Time-dependent Extension of Grimme's Continuous Chirality Measure for Electronic Chirality Flips in Femto- and Attosecond Time Domains.

Grimme's Continuous Chirality Measure (CCM ) was developed for comparisons of the chirality of the electronic wave functions of molecules, typically in their ground states. For example, CCM=14.5, 1.2,  and 0.0 for alanine, hydrogen-peroxide, and for achiral molecules, respectively. Well-designed laser pulses can excite achiral molecules from the electronic ground state to time-dependent chiral superposition states, with chirality flips in the femto- or even attosecond (fs or as) time domains. Here we provide a time-dependent extension CCM(t) of Grimme's CCM for trailing the electronic chirality flips. As examples, we consider two laser driven electronic wavefunctions which represent flips between opposite electronic enantiomers of oriented NaK within 4.76 fs and 433 as. The corresponding  CCM(t) vary respectively from 14.5 or from 13.3 to 0.0, and back.

Ultrafast laser induced charge migration with de- and re-coherences in polyatomic molecules: A general method with application to pyrene.

We develop a general method to study ultrafast laser induced charge migration in molecules, which includes both electronic and nuclear dynamics. The method can be applied to relatively large systems. A detailed analysis of charge migration in pyrene is performed. Decoherences and recoherences of charge migration in pyrene are found and explained in terms of nuclear motions.

Attosecond Charge Migration Can Break Electron Symmetry While Conserving Nuclear Symmetry.

Charge migration moves electrons from one molecular site to another, in a typical time domain from few hundred attoseconds to few femtoseconds. On this timescale, the nuclei stand practically still, implying that the nuclear point group symmetry is conserved. Because electrons move ultrafast, this can lead to a surprising effect, namely, breaking the spatial symmetry of the electron density in spite of the conservation of nuclear framework symmetry. We demonstrate theoretically that attosecond charge migration achieves this electron symmetry breaking if the electrons are prepared in a coherent superposition of nondegenerate electronic ground and excited states which transform according to different irreducible representations. Two simple examples provide a proof-of-principle, namely, periodic attosecond charge migration in the σg + σu superposition state of the aligned H2+ cation (nuclear point group D∞h, but electron symmetry breaking D∞h → C∞v) and in the A1 + B2 superposition state of the oriented H2O molecule (C2v vs C2v → Cs).

Timing the recoherences of attosecond electronic charge migration by quantum control of femtosecond nuclear dynamics: A case study for HCCI.

This work suggests an approach to a new target of laser control of charge migration in molecules or molecular ions. The target is motivated by the fact that nuclear motions can not only cause decoherence of charge migration, typically within few femtoseconds, but they may also enable the reappearance of charge migration after much longer times, typically several tens or even hundreds of femtoseconds. This phenomenon is called recoherence of charge migration, opposite to its decoherence. The details depend on the initiation of the original charge migration by an ultrashort strong intense pump laser pulse. It may reappear quasiperiodically, with reference period Tr. We show that a well-designed pump-dump laser pulse can enforce recoherences of charge migration at different target times Tc, for example, at Tc ≈ Tr/2. The approach is demonstrated by quantum dynamics simulations of the laser driven electronic and nuclear motions in the oriented linear cation HCCI+. First, the concept is explained in terms of a didactic one-dimensional (1D) model that accounts for the decisive CI stretch. The 1D results are then confirmed by a three-dimensional model for the complete set of the CH, CC, and CI stretches.

Attosecond Control of Restoration of Electronic Structure Symmetry.

Laser pulses can break the electronic structure symmetry of atoms and molecules by preparing a superposition of states with different irreducible representations. Here, we discover the reverse process, symmetry restoration, by means of two circularly polarized laser pulses. The laser pulse for symmetry restoration is designed as a copy of the pulse for symmetry breaking. Symmetry restoration is achieved if the time delay is chosen such that the superposed states have the same phases at the temporal center. This condition must be satisfied with a precision of a few attoseconds. Numerical simulations are presented for the C_{6}H_{6} molecule and ^{87}Rb atom. The experimental feasibility of symmetry restoration is demonstrated by means of high-contrast time-dependent Ramsey interferometry of the ^{87}Rb atom.

Communication: Electronic flux induced by crossing the transition state.

We present a new effect of chemical reactions, e.g., isomerizations, that occurs when the reactants pass along the transition state, on the way to products. It is based on the well-known fact that at the transition state, the electronic structure of one isomer changes to the other. We discover that this switch of electronic structure causes a strong electronic flux that is well distinguishable from the usual flux of electrons that travel with the nuclei. As a simple but clear example, the effect is demonstrated here for bond length isomerization of Na2 (21Σu+), with adiabatic crossing the barrier between the inner and outer wells of the double minimum potential that support different "Rydberg" and "ionic" type electronic structures, respectively.

Nuclear spin blockade of laser ignition of intramolecular rotation in the model boron rotor B 13 + 11 .

The boron rotor B 13 + 11 consists of a tri-atomic inner "wheel" that may rotate in its pseudo-rotating ten-atomic outer "bearing"-this concerted motion is called "contorsion." B 13 + 11 in its ground state has zero contorsional angular momentum. Starting from this initial state, it is a challenge to ignite contorsion by a laser pulse. We discover, however, that this is impossible, i.e., one cannot design any laser pulse that induces a transition from the ground to excited states with non-zero contorsional angular momentum. The reason is that the ground state is characterized by a specific combination of irreducible representations (IRREPs) of its contorsional and nuclear spin wavefunctions. Laser pulses conserve these IRREPs because hypothetical changes of the IRREPs would require nuclear spin flips that cannot be realized during the interaction with the laser pulse. We show that all excited target states of B 13 + 11 with non-zero contorsional angular momentum have different IRREPs that are inaccessible by laser pulses. Conservation of nuclear spins thus prohibits laser-induced transitions from the non-rotating ground to rotating target states. We discover various additional constraints imposed by conservation of nuclear spins, e.g., laser pulses can change clockwise to counter-clockwise contorsions or vice versa, but they cannot stop them. The results are derived in the frame of a simple model.

Charge Migration in Eyring, Walter and Kimball's 1944 Model of the Electronically Excited Hydrogen-Molecule Ion.

In an elementary variational treatment of the electronic structure of H2+, Eyring, Walter, and Kimball (EWK) serendipitously discovered charge migration (CM) in 1944. Using an analytic expression for the electronic probability density (EPD), they found that if the electron is initially localized on one of the protons (by taking the initial state to be a superposition of the ground and first excited electronic energy eigenstates), then it oscillates adiabatically between fixed protons with a period T inversely proportional to the energy gap between the eigenstates. At the equilibrium internuclear separation, T = 550.9 as. As shown here, the EWK model also yields an analytic formula for the electronic flux density (EFD). While the EPD indicates where the electron is at any instant, the EFD reveals the pathways the electron follows during its migration. Thus, the EFD complements the EPD, providing valuable new insight into the mechanism of CM. The formula for the EFD is a simple product of a time factor and a spatial factor. This factoring exposes a plethora of spatial-temporal symmetry relations which imply novel and surprising properties. An especially significant finding is that, in contrast to multielectron systems, where electron correlation may play a role in CM, in the EWK model of H2+, CM is due strictly to quantum interference between the ground and first excited electronic states.

Staircase patterns of nuclear fluxes during coherent tunneling in excited doublets of symmetric double well potentials.

Tunneling isomerization of molecules with symmetric double well potentials are associated with periodic nuclear fluxes, from the reactant R to the product P and back to R. Halfway between R and P the fluxes achieve their maximum values at the potential barrier. For molecules in the lowest tunneling doublet (v = 0) the rises and falls to and from the maximum values are approximately bell-shaped. Upon excitation to higher tunneling doublets v = 1, 2, etc., however, this shape is replaced by symmetric "staircase patterns" of the fluxes, with v + 1 stepping up and down in the domains of R and P, respectively. The quantum derivation of the phenomenon is universal. It is demonstrated here for a simple model of nuclear fluxes during tunneling isomerization of ammonia along the umbrella inversion mode, with application to separation of isotopomers.

Concerted Electronic and Nuclear Fluxes During Coherent Tunnelling in Asymmetric Double-Well Potentials.

The quantum theory of concerted electronic and nuclear fluxes (CENFs) during coherent periodic tunnelling from reactants (R) to products (P) and back to R in molecules with asymmetric double-well potentials is developed. The results are deduced from the solution of the time-dependent Schrödinger equation as a coherent superposition of two eigenstates; here, these are the two states of the lowest tunnelling doublet. This allows the periodic time evolutions of the resulting electronic and nuclear probability densities (EPDs and NPDs) as well as the CENFs to be expressed in terms of simple sinusodial functions. These analytical results reveal various phenomena during coherent tunnelling in asymmetric double-well potentials, e.g., all EPDs and NPDs as well as all CENFs are synchronous. Distortion of the symmetric reference to a system with an asymmetric double-well potential breaks the spatial symmetry of the EPDs and NPDs, but, surprisingly, the symmetry of the CENFs is conserved. Exemplary application to the Cope rearrangement of semibullvalene shows that tunnelling of the ideal symmetric system can be suppressed by asymmetries induced by rather small external electric fields. The amplitude for the half tunnelling, half nontunnelling border is as low as 0.218 × 10(-8) V/cm. At the same time, the delocalized eigenstates of the symmetric reference, which can be regarded as Schrödinger's cat-type states representing R and P with equal probabilities, get localized at one or the other minima of the asymmetric double-well potential, representing either R or P.

Multidirectional Angular Electronic Flux during Adiabatic Attosecond Charge Migration in Excited Benzene.

Recently, adiabatic attosecond charge migration (AACM) has been monitored and simulated for the first time, with application to the oriented iodoacetylene cation where AACM starts from the initial superposition of the ground state (φ0) and an electronic excited state (φ1). Here, we develop the theory for electronic fluxes during AACM in ring-shaped molecules, with application to oriented benzene prepared in the superposition of the ground and first excited singlet states. The initial state and its time evolution are analogous to coherent tunneling where φ0 and φ1 have different meanings; however, they denote the wave functions of the lowest tunneling doublet. This analogy suggests to transfer the theory of electronic fluxes during coherent tunneling to AACM, with suitable modifications which account for (i) the different time scales and (ii) the different electronic states, and which make use of (iii) the preparation of the initial state for AACM by a linearly polarized laser pulse. Application to benzene yields the multidirectional angular electronic flux with a pincer-motion type pattern during AACM: this unequivocal result confirms a previous working hypothesis. Moreover, the theory of AACM allows quantification of the electronic flux; that is, the maximum number of electrons (out of 42) which flow concertedly during AACM in benzene is 6 × 0.08 = 0.48.

Laser sculpting of atomic sp, sp(2) , and sp(3) hybrid orbitals.

Atomic sp, sp(2) , and sp(3) hybrid orbitals were introduced by Linus Pauling to explain the nature of the chemical bond. Quantum dynamics simulations show that they can be sculpted by means of a selective series of coherent laser pulses, starting from the 1s orbital of the hydrogen atom. Laser hybridization generates atoms with state-selective electric dipoles, opening up new possibilities for the study of chemical reaction dynamics and heterogeneous catalysis.

Quantum theory of concerted electronic and nuclear fluxes associated with adiabatic intramolecular processes.

An elementary molecular process can be characterized by the flow of particles (i.e., electrons and nuclei) that compose the system. The flow, in turn, is quantitatively described by the flux (i.e., the time-sequence of maps of the rate of flow of particles though specified surfaces of observation) or, in more detail, by the flux density. The quantum theory of concerted electronic and nuclear fluxes (CENFs) associated with electronically adiabatic intramolecular processes is presented. In particular, it is emphasized how the electronic continuity equation can be employed to circumvent the failure of the Born-Oppenheimer approximation, which always predicts a vanishing electronic flux density (EFD). It is also shown that all CENFs accompanying coherent tunnelling between equivalent "reactant" and "product" configurations of isolated molecules are synchronous. The theory is applied to three systems of increasing complexity. The first application is to vibrating, aligned H2(+)((2)Σg(+)), or vibrating and dissociating H2(+)((2)Σg(+), J = 0, M = 0). The EFD maps manifest a rich and surprising structure in this simplest of systems; for example, they show that the EFD is not necessarily synchronous with the nuclear flux density and can alternate in direction several times over the length of the molecule. The second application is to coherent tunnelling isomerization in the model inorganic system B4, in which all CENFs are synchronous. The contributions of core and valence electrons to the EFD are separately computed and it is found that core electrons flow with the nuclei, whereas the valence electrons flow obliquely to the core electrons in distinctive patterns. The third application is to the Cope rearrangement of semibullvalene, which also involves coherent tunnelling. An especially interesting discovery is that the so-called "pericyclic" electrons do not behave in the manner typically portrayed by the traditional Lewis structures with appended arrows. Indeed, it is found that only about 3 pericyclic electrons flow, in contrast to the 6 predicted by the Lewis picture. It is remarkable that the time scales of these three processes vary by 18 orders of magnitude: femtoseconds (H2(+)((2)Σg(+))); picoseconds (B4); kilosceconds (semibullvalene). It is emphasized that results presented herein are appearing in the literature for the first time.

From photoelectron detachment spectra of BrHBr(-), BrDBr(-) and IHI(-), IDI(-) to vibrational bonding of BrMuBr and IMuI.

Photoelectron detachment XLX(-)(00(0)0) + hν → XLX(vib) + e(-) + KER (X = Br or I, L = H or D) at sufficiently low temperatures photoionizes linear dihalogen anions XLX(-) in the vibrational ground state (v1v2 (l)v3 = 00(0)0) and prepares the neutral radicals XLX(vib) in vibrational states (vib). At the same time, part of the photon energy (hν) is converted into kinetic energy release (KER) of the electron [R. B. Metz, S. E. Bradforth, and D. M. Neumark, Adv. Chem. Phys. 81, 1 (1992)]. The process may be described approximately in terms of a Franck-Condon type transfer of the vibrational wavefunction representing XLX(-)(00(0)0) from the domain close to the minimum of its potential energy surface (PES) to the domain close to the linear transition state of the PES of the neutral XLX. As a consequence, prominent peaks of the photoelectron detachment spectra (pds) correlate with the vibrational energies EXLX,vib of states XLX(vib) which are centered at linear transition state. The corresponding vibrational quantum numbers may be labeled vib = (v1v2 (l)v3) = (00(0)v3). Accordingly, the related most prominent peaks in the pds are labeled v3. We construct a model PES which mimics the "true" PES in the domain of transition state such that it supports vibrational states with energies EXLX,pds,00(0)v3 close to the peaks of the pds labeled v3 = 0, 2, and 4. Subsequently, the same model PES is also used to calculate approximate values of the energies EXMuX,00(0)0 of the isotopomers XMuX(00(0)0). For the heavy isotopomers XHX and XDX, it turns out that all energies EXLX,00(0)v3 are above the threshold for dissociation, which means that all heavy XLX(00(0)v3) with wavefunctions centered at the transition state are unstable resonances with finite lifetimes. Turning the table, bound states of the heavy XLX are van der Waals (vdW) bonded. In contrast, the energies EXMuX,00(0)0 of the light isotopomers XMuX(00(0)0) are below the threshold for dissociation, with wavefunctions centered at the transition state. This means that XMuX(00(0)0) are vibrationally bonded. This implies a fundamental change of the nature of chemical bonding, from vdW bonding of the heavy XHX, XDX to vibrational bonding of XMuX. For BrMuBr, the present results derived from experimental pds of BrHBr(-) and BrDBr(-) confirm the recent discovery of vibrational bonding based on quantum chemical ab initio calculations [D. G. Fleming, J. Manz, K. Sato, and T. Takayanagi, Angew. Chem., Int. Ed. 53, 13706 (2014)]. The extension from BrLBr to ILI means the discovery of a new example of vibrational bonding. These empirical results for the vibrational bonding of IMuI, derived from the photoelectron spectra of IHI(-) and IDI(-), are supported by ab initio simulations of the spectra and of the wavefunction representing vibrational bonding of IMuI.

Vibrating H2(+)((2)Σg(+), JM = 00) ion as a pulsating quantum bubble in the laboratory frame.

We present quantum dynamics simulations of the concerted nuclear and electronic densities and flux densities of the vibrating H2(+) ion with quantum numbers (2)Σg(+), JM = 00 corresponding to the electronic and rotational ground state, in the laboratory frame. The underlying theory is derived using the nonrelativistic and Born­Oppenheimer approximations. It is well-known that the nuclear density of the nonrotating ion (JM = 00) is isotropic. We show that the electronic density is isotropic as well, confirming intuition. As a consequence, the nuclear and electronic flux densities have radial symmetry. They are related to the corresponding densities by radial continuity equations with proper boundary conditions. The time evolutions of all four observables, i.e., the nuclear and electronic densities and flux densities, are illustrated by means of characteristic snapshots. As an example, we consider the scenario with initial condition corresponding to preparation of H2(+) by near-resonant weak field one-photon-photoionization of the H2 molecule in its ground state, (1)Σg(+), vJM = 000. Accordingly, the vibrating, nonrotating H2(+) ion appears as pulsating quantum bubble in the laboratory frame, quite different from traditional considerations of vibrating H2+ in the molecular frame, or of the familiar alternative scenario of aligned vibrating H2(+) in the laboratory frame.

Fundamental change in the nature of chemical bonding by isotopic substitution.

Isotope effects are important in the making and breaking of chemical bonds in chemical reactivity. Here we report on a new discovery, that isotopic substitution can fundamentally alter the nature of chemical bonding. This is established by systematic, rigorous quantum chemistry calculations of the isotopomers BrLBr, where L is an isotope of hydrogen. All the heavier isotopomers of BrHBr, BrDBr, BrTBr, and Br(4)HBr, the latter indicating the muonic He atom, the heaviest isotope of H, can only be stabilized as van der Waals bound states. In contrast, the lightest isotopomer, BrMuBr, with Mu the muonium atom, alone exhibits vibrational bonding, in accord with its possible observation in a recent experiment on the Mu+Br2 reaction. Accordingly, BrMuBr is stabilized at the saddle point of the potential energy surface due to a net decrease in vibrational zero point energy that overcompensates the increase in potential energy.

From chiral laser pulses to femto- and attosecond electronic chirality flips in achiral molecules.

Chirality is an important topic in biology, chemistry and physics. Here we show that ultrashort circularly polarized laser pulses, which are chiral, can be fired on achiral oriented molecules to induce chirality in their electronic densities, with chirality flips within femtoseconds or even attoseconds. Our results, obtained by quantum dynamics simulations, use the fact that laser pulses can break electronic symmetry while conserving nuclear symmetry. Here two laser pulses generate a superposition of three electronic eigenstates. This breaks all symmetry elements of the electronic density, making it chiral except at the periodic rare events of the chirality flips. As possible applications, we propose the combination of the electronic chirality flips with Chiral Induced Spin Selectivity.

Nuclear fluxes in diatomic molecules deduced from pump-probe spectra with spatiotemporal resolutions down to 5 pm and 200 asec.

When molecules move, their nuclei flow. The corresponding quantum observable, i.e., the nuclear flux density, was introduced by Schrödinger in 1926, but until now, it has not been measured. Here the first experimental results are deduced from high-resolution pump-probe measurements of the time-dependent nuclear densities in a vibrating diatomic molecule or molecular ion. The nuclear densities are converted to flux densities by means of the continuity equation. The flux densities are much more sensitive to time-dependent quantum effects than the densities. Applications to the sodium molecule and the deuterium molecular ion unravel four new effects; e.g., at the turns from bond stretch to compression, the flux of the nuclei exhibits multiple changes of directions, from small to large bond lengths, a phenomenon that we call the "quantum accordion."

Nuclear flux densities during a model pericyclic reaction with energies well above and below the potential barrier.

Pericyclic reactions with energies E well above the potential energy barrier B (case E>B) proceed with quantum nuclear flux densities 〈j〉 which are essentially proportional to the nuclear densities ρ in the femtosecond time domain. This corresponds to the definition of classical (cl) mechanics, j(cl)=υ(cl) ρ(cl), with almost constant velocity v(cl). For the other case E

Electronic bond-to-bond fluxes in pericyclic reactions: synchronous or asynchronous?

One at a time or all at once? Electronic fluxes during a pericyclic reaction in the electronic ground state--exemplified for the degenerate Cope rearrangement of semibullvalene--may proceed either synchronously or asynchronously. Quantum simulations show that the mechanism is determined by the preparation of the reactants, for example, synchronous at cryogenic temperatures (tunneling) but asynchronous when induced by selective laser pulses (with energy over the barrier).