Sebastian Höfener

The MP2‐F12 method in the TURBOMOLE program package

A detailed description of the explicitly correlated second‐order Møller–Plesset perturbation theory (MP2‐F12) method, as implemented in the TURBOMOLE program package, is presented. The TURBOMOLE implementation makes use of density fitting, which greatly reduces the prefactor for integral evaluation. Methods are available for the treatment of ground states of open‐ and closed‐shell species, using unrestricted as well as restricted (open‐shell) Hartree–Fock reference determinants. Various methodological choices and approximations are discussed. The performance of the TURBOMOLE implementation is illustrated by example calculations of the molecules leflunomide, prednisone, methotrexate, ethylenedioxytetrafulvalene, and a cluster model for the adsorption of methanol on the zeolite H‐ZSM‐5. Various basis sets are used, including the correlation‐consistent basis sets specially optimized for explicitly correlated calculations (cc‐pVXZ‐F12).

Scope and limitations of the SCS-MP2 method for stacking and hydrogen bonding interactions

Fluorobenzenes are pi-acceptor synthons that form pi-stacked structures in molecular crystals as well as in artificial DNAs. We investigate the competition between hydrogen bonding and pi-stacking in dimers consisting of the nucleobase mimic 2-pyridone (2PY) and all fluorobenzenes from 1-fluorobenzene to hexafluorobenzene (n-FB, with n = 1-6). We contrast the results of high level ab initio calculations with those obtained using ultraviolet (UV) and infrared (IR) laser spectroscopy of isolated and supersonically cooled dimers. The 2PY.n-FB complexes with n = 1-5 prefer double hydrogen bonding over pi-stacking, as diagnosed from the UV absorption and IR laser depletion spectra, which both show features characteristic of doubly H-bonded complexes. The 2-pyridone.hexafluorobenzene dimer is the only pi-stacked dimer, exhibiting a homogeneously broadened UV spectrum and no IR bands characteristic for H-bonded species. MP2 (second-order Møller-Plesset perturbation theory) calculations overestimate the pi-stacked dimer binding energies by about 10 kJ/mol and disagree with the experimental observations. In contrast, the MP2 treatment of the H-bonded dimers appears to be quite accurate. Grimmes spin-component-scaled MP2 approach (SCS-MP2) is an improvement over MP2 for the pi-stacked dimers, reducing the binding energy by approximately 10 kJ/mol. When applied to explicitly correlated MP2 theory (SCS-MP2-R12 approach), agreement with the corresponding coupled-cluster binding energies [at the CCSD(T) level] is very good for the pi-stacked dimers, within +/- 1 kJ/mol for the 2PY complexes with 1-fluorobenzene, 1,2-difluorobenzene, 1,2,4,5-tetrafluorobenzene, pentafluorobenzene and hexafluorobenzene. Unfortunately, the SCS-MP2 approach also reduces the binding energy of the H-bonded species, leading to disagreement with both coupled-cluster theory and experiment. The SCS-MP2-R12 binding energies follow the SCS-MP2 binding energies closely, being about 0.5 and 0.7 kJ/mol larger for the H-bonded and pi-stacked forms, respectively, in an augmented correlation-consistent polarized valence quadruple-zeta basis. It seems that the SCS-MP2 and SCS-MP2-R12 methods cannot provide sufficient accuracy to replace the CCSD(T) method for intermolecular interactions where H-bonding and pi-stacking are competitive.

Molecular properties via a subsystem density functional theory formulation: A common framework for electronic embedding

In this article, we present a consistent derivation of a density functional theory (DFT) based embedding method which encompasses wave-function theory-in-DFT (WFT-in-DFT) and the DFT-based subsystem formulation of response theory (DFT-in-DFT) by Neugebauer [J. Neugebauer, J. Chem. Phys. 131, 084104 (2009)] as special cases. This formulation, which is based on the time-averaged quasi-energy formalism, makes use of the variation Lagrangian techniques to allow the use of non-variational (in particular: coupled cluster) wave-function-based methods. We show how, in the time-independent limit, we naturally obtain expressions for the ground-state DFT-in-DFT and WFT-in-DFT embedding via a local potential. We furthermore provide working equations for the special case in which coupled cluster theory is used to obtain the density and excitation energies of the active subsystem. A sample application is given to demonstrate the method.

Coupled‐cluster frozen‐density embedding using resolution of the identity methods

Frozen‐density embedding (FDE) is combined with resolution of the identity (RI) Hartree–Fock and a RI‐variant of a second‐order approximate coupled‐cluster singles and doubles (RI‐CC2) to determine solvatochromic shifts for the lowest excitation energy of acetone and pyridazine, respectively, each solvated in different environments with total system sizes of about 2.5 nm diameter. The combination of FDE and RI‐CC2 increases efficiency and enables the calculation of numerous snapshots with 100 to 300 molecules, also allowing for larger basis sets as well as diffuse functions needed for an accurate treatment of properties. The maximum errors in the solvatochromic shifts amount up to 0.2 eV, which are similar to other approximated studies in the literature.

Solvatochromic shifts from coupled-cluster theory embedded in density functional theory

Building on the framework recently reported for determining general response properties for frozen-density embedding [S. Höfener, A. S. P. Gomes, and L. Visscher, J. Chem. Phys. 136, 044104 (2012)], in this work we report a first implementation of an embedded coupled-cluster in density-functional theory (CC-in-DFT) scheme for electronic excitations, where only the response of the active subsystem is taken into account. The formalism is applied to the calculation of coupled-cluster excitation energies of water and uracil in aqueous solution. We find that the CC-in-DFT results are in good agreement with reference calculations and experimental results. The accuracy of calculations is mainly sensitive to factors influencing the correlation treatment (basis set quality, truncation of the cluster operator) and to the embedding treatment of the ground-state (choice of density functionals). This allows for efficient approximations at the excited state calculation step without compromising the accuracy. This approximate scheme makes it possible to use a first principles approach to investigate environment effects with specific interactions at coupled-cluster level of theory at a cost comparable to that of calculations of the individual subsystems in vacuum.

Fluorescence behavior of (selected) flavonols: a combined experimental and computational study

In this article, results of (time-dependent) density functional theory (DFT and TDDFT) calculations are combined with experimental absorption and fluorescence measurements to explain fluorescence properties of a series of flavonols. The well-understood fluorescence properties of 3- and 5-hydroxyflavone are revisited and validate our combined experimental and theoretical approach. The accuracy of the computational data (energy differences for selected points at the PES, excitation energies and oscillator strengths) allows us to understand quite different experimentally observed fluorescence spectra in the presence of only subtle structural differences. We show that for flavonols with additional hydroxyl groups not the neutral molecule but rather anions lead to fluorescence and that solvation molecules need to be included explicitly in the theoretical calculations to obtain a sufficient accuracy-enabling the understanding and prediction of experimental data for flavonols belonging to different sub-classes.

Calculation of electronic excitations using wave-function in wave-function frozen-density embedding.

Recently, a general framework suitable for general frozen-density embedding (FDE) methods was published [S. Höfener, A. S. P. Gomes, and L. Visscher, J. Chem. Phys. 136, 044104 (2012)]. In the present article, we report the fragmentation of a supermolecule while treating all subsystems with coupled-cluster theory and the interaction of the subsystems with density-functional theory. This variant is denoted wave-function theory in wave-function theory FDE, or coupled-cluster theory in coupled-cluster theory FDE. Main target of this approach is not the embedding of a single molecule in large solvation shells, but rather the possibility to divide a complex system consisting of several molecules when all subsystems are to be treated with, e.g., coupled-cluster methods to provide a balanced and unbiased description. We present numerical results for hydrogen-bonded complexes which exhibit rather strong interactions. Cases with weakly interacting subsystems are expected to exhibit even higher accuracy. This facilitates the study of properties of larger complexes such as DNA base pairs with coupled-cluster methods.

Analytical nuclear gradients of the explicitly correlated Møller–Plesset second-order energy

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.

Analytic Calculation of First-order Molecular Properties at the Explicitly-correlated Second-order Møller-Plesset Level

Abstract Formulae are derived and implemented for the analytic calculation of first-order molecular properties at the level of explicitly-correlated second-order Møller-Plesset perturbation theory. In this theory, which is denoted as MP2-F12 theory, Slater-type geminals are used to expand the first-order wave function. A second-order perturbation theory correction for single excitations into a complementary auxliary basis set is also included. At the MP2-F12 level, it seems sufficient to restrict the analytic calculation of energy derivatives to the level of standard approximation A of MP2-F12 theory and to assume the extended Brillouin condition to hold. Smooth and rapid convergence towards the basis-set limit is observed for the dipole moments of a selection of small closed- and open-shell molecules when calculated at the RI-MP2-F12/2A*[T+V] + CABS singles level in augmented correlation-consistent polarized valence double-, triple-, and quadruple-zeta basis sets that have been optimized especially for use in MP2-F12 theory.

Computing UV/vis spectra using a combined molecular dynamics and quantum chemistry approach: bis-triazin-pyridine (BTP) ligands studied in solution

We report a combined computational and experimental study to investigate the UV/vis spectra of 2,6-bis(5,6-dialkyl-1,2,4-triazin-3-yl)pyridine (BTP) ligands in solution. In order to study molecules in solution using theoretical methods, force-field parameters for the ligand-water interaction are adjusted to ab initio quantum chemical calculations. Based on these parameters, molecular dynamics (MD) simulations are carried out from which snapshots are extracted as input to quantum chemical excitation-energy calculations to obtain UV/vis spectra of BTP ligands in solution using time-dependent density functional theory (TDDFT) employing the Tamm-Dancoff approximation (TDA). The range-separated CAM-B3LYP functional is used to avoid large errors for charge-transfer states occurring in the electronic spectra. In order to study environment effects with theoretical methods, the frozen-density embedding scheme is applied. This computational procedure allows to obtain electronic spectra calculated at the (range-separated) DFT level of theory in solution, revealing solvatochromic shifts upon solvation of up to about 0.6 eV. Comparison to experimental data shows a significantly improved agreement compared to vacuum calculations and enables the analysis of relevant excitations for the line shape in solution.