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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.

The 39th International Symposium on Lattice Field Theory, LATTICE2022, Bonn, Germany, 8 Aug 2022 - 13 Aug 2022; Proceedings of Science / International School for Advanced Studies (LATTICE2022), 262 (2022). doi:10.22323/1.430.0262, We refine our previous study of a $u d \bar{b} \bar{b}$ tetraquark resonance with quantum numbers $I(J^{P})=0(1^{-})$, which is based on antiheavy-antiheavy lattice QCD potentials, by including heavy quark spin effects via the mass difference of the $B$ and the $B^{*}$ meson. This leads to a coupled channel Schrödinger equation, where the two channels correspond to $BB$ and $B^{*}B^{*}$, respectively. We search for $\mbox{T}$ matrix poles in the complex energy plane, but do not find any indication for the existence of a tetraquark resonance in this refined coupled channel approach. We also vary the antiheavy-antiheavy potentials as well as the $b$ quark mass to further understand the dynamics of this four-quark system., Published by SISSA, Trieste

Starting from a re-analysis of previous work, we construct the proper low energy quantum field theory (QFT) limit of a full quantum gravity theory in the Born-Oppenheimer approach. We separate the gravitational sector into a classical background, given by a vacuum diagonal Bianchi I cosmology, and its quantum perturbations represented by the two graviton degrees of freedom; we further include quantum matter in the form of a test scalar field. We then implement a Born-Oppenheimer separation, where the gravitons and matter play the role of "slow" and "fast" quantum components respectively, and perform a Wentzel-Kramers-Brillouin (WKB) expansion in a Planckian parameter. The functional Schr\"odinger evolution for matter is recovered after averaging over quantum gravitational effects, provided that a condition is imposed on the gravitons' wave functional. Such a condition fixes the graviton dynamics and is equivalent to the purely gravitational Wheeler-DeWitt constraint imposed in previous approaches. The main accomplishment of the present work is to clarify that QFT in curved spacetime can be recovered in the low energy limit of quantum gravity only after averaging over the graviton degrees of freedom, in the spirit of effective field theory. Furthermore, it justifies a posteriori the implementation of the gravitational Wheeler-DeWitt equation on the "slow" gravitons' wave functional rather than assuming its validity a priori., Comment: 8 pages. Title updated and discussion expanded; matches published version

We study magnetic traps with very high trap frequencies where the spin is coupled to the motion of the atom. This allows us to investigate how the Born-Oppenheimer approximation fails and how effective magnetic and electric fields appear as the consequence of the non-adiabatic dynamics. The results are based on exact numerical diagonalization of the full Hamiltonian describing the coupling between the internal and external degrees of freedom. The position in energy and the decay rate of the trapping states correspond to the imaginary part of the resonances of this Hamiltonian and are computed using the complex rotation method., 7 pages, 4 figures, 1 table

We show how linear vibronic spectra in molecular systems can be simulated efficiently using first-principles approaches without relying on the explicit use of multiple Born-Oppenheimer potential energy surfaces. We demonstrate and analyze the performance of mean-field and beyond-mean-field dynamics techniques for the H2 molecule in one dimension, in the later case capturing the vibronic structure quite accurately, including quantum Franck-Condon effects. In a practical application of this methodology we simulate the absorption spectrum of benzene in full dimensionality using time-dependent density functional theory at the multitrajectory Ehrenfest level, finding good qualitative agreement with experiment and significant spectral reweighting compared to commonly used single-trajectory Ehrenfest dynamics. These results form the foundation for nonlinear spectral calculations and show promise for future application in capturing phenomena associated with vibronic coupling in more complex molecular and potentially condensed phase systems This work was supported by the European Research Council (ERC-2015-AdG694097), the Cluster of Excellence Advanced Imaging of Matter (AIM), JSPS KAKENHI Grant Number 20K14382, Grupos Consolidados (IT1249-19), and SFB925. The Flatiron Institute is a division of the Simons Foundation

The dynamics of the H + H2+ reaction has been analyzed from the electronically first excited state of diabatic potential energy surfaces constructed by employing the Beyond Born-Oppenheimer theory [J. Chem. Phys. 2014, 141, 204306]. We have employed the coupled 3D time-dependent wavepacket formalism in hyperspherical coordinates for multisurface reactive scattering problems. To be specific, the charge transfer processes have been investigated extensively by calculating state-to-state as well as total reaction probabilities and integral cross sections, when the reaction process is initiated from the first excited electronic state (21A'). We have depicted the convergence profiles of reaction probabilities for the competing charge transfer processes, namely, reactive charge transfer (RCT) and nonreactive charge transfer (NRCT) processes for different total energies with respect to total angular momentum, J. Total and state-to-state integral cross sections are calculated as a function of total energy for the initial rovibrational state, namely, v = 0, j = 0 level of H2+ (2Σg+) molecule and are compared with previous theoretical calculations. Finally, we have calculated temperature-dependent rate constants using our presently evaluated cross sections and compared their average with the experimentally measured one.

Hydroxyl radicals (OH*) play a crucial role in atmospheric chemistry and biological processes. In this study, Born-Oppenheimer molecular dynamics simulations are performed under ambient conditions for a hydroxyl radical in a water nanodroplet containing 191 water molecules. Density functional theory calculations are performed at the BLYP-D3 level with some test calculations at the B3LYP-D3 level. In two 150 ps trajectories, either with OH* initially located in the interior region or at the surface of the water nanodroplet, the OH* radical ends up in the subsurface layer of the nanodroplet, which is different from the "surface preference" predicted from previous empirical force field simulations. The solvation structure of OH* contains fluctuating hydrogen bonds, as well as a two-center three-electron hemibond in some cases. The mobility of OH* is enhanced by hydrogen transfer, which has a free energy barrier of ∼4.6 kcal mol-1. The results presented in this study deepen our understanding of the structure and dynamics of OH* in aqueous solutions, especially around the air-water interface.

Non-adiabatic couplings between Born–Oppenheimer (BO)-derived potential energy surfaces are now recognized as pivotal in describing the non-radiative decay of electronically excited molecules following photon absorption. This opinion piece illustrates how non-BO effects provide photostability to many biomolecules when exposed to ultraviolet radiation, yet in many other cases are key to facilitating ‘reactive’ outcomes like isomerization and bond fission. The examples are presented in order of decreasing molecular complexity, spanning studies of organic sunscreen molecules in solution, through two families of heteroatom containing aromatic molecules and culminating with studies of isolated gas phase H 2 O molecules that afford some of the most detailed insights yet available into the cascade of non-adiabatic couplings that enable the evolution from photoexcited molecule to eventual products. This article is part of the theme issue 'Chemistry without the Born–Oppenheimer approximation'.

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.

We re-examine the (inverse) Fermi accelerator problem by resorting to a quantum trajectory description of the dynamics. Quantum trajectories are generated from the time-independent Schrodinger equation solutions, using a unipolar treatment for the (light) confined particle and a bipolar treatment for the (heavy) movable wall. Analytic results are presented for the exact coupled two-dimensional problem, as well as for the adiabatic and mixed quantum-classical approximations.

Extended Lagrangian Born-Oppenheimer molecular dynamics [ Phys. Rev. Lett. 2008, 100, 123004] is presented for Hartree-Fock theory, where the extended electronic degrees of freedom are represented by a density matrix, including fractional occupation numbers at elevated electronic temperatures. In contrast to regular direct Born-Oppenheimer molecular dynamics simulations, no iterative self-consistent field optimization is required prior to the force evaluations. To sample regions of the potential energy landscape where the gap is small or vanishing, which leads to particular convergence problems in regular direct Born-Oppenheimer molecular dynamics simulations, an adaptive integration scheme for the extended electronic degrees of freedom is presented. The integration scheme is based on a tunable, low-rank approximation of a fourth-order kernel, [Formula: see text], that determines the metric tensor, [Formula: see text], used in the extended harmonic oscillator of the Lagrangian that generates the dynamics of the electronic degrees of freedom. The formulation and algorithms provide a general guide to implement extended Lagrangian Born-Oppenheimer molecular dynamics for quantum chemistry, density functional theory, and semiempirical methods using a density matrix formalism.

The quantum mechanical treatment of both electrons and nuclei is crucial in nonadiabatic dynamical processes such as proton-coupled electron transfer. The nuclear-electronic orbital (NEO) method provides an elegant framework for including nuclear quantum effects beyond the Born-Oppenheimer approximation. To enable the study of nonequilibrium properties, we derive and implement a real-time NEO (RT-NEO) approach based on time-dependent Hatree-Fock or density functional theory, in which the electronic and nuclear degrees of freedom are propagated in a time-dependent variational framework. Nuclear and electronic spectral features can be resolved from the time-dependent dipole moment computed using the RT-NEO method. The test cases show the dynamical interplay between the quantum nuclei and the electrons through vibronic coupling. Moreover, vibrational excitation in the RT-NEO approach is demonstrated by applying a resonant driving field, and electronic excitation is demonstrated by simulating excited state intramolecular proton transfer. This work shows that the RT-NEO approach is a promising tool to study nonadiabatic quantum dynamical processes within a time-dependent variational description for the coupled electronic and nuclear degrees of freedom.

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.

The reaction of chlorine atom Cl(2P) (Cl(2P3/2) and Cl∗(2P1/2)) with D2 was investigated at collision energy from 4.5 kcal/mol to 6.5 kcal/mol with a high-resolution crossed molecular beam apparatus using the technique of D-atom Rydberg tagging detection. The contribution from the spin-orbit excited reaction Cl∗(2P1/2)+D2, which is prohibited by Born-Oppenheimer (BO) approximation, was observed. Collision-energy dependence of differential cross sections (DCSs) near the backward scattering direction was measured. The BO-forbidden reaction Cl∗+D2 was found to be dominant at lower collision energy. As collision energy increases, reactivity of BO-allowed reaction Cl+D2 increases much faster than that of BO-forbidden reaction and becomes dominant at higher collision energy. Our experiment indicates that the additional energy of spin-orbit excitation in Cl∗ facilitates BO-forbidden reaction to pass through the barrier at lower collision energy, while BO approximation is still valid at collision energy near and above the reaction barrier. This tendency of reactivity of Cl/Cl∗+D2 is similar to the isotopic reaction of Cl/Cl∗+H2.

The major bottleneck of first principle based beyond Born–Oppenheimer (BBO) treatment originates from large number and complicated expressions of adiabatic to diabatic transformation (ADT) equation...

The reaction dynamics of a photochemical reaction is typically described by reaction coordinates based on the Born-Oppenheimer (BO) approximation. A strong interaction between electrons and nuclei, conventionally occurring at conical intersections, however, breaks the BO approximation and has major consequences for the efficiency of a photochemical reaction. Despite its importance, related studies into the non-BO dynamics are scarce. Here, we investigate the non-BO dynamics of excited-state intramolecular proton transfer (ESIPT) occurring in 10-hydroxybenzo[h]quinoline (HBQ). Two coherent vibrational modes at 237 and 794 cm-1 representing molecular dynamics on a diabatic surface in HBQ are identified by a wave packet analysis based on a transient absorption measurement with a time resolution of 11 fs and with a density functional theory-based model calculation. It is also revealed that the strong Coulomb field effect in HBQ leads to the completion of ESIPT within about two cycles of the OH stretching mode. The work paves the way for time-domain studies of molecular dynamics beyond the BO approximation in other photochemical reactions.

Mass-dependent diagonal Born–Oppenheimer corrections (DBOCs) to the ab initio electronic ground state potential energy surface for the main 16O3 isotopologue and for homogeneous isotopic substitutions 17O3 and 18O3 of the ozone molecule are reported for the first time. The system being of strongly multiconfigurational character, multireference configuration interaction wave function ansatz with different complete active spaces was used. The reliable DBOC calculations with the targeted accuracy were possible to carry out up to about half of the dissociation threshold D0. The comparison with the experimental band centers shows a significant improvement of the accuracy with respect to the best Born–Oppenheimer (BO) ab initio calculations reducing the total root-mean-squares (calculated–observed) deviations by about a factor of two. For the set of 16O3 vibrations up to five bending and four stretching quanta, the mean (calculated–observed) deviations drop down from 0.7 cm−1 (BO) to about 0.1 cm−1, with the most pronounced improvement seen for bending states and for mixed bending-stretching polyads. In the case of bending band centers directly observed under high spectral resolutions, the errors are reduced by more than an order of magnitude down to 0.02 cm−1 from the observed levels, approaching nearly experimental accuracy. A similar improvement for heavy isotopologues shows that the reported DBOC corrections almost remove the systematic BO errors in vibrational levels below D0/2, though the scatter increases towards higher energies. The possible reasons for this finding, as well as remaining issues are discussed in detail. The reported results provide an encouraging accuracy validation for the multireference methods of the ab initio theory. New sets of ab initio vibrational states can be used for improving effective spectroscopic models for analyses of the observed high-resolution spectra, particularly in the cases of accidental resonances with “dark” states requiring accurate theoretical predictions.

We present an improved Born-Oppenheimer method for the treatment of molecules. Our development is based on taking into account a portion of the kinetic energy which was inadvertently omitted by Born and Oppenheimer. Our theory replaces the set of standard atom-atom potentials by an evolution operator. In particular, in contrast to the traditional Born-Oppenheimer method our amended basis describes the so-called Wannier phenomenon which deforms potential surfaces, and traps one or more threshold electrons into an unstable equilibrium. Within our framework that trapping manifests itself as a Fresnel distribution. Finally we discover a π/2 phase jump in the evolution operator caused by the diffraction of a two-electron wave from a potential ridge.

We employ a recently amended Born-Oppenheimer (hereafter shortly BO) approximation [1] to treat inelastic scattering of slow electrons from highly excited Rydberg atoms like e- + He(1s ns)→He-** for n ≫ 1. Along these lines we replace the standard BO set of potentials by an evolution operator. In this way we take a momentum-momentum coupling inadvertently disregarded by BO into account. The BO eigenvalue problem is now replaced by an evolution equation. One eigen-evolution has been identified as Wanner channel. That channel describes the diffraction of electron pairs from a potential ridge. That diffraction causes a phase jump of π/2 in the channel evolution. Moreover we present a new conservative attractive force controlling the motion of the electron pair as a whole in the nuclear field whose potential is given by . The coupling constant g has been calculated. That potential foreign to the standard BO approximation manifests itself by an entirely new series of isolated resonances located slightly below the double ionization threshold. This resonance ensemble compares favorably with experimental data. Further we present an evolution which forces the electron pair to the electrostatically unstable top of the potential ridge. That evolution may be regarded as quantum version of Wannier’s converging trajectory, and manifests itself here as Fresnel distribution.

Adiabatic potential energy curves (APEC) of the singlet (s) and triplet (t) Sigma+, Pi, and Delta electronic states have been calculated for the NaK molecule. All results of the presented molecular states have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing the interaction of valence electrons with atomic cores. In this approach, only the valence electrons of the Na and K atoms were treated explicitly. The core polarization potential has been also applied in calculations. Additionally, a bespoke basis set, generated and optimized for both ground and excited electronic states of the NaK system was developed. All computations were performed by means of the MOLPRO program package. Reported potentials are ready to compare with the results of other theoretical results and potential energy curves derived from experiments.

We study the Shannon entropy and the Fisher information in a non-Born-Oppenheimer (nBO) regime, where these quantities are constructed from one-particle densities obtained from an exact nBO analytic wave function for a Coulomb-Hooke model of a four-particle system. This model consists of two electrons and two protons with Coulombic interactions between like particles and Hookean interactions otherwise [ Becerra , M. et al. Int. J. Quantum Chem 2013 , 113 ( 10 ), 1584 - 1590 ]. In the nBO case, there arise densities for both the nuclei and electrons. Furthermore, these densities vary with respect to a particular point of reference from which they are calculated. We consider, in the present work, electron and nuclear densities calculated from the following reference points: a global center of mass, the geometric center between the electrons, and the geometric center between the protons. A comparison of the nBO Shannon entropy and Fisher information, with respect to their counterparts computed from Born-Oppenheimer densities, suggests that the former quantities provide more insights into the chemical reactivity because of the nonuniqueness nature of the nBO electron density as well as the availability and access to the nBO nuclear density. Finally, some comments are made concerning the nBO vs the BO regimes in relation to this particular chemical reactivity indicator.

Born–Oppenheimer molecular dynamics simulations with PBE-D3/GTH-DZVP potentials were utilized to explore molecular mechanism of alkali metal cation binding to the calix[4]arene. The calculated standard Gibbs free energy decreased to the higher extent upon binding in case of Cs+ and Rb+ compared to Li+, Na+ and K+. The experimentally observed selectivity was attributed to the stronger coordination shells of Cs+ and Rb+ in the calixarene-bound state compared with the water-coordinated complexes as revealed by electron density analysis.

This paper is devoted to the asymptotic analysis of the eigenvalues of the Laplace operator with a strong magnetic field and Robin boundary condition on a smooth planar domain and with a negative boundary parameter. We study the singular limit when the Robin parameter tends to infinity, which is equivalent to a semi-classical limit involving a small positive semi-classical parameter. The main result is a comparison between the spectrum of the Robin Laplacian with an effective operator defined on the boundary of the domain via the Born–Oppenheimer approximation. More precisely, the low-lying eigenvalue of the Robin Laplacian is approximated by those of the effective operator. When the curvature has a unique non-degenerate maximum, we estimate the spectral gap and find that the magnetic field does not contribute to the three-term expansion of the eigenvalues. In the case of the disc domains, the eigenvalue asymptotics displays the contribution of the magnetic field explicitly.

We present a review of extended Lagrangian Born–Oppenheimer molecular dynamics and its most recent development. The molecular dynamics framework is first derived for general Hohenberg–Kohn density functional theory and it is then presented in explicit forms for thermal Hartree–Fock theory using a density matrix formalism, for self-consistent charge density functional tight-binding theory, and for general non-linear charge relaxation models that can be designed and optimized using modern machine learning methods. Our intention is to give a self-contained but brief and hopefully pedagogical presentation.

The static dipole polarizabilities of the first three lowest states of hydrogen molecules ${\mathrm{H}}_{2}$, HD, and ${\mathrm{D}}_{2}$ are calculated using variationally generated wave functions in Hylleraas coordinates without using the Born-Oppenheimer approximation. Our results for ${\mathrm{H}}_{2}$ and HD are two orders of magnitude more accurate than the best literature values. We also improve the previous best results for ${\mathrm{D}}_{2}$.

The coupling of a molecule and a cavity induces nonadiabaticity in the molecule which makes the description of its dynamics complicated. For polyatomic molecules, reduced-dimensional models and the use of the Born–Oppenheimer approximation (BOA) may remedy the situation. It is demonstrated that contrary to expectation, BOA may even fail in a one-dimensional model and is generally expected to fail in two- or more-dimensional models due to the appearance of conical intersections induced by the cavity., The coupling of a molecule and a cavity induces nonadiabaticity in the molecule which makes the description of its dynamics complicated.

This paper is a continuation of a previous work 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., 37 pages, 1 figure

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 tight-binding 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.

The Born Oppenheimer (BO) and Renner Teller (RT) time dependent quantum dynamics are investigated for the reaction ND a 1 Δ + D ′ ( 2 S ) , considering the NH2 electronic states X ∼ 2 B 1 and A ∼ 2 A 1 . The introduction of RT effects opens the possibility of studying not only the adiabatic reactions (depletion- A N(2D) + D2(a1Δ) and Exchange ND’+(a1Δ) + D) but also non-adiabatic ones (quenching + exchange N D ′ ( X 3 Σ - ) + D , depletion- X N(4S) + D2(a1Δ)). The initial state resolved reaction probabilities, cross sections, and rate constants are obtained considering the Coriolis Coupling (CC) interactions for all the reactions above. To point out the role of RT and CC effect, we compared our results with experimental and semi- classical data.

The nuclear-electronic orbital (NEO) method treats specified nuclei, typically protons, quantum mechanically on the same level as the electrons. This approach invokes the Born-Oppenheimer separation between the quantum and classical nuclei, as well as the conventional separation between the electrons and classical nuclei. To test the validity of this additional adiabatic approximation, herein the diagonal Born-Oppenheimer correction (DBOC) within the NEO framework is derived, analyzed, and calculated numerically for a set of eight molecules. Inclusion of the NEO DBOC is found to change the equilibrium bond lengths by only ∼10

This paper presents molecular dynamics calculations of vibrational energy transfer and nonequilibrium dissociation in O2+O collisions. The O2+O interactions are modeled using nine potential energy ...

The Born-Oppenheimer adiabatic limit applies broadly in chemistry because most reactions occur on the ground electronic state. Photochemical reactions involve two or more electronic states and need not be subject to this adiabatic limit. The spectroscopic signatures of nonadiabatic processes are subtle, and therefore, experimental investigations have been limited to the few systems dominated by single photochemical outcomes. Systems with branched excited-state pathways have been neglected, despite their potential to reveal insights into photochemical reactivity. Here we present experimental evidence from coherent three-dimensional electronic spectroscopy that the E to Z photoisomerization of phytochrome Cph1 is strongly nonadiabatic, and the simulations reproduce the measured features only when the photoisomerization proceeds nonadiabatically near, but not through, a conical intersection. The results broaden the general understanding of photoisomerization mechanisms and motivate future studies of nonadiabatic processes with multiple outcomes arising from branching on excited-state potential energy surfaces.

Fil: Accorinti, Hernán. Universidad de Buenos Aires; Argentina. Fil: Accorinti, Hernán. Agencia Nacional de Promoción Científica y Tecnológica; Argentina. Fil: Martínez González, Juan Camilo. Universidad de Buenos Aires; Argentina. Fil: Martínez González, Juan Camilo. Conicet; Argentina. Accorinti, H. y Martínez González, J. C. (2019). ¿Qué tan cuántica es la química cuántica? Metatheoria, 9(2), 5-18. El propósito del presente trabajo será poner de manifiesto que la química cuántica es una disciplina basada primariamente en modelos, y no en teorías que establecen un marco conceptual específico y autónomo. Esta característica permitirá preguntar qué tan cuántica es la química cuántica que se incorpora precisamente a esos modelos. Para ello analizaremos la aproximación Born-Oppenheimer y los modelos de Enlace de Valencia y de Orbital Molecular. Nuestra intuición es que, en la medida en que sea necesario mantener la noción clásica de estructura molecular para dar cuenta de los comportamientos de las sustancias, la química cuántica adquiere, como propiedad distintiva, un carácter híbrido entre la mecánica clásica y la mecánica cuántica. The purpose of this paper is to show that quantum chemistry is a discipline based primarily on models, and not on theories that establish a specific and autonomous conceptual framework. This feature will allow us to question how quantum is the quantum chemistry incorporated in those models. For this purpose, we will analyze the Born-Oppenheimer approximation and the Valence Bond and Molecular Orbital models. Our intuition is that, to the extent that maintaining the classical notion of molecular structure is necessary to account for the behavior of substances, quantum chemistry acquires, as a distinctive property, a hybrid character between classical mechanics and quantum mechanics.

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.

We report a study of non-covalent complexes of phosphopeptides pXAAAA and N-Ac-pXAAAA (X = Ser, Thr, Tyr) with arginine-containing peptides carrying diazirine 4,4-azipentyl tags at the N-terminus, *LGG(A)nR, or in the photoleucine residue, L*GG(A)nR (n = 3–5). Complexes with *LGG(A)nR were successfully generated as singly charged ions in the gas phase in 0.6–3.5% yields. In contrast, complexes with L*GG(A)nR were formed in negligible ( H bonds (X C, N, O) in the phosphopeptide. BOMD in combination with structural analysis by density functional theory calculations were used to interpret the experimental data and explain the cross-linking efficiencies.

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 σd(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 σp(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.

We report the structural and energetic features of the Mg2+ and Ca2+ cations in ammonia microsolvation environments. Born-Oppenhemier molecular dynamics studies are carried out for [Mg(NH3)n]2+ and [Ca(NH3)n]2+ clusters with n = 2, 3, 4, 6, 8, 20, and 27 at 300 K based on hybrid density functional theory calculations. We determine binding energies per ammonia molecule and the metal cation solvation patterns as a function of the number of molecules. The general trend for Mg2+ is that the Mg-N distances increase as a function of n until the first solvation shell is populated by six ammonia molecules, and then the distances slightly decrease while CN = 6 does not change. For Ca2+, the first solvation shell at room temperature is populated by eight ammonia molecules for clusters with more than one solvation shell, leading to a different structure from that of [Ca(NH3)6]2+ hexamine. The evaporation of NH3 molecules was found at 300 K only for Mg2+ clusters with n ≥ 10; this was not the case for Ca2+ clusters. Vibrational spectra are obtained for all of the clusters, and the evolution of the main features is discussed. EXAFS spectra are also presented for the [Mg(NH3)27(NH3)27]2+ and [Ca(NH3)27]2+ clusters, which yield valuable data to be compared with experimental data in the liquid phase, as previously done for the aqueous solvation of these dications.

Extended Lagrangian Born-Oppenheimer molecular dynamics (XL-BOMD) [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] is formulated for orbital-free Hohenberg-Kohn density-functional theory and for charge equilibration and polarizable force-field models that can be derived from the same orbital-free framework. The purpose is to introduce the most recent features of orbital-based XL-BOMD to molecular dynamics simulations based on charge equilibration and polarizable force-field models. These features include a metric tensor generalization of the extended harmonic potential, preconditioners, and the ability to use only a single Coulomb summation to determine the fully equilibrated charges and the interatomic forces in each time step for the shadow Born-Oppenheimer potential energy surface. The orbital-free formulation has a charge-dependent, short-range energy term that is separate from long-range Coulomb interactions. This enables local parameterizations of the short-range energy term, while the long-range electrostatic interactions can be treated separately. The theory is illustrated for molecular dynamics simulations of an atomistic system described by a charge equilibration model with periodic boundary conditions. The system of linear equations that determines the equilibrated charges and the forces is diagonal, and only a single Ewald summation is needed in each time step. The simulations exhibit the same features in accuracy, convergence, and stability as are expected from orbital-based XL-BOMD.

Using Born–Oppenheimer ab initio molecular dynamics (BOAIMD) simulations, the high-density water (HDW) and low-density water (LDW) structures based on SCAN meta-GGA are compared with those based on PBE GGA. Compared with Car–Parrinello ab initio molecular dynamics (CPAIMD) simulations, BOAIMD simulations can produce more accurate results because no fictitious electron mass is introduced. At each state point, our simulations continue for 100 ps after the system reached equilibrium, which is the longest ab initio simulations of liquid water reported so far and can ensure an accurate statistical average. The influence of the size effect and nuclear quantum effect on structure is not considered in the present work, but only that of two different functionals on the structure is discussed. It is found that, in HDW, just as shown using CPAIMD simulations, the SCAN-based hydrogen-bonds (HBs) are more flexible than the PBE-based ones, which makes the structure based on SCAN obviously closer to the experimental results than that based on PBE. However, it is not the case in LDW, and the difference between the results based on these two functionals is very small.

The precision of the photoassociation spectroscopy of Yb dimer in degenerate gases is enough to improve the constraints on the new short-range gravity-like forces if the theoretical knowledge of the Born-Oppenheimer interatomic potential and non-Born-Oppenheimer interactions is refined [M. Borkowski et al. Sci. Rep. A {\bf 9}, 14807 (2019)]. The ground-state interaction potential of ytterbium dimer is investigated at the eXact 2-component core-correlated CCSD(T) level of {\it ab initio} theory in the complete basis set limit with extensive augmentation by diffuse functions. For the small basis set the comparison is made with the four-component relativistic finite-nuclei CCSD(T) calculations to identify the contraction of the dimer bond length as the main unrecoverable consequence of the scalar-relativistic approximation. Empirical constraint on the number of bound vibrational energy levels of the $^{174}$Yb$_2$ dimer is accounted for by representing the global {\it ab initio}-based Born-Oppenheimer potential with the model semianalytical function containing the scale and shift parameters. The results support the previous evaluation of the Yb dimer potentials from the photoassociation spectroscopy data and provide an accurate and flexible reference for future refinement of the constraints on the short-range gravity-like forces by ultracold atomic spectroscopy., Comment: 1 figure, 18 pages (version of record)

Starting from a Born-Oppenheimer decomposition of the Wheeler-DeWitt equation for the quantum cosmology of the matter-gravity system, we have performed a Wigner-Weyl transformation and obtained equations involving a Wigner function for the scale factor and its conjugate momentum. This has allowed us to study in more detail than previously the approach to the classical limit of gravitation and the way time emerges in such a limit. To lowest order we reproduce the Friedmann equation and the previously obtained equation for the evolution of matter. We also obtain expressions for higher order corrections to the semi-classical limit., Comment: 15 pages, no figures

We analyze the decays of the theoretically predicted lowest bottomonium hybrid $H(1P)$ to open bottom two-meson states. We do it by embedding a quark pair creation model into the Born-Oppenheimer framework which allows for a unified, QCD-motivated description of bottomonium hybrids as well as bottomonium. A new $^{1}\!P_{1}$ decay model for $H(1P)$ comes out. The same analysis applied to bottomonium leads naturally to the well-known $^{3}\!P_{0}$ decay model. We show that $H(1P)$ and the theoretically predicted bottomonium state $\Upsilon(5S)$, whose calculated masses are close to each other, have very different widths for such decays. A comparison with data from $\Upsilon(10860)$, an experimental resonance whose mass is similar to that of $\Upsilon(5S)$ and $H(1P)$, is carried out. Neither a $\Upsilon(5S)$ nor a $H(1P)$ assignment can explain the measured decay widths. However, a $\Upsilon(5S)$-$H(1P)$ mixing may give account of them supporting previous analyses of dipion decays of $\Upsilon(10860)$ and suggesting a possible experimental evidence of $H(1P)$., Comment: 9 pages; v2: new title, major additions and modifications in the article body; v3: slight change in the title, new reference, clarifications and minor modifications in the article body

We report on highly accurate calculations of Born-Oppenheimer potentials for excited n Σ+ states of the hydrogen molecule for all possible combinations of singlet/triplet and gerade/ungerade symmetries up to n = 7. A relative accuracy of 10−10 (0.00002 cm−1) or better is achieved for all the internuclear distances and all the excited states under consideration—an improvement with respect to the best results available in the literature by at least 6 orders of magnitude. Presented variational calculations rely on efficient evaluation of molecular integrals with the explicitly correlated exponential basis in arbitrary precision arithmetics.

International audience; We develop a formalism to accurately account for the renormalization of 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 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 200K and 250 GPa and discuss the optical absorption profile of hydrogen crystal at 200K and carbon diamond at 297K.

The scope of this paper is to compare two different approaches for solving the Wheeler-DeWitt (WDW) equation in the presence of homogeneous matter (inflaton) and perturbations around it. The standard Born-Oppenheimer (BO) decomposition, which consists of factorizing out the gravitational wave function and then defining the flow of the time through it, and a more general BO decomposition where the whole minisuperspace wave function is factorized out. The two approaches are compared, for simplicity, in the case of a minimally coupled inflaton with a flat potential. The consistency of the latter decomposition is checked against the former by comparing the resulting perturbation (Mukhanov-Sasaki) equations. Finally a few solutions to the homogeneous WDW not suitable for the traditional BO treatment are presented and the corresponding Mukhanov-Sasaki equations are evaluated., 21 pages, no figures

We discuss a simple singular system in two dimension, two heavy particles interacting with a light particle via an attractive contact interaction. Although intuitively clear the actual application of the Born-Oppenheimer type approximation to this problem is quite subtle. The light particle ground state energy is not bounded from below when we consider it as a function of heavy particles’ separation. Nevertheless, with due care, we calculate the leading term of the Born-Oppenheimer type approximation and indicate how to get the higher order corrections.

U ovom radu, ispituje se valjanost upotrebe adijabatske Born-Oppenheimer aproksimacije kod opisa interakcije elektrona i jezgara u visoko dopiranom grafenu. Usporedbom rezultata modela čvrste veze i teorije funkcionala gustoće (DFT) za disperziju fonona dopiranog grafena, pokazuje se da adijabatski tretman fonona dovodi do velike renormalizacije E_2g fononskog moda u Γ točki, što nije ispravan rezultat. Kako bi se dobio ispravan vibracijski spektar, potrebno je uključiti dinamičke (neadijabatske) efekte elektron-fonon interakcije. Oni izazivaju velike promjene u dugovalnom dijelu vibracijskog spektra. Neadijabatska korekcija dobivena je kroz vlastitu energiju fonona, a efekt je dokazan i u DFT-u izračunom elektron-fonon interakcije. Metoda je zatim primijenjena na dopirani grafan. Dinamički efekti u dopiranom grafanu izraženiji su nego u dopiranom grafenu. In this seminar the validity of an adiabatic Born-Oppenheimer approximation in the description of electron-phonon interactions in highly doped graphene is examined. Comparing the tight - binding approximation model results and the ones obtained within density functional theory (DFT), it is shown that an adiabatic treatment of phonons leads to a huge renormalization of the E_2g phonon mode in the Brillouin zone center, which is an incorrect result. In order to obtain a correct vibration spectrum, dynamical (nonadiabatic) effects of an electron-phonon interaction should be taken into account. They produce non-negligible changes in the long-wave part of the spectrum. Nonadiabatic correction is obtained through phonon self-energy calculation, while its effect is proved also within a DFT calculation of electron-phonon interaction parameters. This method is then applied to doped graphane. Dynamical effects in doped graphane are more pronounced than in doped graphene.