Comparison of Many-Particle Representations for Selected Configuration Interaction: II. Numerical Benchmark Calculations

The present work is the second part in our three-part series on the comparison of many-particle representations for the selected configuration interaction (CI) method. In this work, we present benchmark calculations based on our selected CI program called the iterative configuration expansion (ICE) that is inspired by the CIPSI method of Malrieu and co-workers (Malrieu J. Chem. Phys. 1973, 58, (12), 5745−5759). We describe the main parameters that enter in this algorithm and perform benchmark calculations on a set of 21 small molecules and compare ground state energies with full configuration interaction (FCI) results (FCI21 test set). The focus is the comparison of the performance of three different types of many-particle basis functions (MPBFs): (1) individual Slater determinants (DETS), (2) individual spin-adapted configuration state functions (CSFs), and (3) all CSFs of a given total spin that can be generated from spatial configurations (CFGs). An analysis of the cost of the calculation in terms of the number of wavefunction parameters and the energy error is evaluated for the DET-, CFG-, and CSF-based ICE. The main differences for the three many-particle basis representations show up in the number of wavefunction parameters and the rate of convergence toward the FCI limit with the thresholds of the ICE. Next, we analyze the best way to extrapolate the ICE energies toward the FCI results as a function of the thresholds. The efficiency of the extrapolation is investigated relative to the FCI21 test set as well as near FCI calculations on three moderately sized hydrocarbon molecules CH4, C2H4, and C4H6. Finally, we comment on the size-inconsistency error for the three many-particle representations and compare it with the error in the total energy. The implication for selected CI implementations with any of the three many-particle representations is discussed

How Can We Predict Accurate Electrochromic Shifts for Biochromophores? A Case Study on the Photosynthetic Reaction Center

Protein-embedded chromophores are responsible for light harvesting, excitation energy transfer, and charge separation in photosynthesis. A critical part of the photosynthetic apparatus are reaction centers (RCs), which comprise groups of (bacterio)chlorophyll and (bacterio)pheophytin molecules that transform the excitation energy derived from light absorption into charge separation. The lowest excitation energies of individual pigments (site energies) are key for understanding photosynthetic systems, and form a prime target for quantum chemistry. A major theoretical challenge is to accurately describe the electrochromic (Stark) shifts in site energies produced by the inhomogeneous electric field of the protein matrix. Here, we present large-scale quantum mechanics/molecular mechanics calculations of electrochromic shifts for the RC chromophores of photosystem II (PSII) using various quantum chemical methods evaluated against the domain-based local pair natural orbital (DLPNO) implementation of the similarity-transformed equation of motion coupled cluster theory with single and double excitations (STEOM-CCSD). We show that certain range-separated density functionals (ωΒ97, ωΒ97X-V, ωΒ2PLYP, and LC-BLYP) correctly reproduce RC site energy shifts with time-dependent density functional theory (TD-DFT). The popular CAM-B3LYP functional underestimates the shifts and is not recommended. Global hybrid functionals are too insensitive to the environment and should be avoided, while nonhybrid functionals are strictly nonapplicable. Among the applicable approximate coupled cluster methods, the canonical versions of CC2 and ADC(2) were found to deviate significantly from the reference results both for the description of the lowest excited state and for the electrochromic shifts. By contrast, their spin-component-scaled (SCS) and particularly the scale-opposite-spin (SOS) variants compare well with the reference DLPNO-STEOM-CCSD and the best range-separated DFT methods. The emergence of RC excitation asymmetry is discussed in terms of intrinsic and protein electrostatic potentials. In addition, we evaluate a minimal structural scaffold of PSII, the D1–D2–CytB559 RC complex often employed in experimental studies, and show that it would have the same site energy distribution of RC chromophores as the full PSII supercomplex, but only under the unlikely conditions that the core protein organization and cofactor arrangement remain identical to those of the intact enzyme

An induced-fit model for asymmetric organocatalytic reactions: a case study of the activation of olefins via chiral Brønsted acid catalysts

We elucidate the stereo-controlling factors of the asymmetric intramolecular hydroalkoxylation of terminal olefins catalyzed by bulky Brønsted acids [Science 2018, 359 (6383), 1501–1505] using high-level electronic structure methods. The catalyst–substrate interaction is described using a dispersion-driven induced-fit model, in which the conformational changes of the catalyst and of the substrate in the transition states are governed to a large extent by London dispersion forces. The distortion energy of the catalyst is dominated by the change in the intramolecular dispersion interactions, while intermolecular catalyst–substrate dispersion interactions are the major stabilizing contribution in the transition state. This model provides a new general framework in which to discuss the stereoselectivity of transformations catalyzed by such confined organocatalysts

Calculation of exchange couplings in the electronically excited state of molecular three-spin systems

Photogenerated molecular three-spin systems, composed of a chromophore and a covalently bound stable radical, are promising candidates for applications in the field of molecular spintronics. Through excitation with light, an excited doublet state and a quartet state are generated, whereby their energy difference depends on the exchange interaction JTR between the chromophore triplet state (T) and the stable radical (R). In order to establish design rules for new materials to be used in molecular spintronics devices, it is of great importance to gain knowledge on the magnitude of JTR as well as the factors influencing JTR on a molecular level. Here, we present a robust and reliable computational method to determine excited state exchange couplings in three-electron-three-centre systems based on a CASSCF/QD-NEVPT2 approach. The methodology is benchmarked and then applied to a series of molecules composed of a perylene chromophore covalently linked to various stable radicals. We calculate the phenomenological exchange interaction JTR between chromophore and radical, which can be compared directly to the experiment, but also illustrate how the individual exchange interactions Jij can be extracted using an effective Hamiltonian that corresponds to the Heisenberg–Dirac–Van-Vleck Hamiltonian. The latter procedure enables a more detailed analysis of the contributions to the exchange interaction JTR and yields additional insight that will be invaluable for future design optimisation

Chlorophyll excitation energies and structural stability of the CP47 antenna of photosystem II: a case study in the first-principles simulation of light-harvesting complexes

Natural photosynthesis relies on light harvesting and excitation energy transfer by specialized pigment–protein complexes. Their structure and the electronic properties of the embedded chromophores define the mechanisms of energy transfer. An important example of a pigment–protein complex is CP47, one of the integral antennae of the oxygen-evolving photosystem II (PSII) that is responsible for efficient excitation energy transfer to the PSII reaction center. The charge-transfer excitation induced among coupled reaction center chromophores resolves into charge separation that initiates the electron transfer cascade driving oxygenic photosynthesis. Mapping the distribution of site energies among the 16 chlorophyll molecules of CP47 is essential for understanding excitation energy transfer and overall antenna function. In this work, we demonstrate a multiscale quantum mechanics/molecular mechanics (QM/MM) approach utilizing full time-dependent density functional theory with modern range-separated functionals to compute for the first time the excitation energies of all CP47 chlorophylls in a complete membrane-embedded cyanobacterial PSII dimer. The results quantify the electrostatic effect of the protein on the site energies of CP47 chlorophylls, providing a high-level quantum chemical excitation profile of CP47 within a complete computational model of “near-native” cyanobacterial PSII. The ranking of site energies and the identity of the most red-shifted chlorophylls (B3, followed by B1) differ from previous hypotheses in the literature and provide an alternative basis for evaluating past approaches and semiempirically fitted sets. Given that a lot of experimental studies on CP47 and other light-harvesting complexes utilize extracted samples, we employ molecular dynamics simulations of isolated CP47 to identify which parts of the polypeptide are most destabilized and which pigments are most perturbed when the antenna complex is extracted from PSII. We demonstrate that large parts of the isolated complex rapidly refold to non-native conformations and that certain pigments (such as chlorophyll B1 and β-carotene h1) are so destabilized that they are probably lost upon extraction of CP47 from PSII. The results suggest that the properties of isolated CP47 are not representative of the native complexed antenna. The insights obtained from CP47 are generalizable, with important implications for the information content of experimental studies on biological light-harvesting antenna systems

An excited state coupled-cluster study on indigo dyes

In the present study, the domain-based pair natural orbital implementation of the similarity-transformed equation of motion method is employed to reproduce the vibrationally resolved absorption spectra of indigo dyes. After an initial investigation of multireference, basis set and implicit solvent effects, our calculated 0–0 transition energies are compared to a benchmark set of experimental absorption band maxima. It is established that the agreement between our method and experimental results is well below the desired 0.1 eV threshold in virtually all cases and that the shift in excitation energies upon chemical substitution is also well reproduced. Finally, the entire spectra of some of the main components of the Tyrian purple dye mixture are reproduced and it is found that our computed spectra match the experimental ones without an empirical shift

Hybrid functional calculations of the Al impurity in silica: Hole localization and electron paramagnetic resonance parameters

We performed first-principle calculations based on the supercell and cluster approaches to investigate the neutral Al impurity in smoky quartz. Electron paramagnetic resonance measurements suggest that the oxygens around the Al center undergo a polaronic distortion which localizes the hole being on one of the four oxygen atoms. We find that the screened exchange hybrid functional successfully describes this localization and improves on standard local density approaches or on hybrid functionals that do not include enough exact exchange such as B3LYP. We find a defect level at about 2.5 eV above the valence band maximum, corresponding to a localized hole in a O 2p orbital. The calculated values of the g tensor and the hyperfine splittings are in excellent agreement with experiment.Comment: 5 pages, 2 figures, 1 tabl

Outer-Sphere Contributions to the Electronic Structure of Type Zero Copper Proteins

Bioinorganic canon states that active-site thiolate coordination promotes rapid electron transfer (ET) to and from type 1 copper proteins. In recent work, we have found that copper ET sites in proteins also can be constructed without thiolate ligation (called “type zero” sites). Here we report multifrequency electron paramagnetic resonance (EPR), magnetic circular dichroism (MCD), and nuclear magnetic resonance (NMR) spectroscopic data together with density functional theory (DFT) and spectroscopy-oriented configuration interaction (SORCI) calculations for type zero Pseudomonas aeruginosa azurin variants. Wild-type (type 1) and type zero copper centers experience virtually identical ligand fields. Moreover, O-donor covalency is enhanced in type zero centers relative that in the C112D (type 2) protein. At the same time, N-donor covalency is reduced in a similar fashion to type 1 centers. QM/MM and SORCI calculations show that the electronic structures of type zero and type 2 are intimately linked to the orientation and coordination mode of the carboxylate ligand, which in turn is influenced by outer-sphere hydrogen bonding

A perturbative approach to multireference equation-of-motion coupled cluster

We introduce a variant of the multireference equation-of-motion coupled-cluster (MR-EOMCC) method where the amplitudes used for the similarity transformations are estimated from perturbation theory. Consequently, the new variant retains the many-body formalism, a reliance on at most two-body densities, and the state-universal character. As a non-iterative variant, computational costs are reduced, and no convergence difficulties with near-singular amplitudes can arise. Its performance was evaluated on several test sets covering transition metal atoms, small diatomics, and organic molecules against (near-)full CI quality reference data. We further highlight its efficacy on the weakly avoided crossing of LiF and place MR-EOMCC and the new variant into context with linear response theory. The accuracy of the variant was found to be at least on par with expectations for multireference perturbation theories, judging by the NEVPT2 method. The variant can be especially useful in multistate situations where the high accuracy of the iterative MR-EOMCC method is not required

Fragment-Based Local Coupled Cluster Embedding Approach for the Quantification and Analysis of Noncovalent Interactions: Exploring the Many-Body Expansion of the Local Coupled Cluster Energy

Herein, we introduce a fragment-based local coupled cluster embedding approach for the accurate quantification and analysis of noncovalent interactions in molecular aggregates. Our scheme combines two different expansions of the domain-based local pair natural orbital coupled cluster (DLPNO-CCSD(T)) energy: the many-body expansion (MBE) and the local energy decomposition (LED). The low-order terms in the MBE are initially computed in the presence of an environment that is treated at a low level of theory. Then, LED is used to decompose the energy of each term in the embedded MBE into additive fragment and fragment-pairwise contributions. This information is used to quantify the total energy of the system while providing at the same time in-depth insights into the nature and cooperativity of noncovalent interactions. Two different approaches are introduced and tested, in which the environment is treated at different levels of theory: the local coupled cluster in the Hartree–Fock (LCC-in-HF) method, in which the environment is treated at the HF level; and the electrostatically embedded local coupled cluster method (LCC-in-EE), in which the environment is replaced by point charges. Both schemes are designed to preserve as much as possible the accuracy of the parent local coupled cluster method for total energies, while being embarrassingly parallel and less memory intensive. These schemes appear to be particularly promising for the study of large and complex molecular aggregates at the coupled cluster level, such as condensed phase systems and protein–ligand interactions