A fast and smooth one-electron approach for investigating charge transfer states and D1-D0 crossings for systems with odd numbers of electrons.

We propose an efficient version of ensemble Hartree-Fock/density functional theory to calculate a set of two charge-transfer states for systems with odd-numbers of electrons. The approach does require definitions of donor/acceptor fragments; however, the approach is not very sensitive to such definitions-even in the limit of very strong electronic coupling. The key ansatz is that, by mandating that the vector space spanned by the active orbitals projects equally onto the donor and acceptor fragments, such a constraint eliminates all intra-molecular local excitations and makes it far easier to generate potential energy surfaces that are smooth over a wide region of configuration space. The method is fast, working with only two electron configurations, and should be useful for ab initio non-adiabatic dynamics in the near future.

On the nature of two-photon transitions for a collection of molecules in a Fabry-Perot cavity.

We investigate the effect of a cavity on nonlinear two-photon transitions of a molecular system and we analyze how such an effect depends on the cavity quality factor, the field enhancement, and the possibility of dephasing. We find that the molecular response to strong light fields in a cavity with a variable quality factor can be understood as arising from a balance between (i) the ability of the cavity to enhance the field of an external probe and promote multiphoton transitions more easily and (ii) the fact that the strict selection rules on multiphoton transitions in a cavity support only one resonant frequency within the excitation range. Although our simulations use a classical level description of the radiation field (i.e., we solve Maxwell-Bloch or Maxwell-Liouville equations within the Ehrenfest approximation for the field-molecule interaction), based on experience with this level of approximation in the past studies of plasmonic and polaritonic systems, we believe that our results are valid over a wide range of external probing.

A simple one-electron expression for electron rotational factors.

Within the context of fewest-switch surface hopping (FSSH) dynamics, one often wishes to remove the angular component of the derivative coupling between states J and K. In a previous set of papers, Shu et al. [J. Phys. Chem. Lett. 11, 1135-1140 (2020)] posited one approach for such a removal based on direct projection, while we isolated a second approach by constructing and differentiating a rotationally invariant basis. Unfortunately, neither approach was able to demonstrate a one-electron operatorÔ whose matrix element JÔK was the angular component of the derivative coupling. Here, we show that a one-electron operator can, in fact, be constructed efficiently in a semi-local fashion. The present results yield physical insight into designing new surface hopping algorithms and are of immediate use for FSSH calculations.

Practical phase-space electronic Hamiltonians for ab initio dynamics.

Modern electronic structure theory is built around the Born-Oppenheimer approximation and the construction of an electronic Hamiltonian Hel(X) that depends on the nuclear position X (and not the nuclear momentum P). In this article, using the well-known theory of electron translation (Γ') and rotational (Γ″) factors to couple electronic transitions to nuclear motion, we construct a practical phase-space electronic Hamiltonian that depends on both nuclear position and momentum, HPS(X,P). While classical Born-Oppenheimer dynamics that run along the eigensurfaces of the operator Hel(X) can recover many nuclear properties correctly, we present some evidence that motion along the eigensurfaces of HPS(X,P) can better capture both nuclear and electronic properties (including the elusive electronic momentum studied by Nafie). Moreover, only the latter (as opposed to the former) conserves the total linear and angular momentum in general.

Spin-Dependent Stereochemistry: A Nonadiabatic Quantum Dynamics Case Study of S + H2 → SH + H Reaction.

We study the spin-dependent stereodynamics of the S + H2 → SH + H reaction by using full-dimensional quantum dynamics calculations with zero total nuclear angular momentum along the triplet 3A″ states and singlet 1A' states. We find that the interplay between the electronic spin direction and the molecular geometry has a measurable influence on the singlet-triplet intersystem crossing reaction probabilities. Our results show that for some incident scattering angles in the body-fixed frame, the relative difference in intersystem crossing reaction probabilities (as determined between spin up and spin down initial states) can be as large as 15%. Our findings are an ab initio demonstration of spin-dependent nonadiabatic dynamics, which we hope will shine light as far as understanding the chiral-induced spin selectivity effect.

Total angular momentum conservation in Ehrenfest dynamics with a truncated basis of adiabatic states.

We show that standard Ehrenfest dynamics does not conserve linear and angular momentum when using a basis of truncated adiabatic states. However, we also show that previously proposed effective Ehrenfest equations of motion [M. Amano and K. Takatsuka, "Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions," J. Chem. Phys. 122, 084113 (2005) and V. Krishna, "Path integral formulation for quantum nonadiabatic dynamics and the mixed quantum classical limit," J. Chem. Phys. 126, 134107 (2007)] involving the non-Abelian Berry force do maintain momentum conservation. As a numerical example, we investigate the Kramers doublet of the methoxy radical using generalized Hartree-Fock with spin-orbit coupling and confirm that angular momentum is conserved with the proper equations of motion. Our work makes clear some of the limitations of the Born-Oppenheimer approximation when using ab initio electronic structure theory to treat systems with unpaired electronic spin degrees of freedom, and we demonstrate that Ehrenfest dynamics can offer much improved, qualitatively correct results.

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.

To guess or not to guess excited state amplitudes during optimization and dynamics.

We report robust initial guesses for the amplitudes and z-vectors in a configuration interaction singles or Tamm-Dancoff approximation calculation that consistently reduce the total number of iterations required for an excited state calculation often by over 50%. The end result of these guesses is that the practicing chemist can expect to generate excited state optimized structures with a total wall time reduced by as much as 30% in the future without any approximations-simply by using information gathered at one geometry and applying it to another geometry.

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.

Nature of Hops, Coordinates, and Detailed Balance for Nonadiabatic Simulations in the Condensed Phase.

Photoinduced processes play a crucial role in a multitude of important molecular phenomena. Accurately modeling these processes in an environment other than a vacuum requires a detailed description of the electronic states involved as well as how energy flows are coupled to the surroundings. Nonadiabatic effects must also be included in order to describe the exchange of energy between electronic and nuclear degrees of freedom correctly. In this work, we revisit the ring-opening reaction 1,3-cylohexadiene (CHD) in a solvent environment. Using our newly developed Interface for Non-Adiabatic Quantum mechanics/molecular mechanics in Solvent (INAQS) we trace the evolution of the reaction via hybrid quantum mechanics/molecular mechanics (QM/MM) surface hopping with a focus on the solvent's participation in the nonadiabatic relaxation process and the long-time approach to equilibrium. We explicitly include the MM solvent contribution to the nonadiabatic coupling vector─enabling an accurate approach to equilibrium at long times─and find that in highly multidimensional systems gradients can have little or nothing to do with the nonadiabatic couplings.

Chiral molecules to transmit electron spin.

Electron transfer through chiral molecules displays a strong spin preference.

Use of QM/MM Surface Hopping Simulations to Understand Thermally Activated Rare-Event Nonadiabatic Transitions in the Condensed Phase.

We implement a rare-event sampling scheme for quantifying the rate of thermally activated nonadiabatic transitions in the condensed phase. Our Quantum mechanics/molecular mechanics (QM/MM) methodology uses the recently developed Interface for NonAdiabatic QM/MM in Solvent (INAQS) package to interface an elementary electronic structure package and a popular open-source molecular dynamics software (GROMACS) to simulate an electron transfer event between two stationary ions in a solution of acetonitrile solvent molecules. Nonadiabatic effects are implemented through a surface hopping scheme, and our simulations allow further quantitative insight into the participation ratio of a solvent and the effect of ion separation distance as far as facilitating electron transfer. We also demonstrate that the standard gas-phase approaches for treating frustrated hops and velocity reversal must be refined when working in the condensed phase with many degrees of freedom. The code and methodology developed here can be easily expanded upon and modified to incorporate other systems and should provide a great deal of new insight into a wide variety of condensed phase nonadiabatic phenomena.

Surface hopping, electron translation factors, electron rotation factors, momentum conservation, and size consistency.

For a system without spin-orbit coupling, the (i) nuclear plus electronic linear momentum and (ii) nuclear plus orbital electronic angular momentum are good quantum numbers. Thus, when a molecular system undergoes a nonadiabatic transition, there should be no change in the total linear or angular momentum. Now, the standard surface hopping algorithm ignores the electronic momentum and indirectly equates the momentum of the nuclear degrees of freedom to the total momentum. However, even with this simplification, the algorithm still does not conserve either the nuclear linear or the nuclear angular momenta. Here, we show that one way to address these failures is to dress the derivative couplings (i.e., the hopping directions) in two ways: (i) we disallow changes in the nuclear linear momentum by working in a translating basis (which is well known and leads to electron translation factors) and (ii) we disallow changes in the nuclear angular momentum by working in a basis that rotates around the center of mass [which is not well-known and leads to a novel, rotationally removable component of the derivative coupling that we will call electron rotation factors below, cf. Eq. (96)]. The present findings should be helpful in the short term as far as interpreting surface hopping calculations for singlet systems (without spin) and then developing the new surface hopping algorithm in the long term for systems where one cannot ignore the electronic orbital and/or spin angular momentum.

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.

A Dynamically Weighted Constrained Complete Active Space Ansatz for Constructing Multiple Potential Energy Surfaces within the Anderson-Holstein Model.

We derive and implement the necessary equations for solving a dynamically weighted, state-averaged constrained CASSCF(2,2) wave function describing a molecule on a metal surface, where we constrain the overlap between two active orbitals and the impurity atomic orbitals to be a finite number. We show that a partial constraint is far more robust than a full constraint. We further calculate the system-bath electronic couplings that arise because, near a metal, there is a continuum (rather than discrete) number of electronic states. This approach should be very useful for simulating heterogeneous electron transfer and electrochemical dynamics going forward.

Spin-Orbit versus Hyperfine Coupling-Mediated Intersystem Crossing in a Radical Pair.

While spin-orbit coupling (SOC) is typically the dominant interaction that couples singlet and triplet states within individual chromophores, hyperfine coupling (HFC) becomes important in multichromophoric systems, particularly in relation to the radical pair mechanism. Here, we use TD-DFT to calculate the spin-orbit coupling and hyperfine coupling between the first singlet and triplet charge transfer states of the radical pair 2Pyrene- and 2N,N-dimethylaniline+. We show that, as the intermolecular donor-acceptor distance grows, SOC decays to zero (as one would expect) because singlet and triplet states are characterized by identical orbitals in space, while the HFC remains comparatively constant. The switching region occurs around 4 Å, beyond which HFC dominates over SOC as far as defining the rate of intersystem crossing (ISC).

A quantum-classical Liouville formalism in a preconditioned basis and its connection with phase-space surface hopping.

We revisit a recent proposal to model nonadiabatic problems with a complex-valued Hamiltonian through a phase-space surface hopping (PSSH) algorithm employing a pseudo-diabatic basis. Here, we show that such a pseudo-diabatic PSSH (PD-PSSH) ansatz is consistent with a quantum-classical Liouville equation (QCLE) that can be derived following a preconditioning process, and we demonstrate that a proper PD-PSSH algorithm is able to capture some geometric magnetic effects (whereas the standard fewest switches surface hopping approach cannot capture such effects). We also find that a preconditioned QCLE can outperform the standard QCLE in certain cases, highlighting the fact that there is no unique QCLE. Finally, we also point out that one can construct a mean-field Ehrenfest algorithm using a phase-space representation similar to what is done for PSSH. These findings would appear extremely helpful as far as understanding and simulating nonadiabatic dynamics with complex-valued Hamiltonians and/or spin degeneracy.