Code generation in ORCA: progress, efficiency and tight integration.

An improved version of ORCA's automated generator environment (ORCA-AGE II) is presented. The algorithmic improvements and the move to C++ as the programming language lead to a performance gain of up to two orders of magnitude compared to the previously developed PYTHON toolchain. Additionally, the restructured modular design allows for far more complex code engines to be implemented readily. Importantly, we have realised an extremely tight integration with the ORCA host program. This allows for a workflow in which only the wavefunction Ansatz is part of the source code repository while all actual high-level code is generated automatically, inserted at the appropriate place in the host program before it is compiled and linked together with the hand written code parts. This construction ensures longevity and uniform code quality. Furthermore the new developments allow ORCA-AGE II to generate parallelised production-level code for highly complex theories, such as fully internally contracted multireference coupled-cluster theory (fic-MRCC) with an enormous number of contributing tensor contractions. We also discuss the automated implementation of nuclear gradients for arbitrary theories. All these improvements enable the implementation of theories that are too complex for the human mind and also reduce development times by orders of magnitude. We hope that this work enables researchers to concentrate on the intellectual content of the theories they develop rather than be concerned with technical details of the implementation.

Big data analysis of ab Initio molecular integrals in the neglect of diatomic differential overlap approximation.

Most modern semiempirical quantum-chemical (SQC) methods are based on the neglect of diatomic differential overlap (NDDO) approximation to ab initio molecular integrals. Here, we check the validity of this approximation by computing all relevant integrals for 32 typical organic molecules using Gaussian-type orbitals and various basis sets (from valence-only minimal to all-electron triple-ζ basis sets) covering in total more than 15.6 million one-electron (1-e) and 10.3 billion two-electron (2-e) integrals. The integrals are calculated in the nonorthogonal atomic basis and then transformed by symmetric orthogonalization to the Löwdin basis. In the case of the 1-e integrals, we find strong orthogonalization effects that need to be included in SQC models, for example, by strategies such as those adopted in the available OMx methods. For the valence-only minimal basis, we confirm that the 2-e Coulomb integrals in the Löwdin basis are quantitatively close to their counterparts in the atomic basis and that the 2-e exchange integrals can be safely neglected in line with the NDDO approximation. For larger all-electron basis sets, there are strong multishell orthogonalization effects that lead to more irregular patterns in the transformed 2-e integrals and thus cast doubt on the validity of the NDDO approximation for extended basis sets. Focusing on the valence-only minimal basis, we find that some of the NDDO-neglected integrals are reduced but remain sizable after the transformation to the Löwdin basis; this is true for the two-center 2-e hybrid integrals, the three-center 1-e nuclear attraction integrals, and the corresponding three-center 2-e hybrid integrals. We consider a scheme with a valence-only minimal basis that includes such terms as a possible strategy to go beyond the NDDO integral approximation in attempts to improve SQC methods. © 2018 Wiley Periodicals, Inc.

Analytic gradient and derivative couplings for the spin-flip extended configuration interaction singles method: Theory, implementation, and application to proton transfer.

We present the formalism of analytic gradients and derivative couplings for the spin-flip extended configuration interaction with single excitations (SF-XCIS) method. We report an efficient implementation of the SF-XCIS method in the framework of semiempirical quantum chemistry that allows fast excited-state calculations for large systems. The performance of the SF-XCIS method in combination with semiempirical orthogonalization-corrected models (OMx) is statistically evaluated for vertical singlet excitation energies. The SF-XCIS method treats the ground state and excited states in a fully balanced manner and properly describes conical intersections involving the ground state. It can thus be used in fewest switches surface hopping (FSSH) simulations of nonadiabatic dynamics processes. This is demonstrated in an OM2/SF-XCIS FSSH pilot study of excited-state proton transfer in 7-(2-pyridyl)indole.

Semiempirical Quantum-Chemical Orthogonalization-Corrected Methods: Benchmarks of Electronically Excited States.

The semiempirical orthogonalization-corrected OMx methods have recently been shown to perform well in extensive ground-state benchmarks. They can also be applied to the computation of electronically excited states when combined with a suitable multireference configuration interaction (MRCI) treatment. We report on a comprehensive evaluation of the performance of the OMx/MRCI methods for electronically excited states. The present benchmarks cover vertical excitation energies, excited-state equilibrium geometries (including an analysis of significant changes between ground- and excited-state geometries), minimum-energy conical intersections, ground- and excited-state zero-point vibrational energies, and 0-0 transition energies for a total of 520 molecular structures and 412 excited states. For comparison, we evaluate the TDDFT/B3LYP method for all benchmark sets, and the CC2, MRCISD, and CASPT2 methods for some of them. We find that the current OMx/MRCI methods perform reasonably well for many of the excited-state properties. However, in comparison to the first-principles methods, there are also a number of shortcomings that should be addressed in future developments.

Semiempirical Quantum-Chemical Orthogonalization-Corrected Methods: Theory, Implementation, and Parameters.

Semiempirical orthogonalization-corrected methods (OM1, OM2, and OM3) go beyond the standard MNDO model by explicitly including additional interactions into the Fock matrix in an approximate manner (Pauli repulsion, penetration effects, and core-valence interactions), which yields systematic improvements both for ground-state and excited-state properties. In this Article, we describe the underlying theoretical formalism of the OMx methods and their implementation in full detail, and we report all relevant OMx parameters for hydrogen, carbon, nitrogen, oxygen, and fluorine. For a standard set of mostly organic molecules commonly used in semiempirical method development, the OMx results are found to be superior to those from standard MNDO-type methods. Parametrized Grimme-type dispersion corrections can be added to OM2 and OM3 energies to provide a realistic treatment of noncovalent interaction energies, as demonstrated for the complexes in the S22 and S66×8 test sets.

Semiempirical Quantum-Chemical Orthogonalization-Corrected Methods: Benchmarks for Ground-State Properties.

The semiempirical orthogonalization-corrected OMx methods (OM1, OM2, and OM3) go beyond the standard MNDO model by including additional interactions in the electronic structure calculation. When augmented with empirical dispersion corrections, the resulting OMx-Dn approaches offer a fast and robust treatment of noncovalent interactions. Here we evaluate the performance of the OMx and OMx-Dn methods for a variety of ground-state properties using a large and diverse collection of benchmark sets from the literature, with a total of 13035 original and derived reference data. Extensive comparisons are made with the results from established semiempirical methods (MNDO, AM1, PM3, PM6, and PM7) that also use the NDDO (neglect of diatomic differential overlap) integral approximation. Statistical evaluations show that the OMx and OMx-Dn methods outperform the other methods for most of the benchmark sets.

Active site structure and absorption spectrum of channelrhodopsin-2 wild-type and C128T mutant.

In spite of considerable interest, the active site of channelrhodopsin still lacks a detailed atomistic description, the understanding of which could strongly enhance the development of novel optogenetics tools. We present a computational study combining different state-of-the-art techniques, including hybrid quantum mechanics/molecular mechanics schemes and high-level quantum chemical methods, to properly describe the hydrogen-bonding pattern between the retinal chromophore and its counterions in channelrhodopsin-2 Wild-Type and C128T mutant. Especially, we show by extensive ground state dynamics that the active site, containing a glutamic acid (E123) and a water molecule, is highly dynamic, sampling three different hydrogen-bonding patterns. This results in a broad absorption spectrum that is representative of the different structural motifs found. A comparison with bacteriorhodopsin, characterized by a pentagonal hydrogen-bonded active site structure, elucidates their different absorption properties.

Nonequilibrium H/D isotope effects from trajectory-based nonadiabatic dynamics.

Ground-state equilibrium kinetic isotope effects can be treated well in the framework of transition state theory, whereas excited-state nonequilibrium isotope effects are theoretically less explored. In this article we show for the first time that trajectory-based nonadiabatic dynamics simulations are able to reproduce experimental values for nonequilibrium H/D isotope effects in excited-state processes. We use high-level electronic structure calculations (MS-CASPT2, DFT/MRCI, and TDDFT) and full-dimensional OM2/MRCI-based nonadiabatic dynamics simulations to study the ultrafast intramolecular excited-state proton transfer (ESIPT) and the subsequent deactivation of 7-(2-pyridyl)indole (7PyIn) and its deuterated analogue (7PyIn-D). We evaluate a total of 1367 surface-hopping trajectories to establish the differences in the dynamical behavior of 7PyIn and 7PyIn-D. The computed H/D isotope effects for ESIPT and excited-state decay are consistent with recent experimental results from femtosecond pump-probe resonance-enhanced multiphoton ionization spectroscopy. We also analyze the influence of temperature fluctuations in the initially prepared sample on the photodynamics of 7PyIn and 7PyIn-D.

Periodic decay in the photoisomerisation of p-aminoazobenzene.

Semiempirical OM2/MRCI surface-hopping simulations have been performed to study the E→Z and Z→E isomerisations of p-aminoazobenzene upon photoexcitation to the S1 state (nπ*). The overall mechanism is similar to the one found previously for the unsubstituted parent system, although there is a moderate speedup of the decay to the ground state because of the steeper excited-state potential between the Franck-Condon region and the conical intersection seam. The decay dynamics to the ground state shows an oscillatory pattern that can be attributed to an out-of-plane rotation of the N2 moiety. The reaction is thus initially driven by N2 rotation, which triggers phenyl rotations around the C-N bonds. The Z isomer is produced most effectively when the phenyl rings rotate in phase.

Photochemical dynamics of E-iPr-furylfulgide.

As an important theoretical step towards unraveling the mechanistic details of the photochemical switching processes in molecules of the fulgide type, we carried out a large-scale, full-dimensional computational study of the ring closure reaction of E-iPr-furylfulgide. Simulated static UV spectra and femtosecond transient spectra are in good agreement with their experimental counterparts. Using surface-hopping photodynamics simulations, we identify three major de-excitation pathways and their interplay. The dominant photochemical pathway (70% of the trajectories) allows for ring closure, while the two minor pathways involve E-Z double bond isomerization rather than cyclization. The relative abundance of the pathways is rationalized by arguments linking structure with dynamics. It should be emphasized, however, that the distinction into three pathways is only a simplified interpretational model, since the actual dynamical trajectories do not strictly follow these idealized pathways but often show mixed behaviour, evolving along two or three of them during the course of the simulation.

Semiempirical Quantum Chemical Calculations Accelerated on a Hybrid Multicore CPU-GPU Computing Platform.

In this work, we demonstrate that semiempirical quantum chemical calculations can be accelerated significantly by leveraging the graphics processing unit (GPU) as a coprocessor on a hybrid multicore CPU-GPU computing platform. Semiempirical calculations using the MNDO, AM1, PM3, OM1, OM2, and OM3 model Hamiltonians were systematically profiled for three types of test systems (fullerenes, water clusters, and solvated crambin) to identify the most time-consuming sections of the code. The corresponding routines were ported to the GPU and optimized employing both existing library functions and a GPU kernel that carries out a sequence of noniterative Jacobi transformations during pseudodiagonalization. The overall computation times for single-point energy calculations and geometry optimizations of large molecules were reduced by one order of magnitude for all methods, as compared to runs on a single CPU core.

Cooperating Dinitrogen and Phenyl Rotations in trans-Azobenzene Photoisomerization.

Semiempirical OM2/MRCI surface-hopping simulations have been performed to study the trans-to-cis photoisomerization of azobenzene upon excitation to the S1 state. The decay dynamics to the ground state shows an oscillatory pattern that can be attributed to an out-of-plane rotation of the N2 moiety. The reaction is thus initially driven by N2 rotation which triggers phenyl rotations around the C-N bonds. The cis isomer is produced most effectively when the phenyl rings rotate in phase. Mode-specific excitations cause variations in the computed decay times and product yields.

Fluorophores as optical sensors for local forces.

The main aim of this study is to investigate correlations between the impact of an external mechanical force on the molecular framework of fluorophores and the resultant changes in their fluorescence properties. Taking into account previous theoretical studies, we designed a suitable custom-tailored oligoparaphenylenevinylene derivative (OPV5) with a twisted molecular backbone. Thin foils made of PVC doped with 100 nM OPV were prepared. By applying uniaxial force, the foils were stretched and three major optical effects were observed simultaneously. First, the fluorescence anisotropy increased, which indicates a reorientation of the fluorophores within the matrix. Second, the fluorescence lifetime decreased by approximately 2.5% (25 ps). Finally, we observed an increase in the emission energy of about 0.2% (corresponding to a blue-shift of 1.2 nm). In addition, analogous measurements with Rhodamine 123 as an inert reference dye showed only minor effects, which can be attributed to matrix effects due to refractive index changes. To relate the observed spectroscopic changes to the underlying changes in molecular properties, quantum-chemical calculations were also performed. Semiempirical methods had to be used because of the size of the OPV5 chromophore. Two conformers of OPV5 (C(2) and C(i) symmetry) were considered and both gave very similar results. Both the observed blue-shift of fluorescence and the reduced lifetime of OPV5 under tensile stress are consistent with the results of the semiempirical calculations. Our study proves the feasibility of fluorescence-based local force probes for polymers under tension. Improved optical sensors of this type should in principle be able to monitor local mechanical stress in transparent samples down to the single-molecule level, which harbors promising applications in polymer science and nanotechnology.

Implementation of a general multireference configuration interaction procedure with analytic gradients in a semiempirical context using the graphical unitary group approach.

The graphical unitary group approach has been applied in an efficient implementation of a general multireference configuration interaction (MRCI) method for use with small active molecular orbital spaces in a semiempirical framework. Gradients can be computed analytically for molecular orbitals from a closed-shell or a half-electron open-shell Hartree-Fock calculation. CPU times for single point energy and gradient calculations are reported. The code allows MRCI geometry optimizations of large molecules, as illustrated for the singlet ground state and the four lowest triplet states of fullerene C(76).

Recent developments in the electronic spectroscopy of amides and alpha-helical polypeptides.

Recent experimental and theoretical advances in understanding the electronic excited states of simple amides are reviewed. Polarized reflection spectroscopy of single crystals of N-acetylglycine shows that the direction of the first pipi* (NV(1)) transition dipole moment of a secondary amide differs by approximately 15 degrees from that of a primary amide. Ab initio calculations on simple amides support this conclusion. Ab initio studies of di- and tri-amides demonstrate that several inter-amide charge-transfer (CT) transitions occur in the 150-175-nm region, between the NV(1) and NV(2) transitions. When the correct dipole transition moment direction for peptides is used in calculations of the circular dichroism of the alpha-helix, the results are much improved over those from earlier calculations that used the direction for primary amides. Studies that consider the mixing of the NV(1) transition with CT transitions are reviewed. These indicate that such mixing is likely to have a significant effect on the absorption and CD spectra of the alpha-helix and other types of peptide conformation. Nevertheless, the independent systems model gives a reasonable first approximation to the absorption and CD spectra of the alpha-helix.