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A route to assess non-linear light–matter interactions from the increasingly popular GW-Bethe–Salpeter equation (GW-BSE) method is outlined. In the present work, the necessary analytic expressions within the static-screened exchange approximation of the BSE are derived. This enables a straightforward implementation of the computation of the first hyperpolarizability as well as two-photon absorption processes for molecular systems. Benchmark calculations on small molecular systems reveal that the GW-BSE method is intriguingly accurate for predicting both first hyperpolarizabilities and two-photon absorption strengths. Using state-of-the-art Kohn–Sham references as a starting point, the accuracy of the GW-BSE method rivals that of the coupled-cluster singles-and-doubles method, outperforming both second-order coupled-cluster and time-dependent density-functional theory. [ABSTRACT FROM AUTHOR]

A two-component contour deformation (CD) based GW method that employs frequency sampling to drastically reduce the computational effort when assessing quasiparticle states far away from the Fermi level is outlined. Compared to the canonical CD-GW method, computational scaling is reduced by an order of magnitude without sacrificing accuracy. This allows for an efficient calculation of core ionization energies. The improved computational efficiency is used to provide benchmarks for core ionized states, comparing the performance of 15 density functional approximations as Kohn–Sham starting points for GW calculations on a set of 65 core ionization energies of 32 small molecules. Contrary to valence states, GW calculations on core states prefer functionals with only a moderate amount of Hartree–Fock exchange. Moreover, modern ab initio local hybrid functionals are also shown to provide excellent generalized Kohn–Sham references for core GW calculations. Furthermore, the core–valence separated Bethe–Salpeter equation (CVS-BSE) is outlined. CVS-BSE is a convenient tool to probe core excited states. The latter is tested on a set of 40 core excitations of eight small inorganic molecules. Results from the CVS-BSE method for excitation energies and the corresponding absorption cross sections are found to be in excellent agreement with those of reference damped response BSE calculations. [ABSTRACT FROM AUTHOR]

The carbonyl cluster compound [GeRu6(CO)18HI] is unique in regard to its structure and bonding with a GeRu6 cluster core, a planar GeRu4HI unit, extensive multi‐center bonding, and an aromatic ring current similar to benzene (9‐10 nA T−1). The open‐shell cluster core is a Ge‐centered five‐membered Ru4(Ru2) ring with CO ligands and an additional H and I atom, each bridging two Ru atoms on opposite sides of the cluster core. The compound is prepared at 130 °C in a weakly‐coordinating ionic liquid. [ABSTRACT FROM AUTHOR]

Nanophotonic concepts can improve measurement techniques by enhancing and tailoring the light–matter interaction. However, the optical response of devices that implement such techniques can be intricate, depending on the sample under investigation. Nanophotonics is therefore a ripe field for applying the concept of a digital twin: a digital representation of an entire real‐world device. In this work, the concept of a digital twin is detailed with the example of a nanophotonically enhanced chiral sensing platform. In that platform, helicity‐preserving cavities enhance the interaction between chiral molecules and light, allowing faster measurement of the circular dichroism of the molecules. The sheer presence of the molecules affects the cavity's functionality, demanding a holistic treatment to understand the device's performance. In the digital twin, optical and quantum chemistry simulations are fused to provide a comprehensive description of the system and predict the circular dichroism spectrum. Performing simulations in lockstep with the experiment will allow a clear interpretation of measurement results. This work also demonstrates how to design a cavity‐enhanced circular dichroism spectrometer by utilizing the digital twin. The digital twin can be used to guide experiments and analyze results, and its underlying concept can be translated to many other optical experiments. [ABSTRACT FROM AUTHOR]

The increasingly popular GW method is becoming a convenient tool to determine vertical ionization energies in molecular systems. However, depending on the formalism used and the range of orbitals investigated, it may be hampered by a steep computational scaling. To alleviate this issue, correlated natural virtual orbitals (NVOs) based on second-order Møller–Plesset (MP2) and direct MP2 correlation energies are implemented, and the resulting correlated NVOs are tested on GW quasiparticle energies. Test cases include the popular GW variants G0W0 and evGW0 as well as more elaborate vertex corrections. We find that for increasingly larger molecular systems and basis sets, NVOs considerably improve efficiency. Furthermore, we test the performance of the truncated (frozen) NVO ansatz on the GW100 test set. For the latter, it is demonstrated that, using a carefully chosen truncation threshold, NVOs lead to a negligible loss in accuracy while providing speedups of one order of magnitude. Furthermore, we compare the resulting quasiparticle energies to very accurate vertical ionization energies obtained from coupled-cluster theory with singles, doubles, and noniterative triples [CCSD(T)], confirming that the loss in accuracy introduced by truncating the NVOs is negligible compared to the methodical errors in the GW approximation. It is also demonstrated that the choice of basis set impacts results far more than using a suitably truncated NVO space. Therefore, at the same computational expense, more accurate results can be obtained using NVOs. Finally, we provide improved reference CCSD(T) values for the GW100 test set, which have been obtained using the def2-QZVPP basis set. [ABSTRACT FROM AUTHOR]

Molecular rotations and vibrations have been extensively studied by chemists for decades, both experimentally using spectroscopic methods and theoretically with the help of quantum chemistry. However, the theoretical investigation of molecular rotations and vibrations in strong magnetic fields requires computationally more demanding tools. As such, proper calculations of rotational and vibrational spectra were not feasible up until very recently. In this work, we present rotational and vibrational spectra for two small linear molecules, H2 and LiH, in strong magnetic fields. By treating the nuclei as classical particles, trajectories for rotations and vibrations are simulated from ab initio molecular dynamics. Born–Oppenheimer potential energy surfaces are calculated at the Hartree–Fock and MP2 levels of theory using London atomic orbitals to ensure gauge origin invariance. For the calculation of nuclear trajectories, a highly efficient Tajima propagator is introduced, incorporating the Berry curvature tensor accounting for the screening of nuclear charges. [ABSTRACT FROM AUTHOR]

[V2(HCyclal)2] is prepared by controlled oxidation of vanadium nanoparticles at 50 °C in toluene. The V(0) nanoparticles are synthesized in THF by reduction of VCl3 with lithium naphthalenide. They exhibit very small particle sizes of 1.2 ± 0.2 nm and a high reactivity (e.g. with air or water). By reaction of V(0) nanoparticles with the azacrown ether H4Cyclal, [V2(HCyclal)2] is obtained with deep green crystals and high yield. The title compound exhibits a V(III) dimer (V⋯V: 304.1(1) pm) with two deprotonated [HCyclal]3− ligands as anions. V(0) nanoparticles as well as the sole coordination of V(III) by a crown ether as the ligand and nitrogen as sole coordinating atom are shown for the first time. Magnetic measurements and computational results point to antiferromagnetic coupling within the V(III) couple, establishing an antiferromagnetic spin S = 1 dimer with the magnetic susceptibility determined by the thermal population of the total spin ranging from ST = 0 to ST = 2. [ABSTRACT FROM AUTHOR]

As quantum-chemical calculations of molecules in static external magnetic fields are becoming increasingly popular, the description of molecular symmetry under such conditions is also becoming more and more relevant. Using group theory, a general scheme of identifying the molecular point group in an external magnetic field is constructed. For both point groups that are non-existent in the absence of a field (C∞ and C∞h) and their double groups, the character tables are presented. General properties of all possible point groups are discussed, and it is mathematically proven that they are all Abelian. [ABSTRACT FROM AUTHOR]

Binuclear coinage metal phosphine complexes are examined under ion trap isolation in order to elucidate their noncovalent binding, structural properties and intrinsic electronic spectra. Our survey shows an intriguing order of electronic transitions obtained by in situ synthesis and mass-spectrometrically supported UV photodissociation spectroscopy on a series of six isolated homo- and heterobinuclear complexes of type [MM′(dcpm)2]2+ (M, M′ = CuI, AgI, AuI; dcpm = bis(dicyclohexyl-phosphino)methane). This approach provides the unique opportunity to study all possible coinage metal interactions within a fixed ligand framework. A successive blue-shift (33 700–38 500 cm−1; 297–260 nm) of the lowest-energy bright electronic transition energy in gas phase was observed in the order of Cu2 < CuAu < CuAg < Au2 < AgAu < Ag2. This order was reproduced by quantum chemical calculations using a scalar-relativistic GW-Bethe–Salpeter-equation (GW-BSE) approach. Theory ascribes the electronic bands of all complexes to metal-centered 1MC(dσ*–pσ) transitions revealing a strengthening of metal–metal′ (M–M′) binding upon excitation, in agreement to mass spetrometric results. A test of the correlation of transition energies with M–M′ distance by quantum chemical calculations of single point energies as a function of intermetallic distance indicates qualitative agreement with experimental results. However, the experimentally observed high sensitivity of spectroscopic shifts towards metal composition cannot be accounted for solely by M–M′ distance variation. The differences in electronic transitions are qualitatively rationalized by the varying (n + 1)s (n = 3, 4, 5) orbital contributions (increase from Cu2via CuAu/CuAg to Au2/AgAu/Ag2) within the nd(n + 1)s/p-hybridization for the ground electronic state of the different complexes, whereas the excited state (of (n + 1)p orbital character) shows significantly less variation in energy. In particular, the observed spectroscopic and mass spectrometric sequence for the Ag/Au complexes is traced back to the interplay of Pauli repulsion and variation in metal–ligand bond strength within the orbital hybridization model. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Ultrafast vibrational coherence with metal-metal stretching mode character is observed for phosphine-bridged d10-d10 complexes of different size, containing the binuclear [Ag2Cl]+ chromophore in an ion trap. Fragmentation pathways are governed by the wave packet's phase.

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. [ABSTRACT FROM AUTHOR]

Quasiparticle energies of the atoms H–Ne have been computed in the GW approximation in the presence of strong magnetic fields with field strengths varying from 0 to 0.25 atomic units (0.25 B 0 = 0.25 ℏ e − 1 a 0 − 2 ≈ 58 763 T). The GW quasiparticle energies are compared with equation-of-motion ionization-potential (EOM-IP) coupled-cluster singles-and-doubles (CCSD) calculations of the first ionization energies. The best results are obtained with the evGW@PBE0 method, which agrees with the EOM-IP-CCSD model to within about 0.20 eV. Ionization potentials have been calculated for all atoms in the series, representing the first systematic study of ionization potentials for the first-row atoms at field strengths characteristic of magnetic white dwarf stars. Under these conditions, the ionization potentials increase in a near-linear fashion with the field strength, reflecting the linear field dependence of the Landau energy of the ionized electron. The calculated ionization potentials agree well with the best available literature data for He, Li, and Be. [ABSTRACT FROM AUTHOR]

We have implemented and applied the GW method and the static screened Bethe–Salpeter equation (BSE) for calculating linear-response properties for quasirelativistic molecular systems. Our ansatz is based on a two-component (2c) scheme that includes spin–orbit coupling as well as scalar relativistic effects. Efficient, state-of-the-art approaches including the analytic continuation (employing Padé approximants, scaling as N 4 with system size N ) and contour deformation schemes are presented to obtain the required 2c quasirelativistic GW quasiparticle energies. Screened exchange contributions are computed within the resolution-of-the-identity approximation, and working equations for the 2c GW/BSE method are given. The performance of the 2c GW/BSE method is assessed, and results are compared to other methods and experimental data. A robust iterative scheme for solving the eigenvalue problems occurring in the 2c GW/BSE and hybrid time-dependent density functional theories is presented. [ABSTRACT FROM AUTHOR]

We report the extended explicitly correlated approximate coupled-cluster singles and doubles CC2(F12*)-XSP method suitable for response properties. Equations are derived using an automated approach and have subsequently been hand-coded into the computer program KOALA, in which for all two-electron integrals, density fitting is employed. Numerical results are presented for the lowest two vertical singlet excitation energies of a set of selected molecules. The results show that the CC2(F12*)-XSP method provides the correct basis-set limit with no bias to the ground state, and an excellent agreement with reference CC2 values using large basis sets is found. Using Dunning's aug-cc-pVTZ basis, the CC2(F12*)-XSP method yields excitation energies which are converged within 1 mEh to the basis-set limit for valence excitations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]