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Experiments have demonstrated that vibrational strong coupling between molecular vibrations and light modes can significantly change molecular properties, such as ground-state reactivity. Theoretical studies toward the origin of this exciting observation can roughly be divided into two categories, with studies based on Hamiltonians that simply couple a molecule to a cavity mode via its ground-state dipole moment on the one hand, and on the other hand ab initio calculations that self-consistently include the effect of the cavity mode on the electronic ground state within the cavity Born-Oppenheimer (CBO) approximation; these approaches are not equivalent. The CBO approach is more rigorous, but unfortunately it requires the rewriting of electronic-structure code, and its results may sometimes be hard to physically interpret. In this work, we exploit the relation between the two approaches and demonstrate on a real molecule (hydrogen fluoride) that for realistic coupling strengths, we can recover CBO energies and spectra to high accuracy using only out-of-cavity quantities from standard electronic-structure calculations. In doing so, we discover what thephysical effects underlying the CBO results are. Our methodology can aid in incorporating more possibly important features in models, play a pivotal role in demystifying CBO results, and provide a practical and efficient alternative to full CBO calculations. [ABSTRACT FROM AUTHOR]

Modern electronic structure theory is built around the Born–Oppenheimer approximation and the construction of an electronic Hamiltonian H ̂ e l (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, H ̂ P S (X , P). While classical Born–Oppenheimer dynamics that run along the eigensurfaces of the operator H ̂ e l (X) can recover many nuclear properties correctly, we present some evidence that motion along the eigensurfaces of H ̂ P S (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. [ABSTRACT FROM AUTHOR]

A time-dependent vibrational electronic coupled-cluster (VECC) approach is proposed to simulate photo-electron/UV-VIS absorption spectra as well as time-dependent properties for non-adiabatic vibronic models, going beyond the Born–Oppenheimer approximation. A detailed derivation of the equations of motion and a motivation for the ansatz are presented. The VECC method employs second-quantized bosonic construction operators and a mixed linear and exponential ansatz to form a compact representation of the time-dependent wave-function. Importantly, the method does not require a basis set, has only a few user-defined inputs, and has a classical (polynomial) scaling with respect to the number of degrees of freedom (of the vibronic model), resulting in a favorable computational cost. In benchmark applications to small models and molecules, the VECC method provides accurate results compared to multi-configurational time-dependent Hartree calculations when predicting short-time dynamical properties (i.e., photo-electron/UV–VIS absorption spectra) for non-adiabatic vibronic models. To illustrate the capabilities, the VECC method is also successfully applied to a large vibronic model for hexahelicene with 14 electronic states and 63 normal modes, developed in the group by Aranda and Santoro [J. Chem. Theory Comput. 17, 1691, (2021)]. [ABSTRACT FROM AUTHOR]

Conical intersections are known to play a vital role in many photochemical processes. The breakdown of the Born–Oppenheimer approximation in the vicinity of a conical intersection causes exciting phenomena, such as the ultrafast radiationless decay of excited states. The passage of a molecule through a conical intersection creates a coherent superposition of electronic states via nonadiabatic couplings. Detecting this coherent superposition may serve as a direct probe of the conical intersection. In this paper, we theoretically demonstrate the use of coherent spontaneous emission in samples with long-range order for probing the occurrence of a conical intersection in a molecule. Our simulations show that the spectrum contains clear signatures of the created coherent superposition of electronic states. We investigate the bandwidth requirements for the x-ray probes, which influence the observation of coherent superposition generated by the conical intersection. [ABSTRACT FROM AUTHOR]

This work combines for the first time ab initio molecular dynamics (AIMD) within the Born–Oppenheimer approximation with a global natural orbital functional (GNOF), an approximate functional of the one-particle reduced density matrix. The most prominent feature of GNOF-AIMD is its ability to display the real-time evolution of natural orbitals, providing detailed information on the time-dependent electronic structure of complex systems and processes, including reactive collisions. The quartet ground-state reaction N(4S) + H2(1Σ) → NH(3Σ) + H(2S) is taken as a validation test. Collision energy influences on integral cross sections for different initial rovibrational states of H2 and rotational-state distributions of the NH product are discussed, showing a good agreement with previous high-quality theoretical results. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Chemical and photochemical reactivity, as well as supramolecular organization and several other molecular properties, can be modified by strong interactions between light and matter. Theoretical studies of these phenomena require the separation of the Schrödinger equation into different degrees of freedom as in the Born–Oppenheimer approximation. In this paper, we analyze the electron–photon Hamiltonian within the cavity Born–Oppenheimer approximation (CBOA), where the electronic problem is solved for fixed nuclear positions and photonic parameters. In particular, we focus on intermolecular interactions in representative dimer complexes. The CBOA potential energy surfaces are compared with those obtained using a polaritonic approach, where the photonic and electronic degrees of freedom are treated at the same level. This allows us to assess the role of electron–photon correlation and the accuracy of CBOA. [ABSTRACT FROM AUTHOR]

Machine-learning potentials provide computationally efficient and accurate approximations of the Born–Oppenheimer potential energy surface. This potential determines many materials properties and simulation techniques usually require its gradients, in particular forces and stress for molecular dynamics, and heat flux for thermal transport properties. Recently developed potentials feature high body order and can include equivariant semi-local interactions through message-passing mechanisms. Due to their complex functional forms, they rely on automatic differentiation (AD), overcoming the need for manual implementations or finite-difference schemes to evaluate gradients. This study discusses how to use AD to efficiently obtain forces, stress, and heat flux for such potentials, and provides a model-independent implementation. The method is tested on the Lennard-Jones potential, and then applied to predict cohesive properties and thermal conductivity of tin selenide using an equivariant message-passing neural network potential. [ABSTRACT FROM AUTHOR]

The quantum chemistry community has developed analytic forces for approximate electronic excited states to enable walking on excited state potential energy surfaces (PES). One can thereby computationally characterize excited state minima and saddle points. Always implicit in using this machinery is the fact that an excited state PES only exists within the realm of the Born-Oppenheimer approximation, where the nuclear and electronic degrees of freedom separate. This work demonstrates through ab initio calculations and simple nonadiabatic dynamics that some excited state minimum structures are fantastical: they appear to exist as stable configurations only as a consequence of the PES construct, rather than being physically observable. Each fantastical structure exhibits an unphysically high predicted harmonic frequency and associated force constant. This fact can serve as a valuable diagnostic of when an optimized excited state structure is non-observable. The origin of this phenomenon can be attributed to the coupling between different electronic states. As PESs approach one another, the upper surface can form a minimum that is very close to a near-touching point. The force constant, evaluated at this minimum, relates to the strength of the electronic coupling rather than to any characteristic excited state vibration. Nonadiabatic dynamics results using a Landau-Zener model illustrate that fantastical excited state structures have extremely short lifetimes on the order of a few femtoseconds. Their appearance in a calculation signals the presence of a nearby conical intersection through which the system will rapidly cross to a lower surface. [ABSTRACT FROM AUTHOR]

A numerical algorithm based on the probabilistic path integral approach for solving Schrödinger equation has been devised to treat molecular systems without Born–Oppenheimer approximation in the nonrelativistic limit at zero temperature as an alternative to conventional variational and perturbation methods. Using high-quality variational trial functions and path integral method based on generalized Feynman–Kac method, we have been able to calculate the non-Born–Oppenheimer energy for hydrogen molecule for the X 1 Σ g 1 state and hydrogen molecular ion. Combining these values and the value for ionization potential for atomic hydrogen, the dissociation energy and ionization potential for hydrogen molecules have been determined to be 36 113.672(3) cm − 1 and 124 446.066(10) cm − 1 , respectively. Our results favorably compare with other theoretical and experimental results and thus show the promise of being a nonperturbative alternative for testing fundamental physical theories. [ABSTRACT FROM AUTHOR]

Nuclear quantum phenomena beyond the Born–Oppenheimer approximation are known to play an important role in a growing number of chemical and biological processes. While there exists no unique consensus on a rigorous and efficient implementation of coupled electron–nuclear quantum dynamics, it is recognized that these problems scale exponentially with system size on classical processors and, therefore, may benefit from quantum computing implementations. Here, we introduce a methodology for the efficient quantum treatment of the electron–nuclear problem on near-term quantum computers, based upon the Nuclear–Electronic Orbital (NEO) approach. We generalize the electronic two-qubit tapering scheme to include nuclei by exploiting symmetries inherent in the NEO framework, thereby reducing the Hamiltonian dimension, number of qubits, gates, and measurements needed for calculations. We also develop parameter transfer and initialization techniques, which improve convergence behavior relative to conventional initialization. These techniques are applied to H2 and malonaldehyde for which results agree with NEO full configuration interaction and NEO complete active space configuration interaction benchmarks for ground state energy to within 10−6 hartree and entanglement entropy to within 10−4. These implementations therefore significantly reduce resource requirements for full quantum simulations of molecules on near-term quantum devices while maintaining high accuracy. [ABSTRACT FROM AUTHOR]

Within the nuclear-electronic orbital (NEO) framework, the real-time NEO time-dependent density functional theory (RT-NEO-TDDFT) approach enables the simulation of coupled electronic-nuclear dynamics. In this approach, the electrons and quantum nuclei are propagated in time on the same footing. A relatively small time step is required to propagate the much faster electronic dynamics, thereby prohibiting the simulation of long-time nuclear quantum dynamics. Herein, the electronic Born–Oppenheimer (BO) approximation within the NEO framework is presented. In this approach, the electronic density is quenched to the ground state at each time step, and the real-time nuclear quantum dynamics is propagated on an instantaneous electronic ground state defined by both the classical nuclear geometry and the nonequilibrium quantum nuclear density. Because the electronic dynamics is no longer propagated, this approximation enables the use of an order-of-magnitude larger time step, thus greatly reducing the computational cost. Moreover, invoking the electronic BO approximation also fixes the unphysical asymmetric Rabi splitting observed in previous semiclassical RT-NEO-TDDFT simulations of vibrational polaritons even for small Rabi splitting, instead yielding a stable, symmetric Rabi splitting. For the intramolecular proton transfer in malonaldehyde, both RT-NEO-Ehrenfest dynamics and its BO counterpart can describe proton delocalization during the real-time nuclear quantum dynamics. Thus, the BO RT-NEO approach provides the foundation for a wide range of chemical and biological applications. [ABSTRACT FROM AUTHOR]

We study the broadening of initially localized wave packets in a quasi one-dimensional diamond ladder with interacting, spinless fermions. The lattice possesses a flat band causing localization. We place special focus on the transition away from the flat band many-body localized case by adding very weak dispersion. By doing so, we allow propagation of the wave packet on significantly different timescales which causes anomalous diffusion. Due to the temporal separation of dynamic processes, an interaction-induced, prethermal equilibrium becomes apparent. A physical picture of light and heavy modes for this prethermal behavior can be obtained within Born–Oppenheimer approximation via basis transformation of the original Hamiltonian. This reveals a detachment between light, symmetric and heavy, anti-symmetric particle species. We show that the prethermal state is characterized by heavy particles binding together mediated by the light particles. [ABSTRACT FROM AUTHOR]

Hot carriers generated from the decay of plasmon excitation can be harvested to drive a wide range of physical or chemical processes. However, their generation efficiency is limited by the concomitant phonon-induced relaxation processes by which the energy in excited carriers is transformed into heat. However, simulations of dynamics of nanoscale clusters are challenging due to the computational complexity involved. Here, we adopt our newly developed Trajectory Surface Hopping (TSH) nonadiabatic molecular dynamics algorithm to simulate plasmon relaxation in Au20 clusters, taking the atomistic details into account. The electronic properties are treated within the Linear Response Time-Dependent Tight-binding Density Functional Theory (LR-TDDFTB) framework. The relaxation of plasmon due to coupling to phonon modes in Au20 beyond the Born–Oppenheimer approximation is described by the TSH algorithm. The numerically efficient LR-TDDFTB method allows us to address a dense manifold of excited states to ensure the inclusion of plasmon excitation. Starting from the photoexcited plasmon states in Au20 cluster, we find that the time constant for relaxation from plasmon excited states to the lowest excited states is about 2.7 ps, mainly resulting from a stepwise decay process caused by low-frequency phonons of the Au20 cluster. Furthermore, our simulations show that the lifetime of the phonon-induced plasmon dephasing process is ∼10.4 fs and that such a swift process can be attributed to the strong nonadiabatic effect in small clusters. Our simulations demonstrate a detailed description of the dynamic processes in nanoclusters, including plasmon excitation, hot carrier generation from plasmon excitation dephasing, and the subsequent phonon-induced relaxation process. [ABSTRACT FROM AUTHOR]

Laser-induced molecular alignment is well understood within the framework of the Born–Oppenheimer (BO) approximation. Without the BO approximation, however, the concept of molecular structure is lost, making it hard to precisely define alignment. In this work, we demonstrate the emergence of alignment from the first-ever non-BO quantum dynamics simulations, using the HD molecule exposed to ultrashort laser pulses as a few-body test case. We extract the degree of alignment from the non-BO wave function by means of an operator expressed in terms of pseudo-proton coordinates that mimics the BO-based definition of alignment. The only essential approximation, in addition to the semiclassical electric-dipole approximation for the matter–field interaction, is the choice of time-independent explicitly correlated Gaussian basis functions. We use a variational, electric-field-dependent basis-set construction procedure, which allows us to keep the basis-set dimension low while capturing the main effects of electric polarization on the nuclear and electronic degrees of freedom. The basis-set construction procedure is validated by comparing with virtually exact grid-based simulations for two one-dimensional model systems: laser-driven electron dynamics in a soft attractive Coulomb potential and nuclear rovibrational dynamics in a Morse potential. [ABSTRACT FROM AUTHOR]

In this paper, we compare and contrast the classical versus quantum dynamics of a cosmological model based on the literature (Modified) Berthelot equation of state for the description of the dark sector of the universe. At the classical background level we identify a Minkowski-like and a de Sitter-like equilibrium epochs, with the latter occurring only beyond a certain threshold for a parameter in the equation of state; at the classical perturbed level we find that this same parameter realizes a duality in the adiabatic speed of sound between the two equilibrium epochs. The quantum evolution of this model is studied in the context of quantum geometrodynamics by solving analytically the Wheeler–DeWitt equation in the Born–Oppenheimer approximation for the scalar field potentials about the two equilibrium epochs. We identify the phenomenon of quantum decoherence to arise at the same threshold which constitutes the bifurcation between the two equilibrium epochs at the classical level. We comment on the quantum modified power spectrum focusing on some consequences dealing with the formation of astrophysical structures within the Press–Schechter framework. Our paper is intended to scrutinize which classical features of a certain cosmological model are preserved at its quantum level, and under which assumptions. [ABSTRACT FROM AUTHOR]

Hydrazoic acid (HN3) is used as a case study for investigating the accuracy and precision by which a molecular structure—specifically, a semi-experimental equilibrium structure (reSE)—may be determined using current state-of-the-art methodology. The influence of the theoretical corrections for effects of vibration–rotation coupling and electron-mass distribution that are employed in the analysis is explored in detail. The small size of HN3 allowed us to deploy considerable computational resources to probe the basis-set dependence of these corrections using a series of coupled-cluster single, double, perturbative triple [CCSD(T)] calculations with cc-pCVXZ (X = D, T, Q, 5) basis sets. We extrapolated the resulting corrections to the complete basis set (CBS) limit to obtain CCSD(T)/CBS corrections, which were used in a subsequent reSE structure determination. The reSE parameters obtained using the CCSD(T)/cc-pCV5Z corrections are nearly identical to those obtained using the CCSD(T)/CBS corrections, with uncertainties in the bond distances and angles of less than 0.0006 Å and 0.08°, respectively. The previously obtained reSE structure using CCSD(T)/ANO2 agrees with that using CCSD(T)/cc-pCV5Z to within 0.000 08 Å and 0.016° for bond distances and angles, respectively, and with only 25% larger uncertainties, validating the idea that reSE structure determinations can be carried out with significantly smaller basis sets than those needed for similarly accurate, strictly ab initio determinations. Although the purely computational re structural parameters [CCSD(T)/cc-pCV6Z] fall outside of the statistical uncertainties (2σ) of the corresponding reSE structural parameters, the discrepancy is rectified by applying corrections to address the theoretical limitations of the CCSD(T)/cc-pCV6Z geometry with respect to basis set, electron correlation, relativity, and the Born–Oppenheimer approximation, thereby supporting the contention that the semi-experimental approach is both an accurate and vastly more efficient method for structure determinations than is brute-force computation. [ABSTRACT FROM AUTHOR]

Hydrazoic acid (HN3) is used as a case study for investigating the accuracy and precision by which a molecular structure—specifically, a semi-experimental equilibrium structure (reSE)—may be determined using current state-of-the-art methodology. The influence of the theoretical corrections for effects of vibration–rotation coupling and electron-mass distribution that are employed in the analysis is explored in detail. The small size of HN3 allowed us to deploy considerable computational resources to probe the basis-set dependence of these corrections using a series of coupled-cluster single, double, perturbative triple [CCSD(T)] calculations with cc-pCVXZ (X = D, T, Q, 5) basis sets. We extrapolated the resulting corrections to the complete basis set (CBS) limit to obtain CCSD(T)/CBS corrections, which were used in a subsequent reSE structure determination. The reSE parameters obtained using the CCSD(T)/cc-pCV5Z corrections are nearly identical to those obtained using the CCSD(T)/CBS corrections, with uncertainties in the bond distances and angles of less than 0.0006 Å and 0.08°, respectively. The previously obtained reSE structure using CCSD(T)/ANO2 agrees with that using CCSD(T)/cc-pCV5Z to within 0.000 08 Å and 0.016° for bond distances and angles, respectively, and with only 25% larger uncertainties, validating the idea that reSE structure determinations can be carried out with significantly smaller basis sets than those needed for similarly accurate, strictly ab initio determinations. Although the purely computational re structural parameters [CCSD(T)/cc-pCV6Z] fall outside of the statistical uncertainties (2σ) of the corresponding reSE structural parameters, the discrepancy is rectified by applying corrections to address the theoretical limitations of the CCSD(T)/cc-pCV6Z geometry with respect to basis set, electron correlation, relativity, and the Born–Oppenheimer approximation, thereby supporting the contention that the semi-experimental approach is both an accurate and vastly more efficient method for structure determinations than is brute-force computation. [ABSTRACT FROM AUTHOR]

The nuclear–electronic orbital (NEO) method is a well-established approach for treating nuclei quantum mechanically in molecular systems beyond the usual Born–Oppenheimer approximation. In this work, we present a strategy to implement the NEO method for periodic electronic structure calculations, particularly focused on multicomponent density functional theory (DFT). The NEO-DFT method is implemented in an all-electron electronic structure code, FHI-aims, using a combination of analytical and numerical integration techniques as well as a resolution of the identity scheme to enhance computational efficiency. After validating this implementation, proof-of-concept applications are presented to illustrate the effects of quantized protons on the physical properties of extended systems, such as two-dimensional materials and liquid–semiconductor interfaces. Specifically, periodic NEO-DFT calculations are performed for a trans-polyacetylene chain, a hydrogen boride sheet, and a titanium oxide–water interface. The zero-point energy effects of the protons as well as electron–proton correlation are shown to noticeably impact the density of states and band structures for these systems. These developments provide a foundation for the application of multicomponent DFT to a wide range of other extended condensed matter systems. [ABSTRACT FROM AUTHOR]

We present a new computational framework to describe polaritons, which treats photons and electrons on the same footing using coupled-cluster theory. As a proof of concept, we study the coupling between the first electronically excited state of carbon monoxide and an optical cavity. In particular, we focus on how the interaction with the photonic mode changes the vibrational spectroscopic signature of the electronic state and how this is affected when tuning the cavity frequency and the light–matter coupling strength. For this purpose, we consider different methodologies and investigate the validity of the Born–Oppenheimer approximation in such situations. [ABSTRACT FROM AUTHOR]

We report on hyperfine-resolved laser spectroscopy of the A2Π ← X2Σ+ transition of magnesium monofluoride (MgF), relevant for laser cooling. We recorded 25 rotational transitions with an absolute accuracy of better than 20 MHz, assigned 56 hyperfine lines, and determined precise rotational, fine, and hyperfine structure parameters for the A2Π state. The radiative lifetime of the A2Π state was determined to be 7.2(3) ns, in good agreement with ab initio calculations. The transition isotope shift between bosonic isotopologues of the molecule is recorded and compared to predicted values within the Born–Oppenheimer approximation. We measured the Stark effect of selected rotational lines of the A2Π ← X2Σ+ transition by applying electric fields of up to 10.6 kV cm−1 and determined the permanent electric dipole moments of 24MgF in its ground X2Σ+ and first excited A2Π states to be μX = 2.88(20) D and μA = 3.20(22) D, respectively. Based on these measurements, we caution for potential losses from the optical cycling transition due to electric field induced parity mixing in the excited state. In order to scatter 104 photons, the electric field must be controlled to below 1 V cm−1. [ABSTRACT FROM AUTHOR]

The rate coefficients k1 and k2 of the reaction $ \hbox{OD}^- + \hbox{HD} \mathop{\rightleftarrows}\limits_{k_2}^{k_1} \hbox{OH}^- + \hbox{D}_2 $ OD − + HD ⇄ k 2 k 1 ⁡ OH − + D 2 in the forward and reverse direction were measured in the temperature ranges of 15 K–273 K and 95 K–300 K, respectively. The experiments were carried out in a temperature-variable cryogenic linear 22-pole radio-frequency ion trap instrument. The temperature dependence of the equilibrium constant $ { {K_{{\rm eq}12}}}(T) $ K e q 12 (T) obtained from the measured data is in good agreement with the value calculated using the detailed balance principle under the Born-Oppenheimer approximation. The enthalpy and the entropy of the reaction obtained from the linear Van't Hoff equation are $ { {\Delta H}} = (20 \pm 2 \pm 3^{{\rm sys}})\,{\rm meV} $ Δ H = (20 ± 2 ± 3 s y s ) m e V and $ { {\Delta S}} = (5.9 \pm 1.8 \pm 1.4^{{\rm sys}})\,{\rm J}/{\rm mol}\,{\rm K} $ Δ S = (5.9 ± 1.8 ± 1.4 s y s ) J / m o l K , respectively. [ABSTRACT FROM AUTHOR]

The incorporation of nuclear quantum effects and non-Born–Oppenheimer behavior into quantum chemistry calculations and molecular dynamics simulations is a longstanding challenge. The nuclear–electronic orbital (NEO) approach treats specified nuclei, typically protons, quantum mechanically on the same level as the electrons with wave function and density functional theory methods. This approach inherently includes nuclear delocalization and zero-point energy in molecular energy calculations, geometry optimizations, reaction paths, and dynamics. It can also provide accurate descriptions of excited electronic, vibrational, and vibronic states as well as nuclear tunneling and nonadiabatic dynamics. Nonequilibrium nuclear–electronic dynamics simulations beyond the Born–Oppenheimer approximation can be used to investigate a wide range of excited state processes. This Perspective provides an overview of the foundational NEO methods and enumerates the prospects for using these methods as building blocks for future developments. The conceptual simplicity and computational efficiency of the NEO approach will enhance its accessibility and applicability to diverse chemical and biological systems. [ABSTRACT FROM AUTHOR]

Laser-induced fluorescence/dispersed fluorescence (LIF/DF) and cavity ring-down spectra of the A 1 ̃ 2 A ′ ′ / A 2 ̃ 2 A ′ − X ̃ 2 A ′ electronic transition of the calcium ethoxide (CaOC2H5) radical have been obtained under jet-cooled conditions. An essentially constant A ̃ 2 − A ̃ 1 energy separation for different vibronic levels is observed in the LIF spectrum, which is attributed to both the spin–orbit (SO) interaction and non-relativistic effects. Electronic transition energies, vibrational frequencies, and spin–vibrational eigenfunctions calculated using the coupled-cluster method, along with results from previous complete active space self-consistent field calculations, have been used to predict the vibronic energy level structure and simulate the recorded LIF/DF spectra. Although the vibrational frequencies and Franck–Condon (FC) factors calculated under the Born–Oppenheimer approximation and the harmonic oscillator approximation reproduce the dominant spectral features well, the inclusion of the pseudo-Jahn–Teller (pJT) and SO interactions, especially those between the A 1 ̃ 2 A ″ / A 2 ̃ 2 A ′ and the B ̃ 2 A ′ states, induces additional vibronic transitions and significantly improves the accuracy of the spectral simulations. Notably, the spin–vibronic interactions couple vibronic levels and alter transition intensities. The calculated FC matrix for the A 1 ̃ 2 A ′ ′ / A 2 ̃ 2 A ′ − X ̃ 2 A ′ transition contains a number of off-diagonal matrix elements that connect the vibrational ground levels to the levels of the ν8 (CO stretch), ν11 (OCC bending), ν12 (CaO stretch), ν13 (in-plane CaOC bending), and ν21 (out-of-plane CaOC bending) modes, which are used for vibrational assignments. Transitions to the ν21(a″) levels are allowed due to the pJT effect. Furthermore, when LIF transitions to the A ̃ -state levels of the CaOC-bending modes, ν13 and ν21, are pumped, A 1 ̃ 2 A ′ ′ / A 2 ̃ 2 A ′ → X ̃ 2 A ′ transitions to the combination levels of these two modes with the ν8, ν11, and ν12 modes are also observed in the DF spectra due to the Duschinsky mixing. Implications of the present spectroscopic investigation to laser cooling of asymmetric-top molecules are discussed. [ABSTRACT FROM AUTHOR]

The complex-scaling method can be used to calculate molecular resonances within the Born–Oppenheimer approximation, assuming that the electronic coordinates are dilated independently of the nuclear coordinates. With this method, one will calculate the complex energy of a non-Hermitian Hamiltonian, whose real part is associated with the resonance position and imaginary part is the inverse of the lifetime. In this study, we propose techniques to simulate resonances on a quantum computer. First, we transformed the scaled molecular Hamiltonian to second quantization and then used the Jordan–Wigner transformation to transform the scaled Hamiltonian to the qubit space. To obtain the complex eigenvalues, we introduce the direct measurement method, which is applied to obtain the resonances of a simple one-dimensional model potential that exhibits pre-dissociating resonances analogous to those found in diatomic molecules. Finally, we applied the method to simulate the resonances of the H 2 − molecule. The numerical results from the IBM Qiskit simulators and IBM quantum computers verify our techniques. [ABSTRACT FROM AUTHOR]

A model of a planar tri-atomic molecule is presented, which is integrable in the Born–Oppenheimer adiabatic approximation. The molecular Hamiltonian is the sum of a nuclear vibrational energy operator and an electronic Hamiltonian, where vibrations of nuclei are defined to be motions with vanishing total angular momentum in the center-of-mass system, and where the electronic Hamiltonian is assumed to be a traceless 2 × 2 Hermitian matrix defined on R ̇ 3 , the shape space of the planar three-body system. Once an eigenvalue of the electronic Hamiltonian is chosen, vibrational-electronic interaction is introduced through covariant differential operators acting on sections of the eigen-line bundle associated with the chosen eigenvalue. The Hamiltonian for nuclear motion coupled with electronic state is then described in terms of these covariant differential operators together with the chosen eigenvalue as a potential for nuclear motion. The eigenvalues of the nuclear Hamiltonian are evaluated for bound states. In the case that vibrational-electronic interaction is restricted to small vibrational-electronic one around a symmetric configuration of the nuclei, a remark is made on a relation to a well-known Hamiltonian describing the dynamic Jahn–Teller effect for a planar tri-atomic molecule X3. [ABSTRACT FROM AUTHOR]

Heavy-quark spin symmetry is explicitly broken by the mass splitting between a heavy-light pseudoscalar meson and its vector partner. This fact plays a pivotal role in the physics of states whose mass lies close to the threshold of an open-flavor meson pair, like X(3872). We show that this source of heavy-quark spin symmetry breaking can be systematically included within the diabatic representation of the Born-Oppenheimer approximation. We verify that including all the appropriate coupled channels guarantees conservation of total angular momentum, parity, and charge-conjugation parity. This marks a fundamental step towards a unified, first-principles study of quarkonia and meson molecules with hidden flavor. [ABSTRACT FROM AUTHOR]

We consider a molecule in the Born–Oppenheimer approximation interacting with a plate of infinite thickness, i.e., a half-space, which is perfectly conducting or dielectric. It is well known in the physics literature that in this case the atom or molecule is attracted by the plate at sufficiently large distances. This effect is analogous to the well-known van der Waals interaction between neutral atoms or molecules. We prove that the interaction energy W of the system is given by W (r , v) = − C (v) r − 3 + O ( r − 4 ) , where r is the distance between the molecule and the plate and v indicates their relative orientation. Moreover, C(v) is positive and continuous, thus the atom or molecule is always pulled toward the plate at sufficiently large distances, for all relative orientations v. For some specific systems, we provide sharper estimates of W(r, v). This asymptotic behavior is well known in the physics literature; however, we are not aware of any previous rigorous results, even on the existence of a ground state of the system. For pedagogical reasons, we often start with the case of a hydrogen atom and then we generalize the arguments to deal with a general molecule. [ABSTRACT FROM AUTHOR]

A calibration free laser ablation molecular isotopic spectrometry (CF-LAMIS) approach for boron isotopic concentration determination has been investigated under ambient atmospheric air conditions. Using non-rigid rotor and anharmonic equations and diatomic constants, a database for ro-vibrational transitions of both the 11BO B-X band and the 10BO B-X band was developed. The selected molecular transition of boron oxide (BO) was computed using this database. The computed molecular transitions combined with an in-house developed molecular spectrum fitting algorithm based on Born–Oppenheimer approximation and Boltzmann equilibrium provides compositional information from an experimental spectrum. The parameters such as laser energy, acquisition delay time and spectral wavelength with respect to the degree of differentiability are optimized to predict the result. This CF-LAMIS method predicts the 10B isotopic concentration with an accuracy and % RSD of 1.1% and 2.7%. The method introduces a new outlook to calibration-free analytical analysis, as boron isotopic concentrations were predicted accurately and precisely under ambient air conditions without any standard samples. [ABSTRACT FROM AUTHOR]

Elastic modeling of spin-crossover materials has boomed remarkably these last years. Among these models, the electro-elastic model combining spin and lattice degrees of freedom showed good abilities of fair description of the thermodynamics and spin-crossover solids. In the present work, we explore a new treatment of this model based on a homogeneous description of the lattice spacing with well separate relaxation timescales for the lattice and spin state degrees of freedom. This description is analogous to the Born–Oppenheimer approximation and allows analytic treatment of the elastic part of the model, thus simplifying considerably the model resolution. As a result, we have been able to demonstrate the equivalence between the genuine electro-elastic model and an Ising-like Hamiltonian with competing long-range ferro-like and short-range (nearest neighbors and next-nearest neighbors along diagonals) antiferro-like interactions, whose relationship with the high-spin to low-spin misfit elastic energy has been established. This model generates intrinsic elastic frustration in the lattice, which leads to a rich variety of hysteretic first-order transitions made of one- two-, three-, or four-step behaviors. Complex self-organizations of the spin states are evidenced in the plateau regions in the form of checkerboard-like, stripes-like patterns, constituted of alternate high-spin and low-spin ferro-like stripes or alternate ferro high-spin (or low-spin) and antiferro-like chains, as well labyrinth structures. [ABSTRACT FROM AUTHOR]

The nuclear–electronic orbital (NEO) method is a multicomponent quantum chemistry theory that describes electronic and nuclear quantum effects simultaneously while avoiding the Born–Oppenheimer approximation for certain nuclei. Typically specified hydrogen nuclei are treated quantum mechanically at the same level as the electrons, and the NEO potential energy surface depends on the classical nuclear coordinates. This approach includes nuclear quantum effects such as zero-point energy and nuclear delocalization directly into the potential energy surface. An extended NEO potential energy surface depending on the expectation values of the quantum nuclei incorporates coupling between the quantum and classical nuclei. Herein, theoretical methodology is developed to optimize and characterize stationary points on the standard or extended NEO potential energy surface, to generate the NEO minimum energy path from a transition state down to the corresponding reactant and product, and to compute thermochemical properties. For this purpose, the analytic coordinate Hessian is developed and implemented at the NEO Hartree–Fock level of theory. These NEO Hessians are used to study the SN2 reaction of ClCH3Cl− and the hydride transfer of C4H9+. For each system, analysis of the single imaginary mode at the transition state and the intrinsic reaction coordinate along the minimum energy path identifies the dominant nuclear motions driving the chemical reaction. Visualization of the electronic and protonic orbitals along the minimum energy path illustrates the coupled electronic and protonic motions beyond the Born–Oppenheimer approximation. This work provides the foundation for applying the NEO approach at various correlated levels of theory to a wide range of chemical reactions. [ABSTRACT FROM AUTHOR]

We develop a formalism to accurately account for the renormalization of the electronic structure due to quantum and thermal nuclear motions within the Born–Oppenheimer approximation. We focus on the fundamental energy gap obtained from electronic addition and removal energies from quantum Monte Carlo calculations in either the canonical or grand-canonical ensembles. The formalism applies as well to effective single electron theories such as those based on density functional theory. We show that the electronic (Bloch) crystal momentum can be restored by marginalizing the total electron–ion wave function with respect to the nuclear equilibrium distribution, and we describe an explicit procedure to establish the band structure of electronic excitations for quantum crystals within the Born–Oppenheimer approximation. Based on the Kubo–Greenwood equation, we discuss the effects of nuclear motion on optical conductivity. Our methodology applies to the low temperature regime where nuclear motion is quantized and, in general, differs from the semi-classical approximation. We apply our method to study the electronic structure of C2/c-24 crystalline hydrogen at 200 K and 250 GPa and discuss the optical absorption profile of hydrogen crystals at 200 K and carbon diamond at 297 K. [ABSTRACT FROM AUTHOR]

We study the generation of electronic ring currents in the presence of nonadiabatic coupling using circularly polarized light. For this, we introduce a solvable model consisting of an electron and a nucleus rotating around a common center and subject to their mutual Coulomb interaction. The simplicity of the model brings to the forefront the non-trivial properties of electronic ring currents in the presence of coupling to the nuclear coordinates and enables the characterization of various limiting situations transparently. Employing this model, we show that vibronic coupling effects play a crucial role even when a single E degenerate eigenstate of the system supports the current. The maximum current of a degenerate eigenstate depends on the strength of the nonadiabatic interactions. In the limit of large nuclear to electronic masses, in which the Born–Oppenheimer approximation becomes exact, constant ring currents and time-averaged oscillatory currents necessarily vanish. [ABSTRACT FROM AUTHOR]

A first principles quantum formalism to describe the non-adiabatic dynamics of electrons and nuclei based on a second quantization representation (SQR) of the electronic motion combined with the usual representation of the nuclear coordinates is introduced. This procedure circumvents the introduction of potential energy surfaces and non-adiabatic couplings, providing an alternative to the Born–Oppenheimer approximation. An important feature of the molecular Hamiltonian in the mixed first quantized representation for the nuclei and the SQR representation for the electrons is that all degrees of freedom, nuclear positions and electronic occupations, are distinguishable. This makes the approach compatible with various tensor decomposition Ansätze for the propagation of the nuclear–electronic wavefunction. Here, we describe the application of this formalism within the multi-configuration time-dependent Hartree framework and its multilayer generalization, corresponding to Tucker and hierarchical Tucker tensor decompositions of the wavefunction, respectively. The approach is applied to the calculation of the photodissociation cross section of the HeH+ molecule under extreme ultraviolet irradiation, which features non-adiabatic effects and quantum interferences between the two possible fragmentation channels, He + H+ and He+ + H. These calculations are compared with the usual description based on ab initio potential energy surfaces and non-adiabatic coupling matrix elements, which fully agree. The proof-of-principle calculations serve to illustrate the advantages and drawbacks of this formalism, which are discussed in detail, as well as possible ways to overcome them. We close with an outlook of possible application domains where the formalism might outperform the usual approach, for example, in situations that combine a strong static correlation of the electrons with non-adiabatic electronic–nuclear effects. [ABSTRACT FROM AUTHOR]

We introduce a new theoretical and computational framework for treating molecular quantum mechanics without the Born–Oppenheimer approximation. The molecular wavefunction is represented in a tensor-product space of electronic and vibrational basis functions, with electronic basis chosen to reproduce the mean-field electronic structure at all geometries. We show how to transform the Hamiltonian to a fully second-quantized form with creation/annihilation operators for electronic and vibrational quantum particles, paving the way for polynomial-scaling approximations to the tensor-product space formalism. In addition, we make a proof-of-principle application of the new Ansatz to the vibronic spectrum of C2. [ABSTRACT FROM AUTHOR]

Reactions of methane with different atoms are benchmark examples of elementary reaction processes intensively studied by theory and experiment. Due to the presence of conical intersections and spin–orbit coupling, non-adiabatic transitions can occur in reactions with F, Cl, or O atoms. Extending detailed quantum theory beyond the Born–Oppenheimer approximation for polyatomic reaction processes, non-adiabatic wave packet dynamics calculations studying the F(2P3/2)/F*(2P1/2) + CHD3 → HF + CD3 reaction on accurate vibronically and spin–orbit coupled diabatic potential energy surfaces are presented. Non-adiabatic transitions are found to increase the reactivity compared to Born–Oppenheimer theory and are more prominent than in triatomic reactions previously studied. Furthermore, the lifetimes of reactive resonances are reduced. The reactivity of F(2P3/2) is found to exceed the one of F*(2P1/2) even at low collision energies. [ABSTRACT FROM AUTHOR]

We have developed an algorithm to detect holes in multi-dimensional real-valued surfaces—such as the potential energy surfaces (PESs) that describe the nuclear motion of molecules in the context of the Born–Oppenheimer approximation. For our purposes, a PES "hole" is defined as an unphysical saddle point, beyond which the potential energy drops (typically) without limit to negative infinity. PES holes are numerical artifacts that can arise when fitting PES functional forms to discrete ab initio data—even when the data is of high quality, and/or for comparatively few degrees of freedom (DOF). Often undetected, PES holes can have devastating effects on subsequent dynamical calculations, especially if they occur at low energies. In this paper, we present a highly efficient algorithm designed to systematically identify hole configurations and energies. The method is applied to a variety of molecular PESs ranging up to 30 DOF. A number of evidently previously undetected PES holes are reported here—surprisingly, even for PESs that have been available for decades. The code itself (Crystal) is presented together with a user manual. These tools may be of great benefit for PES developers, who can use the information they provide to fix holes, once identified. More generally, the methodology can be applied in any context involving multi-dimensional surfaces. [ABSTRACT FROM AUTHOR]

In this work, we describe a computer program called ATOM-MOL-nonBO for performing bound state calculations of small atoms and molecules without assuming the Born–Oppenheimer approximation. All particles forming the systems, electrons and nuclei, are treated on equal footing. The wave functions of the bound states are expanded in terms of all-particle one-center complex explicitly correlated Gaussian functions multiplied by Cartesian angular factors. As these Gaussian functions are eigenfunctions of the operator representing the square of the total angular momentum of the system, the problem separates and calculations of states corresponding to different values of the total rotational quantum number can be solved independently from each other. Due to thorough variational optimization of the Gaussian exponential parameters, the method allows us to generate very accurate wave functions. The optimization is aided by analytically calculated energy gradient determined with respect to the parameters. Three examples of calculations performed for diatomic and triatomic molecules are shown as an illustration of calculations that can be performed with this program. Finally, we discuss the limitations, applicability range, and bottlenecks of the program. [ABSTRACT FROM AUTHOR]

Inspired by the possibility to experimentally manipulate and enhance chemical reactivity in helium nanodroplets, we investigate the effective interaction and the resulting correlations between two diatomic molecules immersed in a bath of bosons. By analogy with the bipolaron, we introduce the biangulon quasiparticle describing two rotating molecules that align with respect to each other due to the effective attractive interaction mediated by the excitations of the bath. We study this system in different parameter regimes and apply several theoretical approaches to describe its properties. Using a Born–Oppenheimer approximation, we investigate the dependence of the effective intermolecular interaction on the rotational state of the two molecules. In the strong-coupling regime, a product-state ansatz shows that the molecules tend to have a strong alignment in the ground state. To investigate the system in the weak-coupling regime, we apply a one-phonon excitation variational ansatz, which allows us to access the energy spectrum. In comparison to the angulon quasiparticle, the biangulon shows shifted angulon instabilities and an additional spectral instability, where resonant angular momentum transfer between the molecules and the bath takes place. These features are proposed as an experimentally observable signature for the formation of the biangulon quasiparticle. Finally, by using products of single angulon and bare impurity wave functions as basis states, we introduce a diagonalization scheme that allows us to describe the transition from two separated angulons to a biangulon as a function of the distance between the two molecules. [ABSTRACT FROM AUTHOR]

Analytic gradients of electronic eigenvalues require one calculation per nuclear geometry, compared to at least 3n + 1 calculations for finite difference methods, where n is the number of nuclei. Analytic nonadiabatic derivative coupling terms (DCTs), which are calculated in a similar fashion, are used to remove nondiagonal contributions to the kinetic energy operator, leading to more accurate nuclear dynamics calculations than those that employ the Born-Oppenheimer approximation, i.e., that assume off-diagonal contributions are zero. The current methods and underpinnings for calculating both of these quantities, gradients and DCTs, for the State-Averaged MultiReference Configuration Interaction with Singles and Doubles (MRCI-SD) wavefunctions in COLUMBUS are reviewed. Before this work, these methods were not available for wavefunctions of a relativistic MRCI-SD Hamiltonian. Calculation of these terms is critical in successfully modeling the dynamics of systems that depend on transitions between potential energy surfaces split by the spin-orbit operator, such as diode-pumped alkali lasers. A formalism for calculating the transition density matrices and analytic derivative coupling terms for such systems is presented. [ABSTRACT FROM AUTHOR]

According to relativistic quantum mechanics, particles can be of negative kinetic energies (NKE). The author asserts in his previous works that the NKE substances are dark matters. Some NKE particles, say a pair of NKE electrons, can constitute a stable system by means of the repulsive interaction between them. In the present work, two simplest three-particle systems are investigated. One consists of two NKE positrons and one NKE proton, called dark hydrogen anion. The other is composed of two NKE protons and one NKE positron, called dark hydrogen molecule cation. They are so named because the Hamiltonians of them can correspond to those of the hydrogen anion and hydrogen molecule cation. In evaluating the dark hydrogen molecule cation, the famous Born-Oppenheimer approximation does not apply, i.e., the NKE of the protons cannot be neglected. Without the NKE, the system cannot be stable. Our study reveals that in a NKE system, the particles with the same kind of electric charge combine tightly. This is to enhance the repulsive Coulomb potential so as to raise the total energy as far as possible. A great amount of NKE particles can compose a dense and dark macroscopic NKE body. Thus, it is conjectured that some remote dark celestial bodies may be NKE ones other than the well-known black holes. The discrepancies between the black holes and macroscopic NKE bodies are pointed out. [ABSTRACT FROM AUTHOR]

A closed interpolation equation is derived based on exact relations of quantum statistical theory for Coulomb systems and the Born–Oppenheimer approximation. This equation relates pressure and its derivative to density at a fixed temperature for a simple quasi-classical liquid, in which the effective pair potential of particle–particle interaction has a Fourier transform. [ABSTRACT FROM AUTHOR]