction channels, an exact quantum scattering solution in two dimensions shows that the presence of a significant Berry force can sometimes lead to spin selectivity as large as 100%. Thus, this article opens the door for organic chemists to start designing spintronic devices that use nuclear motion and conical intersections (combined with standard spin-orbit coupling) in order to achieve spin selection. Vice versa, for physical chemists, this article also emphasizes that future semiclassical simulations of intersystem crossing (which have heretofore ignored Berry force) should be corrected to account for the spin polarization that inevitably arises when dynamics pass near conical intersections.

Spin polarization is at the basis of quantum information and underlies some natural processes, but many aspects still need to be explored. Here, the authors, by quantum mechanical computations, show that even a weak spin-orbit coupling near a conical intersection can induce large spin selection, with consequences for spin manipulation in photochemical or electrochemical reactions.