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4,4 ′ -bis(carbazol-9-yl)biphenyl (CBP) is a commonly used hole-transport host material in phosphorescent organic light-emitting devices (PhOLEDs). Despite its widespread use, device degradation is observed that most likely involves excited states and ionic species. The present work aims at providing a first step towards a detailed CBP characterisation by computing excited-state properties and ionised species of CBP using time-dependent density functional theory (TD-DFT) and the Bethe-Salpeter equation (BSE) based on the GW method. The investigation reveals a strong dependence of the absorption spectrum on the interactions of the phenyl and carbazole units, which is computed for 1.6 k ground-state rotamers using the efficient GW-BSE method. A similar approach using a set of 1.6 k excited-state rotamers shows a significantly smaller dependence on fragment orientation for emission. In order to model ensembles of gas-phase CBP molecules, spectra are simulated employing a Boltzmann distribution for different temperatures based on the relative ground-state energies of the rotamers. This approach reveals that certain absorption bands experience almost no change in the ensemble picture while others vanish, which can be understood in terms of the geometry-dependence of the excited states due to the phenyl-carbazole interactions. [ABSTRACT FROM AUTHOR]

From the 30th of June until the 5th of July 2019, the 9th Molecular Quantum Mechanics conference (MQM 2019) took place in the 'Kongresshaus Stadthalle' in Heidelberg, Germany. The conference had been organised to celebrate the 'German School' of quantum chemistry by honouring four quantum chemists that had pioneered the field in Germany. In particular, the 9th MQM conference was held to the memory of Reinhart Ahlrichs and in honour of Werner Kutzelnigg, Wilfried Meyer, and Sigrid Peyerimhoff. The authors of this article are very thankful to have had the opportunity to chair the historical session, respectively, to deliver the laudation for Werner Kutzelnigg. In what follows, we would like to give a few biographical notes on the life of Werner, say a few words about his personality, and highlight his most important and pioneering contributions to the field of quantum chemistry. [ABSTRACT FROM AUTHOR]

The nonperturbative calculation of molecular properties in magnetic fields requires the evaluation of integrals over complex-valued Gaussian-type London atomic orbitals (LAOs). With these orbitals, the calculation of four-centre electron-repulsion integrals (ERIs) is particularly demanding, because their permutational symmetry is lowered, and because complex algebra is required. We have implemented the resolution-of-the-identity (RI) approximation for LAOs in the TURBOMOLE program package. With respect to LAOs, employing the RI approximation is particularly beneficial, because the auxiliary basis set may always be chosen to be real-valued. As a consequence, the two-centre integrals in the RI approximation remain real-valued, and the three-centre integrals possess the same permutational symmetry as their real-valued counterparts. Compared to a direct calculation of four-centre ERIs over LAOs, using the RI approximation thus not only reduces the scaling of the integral evaluation, but also increases the efficiency by an additional factor of at least two. By using other well-established methods such as Cauchy–Schwarz screening, the difference-density approach, and Pulay's direct inversion in the iterative subspace (DIIS), the efficiency of nonperturbative calculations in magnetic fields can be increased even further. [ABSTRACT FROM AUTHOR]

A damped-response formalism in the GW approximation to the Bethe–Salpeter equation (BSE) is presented and implemented. It is based on a quasirelativistic two-component (2c) approach that includes scalar-relativistic and spin–orbit effects derived from the one-electron Dirac equation. A generalised solver, which also allows to calculate static, dynamic and damped-response polarisabilites, is discussed in detail. Throughout our implementation, the resolution-of-the-identity approximation is employed to reduce the computational effort. The performance of 2c GW-BSE is benchmarked against experimental and high-level ab initio data and compared to standard density-functional theory approaches, including modern local hybrid functionals for which a proper non-collinear kernel for Kramers-restricted systems is reported. [ABSTRACT FROM AUTHOR]

A method for computing quasi-relativistic two-component dispersion energies is developed and implemented in the TURBOMOLE program package. The method is based on the Casimir–Polder formula for dispersion energies, which occurs in symmetry-adapted perturbation theory. The method is applied to evaluate the dispersion energies of a small set of van der Waals complexes involving heavy elements such as gold, mercury and bismuth. [ABSTRACT FROM PUBLISHER]

The vertical ionisation energies of the molecules of the GW27 (27 molecules) and GW100 (100 molecules) test sets are computed in a polarised triple-zeta-valence basis set in the framework of coupled-cluster theory with single, double, and non-iterative triple substitutions. The molecular geometries were kept fixed to those of the two test sets. To demonstrate the usefulness of the coupled-cluster reference values, they are compared with quasi-particle energies obtained in the G0W0approximation for functionals commonly used in Kohn–Sham density-functional theory (DFT). Furthermore, an approximation is assessed, in which only exchange contributions are added to the DFT orbital energies. [ABSTRACT FROM PUBLISHER]

A systematic way to construct compact complementary auxiliary basis sets (ABSs) from and for atomic natural orbital basis sets for the use as resolution-of-the-identity sets in explicitly correlated F12 calculations is presented. The performance of these newly constructed ABSs has been benchmarked in explicitly correlated calculations of absolute energies, ionisation potentials and electron affinities. [ABSTRACT FROM PUBLISHER]

Non-covalent interactions can usually be described accurately at the coupled-cluster level of theory using single, double and triple excitations, the latter within a perturbation-theory framework. However, since the computations with the corresponding coupled-cluster model, CCSD(T), are computationally very demanding, they can often not be carried out in large enough basis sets. This leads to a basis-set truncation error. To correct this error, a basis-set correction can be computed at the level of second-order Møller–Plesset (MP2) perturbation theory in the limit of a complete basis set, but such a correction tends to overestimate the magnitude of the basis-set truncation error. In the present work, we suggest to damp the basis-set correction obtained at the complete-basis-set MP2 level using interference factors for individual occupied orbital pairs. The approach is applied to the non-covalent interactions of the S22B database, where the interference correction turns out to be very small. [ABSTRACT FROM AUTHOR]

We present a new method for the evaluation of four-centre electron-repulsion integrals that combines density fitting (DF) with numerical integration by quadrature (QD). In this composite DF-QD approach, the orbital product density is fitted by a truncated spectral set of auxiliary functions and the fitting residual is expanded in a discrete space of functions localised at the eigenvalues of the coordinate operator. The new DF-QD approach has the advantage of DF of reducing computational effort and storage requirements of conventional quantum chemical algorithms, and allows for high accuracy and error control by means of QD. Systematic improvement of the accuracy is achieved for a chosen DF basis set by enlarging the number of grid points used for QD. Test calculations on a set of small molecules reveal that errors in absolute energy of the DF-QD approximation with less than 1000 and 3000 grid points per atom do not exceed one milli- and one microhartree, respectively, even if standard (non-optimised) AO basis sets are used for DF. [ABSTRACT FROM AUTHOR]

Data intense processes such as the establishment of quantitative structure–property relationships, the design of novel compounds and also the validation of new quantum chemical methods call for a structured approach for the processing of the results. Whereas in quantum chemistry there are established de facto standards for the computational methods, community standards for [exchange-] data formats are still under development. In this article we present a benchmark study of the (auxiliary-) basis set dependence of the binding energies of an array of conformers of the ethene dimer using the RI-MP2-F12 method. The study was performed using a version of the TURBOMOLE program package modified to provide output in an extended CML format to be imported in an eXist database. This infrastructure for the generation, archival, analysis, and exchange of quantum chemical data is briefly introduced in this article. [ABSTRACT FROM AUTHOR]

The analytical computation of nuclear gradients has been derived and implemented for the explicitly correlated second-order Møller-Plesset method (MP2-F12). The implementation has been accomplished in the TURBOMOLE program package for ansatz MP2-F12/2*A. A Slater-type geminal expanded in six Gaussian geminals (STG-6G), a complementary auxiliary basis set (CABS), and robust density fitting approximations are used. In addition, a second-order perturbation theory correction for single excitations into the complementary auxiliary basis set (CABS singles) is included to reduce the Hartree-Fock error. Smooth convergence towards the basis set limit is observed for a selection of molecules. For computations on dimers of weakly interacting molecules in small basis sets, explicitly correlated second-order Møller-Plesset theory outperforms conventional second-order Møller-Plesset theory because basis set superposition errors are largely avoided at the MP2-F12/2*A level. [ABSTRACT FROM AUTHOR]

In calculations on open-shell systems, spin-flipped geminals must be used in explicitly correlated F12 methods with spin-unrestricted or restricted open-shell Hartree-Fock reference wave functions. We suggest the use of the sp ansatz of Bokhan et al. [J. Chem. Phys. 131, 084105 (2009)] for calculations with fixed F12 amplitudes, but to use a novel contracted geminal approach if the F12 amplitudes are to be optimised. This new approach is denoted MP2-F12-o (CCSD(F12)-o). The performance of the new approach is assessed by calculating the atomisation energies of a test set comprising 106 molecules containing the atoms H, C, N, O and F, and by calculating the ionisation energies and electron affinities of the atoms C, N, O and F. [ABSTRACT FROM AUTHOR]

One-electron basis sets for F12 explicitly-correlated molecular electronic-structure methods are assessed by analysing the accuracy of Hartree-Fock energies and valence-only second-order correlation energies of a test set of 106 small molecules containing the atoms H, C, N, O and F. For these molecules, near Hartree-Fock-limit energies and benchmark second-order correlation energies (accurate to within 99.95% of the basis-set limit) are provided. Absolute energies are analysed as well as the Hartree-Fock and second-order correlation contributions to the atomisation energies of the molecules. Standard basis sets such as the Karlsruhe def2-TZVPP and def2-QZVPP sets and the augmented correlation-consistent polarised valence X-tuple zeta (aug-cc-p VXZ, X = D, T, Q, 5) sets are compared with the specialised cc-pVXZ-F12 (X = D, T, Q) sets that were recently optimised by Peterson and co-workers [J. Chem. Phys. 128, 084102 (2008)] for use in F12 theory. The results obtained from F12 explicitly-correlated molecular electronic-structure calculations are compared with those that are obtained by standard electronic-structure calculations followed by basis-set extrapolation based on the X-3 convergence behaviour of the aug-cc-pVXZ basis sets. The most important conclusions are that the cc-pVXZ-F12 sets are the preferred basis sets for F12 theory and that the X-3 extrapolation from the aug-cc-pVQZ and aug-cc-pV5Z is slightly more accurate than F12 theory in the cc-pVTZ-F12 basis but less accurate than F12 theory in the cc-pVQZ-F12 basis. [ABSTRACT FROM AUTHOR]

We review the current status of quantum chemistry as a predictive tool of chemistry and molecular physics, capable of providing highly accurate, quantitative data about molecular systems. We begin by reviewing wave-function based electronic-structure theory, emphasizing the N-electron hierarchy of coupled-cluster theory and the one-electron hierarchy of correlation-consistent basis sets. Following a discussion of the slow basis-set convergence of dynamical correlation and basis-set extrapolations, we consider the methods of explicit correlation, from the early work of Hylleraas in the 1920s to the latest developments in such methods, capable of yielding high-accuracy results in medium-sized basis sets. Next, we consider the small corrections to the electronic energy (high-order virtual excitations, vibrational, relativistic, and diagonal Born-Oppenheimer corrections) needed for high accuracy and conclude with a review of the composite methods and computational protocols of electronic-structure theory. [ABSTRACT FROM AUTHOR]

The past few years have seen a particularly rich period in the development of the explicitly correlated R12 theories of electron correlation. These theories bypass the slow convergence of conventional methods, by augmenting the traditional orbital expansions with a small number of terms that depend explicitly on the interelectronic distance r 12 . Amongst the very numerous discoveries and developments that we will review here, two stand out as being of particular interest. First, the fundamental numerical approximations of the R12 methods withstand the closest scrutiny: Kutzelnigg's use of the resolution of the identity and the generalized Brillouin condition to avoid many-electronic integrals remains sound. Second, it transpires that great gains in accuracy can be made by changing the dependence on the interelectronic coordinate from linear ( r 12 ) to some suitably chosen short-range form (e.g., exp(-α r 12 )). Modern R12 (or F12) methods can deliver MP2 energies (and beyond) that are converged to chemical accuracy (1  kcal/mol) in triple- or even double-zeta basis sets. Using a range of approximations, applications to large molecules become possible. Here, the major developments in the field are reviewed, and recommendations for future directions are presented. By comparing with commonly used extrapolation techniques, it is shown that modern R12 methods can deliver high accuracy dramatically faster than by using conventional methods. [ABSTRACT FROM AUTHOR]

The very good performance of modern density functional theory for molecular geometries and harmonic vibrational frequencies has been well established. We investigate the performance of density functional theory (DFT) for quartic force fields, vibrational anharmonicity and rotation–vibration coupling constants, and thermodynamic functions beyond the RRHO (rigid rotor–harmonic oscillator) approximation of a number of small polyatomic molecules. Convergence in terms of basis set, integration grid and the numerical step size for determining the quartic force field by using central differences of analytical second derivatives has been investigated, as well as the performance of various exchange-correlation functionals. DFT is found to offer a cost-effective approach with manageable scalability for obtaining anharmonic molecular properties, and particularly as a source for anharmonic zero-point and thermal corrections for use in conjunction with benchmark ab initio thermochemistry methods. [ABSTRACT FROM AUTHOR]

The second-order Møller-Plesset (MP2) correlation energies of the valence shells of C 2 H 4 and C 2 H 6 (with fixed nuclear coordinates) were computed as accurately as technically feasible. The pair energies for singlet and triplet pairs are reported for localized molecular orbitals. An accuracy of the order of 0.01m E h is achieved for all of the individual pair energies. The best estimates of the total valence-shell MP2 correlation energies of C 2 H 4 and C 2 H 6 in the chosen geometries are -373.6±0. and -410.0±0.1m E h , respectively. In the aug-cc-pVQZ, aug-cc-pV5Z and aug-cc-pV6Z basis sets, 96.2, 98.0 and 98.8% of the these values are recovered, respectively. The percentages are improved to 99.8% by means of spin-adapted two-point extrapolations from the aug-cc-pVQZ and aug-cc-pV5Z results. An extrapolation based on the aug-cc-pV5Z and aug-cc-pV6Z correlation energies yields 99.9%. [ABSTRACT FROM AUTHOR]

Relativistic energy corrections which arise from the use of the Dirac-Coulomb Hamiltonian, and the Gaunt and Breit interaction operators, plus Lamb-shift effects have been determined for the global minima of the ground electronic states of C[sub 2]H[sub 6], NH[sub 3], H[sub 2]O, [H,C,N], HNCO, HCOOH, SiC[sub 2], SiH[sub 3][sup -], and H[sub 2]S, and for barrier characteristics for these molecular systems (inversion barrier of NH[sub 3] and SiH[sub 3][sup -], barrier to linearity of H[sub 2]O, H[sub 2]S, and HNCO, rotational barrier of C[sub 2]H[sub 6], difference between conformations of HCOOH (Z/E) and SiC[sub 2] (linear/T-shaped), and isomerization barrier of HCN/HNC). The relativistic calculations performed at the Hartree-Fock and the highly correlated CCSD(T) levels employed a wide variety of basis sets. Comparison of the perturbational and the four-component fully variational results indicate that the Coulomb-Pauli Hamiltonian and the lowest order Hamiltonian of direct perturbation theory (DPT(2)) are highly successful for treating the relativistic energy effects in light molecular systems both at a single point on the potential energy hypersurface and along the surface. Electron correlation contributions to the relativistic corrections are relatively small for the systems studied, and are comparable with the 2-electron Darwin correction. Corrections beyond the Dirac-Coulomb treatment are usually rather small, but may become important for high accuracy ab initio calculations. [ABSTRACT FROM AUTHOR]

Coupled-cluster singles and doubles (CCSD) valence shell correlation energies of the systems CH[sub 2] ([sup 1]A[sub 1] state), H[sub 2]O, HF, N[sub 2], CO, Ne, and F[sub 2] are computed by means of standard calculations with correlation-consistent basis sets of the type cc-pV x Z (x = D, T, Q, 5, 6) and by means of explicitly correlated coupled-cluster calculations (CCSD-R12/B) with large uncontracted basis sets of the type 19s14p8d6f4g3h for C, N, O, F, and Ne and 9s6p4d3f for H. These CCSD-R12/B calculations provide reference values for the basis set limit of CCSD theory. The computed correlation energies are decomposed into singlet and triplet pair energies. It is established that the singlet pair energies converge as X[sup -3] and the triplet pair energies as X[sup -5] with the cardinal number of the correlation-consistent basis sets, and an extrapolation technique is proposed that takes into account their different convergence behaviour. Applied to the cc-pV5Z and cc-pV6Z results, this new extrapolation yields pair energies with a mean absolute deviation of 0.02 m E [sub h] from the CCSD-R12/B reference values. For the seven systems under study, the extrapolated total valence shell correlation energies agree to within 0.2 m E[sub h] with the CCSD-R12/B benchmark data. [ABSTRACT FROM AUTHOR]

A new global, ground-state, Born-Oppenheimer surface is presented for the H[sup +] [sub 3] system. The energy switching approach has been used to combine different functional forms for three different regimes: a spectroscopic expansion at low energy, a Sorbie-Murrell function at high energy and known long-range terms combined with accurate diatomic potentials at large separations. At low energies we have used the ultra high accuracy ab initio data of Cencek et al. (1998, J. chem. Phys., 108, 2831). At intermediate energy we have calculated 134 new ab initio energies using a high accuracy, explicitly correlated procedure. The ab initio data of Schinke et al. (1980, J. chem. Phys., 72, 3909) has been used to constrain the high energy region. Two fits are presented which differ somewhat in their behaviour at energies over 45000cm[sup -1] above the H[sup +] [sub 3] minimum. Below this energy, the fits reproduce each set of ab initio data close to their intrinsic accuracy. The ground state surface should provide a suitable starting point for renewed studies of the near-threshold photodissociation spectrum originally reported by Carrington et al. (1982, Molec. Phys., 45, 753). [ABSTRACT FROM AUTHOR]

The basis set convergence of ab initio computed electronic dissociation energies is reported for the hydrogen bonded complexes (HF)2(H2O)2. At the level of CCSD(T) theory (coupled cluster model with singles, doubles, and approximate connected triples), the interaction energy is split into one- and two-body terms, and corrections such as the counterpoise (CP) and the MP2 limit are explored. The MP2-limit correction consists of substituting the second-order Moller-Plesset (MP2) perturbation theory contribution computed with the actual basis set by the limiting value that is obtained in a complete basis. Clearly the basis set convergence of the CCSD(T) calculations is improved by the MP2 limit correction. Moreover, the MP2-limit correction can be applied irrespective of whether or not the two-body term has been CP corrected beforehand. Little difference is found between the two possibilities, but the most accurate results are obtained by applying the MP2 limit correction to CP corrected CCSD(T) two-body terms. Best estimates of De = 19.1(2)kJ mol-1 for (HF)2 and 21.1(3)kJ mol-1 for (H2O) are inferred. [ABSTRACT FROM AUTHOR]

The ab initio calculation of molecular geometrical properties in the Hellmann-Feynman approximation is discussed in which the atomic orbitals are fixed at the positions of the nuclei at the reference geometry, thereby avoiding the calculation of derivatives of the molecular integrals with respect to the positions of the atomic orbitals. For the molecular gradient, the molecular Hessian, and the molecular dipole gradient, the convergence of the calculated properties is studied for a large number of basis sets at the Hartree-Fock level and at the CCSD(T)-R12 level. In the Hellmann-Feynman approximation, it is found to be necessary to impose explicitly rotational and translational invariance. Although small basis sets perform poorly in the Hellmann-Feynman approximation (compared with the standard approach where the atomic orbitals are moving with the displaced nuclei), satisfactory convergence is obtained for geometries and harmonic frequencies (to within 1% of the standard approximation) with the larger of the correlation-consistent core-valence cc-pCVXZ basis sets. For the infrared intensities, the agreement with the standard approach is still poor (only within 15% for the largest correlation-consistent basis). The best results are obtained with an R12 basis previously developed for the calculation of energies in the explicitly correlated R12 approximation. In this basis, the geometrical parameters and harmonic frequencies are within 0.5% of the standard approach and the infrared intensities within 5% , suggesting that the Hellmann-Feynman approximation may be useful for applications at the highly accurate MP2-R12, CCSD-R12, and CCSD(T)-R12 levels of theory. [ABSTRACT FROM AUTHOR]

The electronic dissociation energies and barriers to concerted hydrogen exchange of (HF)n oligomers with n = 2 ,...,5 are computed by means of a many-body decomposition of the total electronic energy. The one- and two-body terms are obtained from explicitly correlated coupled cluster calculations including singles, doubles, and a perturbative triples correction (CCSD(T)-R12), in a large Gaussian basis set consisting of 276 contracted atomic functions. The three-body term is computed at the conventional CCSD(T) level in a basis set containing 228 functions. The four- and five-body terms are obtained from explicitly correlated secondorder perturbation theory calculations (MP2-R12), using basis sets with 305 (tetramer) and 380 (pentamer) functions. Since the many-body terms are computed using the same basis set (i.e. the basis of the largest fragment) for all fragments and subfragments, our calculations implicitly include a counterpoise correction. The results of the calculations are compared with semi-empirical one-, two-, and three-body potentials, and new best estimates of the electronic dissociation energies and barriers are inferred. For (HF)2, (HF)3, (HF)4, and (HF)5, respectively, we obtain for the electronic dissociation energies into monomers 19.1(2), 64(2), 116(3) and 158(4)kJmol-1, and for the electronic barriers to concerted hydrogen exchange 175(10), 85(10), 60(10) and 65(10)kJmol 1. The results are shown to be consistent with NMR line broadening data within the framework of transition state theory. [ABSTRACT FROM AUTHOR]

In 1987, Seiler et al. (1987, Angew. Chem. Int. Edn Engl., 26, 1175) reported the observation of an eclipsed Csp3-CH3 bond in the low-temperature X-ray analysis of a crystalline trihydrate tricyclic orthoamide. This contrasts with the observed staggered conformation in an anhydrous crystal of the tricyclic orthoamide. Modest quantum chemical calculations estimated that a 5.5 kcal-mol-1 energy difference between the eclipsed form and the expected staggered form could be accounted for by unprecedented hydrogen bonding interaction strengths due to cooperative effects. In 1993, Novoa et al. (1993, Angew. Chem. Int. Edn Engl, 32, 588) showed that the earlier calculations were in error since they did not correct for basis set superposition error (BSSE). The BSSE corrected results of Novoa et al. could not account for the necessary 5.5 kcal mol-1 and this led them to question the original X-ray analysis of Seiler et al. Both sets of calculations suffered from the use of insufficiently accurate levels of theory and an inappropriate choice of model system. A current best estimate for the barrier to rotation is 1.4 kcal mol-1, far below that of the earlier studies. The stabilization of the eclipsed geometry due to hydrogen bonding after correction for BSSE is enough to match this small barrier. At today's best level of theory, the experimentally observed structure is 0.2 kcal mol-1 more stable than the staggered geometry. [ABSTRACT FROM AUTHOR]