The GW/BSE Method in Magnetic Fields

The GW approximation and the Bethe–Salpeter equation have been implemented into the Turbomole program package for computations of molecular systems in a strong, finite magnetic field. Complex-valued London orbitals are used as basis functions to ensure gauge-invariant computational results. The implementation has been benchmarked against triplet excitation energies of 36 small to medium-sized molecules against reference values obtained at the approximate coupled-cluster level (CC2 approximation). Finally, a spectacular change of colour from orange to green of the tetracene molecule is induced by applying magnetic fields between 0 and 9,000 T perpendicular to the molecular plane

Robust relativistic many-body Green’s function based approaches for assessing core ionized and excited states

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

Reaching strong absorption up to 700 nm with new benzo[ g ]quinoxaline-based heteroleptic copper( i ) complexes for light-harvesting applications

Heteroleptic copper(I) complexes, with a diimine as a chromophoric unit and a bulky diphosphine as an ancillary ligand, have the advantage of a reduced pseudo Jahn–Teller effect in their excited state over the corresponding homoleptic bis(diimine) complexes. Nevertheless, their lowest absorption lies generally between 350 to 500 nm. Aiming at a strong absorption in the visible by stable heteroleptic Cu(I) complexes, we designed a novel diimine based on 4-(benzo[g]quinoxal-2′-yl)-1,2,3-triazole derivatives. The large π-conjugation of the benzoquinoxaline moiety shifted bathochromically the absorption with regard to other diimine-based Cu(I) complexes. Adding another Cu(I) core broadened the absorption and extended it to considerably longer wavelengths. Moreover, by fine-tuning the structure of the dichelating ligand, we achieved a panchromatic absorption up to 700 nm with a high molar extinction coefficient of 8000 M$^{-1}$ cm$^{-1}$ at maximum (λ = 570 nm), making this compound attractive for light-harvesting antennae

Computation of Electromagnetic Properties of Molecular Ensembles

We outline a methodology for efficiently computing the electromagnetic response of molecular ensembles. The methodology is based on the link that we establish between quantum‐chemical simulations and the transfer matrix (T‐matrix) approach, a common tool in physics and engineering. We exemplify and analyze the accuracy of the methodology by using the time‐dependent Hartree‐Fock theory simulation data of a single chiral molecule to compute the T‐matrix of a cross‐like arrangement of four copies of the molecule, and then computing the circular dichroism of the cross. The results are in very good agreement with full quantum‐mechanical calculations on the cross. Importantly, the choice of computing circular dichroism is arbitrary: Any kind of electromagnetic response of an object can be computed from its T‐matrix. We also show, by means of another example, how the methodology can be used to predict experimental measurements on a molecular material of macroscopic dimensions. This is possible because, once the T‐matrices of the individual components of an ensemble are known, the electromagnetic response of the ensemble can be efficiently computed. This holds for arbitrary arrangements of a large number of molecules, as well as for periodic or aperiodic molecular arrays. We identify areas of research for further improving the accuracy of the method, as well as new fundamental and technological research avenues based on the use of the T‐matrices of molecules and molecular ensembles for quantifying their degrees of symmetry breaking. We provide T‐matrix‐based formulas for computing traditional chiro‐optical properties like (oriented) circular dichroism, and also for quantifying electromagnetic duality and electromagnetic chirality. The formulas are valid for light‐matter interactions of arbitrarily‐high multipolar orders

Systematic investigation of the influence of electronic substituents on dinuclear gold( i ) amidinates: synthesis, characterisation and photoluminescence studies

Dinuclear gold(I) compounds are of great interest due to their aurophilic interactions that influence their photophysical properties. Herein, we showcase that gold–gold interactions can be influenced by tuning the electronic properties of the ligands. Therefore, various para substituted (R) N,N′-bis(2,6-dimethylphenyl)formamidinate ligands (pRXylForm; Xyl = 2,6-dimethylphenyl and Form = formamidinate) were treated with Au(tht)Cl (tht = tetrahydrothiophene) to give via salt metathesis the corresponding gold(I) compounds [pRXylForm$_2$Au$_2$] (R = –OMe, –Me, –Ph, –H, –SMe, and –CO$_2$Me). All complexes showed intense luminescence properties at low temperatures. Alignment with the Hammett parameter σ$_p$ revealed the trends in the $^1$H and $^{13}$C NMR spectra. These results showed the influence of the donor–acceptor abilities of different substituents on the ligand system which were confirmed with calculated orbital energies. Photophysical investigations showed their lifetimes in the millisecond range indicating phosphorescence processes and revealed a redshift with the decreasing donor ability of the substituents in the solid state

Synthesis of New Donor‐Substituted Biphenyls: Pre‐ligands for Highly Luminescent (C^C^D) Gold(III) Pincer Complexes

We herein report on new synthetic strategies for the preparation of pyridine and imidazole substituted 2,2’‐dihalo biphenyls. These structures are pre‐ligands suitable for the preparation of respective stannoles. The latter can successfully be transmetalated to K[AuCl$_{4}$] forming non‐palindromic [(C^C^D)Au$^{III}$] pincer complexes featuring a lateral pyridine (D=N) or N‐heterocyclic carbene (NHC, D=C’) donor. The latter is the first report on a pincer complex with two formally anionic sp$^{2}$ and one carbenic carbon donor. The [(C^C^D)Au$^{III}$] complexes show intense phosphorescence in solution at room temperature. We discuss the developed multistep strategy and touch upon synthetic challenges. The prepared complexes have been fully characterized including X‐ray diffraction analysis. The gold(III) complexes’ photophysical properties have been investigated by absorption and emission spectroscopy as well as quantum chemical calculations on the quasi‐relativistic two‐component TD‐DFT and GW/Bethe–Salpeter level including spin–orbit coupling. Thus, we shed light on the electronic influence of the non‐palindromic pincer ligand and reveal non‐radiative relaxation pathways of the different ligands employed

Cooperativity in luminescent heterobimetallic diphosphine-β-diketiminate complexes

The bis(phosphine)-functionalized β-diketiminate ligand [HC{(CH$_3$)C}$_2${(o-[P(C$_6$H$_5$)$_2$]$_2$C$_6$H$_4$)N}$_2$]$^−$(PNac) was used for the synthesis of luminescent closed-shell bimetallic complexes. The PNNP pocket combining both soft and hard donor sites can act as an orthogonal ligand scaffold to selectively coordinate two different metal ions. Deprotonation and subsequent salt elimination with [AuCl(tht)] (tht = tetrahydrothiophene) or AgI yielded the mononuclear complexes [PNacAu] (1) or [PNacAg] (2), respectively. The AuI ion is linearly coordinated by the two phosphines, forming a 12-membered metalla-macrocycle with an empty β-diketiminate pocket available for complexation of hard d$^{10}$ metal ions (Zn$^{II}$, Cd$^{II}$, and Hg$^{II}$). According to this synthetic protocol, a series of heterobimetallic complexes were isolated. The complexation of the second metal ion in close spatial proximity has led to drastic changes in the photophysical properties. For further studies and understanding, quantum chemical calculations were performed

GW quasiparticle energies of atoms in strong magnetic fields

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 ℏe −1 a −2 0 ≈58 763 0.25 B0=0.25 ℏe−1a0−2≈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