Approaching the basis-set limit of the dRPA correlation energy with explicitly correlated and projector augmented-wave methods.

The direct random-phase approximation (dRPA) is used to calculate and compare atomization energies for the HEAT set and ten selected molecules of the G2-1 set using both plane waves and Gaussian-type orbitals. We describe detailed procedures to obtain highly accurate and well converged results for the projector augmented-wave method as implemented in the Vienna Ab initio Simulation Package as well as the explicitly correlated dRPA-F12 method as implemented in the TURBOMOLE package. The two approaches agree within chemical accuracy (1 kcal/mol) for the atomization energies of all considered molecules, both for the exact exchange as well as for the RPA. The root mean-square deviation is 0.41 kcal/mol for the exact exchange (evaluated using density functional theory orbitals) and 0.33 kcal/mol for exact exchange plus correlation from the RPA.

A litmus test for the balanced description of dispersion interactions and coordination chemistry of lanthanoids.

The influence of long-range interactions on the structure of complexes of Eu(III) with four 9-hydroxy-phenalen-1-one ligands (HPLN) and one alkaline earth metal dication [Eu(PLN)4AE]+ (AE: Mg, Ca, Sr, and Ba) is analyzed. Through the [Eu(PLN)4Ca]+ complex, which is a charged complex with two metals-one of them a lanthanoid-and with four relatively fluxional π-ligands, the difficulties of describing such systems are identified. The inclusion of the D3(BJ) or D4 corrections to different density functionals introduces significant changes in the structure, which are shown to stem from the interaction between pairs of PLN ligands. This interaction is studied further with a variety of density functionals, wave-function based methods, and by means of the random phase approximation. By comparing the computed results with those from experimental evidence of gas-phase photoluminescence and ion mobility measurements it is concluded that the inclusion of dispersion corrections does not always yield structures that are in agreement with the experimental findings.

The He-H3 + complex. II. Infrared predissociation spectrum and energy term diagram.

The rotationally resolved infrared (IR) spectrum of the He-H3 + complex has been measured in a cryogenic ion trap experiment at a nominal temperature of 4 K. Predissociation of the stored complex has been invoked by excitation of the degenerate ν2 mode of the H3 + sub-unit using a pulsed optical parametric oscillator system. An assignment of the experimental spectrum became possible through one-to-one correlations with bands of the spectrum theoretically predicted in Paper I [Harding et al., J. Chem. Phys. 156, 144307 (2022)]. 19 bands have been assigned and analyzed, and the energy term diagram of the lower states of this floppy molecular complex has been derived from combination differences (CDs) in the experimental spectrum. Ground state combination differences (GSCDs) reveal a large part of the energy term diagram for the He-H3 + complex in its vibrational ground state, v = 0. Experimental and theoretical term energies agree within experimental accuracy for the rotational fine structure associated with the total angular momentum quantum number J and the parity e/f as well as for the coarse spacing of the lowest K states of the complex. This favorable comparison shows that the potential energy surface (PES) calculated in Paper I is accurate. The barriers between the three equivalent global minima in this PES are relatively low and the He-H3 + complex is extremely floppy, with nearly unhindered internal rotation of the H3 + sub-unit. The resulting Coriolis interactions couple the internal and end-over-end rotation of the complex and contribute significantly to the energy terms. They are observed both in experiment and theory and are, e.g., the origin of different rotational constants for states of e and f parity. Also in this respect, experiment and theory agree very well. Despite the assignment and analysis of many bands of the extremely rich IR spectrum of He-H3 +, higher levels of excitation, including the complex stretching mode, need further attention.

The He-H3 + complex. I. Vibration-rotation-tunneling states and transition probabilities.

With a He-H3 + interaction potential obtained from advanced electronic structure calculations, we computed the vibration-rotation-tunneling (VRT) states of this complex for total angular momenta J from 0 to 9, both for the vibrational ground state and for the twofold degenerate v2 = 1 excited state of H3 +. The potential has three equivalent global minima with depth De = 455.3 cm-1 for He in the plane of H3 +, three equatorial saddle points that separate these minima with barriers of 159.5 cm-1, and two axial saddle points with energies of 243.1 cm-1 above the minima. The dissociation energies calculated for the complexes of He with ortho-H3 + (oH3 +) and para-H3 + (pH3 +) are D0 = 234.5 and 236.3 cm-1, respectively. Wave function plots of the VRT states show that they may be characterized as weakly hindered internal rotor states, delocalized over the three minima in the potential and with considerable amplitude at the barriers. Most of them are dominated by the jk = 10 and 11 rotational ground states of oH3 + and pH3 +, with the intermolecular stretching mode excited up to v = 4 inclusive. However, we also found excited internal rotor states: 33 in He-oH3 +, and 22 and 21 in He-pH3 +. The VRT levels and wave functions were used to calculate the frequencies and line strengths of all allowed v2 = 0 → 1 rovibrational transitions in the complex. Theoretical spectra generated with these results are compared with the experimental spectra in Paper II [Salomon et al., J. Chem. Phys. 156, 144308 (2022)] and are extremely helpful in assigning these spectra. This comparison shows that the theoretical energy levels and spectra agree very well with the measured ones, which confirms the high accuracy of our ab initio He-H3 + interaction potential and of the ensuing calculations of the VRT states.

Hyperfine-Resolved Near-Infrared Spectra of H217O.

Huge efforts have recently been taken in the derivation of accurate compilations of rovibrational energies of water, one of the most important reference systems in spectroscopy. Such precision is desirable for all water isotopologues, although their investigation is challenged by hyperfine effects in their spectra. Frequency-comb locked noise-immune cavity-enhanced optical-heterodyne molecular spectroscopy (NICE-OHMS) allows for achieving high sensitivity, resolution, and accuracy. This technique has been employed to resolve the subtle hyperfine splittings of rovibrational transitions of H217O in the near-infrared region. Simulation and interpretation of the H217O saturation spectra have been supported by coupled-cluster calculations performed with large basis sets and accounting for high-level corrections. Experimental 17O hyperfine parameters are found in excellent agreement with the corresponding computed values. The need of including small hyperfine effects in the analysis of H217O spectra has been demonstrated together with the ability of the computational strategy employed for providing quantitative predictions of the corresponding parameters.

Coupled-cluster techniques for computational chemistry: The CFOUR program package.

An up-to-date overview of the CFOUR program system is given. After providing a brief outline of the evolution of the program since its inception in 1989, a comprehensive presentation is given of its well-known capabilities for high-level coupled-cluster theory and its application to molecular properties. Subsequent to this generally well-known background information, much of the remaining content focuses on lesser-known capabilities of CFOUR, most of which have become available to the public only recently or will become available in the near future. Each of these new features is illustrated by a representative example, with additional discussion targeted to educating users as to classes of applications that are now enabled by these capabilities. Finally, some speculation about future directions is given, and the mode of distribution and support for CFOUR are outlined.

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations.

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy-cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe-Salpeter methods, second-order Møller-Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE's functionality, including excited-state methods, RPA and Green's function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE's current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE's development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

The first microsolvation step for furans: New experiments and benchmarking strategies.

The site-specific first microsolvation step of furan and some of its derivatives with methanol is explored to benchmark the ability of quantum-chemical methods to describe the structure, energetics, and vibrational spectrum at low temperature. Infrared and microwave spectra in supersonic jet expansions are used to quantify the docking preference and some relevant quantum states of the model complexes. Microwave spectroscopy strictly rules out in-plane docking of methanol as opposed to the top coordination of the aromatic ring. Contrasting comparison strategies, which emphasize either the experimental or the theoretical input, are explored. Within the harmonic approximation, only a few composite computational approaches are able to achieve a satisfactory performance. Deuteration experiments suggest that the harmonic treatment itself is largely justified for the zero-point energy, likely and by design due to the systematic cancellation of important anharmonic contributions between the docking variants. Therefore, discrepancies between experiment and theory for the isomer abundance are tentatively assigned to electronic structure deficiencies, but uncertainties remain on the nuclear dynamics side. Attempts to include anharmonic contributions indicate that for systems of this size, a uniform treatment of anharmonicity with systematically improved performance is not yet in sight.

Understanding UV-Vis Spectra of Halogenated Tetraazaperopyrenes (TAPPs): A Computational Study.

The UV-vis absorption and emission spectra of halogenated tetraazaperopyrenes (TAPPs) have been investigated employing second-order approximate coupled cluster (CC2) and (time-dependent) density functional theory (DFT). We have found that the qualitative estimates of (vertical) absorption and excitation energies are possible within a single particle picture based on frontier orbitals, but the single particle picture is not sufficient to achieve quantitative accuracy. Going from the single-particle picture to the many-particle picture improves the agreement with experimental results, but still no satisfying correlation of theory and experiment is obtained. The comparison of CC2- and DFT-based methods reveals that deviations from the experimental results cannot be explained by deficiencies of the electronic-structure methods but rather stem from neglecting vibrational effects. An agreement of theoretical results and experimental spectra is found for adiabatic excitation energies, which are given as energy differences of vibronic states, which are directly accessible using both theoretical and experimental methods. The most pronounced vibronic influence is found for the Stokes shifts, which are significantly overestimated by computing the vertical electronic transitions only. Based on the vibronic contributions, the small Stokes shift of the TAPP compounds can be explained by the temperature dependence of the vibrationally resolved UV-vis spectra.

Bethe-Salpeter correlation energies of atoms and molecules.

A variety of approaches are presented for the computation of atomic and molecular correlation energies based on the Bethe-Salpeter equation in the framework of the adiabatic-connection fluctuation-dissipation theorem. The performance of the approaches is assessed by computing the total energies of the atoms H-Ne and the atomization energies of the high-accuracy extrapolated ab initio thermochemistry set of small molecules as well as by determining the bond lengths and harmonic vibrational frequencies of the metal monoxides MO with M=Ca-Zn.

A highly flexible molecule: The peculiar case of ethynyl isothiocyanate HCCNCS.

The rotational spectrum of the parent isotopic species of HCCNCS, along with those of three 13C singly substituted variants and one 34S minor isotopologue, has been observed with high resolution using Fourier transform microwave spectroscopy from 4 to 26 GHz. Based on the observed spectral pattern and assignment of the 14N nuclear quadrupole hyperfine structure, the geometry of HCCNCS is effectively linear, which is further supported by the observation of ℓ -type doubling for rotational transitions in an excited bending state of the parent HCCNCS. The experimental observations are supported by high level quantum chemical calculations using the coupled-cluster singles and doubles model augmented by a perturbative correction for triple excitations, CCSD(T), level of theory that reveal an extremely shallow potential energy well along the CNC bending angle with a surprising basis set dependence.

Vibronic Coupling Analysis of the Ligand-Centered Phosphorescence of Gas-Phase Gd(III) and Lu(III) 9-Oxophenalen-1-one Complexes.

The gas-phase laser-induced photoluminescence of cationic mononuclear gadolinium and lutetium complexes involving two 9-oxophenalen-1-one ligands is reported. Performing measurements at a temperature of 83 K enables us to resolve vibronic transitions. Via comparison to Franck-Condon computations, the main vibrational contributions to the ligand-centered phosphorescence are determined to involve rocking, wagging, and stretching of the 9-oxophenalen-1-one-lanthanoid coordination in the low-energy range, intraligand bending, and stretching in the medium- to high-energy range, rocking of the carbonyl and methine groups, and C-H stretching beyond. Whereas Franck-Condon calculations based on density-functional harmonic frequency computations reproduce the main features of the vibrationally resolved emission spectra, the absolute transition energies as determined by density functional theory are off by several thousand wavenumbers. This discrepancy is found to remain at higher computational levels. The relative energy of the Gd(III) and Lu(III) emission bands is only reproduced at the coupled-cluster singles and doubles level and beyond.

The furan microsolvation blind challenge for quantum chemical methods: First steps.

Herein we present the results of a blind challenge to quantum chemical methods in the calculation of dimerization preferences in the low temperature gas phase. The target of study was the first step of the microsolvation of furan, 2-methylfuran and 2,5-dimethylfuran with methanol. The dimers were investigated through IR spectroscopy of a supersonic jet expansion. From the measured bands, it was possible to identify a persistent hydrogen bonding OH-O motif in the predominant species. From the presence of another band, which can be attributed to an OH-π interaction, we were able to assert that the energy gap between the two types of dimers should be less than or close to 1 kJ/mol across the series. These values served as a first evaluation ruler for the 12 entries featured in the challenge. A tentative stricter evaluation of the challenge results is also carried out, combining theoretical and experimental results in order to define a smaller error bar. The process was carried out in a double-blind fashion, with both theory and experimental groups unaware of the results on the other side, with the exception of the 2,5-dimethylfuran system which was featured in an earlier publication.

Correlation of the structural information obtained for europium-chelate ensembles from gas-phase photoluminescence and ion-mobility spectroscopy with density-functional computations and ligand-field theory.

We report a combined investigation of europium(iii)9-oxo-phenalen-1-one (PLN) coordination complexes, [Eu(PLN)4AE]+ with AE = Mg, Ca, and Sr, using gas-phase photoluminescence, trapped ion-mobility spectrometry and density-functional computations. In order to sort out the structural impact of the alkali earth dications on the photoluminescence spectra, the experimental data are compared to the predicted ligand-field splittings as well as to the collision cross-sections for different isomers of [Eu(PLN)4AE]+. The best fitting interpretation is that one isomer family predominantly contributes to the recorded luminescence. The present work demonstrates the complexity of the coordination patterns of multicenter lanthanoid chelates involved in dynamical equilibria and the pertinence of using isolation techniques to elucidate their photophysical properties.

Gas-Phase Photoluminescence Characterization of Stoichiometrically Pure Nonanuclear Lanthanoid Hydroxo Complexes Comprising Europium or Gadolinium.

Gas-phase photoluminescence measurements involving mass-spectrometric techniques enable determination of the properties of selected molecular systems with knowledge of their exact composition and unaffected by matrix effects such as solvent interactions or crystal packing. The resulting reduced complexity facilitates a comparison with theory. Herein, we provide a detailed report of the intrinsic luminescence properties of nonanuclear europium(III) and gadolinium(III) 9-hydroxyphenalen-1-one (HPLN) hydroxo complexes. Luminescence spectra of [Eu9(PLN)16(OH)10](+) ions reveal an europium-centered emission dominated by a 4-fold split Eu(III) hypersensitive transition, while photoluminescence lifetime measurements for both complexes support an efficient europium sensitization via a PLN-centered triplet-state manifold. The combination of gas-phase measurements with density functional theory computations and ligand-field theory is used to discuss the antiprismatic core structure of the complexes and to shed light on the energy-transfer mechanism. This methodology is also employed to fit a new set of parameters, which improves the accuracy of ligand-field computations of Eu(III) electronic transitions for gas-phase species.

Differential Many-Body Cooperativity in Electronic Spectra of Oligonuclear Transition-Metal Complexes.

In computational chemistry, non-additive and cooperative effects can be defined in terms of a (differential) many-body expansion of the energy or any other physical property of the molecular system of interest. One-body terms describe energies or properties of the subsystems, two-body terms describe non-additive but pairwise contributions and three-body as well as higher-order terms can be interpreted as a measure for cooperativity. In the present article, this concept is applied to the analysis of ultraviolet/visible (UV/Vis) spectra of homotrinuclear transition-metal complexes by means of a many-body expansion of the change in the spectrum induced by replacing each of the three transition-metal ions by another transition-metal ion to yield a different homotrinuclear transition-metal complex. Computed spectra for the triangulo-complexes [M3 {Si(mt(Me) )3}2] (M=Pd/Pt, mt(Me) =methimazole) and tritopic triphenylene-based N-heterocyclic carbene Rh/Ir complexes illustrate the concept, showing large and small differential three-body cooperativity, respectively.

The hyperfine structure in the rotational spectra of D2(17)O and HD(17)O: Confirmation of the absolute nuclear magnetic shielding scale for oxygen.

Guided by theoretical predictions, the hyperfine structures of the rotational spectra of mono- and bideuterated-water containing (17)O have been experimentally investigated. To reach sub-Doppler resolution, required to resolve the hyperfine structure due to deuterium quadrupole coupling as well as to spin-rotation (SR) and dipolar spin-spin couplings, the Lamb-dip technique has been employed. The experimental investigation and in particular, the spectral analysis have been supported by high-level quantum-chemical computations employing coupled-cluster techniques and, for the first time, a complete experimental determination of the hyperfine parameters involved was possible. The experimentally determined (17)O spin-rotation constants of D2 (17)O and HD(17)O were used to derive the paramagnetic part of the corresponding nuclear magnetic shielding constants. Together with the computed diamagnetic contributions as well as the vibrational and temperature corrections, the latter constants have been employed to confirm the oxygen nuclear magnetic shielding scale, recently established on the basis of spin-rotation data for H2 (17)O [Puzzarini et al., J. Chem. Phys. 131, 234304 (2009)].

Effect of Proton Substitution by Alkali Ions on the Fluorescence Emission of Rhodamine B Cations in the Gas Phase.

The photophysics of chromophores is strongly influenced by their environment. Solvation, charge state, and adduct formation significantly affect ground and excited state energetics and dynamics. The present study reports on fluorescence emission of rhodamine B cations (RhBH+) and derivatives in the gas phase. Substitution of the acidic proton of RhBH+ by alkali metal cations, M+, ranging from lithium to cesium leads to significant and systematic blue shifts of the emission. The gas-phase structures and singlet transition energies of RhBH+ and RhBM+, M = Li, Na, K, Rb, and Cs, were investigated using Hartree-Fock theory, density functional methods, second-order Møller-Plesset perturbation theory, and the second-order approximate coupled-cluster model CC2. Comparison of experimental and theoretical results highlights the need for improved quantum chemical methods, while the hypsochromic shift observed upon substitution appears best explained by the Stark effect due to the inhomogeneous electric field generated by the alkali ions.

Substitutional photoluminescence modulation in adducts of a europium chelate with a range of alkali metal cations: a gas-phase study.

We present gas-phase dispersed photoluminescence spectra of europium(III) 9-hydroxyphenalen-1-one (HPLN) complexes forming adducts with alkali metal ions ([Eu(PLN)3M](+) with M = Li, Na, K, Rb, and Cs) confined in a quadrupole ion trap for study. The mass selected alkali metal cation adducts display a split hypersensitive (5)D0 → (7)F2 Eu(3+) emission band. One of the two emission components shows a linear dependence on the radius of the alkali metal cation whereas the other component displays a quadratic dependence thereon. In addition, the relative intensities of both components invert in the same order. The experimental results are interpreted with the support of density functional calculations and Judd-Ofelt theory, yielding also structural information on the isolated [Eu(PLN)3M](+) chromophores.

Characterization of Nonanuclear Europium and Gadolinium Complexes by Gas-Phase Luminescence Spectroscopy.

Gas-phase measurements using mass-spectrometric techniques allow determination of the luminescence properties of selected molecular systems with knowledge of their exact composition. Furthermore, isolated luminophores are unaffected by matrix effects like solvent interactions or crystal packing. As a result, the system complexity is reduced relative to the condensed phase and a direct comparison with theory is facilitated. Herein, we report the intrinsic luminescence properties of nonanuclear europium(III) and gadolinium(III) 9-hydroxyphenalen-1-one (HPLN)-hydroxo complexes. Luminescence spectra of [Eu9(PLN)16(OH)10](+) ions reveal an europium-centered emission dominated by a 4-fold split Eu(III) hypersensitive transition. The corresponding Gd(III) complex, [Gd9(PLN)16(OH)10](+), shows a broad emission from a ligand based triplet state with an onset of about 1000 wavenumbers in excess of the europium emission. As supported by photoluminescence lifetime measurements for both complexes, we deduce an efficient europium sensitization via PLN-based triplet states. The luminescence spectra of the complexes are discussed in terms of a square antiprismatic europium/gadolinium core structure as suggested by density functional computations.