Beyond Born-Oppenheimer

An “inverse” harpoon mechanism
Gope, K. ; Livshits, E. ; Bittner, D. M. ; Baer, R. ; Strasser, D. An “inverse” harpoon mechanism. Science Advances 2022, 8 eabq8084. Publisher's VersionAbstract

Electron-transfer reactions are ubiquitous in chemistry and biology. The electrons quantum nature allows its transfer across long distances. In the well-known harpoon mechanism, electron-transfer results in Coulombic attraction between initially neutral reactants that leads to dramatic increase in the reaction rate. Here we present a different mechanism, in which electron-transfer from a neutral reactant to a multiply charged cation results in strong repulsion that encodes the electron-transfer distance in the kinetic energy release. 3D coincidence-imaging allows to identify such “inverse” harpoon products, predicted by non adiabatic molecular dynamics simulations to occur between H2 and HCOH2+ following double-ionization of isolated methanol molecules. Detailed comparison of measured and simulated data indicates that while the relative probability of long-range electron-transfer events is correctly predicted, theory overestimates the electron-transfer distance.

Sequential and concerted C-C and C-O bond dissociation in the Coulomb explosion of 2-propanol
Bittner, D. ; Gope, K. ; Livshits, E. ; Baer, R. ; Strasser, D. Sequential and concerted C-C and C-O bond dissociation in the Coulomb explosion of 2-propanol. Journal of Chemical Physics 2022, 157, 074309. Publisher's Version
Two pathways and an isotope effect in H3+ formation following double ionization of methanol
Gope, K. ; Livshits, E. ; Bittner, D. M. ; Baer, R. ; Strasser, D. Two pathways and an isotope effect in H3+ formation following double ionization of methanol. Natural Sciences 2021, ntls.10022. Publisher's VersionAbstract

The trihydrogen ion has a central role in creating complex molecules in the interstellar medium. Therefore, its formation and destruction mechanisms in high photon energy environments involving organic molecules are drawing significant experimental and theoretical attention. Here, we employ a combination of time-resolved ultrafast extreme-ultraviolet pump and near-infrared probe spectroscopy applied to the deuterated CH3OD methanol molecule. Similar to other double-ionization studies, the isotopic labeling reveals two competing pathways for forming trihydrogen: A) H+3 + COH+ and B) H+3 + HCO+. We validate our high-level ab initio nonadiabatic molecular dynamic simulations by showing that it closely reproduces the essential features of the measured kinetic energy release distribution and branching ratios of the two pathways of the deuterated system. The success of ab initio simulation in describing single photon double-ionization allows for an unprecedented peek into the formation pathways for the undeuterated species, beyond present experimental reach. For this case, we find that the kinetic energy release of pathway B shifts to lower energies by more than 0.6 eV due to a dynamical isotope effect. We also determine the mechanism for trihydrogen formation from excited states of the dication and elucidate the isotope effect’s role in the observed dynamics.

Time-resolving the ultrafast H2 roaming chemistry and H3+ formation using extreme-ultraviolet pulses
Livshits, E. ; Luzon, I. ; Gope, K. ; Baer, R. ; Strasser, D. Time-resolving the ultrafast H2 roaming chemistry and H3+ formation using extreme-ultraviolet pulses. Communications Chemistry 2020, 3 49. Publisher's Version livshits2020time.pdf
Absence of Triplets in Single-Photon Double Ionization of Methanol
Gope, K. ; Livshits, E. ; Bittner, D. M. ; Baer, R. ; Strasser, D. Absence of Triplets in Single-Photon Double Ionization of Methanol. The Journal of Physical Chemistry Letters 2020, 11, 8108–8113. Publisher's VersionAbstract

Despite the abundance of data concerning single-photon double ionization of methanol, the spin state of the emitted electron pair has never been determined. Here we present the first evidence that identifies the emitted electron pair spin as overwhelmingly singlet when the dication forms in low-energy configurations. The experimental data show that while the yield of the CH2O+ + H3+ Coulomb explosion channel is abundant, the metastable methanol dication is largely absent. According to high-level ab initio simulations, these facts indicate that photoionization promptly forms singlet dication states, where they quickly decompose through various channels, with significant H3+ yields on the low-lying states. In contrast, if we assume that the initial dication is formed in one of the low-lying triplet states, the ab initio simulations exhibit a metastable dication, contradicting the experimental findings. Comparing the average simulated branching ratios with the experimental data suggests a \textgreater3 order of magnitude enhancement of the singlet:triplet ratio compared with their respective 1:3 multiplicities.

Making Sense of Coulomb Explosion Imaging
Luzon, I. ; Livshits, E. ; Gope, K. ; Baer, R. ; Strasser, D. Making Sense of Coulomb Explosion Imaging. J. Phys. Chem. Lett. 2019, 10, 1361–1367. Publisher's VersionAbstract

A multifaceted agreement between ab initio theoretical predictions and experimental measurements, including branching ratios, channel-specific kinetic energy release, and three-body momentum correlation spectra, leads to the identification of new mechanisms in Coulomb-explosion (CE) induced two- and three-body breakup processes in methanol. These identified mechanisms include direct nonadiabatic Coulomb explosion responsible for CO bond-breaking, a long-range “ inverse harpooning” dominating the production of H2+ + HCOH+, a transient proton migration leading to surprising energy partitioning in three-body fragmentation and other complex dynamics forming products such as H2O+ and H3+. These mechanisms provide general concepts that should be useful for analyzing future time-resolved Coulomb explosion imaging of methanol as well as other molecular systems. These advances are enabled by a combination of recently developed experimental and computational techniques, using weak ultrafast EUV pulses to initiate the CE and a high-level quantum chemistry approach to follow the resulting field-free nonadiabatic molecular dynamics.

Paul, A. K. ; Adhikari, S. ; Baer, M. ; Baer, R. H2 + photodissociation by an intense pulsed photonic Fock state. Phys. Rev. A 2010, 81, 013412.Abstract

We study the photodissociation of the H+2 molecule by ultrashort Fock-state electromagnetic pulses (EMPs). We use the Born-Oppenheimer treatment combined with an explicit photon number representation via diabatic electrophoton potential surfaces for simplification of the basic equations. We discuss the issue of the number of photon states required and show that six photon states enable good accuracy for photoproduct kinetic energies of up to 3 eV. We calculate photodissociation probabilities and nuclear kinetic-energy (KE) distributions of the photodissociation products for 800 nm, 50-TW/cm2 pulses. We show that KE distributions depend on three pulse durations of 10, 20, and 45 fs and on various initial vibrational states of the molecule. We compare the Fock-state results to those obtained by “conventional,” i.e., coherent-state, laser pulses of equivalent electric fields and durations. The effects of the quantum state of EMPs on the photodissociation dynamics are especially strong for high initial vibrational states of H+2. While coherent-state pulses suppress photodissociation for the high initial vibrational states of H+2, the Fock-state pulses enhance it.

Baer, R. Ground-State Degeneracies Leave Recognizable Topological Scars in the Electronic Density. Phys. Rev. Lett. 2010, 104, 073001.Abstract

In Kohn-Sham density functional theory (KS DFT) a fictitious system of noninteracting particles is constructed having the same ground-state (GS) density as the physical system of interest. A fundamental open question in DFT concerns the ability of an exact KS calculation to spot and characterize the GS degeneracies in the physical system. In this Letter we provide theoretical evidence suggesting that the GS density, as a function of position on a 2D manifold of parameters affecting the external potential, is â€øe}topologically scarredâ€ï¿½ in a distinct way by degeneracies. These scars are sufficiently detailed to enable determination of the positions of degeneracies and even the associated Berry phases. We conclude that an exact KS calculation can spot and characterize the degeneracies of the physical system.

Paul, A. K. ; Adhikari, S. ; Mukhopadhyay, D. ; Halasz, G. J. ; Vibok, A. ; Baer, R. ; Baer, M. Photodissociation of H2+ upon Exposure to an Intense Pulsed Photonic Fock State. J. Phys. Chem. A 2009, 113, 7331–7337.Abstract

Producing and controlling nonclassical light states are now the subject of intense experimental efforts. In this paper we consider the interaction of such a light state with a small molecule. Specifically, we develop the theory and apply it numerically to calculate in detail how a short pulse of nonclassical light, such as the high intensity Fock state, induces photodissociation in H2+. We compare the kinetic energy distributions and photodissociation yields with the analogous results of quasi-classical light, namely a coherent state. We find that Fock-state light decreases the overall probability of dissociation for low vibrational states of H2+ as well as the location of peaks and line shapes in the kinetic energy distribution of the nuclei.

Halász, G. J. ; Vibók, Á. ; Baer, R. ; Baer, M. Conical intersections induced by the Renner effect in polyatomic molecules. J. Phys. A: Math. Theor. 2007, 40, F267.Abstract

Characterizing and localizing electronic energy degeneracies is important for describing and controlling electronic energy flow in molecules. We show, using topological phase considerations, that the Renner effect in polyatomic molecules with more than three nuclei is necessarily accompanied by 'satellite' conical intersections. In these intersections the non-adiabatic coupling term is on average half an integer. We present ab initio results on the tetra-atomic radical cation C2H+2 to demonstrate the theory.

Halász, G. J. ; Vibók, Á. ; Baer, R. ; Baer, M. Renner-Teller nonadiabatic coupling terms: An ab-initio study of the HNH molecule, 2006. halasz2006renner.pdf
Halász, G. J. ; Vibók, Á. ; Baer, R. ; Baer, M. D matrix analysis of the Renner-Teller effect: an accurate three-state diabatization for NH2. J. Chem. Phys. 2006, 125, 094102. halasz2006c.pdf
Ryb, I. ; Baer, R. Combinatorial invariants and covariants as tools for conical intersections. J. Chem. Phys. 2004, 121, 10370–10375.Abstract

The combinatorial invariant and covariant are introduced as practical tools for analysis of conical intersections in molecules. The combinatorial invariant is a quantity depending on adiabatic electronic states taken at discrete nuclear configuration points. It is invariant to the phase choice (gauge) of these states. In the limit that the points trace a loop in nuclear configuration space, the value of the invariant approaches the corresponding Berry phase factor. The Berry phase indicates the presence of an odd or even number of conical intersections on surfaces bounded by these loops. Based on the combinatorial invariant, we develop a computationally simple and efficient method for locating conical intersections. The method is robust due to its use of gauge invariant nature. It does not rely on the landscape of intersecting potential energy surfaces nor does it require the computation of nonadiabatic couplings. We generalize the concept to open paths and combinatorial covariants for higher dimensions obtaining a technique for the construction of the gauge-covariant adiabatic-diabatic transformation matrix. This too does not make use of nonadiabatic couplings. The importance of using gauge-covariant expressions is underlined throughout. These techniques can be readily implemented by standard quantum chemistry codes.

Baer, R. ; Siam, N. Real-time study of the adiabatic energy loss in an atomic collision with a metal cluster. The Journal of chemical physics 2004, 121, 6341–6345. baer2004d.pdf
Baer, R. ; Kouri, D. J. ; Baer, M. ; Hoffman, D. K. General Born–Oppenheimer–Huang approach to systems of electrons and nuclei. The Journal of chemical physics 2003, 119, 6998–7002.Abstract

We reconsider the Born-Oppenheimer-Huang treatment of systems of electrons and nuclei for the case of their interaction with time-dependent fields. Initially, we present a framework in which all expressions derived are formally exact since no truncations are introduced. The objective is to explore the general structure of the equations under the most unrestricted conditions, including the possibility that the electronic basis is dependent both on the nuclear coordinates and on time. We then derive an application of the theory applicable to cases of interaction with strong time-dependent fields. The method truncates the electronic basis only after the time-dependent interaction is taken into account in the electronic wave functions. This leads to theory which is similar to a Born-Oppenheimer-type truncation within the interaction picture. (C) 2003 American Institute of Physics.

Baer, R. Born-Oppenheimer invariants along nuclear paths. J. Chem. Phys. 2002, 117, 7405. baer2002c.pdf
Baer, R. Non-adiabatic couplings by time-dependent density functional theory. Chem. Phys. Lett. 2002, 364, 75–79. baer2002.pdf
Charutz, D. M. ; Baer, R. ; Baer, M. A study of degenerate vibronic coupling effects on scattering processes: Are resonances affected by degenerate vibronic coupling?. Chem. Phys. Lett. 1997, 265, 629–637.Abstract

Recently the Jahn-Teller model was extended to treat (reactive) scattering processes. The present study is devoted to possible effects of a degenerate vibronic coupling (DVC) on resonances. The main conclusions are: (a) The DVC affects dramatically the state-to-state transition processes and as a result it shuffles resonances attached to given transitions and may cause existing resonances to be masked by other processes. (b) The DVC may affect the widths and the heights of resonances but change only slightly their position.

Baer, R. ; Zeiri, Y. ; Kosloff, R. Hydrogen transport in nickel (111). Phys. Rev. B 1997, 55, 10952. baer1997e.pdf