A semiclassical non-adiabatic phase-space approach to molecular translations and rotations: Surface hopping with electronic inertial effects.

We demonstrate that working with a correct phase-space electronic Hamiltonian captures electronic inertial effects. In particular, we show that phase space surface hopping dynamics do not suffer (at least to very high order) from non-physical non-adiabatic transitions between electronic eigenstates during the course of pure nuclear translational and rotational motion. This work opens up many new avenues for quantitatively investigating complex phenomena, including angular momentum transfer between chiral phonons and electrons as well as chiral-induced spin selectivity effects.

An electronic phase-space Hamiltonian approach for electronic current density and vibrational circular dichroism.

The Born-Oppenheimer framework stipulates that chemistry and physics occur on potential energy surfaces VBO(X) parameterized by a nuclear coordinate X, which are built by diagonalizing a BO Hamiltonian ĤBO(X). However, such a framework cannot recover many measurable chemical and physical features, including vibrational circular dichroism spectra. In this article, we show that a phase-space electronic Hamiltonian ĤPS(X,P), parameterized by both nuclear position X and momentum P, with a similar computational cost as solving ĤBO(X), can recover not just experimental vibrational circular dichroism signals but also a meaningful electronic current density that explains the features of the vibrational circular dichroism rotational strengths.

A Constrained CASSCF(2,2) Approach to Study Electron Transfer between a Molecule and Metal Cluster.

We have implemented a constrained CASSCF(2,2) calculation so as to study thermal electron transfer between a chlorine ion and a cluster of lithium atoms of variable size (from 1 to 17). Our calculations illustrate how the geometry of the ground state-charge transfer state crossing point (as well as the strength of a diabatic coupling) can depend sensitively on the number of metal ions (i.e.

An Efficient Algorithm for Constrained CASSCF(1,2) and CASSCF(3,2) Simulations as Relevant to Electron and Hole Transfer Problems.

We propose an efficient algorithm for the recently published electron/hole-transfer Dynamical-weighted State-averaged Constrained CASSCF (eDSC/hDSC) method studying charge transfer states and D-D crossings for systems with odd numbers of electrons. By separating the constrained minimization problem into an unconstrained self-consistent-field (SCF) problem and a constrained nonself-consistent-field (nSCF) problem, as well as accelerating the direct inversion in the iterative subspace (DIIS) technique to solve the SCF problem, the overall computational cost is reduced by a factor of 8-20 compared with directly using sequential quadratic programming (SQP). This approach should be applicable for other constrained minimization problems, and in the immediate future, once gradients are available, the present eDSC/hDSC algorithm should allow for speedy nonadiabatic dynamics simulations.

A Phase-Space Electronic Hamiltonian For Vibrational Circular Dichroism.

We show empirically that a phase-space non-Born-Oppenheimer electronic Hamiltonian approach to quantum chemistry (where the electronic Hamiltonian is parametrized by both nuclear position and momentum, (,)) is both a practical and accurate means to recover vibrational circular dichroism spectra. We further hypothesize that such a phase-space approach may lead to very new dynamical physics beyond spectroscopic circular dichroism, with potential implications for understanding chiral induced spin selectivity (CISS), noting that classical phase-space approaches conserve the total nuclear plus electronic momentum, whereas classical Born-Oppenheimer approaches do not (they conserve only the nuclear momentum).

Angular Momentum Transfer between a Molecular System and a Continuous Circularly Polarized Light Field within a Semiclassical Born-Oppenheimer Surface Hopping Framework.

We simulate semiclassically angular momentum transfer for a molecular system subject to a circularly polarized light (CPL) field either moving along a single Born-Oppenheimer (BO) surface or moving along multiple BO surfaces. Both sets of simulations are able to conserve the total angular momentum around the propagation direction of the CPL field, the former requiring a Berry force and the latter requiring a surface parametrized by both nuclear position and momentum (a so-called phase-space approach). Our results provide new insight into the nature of semiclassical nonadiabatic dynamics methods and further demonstrate the power of such methods to capture angular momentum transfer between different media, highlighting the need for accurate algorithms that conserve the total angular momentum.

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.

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 Ĥel(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, ĤPS(X,P). While classical Born-Oppenheimer dynamics that run along the eigensurfaces of the operator Ĥel(X) can recover many nuclear properties correctly, we present some evidence that motion along the eigensurfaces of ĤPS(X,P) can better capture both nuclear and electronic properties (including the elusive electronic momentum studied by Nafie).

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.

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

We study the spin-dependent stereodynamics of the S + H → SH + H reaction by using full-dimensional quantum dynamics calculations with zero total nuclear angular momentum along the triplet ″ states and singlet ' 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%.

Diagonalizing the Born-Oppenheimer Hamiltonian via Moyal perturbation theory, nonadiabatic corrections, and translational degrees of freedom.

This article describes a method for calculating higher order or nonadiabatic corrections in Born-Oppenheimer theory and its interaction with the translational degrees of freedom. The method uses the Wigner-Weyl correspondence to map nuclear operators into functions on the classical phase space and the Moyal star product to represent operator multiplication on those functions. These are explained in the body of the paper.

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.

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.

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.

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.

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.

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.

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.