Potassium Dimer Research Articles

The C[formula omitted] state of potassium dimer revisited: An extensive study by polarisation labelling spectroscopy method

The polarisation labelling spectroscopy technique was applied to study the C1Πu← X1Σg+ band system in potassium dimer. About 1100 new rotationally resolved molecular lines were measured in the 22100–24100 cm−1 spectral range. Perturbations of the lowest vibrational levels of the C state were localised and their origin discussed. A set of Dunham coefficients was deduced to fit the unperturbed levels of the C1Πu state with 0≤v≤38 and 18≤J≤101 and the potential energy curve of the state was constructed.

Cerium cyclotrisilazides

The 6-membered 3,5-bis(dimethylsilyl)-2,2,4,4,6,6-hexamethyl-1,3,5,2,4,6-triazatrisilinan-1-ido ligand (dhts) was accessed in the potassium dimer [K(dhts)(thf)]2 (1thf), when treating KH with excess HN(SiHMe2)2 in the presence of THF. 1thf engaged in salt metathesis with CeCl3(thf)1.05 in THF, giving Ce(dhts)3(thf) (2thf). An attempted metathesis reaction in toluene failed, leading only to the recovery of 1thf. Attempts at generating potassium-ate complex {KCe(dhts)4} from salt metathesis between CeCl3(thf)1.05 and four equivalents of 1thf in THF, followed by crystallisation from toluene, resulted in the formation of both 2thf and [K(dhts)(toluene)]2 (1tol). Oxidation of 2thf with trityl chloride led to the isolation of the metastable tetravalent heteroleptic cerium complex Ce(dhts)3Cl (3), characterised by both 1H NMR spectroscopy and X-ray crystallography. Compound 3 is a new addition to a prominent class of cerium(IV) silylamides, and an understudied class of triazatrisilinanides.

Excitation of higher lying states in a potassium diode-pumped alkali laser

A kinetic model for the performance of a potassium DPAL, including the role of higher lying states, is developed to assess the impact on device efficiency and performance. A rate package for a nine-level kinetic model including recommended rate parameters is solved under steady-state conditions. Energy pooling and far wing absorption populates higher lying states, with single photon and Penning ionization leading to modest potassium dimer ion concentrations. The fraction of the population removed from the basic three levels associated with the standard model is less than 10% for all reasonable laser conditions, including pump intensities up to 100 kW cm $$^{-2}$$ and K densities as high as $$10^{16}$$ cm $$^{-3}$$ . The influence of these effects can largely be mitigated by proper control of the inlet alkali density.

Short-Lived K2S Molecules in Superionic Potassium Sulfide

First principles molecular dynamics study enables us to elucidate the formation of short-lived K2S molecules in superionic potassium sulfide. Covalent electron densities exist between the ionized immobile sulfurs and their coordinated ionized mobile potassiums forming the respective covalent and the Coulomb bonds between them. Both the bonds induce indirect covalent and indirect Coulomb attractions between the di-interstitial potassiums on the mid-sulfurs forming the molecules. The lifetime of the molecules is 120 fs at 1050 K. The covalent density also exists in short-lived potassium pairs with the lifetime of 110 fs. The three attractions constrain the self-diffusion of the potassiums in the sulfide which reduces Haven’s ratios of the potassiums. The absence of the rigid potassium dimers indicates a failure of the chain models for the superionic diffusion. The attractions reduce the Coulomb attractions between them comparing with their completely ionized states which induces the melting of the sublattic...

Coupled electron-nuclear wavepacket dynamics in potassium dimers

Recently we have demonstrated control of valence-bond excitation of a molecule due to the interplay of the induced charge oscillation with the precisely tailored phase of the driving laser field (Bayer et al 2013 Phys. Rev. Lett. 110 123003). In this contribution we describe in more detail the two-colour experiment—a control pulse sequence followed by an ionizing probe pulse of a different wavelength. We provide details on the quantum dynamics simulations carried out to reproduce and to analyse the experimental results. The procedure for averaging over the focal intensity distribution in the interaction region and the method for orientation averaging, which are both crucial for the reproduction of our strong-field measurements, are also described in detail. The analysis of the temporal evolution of the expectation values of the wavepackets on the relevant potentials, the induced energetic shifts in the molecule and the modulation in the charge oscillation provides further insights into the interplay of the coupled nuclear-electron dynamics. Because the measured photoelectron spectra reveal the population of the target states we describe the quantum mechanical approach to calculate the photoelectron spectra and rationalize the results using Mulliken's difference potential method.

On the use of effective core potentials in the calculation of magnetic properties, such as magnetizabilites and magnetic shieldings

State-of-the art effective core potentials (ECPs) that replace electrons of inner atomic cores involve non-local potentials. If such an effective core potential is added to the Hamiltonian of a system in a magnetic field, the resulting Hamiltonian is not gauge invariant. This means, magnetic properties such as magnetisabilities and magnetic shieldings (or magnetic susceptibilities and nuclear magnetic resonance chemical shifts) calculated with different gauge origins are different even for exact solutions of the Schrödinger equation. It is possible to restore gauge invariance of the Hamiltonian by adding magnetic field dependent terms arising from the effective core potential. Numerical calculations on atomic and diatomic model systems (potassium mono-cation and potassium dimer) clearly demonstrate that the standard effective core potential Hamiltonian violates gauge invariance, and this affects the calculation of magnetisabilities more strongly than the calculation of magnetic shieldings. The modified magnetic field dependent effective core potential Hamiltonian is gauge invariant, and therefore it is the correct starting point for distributed gauge origin methods. The formalism for gauge including atomic orbitals (GIAO) and individual gauge for localized orbitals methods is worked out. ECP GIAO results for the potassium dimer are presented. The new method performs much better than a previous ECP GIAO implementation that did not account for the non-locality of the potential. For magnetic shieldings, deviations are clearly seen, but they amount to few ppm only. For magnetisabilities, our new ECP GIAO implementation is a major improvement, as demonstrated by the comparison of all-electron and ECP results.

Electronic coherence within the semiclassical field-induced surface hopping method: strong field quantum control in K2

We demonstrate that the semiclassical field-induced surface hopping (FISH) method (Mitrićet al., Phys. Rev. A: At., Mol., Opt. Phys., 2009, 79, 053416.) accurately describes the selective coherent control of electronic state populations. With the example of the strong field control in the potassium dimer using phase-coherent double pulse sequences, we present a detailed comparison between FISH simulations and exact quantum dynamics. We show that for short pulses the variation of the time delay between the subpulses allows for a selective population of the desired final state with high efficiency. Furthermore, also for pulses of longer time duration, when substantial nuclear motion takes place during the action of the pulse, optimized pulse shapes can be obtained which lead to selective population transfer. For both types of pulses, the FISH method almost perfectly reproduces the exact quantum mechanical electronic population dynamics, fully taking account of the electronic coherence, and describes the leading features of the nuclear dynamics accurately. Due to the significantly higher computational efficiency of FISH as a trajectory-based method compared to full quantum dynamics simulations, this offers the possibility to theoretically investigate control experiments on realistic systems including all nuclear degrees of freedom.

Failure of potassium dimer formation on the β-SiC(100)-c (4 × 2) surface

Using ab initio molecular dynamics, we study the formation of dimers on the β-SiC(100)-c(4 × 2) surface. According to previously published experimental results of Derycke et al. [Appl. Phys. Lett. 88(2), 022105 (2006)] (using scanning tunneling spectroscopy, core-level photoemission spectroscopy, and low-energy electron diffraction) the (100)-c(4 × 2) surface is highly prone to form potassium dimers. In their work, potassium atoms fill adjacent well-defined pedestal sites when there are lower coverages of potassium deposited onto the surface (∼0.16 monolayers). Contrary to the work by Derycke et al., we find that potassium does not prefer to form dimers on the (100)-c(4 × 2) surface, but rather potassium tends to reconstruct (after annealing simulations) by choosing distant pedestal sites in order to minimize the overlap of the ionic radii of the potassium atoms.

Searching for pathways involving dressed states in optimal control theory

Selective population of dressed states has been proposed as an alternative control pathway in molecular reaction dynamics [Wollenhaupt et al., J. Photochem. Photobiol. A: Chem., 2006, 180, 248]. In this article we investigate if, and under which conditions, this strong field pathway is included in the search space of optimal control theory. For our calculations we used the proposed example of the potassium dimer, in which the different target states can be reached via dressed states by resonant transition. Especially, we investigate whether the optimization algorithm is able to find the route involving the dressed states although the target state lies out of resonance in the bare state picture.

Parametrically polarization shaped pulses guided via a hollow core photonic crystal fiber for coherent control

We present ultrafast polarization pulse shaping through a micro structured hollow core photonic crystal fiber. The pulses are shaped in pulse sequences in which the energy, distance, phases, and chirps as well as the state of polarization of each individual sub-pulse can be independently controlled. The application of these pulses for coherent control is demonstrated for feedback loop optimization of the multi-photon ionization of potassium dimers. In a second experiment, this process is investigated by shaper-assisted pump-probe spectroscopy which is likewise performed with pulses that are transmitted through the fiber. Both techniques reveal the excitation pathway including the dynamics in the participating electronic states and expose the relevance of the polarization. These methods will be valuable for endoscopic applications.

Dissipative vibrational wave packet dynamics of alkali dimers attached to helium nanodroplets

Femtosecond pump–probe spectroscopy has been used to study vibrational dynamics of potassium dimers attached to superfluid helium nanodroplets. Comparing the measured data with theoretical results based on dissipative quantum dynamics we propose that the most important effect of the helium environment is a general damping of the vibrational dynamics. The calculations allow us to explain crucial experimental findings that are unobserved in gas phase measurements. Remarkably, wave packet velocities of such alkali dimer vibrations are just about in the range of the Landau critical velocity of superfluid helium. We therefore also discuss a possible influence of superfluidity on the induced wave packet dynamics.

Coherent Control of Decoherence

Manipulation of quantum interference requires that the system under control remains coherent, avoiding (or at least postponing) the phase randomization that can ensue from coupling to an uncontrolled environment. We show that closed-loop coherent control can be used to mitigate the rate of quantum dephasing in a gas-phase ensemble of potassium dimers (K2), which acts as a model system for testing the general concepts of controlling decoherence. Specifically, we adaptively shaped the light pulse used to prepare a vibrational wave packet in electronically excited K2, with the amplitude of quantum beats in the fluorescence signal used as an easily measured surrogate for the purpose of optimizing coherence. The optimal pulse increased the beat amplitude from below the noise level to well above it, and thereby increased the coherence life time as compared with the beats produced by a transform-limited pulse. Closed-loop methods can thus effectively identify states that are robust against dephasing without any previous information about the system-environment interaction.

Multi-objective optimization on alkali dimers

We present experimental results of a multi-objective evolutionary algorithm that controls the ionization of the NaK molecule and the fragmentation/ionization of potassium dimers. The two physically contradictive goals are dimer ionization and fragmentation into the atomic isotopes. In the NaK case, we use an approach to simplify the usually complex results of feedback-loop coherent control experiments and implement the ‘pulse cleaning’ method. It defines the objective function in a way that unnecessary spectral features are reduced and the most important vibronic transitions are enhanced. This method will be developed in terms of a classical multi-objective optimization and we present some corresponding Pareto-optimal solutions.

Coherent control of electrons, atoms and molecules with intense shaped light pulses

We report on a physical mechanism of coherent control with intense shaped femtosecond laser pulses. We study photoelectron spectra from multi-photon ionization of potassium atoms and dimers using tailored femtosecond laser pulses. Our results are interpreted in terms of Selective Population of Dressed States (SPODS). Two realizations of SPODS by Photon Locking (PL) via pulse sequences and Rapid Adiabatic Passage (RAP) via chirped pulses are discussed. New physical mechanisms arise, when both PL and RAP are at play simultaneously. Control by the combined effect of PL and RAP is studied by mapping out a two-parameter Quantum Control Landscape (QCL) for selective population of dressed states.

The potential energy curve of the ground state of the potassium dimer, XΣg+1 K2

The most recently published listings of vibrational term values and corresponding turning points of the potential energy curve of X (1)Sigma(g) (+) K(2) consist of two sets of data: energy levels v(")=0-73 and v(")=74-81. The two sets of data are found to exhibit a discontinuity. This is due to different Dunham coefficients used to produce a listing of turning points for levels v(")=0-73 and for levels v(")=74-81. This work provides an explicit, self-consistent listing of turning points for the entire domain of observed vibrational term values. New values are reported for levels v(")=53-81. This potential yields eigenvalues in excellent agreement with experimental vibrational term values and predicts two more bound levels. A "universal" function proposed in 1991 for predicting potential energy curves yields eigenvalues for levels v(")=0-81 (99.96% of dissociation) that have an average absolute deviation from the experiment of 0.95 cm(-1).

Optimal control of isotope selective fragmentation

We demonstrate coherent control of isotope selective fragmentation processes of potassium dimers into differing atomic isotopes using shaped fs-laser pulses. When applying evolution strategies in a feedback loop, optimizing 39K + vs. 41K + for different center wavelengths, we astonishingly exposed molecular fingerprints. Moreover, we performed two criteria optimizations by maximizing the fragment vs. the dimer ion isotope ratio with selected weighting factors. Insight into the coherent ultrafast interaction of spectral pulse components with the dimer wave functions is provided by analyzing the optimized pulse forms.

“Hooked-on” Calix[8]arenes: A (H2O)10 Cluster with an Unprecedented Structure

Calix[8]arene was crystallized at the THF/water interface in the presence of K 2 CO 3 to yield a one-dimensional channel structure. Between two neighboring macrocyclic ligands, two potassium ions are bridged via water molecules, whereas the next two calix[8]arenes are sandwiching a water cluster made of 10 water molecules. The water cluster and the potassium dimer are further coordinated by THF molecules. The channel is thus formed by the calix[8]arene and the THF ligands, their oxygen atoms pointing inward.

Learning from the acquired optimized pulse shapes about the isotope selective ionization of potassium dimers

Selective optimization of the 39,39K2 and 39,41K2 isotopomers in a three-photon ionization process is presented by applying evolution strategies on shaped fs pulses in a feedback loop. The optimizations at different center wavelengths show considerably large enhancements of one isotope compared to the other and reversed. We compare the acquired optimized pulse shapes for combined phase and amplitude with pure amplitude modulation. Particularly from their spectra we are able to extract information about the optimally chosen differing ionization paths via the involved vibrational states. Furthermore, a comparison of the temporal shape of the optimized pulse forms for combined phase and amplitude with pure phase optimization is given. The presented pulse form analysis demonstrates the potential of restricted optimization to gain insight into the underlying dynamical processes. Our approach reveals how the optimization algorithm precisely addresses the vibrational wave functions both spectrally and temporally.

Quantum control by ultrafast polarization shaping.

We demonstrate that the use of time-dependent light polarization opens a new level of control over quantum systems. With potassium dimer molecules from a supersonic molecular beam, we show that a polarization-shaped laser pulse increases the ionization yield beyond that obtained with an optimally shaped linearly polarized laser pulse. This is due to the different multiphoton ionization pathways in K2 involving dipole transitions which favor different polarization directions of the exciting laser field. This experiment is a qualitative extension of quantum control mechanisms which opens up new directions giving access to the three-dimensional temporal response of molecular systems.

Calculation of molecular constants for the X 1Σ g + , A 1Σ u + , B 1Πu, and a 3Σ u + electronic states of 39K2

The molecular constants are calculated for the X 1Σ g + , A 1Σ u + , B 1Πu, and a 3Σ u + and electronic states of a potassium dimer. The wave functions and vibrational energies necessary for calculating the molecular constants are determined by solving the radial wave equation with the use of potential energy curves constructed by the semiempirical method. The vibrational terms, the rotational constants, and the centrifugal distortion constants calculated from the potential curves are compared with those determined from the experimental data.