We give an explicit and general description of the energy, linear momentum, angular momentum and boost momentum of a molecule to order $1/c^2$, where it necessary to take account of kinetic contributions made by the electrons and nuclei as well as electromagnetic contributions made by the intramolecular field. A wealth of interesting subtleties are encountered that are not seen at order $1/c^0$, including relativistic Hall shifts, anomalous velocities and hidden momenta. Some of these have well known analogues in solid state physics.
Photoelectron circular dichroism refers to the forward/backward asymmetry in the photoelectron angular distribution with respect to the propagation axis of circularly polarized light. It has recently been demonstrated in femtosecond multi-photon photoionization experiments with randomly oriented camphor and fenchone molecules [C. Lux et al., Angew. Chem. Int. Ed. 51, 5001 (2012);C. S. Lehmann et al., J. Chem. Phys. 139, 234307 (2013)]. A theoretical framework describing this process as (2+1) resonantly enhanced multi-photon ionization is constructed, which consists of two-photon photoselection…
The application of a matrix-based reconstruction protocol for obtaining Molecular Frame (MF) photoelectron angular distributions (MFPADs) from laboratory frame (LF) measurements (LFPADs) is explored. Similarly to other recent works on the topic of MF reconstruction, this protocol makes use of time-resolved LF measurements, in which a rotational wavepacket is prepared and probed via photoionization, followed by a numerical reconstruction routine; however, in contrast to other methodologies, the protocol developed herein does not require determination of photoionization matrix elements, and cons…
Photoelectron angular distributions (PADs) of oriented polar molecules in response to different polarized lasers are systematically investigated. It is found that the PADs of polar CO molecules show three distinct styles excited by linearly, elliptically and circularly polarized lasers respectively. In the case of elliptical polarization, a deep suppression is observed along the major axis and the distribution concentrates approximately along the minor axis. Additionally, it is also found that the concentrated distributions rotate clockwise as the ellipticity increases. Our investigation prese…
We show that in non-collinear magnetic molecules, non-adiabatic (dynamical) effects due to the electron-vibron coupling are time-reversal symmetry breaking interactions for the vibrational field. As in these systems the electronic wavefunction can not be chosen as real, a nonzero geometric vector potential (Berry connection) arises. As a result, an intrinsic nonzero vibrational angular momentum occurs even for non-degenerate modes and in the absence of external probes. The vibronic modes can then be seen as elementary quantum particles carrying a sizeable angular momentum. As a proof of concep…
Recently it was shown that a molecule rotating in a quantum solvent can be described in terms of the `angulon' quasiparticle [Phys. Rev. Lett. 118, 095301 (2017)]. Here we extend the angulon theory to the case of molecules possessing an additional spin-1/2 degree of freedom and study the behavior of the system in the presence of a static magnetic field. We show that exchange of angular momentum between the molecule and the solvent can be altered by the field, even though the solvent itself is non-magnetic. In particular, we demonstrate a possibility to control resonant emission of phonons with…
Molecular line lists, particularly those computed for high temperature applications, often have very few states assigned local quantum numbers. These are often important components for accurately determining line shape parameters required for radiative transfer simulations. The projection of the total angular momentum onto the molecule fixed axis ($k$) is investigated in the Radau internal coordinate system to determine when it can be considered a good quantum number. In such a coordinate system, when the square of the $k^{th}$ component of the wavefunction is greater than one half, then we ca…
We present a new extension of the UKRmol electron-molecule scattering code suite, which allows one to compute ab initio photoionization and photorecombination amplitudes for complex molecules, resolved both on the molecular alignment (orientation) and the emission angle and energy of the photoelectron. We illustrate our approach using CO$_2$ as an example, and analyze the importance of multi-channel effects by performing our calculations at different, increasing levels of complexity. We benchmark our method by comparing the results of our calculations with experimental data and with theoretica…
It is shown that the atom-molecule collision problem in the presence of an external electric field can be solved using the total angular momentum representation in the body-fixed coordinated frame, leading to a computationally efficient method for ab initio modeling of low-temperature scattering phenomena. Our calculations demonstrate rapid convergence of the cross sections for vibrational and Stark relaxation in He-CaD collisions with the number of total angular momentum states in the basis set, leading to a 5-100 fold increase in computational efficiency over the previously used methods base…
In this paper a coherent superposition of angular momentum states created by absorption of polarized light by molecules is analyzed. Attention is paid to the time evolution of wave packets representing spatial orientation of internuclear axis of diatomic molecule. Two examples are considered in detail. Molecules absorbing light in a permanent magnetic field experiencing Zeeman effect and molecules absorbing light in a permanent electric field experiencing quadratic Stark effect. In a magnetic field we have a wave packet that evolves in time exactly as classical dipole oscillator in a permanent…
In this paper, we discuss the dissociative electron attachment process in Ammonia. Kinetic energy and angular distributions of H^{-} and NH_{2}^{-} fragment anions across the two well known resonances at 5.5 eV and 10.5 eV are reported. The angular distributions show deviation of axial recoil approximation akin to that observed in water.
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…
We provide a theory of the deflection of polar and non-polar rotating molecules by inhomogeneous static electric field. Rainbow-like features in the angular distribution of the scattered molecules are analyzed in detail. Furthermore, we demonstrate that one may efficiently control the deflection process with the help of short and strong femtosecond laser pulses. In particular the deflection process may by turned-off by a proper excitation, and the angular dispersion of the deflected molecules can be substantially reduced. We study the problem both classically and quantum mechanically, taking i…
In this paper, we discuss the dissociative electron attachment process in Methane. Kinetic energy and angular distributions of H^{-} and CH_{2}^{-} fragment anions across the broad resonance about 10 eV is reported. Angular distribution of H^{-} ions changes from being perpendicular to forward-backward scattering across the resonance. Possibility of Jahn-Teller effect on excitation of the triply degenerate 1t2 molecular orbital is inferred.
The formation of vortices is usually considered to be the main mechanism of angular momentum disposal in superfluids. Recently, it was predicted that a superfluid can acquire angular momentum via an alternative, microscopic route -- namely, through interaction with rotating impurities, forming so-called `angulon quasiparticles' [Phys. Rev. Lett. 114, 203001 (2015)]. The angulon instabilities correspond to transfer of a small number of angular momentum quanta from the impurity to the superfluid, as opposed to vortex instabilities, where angular momentum is quantized in units of $\hbar$ per atom…
The combination of photoelectron spectroscopy and ultrafast light sources is on track to set new standards for detailed interrogation of dynamics and reactivity of molecules. A crucial prerequisite for further progress is the ability to not only detect the electron kinetic energy, as done in traditional photoelectron spectroscopy, but also the photoelectron angular distributions (PADs) in the molecular frame. Here carbonylsulfide (OCS) and benzonitrile molecules, fixed in space by combined laser and electrostatic fields, are ionized with intense, circularly polarized, 30 femtosecond laser puls…
We show that the integral cross sections for state-to-state quantum scattering of cold molecules in a magnetic field can be efficiently computed using the total angular momentum representation despite the presence of unphysical Zeeman states in the eigenspectrum of the asymptotic Hamiltonian. We demonstrate that the unphysical states arise due to the incompleteness of the space-fixed total angular momentum basis caused by using a fixed cutoff value $J_\text{max}$ for the total angular momentum of the collision complex $J$. As a result, certain orbital angular momentum ($l$) basis states lack t…
We use laser-induced rotation of single molecules embedded in superfluid helium nanodroplets to reveal angular momentum dynamics and transfer in a controlled setting, under far-from-equilibrium conditions. As an unexpected result, we observe pronounced oscillations of time-dependent molecular alignment that have no counterpart in gas-phase molecules. Angulon theory reveals that these oscillations originate from the unique rotational structure of molecules in He droplets and quantum-state-specific transfer of rotational angular momentum to the many-body He environment on picosecond timescales. …
We present a simple quantum mechanical model describing excited rotational states of molecules in superfluid helium nanodroplets, as recently studied in non-adiabatic molecular alignment experiments [Cherepanov et al., Phys. Rev. A 104, L061303 (2021)]. We show that a linear molecule immersed in a superfluid can be seen as an effective symmetric top, similar to the rotational structure of radicals, such as OH or NO, but with the angular momentum of the superfluid playing the role of the electronic angular momentum in free molecules. The model allows to evaluate the effective rotational and cen…
In the present paper, we report the details of the kinetic energy and angular distributions of the H^{-}, S^{-}/SH^{-} fragment ions produced due to dissociative electron attachment in H_{2}S molecules at resonances peaking at 2.2 eV, 5.2 eV, 7.5 eV and 10 eV.
Resonant scattering of optically state-prepared and aligned molecules in the cold regime allows the most detailed interrogation and control of bimolecular collisions. This technique has recently been applied to collisions of two aligned ortho-D2 molecules prepared in the j=2 rotational level of the v=2 vibrational manifold using the Stark-induced adiabatic Raman passage technique. Here, we develop the theoretical formalism for collisions of two aligned molecules and apply our approach to state-prepared D2(v=2,j=2) + D2(v=2,j=2) --> D2(v=2,j=2) + D2(v=2,j=0) collisions. Quantum scattering calcu…
We present a new variation of Young's double-slit formula for polarization-averaged molecular-frame photoelectron angular distributions (PA-MFPADs) of hetero-diatomic molecules, which may be used to extract the bond length. So far, empirical analysis of the PA-MFPADs has often been carried out employing Young's formula in which each of the two atomic centers emits a $s$-photoelectron wave. The PA-MFPADs, on the other hand, can consist of an interference between the $p$-wave from the X-ray absorbing atom emitted along the molecular axis and the $s$-wave scattered by neighboring atom, within the…
A new iterative version of population projection analysis is formulated and applied to determine relativistic effective atomic configurations of superheavy elements Cn and Fl and their lighter homologues (Hg and Pb) in the molecules of their fluorides and oxides. The dependence of the computed populations on the initial reference atomic spinors is completely avoided. The difference in population of atomic spinors with the same orbital angular momentum and different total angular momenta is demonstrated to be essential for understanding the peculiarities of chemical bonding in superheavy elemen…
Measuring inelastic rates with partial wave resolution requires temperatures close to a Kelvin or below, even for the lightest molecule. In a recent experiment Perreault et al. [1] studied collisional relaxation of excited HD molecules in the v = 1, j = 2 state by para- and ortho-H2 at a temperature of about 1 K, extracting the angular distribution of scattered HD in the v = 1,j = 0 state. By state-preparation of the HD molecules, control of the angular distribution of scattered HD was demonstrated. Here, we report a first-principles simulation of that experiment which enables us to attribute …
Zepto to Attosecond core-level photoemission time delays in homonuclear diatomic molecules and non-dipole effects in the framework of Multiple Scattering theory
Theory of long-range interactions between an atom in its ground S state and a linear molecule in a degenerate state with a non-zero projection of the electronic orbital angular momentum is presented. It is shown how the long-range coefficients can be related to the first and second-order molecular properties. The expressions for the long-range coefficients are written in terms of all components of the static and dynamic multipole polarizability tensor, including the nonadiagonal terms connecting states with the opposite projection of the electronic orbital angular momentum. It is also shown th…
Semiclassical oscillation of the electron through the nucleus of the H atom yields both the exact energy and the correct orbital angular momentum for l=0 quantum states. Similarly, electron oscillation through the nuclei of H2+ accounts for a stable molecule ion with energy close to the quantum mechanical solution. The small discrepancy arises from the neglect of the electron's wave nature.
We show that the cross sections for molecule - molecule collisions in the presence of an external field can be computed efficiently using a total angular momentum basis, defined either in the body-fixed frame or in the space-fixed coordinate system. This method allows for computations with much larger basis sets than previously possible. We present calculations for 15NH - 15NH collisions in a magnetic field. Our results support the conclusion of the previous study that the evaporative cooling of rotationally ground 15NH molecules in a magnetic trap has a prospect of success.
The ro--vibrational spectra of molecules dissolved in liquid $^4$He nanodroplets display rotational structure. Where resolved, this structure has been used to determine a temperature that has been assumed to equal that of the intrinsic excitations of the helium droplets containing the molecules. Consideration of the density of states as a function of energy and total angular momentum demonstrates that there is a small but significant bias of the rotor populations that make the temperature extracted from a fit to its rotational level populations slightly higher than the temperature of the rippl…
The Angular Localization Function (ALF): a practical tool to measure solvent angular order with Molecular Density Functional Theory
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux, PHENIX（界面电解质与纳米系统物理化学 PHENIX）；Réseau sur le Stockage Électrochimique de l’Énergie (RS2E)（电化学储能网络 RS2E）
An electrical molecular motor driven by angular momentum transfer
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Charles University（查理大学）；UPV/EHU（巴斯克国立大学）；CSIC-UPV/EHU（西班牙国家研究委员会-巴斯克国立大学）；University of Regensburg（雷根斯堡大学）；University of Basel（巴塞尔大学）
The photoionization of chiral molecules prepared in a coherent superposition of excited states can give access to the underlying chiral coherent dynamics in a procedure known as photoexcitation induced photoelectron circular dichroism (PXECD). This exclusive dependence on coherence can also be seen in a different part of the angular spectrum, where it is not contingent on the chirality of the molecule, thus allowing extension of PXECD's sensitivity to tracking coherence to non-chiral molecules. Here we present a general theory of PXECD based on angular momentum algebra and derive explicit expr…
A new, hitherto unknown bound state of the positronium molecule, with orbital angular momentum L=1 and negative parity is reported. This state is stable against autodissociation even if the masses of the positive and negative charges are not equal. The existence of a similar state in two-dimension has also been investigated. The fact that the biexcitons have a second bound state may help the better understanding of their binding mechanism.
The aim of this article is to present the interference effects which occur during the time evolution of simple angular wave packets (WP) which can be associated to a diatomic rigid molecule (heteronuclear) or to a quantum rigid body with axial symmetry like a molecule or a nucleus. The time evolution is understood entirely within the frame of fractional revivals discovered by Averbukh and Perelman since the energy spectrum is exactly quadratic. Our objectives are to study how these interference effects differ when there is a change of the initial WP. For this purpose we introduce a two paramet…
A classical microscopic theory of rovibrational motion at high angular momenta in symmetrical non-linear molecules AB$_2$ is derived within the framework of small oscillations near the stationary states of a rotating molecule. The full-dimensional analysis including stretching vibrations has confirmed the existence of the bifurcation predicted previously by means of the rigid-bender model. The formation of fourfold energy clusters has already been experimentally verified for H$_2$Se and it has been demonstrated in fully-dimensional quantum mechanical calculations using the MORBID computer prog…
