Molecular Orbital Tomography Research Articles

SLIMP 2.0: A new version of strong laser interaction model package for atoms and molecules, now with molecular orbital tomography based on high-order harmonic spectra

A new version of strong laser interaction model package for atoms and molecules is presented. Its capacities are enhanced by incorporating modules related to molecular orbital tomography (MOT) in length and velocity forms based on high-order harmonic spectra (HHS). This advanced package enables two-dimensional and three-dimensional MOT of both symmetric and asymmetric molecules using HHS, providing an efficient means for both experimental and theoretical investigations of molecular orbital structures. In addition, it can calculate the precise theoretical orbitals corresponding to those reconstructed by MOT. Furthermore, the package can calculate the transition dipole moment (TDM) in the plane wave approximation and allow for reference MOT based on TDM. It can evaluate the quality of reconstructed orbitals based on HHS and reveal the physical and numerical effects on MOT. This package is suitable for MOT under conditions of driving laser at different intensities and wavelengths, and can be applied to different molecules with various structures. It is designed to facilitate easy expansion for additional capabilities. Program summaryProgram Title: SLIMP, version 2.0CPC Library link to program files:https://doi.org/10.17632/jgcb7m7wwv.1Licensing provisions: GPLv3Programming language: Fortran 90Journal reference of previous version: Comput. Phys. Commun. 192 (2015) 330-341.Does the new version supersede the previous version?: Yes.Reasons for the new version: Molecular orbital tomography (MOT) [1] based on high-order harmonic spectra (HHS) [2] is an important research topic in the field of strong-field physics. It provides an efficient way to probe molecular orbital structures experimentally, which was not considered in the former version of SLIMP [3] and is now included in SLIMP 2.0. The new version package allows performing two-dimensional (2D) and three-dimensional (3D) MOT [4] based on HHS obtained from experiments or simulations, providing reliable detections for many orbitals of interest, either symmetric or asymmetric molecules.Summary of revisions: Extending capacities focus on enabling performing 2D and 3D MOT on symmetric and asymmetric molecules based on HHS, and together the relevantly precise theoretical orbital output, calculation of transition dipole moment (TDM) and reference MOT based on TDM. For 2D MOT, MOT in both length and velocity forms are implemented.Nature of problem: To perform MOT based on HHS, the user needs general reconstruction programs, taking symmetric and asymmetric molecules, 2D and 3D orbitals, and MOT in length and velocity forms into account. In addition, evaluation of imaging quality is required, which can reveal the physical and numerical effects on reconstructions.Solution method: The 2D symmetric and asymmetric, length- and velocity-form, and 3D reconstruction algorithms are implemented based on Fortran 90. Furthermore, this package provides a reference MOT based on directly calculated TDM, served as a comparable result to the reconstructed orbital based on HHS. The comparison between reconstructions based on HHS and TDM can reveal the effects on MOT in physical and numerical aspects.Additional comments including restrictions and unusual features: This package does not include MOT of asymmetric molecules in velocity form. For the 2D MOT based on HHS, the reconstructed 2D projection of gerade, ungerade orbital or the gerade and ungerade components of asymmetric orbital must have the axial symmetry about the x- and z-axis. For the 3D MOT, the reconstructed 3D orbital has to be cylindrically symmetric.

Molecular orbital tomography of HOMO and HOMO-1 of the nonlinear molecule H2O: The study on multi-orbital effects

Molecular orbital tomography (MOT) through high-order harmonic generation (HHG) is a crucial method for probing individual molecular orbitals. Previous studies mainly focused on linear molecules such as N2, and CO, where valence orbitals were imaged by detecting harmonic emission at various alignments. In this study, we investigate the HHG from the water molecules, with the aim of exploring MOT for nonlinear molecules. By employing the time-dependent density functional theory, we obtain HHG spectra for different angles between the laser polarization and molecular symmetry axis. By manipulating the scanning planes (planes perpendicular to the laser propagation direction and contain the field polarization direction), specific orbitals can be selectively imaged. Particularly, a well-reconstructed highest occupied molecular orbital (HOMO) is obtained when the laser scanning plane approximately aligns with the nodal plane of HOMO-1. However, when the laser polarization deviates from the nodal plane, multiple orbitals contribute to the HHG process, and we visualize the orbital distortions resulting from such effects. Furthermore, HOMO-1, can be reconstructed when the laser scanning plane aligns with the nodal plane of HOMO. This research significantly advances the development of MOT and opens up intriguing possibilities for reconstructing orbitals of more complex molecules.

Rydberg state excitation of atoms and molecules in ultrafast intense laser field

When atoms or molecules are irradiated by a strong laser field with pulse duration of tens of femtoseconds and intensity larger than 10<sup>13</sup> W/cm<sup>2</sup>, they will generally undergo tunneling ionization, which will induce various non-perturbative and highly nonlinear phenomena. Investigations into the strong field physical processes is of significance in studying attosecond physics, molecular orbital imaging, ultrafast electron diffraction and advanced short ultraviolet light sources. While there is a relatively long history of the studies of tunneling ionization induced physics including high-order above threshold ionization (HATI), high-order harmonic generation (HHG) and non-sequential double ionization (NSDI), it is until recently to surprisedly find that in the tunneling ionization region, neutral atoms or molecules can survive in strong laser fields in highly excited Rydberg states. As a basic process of the interaction between ultrafast strong laser fields and atoms or molecules, such a Rydberg state excitation (RSE) has been viewed as an important supplement to the physical picture of the tunneling ionization. During the past several years, the extensive research attention has been paid to the RSE process in strong laser field. Various theoretical and experimental methods have been developed to investigate the strong field RSE of both atoms and molecules, to understand the underlying physical mechanism behind the recapture of the tunneling electrons and to reveal the quantum features and molecular structure effect in RSE. These advances have brought about an in-depth understanding and a systematic view of the atomic and molecular RSE in strong laser fields, as well as their relations to the other tunneling ionization induced physical processes such as ATI, HHG and NSDI. Here, we systematically review recent research progress of the atomic and molecular RSE in strong laser fields. We particularly focus on several aspects of this strong field process, i.e. the physical mechanism of the recapture, the quantum feature and the interference of different orbits, and the structure effect in molecular RSE. In addition, neutral particle acceleration and coherent radiation which can be induced by the strong field RSE, are also discussed. Finally, we provide a short summary and prospect of the future studies on the strong field RSE.

Three-dimensional tomographic imaging of CO molecular orbitals reveals multi-electron effects

According to the asymmetric molecular orbital reconstruction algorithm, which divides orbital into gerade and ungerade components and which does not depend on the unidirectional recollisional condition, we obtain the two-dimensional highest occupied molecular orbital (HOMO) of CO based on the directly calculated transition dipole moment and the harmonic spectra calculated by the Lewenstein model, respectively, which is the three-dimensional (3D) HOMO projected onto the plane perpendicular to the laser propagation direction. In order to retrieve the full orbital function, a 3D molecular orbital tomography (MOT) method is developed and is successfully applied to the reconstructions of the HOMO of CO, which simplifies the 3D imaging process of orbitals of linear molecules, and is expected to be extended to reconstruct the 3D orbitals of nonlinear molecules. In addition, the time-dependent density functional theory is employed to acquire the harmonic spectra of CO in a 800 nm and 1500 nm wavelength laser, respectively. The comparison of these two reconstruction results helps identify the multi-electron effects for asymmetric MOT, which requires further study. This work advances the development of MOT and is expected to reveal multi-electron effects in orbital imaging of complex polyatomic molecules.

Long-Lasting Molecular Orientation Induced by a Single Terahertz Pulse.

We present a novel, previously unreported phenomenon appearing in a thermal gas of nonlinear polar molecules excited by a single THz pulse. We find that the induced orientation lasts long after the excitation pulse is over. In the case of symmetric-top molecules, the time-averaged orientation remains indefinitely constant, whereas in the case of asymmetric-top molecules the orientation persists for a long time after the end of the pulse. We discuss the underlying mechanism, study its nonmonotonous temperature and amplitude dependencies, and show that there exist optimal parameters for maximal residual orientation. The persistent orientation implies a long-lasting macroscopic dipole moment, which may be probed by even harmonic generation and may enable deflection by inhomogeneous electrostatic fields.

Principle and application of two-color attoclock

Time-resolving ultrafast electron dynamics driven by lights in atoms and molecules is one of the central topics in both science and technology, as a prerequisite for controlling the electron dynamics and creating unprecedented functions to serve for human. Photoionization by intense lasers is the fundamental interaction between lights and atoms. For strong-field ionization, the amplitude and the phase of the ionized electron wave packet could give direct insights of electron dynamics in the classically forbidden, sub-Coulomb-barrier region. Electron tunneling through the suppressed Coulomb potential and traveling in continuum leave fingerprints not only on the amplitude of the electron wave packet, but also on its phase distribution. Recently, benefiting from that the laser pulse duration approaches to the natural time scale of intra-atomic electron dynamics, one was allowed to image the amplitude and the phase of an electron wave function on the attosecond scale using new metrologies combined with attosecond light pulses, such as attosecond streaking camera and the technique of reconstruction of attosecond beating by interference of two-photon transition. Alternatively, attoclock is based on the angle-time mapping principle in one-color circularly polarized femtosecond light fields, without resorting to the attosecond light pulses. It is originally introduced as a powerful method to address the issue of tunneling time delays with the attosecond time resolution in strong-field physics. In recent years, due to the flexible manipuility and the rich diversity of the two-color femtosecond light fields, the two-color fields have gradually become an important method to control the ultrafast electron dynamics driven by intense lasers. The two-color attoclock combined with attoclock and two-color fields, then attracts the increasing attention, and hence becomes the research front of strong-field physics. In this review, we will introduce two kinds of the two-color attoclock. First, based on the co-rotating two-color light fields, we demonstrate a novel time-resolved photoelectron interferometry, i.e., double-hand attoclock. Using this technique, one can extract the phase information and the amplitude information of the ionized electron wavepackets by strong-field ionization with intense light pulses. From the extracted time-resolved distributions of electron phase and amplitude, we reveal the electron sub-barrier dynamics with attosecond time resolution. As to the second two-color attoclock, we study the old and controversial question, i.e., tunneling time delay. Introducing a linearly polarized second harmonic field to calibrate the attoclock constructed by a circularly polarized fundamental-frequency light field, we demonstrate an improved attoclock. The improved attoclock can measure the photoelectron offset angle more accurately, which corresponds to tunneling time delay. Theoretically, we also demonstrate that the instantaneous tunneling picture and the Wigner delay picture for tunneling, which seem contradictory with each other, can be unified within the same theoretical framework, i.e., strong-field approximation theory. For the result of the improved attoclock, the two tunneling pictures can both agree with the experiment. To conclude, the two-color attoclock possesses not only very high time resolution but also good space resolution. Therefore, the two-color attclock has a very exciting potential in molecular orbital imaging, tunneling ionization of molecules and so on.

Can photoemission tomography be useful for small, strongly-interacting adsorbate systems?

Molecular orbital tomography, also termed photoemission tomography, which considers the final state as a simple plane wave, has been very successful in describing the photoemisson distribution of large adsorbates on noble metal surfaces. Here, following a suggestion by Bradshaw and Woodruff (2015 New J. Phys. 17 013033), we consider a small and strongly-interacting system, benzene adsorbed on palladium (110), to consider the extent of the problems that can arise with the final state simplification. Our angle-resolved photoemission experiments, supported by density functional theory calculations, substantiate and refine the previously determined adsorption geometry and reveal an energetic splitting of the frontier π-orbital due to a symmetry breaking which has remained unnoticed before. We find that, despite the small size of benzene and the comparably strong interaction with palladium, the overall appearance of the photoemission angular distributions can basically be understood within a plane wave final state approximation and yields a deeper understanding of the electronic structure of the interface. There are, however, noticeable deviations between measured and simulated angular patterns which we ascribe to molecule-substrate interactions and effects beyond a plane-wave final state description.

Three-dimensional tomographic imaging of molecular orbitals by photoelectron momentum microscopy

As one of the fundamental concepts of quantum mechanics, electrons in atoms and molecules are assigned to respective orbitals. The geometric distribution of these orbitals is immediately connected to many chemical and physical properties of the system. Consequently, measuring electron orbitals directly has been highly desired. In this study, we demonstrate how a combination of a photoemission electron microscope with a synchrotron UV-light source can be utilised to record a three-dimensional set of tomographic data and present a detailed procedure to reconstruct the orbitals under investigation in real space.

Images of molecular orbitals in strong-field photoelectron momentum distributions generated by circularly polarized pulses

Strong-field photoelectron momentum distributions (PEMDs) generated in the ionization of molecules by circularly polarized laser pulses contain valuable information on the structure of the ionizing molecular orbital. In this paper, we investigate using the adiabatic theory how this information is imprinted in and can be extracted from such PEMDs. The PEMDs have a donutlike shape. The variation of a PEMD along the donut reproduces the orientation dependence of the ionization rate of the ionizing orbital, and hence reflects its nodal structure and shape. The transverse structure of the PEMD in cross sections of the donut corresponding to orientations of the molecule at which the ionizing orbital has a node in the direction opposite to that of the instantaneous laser field reflects the interplay of two competing ionization channels, which provides additional information on the orbital structure. We illustrate these features by the analysis of PEMDs for three states of different symmetries of the hydrogen molecular ion ${\mathrm{H}}_{2}{}^{+}$.

Tomography of asymmetric molecular orbitals with a one-color inhomogeneous field.

We demonstrate image asymmetric molecular orbitals via high-order harmonic generation in a one-color inhomogeneous field. Due to the broken inversion symmetry of the inhomogeneous field in space, the returning electrons with energy in a broad range can be forced to recollide from only one direction for all the orientation angles of molecules, which therefore can be used to reconstruct asymmetric molecular orbitals. Following the procedure of molecular orbital tomography, the highest occupied molecular orbital of carbon monoxide (CO) is satisfactorily reconstructed with high-order harmonic spectra driven by the inhomogeneous field. This scheme is helpful to relax the requirement of laser conditions and is also applicable to other asymmetric molecules.

Symmetry in circularly polarized molecular high-order harmonic generation with intense bicircular laser pulses

We present symmetry effects of laser fields and molecular geometries in circularly polarized high-order harmonic generation by bichromatic counter-rotating circularly polarized laser pulses. Simulations are performed on oriented molecules by numerically solving time-dependent Schr\odinger equations. We discuss how electron recollision trajectories by the orthogonal laser field polarizations influence the harmonic polarization by using a time-frequency analysis of harmonics. It is found that orientation-dependent asymmetric ionization in linear molecules due to Coulomb potentials gives rise to a dependence of the polarization on the harmonic frequency. Effects of Coriolis forces are also presented on harmonic generation. Electron recollision trajectories illustrate the effects of the relative symmetry of the field and the molecule, thus paving a method for circularly polarized attosecond pulse generation and molecular orbital imaging in more complex systems.

Single-shot molecular orbital tomography with orthogonal two-color fields.

Molecular orbital tomography (MOT) based on high-order-harmonic generation opens a way to track the molecular electron dynamics or even follow a chemical reaction. However, the real-time imaging of the evolution of electron orbitals is hampered by the multi-shot measurement of high-order harmonics. Here, we report a single-shot MOT scheme with orthogonal two-color (OTC) fields. This scheme enables the tomographic imaging of molecular orbital with single-shot measurement in experiment, owing to the two-dimensional manipulation of the electron motion in OTC fields. Our work paves the way towards tracking the molecular electron dynamics with combined attosecond temporal and sub-Ångström spatial resolutions.

Laser-induced blurring of molecular structure information in high harmonic spectroscopy

High harmonic spectroscopy gives access to molecular structure with Angström resolution. Such information is encoded in the destructive interferences occurring between the harmonic emissions from the different parts of the molecule. By solving the time-dependent Schrödinger equation, either numerically or with the molecular strong-field approximation, we show that the electron dynamics in the emission process generally results in a strong spectral smoothing of the interferences, blurring the structural information. However we identify specific generation conditions where they are unaffected. These findings have important consequences for molecular imaging and orbital tomography using high harmonic spectroscopy.

Asymmetric molecular-orbital tomography by manipulating electron trajectories

We present a scheme for tomographic imaging of asymmetric molecular orbital based on high-order harmonic generation with a two-color orthogonally polarized multicycle laser field. With the two-dimensional manipulation of the electron trajectories, the electrons can recollide with the target molecule from two noncollinear directions, and then the dipole moment generated from the single direction can be obtained to reconstructed the asymmetric molecular orbital. The recollision is independent from the molecular structure and the angular dependence of the ionization rate in the external field. For this reason, this scheme can avoid the negative effects arising from the modification of the angle-dependent ionization rate induced by Stark shift and be applied to various molecules.

Engaged student learning through the ACS-certified bachelor’s degree

The National Science Foundation’s primary grant program that supports undergraduate curriculum development activities—Improving Undergraduate STEM Education—has two tracks, one of which is Engaged Student Learning. The program recognizes that passive forms of teaching and learning, such as lectures and “cookbook” laboratory experiments, do not promoting meaningful learning among many students. Research on how people learn supports the desirability of engaged student learning. These studies show that learning is a constructive process and is improved when learners properly connect a new concept to knowledge they already possess. Those who teach will realize that while lecturing, the instructor frequently makes connections for students by describing prior knowledge that informs new material—for example, how knowledge of atomic orbitals can help us construct visual images of certain molecular orbitals. However, there are two drawbacks when the instructor makes the connection for students. The first is that s...

Diffractive molecular-orbital tomography

High harmonic generation in the interaction of femtosecond lasers with atoms and molecules opens the path to molecular orbital tomography and to probe the electronic dynamics with attosecond-{\AA}ngstr\"{o}m resolutions. Molecular orbital tomography requires both the amplitude and phase of the high harmonics. Yet the measurement of phases requires sophisticated techniques and represents formidable challenges at present. Here we report a novel scheme, called diffractive molecular orbital tomography, to retrieve the molecular orbital solely from the amplitude of high harmonics without measuring any phase information. We have applied this method to image the molecular orbitals of N$_2$, CO$_2$ and C$_2$H$_2$. The retrieved orbital is further improved by taking account the correction of Coulomb potential. The diffractive molecular orbital tomography scheme, removing the roadblock of phase measurement, significantly simplifies the molecular orbital tomography procedure and paves an efficient and robust way to the imaging of more complex molecules.

Laser-induced electron diffraction: inversion of photo-electron spectra for molecular orbital imaging

ABSTRACTIn this paper, we discuss the possibility of imaging molecular orbitals from photoelectron spectra obtained via laser -induced electron diffraction in linear molecules. This is an extension of our recent work to the case of the HOMO-1 orbital of the carbon dioxide molecule. We show that such an imaging technique has the potential to image molecular orbitals at different internuclear distances in a sub-femtosecond time scale and with a resolution of a fraction of an Angström.

Tunneling wave packets of atoms from intense elliptically polarized fields in natural geometry

We study strong-field tunneling of atoms in intense elliptically polarized laser fields in natural tunneling geometry. We obtain the temporal- and spatial-dependent tunneling ionization rates, the transverse and longitudinal momentum distributions, and the position distributions of the tunnel exit in parabolic coordinates. The tunneling electron wave packets at the tunnel exit are three dimensionally characterized for both momentum and spatial distributions. The conjunction between the tunneling point and the classical propagation of the widely used semiclassical model are naturally connected. We further calculate the ellipticity-dependent photoelectron momentum distributions on the detector, which are validated by comparison with the exact results through numerically solving the time-dependent Schr\odinger equation. The theory clarifies crucial questions about strong-field tunneling ionization, which has important implications for the attoclock with elliptical or circular fields, photoelectron holography, molecular orbital imaging, etc.

多次元電子分光による分子軌道イメージング

多次元電子分光による分子軌道イメージング

Tracking the ultrafast motion of a single molecule by femtosecond orbital imaging.

Watching a single molecule move on its intrinsic time scale—one of the central goals of modern nanoscience—calls for measurements that combine ultrafast temporal resolution1–8 with atomic spatial resolution9–30. Steady-state experiments achieve the requisite spatial resolution, as illustrated by direct imaging of individual molecular orbitals using scanning tunnelling microscopy9–11 or the acquisition of tip-enhanced Raman and luminescence spectra with sub-molecular resolution27–29. But tracking the dynamics of a single molecule directly in the time domain faces the challenge that single-molecule excitations need to be confined to an ultrashort time window. A first step towards overcoming this challenge has combined scanning tunnelling microscopy with so-called ‘lightwave electronics”1–8, which uses the oscillating carrier wave of tailored light pulses to directly manipulate electronic motion on time scales faster even than that of a single cycle of light. Here we use such ultrafast terahertz scanning tunnelling microscopy to access a state-selective tunnelling regime, where the peak of a terahertz electric-field waveform transiently opens an otherwise forbidden tunnelling channel through a single molecular state and thereby removes a single electron from an individual pentacene molecule’s highest occupied molecular orbital within a time window shorter than one oscillation cycle of the terahertz wave. We exploit this effect to record ~100 fs snapshot images of the structure of the orbital involved, and to reveal through pump-probe measurements coherent molecular vibrations at terahertz frequencies directly in the time domain and with sub-angstrom spatial resolution. We anticipate that the combination of lightwave electronics1–8 and atomic resolution of our approach will open the door to controlling electronic motion inside individual molecules at optical clock rates.