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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]

Regarding the correlated electron-nuclear motion in a model system, we investigate the dynamics in the vicinity of a conical intersection (CoIn) between two excited state potential surfaces. It is documented that an ensemble of classical trajectories which move in the complete electronic-nuclear phase space tracks the quantum wave-packet motion through the CoIn which is accompanied by a non-adiabatic population transfer. On the contrary, for an adiabatic circular motion around the position of the CoIn, the quantum mechanical and classical densities deviate substantially. In the latter case, the Born-Oppenheimer classical nuclear motion on a single potential surface is able to track the quantum dynamics. [ABSTRACT FROM AUTHOR]

The diagonal Born-Oppenheimer correction (DBOC) stems from the diagonal second derivative coupling term in the adiabatic representation, and it can have an arbitrary large magnitude when a gap between neighbouring Born-Oppenheimer (BO) potential energy surfaces (PESs) is closing. Nevertheless, DBOC is typically neglected in mixed quantum-classical methods of simulating nonadiabatic dynamics (e.g., fewest-switch surface hopping (FSSH) method). A straightforward addition of DBOC to BO PESs in the FSSH method, FSSH+D, has been shown to lead to numerically much inferior results for models containing conical intersections. More sophisticated variation of the DBOC inclusion, phase-space surface-hopping (PSSH) was more successful than FSSH+D but on model problems without conical intersections. This work comprehensively assesses the role of DBOC in nonadiabatic dynamics of two electronic state problems and the performance of FSSH, FSSH+D, and PSSH methods in variety of one- and two-dimensional models. Our results show that the inclusion of DBOC can enhance the accuracy of surface hopping simulations when two conditions are simultaneously satisfied: (1) nuclei have kinetic energy lower than DBOC and (2) PESs are not strongly nonadiabatically coupled. The inclusion of DBOC is detrimental in situations where its energy scale becomes very high or even diverges, because in these regions PESs are also very strongly coupled. In this case, the true quantum formalism heavily relies on an interplay between diagonal and off-diagonal nonadiabatic couplings while surface hopping approaches treat diagonal terms as PESs and off-diagonal ones stochastically. [ABSTRACT FROM AUTHOR]

The influence of nuclear dynamics in the electronic ground state on the (e,2e) momentum profiles of dimethyl ether has been analyzed using the harmonic analytical quantum mechanical and Born- Oppenheimer molecular dynamics approaches. In spite of fundamental methodological differences, results obtained with both approaches consistently demonstrate that molecular vibrations in the electronic ground state have a most appreciable influence on the momentum profiles associated to the 2b1, 6a1, 4b2, and 1a2 orbitals. Taking this influence into account considerably improves the agreement between theoretical and newly obtained experimental momentum profiles, with improved statistical accuracy. Both approaches point out in particular the most appreciable role which is played by a few specific molecular vibrations of A1, B1, and B2 symmetries, which correspond to C-H stretching and H-C-H bending modes. In line with the Herzberg-Teller principle, the influence of these molecular vibrations on the computed momentum profiles can be unraveled from considerations on the symmetry characteristics of orbitals and their energy spacing. [ABSTRACT FROM AUTHOR]

With recent developments in simulating nonadiabatic systems to high accuracy, it has become possible to determine how much energy is attributed to nuclear quantum effects beyond zero-point energy. In this work, we calculate the non-relativistic ground-state energies of atomic and molecular systems without the Born-Oppenheimer approximation. For this purpose, we utilize the fixed-node diffusion Monte Carlo method, in which the nodes depend on both the electronic and ionic positions. We report ground-state energies for all systems studied, ionization energies for the first-row atoms and atomization energies for the first-row hydrides. We find the ionization energies of the atoms to be nearly independent of the Born-Oppenheimer approximation, within the accuracy of our results. The atomization energies of molecular systems, however, show small effects of the nonadiabatic coupling between electrons and nuclei. [ABSTRACT FROM AUTHOR]

The influence of thermally induced nuclear dynamics (molecular vibrations) in the initial electronic ground state on the valence orbital momentum profiles of furan has been theoretically investigated using two different approaches. The first of these approaches employs the principles of Born-Oppenheimer molecular dynamics, whereas the so-called harmonic analytical quantum mechanical approach resorts to an analytical decomposition of contributions arising from quantized harmonic vibrational eigenstates. In spite of their intrinsic differences, the two approaches enable consistent insights into the electron momentum distributions inferred from new measurements employing electron momentum spectroscopy and an electron impact energy of 1.2 keV. Both approaches point out in particular an appreciable influence of a few specific molecular vibrations of A1 symmetry on the 9a1 momentum profile, which can be unravelled from considerations on the symmetry characteristics of orbitals and their energy spacing. [ABSTRACT FROM AUTHOR]

We propose a methodology to unify electronic and nuclear quantum wavepacket dynamics in molecular processes including nonadiabatic chemical reactions. The canonical and traditional approach in the full quantum treatment both for electrons and nuclei rests on the Born–Oppenheimer fixed nuclei strategy, the total wavefunction of which is described in terms of the Born–Huang expansion. This approach is already realized numerically but only for small molecules with several number of coupled electronic states for extremely hard technical reasons. Besides, the stationary-state view of the relevant electronic states based on the Born–Oppenheimer approximation is not always realistic in tracking real-time electron dynamics in attosecond scale. We therefore incorporate nuclear wavepacket dynamics into the scheme of nonadiabatic electron wavepacket theory, which we have been studying for a long time. In this scheme thus far, electron wavepackets are quantum mechanically propagated in time along nuclear paths that can naturally bifurcate due to nonadiabatic interactions. The nuclear paths are in turn generated simultaneously by the so-called matrix force given by the electronic states involved, the off-diagonal elements of which represent the force arising from nonadiabatic interactions. Here we advance so that the nuclear wavepackets are directly taken into account in place of path (trajectory) approximation. The nuclear wavefunctions are represented in terms of the Cartesian Gaussians multiplied by plane waves, which allows for feasible calculations of atomic and molecular integrals together with the electronic counterparts in a unified manner. The Schrödinger dynamics of the simultaneous electronic and nuclear wavepackets are to be integrated by means of the dual least action principle of quantum mechanics [K. Takatsuka, J. Phys. Commun. 4, 035007 (2020)], which is a time-dependent variational principle. Great contributions of Vincent McKoy in the electron dynamics in the fixed nuclei approximation and development in time-resolved photoelectron spectroscopy are briefly outlined as a guide to the present work. [ABSTRACT FROM AUTHOR]

We present an efficient general approach to first principles molecular dynamics simulations based on extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] in the limit of vanishing self-consistent field optimization. The reduction of the optimization requirement reduces the computational cost to a minimum, but without causing any significant loss of accuracy or long-term energy drift. The optimization-free first principles molecular dynamics requires only one single diagonalization per time step, but is still able to provide trajectories at the same level of accuracy as 'exact,' fully converged, Born-Oppenheimer molecular dynamics simulations. The optimization-free limit of extended Lagrangian Born-Oppenheimer molecular dynamics therefore represents an ideal starting point for robust and efficient first principles quantum mechanical molecular dynamics simulations. [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]

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]

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]

Abstract: In this work, we present a quantum mechanical treatment of the three‐body LiH 2 + molecular system in the Born–Oppenheimer (BO) approximation, were the nuclei dynamics is evaluated over the potential energy surfaces (PES) induced by the electronic states. The PES corresponding to the two lowest electronic levels are the ones described by Martinazzo et al. (Chem. Phys. 2003, 287, 335), and are used to write the three‐body Schrdinger equation of the three atomic system. We use the generalized Sturmian functions method to expand the wave functions in each (distinguishable) pair of relative coordinates or Jacobi pairs, and analyze the convergence differences between the series. A partial‐wave decomposition of the potential is proposed to simplify the Hamiltonian matrix element calculation. Bound states are considered for the ground and first excited electronic PES, the spreading of energies after sudden electronic transitions studied, and the break‐up probability induced by the sudden change of the PES evidenced. [ABSTRACT FROM AUTHOR]

Recently a new formulation of quantum mechanics has been suggested which is based on the concept of signed particles, that is, classical objects provided with a position, a momentum and a sign simultaneously. In this article, we comment on the plausibility of simulating atomic systems beyond the Born-Oppenheimer approximation by means of the signed particle formulation of quantum mechanics. First, to show the new perspective offered by this new formalism, we provide an example studying quantum tunnelling through a simple Gaussian barrier in terms of the signed particle formulation. Then, we perform a direct simulation of the hydrogen atom as a full quantum two-body system, showing that the formalism can be a very promising tool for first-principle-only quantum chemistry. [ABSTRACT FROM AUTHOR]

Techniques developed for investigating nonadiabatic processes in molecular systems are adapted to study the structure and properties of holomorphic and meromorphic functions of a complex variable, $$f(z)=\mathfrak {R}(f)+i\,\mathfrak {I}(f)$$ . The connection is that $$\mathfrak {R}(f)$$ and $$\mathfrak {I}(f)$$ are correlated two-dimensional scalar functions, interrelated by the Cauchy-Riemann equations. Exploiting this fact, it is demonstrated that $$\mathfrak {R}(f)$$ and $$\mathfrak {I}(f)$$ of f can be envisaged in Euclidean $${\mathbb {R}}^{3}$$ space as a two-state set of constrained, intersecting two-dimensional potential energy surfaces ( PESs), called the graph of f. Importantly, the analytic and algebraic properties of f dictate the geometric structure evinced in the graph of f. This parallels multi-state sets of higher-dimensional, constrained, intersecting PESs linked with correlated electronic eigenstates of the parameterized molecular Hamiltonian operator. In view of this association, the language and mathematical infrastructure devised by chemists for discussing and analyzing intersections in higher-dimensional PESs are suitably modified for f. Notably, an algorithm capable of optimizing roots and poles of f through analysis of the real, two-dimensional $$\mathfrak {R}(f)$$ and $$\mathfrak {I}(f)$$ functions is derived, which is based on intersection-adapted coordinate and constrained Lagrangian methodologies. As constrained, intersecting PESs are indispensible for conceptualizing and characterizing the physics governing nonadiabatic phenomena, f represents a foundational bridge to these more abstract constructions. [ABSTRACT FROM AUTHOR]

Quantum mechanical, non-relativistic, non-Born-Oppenheimer (non-BO) calculations are performed for the rovibrational spectrum of H 2 excited to the second rotational level. The non-BO wave functions of the considered states are expanded in terms of all-particle explicitly correlated Gaussian functions. The dissociation energies and rovibrational transition energies are calculated and compared with experimental values and values obtained in calculations performed by others. The average interparticle distances are calculated and compared with the corresponding values for HD. They show that H 2 is a more “diffuse molecule”. The nuclear-nuclear correlation functions are calculated and plotted to visualize the “non-BO molecular structure” of H 2 . [ABSTRACT FROM AUTHOR]

An exact single-product factorisation of the molecular wave function for the timedependent Schrödinger equation is investigated by using an ansatz involving a phase factor. By using the Frenkel variational method, we obtain the Schrödinger equations for the electronic and nuclear wave functions. The concept of a potential energy surface (PES) is retained by introducing a modified Hamiltonian as suggested earlier by Cederbaum. The parameter ω in the phase factor is chosen such that the equations of motion retain the physically appealing Born– Oppenheimer-like form, and is therefore unique. [ABSTRACT FROM AUTHOR]

A discussion about the classical Coulomb repulsion via point-like nuclear charges, usually employed within Born-Oppenheimer approximation, leads to the description of Dirac paradox: an inconsistency found when describing nuclear charges by means of Dirac's distributions and computing with them nuclear Coulomb repulsion integrals. The way of overcoming Dirac paradox is bound to the description of soft Gaussian nuclear charge density and also to adopting a nuclear hypermultiplet Coulomb repulsion formulation. Such theoretical prospect produces a quantum mechanically compliant but simple algorithm in order to compute nuclear repulsion, which also appears to be consistently related to classical Coulomb repulsion energy, while avoiding singularities when nuclei collapse. [ABSTRACT FROM AUTHOR]

Many of the XYZ mesons discovered in the last decade can be identified as bound states of a heavy quark and antiquark in Born-Oppenheimer (BO) potentials defined by the energy of gluon and light-quark fields in the presence of static color sources. The mesons include quarkonium hybrids, which are bound states in excited flavor-singlet BO potentials, and quarkonium tetraquarks, which are bound states in BO potentials with light-quark+antiquark flavor. The deepest hybrid potentials are known from lattice QCD calculations. The deepest tetraquark potentials can be inferred from lattice QCD calculations of static adjoint mesons. Selection rules for hadronic transitions are derived and used to identify XYZ mesons that are candidates for ground-state energy levels in the BO potentials for charmonium hybrids and tetraquarks. [ABSTRACT FROM AUTHOR]

ording to ontological reductionism, molecular chemistry refers, at last, to the quantum ontology; therefore, the ontological commitments of chemistry turn out to be finally grounded on quantum mechanics. The main problem of this position is that nobody really knows what quantum ontology is. The purpose of this work is to argue that the confidence in the existence of the physical entities described by quantum mechanics does not take into account the interpretative problems of the theory: in the discussions about the relationship between chemistry and physics, difficulties are seen only on the side of chemistry, whereas matters highly controversial on the side of physics are taken for granted. For instance, it is usually supposed that the infinite mass limit in the Born-Oppenheimer approximation leads by itself to the concept of molecular framework used in molecular chemistry. We will argue that this assumption is implicitly based on an interpretative postulate for quantum mechanics, which, in turn, runs into difficulties when applied to the explanation of the simplest model of the hydrogen atom. [ABSTRACT FROM AUTHOR]

I was born in Budapest, Hungary, on July 7, 1907, and this first part of my interview with Andor Frenkel focuses on my life and work in Europe. After my elementary and secondary education I studied mathematics at the University of Budapest for two years. I went to the University of Göttingen in 1928 where I attended Max Born’s lectures on quantum mechanics, which influenced me to change from mathematics to physics, and as a consequence I focused on filling the gaps in my physics background. When ready to turn to research work I followed the advice of my friend Edward Teller and spent three months in Werner Heisenberg’s group at the University of Leipzig in the summer of 1930. That fall I returned to the University of Budapest, where I received my Ph.D.degree in the summer of 1932. Two months later, because I had become entangled in the illegal Communist Party, I was arrested and sentenced to fourteen months in prison. Fifteen months after my release, I joined Lev Landau’s group at the Ukrainian Physical-Technical Institute in Kharkov, passed Landau’s so-called “theorminimum” program on my second attempt, began research on the theory of liquid helium, and lost my faith in communism following Stalin’s repressive measures. I obtained an exit visa through the Hungarian Legation and returned to Budapest in June 1937. That September, again with the help of my friend Edward Teller, I attended a conference in Paris where I met Fritz London and Edmond Bauer, who arranged for me a small scholarship and an association with the Langevin laboratory at the Collège de France. Four months later, in January 1938 Kapitza, and John F. Allen and A. Donald Misener reported their independent discovery of the superfluidity of helium, which London and I explored theoretically and I explained with my two-fluid theory later in 1938. Following the German invasion of France, my wife and I left Paris for Toulouse in June 1940, obtained exit visas to enter Spain and Portugal in February 1941, and boarded a Portuguese ship for New York the following month. The second part of this interview, covering my life and work in America, will appear in the next issue. [ABSTRACT FROM AUTHOR]