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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]

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]

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]

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]

The mathematics used in physical chemistry has changed greatly in the past forty years and it will certainly continue to change more quickly. Theoretical chemists and physicists must have an acquaintance with abstract mathematics if they are to keep up with their field, as the mathematical language in which it is expressed changes. Thinking about it, in this article, we want to show some of the most important concepts of Mathematical Analysis involved in obtaining analytical functions to represent the potential energy interaction for diatomic systems. A basic guide for the construction of a potential based on Dunham's coefficients and an example of a new potential obtained from this methodology is also presented.

In this paper, we study the spectral properties of polarobreathers, that is, breathers carrying charge in a one-dimensional semiclassical model. We adapt recently developed numerical methods that preserve the charge probability at every step of time integration without using the Born–Oppenheimer approximation, which is the assumption that the electron is not at equilibrium with the atoms or ions. We develop an algorithm to obtain exact polarobreather solutions. The properties of polarobreathers, both stationary and moving ones, are deduced from the lattice and charge variable spectra in the frequency–momentum space. We consider an efficient approach to produce approximate polarobreathers with long lifespans. Their spectrum allows for the determination of the initial conditions and the necessary parameters to obtain numerically exact polarobreathers. The spectra of exact polarobreathers become extremely simple and easy to interpret. We also solve the problem that the charge frequency is not an observable, but the frequency of the charge probability certainly is an observable. [ABSTRACT FROM AUTHOR]

We study compact hidden charm pentaquarks in the Born–Oppenheimer approximation, previously introduced for tetraquarks, assuming the heavy pair to be in a color octet. We show that Fermi statistics applied to the complex of the three light quarks, also in color octet, requires S-wave pentaquark ground states to consist of three octets of flavour-SU(3) f , two with spin 1/2 and one with spin 3/2, in line with the observed, strangeness S = 0 , - 1 , spectrum. Additional lines corresponding to decays into J / ψ + Σ and J / ψ + Ξ are predicted. In the language of non-relativistic SU(6), ground state pentaquarks form either a 56 or a 20 representation, distinguished by presence or absence of pentaquarks decaying in the spin 3/2 decuplet, e.g. in J / ψ + Δ + + . Observation of a strangeness S = - 2 or isospin I = 3 / 2 pentaquarks would be a clear signature of compact, QCD bound pentaquarks. [ABSTRACT FROM AUTHOR]

The question of whether chemical structure is reducible to Everettian Quantum Mechanics (EQM) should be of interest to philosophers of chemistry and philosophers of physics alike. Among the three realist interpretations of quantum mechanics, EQM resolves the measurement problem by claiming that measurements (now interpreted as instances of decoherence) have indeterminate outcomes absolutely speaking, but determinate outcomes relative to emergent worlds—Maudlin (Topoi, 14:7-15, 1995). Philosophers who wish to be sensitive to the practice of quantum chemistry e.g. Scerri (The changing views of a philosopher of chemistry on the question of reduction, 2016) should be interested in EQM because Franklin and Seifert (J. Philos. Sci, 2020) claim that resolving the measurement problem also resolves the reducibility of chemical structure, and EQM is the interpretation which involves no mathematical structure beyond that used by practicing scientists. Philosophers interested in the quantum interpretation debate should be interested in the reducibility of chemistry because chemical structure is precisely the kind of determinate three-dimensional fact which EQM should be able to ground if it is to be empirically coherent—see Allori (Quantum Rep, 5:80-101, 2023). The prospects for reduction of chemical structure are poor if it cannot succeed in EQM; the prospects for EQM as a guide to ontology are poor if it cannot reduce chemical structure. Unfortunately for proponents of chemical reduction and EQM, there are three serious barriers to the reduction of chemistry to EQM. The first concern is that quantum treatments of chemical structure rely on the Born-Oppenheimer approximation, which holds nuclear locations fixed while minimizing the energy of the electronic configuration—Hendry (Philosophical Perspectives in Quantum Chemistry, 147-172, 2022), but this approximation is not licensed by EQM. The Born-Oppenheimer approximation relies on nuclei and molecular orbitals being simultaneously present, but in the three-dimensional ontology following from the Everett interpretation these only emerge at different energy scales and are not simultaneously present—Miller (Found. Chem, 25:405-417, 2023). The second concern is that the emergent worlds of EQM are supposed to be decoherent at the macro-scale—Wilson (The Nature of Contingency: Quantum Physics as Modal Realism 2020), but the recent development of superchemistry suggests that chemical reactions can occur in coherent states—Zhang et al. (Nat. Phys, 1-5, 2023). The third concern is that emergent worlds are only pragmatic pseudo-processes—Wallace (The Emergent Multiverse: Quantum Theory According to the Everett Interpretation, 2012b), but this means EQM trades realist physics for mere instrumentalism about chemistry. Absent a commitment to chemical realism, reduction is an empty promise. The prospects for reduction of chemical structure to EQM are therefore poor. [ABSTRACT FROM AUTHOR]

A possible solution of the problem of time in the Wheeler–DeWitt quantum geometrodynamics is that time appears within a semiclassical limit. Following this line of thinking, one can come to the Schrodinger equation for matter fields in curved spacetime with quantum-gravitational corrections. In the present paper, we study the semiclassical limit in the case of a closed isotropic model with a scalar field decomposed into modes. We analyse calculations made within frameworks of three approaches. The first approach was proposed by Kiefer and Singh. Since the Wheeler–DeWitt equation does not contain a time derivative, it is constructed by means of a special mathematical procedure, a time variable being a parameter along a classical trajectory of gravitational field. The second method was suggested in the paper of Maniccia and Montani, who introduced the Kuchař–Torre reference fluid as an origin of time. Furthermore, the third is the extended phase space approach to the quantisation of gravity. In this approach, the temporal Schrodinger equation is argued to be more fundamental than the Wheeler–DeWitt equation, and there is no problem of time. Time is introduced due to fixing a reference frame of a certain observer, who can register the macroscopic consequences of quantum gravitational phenomena in the Very Early Universe. To go to the semiclassical limit, the Born–Oppenheimer approximation for gravity is used. In each of the approaches, in the order of O (1 / M) , a temporal Schrödinger equation for matter fields in curved spacetime with quantum gravitational corrections is obtained. However, equations and corrections are different in various approaches, and the results depend on the additional assumptions made within the scopes of these approaches. [ABSTRACT FROM AUTHOR]

Until about a decade or so, till the fast-paced development and usage of computers, organic chemistry students often chose experimental projects during an internship. Presently, there are software packages that solve quantum chemical equations and present the possibility of a 'black-box' type of approach to getting exposed to computational organic chemistry. Encouraging as this may seem, Indian university students can find the entry to and an understanding of computational chemistry daunting due to a lack of exposure to research. This article attempts to bridge the gap for such students by providing a gentle introduction to the field of quantum chemistry. [ABSTRACT FROM AUTHOR]

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For decades, the light-matter interaction (LMI) based on Born-Oppenheimer (BO) approximation has dominated the fields of photonics, materials, and condensed-matter physics. However, in polar crystals, the BO approximation is not applicable when stimulated phonon polaritons are excited. Unlike the studies on topological physics and physical chemistry that go beyond BO approximation, here we unravel a stimulated phonon polariton-mediated LMI mechanism in polar crystals, which is radically different from the traditional LMI interpreted by BO approximation. In the regime of stimulated phonon polariton-mediated LMI, two exemplary experiments were conducted at different wavelengths: Q-factor increase of a LiNbO3 terahertz microcavity, and a five orders-of-magnitude enhancement of second-harmonic generation of infrared laser pulses in a LiNbO3 slab. Our study enhances the understanding of the LMI mechanism and shows potential for applications in the fields of optics/photonics and condensed-matter physics. Light-matter interaction has been dominated by Born-Oppenheimer approximation for centuries. Here the authors proposed a light-matter interaction mechanism beyond this approximation, proposing stimulated phonon polariton-mediated light-matter interaction, showing further understanding and applications in the fields of optics/photonics and condensed-matter physics. [ABSTRACT FROM AUTHOR]

Pendekatan Born-Oppenheimer diterapkan untuk menghitung tingkat energi vibrasi keadaan dasar molekul hidrogen. Persamaan Schrodinger untuk inti atom diselesaikan dengan menggunakan metode semi-klasik, di mana inti atom diasumsikan bergerak secara klasik dalam sumur potensial dan energi vibrasi ditentukan dengan menerapkan aturan kuantisasi kuantum. Potensial yang digunakan pada penelitian adalah potensial Morse. Dalam penelitian ini, tingkat energi vibrasi dihitung dengan metode numerik, yaitu metode integrasi Simpson dan metode regula falsi. 15 Tingkat energi vibrasi dari molekul H2 diperoleh dan dibandingkan dengan data hasil eksperimen. Perbandingan ini mengindikasikan pendekatan yang digunakan pada penelitian ini memberikan hasil yang sangat akurat pada tingkat energi vibrasi yang relatif rendah (0≤n≤4), dengan kesalahan kurang dari 0,7%, dan untuk 5≤n≤8 dengan kesalahan maksimum 7,3%. Keakuratan menurun ketika tingkat energi vibrasi meningkat. Secara khusus, untuk n = 13 dan n = 14, kesalahan meningkat secara signifikan, menunjukkan gagalnya pendekatan ini untuk tingkat energi vibrasi yang relatif tinggi, khususnya untuk dua tingkat energi ini. Born-Oppenheimer approximation was applied to calculate vibrational energy levels of ground state of Hydrogen molecule. The Schrodinger equation for the nuclei was solved using a semi-classical method, in which the nuclei are assumed to move classically in a potential well and the vibrational energies are determined by applying the quantum mechanical quantization rules. Potential used in this research was the Morse potential. Here, vibrational energy levels of the molecule were calculated using numerical methods, i.e. Simpson integration method and false position method. 15 Vibrational energy levels of the H2 molecule were obtained and compared to the corresponding results from experiments. The comparison indicated that the approximation used in this research yielded very accurate results for relatively low vibrational levels (0≤n≤4), with errors being less than 0.7% and for 5≤n≤8 with maximum of 7.3% errors. The accuracy decreased as the vibrational levels increased, as expected. In particular, for n=13 and n=14, errors significantly increased, indicating the breakdown of the approximation for relatively high vibrational levels, in particular for these two energy levels.

The process of stress-strain nonlinear deformation is fundamental to almost all branches of science and engineering. Although the mechanical mechanisms of such process are well studied, the governing atomic processes that take place inside solids during mechanical loading remains unclear. In this work, new equations to characterize the stress-strain nonlinear deformation from entropy changes on surface wetting are presented. The evolution of entropy changes during mechanical loading is calculated based on the Born-Oppenheimer approximation, wherein electronic, nuclear, electron-phonon, and phonon-phonon coupling interactions are treated independently. Further measurement and modelling of water contact angles at different strain loadings for NiTi, steel, and aluminum systems, within the elastic and the early plastic domain, are performed to validate the derived equation. These results may enable a paradigm shift from energy-force to entropy-centric research while offering exciting possibilities in NDT inspection, featureless fluid navigation, and anti-biofouling fields.

The cross sections and rate coefficients for inelastic processes in low-energy collisions of nickel atoms and positive ions with hydrogen atoms and negative ions are calculated for the collisional energy range 10−4–100 eV and for the temperature range 1000–10,000 K. 74 covalent and three ionic states correlated to 11 molecular symmetries are considered. 3380 partial inelastic processes are treated in total. The study of nickel–hydrogen collisions is performed by the quantum model methods within the Born–Oppenheimer formalism. The electronic structure of the collisional quasimolecule is calculated by the semiempirical asymptotic method for each considered molecular symmetry. For nuclear dynamic calculations the simplified method in combination with the Landau–Zener model is used. Nuclear dynamics within each considered symmetry is treated separately, and the total rate coefficients for each inelastic process have been summed over all symmetries. The largest values of the rate coefficients (exceeding 10−8 cm3 s−1) correspond to the mutual neutralization processes in collisions Ni+(3d92D) + H−(1s21S) (the ground ionic state being the initial state), as well as in Ni+(3d84s4,2F) + H−(1s21S) (the first excited and the second excited ionic states being the initial states) collisions. At the temperature of 6000 K, the rate coefficients with large magnitudes have the values from the ranges (1.35−5.87) × 10−8 cm3 s−1 and (1.02−6.77) × 10−8 cm3 s−1, respectively. The calculated rate coefficients with large and moderate values are important for non–local thermodynamic equilibrium stellar atmosphere modeling. [ABSTRACT FROM AUTHOR]

The interaction between phonons and 4f electrons, which is forming a new quantum state (quasi-bound state) beyond Born-Oppenheimer approximation, is very prominent and lattice dynamics plays here a key role. There is only a small number of compounds in which the experimental observation suggest such a scenario. One of these compounds is CePd2Al2. Here the study of phonon dispersion curves of (Ce,La)Pd2Al2 at 1.5, 7.5, 80 and 300 K is presented. The inelastic X-ray scattering technique was used for mapping the phonon modes at X and Z points as well as in Λ and Δ directions, where the symmetry analysis of phonon modes was performed. The measured spectra are compared with the theoretical calculation, showing very good agreement. The measurements were performed in several Brillouin zones allowing the reconstruction of phonon dispersion curves. The results are discussed with respect to the magneto-elastic interaction and are compared with other cerium compounds. The phonon mode symmetry A1g was found to be unaffected by the interaction, which is in contrast to previous assumptions. [ABSTRACT FROM AUTHOR]

The interaction between phonons and 4f electrons, which is forming a new quantum state (quasi-bound state) beyond Born-Oppenheimer approximation, is very prominent and lattice dynamics plays here a key role. There is only a small number of compounds in which the experimental observation suggest such a scenario. One of these compounds is CePd2Al2. Here the study of phonon dispersion curves of (Ce,La)Pd2Al2 at 1.5, 7.5, 80 and 300 K is presented. The inelastic X-ray scattering technique was used for mapping the phonon modes at X and Z points as well as in Λ and Δ directions, where the symmetry analysis of phonon modes was performed. The measured spectra are compared with the theoretical calculation, showing very good agreement. The measurements were performed in several Brillouin zones allowing the reconstruction of phonon dispersion curves. The results are discussed with respect to the magneto-elastic interaction and are compared with other cerium compounds. The phonon mode symmetry A1g was found to be unaffected by the interaction, which is in contrast to previous assumptions. [ABSTRACT FROM AUTHOR]

We study the potential of X (3872) at finite temperature in the Born-Oppenheimer approximation under the assumption that it is a tetraquark. We argue that, at large number of colors, it is a good approximation to assume that the potential consists in a real part plus a constant imaginary term. The real part is then computed adapting an approach by Rothkopf and Lafferty and using as input lattice QCD determinations of the potential for hybrids. This model allows us to qualitatively estimate at which temperature range the formation of a heavy tetraquark is possible, and to propose a qualitative picture for the dissociation of the state in a medium. Our approach can be applied to other suggested internal structures for the X (3872) and to other exotic states. [ABSTRACT FROM AUTHOR]

Pressure-induced superconductivity has been widely explored and observed in Bi2Se3-based topological materials to hunt for topological superconductors. Although their triggered superconductivity has a close connection to their pressure-induced structural phase transitions, the quest for the electron pairing mechanism of these superconducting semiconductors in both their initial rhombohedral and high-pressure phases remains unknown. In this work, we present a systematic study of the pressure effect on superconducting properties and lattice dynamics using a combination of electrical transport, Raman-scattering, and synchrotron x-ray diffraction measurements using diamond anvil cells. One key finding is our observation of a cooperative connection between the strength of the electron–phonon interaction (EPI) generated by optical branches and the pressure-tunable superconductivity in rhombohedral SrxBi2Se3 crystal. The underlying suppression mechanism of the Tc by pressure is ascribed to the weakening of the electrons' interaction with the optical phonon modes in the rhombohedral phase. In the intermediate monoclinic phase, the Tc value underwent a sharp increase with carrier density accumulation accompanying the concurrent enhanced EPI. This is intuitively unusual since it is expected that the EPI shall be weakened by inducing more conducting carriers in a normal metal. In the tetragonal phase, the superconductivity is interpreted within BCS theory, since it is fully metallized and obeys the adiabatic Born–Oppenheimer approximation well. Our findings are important to fully understand unconventional superconductivity and the unusual pairing mechanism in the layered rhombohedral Bi2Se3-based superconductors. [ABSTRACT FROM AUTHOR]

In the framework of the Born–Oppenheimer (BO) method, we illustrate our ab-initio spectroscopic study of the of silver hydride molecule. The calculation of 48 electrons for this system is very difficult, so we have been employed a pseudo-potential (P.P) to reduce the big number of electrons to two electrons of valence, which is proposed by Barthelat and Durant. This allowed us to make a configuration interaction (CI). The potential energy curves (PECs) and the spectroscopic constants of AgH have been investigated for Σ+, Π and Δ symmetries. We have been determined the permanent and transition dipole moments (PDM and TDM), the vibrational energies levels and their spacing. We compared our results with the available experimental and theoretical results in the literature. We found a good accordance with the experimental and theoretical data that builds a validation of the choice of our approach. [ABSTRACT FROM AUTHOR]

This paper deals with new approaches towards the Jablonski diagram and the ¿ state concepts from the viewpoint of the relationship between electronic deactivation and vibrational relaxation processes in electronically excited species. In both concepts, vibrational relaxation precedes the electronic deactivation processesofexcited molecules. The experimental data accumulated up to the present using mainly time-resolved luminescence and transient absorption spectroscopy from the field of the photophysics of transition metal compounds and different organic molecules have clearly demonstrated that even spin-forbidden electronic deactivations are in many cases faster processes that vibrational relaxation. It means that the classical Jablonski diagram indicating that electronic deactivation processes occur after vibrational relaxation should be modified. In general, electronic deactivations occur from vibrationally higher states. [ABSTRACT FROM AUTHOR]

With an intense femtosecond two-color pulse optimized for the generation of even-order harmonics from CO molecules, we directly measure the actual degrees of orientation by utilizing the Coulomb explosion imaging technique with appropriate probe polarization. We find that the macroscopic orientation of CO molecules is negligible even when significant even-order harmonics are observed. This finding shows that the generation of even-order harmonics cannot be ascribed to the macroscopic orientation of CO molecules. The rotational wave packet of CO molecules created with an intense femtosecond two-color pulse is thought to be in an uninvestigated quantum state, which cannot be explained by the theoretical model based on the Born–Oppenheimer approximation, without inversion symmetry at any of the three steps of high-order harmonic generation, leading to the generation of even-order harmonics. [ABSTRACT FROM AUTHOR]

Uncertainty estimates have long been a standard part of experimental physics, but the same has not been true on the theoretical side. However, the culture is now changing, and it is becoming more common to include uncertainty estimates in theoretical calculations of atomic and molecular properties. This tutorial paper discusses the progress that has been made in assessing the accuracy of both theory and experiment in a wide variety of circumstances, ranging from the most fundamental measurements of atomic properties such as the electron anomalous magnetic moment and the proton size puzzle in the hydrogen atom to uncertainty estimates for two- and three-electron atoms (helium and lithium), for many-electron atoms and for electron–atom scattering processes. This is followed by a discussion of uncertainties for molecules, and especially the recent remarkable progress for and H2 treated as full three- and four-body problems without the use of the Born–Oppenheimer approximation. The paper includes a discussion of variational methods and the Hylleraas–Undheim–MacDonald theorem, which guarantees variational bounds for excited states as well as for the ground state. This leads naturally to a discussion of the use of pseudostates to perform perturbation sums over intermediate states, and a demonstration calculation for the polarizability of hydrogen. The results of well-defined uncertainty estimates have important implications for both the search for new physics beyond the standard model from high-precision measurements, and for the application of theoretical atomic and molecular data to plasma physics and to astrophysics. [ABSTRACT FROM AUTHOR]

The stability of four fermionic particles with unit charge, of which two are positively and two negatively charged, is discussed. Except for using the simplest approximation of a single Gaussian orbital per particle, the problem is exactly solved variationally by varying the masses to simulate molecular di-hydrogen, mono-muonated di-hydrogen, and di-muonated di-hydrogen. We illustrate the celebrated Born–Oppenheimer approximation 2 years after the occasion of its 90th anniversary. It is suggested that this method is valid only for di-hydrogen. [ABSTRACT FROM AUTHOR]

Quantum chemistry is the branch of chemistry whose primary focus is the application of quantum mechanics to chemical systems at the molecular level. Precisely due to its peculiar position between chemistry and physics, in the last times it has begun to engage the interest of the philosophers of chemistry. Nevertheless, in this philosophical field, quantum chemistry has been studied mainly from a historical viewpoint or from a perspective interested on methodological issues. By contrast, the question that will guide this article is: what kind of ontic items are those studied by quantum chemistry? In order to develop the argumentation, first the relevance of the ontological questions will be addressed. Then, it will be considered in what measure the Born-Oppenheimer approximation and the quantum-chemistry concept of electron fit in the quantum theoretical context. Finally, some issues about what quantum chemistry refers to will be discussed. [ABSTRACT FROM AUTHOR]

We make a critical review of the semiclassical interpretation of quantum cosmology and emphasise that it is not necessary to consider that a concept of time emerges only when the gravitational field is (semi)classical. We show that the usual results of the semiclassical interpretation and its generalisation known as the Born–Oppenheimer approach to quantum cosmology can be obtained by gauge fixing, both at the classical and quantum levels. By "gauge fixing," we mean a particular choice of the time coordinate, which determines the arbitrary Lagrange multiplier that appears in Hamilton's equations. In the quantum theory, we adopt a tentative definition of the (Klein–Gordon) inner product, which is positive definite for solutions of the quantum constraint equation found via an iterative procedure that corresponds to a weak coupling expansion in powers of the inverse Planck mass. We conclude that the wave function should be interpreted as a state vector for both gravitational and matter degrees of freedom, the dynamics of which is unitary with respect to the chosen inner product and time variable. [ABSTRACT FROM AUTHOR]

This paper is a continuation of a previous work [2] about the study of the survival probability modelizing the molecular predissociation in the Born-Oppenheimer framework. Here we consider the critical case where the reference energy corresponds to the value of a crossing of two electronic levels, one of these two levels being confining while the second dissociates. We show that the survival probability associated to a certain initial state is a sum of the usual time-dependent exponential contribution, and a reminder term that is jointly polynomially small with respect to the time and the semiclassical parameter. We also compute explicitly the main contribution of the remainder. [ABSTRACT FROM AUTHOR]

We have calculated ground state interaction energies for an antihydrogen atom and a hydrogen molecule within the Born–Oppenheimer approximation. Leptonic energies were calculated using a large basis set of explicitly correlated Gaussian functions. Energies were calculated at over 2800 geometries including different proton–proton distances. The energies have been fit to functional forms using a neural network for the short-range interaction which is combined with asymptotic formulas at long range. A two-dimensional rigid rotor and a three-dimensional atom–molecule potential energy surface (PES) have been determined. Rigid-rotor scattering calculations on these surfaces have been carried out using the S-matrix Kohn variational method with a two-dimensional Gaussian basis set. We have calculated cross sections for elastic, rotationally inelastic and annihilation collisions on the two-dimensional PES. This includes the first calculation of leptonic annihilation for this system. [ABSTRACT FROM AUTHOR]

Within a tight-binding approximation, we numerically determine the time evolution of graphene electronic states in the presence of classically vibrating nuclei. There is no reliance on the Born-Oppenheimer approximation within the p-orbital tightbinding basis, although our approximation is "atomically adiabatic": the basis p-orbitals are taken to follow nuclear positions. Our calculations show that the strict adiabatic Born-Oppenheimer approximation fails badly. We find that a diabatic (lazy electrons responding weakly to nuclear distortions) Born-Oppenheimer model provides a much more accurate picture and suggests a generalized many-body Bloch orbital-nuclear basis set for describing electron-phonon interactions in graphene. [ABSTRACT FROM AUTHOR]

SCCS- was detected by laser-induced fluorescence spectroscopy in 2003 (M. Nakajima, Y. Yoneda, Y. Sumiyoshi, T. Nagata, Y. Endo, J. Chem. Phys. 119 (2003) 7805) and its spectrum was analyzed and the results presented together with ab initio calculations data. Symmetrical stretching vibrations were assigned in both the ground X 2Πu and the first excited A 2Πg electronic states, but no data about spin-orbit splitting and bending vibrational modes were given. In the present work, the vibronic levels in the ground electronic state of SCCS- were calculated by means of a model developed by Perić and coworkers for the treatment of the Renner-Teller effect in any-atomic linear species in its variational form (M. Mitić, R. Ranković, M. Milovanović, S. Jerosimić, M. Perić, Chem. Phys. 464 (2016) 55) using the ab initio multireference configuration interaction calculations for obtaining potential energy curves in the Born-Oppenheimer approximation. Additionally, the spin-orbit splitting in the ground state was investigated taking into account the interaction with the first excited state, and the energies obtained from combined treatment of vibronic and spin-orbit interactions in the ground state are reported. Finally, based on the present results, several assignments of unidentified bands reported by Nakajima et al. are proposed. [ABSTRACT FROM AUTHOR]

We have investigated the effect of the finite size of the constituent quarks on singlet and triplet nucleon–nucleon potentials, obtained in the framework of the SU(2) nonrelativistic quark model using the resonating group method in the Born–Oppenheimer approximation. The full Hamiltonian used in the investigation includes the kinetic energy, two-body confinement potential, one gluon exchange potential, and instanton induced interaction. The effects of the smearing of the contact interactions and the variation of the constituent mass of the quarks are discussed. [ABSTRACT FROM AUTHOR]

Nearly a century of research has established the Born–Oppenheimer approximation as a cornerstone of condensed-matter systems, stating that the motion of the atomic nuclei and electrons may be treated separately. Interactions beyond the Born– Oppenheimer approximation are at the heart of magneto-elastic functionalities and instabilities. We report comprehensive neutron spectroscopy and ab initio phonon calculations of the coupling between phonons, CEF-split localized 4f electron states, and conduction electrons in the paramagnetic regime of CeAuAl3, an archetypal Kondo lattice compound. We identify two distinct magneto-elastic hybrid excitations that form even though all coupling constants are small. First, we find a CEF–phonon bound state reminiscent of the vibronic bound state (VBS) observed in other materials. However, in contrast to an abundance of optical phonons, so far believed to be essential for a VBS, the VBS in CeAuAl3 arises from a comparatively low density of states of acoustic phonons. Second, we find a pronounced anticrossing of the CEF excitations with acoustic phonons at zero magnetic field not observed before. Remarkably, both magneto-elastic excitations are well developed despite considerable damping of the CEFs that arises dominantly by the conduction electrons. Taking together the weak coupling with the simultaneous existence of a distinct VBS and anticrossing in the same material in the presence of damping suggests strongly that similarly well-developed magneto-elastic hybrid excitations must be abundant in a wide range of materials. In turn, our study of the excitation spectra of CeAuAl3 identifies a tractable point of reference in the search for magneto-elastic functionalities and instabilities. [ABSTRACT FROM AUTHOR]

Nearly a century of research has established the Born–Oppenheimer approximation as a cornerstone of condensed-matter systems, stating that the motion of the atomic nuclei and electrons may be treated separately. Interactions beyond the Born– Oppenheimer approximation are at the heart of magneto-elastic functionalities and instabilities. We report comprehensive neutron spectroscopy and ab initio phonon calculations of the coupling between phonons, CEF-split localized 4f electron states, and conduction electrons in the paramagnetic regime of CeAuAl3, an archetypal Kondo lattice compound. We identify two distinct magneto-elastic hybrid excitations that form even though all coupling constants are small. First, we find a CEF–phonon bound state reminiscent of the vibronic bound state (VBS) observed in other materials. However, in contrast to an abundance of optical phonons, so far believed to be essential for a VBS, the VBS in CeAuAl3 arises from a comparatively low density of states of acoustic phonons. Second, we find a pronounced anticrossing of the CEF excitations with acoustic phonons at zero magnetic field not observed before. Remarkably, both magneto-elastic excitations are well developed despite considerable damping of the CEFs that arises dominantly by the conduction electrons. Taking together the weak coupling with the simultaneous existence of a distinct VBS and anticrossing in the same material in the presence of damping suggests strongly that similarly well-developed magneto-elastic hybrid excitations must be abundant in a wide range of materials. In turn, our study of the excitation spectra of CeAuAl3 identifies a tractable point of reference in the search for magneto-elastic functionalities and instabilities. [ABSTRACT FROM AUTHOR]

Perhaps the hottest topic in the philosophy of chemistry is that of the relationship between chemistry and physics. The problem finds one of its main manifestations in the debate about the nature of molecular structure, given by the spatial arrangement of the nuclei in a molecule. The traditional strategy to address the problem is to consider chemical cases that challenge the definition of molecular structure in quantum–mechanical terms. Instead of taking that top-down strategy, in this paper we face the problem of the reduction of molecular structure to quantum mechanics from a bottom-up perspective: our aim is to show how the theoretical peculiarities of quantum mechanics stand against the possibility of molecular structure, defined in terms of the spatial relations of the nuclei conceived as individual localized objects. We will argue that, according to the theory, quantum "particles" are not individuals that can be identified as different from others and that can be reidentified through time; therefore, they do not have the ontological stability necessary to maintain the relations that can lead to a spatially definite system with an identifiable shape. On the other hand, although quantum chemists use the resources supplied by quantum mechanics with successful results, this does no mean reduction: their "approximations" add certain assumptions that are not justified in the context of quantum mechanics or are even inconsistent with the very formal structure of the theory. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • A new non-Born-Oppenheimer molecular method is presented and used to calculate all 23 bound states of HD+ with L = 1. Abstract In our previous work (Bubin et al., 2016) it was established that complex explicitly-correlated one-center all-particle Gaussian functions (CECGs) provide an effective basis set for very accurate non-relativistic molecular non-Born-Oppenheimer (non-BO) calculations for vibrational ground and excited states corresponding to the rotational ground state. In this work we advance the molecular CECGs approach further by implementing and testing the algorithms for calculating the vibrational states corresponding to the first rotational excited state (the J = 1 state). The test concerns all bound J = 1 rovibrational states of the HD+ ion. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • The pressure-induced order-disorder transition of ice VIII to VII is reproduced. • The measured infrared and Raman spectra are well reproduced by our simulations. • A definite role of the nuclear quantum effects in H 2 O ice is found even at 270 K. Abstract To assess the performance of our implemented first principles isothermal-isobaric centroid molecular dynamics (CMD) we performed Born-Oppenheimer (BO) CMD simulations in the NPT ensemble for high pressure ices (HPIs) VIII, VII, and X at 270 K. By elevating pressure the crystal system is found to transform from tetragonal to cubic at ∼ 30 GPa, accompanying the proton order (ice VIII)-disorder (ice VII) transition observed to occur in our BO-CMD simulations. Moreover, our simulations are proved to be able to reproduce well both infrared and Raman spectra for HPIs in the frequency range above ∼ 500 cm−1. [ABSTRACT FROM AUTHOR]

Abstract Magnetic properties are a very sensitive probe of hydrogen bond interactions. In this work, the magnetic shielding constants of liquid hydrogen cyanide (HCN) were investigated through a combined approach, where quantum mechanical calculations are carried out by using configurations generated by Born-Oppenheimer molecular dynamics (BOMD). Following the trends observed in small HCN clusters, the results for liquid HCN show that the magnetic shielding constant σ (15N) is increased by 10.5 ± 12 ppm relative to its gas phase value, which is in very good agreement with experiment (10 ppm). The shielding of the N atom in the liquid phase of HCN is in contrast to what is observed in liquid ammonia, where the N atom is deshielded relative to the gas phase. By adopting a natural chemical shielding (NCS) analysis, it is shown that the σ d (15N) diamagnetic shielding constant of HCN is not changed when we move from the gas to the liquid phase. Moreover, the results strongly indicate that the gas-to-liquid chemical shift of the 15N atom is essentially determined by the difference between the nitrogen lone-pair (LP) orbital paramagnetic contribution to σ p (15N). The importance of coupling NCS to BOMD configurations for a better understanding of the relationship between hydrogen bonding and the somewhat anomalous shielding of the 15N atom in liquid HCN is stressed. Graphical Abstract Highlights • Born-Oppenheimer molecular dynamics and magnetic properties of liquid HCN • Coupling of natural chemical shielding analysis to Born-Oppenheimer molecular dynamics configurations • The gas-to-liquid chemical shielding of the N atom in HCN is determined by the change of the paramagnetic contribution. • Molecular understanding of the anomalous shielding of the N atom in liquid HCN through natural shielding analysis [ABSTRACT FROM AUTHOR]