DataSheet1_The GW/BSE Method in Magnetic Fields.zip

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.</p

Accuracy Assessment of <i>GW</i> Starting Points for Calculating Molecular Excitation Energies Using the Bethe–Salpeter Formalism

The performance of the Bethe–Salpeter equation (BSE) approach for the first-principles computation of singlet and triplet excitation energies of small organic, closed-shell molecules has been assessed with respect to the quasiparticle energies used on input, obtained at various levels of <i>GW</i> theory. In the corresponding <i>GW</i> computations, quasiparticle energies have been computed for <i>all</i> orbital levels by means of using full spectral functions. The assessment reveals that, for valence excited states, quasiparticle energies obtained at the levels of eigenvalue-only self-consistent (ev<i>GW</i>) or quasiparticle self-consistent theory (qs<i>GW</i>) are required to obtain results of comparable accuracy as in time-dependent density-functional theory (TDDFT) using a hybrid functional such as PBE0. In contrast to TDDFT, however, the BSE approach performs well not only for valence excited states but also for excited states with Rydberg or charge-transfer character. To demonstrate the applicability of the BSE approach, computation times are reported for a set of aromatic hydrocarbons. Furthermore, examples of computations of ordinary photoabsorption and electronic circular dichroism spectra are presented for (C₆₀)₂ and C₈₄, respectively

Efficient Calculation of Magnetic Circular Dichroism Spectra Using Spin-Noncollinear Linear-Response Time-Dependent Density Functional Theory in Finite Magnetic Fields

Excited-state calculations in finite magnetic fields are presented in the framework of spin-noncollinear linear-response time-dependent density functional theory. To ensure gauge-origin invariance, London atomic orbitals are employed throughout. An efficient implementation into the Turbomole package, which also includes the resolution of the identity approximation, allows for the investigation of excited states of large molecular systems. The implementation is used to investigate the magnetic circular dichroism spectra of sizable organometallic molecules such as a zinc tetraazaporphyrin with two fused naphthalene units, which is a molecule with 57 atoms

Approaching Phosphorescence Lifetimes in Solution: The Two-Component Polarizable-Embedding Approximate Coupled-Cluster Method

Theoretical description of phosphorescence lifetimes in the condensed phase requires a method that takes into account both spin–orbit coupling and solvent–solute interactions. To obtain such a method, we have coupled our recently developed two-component coupled-cluster method with singles and approximated doubles to a polarizable environment. With this new method, we investigate how different solvents effect the electronic phosphorescence energies and lifetimes of 4<i>H</i>-pyran-4-thione

Efficient Calculation of Magnetic Circular Dichroism Spectra Using Spin-Noncollinear Linear-Response Time-Dependent Density Functional Theory in Finite Magnetic Fields

Excited-state calculations in finite magnetic fields are presented in the framework of spin-noncollinear linear-response time-dependent density functional theory. To ensure gauge-origin invariance, London atomic orbitals are employed throughout. An efficient implementation into the Turbomole package, which also includes the resolution of the identity approximation, allows for the investigation of excited states of large molecular systems. The implementation is used to investigate the magnetic circular dichroism spectra of sizable organometallic molecules such as a zinc tetraazaporphyrin with two fused naphthalene units, which is a molecule with 57 atoms

Non-covalent Interactions of CO₂ with Functional Groups of Metal–Organic Frameworks from a CCSD(T) Scheme Applicable to Large Systems

The strength of interactions between CO₂ and 23 building blocks of metal–organic frameworks are reported in this paper. This theoretical study is based on an incremental, explicitly correlated coupled-cluster scheme with interference effects. This scheme allows the accurate calculation of molecular complexes such as zinc acetate (32 non-hydrogen atoms) at the CCSD­(T) level, close to the basis set limit. Higher CO₂ affinity for complexes with nitrogen-containing heterocycles is predicted from the calculated interaction energies. The good agreement between the interaction energies obtained from the CCSD­(T) scheme and DFT-D3 is discussed

Explicitly Correlated Dispersion and Exchange Dispersion Energies in Symmetry-Adapted Perturbation Theory

The individual interaction energy terms in symmetry-adapted perturbation theory (SAPT) not only have different physical interpretations but also converge to their complete basis set (CBS) limit values at quite different rates. Dispersion energy is notoriously the slowest converging interaction energy contribution, and exchange dispersion energy, while smaller in absolute value, converges just as poorly in relative terms. To speed up the basis set convergence of the lowest-order SAPT dispersion and exchange dispersion energies, we borrow the techniques from explicitly correlated (F12) electronic structure theory and develop practical expressions for the closed-shell Edisp(20)-F12 and Eexch–disp(20)-F12 contributions. While the latter term has been derived and implemented for the first time, the former correction was recently proposed by Przybytek [J. Chem. Theory Comput. 2018, 14, 5105−5117] using an Ansatz with a full optimization of the explicitly correlated amplitudes. In addition to reimplementing the fully optimized variant of Edisp(20)-F12, we propose three approximate Ansätze that substantially improve the scaling of the method and at the same time avoid the numerical instabilities of the unrestricted optimization. The performance of all four resulting flavors of Edisp(20)-F12 and Eexch–disp(20)-F12 is first tested on helium, neon, argon, water, and methane dimers, with orbital and auxiliary basis sets up to aug-cc-pV5Z and aug-cc-pV5Z-RI, respectively. The double- and triple-ζ basis set calculations are then extended to the entire A24 database of noncovalent interaction energies and compared with CBS estimates for Edisp(20) and Eexch–disp(20) computed using conventional SAPT with basis sets up to aug-cc-pV6Z with midbond functions. It is shown that the F12 treatment is highly successful in improving the basis set convergence of the SAPT terms, with the F12 calculations in an X-tuple ζ basis about as accurate as conventional calculations in bases with cardinal numbers (X + 2) for Edisp(20) and either (X + 1) or (X + 2) for Eexch–disp(20). While the full amplitude optimization affords the highest accuracy for both corrections, the much simpler and numerically stable optimized diagonal Ansatz is a very close second. We have also tested the performance of the simple F12 correction based on the second-order Møller–Plesset perturbation theory, SAPT-F12­(MP2) [Frey, J. A.; Chem. Rev. 2016, 116, 5614−5641] and observed that it is also quite successful in speeding up the basis set convergence of conventional Edisp(20) + Eexch–disp(20), albeit with some outliers

Basis Set Limit Coupled Cluster Study of H-Bonded Systems and Assessment of More Approximate Methods

Hydrogen bonds are of utmost importance in both chemistry and biology. As the applicability of density functional theory and ab initio methods extends to ever larger systems and to liquids, an accurate description of such interactions is desirable. However, reference data are often lacking, and ab initio calculations are only possible and done in very small basis sets. Here, we present high level [CCSD(T)] ab initio reference calculations at the basis set limit on a large set of hydrogen-bonded systems and assess the accuracy of second-order perturbation theory (MP2). The possibilities of using basis set extrapolations for geometries and dissociation energies are discussed as well as the results of R12 methods and density functional and local correlation methods

Global Analytical Potential Energy Surface for Large Amplitude Nuclear Motions in Ammonia^†

An analytical, full-dimensional, and global representation of the potential energy surface of NH3 in the lowest adiabatic electronic state is developed, and parameters are determined by adjustment to ab initio data and thermochemical data for several low-lying dissociation channels. The electronic structure is calculated at the CASPT2 level within an [8,7] active space. The representation is compared to other recently published potential energy surfaces for this molecule. The present representation is distinguished by giving a qualitatively correct description of the potential energy for very large amplitude displacements of the nuclei from equilibrium. Other characteristic features of the present surface are the equilibrium geometries req(NH3) ≈ 101.24 pm, req(NH2) ≈ 102.60 pm, αeq(NH3) ≈ 106.67°, and the inversion barrier at rinv(NH3) ≈ 99.80 pm and 1781 cm-1 above the NH3 minimum. The barrier to linearity in NH2 is 11 914 cm-1 above the NH2(2B1) minimum. While the quartic force field for NH3 from the present representation is significantly different from that of the other potential energy surfaces, the vibrational structures obtained from perturbation theory are quite similar for all representations studied here

Tuning the Gap: Electronic Properties and Radical-Type Reactivities of Heteronuclear [1.1.1]Propellanes of Heavier Group 14 Elements

Two heteronuclear [1.1.1]propellanes of group 14, Ge2Si3Mes6 (1) and Sn2Si3Mes6 (2) (Mes = 2,4,6-Me3C6H2), were prepared by reductive coupling of Mes2SiCl2 and GeCl2·dioxane or SnCl2. Both compounds were characterized in detail, including X-ray structure analyses on single crystals. In each case it was found that the E2Si3 cluster core consists of three bridging {SiMes2} units and two ligand-free bridgehead atoms (Eb). As a result of the different size of the bridging units, the distances between the bridgehead atoms are considerably shorter (0.10 Å for 1 and 0.27 Å for 2) than in the homonuclear counterparts Ge5Mes6 and Sn5Dep6 (Dep = 2,6-Et2C6H3) known from the literature. The stronger Eb···Eb interactions in 1 and 2 were confirmed by electrochemical studies using cyclic voltammetry. UV/vis studies, together with density functional theory (DFT) calculations, further supported these findings. A correlation of the Eb···Eb distances and the singlet and triplet A2 transitions for a series of homo- and heteronuclear [1.1.1]propellanes revealed that higher 3A2 excitation wavelengths, and thus lower ΔES→T energies, are obtained either by increasing the distances between the bridgehead atoms or by arranging the involved orbitals in close spatial proximity. Reactivity studies on 1 and 2 using selected reagents showed that Me3SnH or the disulfide FcS−SFc (Fc = ferrocenyl), which are prone to radical-type reactivity, can be readily added across the bridge (the tin hydride reacts only with 1). The resulting 1,3-disubstituted bicyclo[1.1.1]pentane derivatives Me3Sn−Ge(SiMes2)3Ge−H (3) and FcS−E(SiMes2)3E−SFc (4 (E = Ge) and 5 (E = Sn)) were characterized in detail, including X-ray structures of 4 and 5. Interestingly, the homolytic S−S bond addition reactions were found to be susceptible to light. Even though the tin-containing propellane 2 turned out to be more reactive than 1, both conversions can be drastically enhanced simply by using daylight in the lab