We have theoretically investigated the double core-hole (DCH) states of the open-shell molecules and examined the possibility of DCH spectroscopy by means of X-ray two-photon photoelectron spectroscopy (XTPPS). Energies of many DCH states were obtained by the CASSCF calculations and the generalized intra- and interatomic relaxation energies were evaluated. We show that XTPPS can extract these quantities by the measurement of single and double core-hole ionization potentials. We discuss the influence of chemical environment on the DCH states with two holes at the same atomic site and at two different atomic sites.
We present a theoretical study of the impact of an electric field combined with a magnetic field on the rotational dynamics of open shell diatomic molecules. Within the rigid rotor approximation, we solve the time-independent Schrödinger equation including the fine-structure interactions and the Λ-doubling effects. We consider three sets of molecule specific parameters and several field regimes and investigate the interplay between the different interactions identifying the dominant one. The possibility of inducing couplings between the spin and rotational degrees of freedom is demonstrated.
The scaling of nuclear spin-dependent parity violating effects with increasing nuclear charge $Z$ is discussed in two series of isovalent open-shell diatomic molecules. The parameter $W_\mathrm{a}$ characterising the strength of parity violation in diatomic molecules is calculated in the framework of the zeroth-order regular approximation (ZORA) and found to be in good agreement with the $R(Z) Z^k$ scaling law derived for atoms in which $R(Z)$ represents a relativistic enhancement factor. The influence of electron correlation is studied on the molecular level, with spin-polarisation effects be…
We demonstrate cryogenic buffer-gas cooling of gas-phase methyltrioxorhenium (MTO). This molecule is closely related to chiral organometallic molecules where the parity-violating energy differences between enantiomers may be measurable. The molecules are produced with a rotational temperature of approximately 6~K by laser ablation of an MTO pellet inside a cryogenic helium buffer gas cell. Facilitated by the low temperature, we demonstrate absorption spectroscopy of the 10.2~$μ$m antisymmetric Re=O stretching mode of MTO with a resolution of 8~MHz and a frequency accuracy of 30~MHz. We partial…
We report an experimental investigation on the Doppler-free saturated absorption spectroscopy of buffer-gas-cooled Barium monofluoride (BaF) molecules in a 4~K cryogenic cell. The obtained spectra with a resolution of 19~MHz, much smaller than previously observed in absorption spectroscopy, clearly resolve the hyperfine transitions. Moreover, we use these high-resolution spectra to fit the hyperfine splittings of excited $A(v=0)$ state and find the hyperfine splitting of the laser-cooling-relevant $A^2Π_{1/2}(v=0, J=1/2, +)$ state is about 18 MHz, much higher than the previous theoretically pr…
The spin-exchange effect in spin-polarized electron collisions with unpolarized open-shell molecules, O$_2$, B$_2$, S$_2$ and Si$_2$, has been studied by the R-matrix method with the fixed-bond approximation. All of these molecules have ${}^3 Σ_{g}^{-}$ symmetry in their ground states. Usual integrated cross sections with unpolarized electrons has also been studied. We used the complete active space self consistent field orbitals and put more than 10 target electronic states in the R-matrix models. In electron O$_2$ elastic collisions, calculated polarization fractions agree well with the expe…
We present quantum-theoretical studies of collisions between an open-shell S-state atom and a ^2Pi-state molecule in the presence of a magnetic field. We analyze the collisional Hamiltonian and discuss possible mechanisms for inelastic collisions in such systems. The theory is applied to the collisions of the nitrogen atom (^4S) with the OH molecule, with both collision partners initially in fully spin-stretched (magnetically trappable) states, assuming that the interaction takes place exclusively on the two high-spin (quintet) potential energy surfaces. The surfaces for the quintet states are…
Magnetic Feshbach resonances play a central role in experimental research of atomic gases at ultracold temperatures, as they allow one to control the microscopic interactions between ultracold atoms by tuning an applied magnetic field. These resonances arise due to strong hyperfine interactions between the unpaired electron and the nuclear magnetic moment of the alkali metal atoms. A major thrust of current research is to create an ultracold gas of diatomic alkali-metal molecules in the ground rovibrational state of the ground electronic $^1Σ$ state. Unlike alkali metal atoms, $^1Σ$ diatomic m…
Implementing a scalable quantum information processor using polar molecules in optical lattices requires precise control over the long-range dipole-dipole interaction between molecules in selected lattice sites. We present here a scheme using trapped open-shell $^2Σ$ polar molecules that allows dipolar exchange processes between nearest and next-nearest neighbors to be controlled to construct a generalized transverse Ising spin Hamiltonian with tunable $XX$, $YY$ and $XY$ couplings in the rotating frame of the driving lasers. The scheme requires a moderately strong bias magnetic field with nea…
We present a high-resolution laser spectroscopic study of the $\tilde{A}\,^2B_2- \tilde{X}\,^2A_1$ and $\tilde{B}\,^2B_1- \tilde{X}\,^2A_1$ transitions of calcium (I) phenoxide, CaOPh (CaOC$_6$H$_5$). The rotationally resolved band systems are analyzed using an effective Hamiltonian model and are accurately modeled as independent perpendicular ($b$- or $c$-type) transitions. The structure of calcium monophenoxide is compared to previously observed Ca-containing radicals and implications for direct laser cooling are discussed. This work demonstrates that functionalization of aromatic molecules …
Open-shell systems such as magnetic molecules or defects with a triplet ground state are challenging to describe in electronic structure methods, but are of great interest for quantum information applications. We demonstrate a spin-flip approach within the Bethe-Salpeter equation to calculate ground and excited states of open-shell molecules and defected solids. The approach works in periodic boundary conditions without any need for embedding or selection of a subspace. Our benchmark results for the torsion potential-energy surface of ethylene and the optical excitations of the diamond NV$^{-}…
Understanding inner-shell excitations in molecules through spectroscopy of the 4f hole states of YbF
Center for Cold Matter, Blackett Laboratory, Imperial College London（帝国理工学院冷物质中心布莱克特实验室）；Fritz-Haber-Institut der Max-Planck-Gesellschaft（马克斯·普朗克学会弗里茨·哈伯研究所）
We fabricate OLEDs using a stable neutral π radical, BDPA, as the emitter. There is only one electron in the singly occupied molecular orbital (SOMO) of this open-shell molecule. This feature makes the excited state of open-shell molecules be neither singlet nor triplet, but doublet. The key issue of how to harvest the triplet energy in an OLED is thus bypassed, due to the radiative decay of doublet is totally spin allowed. In the BDPA-based OLED, the emission was confirmed to be from the electronic transition from LUMO to SOMO, via the frontier molecular orbital analysis combined with the spe…
The study of ultracold molecules tightly trapped in an optical lattice can expand the frontier of precision measurement and spectroscopy, and provide a deeper insight into molecular and fundamental physics. Here we create, probe, and image microkelvin $^{88}$Sr$_2$ molecules in a lattice, and demonstrate precise measurements of molecular parameters as well as coherent control of molecular quantum states using optical fields. We discuss the sensitivity of the system to dimensional effects, a new bound-to-continuum spectroscopy technique for highly accurate binding energy measurements, and prosp…
The spectra (rotational, rotation-vibrational or electronic) of diatomic molecules due to transitions involving only closed-shell ($^1Σ$) electronic states follow very regular, simple patterns and their theoretical analysis is usually straightforward. On the other hand, open-shell electronic states lead to more complicated spectral patterns and, moreover, often appear as a manifold of closely lying electronic states, leading to perturbations with even larger complexity. This is especially true when at least one of the atoms is a transition metal. Traditionally these complex cases have been ana…
Rapid progress in cooling and trapping of molecules has enabled first experiments on high resolution spectroscopy of trapped diatomic molecules, promising unprecedented precision. Extending this work to polyatomic molecules provides unique opportunities due to more complex geometries and additional internal degrees of freedom. Here, this is achieved by combining a homogeneous-field microstructured electric trap, rotational transitions with minimal Stark broadening at a 'magic' offset electric field, and optoelectrical Sisyphus cooling of molecules to the low millikelvin temperature regime. We …
Trapped atoms and ions are among the best controlled quantum systems which find widespread applications in quantum information, sensing and metrology. For molecules, however, a similar degree of control is currently lacking owing to their complex energy-level structure. Quantum-logic protocols in which atomic ions serve as probes for molecular ions are a promising route for achieving this level of control, especially with homonuclear molecules that decouple from black-body radiation. Here, a quantum-non-demolition protocol on single trapped N$_2^+$ molecules is demonstrated. The spin-rovibroni…
Electron density distribution plays an essential role in predicting molecular properties. It is also a simple observable from which machine-learning models for molecular electronic structure can be derived. In the present work, we present the performance of the one-body Møller-Plesset second-order perturbation (OBMP2) theory that we have recently developed. In OBMP2, an effective one-body Hamiltonian including dynamic correlation at the MP2 level is derived using the canonical transformation followed by the cumulant approximation. We evaluate electron density and related properties of three gr…
The program {\sc Duo} (Yurchenko {\it et al.}, Computer Phys. Comms., 202 (2016) 262) provides direct solutions of the nuclear motion Schrödinger equation for the (coupled) potential energy curves of open shell diatomic molecules. Wavefunctions from {\sc Duo} are used to compute Landé $g$-factors valid for weak magnetic fields, the results are compared with the idealized predictions of both Hund's case (a) and Hund's case (b) coupling schemes. Test calculations are performed for AlO, NO, CrH and C$_2$. The computed $g_J$'s both provide a sensitive test of the underlying spectroscopic model use…
We have studied the X 1Σ+ and B 1Π states of 7Li85Rb using Laser Induced Fluorescence (LIF) spectroscopy and Fluorescence Excitation Spectroscopy (FES). We extract molecular constants for levels v" = 0-2 of the X 1Σ+ state and levels v' = 0-20 of the B 1Π state. For the B 1Π state, we have observed rotational perturbations in the e-parity component of the v' = 2 level, and determined the dissociation energy. We discuss implications of our measurements in finding efficient photoassociation pathways for production of ultra-cold ground state LiRb molecules, and their detection via state selective…
This review article discusses advances in the use of time-resolved photoelectron spectroscopy for the study of non-adiabatic processes in molecules. A theoretical treatment of the experiments is presented together with a number of experimental examples.
Due to its element- and site-specificity, inner-shell photoelectron spectroscopy is a widely used technique to probe the chemical structure of matter. Here we show that time-resolved inner-shell photoelectron spectroscopy can be employed to observe ultrafast chemical reactions and the electronic response to the nuclear motion with high sensitivity. The ultraviolet dissociation of iodomethane (CH$_3$I) is investigated by ionization above the iodine 4d edge, using time-resolved inner-shell photoelectron and photoion spectroscopy. The dynamics observed in the photoelectron spectra appear earlier …
Cavity-enhanced frequency comb spectroscopy for molecule detection in the mid-infrared powerfully combines high resolution, high sensitivity, and broad spectral coverage. However, this technique, and essentially all spectroscopic methods, is limited in application to relatively small, simple molecules. Here we integrate comb spectroscopy with continuous, cold samples of molecules produced via buffer gas cooling, thus enabling the study of significantly more complex molecules. We report simultaneous gains in resolution, sensitivity, and bandwidth and demonstrate this combined capability with th…
Single molecule spectroscopy aims at unveiling often hidden but potentially very important contributions of single entities to a system's ensemble response. Albeit contributing tremendously to our ever growing understanding of molecular processes the fundamental question of temporal evolution, or change, has thus far been inaccessible, resulting in a static picture of a dynamic world. Here, we finally resolve this dilemma by performing the first ultrafast time-resolved transient spectroscopy on a single molecule. By tracing the femtosecond evolution of excited electronic state spectra of singl…
The interaction between excitons and phonons in semiconductor nanocrystals plays a crucial role in the exciton energy spectrum and dynamics, and thus in their optical properties. We investigate the exciton2 phonon coupling in giant-shell CdSe/CdS core-shell nanocrystals via resonant Raman spectroscopy. The Huang-Rhys parameter is evaluated by the intensity ratio of the longitudinal-optical (LO) phonon of CdS with its first multiscattering (2LO) replica. We used four different excitation wavelengths in the range from the onset of the CdS shell absorption to well above the CdS shell band edge to…
A quantitative single-molecule tip-enhanced Raman spectroscopy (TERS) study at room temperature remained a challenge due to the rapid structural dynamics of molecules exposed to air. Here, we demonstrate the single-molecule level hyperspectral TERS imaging of brilliant cresyl blue (BCB) at room temperature for the first time, along with quantitative spectral analyses. Freeze-frame approach using a thin Al2O3 capping layer, which suppresses spectral diffusions and inhibits chemical reactions and contaminations in air, enabled reliable and robust chemical imaging. For the molecules resolved spat…
We report on two-photon photoassociation (PA) spectroscopy of ultracold heteronuclear LiRb molecules. This is used to determine the binding energies of the loosely bound levels of the electronic ground singlet and the lowest triplet states of LiRb. We observe strong two-photon PA lines with power broadened line widths greater than 20 GHz at relatively low laser intensity of 30 W/cm$^{2}$. The implication of this observation on direct atom to molecule conversion using stimulated Raman adiabatic passage (STIRAP) is discussed and the prospect for electronic ground state molecule production is the…
For over five decades, studies in the field of chemical physics and physical chemistry have primarily aimed to understand the quantum properties of molecules. However, high-resolution rovibronic spectroscopy has been limited to relatively small and simple systems because translationally and rotationally cold samples have not been prepared in sufficiently large quantities for large and complex systems. In this study, we present high-resolution rovibronic spectroscopy results for large gas-phase molecules, namely, free-base phthalocyanine (FBPc). The findings suggest that buffer-gas cooling may …
Parity violation (PV) effects in chiral molecules have so far never been experimentally observed. To take this challenge up, a consortium of physicists, chemists, theoreticians and spectroscopists has been established and aims at measuring PV energy differences between two enantiomers by using high-resolution laser spectroscopy. In this article, we present our common strategy to reach this goal, the progress accomplished in the diverse areas, and point out directions for future PV observations. The work of André Collet on bromochlorofluoromethane enantiomers, their synthesis and their chiral r…
Interacting dipole ($p$) bosons along with scalar ($s$) bosons, based on the ideas drawn from the interacting boson model of atomic nuclei, led to the development of the vibron model based on $U(4)$ spectrum generating algebra for diatomic molecules. The $U(4) \supset SO(4) \supset SO(3)$ algebra generates rotation-vibration spectra. Extending this to two coupled $SO(4)$ algebras and three $SO(4)$ algebras describe triatomic and four-atomic molecules respectively. Similarly, appropriately coupled $U(2) \supset SO(2)$ algebras will describe the stretching vibrations, with proper point group sym…
We consider the theory of the non-linear spectroscopy for a single molecule undergoing stochastic dynamics and interacting with a sequence of two laser pulses. General expressions for photon counting statistics are obtained, and an exact solution to the problem of the Kubo-Anderson process is found. In the limit of impulsive pulses the information on the photon statistics is contained in the molecule's dipole correlation function. The selective limit where temporal resolution is maintained, the semi-classical approximation and the fast modulation limit exhibit general behaviors of this new typ…
The electronic excitation of molecules triggers diverse phenomena such as luminescence and photovoltaic effects, which are the bases of various energy-converting devices. Understanding and control of the excitations at the single-molecule level are long standing targets, however, they have been hampered by the limited spatial resolution in optical probing techniques. Here we investigate the electronic excitation of a single molecule with sub-molecular precision using a localised plasmon at the tip apex of a scanning tunnelling microscope (STM) as an excitation probe. Coherent energy transfer b…
In Surface Enhanced Raman Scattering (SERS) the problem of drawing molecules to the places where surface plasmon resonance enhancements will produce signals is one of the most basic ones, and the initial obstacle to every application of the effect. We explore the possibility of using electrostatic forces as a means to "guide" charged molecules in solution toward SERS active substrates. We also show explicitly the possibility of selectively enhancing different types of dyes according to their charge, and we discuss briefly possible extensions for other applications where "electrostatic guiding"…
Tracing ultrafast processes induced by interaction of light with matter is often very challenging. In molecular systems, the initially created electronic coherence becomes damped by the slow nuclear rearrangement on a femtosecond timescale which makes real-time observations of electron dynamics in molecules particularly difficult. In this work, we report an extension of the theory underlying the attosecond transient absorption spectroscopy (ATAS) for the case of molecules, including a full account for the coupled electron-nuclear dynamics in the initially created wave packet, and apply it to p…
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…
We discuss implications of a recent experimental breakthrough which uses a fluorescence-doped flexible semiconducting polymer to construct a single-molecule sensor which can detect ultra-weak forces in the molecular environment, with a grey scale down to 300 femtonewtons.
The computational prediction of atomistic structure is a long-standing problem in physics, chemistry, materials, and biology. Within conventional force-field or {\em ab initio} calculations, structure is determined through energy minimization, which is either approximate or computationally demanding. Alas, the accuracy-cost trade-off prohibits the generation of synthetic big data records with meaningful energy based conformational search and structure relaxation output. Exploiting implicit correlations among relaxed structures, our kernel ridge regression model, dubbed Graph-To-Structure (G2S)…
Hypericin can be found in nature in Hypericum perforatum (St. John's Wort) and has become subject of intense biochemical research. Studies report of antidepressive, antineoplastic, antitumor and antiviral activity of hypericin. Among the variety of potential applications hypericin can be used as photosensitizer in photodynamic therapy (PDT), where it is brought into cancer cells and produces singlet oxygen upon irradiation with a suitable light source. Therefore, the photophysical properties of hypericin are crucial for a successful application in a medical treatment. Here, we present the firs…
Because of their central importance in chemistry and biology, water molecules have been the subject of decades of intense spectroscopic investigations. Rotational spectroscopy of water vapor has yielded detailed information about the structure and dynamics of isolated water molecules as well as water dimers and clusters. Nonlinear rotational spectroscopy in the terahertz regime has been developed recently to investigate the rotational dynamics of linear and symmetric-top molecules whose rotational energy levels are regularly spaced, but it has not previously been applied to water or other lowe…
We report a novel experimental technique to investigate ultrafast dynamics in photoexcited molecules by probing the third-order nonlinear optical susceptibility. A non-colinear 3-pulse scheme is developed to probe the ultrafast dynamics of excited electronic states using the optical Kerr effect by time-resolved polarization spectroscopy. Optical heterodyne and optical homodyne detection are demonstrated to measure the third-order nonlinear optical response for the S1 excited state of liquid nitrobenzene, which is populated by 2-photon absorption of a 780 nm 35 fs excitation pulse.
Semiclassical description, based on electrostatics and Thomas-Fermi model is applied here to calculate dimensions of the electronic shell of a fullerene molecule and a nanotube. The internal radius of the electronic shell of a fullerene molecule, calculated within the framework of the model is 0.2808 nm. The external radius is 0.4182 nm. The experimental values are 0.279 nm and 0.429 nm correspondingly. This shows that semiclassical approach provides rather good description of the dimensions of the electronic shell in a fullerene molecule. Two types of dipole oscillations in a fullerene molecu…
Enantiodetection of chiral molecules is important to pharmaceutical drug production, chemical reaction control, and biological function designs. Traditional optical methods of enantiodetection rely on the weak magnetic-dipole or electric-quadrupole interactions, and in turn suffer from the weak signal and low sensitivity. We propose a new optical enantiodetection method to determine the enantiomeric excess via two-dimensional (2D) spectroscopy of the chiral mixture driven by three electromagnetic fields. The quantities of left- and right- handed chiral molecules are reflected by the intensitie…
We present an extension of our one-body Møller-Plesset second-order perturbation (OBMP2) method for open-shell systems. We derived the OBMP2 Hamiltonian through the canonical transformation followed by the cumulant approximation to reduce many-body operators into one-body ones. The resulting Hamiltonian consists of an uncorrelated Fock (unperturbed Hamiltonian) and a one-body correlation potential (perturbed Hamiltonian) composed of only double excitations. Molecular orbitals and associated energy levels are then relaxed via self-consistency, similar to Hartree-Fock, in the presence of the cor…
Three-wave mixing spectroscopy of chiral molecules, which exist in left-handed and right-handed conformations, allows for enantio-selective population transfer despite random orientation of the molecules. This is based on constructive interference of the three-photon pathways for one enantiomer and destructive one for the other. We prove here that three mutually orthogonal polarization directions are required to this end. Two different dynamical regimes exist to realize enantio-selective population transfer, and we show that they correspond to different phase conditions in the three-wave mixin…
Accurate low and high-lying bound states of Tietz-Hua oscillator potential are presented. The radial Schrödinger equation is solved efficiently by means of the generalized pseudospectral method that enables optimal spatial discretization. Both $\ell=0$ and rotational states are considered. Ro-vibrational levels of six diatomic molecules \emph{viz.}, H$_2$, HF, N$_2$, NO, O$_2$, O$_2^+$ are obtained with good accuracy. Most of the states are reported here for the first time. A detailed analysis of variation of eigenvalues with $n, \ell$ quantum numbers is made. Results are compared with literat…
An effective Hamiltonian without symmetry restriction has been developed to model the rotational and fine structure of two nearly degenerate electronic states of an open-shell molecule. In addition to the rotational Hamiltonian for an asymmetric top, this spectroscopic model includes energy separation between the two states due to difference potential and zero-point energy difference, as well as the spin-orbit (SO), Coriolis, and electron spin-molecular rotation (SR) interactions. Hamiltonian matrices are computed using orbitally and fully symmetrized case (a) and case (b) basis sets. Intensit…
Nonadiabatic dynamics around an avoid crossing or a conical intersection play a crucial role in the photoinduced processes of most polyatomic molecules. The present work shows that the topological phase in conical intersection makes the behavior of pump-probe high-order harmonic spectroscopy different from the case of avoid crossing. The coherence built up when the system crosses the avoid crossing will lead to the oscillatory behavior of the spectrum, while the geometric phase erodes these oscillations in the case of conical intersection. Additionally, the dynamical blueshift and the splittin…
Probing the real time dynamics of a reacting molecule remains one of the central challenges in chemistry. In this letter we show how the time-dependent wavefunction of an excited-state reacting molecule can be completely reconstructed from resonant coherent anti-Stokes Raman spectroscopy. The method assumes knowledge of the ground-state potential but not of any excited-state potential, although we show that the latter can be computed once the time-dependent excited-state wavefunction is known. The formulation applies to polyatomics as well as diatomics and to bound as well as dissociative exci…
We present new interaction potential curves, calculated from first-principle, for the He$(^3$S)$...$H$_2$ and He$(^3$S)$...$Ar systems, relevant in Penning's ionization experiments. Two different approaches were applied: supermolecular using coupled cluster theory (CC) and perturbational within symmetry-adapted perturbation theory (SAPT). Both methods gave consistent results and the potentials were used to determine the positions of shape resonances in low collision energy scattering regime. We found a good agreement with the most recent scattering experiment of Henson {\em et al.} [Science {\…
Expressions for the two-dimensional Stimulated x-ray Raman Spectroscopy (2D-SXRS) signal obtained using attosecond x-ray pulses are derived. The 1D- and 2D-SXRS signals are calculated for trans-N-methyl acetamide (NMA) with broad bandwidth (FWHM ~14.2eV, 181 as) pulses tuned to the oxygen and nitrogen K-edges. Crosspeaks in 2D signals reveal electronic Franck-Condon overlaps between valence orbitals and relaxed orbitals in the presence of the core hole.
