TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations.

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy-cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe-Salpeter methods, second-order Møller-Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE's functionality, including excited-state methods, RPA and Green's function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE's current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE's development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

How a linear triazene photoisomerizes in a volume-conserving fashion.

Understanding deactivation mechanisms of functional groups is a key step to design novel photo-active devices and molecular imaging agents. Here, we elucidate the photochemistry of linear triazenes, an extended analogue of the photo-switchable azo group, exemplarily for the widely used DNA-minor-groove binder berenil. Combining ultrafast spectroscopy and ab initio calculations unveils that the E-azo,s-trans structure of berenil predominates in the gas phase and in aqueous solution, and ADC(2) intrinsic reaction coordinate calculations disclose that the excited-state relaxation to the S1 minima/conical intersections follows a two-step mechanism: N[double bond, length as m-dash]N bond stretching followed by a bicycle-pedal rotation in the triazene bridge. Furthermore, studying the ground-state pathways shows that a fraction of the molecules relaxes back to the E-azo,s-trans isomer while the other part photoisomerizes to the Z-azo,s-trans via a hula-twist motion, as evidenced by experimental quantum yields of Φ ≈ 0.5 found for berenil in water, ethylene glycol, or bound to ß-trypsin. Moreover, our studies show that while the excited-state relaxation is insensitive to the environment, the ground-state dynamics depend on biomolecular binding partners.

COSMO-RI-ADC(2) excitation energies and excited state gradients.

We present an implementation of analytic gradients for electronically excited states for the algebraic-diagrammatic construction through second order, ADC(2), in combination with the conductor-like screening model (COSMO) as an implicit solvent model. The implementation uses a post-SCF reaction field scheme for the coupling between the environment and the quantum system which retains the computational efficiency of the gas-phase RI-ADC(2) calculations. Applying this approach, we computed solvatochromic shifts for UV absorption and fluorescence transitions of 4-(N,N-dimethylamino)benzonitrile using equilibrium geometries for the ground and the first excited states optimized in the presence of acetonitrile as solvent. Furthermore, we investigated the excited state energies and geometries of the 2-iodobenzimidazolium·triflate ion pair in aqueous solution as an example where solvent effects have a large influence on the structure and the UV spectrum.

Comparison of Reaction Field Schemes for Coupling Continuum Solvation Models with Wave Function Methods for Excitation Energies.

We address in this work the question to which extend reaction field schemes for correlated wave function methods give accurate excitation energies and, at the same time, physically consistent potential energy surfaces. The performance of the perturbation on energy (PTE), perturbation on energy and density (PTED), and post-SCF reaction field schemes is compared for the algebraic diagrammatic construction through second-order, ADC(2), as electronic structure and the conductor-like screening model COSMO as solvation model. The conditions on reaction field schemes to give physically consistent potential energies surfaces are discussed at the example of 4-(N,N-dimethylamino)benzonitrile, which is used as a test case to assess the artifacts introduced by state-specific contributions to the effective Hamiltonian. To evaluate the accuracy for excitation energies, we use two benchmark sets with data in gas phase and solution for ππ* and nπ* electronic transitions. The experimental solvatochromic shifts are compared to the corresponding calculated values at the COSMO-ADC(2) level with the PTE scheme within the frozen solvent approximation, PTED with the linear response (LR) and corrected linear response (cLR) and post-SCF with LR schemes and with the approximate coupled-cluster singles and doubles method CC2 combined with COSMO in the post-SCF (LR) scheme. The PTE scheme gives at the COSMO-ADC(2) level less accurate solvent shifts than the PTED(LR), PTED(cLR), and post-SCF(LR) schemes. The most accurate prediction of solvatochromism is obtained with the post-SCF(LR) scheme. In most cases, PTED(cLR) performs similar to post-SCF, although its nonlinear perturbative correction causes problems for potential energy surfaces.

Relaxation Dynamics of the Triazene Compound Berenil in DNA-Minor-Groove Confinement after Photoexcitation.

The effects of biomolecular embedding on the photoinduced relaxation process of the DNA-minor-groove binder berenil, diminazene aceturate, are studied with quantum mechanics/molecular mechanics, QM/MM, calculations that employ the algebraic diagrammatic construction through second-order, ADC(2), for the quantum mechanical part and an atomistic polarizable embedding for the classical part. The lowest singlet excitation to the S1 state is a bright transition with a ππ* character and a perichromatic red shift, due to the interactions with the solvent and DNA. The excited-state relaxation pathway is a two-step mechanism, an N═N azo-bond stretch followed by a volume-conserving bicycle-pedal twist. The DNA confinement and the coupling to solvent molecules via hydrogen bonds lead, for the excited-state relaxation process, only to small deviations from the ideal bicycle-pedal relaxation. Because of its volume-conserving character, the S1 excited-state relaxation proceeds almost unhindered, even in a fully rigid minor-groove confinement. With a fully frozen DNA minor groove and solvent, the energy gap for deexcitation from S1 to the ground state increased to 2.0 eV compared to 0.16 eV in aqueous solution. When the relaxation of the first solvation shell is included, the relaxation process on the S1 potential energy surface proceeds to a region on the potential energy surface, where only a small gap to the ground-state potential energy surface remains, 0.43 eV. These results show that the solvent relaxation has a significant effect in controlling the energy gap between the ground and S1 electronically excited states, which explains the experimental observations of the fluorescence characteristics of berenil in DNA confinement.

Avoiding Electron Spill-Out in QM/MM Calculations on Excited States with Simple Pseudopotentials.

QM/MM calculations of electronic excitations with diffuse basis sets often have large errors due to spill-out of electrons from the quantum subsystem. The Pauli repulsion of the electrons by the environment has to be included to avoid this. We propose transferable atomic all-electron pseudopotentials that can readily be combined with most MM force fields to avoid electron spill-out. QM/MM excitation energies computed with time-dependent Hartree-Fock and the algebraic diagrammatic construction through second-order are benchmarked against supermolecular calculations to validate these new pseudopotentials. The QM/MM calculations with pseudopotentials give accurate results that are stable with augmentation of the basis set with diffuse functions. We show that the largest contribution to residual deviations from full QM calculations is caused by the missing London dispersion interaction.

Analytic Excited State Gradients for the QM/MM Polarizable Embedded Second-Order Algebraic Diagrammatic Construction for the Polarization Propagator PE-ADC(2).

An implementation of a QM/MM embedding in a polarizable environment is presented for second-order Møller-Plesset perturbation theory, MP2, for ground state energies and molecular gradients and for the second-order Algebraic Diagrammatic Construction, ADC(2), for excitation energies and excited state molecular gradients. In this implementation of PE-MP2 and PE-ADC(2), the polarizable embedded Hartree-Fock wave function is used as uncorrelated reference state. The polarization-correlation cross terms for the ground and excited states are included in this model via an approximate coupling density. A Lagrangian formulation is used to derive the relaxed electron densities and molecular gradients. The resolution-of-the-identity approximation speeds up the calculation of four-index electron repulsion integrals in the molecular orbital basis. As a first application, the method is used to study the photophysical properties of host-guest complexes where the accuracy and weaknesses of the model are also critically examined. It is demonstrated that the ground state geometries of the full quantum mechanical calculation for the supermolecule can be well reproduced. For excited state geometries, the deviations from the supermolecular calculation are slightly larger, but still the environment effects are captured qualitatively correctly, and energy gaps between the ground and excited states are obtained with sufficient accuracy.

Ultrafast Dynamics of a Triazene: Excited-State Pathways and the Impact of Binding to the Minor Groove of DNA and Further Biomolecular Systems.

Many synthetic DNA minor groove binders exhibit a strong increase in fluorescence when bound to DNA. The pharmaceutical-relevant berenil (diminazene aceturate) is an exception with an extremely low fluorescence quantum yield (on the order of 10-4). We investigate the ultrafast excited-state dynamics of this triazene by femtosecond time-resolved fluorescence experiments in water, ethylene glycol, and buffer and bound to the enzyme ß-trypsin, the minor groove of AT-rich DNA, and G-quadruplex DNA. Ab initio calculations provide additional mechanistic insight. The complementing studies unveil that the excited-state motion initiated by ππ* excitation occurs in two phases: a subpicosecond phase associated with the lengthening of the central N═N double bond, followed by a bicycle-pedal-type motion of the triazene bridge, which is almost volume-conserving and can proceed efficiently within only a few picoseconds even under spatially confined conditions. Our results elucidate the excited-state relaxation mechanism of aromatic triazenes and explain the modest sensitivity of the fluorescence quantum yield of berenil even when it is bound to various biomolecules.

Polarizable Embedded RI-CC2 Method for Two-Photon Absorption Calculations.

We present a novel polarizable embedded resolution-of-identity coupled cluster singles and approximate doubles (PERI-CC2) method for calculation of two-photon absorption (TPA) spectra of large molecular systems. The method was benchmarked for three types of systems: a water-solvated molecule of formamide, a uracil molecule in aqueous solution, and a set of mutants of the channelrhodopsin (ChR) protein. The first test case shows that the PERI-CC2 method is in excellent agreement with the PE-CC2 method and in good agreement with the PE-CCSD method. The uracil test case indicates that the effects of hydrogen bonding on the TPA of a chromophore with the nearest environment is well-described with the PERI-CC2 method. Finally, the ChR calculation shows that the PERI-CC2 method is well-suited and efficient for calculations on proteins with medium-sized chromophores.