The multi-component quantum theory of atoms in molecules (MC-QTAIM) analysis is done on methane, ethylene, acetylene and benzene as selected basic hydrocarbons. This is the first report on applying the MC-QTAIM analysis on polyatomic species. In order to perform the MC-QTAIM analysis, at first step the nuclear-electronic orbital method at Hartree-Fock level (NEO-HF) is used as a non-Born-Oppenheimer (nBO) ab initio computational procedure assuming both electrons and protons as quantum waves while carbon nuclei as point charges in these systems. The ab initio calculations proceed substituting all the protons of each species first with deuterons and then tritons. At the next step, the derived nBO wavefunctions are used for the "atoms in molecules" (AIM) analysis. The results of topological analysis and integration of atomic properties demonstrate that the MC-QTAIM is capable of deciphering the underlying AIM structure of all the considered species. Also, the results of the analysis for each isotopic composition are distinct and the fingerprint of the mass difference of hydrogen isotopes is clearly seen in both topological and AIM analyses. This isotopic distinction is quite unique in the MC-QTAIM and not recovered by the orthodox QTAIM that treats nuclei as clamped particles. The results of the analysis also demonstrate that each quantum nucleus that forms an atomic basin resides within its own basin. The confinement of quantum nuclei within a single basin is used to simplify the basic equations of the MC-QTAIM paving the way for future theoretical studies.
The coupling of a molecule and a cavity induces non-adiabaticity 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 generally expected to fail in two- or more-dimensional models due to the appearance of conical intersections induced by the cavity.
Extended Lagrangian Born-Oppenheimer molecular dynamics (XL-BOMD) [Phys. Rev. Lett. vol. 100, 123004 (2008)] is combined with Kohn-Sham density functional theory (DFT) using a DFT+U correction based on the Hubbard model. This combined XL-BOMD and DFT+U approach allows efficient Born-Oppenheimer molecular dynamics simulations with orbital-dependent corrections beyond regular Kohn-Sham density functional theory. The extended Lagrangian formulation eliminates the need for the iterative self-consistent-field optimization of the electronic ground state prior to the force evaluations, which is requi…
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 and, by varying the masses to simulate molecular di-hydrogen, mono-muonated di-hydrogen and di-muonated di-hydrogen, employed to illustrate the celebrated Born-Oppenheimer approximation on the occasion of its 90th anniversary. It is suggested that it is valid only for di-hydrogen.
The main motivation for this work is the exploration of rotational-vibrational states corresponding to electronic excitations in a pre-Born-Oppenheimer quantum theory of molecules. These states are often embedded in the continuum of the lower-lying dissociation channel of the same symmetry, and thus are thought to be resonances. In order to calculate rovibronic resonances, the pre-Born-Oppenheimer variational approach of [J. Chem. Phys. 137, 024104 (2012)], based on the usage of explicitly correlated Gaussian functions and the global vector representation, is extended with the complex coordina…
Theory of proton coupled electron transfer reactions: Assessing the Born-Oppenheimer approximation for the proton motion using an analytically solvable model
Describing the dynamics of nuclei in molecules requires a potential energy surface, which is traditionally provided by the Born-Oppenheimer or adiabatic approximation. However, we also need to assign masses to the nuclei. There, the Born-Oppenheimer picture does not account for the inertia of the electrons and only bare nuclear masses are considered. Nowadays, experimental accuracy challenges the theoretical predictions of rotational and vibrational spectra and requires to include the participation of electrons in the internal motion of the molecule. More than 80 years after the original work …
This paper concerns the representation of angular momentum operators in the Born-Oppenheimer theory of polyatomic molecules and the various forms of the associated conservation laws. Topics addressed include the question of whether these conservation laws are exactly equivalent or only to some order of the Born-Oppenheimer parameter $κ=(m/M)^{1/4}$, and what the correlation is between angular momentum quantum numbers in the various representations. These questions are addressed both in problems involving a single potential energy surface, and those with multiple, strongly coupled surfaces; and…
Born-Oppenheimer Molecular Dynamics (BOMD) is a powerful but expensive technique. The main bottleneck in a density functional theory bomd calculation is the solution to the Kohn-Sham (KS) equations, that requires an iterative procedure that starts from a guess for the density matrix. Converged densities from previous points in the trajectory can be used to extrapolate a new guess, however, the non-linear constraint that an idempotent density needs to satisfy make the direct use of standard linear extrapolation techniques not possible. In this contribution, we introduce a locally bijective map …
It was recently shown [G. Albareda, et al., Phys. Rev. Lett. 113, 083003 (2014)] that within the conditional decomposition approach to the coupled electron-nuclear dynamics, the electron-nuclear wave function can be exactly decomposed into an ensemble of nuclear wavepackets effectively governed by nuclear conditional time-dependent potential-energy surfaces (C-TDPESs). Employing a one-dimensional model system we show that for strong nonadiabatic couplings the nuclear C-TDPESs exhibit steps that bridge piecewise adiabatic Born-Oppenheimer PESs. The nature of these steps is identified as an effe…
Can The Mystery of The Born-Oppenheimer Electronic Current Density Be Explained With A Simple Phase Space Electronic Hamiltonian? Yes (And A Lot More Too)
An alternative method is introduced to solve a simple two-dimensional models describing vibrational excitation and dissociation processes during the electron-molecule collisions. The model works with one electronic and one nuclear degree of freedom. The two-dimensional $R$-matrix can be constructed simultaneously on the electronic and nuclear surfaces using all three forms developed previously for electron-atom and electron-molecule collisions. These are the eigenchannel $R$-matrix form, inversion technique of Nesbet and Robicheaux, and the Wigner-Eisenbud-type form using expansion over the po…
We report on accurate variational calculations of the Born-Oppenheimer potential for excited states of the hydrogen molecule with $Π$, $Δ$, and $Φ$ symmetries. The obtained potential energy curves reach the relative precision of $10^{-9}$ or better along internuclear distances of 0.01 -- 20 au. Calculations rely on recursive evaluation of two-center two-electron molecular integrals with exponential functions in arbitrary precision arithmetics. Our results for most of the states are the first ever reported, and for the previously calculated states constitute an improvement by several orders of …
Laser-induced molecular alignment is well understood within the framework of the Born-Oppenheimer (BO) approximation Without the BO approximation, however, the concept of molecular structure is lost, making alignment hard to define precisely. In this work, we demonstrate the emergence of alignment from the first-ever non-BO quantum dynamics simulations, using the HD molecule exposed to ultrashort laser pulses as a few-body test case We extract the degree of alignment from the non-BO wave function by means of an operator expressed in terms of pseudo-proton coordinates that mimics the BO-based d…
The diagonal nonadiabatic term arising from the Born--Oppenheimer wave-function ansatz contains contributions from a vector and scalar potential. The former is provably zero when the wave function can be taken to be real valued, and the latter, known as the diagonal Born--Oppenheimer correction (DBOC), is typically small in magnitude. Therefore, unless high accuracy is sought, the diagonal nonadiabatic term is usually neglected when calculating molecular properties. In the presence of a magnetic field, the wave function is generally complex, and the geometric vector potential gives rise to a s…
We present a generalization of Extended Lagrangian Born-Oppenheimer molecular dynamics [Phys. Rev. Lett. vol. 100, 123004 (2008); Eur. Phys. J. B vol. 94, 164 (2021)] that also includes the electronic spin-degrees of freedom as extended dynamical variables. To integrate the combined spin and charge degrees of freedom, we use a preconditioned low-rank Krylov subspace approximation. Our approach is demonstrated for quantum-mechanical molecular dynamics simulations of iron, using spin-polarized self-consistent charge density functional tight-binding theory. We also show how the low-rank Krylov su…
For rovibronic states corresponding to the $B$ and $B'\ ^1Σ_\text{u}^+$ electronic states of the hydrogen molecule, the pre-Born--Oppenheimer (four-particle) non-relativistic energy is converged to a 1-3 parts-per-billion relative precision. The four-particle non-relativistic energy is appended with leading-order relativistic, leading- and estimated higher-order quantum-electrodynamics corrections. The resulting term values referenced to the rovibronic ground state are obtained in an excellent agreement with the experimental results. Further results are reported and discussed for other rovibro…
Extended Lagrangian Born-Oppenheimer molecular dynamics [{\em Phys.\ Rev.\ Lett.\ } {\bf 2008}, {\em 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 particula…
We perform model calculations for a stretched LiF molecule, demonstrating that nonadiabatic charge transfer effects can be accurately and seamlessly described within a density functional framework. In alkali halides like LiF, there is an abrupt change in the ground state electronic distribution due to an electron transfer at a critical bond length $R=R_c$, where a barely avoided crossing of the lowest adiabatic potential energy surfaces calls the validity of the Born-Oppenheimer approximation into doubt. Modeling the $R$-dependent electronic structure of LiF within a two-site Hubbard model, we…
Within the nuclear-electronic orbital (NEO) framework, the real-time NEO time-dependent density functional theory (RT-NEO-TDDFT) approach enables the simulation of coupled electronic-nuclear dynamics. In this approach, the electrons and quantum nuclei are propagated in time on the same footing. A relatively small time step is required to propagate the much faster electronic dynamics, thereby prohibiting the simulation of long-time nuclear quantum dynamics. Herein, the electronic Born--Oppenheimer (BO) approximation within the NEO framework is presented. In this approach, the electronic density…
In two recent publications ( Int. J. Quant. Chem. 114, 1645 (2014) and Molec. Phys. 114, 227 (2016)) it was shown that the Born -Hwang (BH) treatment of a molecular system perturbed by an external field yields a set of decoupled vectorial Wave Equations, just like in Electromagnetism. This finding led us to declare on the existence of a new type of Fields, which were termed Molecular Fields. The fact that such fields exist implies that at the vicinity of conical intersections exist a mechanism that transforms a passing-by electric beam into a field which differs from the original electric fiel…
Toward Accurate Post-Born-Oppenheimer Molecular Simulations on Quantum Computers: An Adaptive Variational Eigensolver with Nuclear-Electronic Frozen Natural Orbitals
A system of two bilinearly coupled harmonic oscillators has been solved analytically by using the Born-Oppenheimer (BO) product wavefunction ansatz and the phase-space bound trajectory approach [J. S. Molano et al., Chem. Phys. Lett. \textbf{76}(12), 138171 (2021)]. The bilinearly coupled oscillator system allows to obtain the analytical expression of the quantum system, facilitating comparison with the results of using the BO ansatz product. The analytical and BO wavefunctions are obtained as a product of parabolic cylinder functions. The arguments of the parabolic cylinder functions of the e…
Numerical projection methods are elaborated for the calculation of eigenstates of the non-relativistic many-particle Coulomb Hamiltonian with selected rotational and parity quantum numbers employing shifted explicitly correlated Gaussian functions, which are, in general, not eigenfunctions of the total angular momentum and parity operators. The increased computational cost of numerically projecting the basis functions onto the irreducible representations of the three dimensional rotation-inversion group is the price to pay for the increased flexibility of the basis functions. This increased fl…
In pre-Born-Oppenheimer (pre-BO) theory a molecule is considered as a quantum system as a whole, including the electrons and the atomic nuclei on the same footing. This approach is fundamentally different from the traditional quantum chemistry treatment, which relies on the separation of the motion of the electrons and the atomic nuclei. A fully quantum mechanical treatment of molecules has a great promise for future developments and applications. Its most accurate versions may contribute to the definition of new schemes for metrology and testing fundamental physical theories; its approximate …
We investigate Born-Oppenheimer breakdown (BOB) effects (beyond the usual mass scaling) for the electronic ground states of a series of homonuclear and heteronuclear alkali-metal diatoms, together with the Sr$_2$ and Yb$_2$ diatomics. Several widely available electronic structure software packages are used to calculate the leading contributions to the total isotope shift for commonly occurring isotopologs of each species. Computed quantities include diagonal Born-Oppenheimer corrections (mass shifts) and isotopic field shifts. Mass shifts dominate for light nuclei up to and including K, but fi…
The role of electron-nuclear entanglement on the validity of the Born-Oppenheimer (BO) approximation is investigated. While nonadiabatic couplings generally lead to entanglement and to a failure of the BO approximation, surprisingly the degree of electron-nuclear entanglement is found to be uncorrelated with the degree of validity of the BO approximation. This is because while the degree of entanglement of BO states is determined by their deviation from the corresponding states in the crude BO approximation, the accuracy of the BO approximation is dictated, instead, by the deviation of the BO …
Strong Electronic Polarization of the C60 Fullerene by the Imidazolium-Based Ionic Liquids: Accurate Insights from Born-Oppenheimer Molecular Dynamics Simulations
The underlying physics behind the molecular harmonic emission in relatively long sin$^2$-like laser pulses is investigated. We numerically solved the full-dimensional electronic time-dependent Schrödinger equation beyond the Born-Oppenheimer approximation for simple molecular ion H$_2^+$. The occurrence and the effect of electron localization, non-adiabatic redshift and spatially asymmetric emission are evaluated to understand better complex patterns appearing in the high-order harmonic generation (HHG) spectrum. Results show that the complex patterns in the HHG spectrum originate mainly from …
This paper presents the calculation of the electric transition dipole moment in a pre-Born-Oppenheimer framework. Electrons and nuclei are treated equally in terms of the parametrization of the non-relativistic total wave function, which is written as a linear combination of basis functions constructed with explicitly correlated Gaussian functions and the global vector representation. The integrals of the electric transition dipole moment are derived corresponding to these basis functions in both the length and the velocity representation. The complete derivation and the calculations are perfo…
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…
While the treatment of conical intersections in molecular dynamics generally requires nonadiabatic approaches, the Born-Oppenheimer adiabatic approximation is still adopted as a valid alternative in certain circumstances. In the context of Mead-Truhlar minimal coupling, this paper presents a new closure of the nuclear Born-Oppenheimer equation, thereby leading to a molecular dynamics scheme capturing geometric phase effects. Specifically, a semiclassical closure of the nuclear Ehrenfest dynamics is obtained through a convenient prescription for the nuclear Bohmian trajectories. The conical int…
