Gaussian process regression adaptive density-guided approach: Toward calculations of potential energy surfaces for larger molecules.

We present a new program implementation of the Gaussian process regression adaptive density-guided approach [Schmitz et al., J. Chem. Phys. 153, 064105 (2020)] for automatic and cost-efficient potential energy surface construction in the MidasCpp program. A number of technical and methodological improvements made allowed us to extend this approach toward calculations of larger molecular systems than those previously accessible and maintain the very high accuracy of constructed potential energy surfaces. On the methodological side, improvements were made by using a Δ-learning approach, predicting the difference against a fully harmonic potential, and employing a computationally more efficient hyperparameter optimization procedure. We demonstrate the performance of this method on a test set of molecules of growing size and show that up to 80% of single point calculations could be avoided, introducing a root mean square deviation in fundamental excitations of about 3 cm-1. A much higher accuracy with errors below 1 cm-1 could be achieved with tighter convergence thresholds still reducing the number of single point computations by up to 68%. We further support our findings with a detailed analysis of wall times measured while employing different electronic structure methods. Our results demonstrate that GPR-ADGA is an effective tool, which could be applied for cost-efficient calculations of potential energy surfaces suitable for highly accurate vibrational spectra simulations.

Reliable Isotropic Electron-Paramagnetic-Resonance Hyperfine Coupling Constants from the Frozen-Density Embedding Quasi-Diabatization Approach.

We present a systematic benchmark of isotropic electron-paramagnetic-resonance hyperfine coupling constants calculated for radical cation and anion complexes of molecules contained in the S22 test set using the frozen-density embedding quasi-diabatization (FDE-diab) approach. The results are compared to those from Kohn-Sham density-functional theory and frozen-density embedding, employing the domain-based local pair natural orbital coupled cluster singles and doubles method as a reference. We demonstrate that our new approach outperforms frozen-density embedding in all cases and provides reliable hyperfine couplings for radical cations using rather simple generalized-gradient approximation-type functionals. By contrast, more sophisticated and computationally less efficient exchange-correlation approximations are required for Kohn-Sham density-functional theory. For the radical anions, FDE-diab can at least provide an accuracy similar to that of Kohn-Sham density-functional theory. Finally, we demonstrate the computational advantages of FDE-diab for a π-stacked benzene octamer radical cation.

Multi-state formulation of the frozen-density embedding quasi-diabatization approach.

We present a multi-state implementation of the recently developed frozen-density embedding diabatization (FDE-diab) methodology [D. G. Artiukhin and J. Neugebauer, J. Chem. Phys. 148, 214104 (2018)] in the Serenity program. The new framework extends the original approach such that any number of charge-localized quasi-diabatic states can be coupled, giving an access to calculations of ground and excited state spin-density distributions as well as to excitation energies. We show that it is possible to obtain results similar to those from correlated wave function approaches such as the complete active space self-consistent field method at much lower computational effort. Additionally, we present a series of approximate computational schemes, which further decrease the overall computational cost and systematically converge to the full FDE-diab solution. The proposed methodology enables computational studies on spin-density distributions and related properties for large molecular systems of biochemical interest.

Theoretical Assessment of Hinge-Type Models for Electron Donors in Reaction Centers of Photosystems I and II as well as of Purple Bacteria.

Hinge-type molecular models for electron donors in reaction centers of Photosystems I and II and purple bacteria were investigated using a two-state computational approach based on frozen-density embedding (FDE). This methodology, dubbed FDE-diab, is known to avoid consequences of the self-interaction error as far as intermolecular phenomena are concerned, which allows a prediction of qualitatively correct spin densities for large biomolecular systems. The calculated spin density distributions are in a good agreement with available experimental results and demonstrated a very high sensitivity to changes in the relative orientation of cofactors and amino acid protonation states. This allows a validation of the previously proposed hinge-type models providing hints on possible protonation states of axial histidine molecules.

Computational Investigation of the Spin-Density Asymmetry in Photosynthetic Reaction Center Models from First Principles.

We present a computational analysis of the spin-density asymmetry in cation radical states of reaction center models from photosystem I, photosystem II, and bacteria from Synechococcus elongatus, Thermococcus vulcanus, and Rhodobacter sphaeroides, respectively. The recently developed frozen-density embedding (FDE)-diab methodology [J. Chem. Phys., 2018, 148, 214104] allowed us to effectively avoid the spin-density overdelocalization error characteristic for the standard Kohn-Sham density functional theory and to reliably calculate spin-density distributions and electronic couplings for a number of molecular systems ranging from inner pairs of (bacterio)chlorophyll a molecules in vacuum to large proteins including up to about 2000 atoms. The calculated spin densities show a good agreement with available experimental results and were used to validate reaction center models reported in the literature. Here, we demonstrate that the applied theoretical approach is very sensitive to changes in molecular structures and the relative orientation of molecules. This makes FDE-diab a valuable tool for electronic structure calculations of large photosynthetic models effectively complementing the existing experimental techniques.

Adaptive density-guided approach to double incremental potential energy surface construction.

We present a combination of the recently developed double incremental expansion of potential energy surfaces with the well-established adaptive density-guided approach to grid construction. This unique methodology is based on the use of an incremental expansion for potential energy surfaces, known as n-mode expansion; an incremental many-body representation of the electronic energy; and an efficient vibrational density-guided approach to automated determination of grid dimensions and granularity. The reliability of the method is validated calculating potential energy surfaces and obtaining fundamental excitation energies for three moderate-size chain-like molecular systems. The use of our methodology leads to considerable computational savings for potential energy surface construction compared to standard approaches while maintaining a high level of accuracy in the resulting potential energy surfaces. Additional investigations indicate that our method can be applied to covalently bound and strongly interacting molecular systems, even though these cases are known to be very unfavorable for fragmentation schemes. We therefore conclude that the presented methodology is a robust and flexible approach to potential energy surface construction, which introduces considerable computational savings without compromising the accuracy of vibrational spectra calculations.

Approximate high mode coupling potentials using Gaussian process regression and adaptive density guided sampling.

We present a new efficient approach for potential energy surface construction. The algorithm employs the n-mode representation and combines an adaptive density guided approach with Gaussian process regression for constructing approximate higher-order mode potentials. In this scheme, the n-mode potential construction is conventionally done, whereas for higher orders the data collected in the preceding steps are used for training in Gaussian process regression to infer the energy for new single point computations and to construct the potential. We explore different delta-learning schemes which combine electronic structure methods on different levels of theory. Our benchmarks show that for approximate 2-mode potentials the errors can be adjusted to be in the order of 8 cm-1, while for approximate 3-mode and 4-mode potentials the errors fall below 1 cm-1. The observed errors are, therefore, smaller than contributions due to missing higher-order electron excitations or relativistic effects. Most importantly, the approximate potentials are always significantly better than those with neglected higher-order couplings.

Photochemically induced dynamic nuclear polarization NMR on photosystem II: donor cofactor observed in entire plant.

The solid-state photo-CIDNP (photochemically induced dynamic nuclear polarization) effect allows for increase of signal and sensitivity in magic-angle spinning (MAS) NMR experiments. The effect occurs in photosynthetic reaction centers (RC) proteins upon illumination and induction of cyclic electron transfer. Here we show that the strength of the effect allows for observation of the cofactors forming the spin-correlated radical pair (SCRP) in isolated proteins, in natural photosynthetic membranes as well as in entire plants. To this end, we measured entire selectively 13C isotope enriched duckweed plants (Spirodela oligorrhiza) directly in the MAS rotor. Comparison of 13C photo-CIDNP MAS NMR spectra of photosystem II (PS2) obtained from different levels of RC isolation, from entire plant to isolated RC complex, demonstrates the intactness of the photochemical machinery upon isolation. The SCRP in PS2 is structurally and functionally very similar in duckweed and spinach (Spinacia oleracea). The analysis of the photo-CIDNP MAS NMR spectra reveals a monomeric Chl a donor. There is an experimental evidence for matrix involvement, most likely due to the axial donor histidine, in the formation of the SCRP. Data do not suggest a chemical modification of C-131 carbonyl position of the donor cofactor.

Frozen-density embedding as a quasi-diabatization tool: Charge-localized states for spin-density calculations.

We present an effective approach for (spin-)density calculations of open-shell molecular complexes that avoid both an overdelocalization of spin densities as often observed in approximate Kohn-Sham-density functional theory (KS-DFT) calculations and an overlocalization of spin densities as may occur in fragment approaches with non-suitable fragment choices. The method is based on the frozen-density embedding formalism and makes use of non-orthogonal, spin-/charge-localized Slater determinants, which provides a basis for qualitatively correct descriptions of intersystem spin-density delocalization. The reliability of this method is tested on four complexes featuring different molecular sizes and interactions and showing different degrees of spin-density delocalization, ranging from fully localized to fully delocalized. The resulting spin densities are compared to accurate ab initio results. The method is clearly more robust than the corresponding KS-DFT approximations, as it works qualitatively correct in all cases studied.

Photocatalytic E → Z Isomerization of Polarized Alkenes Inspired by the Visual Cycle: Mechanistic Dichotomy and Origin of Selectivity.

Iteratively executed with exquisite spatial and temporal control, the selective isomerization of polarized alkenes underpins a plethora of complex biological processes ranging from natural product biosynthesis through to the mammalian visual cycle. However, nature's proficiency conceals the inherent difficulties in replicating this contra-thermodynamic transformation in the laboratory. Recently, we disclosed the first highly Z-selective isomerization of polarized alkenes, employing the cinnamoyl chromophore as a retinal surrogate under UV-irradiation (402 nm) with (-)-riboflavin (vitamin B2) as an inexpensive, organic photocatalyst (J. Am. Chem. Soc. 2015, 137, 11254-11257). This study was inspired by the propensity of crystalline (-)-riboflavin in the eyes of vertebrates to invert the intrinsic directionality of retinal isomerization. Herein, we extend this methodology to include a bioinspired, catalytic E → Z isomerization of α,ß-unsaturated nitriles, thereby mimicking the intermediate Opsin-derived, protonated Schiff base in the visual cycle with simple polarized alkenes. Replacement of the iminium motif by a cyano group is well tolerated and gives an additional degree of versatility for postisomerization functionalization. Broad substrate scope is demonstrated (up to 99:1 Z:E) together with evidence of mechanistic dichotomy via both singlet and triplet energy transfer mechanisms. Kinetic studies, temperature dependent photostationary state correlations and investigation of substituent-based electronic perturbation of the alkene identified polarization combined with increased Z-isomer activation barriers as the selectivity governing factors in catalysis. This investigation demonstrates the importance of internal structural preorganization on photostationary composition and explicates the augmented Z-selectivity upon hydrogen-alkyl exchange at the ß-position of the alkene.

Quantum Chemical Spin Densities for Radical Cations of Photosynthetic Pigment Models.

The spin densities of radical cations of magnesium porphyrin, magnesium chlorine and a truncated chlorophyll a model are calculated with density-functional theory and multiconfigurational quantum chemical methods. The latter serve as a reference for approximate density-functional theory which yields spin densities that may suffer from the self-interaction error. We carried out complete active space self-consistent field calculations with increasing active orbital spaces to systematically converge qualitatively correct spin densities. In particular, for the magnesium chlorine and chlorophyll a model radical cations, this is not easy to achieve because of the lower symmetry compared to magnesium porphyrin. Strategies had to be employed which allowed us to consider very large active orbital spaces. We explored restricted active space self-consistent field and density-matrix renormalization group calculations. Based on these reference data, we assessed the accuracy of different density-functional approximations. We show that in particular, exchange-correlation model potentials with correct asymptotic behavior yield good spin densities, and we find, in agreement with previous studies on different classes of compounds, that hybrid functionals systematically increase spin-polarization effects with increasing amounts of exact exchange. Our results provide a starting point for investigations of spin densities of more complex systems such as the hinge model for the primary electron donor in photosystem II.

Radical perfluoroalkylation - easy access to 2-perfluoroalkylindol-3-imines via electron catalysis.

Arylisonitriles (2 equivalents) react with alkyl and perfluoroalkyl radicals to form 2-alkylated indole-3-imines via two sequential additions to the isonitrile moiety followed by homolytic aromatic substitution. The three component reaction comprises three C-C bond formations. The endocyclic imine functionality in the products is more reactive in follow up chemistry and hydrolysis of the exocyclic imine leads to 3-oxindoles that show fluorescence properties.

Ab Initio Characterization of the Electrostatic Complexes Formed by H2 Molecule and Cr(+), Mn(+), Cu(+), and Zn(+) Cations.

Equilibrium structures, dissociation energies, and rovibrational energy levels of the electrostatic complexes formed by molecular hydrogen and first-row S-state transition metal cations Cr(+), Mn(+), Cu(+), and Zn(+) are investigated ab initio. Extensive testing of the CCSD(T)-based approaches for equilibrium structures provides an optimal scheme for the potential energy surface calculations. These surfaces are calculated in two dimensions by keeping the H-H internuclear distance fixed at its equilibrium value in the complex. Subsequent variational calculations of the rovibrational energy levels permits direct comparison with data obtained from equilibrium thermochemical and spectroscopic measurements. Overall accuracy within 2-3% is achieved. Theoretical results are used to examine trends in hydrogen activation, vibrational anharmonicity, and rotational structure along the sequence of four electrostatic complexes covering the range from a relatively floppy van der Waals system (Mn(+)···H2) to an almost a rigid molecular ion (Cu(+)···H2).

Excitation energies from frozen-density embedding with accurate embedding potentials.

We present calculations of excitation energies within the time-dependent density functional theory (TDDFT) extension of frozen-density embedding (FDE) using reconstructed accurate embedding potentials. Previous applications of FDE showed significant deviations from supermolecular calculations; our current approach eliminates one potential error source and yields excitation energies of generally much better agreement with Kohn-Sham-TDDFT. Our results demonstrate that the embedding potentials represent the main error source in FDE-TDDFT calculations using standard approximate kinetic-energy functionals for excitations localized within one subsystem.

Interaction of the beryllium cation with molecular hydrogen and deuterium.

The structural and spectroscopic properties of the Be(+)-H2 and Be(+)-D2 electrostatic complexes are investigated theoretically. A three-dimensional ground-state potential energy surface is generated ab initio at the CCSD(T) level and used for calculating the lower rovibrational energy levels variationally. The minimum of the potential energy surface corresponds to a well depth of 3168 cm(-1), an intermolecular separation of 1.776 Å, with the bond of the H2 subunit being 0.027 Å longer than for the free molecule. Taking vibrational zero point energy into account, the complexes containing para H2 and ortho D2 are predicted to have dissociation energies of 2678 and 2786 cm(-1), respectively. The νHH band of Be(+)-H2 is predicted to be red-shifted from the free dihydrogen transition by -323 cm(-1), whereas the corresponding shift for Be(+)-D2 is predicted to be -229 cm(-1). The dissociation energy of the Be(+)-D2 complex is calculated to be slightly higher than the energy required to vibrationally excite the D2 subunit, raising the possibility that the onset of dissociation can be observed in the infrared predissociation spectrum at a particular rotational energy level in the νDD manifold.