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We present a phase-space electronic Hamiltonian ĤPS (parameterized by both nuclear position X and momentum P) that boosts each electron into the moving frame of the nuclei that are closest in real space. The final form for the phase space Hamiltonian does not assume the existence of an atomic orbital basis, and relative to standard Born–Oppenheimer theory, the newly proposed one-electron operators can be expressed directly as functions of electronic and nuclear positions and momentum. We show that (i) quantum–classical dynamics along such a Hamiltonian maintains momentum conservation and that (ii) diagonalizing such a Hamiltonian can recover the electronic momentum and electronic current density reasonably well. In conjunction with other reports in the literature that such a phase-space approach can also recover vibrational circular dichroism spectra, we submit that the present phase-space approach offers a testable and powerful approach to post-BO electronic structure theory. Moreover, the approach is inexpensive and can be immediately applied to simulations of chiral induced spin selectivity experiments (where the transfer of angular momentum between nuclei and electrons is considered critical). 

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. 

Abstract The invention of the laser unleashed the potential of optical metrology, leading to numerous advancements in modern science and technology. This reliance on lasers, however, also introduces a bottleneck for precision optical metrology, as it requires sophisticated photonic infrastructure for precise laser-wave control, leading to limited metrology performance and significant system complexity. Here, we take a key step toward overcoming this challenge by demonstrating a Pockels laser with multifunctional capabilities that elevate optical metrology to a new level. The chip-scale laser achieves a narrow intrinsic linewidth down to 167 Hz and a broad mode-hop-free tuning range up to 24 GHz. In particular, it delivers an unprecedented frequency chirping rate of up to 20 EHz/s and an exceptional modulation bandwidth exceeding 10 GHz, both of which are orders of magnitude greater than those of existing lasers. Leveraging this laser, we successfully achieve velocimetry at 40 m/s over a short distance of 0.4 m, and measurable velocities up to the first cosmic velocity at 1 m away—a feat unattainable with conventional ranging approaches. At the same time, we achieve distance metrology with a ranging resolution of <2 cm. Furthermore, for the first time to our knowledge, we implement a dramatically simplified architecture for laser frequency stabilization by directly locking the laser to an external reference gas cell without requiring additional external light control. This approach enables long-term laser stability with a frequency fluctuation of only ±6.5 MHz over 60 min. The demonstrated Pockels laser combines elegantly high laser coherence with ultrafast frequency reconfigurability and superior multifunctional capability. We envision its profound impact across diverse fields including communication, sensing, autonomous driving, quantum information processing, and beyond. 

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. 

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). Moreover, only the latter (as opposed to the former) conserves the total linear and angular momentum in general. 

Using ai-GCMC simulations,operandoWAXS, and kinetics analysis, we found that the high-rate performance of Sb as an alloy anode in Na-ion batteries is due to the presence of an amorphous intermediate phase formed during sodiation and desodiation. 

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.