Formulation and Implementation of Frequency-Dependent Linear Response Properties with Relativistic Coupled Cluster Theory for GPU-Accelerated Computer Architectures.

We present the development and implementation of relativistic coupled cluster linear response theory (CC-LR), which allows the determination of molecular properties arising from time-dependent or time-independent electric, magnetic, or mixed electric-magnetic perturbations (within a common gauge origin for the magnetic properties) as well as taking into account the finite lifetime of excited states in the framework of damped response theory. We showcase our implementation, which is capable to offload the computationally intensive tensor contractions characteristic of coupled cluster theory onto graphical processing units, in the calculation of (a) frequency-(in)dependent dipole-dipole polarizabilities of IIB atoms and selected diatomic molecules, with a particular emphasis on the calculation of valence absorption cross sections for the I2 molecule; (b) indirect spin-spin coupling constants for benchmark systems such as the hydrogen halides (HX, X = F-I) as well the H2Se-H2O dimer as a prototypical system containing hydrogen bonds; and (c) optical rotations at the sodium D line for hydrogen peroxide analogues (H2Y2, Y = O, S, Se, Te). Thanks to this implementation, we are able to show the similarities in performance, but often the significant discrepancies, between CC-LR and approximate methods such as density functional theory. Comparing standard CC response theory with the flavor based upon the equation of motion formalism, we find that for valence properties such as polarizabilities, the two frameworks yield very similar results across the periodic table as found elsewhere in the literature; for properties that probe the core region, such as spin-spin couplings, on the other hand, we show a progressive differentiation between the two as relativistic effects become more important. Our results also suggest that as one goes down the periodic table, it may become increasingly difficult to measure pure optical rotation at the sodium D line due to the appearance of absorbing states.

Vibronic Coupling in Spherically Encapsulated, Diatomic Molecules: Prediction of a Renner-Teller-like Effect for Endofullerenes.

In the year 1933, Herzberg and Teller realized that the potential energy surface of a triatomic, linear molecule splits into two as soon as the molecule is bent. The phenomenon, later dubbed the Renner-Teller effect due to the detailed follow-up work of Renner on the subject, describes the coupling of a symmetry-reducing molecular vibration with degenerate electronic states. In this article, we show that a very similar type of nonadiabatic coupling can occur for certain translational degrees of freedom of diatomic, electronically degenerate molecules when trapped in a nearly spherical or cylindrical quantum confinement, e.g., realized through electromagnetic fields or molecular encapsulation. We illustrate this on the example of fullerene-encapsulated nitric oxide, and provide a prediction of its interesting, perturbed vibronic spectrum.

Electronic spectra of ytterbium fluoride from relativistic electronic structure calculations.

We report an investigation of the low-lying excited states of the YbF molecule-a candidate molecule for experimental measurements of the electron electric dipole moment-with 2-component based multi-reference configuration interaction (MRCI), equation of motion coupled cluster (EOM-CCSD) and the extrapolated intermediate Hamiltonian Fock-space coupled cluster (XIHFS-CCSD). Specifically, we address the question of the nature of these low-lying states in terms of configurations containing filled or partially-filled Yb 4f shells. We show that while it does not appear possible to carry out calculations with both kinds of configurations contained in the same active space, reliable information can be extracted from different sectors of Fock space-that is, by performing electron attachment and detachment IHFS-CCSD and EOM-CCSD calculation on the closed-shell YbF+ and YbF- species, respectively. From these calculations we predict Ω = 1/2, 3/2 states, arising from the 4f13σ26s, 4f145d1/6p1, and 4f135d1σ16s configurations to be able to interact as they appear in the same energy range around the ground-state equilibrium geometry. As these states are generated from different sectors of Fock space, they are almost orthogonal and provide complementary descriptions of parts of the excited state manifold. To obtain a comprehensive picture, we introduce a simple adiabatization model to extract energies of interacting Ω = 1/2, 3/2 states that can be compared to experimental observations.

Implementation of Relativistic Coupled Cluster Theory for Massively Parallel GPU-Accelerated Computing Architectures.

In this paper, we report reimplementation of the core algorithms of relativistic coupled cluster theory aimed at modern heterogeneous high-performance computational infrastructures. The code is designed for parallel execution on many compute nodes with optional GPU coprocessing, accomplished via the new ExaTENSOR back end. The resulting ExaCorr module is primarily intended for calculations of molecules with one or more heavy elements, as relativistic effects on the electronic structure are included from the outset. In the current work, we thereby focus on exact two-component methods and demonstrate the accuracy and performance of the software. The module can be used as a stand-alone program requiring a set of molecular orbital coefficients as the starting point, but it is also interfaced to the DIRAC program that can be used to generate these. We therefore also briefly discuss an improvement of the parallel computing aspects of the relativistic self-consistent field algorithm of the DIRAC program.

Effects of ligands on (de-)enhancement of plasmonic excitations of silver, gold and bimetallic nanoclusters: TD-DFT+TB calculations.

Metal nanoclusters can be synthesized in various sizes and shapes and are typically protected with ligands to stabilize them. These ligands can also be used to tune the plasmonic properties of the clusters as the absorption spectrum of a protected cluster can be significantly altered compared to the bare cluster. In this paper, we computationally investigate the influence of thiolate ligands on the plasmonic intensity for silver, gold and alloy clusters. Using time-dependent density functional theory with tight-binding approximations, TD-DFT+TB, we show that this level of theory can reproduce the broad experimental spectra of Au144(SR)60 and Ag53Au91(SR)60 (R = CH3) compounds with satisfactory agreement. As TD-DFT+TB does not depend on atom-type parameters we were able to apply this approach on large ligand-protected clusters with various compositions. With these calculations we predict that the effect of ligands on the absorption can be a quenching as well as an enhancement. We furthermore show that it is possible to unambiguously identify the plasmonic peaks by the scaled Coulomb kernel technique and explain the influence of ligands on the intensity (de-)enhancement by analyzing the plasmonic excitations in terms of the dominant orbital contributions.

Conservation of Hot Thermal Spin-Orbit Population of 2P Atoms in a Cold Quantum Fluid Environment.

The 0.4 K internal temperature of superfluid helium nanodroplets is believed to guarantee a corresponding ground-state population of dopant atoms and molecules inside this cryogenic matrix. We have recorded 6s ← 5p excitation spectra of indium atoms in helium droplets and found two absorption bands separated by about 2000 cm-1, a value close to the spin-orbit (SO) splitting of the In 2P ground state. The intensities of the bands agree with a thermal population of the 2P1/2 and 2P3/2 states at 870 K, the temperature of the In pick-up cell. Applying femtosecond pump-probe spectroscopy, we found the same dynamical response of the helium solvation shell after the photoexcitation of the two bands. He-density functional theory simulations of the excitation spectra are in agreement with the bimodal structure. Our findings show that the population of SO levels of hot dopants is conserved after pick-up inside the superfluid droplet. Implications for the interpretation of experiments on molecular aggregates are discussed.

Spectroscopy of gold atoms and gold oligomers in helium nanodroplets.

The 6p 2P1/2 ← 6s 2S1/2 and 6p 2P3/2 ← 6s 2S1/2 transitions (D lines) of gold atoms embedded in superfluid helium nanodroplets have been investigated using resonant two-photon ionization spectroscopy. Both transitions are strongly blue-shifted and broadened due to the repulsive interaction between the Au valence electron and the surrounding helium. The in-droplet D lines are superimposed by the spectral signature of Au atoms relaxed into the metastable 2D states. These features are narrower than the in-droplet D lines and exhibit sharp rising edges that coincide with bare atom transitions. It is concluded that they originate from metastable 2D state AuHen exciplexes that have been ejected from the helium droplets during a relaxation process. Interestingly, the mechanism that leads to the formation of these complexes is suppressed for very large helium droplets consisting of about 2 × 106 He atoms, corresponding to a droplet diameter on the order of 50 nm. The assignment of the observed spectral features is supported by ab initio calculations employing a multiconfigurational self-consistent field method and a multi-reference configuration interaction calculation. For large helium droplets doped with Au oligomers, excitation spectra for mass channels corresponding to Aun with n = 2, 3, 4, 5, 7, and 9 are presented. The mass spectrum reveals even-odd oscillations in the number of Au atoms that constitute the oligomer, which is characteristic for coinage metal clusters. Resonances are observed close by the in-droplet D1 and D2 transitions, and the corresponding peak forms are very similar for different oligomer sizes.

Rydberg states of alkali atoms on superfluid helium nanodroplets: inside or outside?

Electronic excitations of an electron bound to an alkali metal ion inside a droplet of superfluid 4He are computed via a combination of helium density functional theory and the numerical integration of the Schrödinger equation for a single electron in a modified, He density dependent atomic pseudopotential. The application of a spectral method to the radial part of the valence electron wavefunction allows the computation of highly excited Rydberg states. For low principal quantum numbers, the energy required to push the electron outward is larger than the solvation energy of the ion. However, for higher principal quantum numbers the situation is reversed, which suggests the stability of a system where the ion sits inside the droplet while the valence electron orbits the nanodroplet.

Electric dipole moments and chemical bonding of diatomic alkali-alkaline earth molecules.

We investigate the properties of alkali-alkaline earth diatomic molecules in the lowest Σ(+) states of the doublet and quartet multiplicity by ab initio calculations. In all sixteen cases studied, the permanent electric dipole moment points in opposite directions for the two spin states. This peculiarity can be explained by molecular orbital theory. We further discuss dissociation energies and bond distances. We analyze trends and provide an empirically motivated model for the prediction of the permanent electric dipole moment for combinations of alkali and alkaline earth atoms not studied in this work.

Investigation of the RbCa molecule: Experiment and theory.

We present a thorough theoretical and experimental study of the electronic structure of RbCa. The mixed alkali-alkaline earth molecule RbCa was formed on superfluid helium nanodroplets. Excited states of the molecule in the range of 13 000-23 000 cm-1 were recorded by resonance enhanced multi-photon ionization time-of-flight spectroscopy. The experiment is accompanied by high level ab initio calculations of ground and excited state properties, utilizing a multireference configuration interaction method based on multiconfigurational self consistent field calculations. With this approach the potential energy curves and permanent electric dipole moments of 24 electronic states were calculated. In addition we computed the transition dipole moments for transitions from the ground into excited states. The combination of experiment and theory allowed the assignment of features in the recorded spectrum to the excited [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] states, where the experiment allowed to benchmark the calculation. This is the first experimental work giving insight into the previously unknown RbCa molecule, which offers great prospects in ultracold molecular physics due to its magnetic and electronic dipole moment in the [Formula: see text] ground state.

Ab initio study of the RbSr electronic structure: potential energy curves, transition dipole moments, and permanent electric dipole moments.

Excited states and the ground state of the diatomic molecule RbSr were calculated by post Hartree-Fock molecular orbital theory up to 22 000 cm(-1). We applied a multireference configuration interaction calculation based on multiconfigurational self-consistent field wave functions. Both methods made use of effective core potentials and core polarization potentials. Potential energy curves, transition dipole moments, and permanent electric dipole moments were determined for RbSr and could be compared with other recent calculations. We found a good agreement with experimental spectra, which have been obtained recently by helium nanodroplet isolation spectroscopy. For the lowest two asymptotes (Rb (5s (2)S) + Sr (5s4d (3)P°) and Rb (5p (2)P°) + Sr (5s(2) (1)S)), which exhibit a significant spin-orbit coupling, we included relativistic effects by two approaches, one applying the Breit-Pauli Hamiltonian to the multireference configuration interaction wave functions, the other combining a spin-orbit Hamiltonian and multireference configuration interaction potential energy curves. Using the results for the relativistic potential energy curves that correspond to the Rb (5s (2)S) + Sr (5s4d (3)P°) asymptote, we have simulated dispersed fluorescence spectra as they were recently measured in our lab. The comparison with experimental data allows to benchmark both methods and demonstrate that spin-orbit coupling has to be included for the lowest states of RbSr.

Helium-droplet-assisted preparation of cold RbSr molecules.

We present a combined experimental and theoretical study of the RbSr molecule. The experimental approach is based on the formation of RbSr molecules on helium nanodroplets. Utilizing two-photon ionization spectroscopy, an excitation spectrum ranging from 11,600 up to 23,000 cm(-1) was recorded. High level ab initio calculations of potential energy curves and transition dipole moments accompany the experiment and facilitate an assignment of transitions. We show that RbSr molecules desorb from the helium droplets upon excitation, which enables dispersed fluorescence spectroscopy of free RbSr. These spectra elucidate X(2)Σ(+) ground and excited state properties. Emission spectra originating from states corresponding to the Rb(5s(2)S) + Sr(5s5p(3)P) asymptote were recorded; spin-orbit coupling was included for the simulation. The results should provide a good basis for achieving the formation of this molecule in cold collisions, thus offering intriguing prospects for ultracold molecular physics.

Characterization of RbSr molecules: spectral analysis on helium droplets.

We report an experimental investigation of RbSr molecules attached to helium nanodroplets. The molecules are prepared on the surface of helium droplets by utilizing a sequential pickup scheme. We provide a detailed analysis of the excitation spectrum in the wavelength range 11,600-23,000 cm(-1). The spectrum has been recorded by resonance enhanced multi-photon ionization time-of-flight spectroscopy. The inherent mass sensitivity of the method allows for an unraveling of the RbSr spectrum, which is influenced by Rb and Sr dimer contributions, because of the proximity of their respective isotopologues. In addition, the vibrationally resolved 4(2)Σ(+) band was investigated using laser induced fluorescence spectroscopy. The vibronic transitions exhibit a lambda-shaped peak form, which is characteristic of excitations on helium droplets and indicative of strong coupling of the molecule to the superfluid helium environment. Furthermore, the vibrationally resolved 4(2)Σ(+) state enables the determination of molecular parameters, which are in excellent agreement with previously measured dispersed fluorescence spectra, originating from bare RbSr molecules. The assignment of recorded transitions is based on calculated transition dipole moments and potential energy curves. The theoretical results allow for the identification of transitions from the vibronic X(2)Σ(+) ground state to the 2(2)Π, 3(2)Σ(+), 4(2)Σ(+), 3(2)Π, 4(2)Π and 6(2)Σ(+) states. The detailed investigation of RbSr on helium droplets provides a solid basis for further high resolution gas phase studies of this diatomic molecule that holds promise in the area of cold molecular physics.

Solvation and spectral line shifts of chromium atoms in helium droplets based on a density functional theory approach.

The interaction of an electronically excited, single chromium (Cr) atom with superfluid helium nanodroplets of various size (10 to 2000 helium (He) atoms) is studied with helium density functional theory. Solvation energies and pseudo-diatomic potential energy surfaces are determined for Cr in its ground state as well as in the y(7)P, a(5)S, and y(5)P excited states. The necessary Cr-He pair potentials are calculated by standard methods of molecular orbital-based electronic structure theory. In its electronic ground state the Cr atom is found to be fully submerged in the droplet. A solvation shell structure is derived from fluctuations in the radial helium density. Electronic excitations of an embedded Cr atom are simulated by confronting the relaxed helium density (ρHe), obtained for Cr in the ground state, with interaction pair potentials of excited states. The resulting energy shifts for the transitions z(7)P ← a(7)S, y(7)P ← a(7)S, z(5)P ← a(5)S, and y(5)P ← a(5)S are compared to recent fluorescence and photoionization experiments.

An ab initio study of the CrHe diatomic molecule: the effect of van der Waals distortion on a highly magnetic multi-electron system.

The interaction between He and Cr is investigated by means of post-Hartree-Fock molecular orbital theory. We analyze the influence of the van der Waals forces on the complex electronic structure of the chromium atom, starting with its septet manifold and cover the first few electronically excited states up to 30 000 cm(-1). For the sake of a direct comparison with ongoing experiments on Cr-doped helium nanodroplets we extend our analysis to selected states of the quintet manifold in order to explain a non-radiating relaxation from y (7)P(o) to z (5)P(o).

Spectroscopy of cold LiCa molecules formed on helium nanodroplets.

We report on the formation of mixed alkali-alkaline earth molecules (LiCa) on helium nanodroplets and present a comprehensive experimental and theoretical study of the ground and excited states of LiCa. Resonance enhanced multiphoton ionization time-of-flight (REMPI-TOF) spectroscopy and laser induced fluorescence (LIF) spectroscopy were used for the experimental investigation of LiCa from 15000 to 25500 cm(-1). The 4(2)Σ(+) and 3(2)Π states show a vibrational structure accompanied by distinct phonon wings, which allows us to determine molecular parameters as well as to study the interaction of the molecule with the helium droplet. Higher excited states (4(2)Π, 5(2)Σ(+), 5(2)Π, and 6(2)Σ(+)) are not vibrationally resolved and vibronic transitions start to overlap. The experimental spectrum is well reproduced by high-level ab initio calculations. By using a multireference configuration interaction (MRCI) approach, we calculated the 19 lowest lying potential energy curves (PECs) of the LiCa molecule. On the basis of these calculations, we could identify previously unobserved transitions. Our results demonstrate that the helium droplet isolation approach is a powerful method for the characterization of tailor-made alkali-alkaline earth molecules. In this way, important contributions can be made to the search for optimal pathways toward the creation of ultracold alkali-alkaline earth ground state molecules from the corresponding atomic species. Furthermore, a test for PECs calculated by ab initio methods is provided.

Spectroscopy of lithium atoms and molecules on helium nanodroplets.

We report on the spectroscopic investigation of lithium atoms and lithium dimers in their triplet manifold on the surface of helium nanodroplets (He(N)). We present the excitation spectrum of the 3p ← 2s and 3d ← 2s two-photon transitions for single Li atoms on He(N). The atoms are excited from the 2S(Σ) ground state into Δ, Π, and Σ pseudodiatomic molecular substates. Excitation spectra are recorded by resonance enhanced multiphoton ionization time-of-flight (REMPI-TOF) mass spectroscopy, which allows an investigation of the exciplex (Li*­He(m), m = 1­3) formation process in the Li­He(N) system. Electronic states are shifted and broadened with respect to free atom states, which is explained within the pseudodiatomic model. The assignment is assisted by theoretical calculations, which are based on the Orsay­Trento density functional where the interaction between the helium droplet and the lithium atom is introduced by a pairwise additive approach. When a droplet is doped with more than one alkali atom, the fragility of the alkali­He(N) systems leads preferably to the formation of high-spin molecules on the droplets. We use this property of helium nanodroplets for the preparation of Li dimers in their triplet ground state (13Σu(+)). The excitation spectrum of the 23Πg(ν' = 0­11) ← 13Σu(+)(ν″ = 0) transition is presented. The interaction between the molecule and the droplet manifests in a broadening of the transitions with a characteristic asymmetric form. The broadening extends to the blue side of each vibronic level, which is caused by the simultaneous excitation of the molecule and vibrations of the droplet (phonons). The two isotopes of Li form 6Li2 and 7Li2 as well as isotope mixed 6Li7Li molecules on the droplet surface. By using REMPI-TOF mass spectroscopy, isotope-dependent effects could be studied.