Quantum-classical rate coefficient datasets of vibrational energy transfer in carbon monoxide based on highly accurate potential energy surface.

A merged potential energy surface (PES) is introduced for CO + CO collisions by combining a recent full-dimensional ab initio PES [Chen et al. J. Chem. Phys. 153, 054310 (2020)] and analytical long-range multipolar interactions. This merged PES offers a double advantage: it retains the precision of the ab initio PES in describing the van der Waals well and repulsive short range while providing an accurate physical description of long-range interaction; it significantly reduces the computational time required for trajectory integration since the long-range portion of the ab initio PES (involving numerous neural network fitting parameters) is now replaced by the analytical model potential. Based on the present merged PES, mixed Quantum-Classical (MQC) calculations, which capture quantum effects related to vibrational motion, align with a range of experimental data, including transport properties, vibrational energy transfer between CO and its isotoplogues, as well as rate coefficients for V-V and V-T/R processes. Notably, the original ab initio PES yields V-T/R rate coefficients at low temperatures that are significantly higher than the experimental data due to the artificial contribution of its unphysical long-range potential. In addition to conducting extensive MQC calculations to obtain raw data for V-V and V-T/R rate coefficients, we employ Gaussian process regression to predict processes lacking computed MQC data, thereby completing the considered V-V and V-T/R datasets. These extensive rate coefficient datasets, particularly for V-T/R processes, are unprecedented and reveal the significant role played by V-T/R processes at high temperatures, emphasizing the necessity of incorporating both V-V and V-T/R processes in the applications.

DeepGRID: Deep Learning Using GRID Descriptors for BBB Prediction.

Deep Learning approaches are able to automatically extract relevant features from the input data and capture nonlinear relationships between the input and output. In this work, we present the GRID-derived AI (GrAId) descriptors, a simple modification to GRID MIFs that facilitate their use in combination with Convolutional Neural Networks (CNNs) to build Deep Learning models in a rotationally, conformationally, and alignment-independent approach we are calling DeepGRID. To our knowledge, this is the first time that GRID MIFs have been combined with CNNs in a Deep Learning approach. We applied the approach to build regression and classification models for blood-brain barrier permeation, an important factor when designing CNS drugs and conversely when designing to avoid off-target effects for CNS-inactive drugs. The VolSurf approach was one of the first to successfully model this property from three-dimensional structures, using descriptors derived from their GRID Molecular Interaction Fields (MIFs) in combination with PLS. We compared the DeepGRID models with others built using the hand-crafted VolSurf descriptors in combination with both PLS and Random Forest (RF). Both the DeepGRID and RF regression models performed best according to the % of compounds with a Geometric Mean Fold Error (GMFE) within 2-fold of the experimental data. Applying these regression models as classifiers, for the smaller 332 and 416 compound data sets all models performed well with ROC AUC values of ∼0.9 on the external test set. For the larger 2105 compound data set, the DeepGRID classifier performed the best with an AUC of 0.87 on the external test set with the RF model having an AUC of 0.84 and the original VolSurf lgBB model having an AUC of 0.83.

Structural Reshaping of the Zinc-Finger Domain of the SARS-CoV-2 nsp13 Protein Using Bismuth(III) Ions: A Multilevel Computational Study.

The identification of novel therapeutics against the pandemic SARS-CoV-2 infection is an indispensable new address of current scientific research. In the search for anti-SARS-CoV-2 agents as alternatives to the vaccine or immune therapeutics whose efficacy naturally degrades with the occurrence of new variants, the salts of Bi3+ have been found to decrease the activity of the Zn2+-dependent non-structural protein 13 (nsp13) helicase, a key component of the SARS-CoV-2 molecular tool kit. Here, we present a multilevel computational investigation based on the articulation of DFT calculations, classical MD simulations, and MIF analyses, focused on the examination of the effects of Bi3+/Zn2+ exchange on the structure and molecular interaction features of the nsp13 protein. Our calculations confirmed that Bi3+ ions can replace Zn2+ in the zinc-finger metal centers and cause slight but appreciable structural modifications in the zinc-binding domain of nsp13. Nevertheless, by employing an in-house-developed ATOMIF tool, we evidenced that such a Bi3+/Zn2+ exchange may decrease the extension of a specific hydrophobic portion of nsp13, responsible for the interaction with the nsp12 protein. The present study provides for a detailed, atomistic insight into the potential anti-SARS-CoV-2 activity of Bi3+ and, more generally, evidences the hampering of the nsp13-nsp12 interaction as a plausible therapeutic strategy.

Combining machine learning and quantum mechanics yields more chemically aware molecular descriptors for medicinal chemistry applications.

Molecular interaction fields (MIFs), describing molecules in terms of their ability to interact with any chemical entity, are one of the most established and versatile concepts in drug discovery. Improvement of this molecular description is highly desirable for in silico drug discovery and medicinal chemistry applications. In this work, we revised a well-established molecular mechanics' force field and applied a hybrid quantum mechanics and machine learning approach to parametrize the hydrogen-bonding (HB) potentials of small molecules, improving this aspect of the molecular description. Approximately 66,000 molecules were chosen from available drug databases and subjected to density functional theory calculations (DFT). For each atom, the molecular electrostatic potential (EP) was extracted and used to derive new HB energy contributions; this was subsequently combined with a fingerprint-based description of the structural environment via partial least squares modeling, enabling the new potentials to be used for molecules outside of the training set. We demonstrate that parameter prediction for molecules outside of the training set correlates with their DFT-derived EP, and that there is correlation of the new potentials with hydrogen-bond acidity and basicity scales. We show the newly derived MIFs vary in strength for various ring substitution in accordance with chemical intuition. Finally, we report that this derived parameter, when extended to non-HB atoms, can also be used to estimate sites of reaction.

Hampering the early aggregation of PrP-E200K protein by charge-based inhibitors: a computational study.

A multilayered computational workflow was designed to identify a druggable binding site on the surface of the E200K pathogenic mutant of the human prion protein, and to investigate the effect of the binding of small molecules in the inhibition of the early aggregation of this protein. At this purpose, we developed an efficient computational tool to scan the molecular interaction properties of a whole MD trajectory, thus leading to the characterization of plausible binding regions on the surface of PrP-E200K. These structural data were then employed to drive structure-based virtual screening and fragment-based approaches to the seeking of small molecular binders of the PrP-E200K. Six promising compounds were identified, and their binding stabilities were assessed by MD simulations. Therefore, analyses of the molecular electrostatic potential similarity between the bound complexes and unbound protein evidenced their potential activity as charged-based inhibitors of the PrP-E200K early aggregation.

Characterization of PD-L1 binding sites by a combined FMO/GRID-DRY approach.

The programmed cell death protein 1 (PD-1) and its ligand, PD-L1, constitute an important co-inhibitory immune checkpoint leading to downregulation of immune system. Tumor cells developed a strategy to trigger PD-1/PD-L1 pathway reducing the T cell anticancer activity. Anti-PD-L1 small drugs, generally with improved pharmacokinetic and technological profiles than monoclonal antibodies, became an attractive research topic. Nevertheless, still few works have been published on the chemical features of possible binding sites. In this work, we applied a novel computational protocol based on the combination of the ab initio Fragment Molecular Orbital (FMO) method and a newly developed GRID-DRY approach in order to characterize the PD-L1 binding sites, starting from PD-1/PD-L1 and PD-L1/BMS-ligands (Bristol-Mayers Squibb ligands) complexes. The FMO method allows the calculation of the pair-residues as well as the ligand-residues interactions with ab initio accuracy, whereas the GRID-DRY approach is an effective tool to investigate hydrophobic interactions, not easily detectable by ab initio methods. The present GRID-DRY protocol is able to determine the energy contributions of each ligand atoms to each hydrophobic interaction, both qualitatively and quantitatively. We were also able to identify the three specific hot regions involved in PD-1/PD-L1 protein-protein interaction and in PD-L1/BMS-ligand interactions, in agreement with preceding theoretical/experimental results, and to suggest a specific pharmacophore for PD-L1 inhibitors.

Spin-orbit coupling is the key to unraveling intriguing features of the halogen bond involving astatine.

The effect of spin-orbit coupling (SOC) on the halogen bond involving astatine has been investigated using state-of-the-art two- and four-component relativistic calculations. Adducts between Cl-X (X = Cl, Br, I and At) and ammonia have been selected to establish a trend on going down the periodic table. The SOC influence has been explored not only on the geometric and energetic features that can be used to characterize the halogen bond strength but also on the three main contributions to it that are the charge transfer, the "σ-hole" (i.e. the localized region with a net positive electrostatic potential at the halogen site) and the "polar flattening" (which is related to the effective shape of the halogen site). A surprisingly large increase of the Cl-At dipole moment, due to the inclusion of SOC, has been worked out using four-component CCSD(T) reference calculations, indicating that this bond is significantly more ionic than one may predict. Due to the SOC effect, which induces a peculiar charge accumulation on the At side in the Cl-At dimer, a weakening of the astatine-mediated halogen bond occurs arising from the (i) reduced amount of charge transfer, (ii) decrease of the polar flattening and (iii) lowering of the short-range Coulomb potential. The analysis of the electronic structure of the Cl-At moiety allows for a rationalization of the SOC effects on all the considered features of the halogen bond, including an unprecedented unsymmetrical charge back-donation from Cl-At to ammonia.

BERTHA: Implementation of a four-component Dirac-Kohn-Sham relativistic framework.

In this paper, we present and review the most recent computational advances in the BERTHA code. BERTHA can be regarded as the state of the art in fully relativistic four-component Dirac-Kohn-Sham (DKS) software. Thanks to the implementation of various parallelization and memory open-ended distribution schemes in combination with efficient "density fitting" algorithms, it greatly reduces the computational burden of four-component DKS calculations. We also report the newly developed OpenMP version of the code, that, together with the berthmod Python module, provides a significant leap forward in terms of usability and applicability of the BERTHA software. Some applications of the recently developed natural orbitals for chemical valence/charge displacement bonding analysis and the real-time time dependent DKS implementation are also reported.

An insight of early PrP-E200K aggregation by combined molecular dynamics/fragment molecular orbital approaches.

Unveiling the events leading to the formation of prion particles is a nowadays challenge in the field of neurochemistry. Pathogenic mutants of prion protein (PrP) are characterized by both an intrinsic tendency to aggregation and scrapie conversion propensity. However, the question about a possible correlation between these two events lasts still unanswered. Here, a multilayered computational workflow was employed to investigate structure, stability, and molecular interaction properties of a dimer of PrPC -E200K, a well-known mutant of the PrP that represents a reduced model of early aggregates of this protein. Based on the combination of molecular dynamics and quantum mechanical approaches, this study provided for an in depth insight of PrPC -E200K dimer in terms of residue-residue interactions. Assembly hypotheses for the early aggregation of PrPC -E200K are paved and compared with PrPSc models reported in the literature to find a structural link between early and late (scrapie) aggregates of this protein.

The Chemical Bond and s-d Hybridization in Coinage Metal(I) Cyanides.

We present a four-component relativistic density functional theory study of the chemical bond and s-d hybridization in the group 11 cyanides M-CN (M = Cu, Ag, and Au). The analysis is carried out within the charge-displacement/natural orbital for chemical valence (CD-NOCV) scheme, which allows us to single out meaningful contributions to the total charge rearrangement that arises upon bond formation and to quantify the components of the Dewar-Chatt-Duncanson bonding model (the ligand-to-metal donation and metal-to-ligand back-donation). The M-CN bond is characterized by a large donation from the cyanide ion to the metal cation and by two small back-donation components from the metal toward the cyanide anion. The case of gold cyanide elucidates the peculiar role of the relativistic effects in determining the characteristics of the Au-C bond with respect to the copper and silver homologues. In AuCN, the donation and back-donation components are significantly enhanced, and the spin-orbit coupling, removing the degeneracy of the 5d atomic orbitals, induces a substantial split in the back-donation components. A simple spatial analysis of the NOCV-pair density, related to the ligand-to-metal donation component, allows us to quantify, with unprecedented accuracy, the charge rearrangement due to the s-d hybridization occurring at the metal site. The s-d hybridization plays a key role in determining the shape and size of the metal; it removes electron density from the bond axis and induces a significant flattening at the metal site in the position trans to the ligand. The s-d hybridization is present in all noble metal complexes, influencing the bond distances, and its effect is enhanced for Au, which is consistent with the preference of gold to form linear complexes. A comparative investigation of simple complexes [AuL]+/0 of Au+ with different ligands (L = F-, N-heterocyclic carbene, CO, and PH3) shows that the s-d hybridization mechanism is also influenced by the nature of the ligand.

Investigation of the molecular similarity in closely related protein systems: The PrP case study.

The amyloid conversion is a massive detrimental modification affecting several proteins upon specific physical or chemical stimuli characterizing a plethora of diseases. In many cases, the amyloidogenic stimuli induce specific structural features to the protein conferring the propensity to misfold and form amyloid deposits. The investigation of mutants, structurally similar to their native isoform but inherently prone to amyloid conversion, may be a viable strategy to elucidate the structural features connected with amyloidogenesis. In this article, we present a computational protocol based on the combination of molecular dynamics (MD) and grid-based approaches suited for the pairwise comparison of closely related protein structures. This method was applied on the cellular prion protein (PrP(C)) as a case study and, in particular, addressed to the quali/quantification of the structural features conferred by either E200K mutations and treatment with CaCl(2), both able to induce the scrapie conversion of PrP. Several schemes of comparison were developed and applied to this case study, and made up suitable of application to other protein systems. At this purpose an in-house python codes has been implemented that, together with the parallelization of the GRID force fields program, will spread the applicability of the proposed computational procedure.

Gold-superheavy-element interaction in diatomics and cluster adducts: A combined four-component Dirac-Kohn-Sham/charge-displacement study.

The chemistry of superheavy elements (Z ≥ 104) is actively investigated in atom-at-a-time experiments of volatility through adsorption on gold surfaces. In this context, common guidelines for interpretation based on group trends in the periodic table should be used cautiously, because relativistic effects play a central role and may cause predictions to fall short. In this paper, we present an all-electron four-component Dirac-Kohn-Sham comparative study of the interaction of gold with Cn (Z = 112), Fl (Z = 114), and Uuo (Z = 118) versus their lighter homologues of the 6th period, Hg, Pb, and Rn plus the noble gas Xe. Calculations were carried out for Au-E (E = Hg, Cn, Pb, Fl, Xe, Rn, Uuo), Au7- and Au20-E (E = Hg, Cn, Pb, Fl, Rn) complexes, where Au7 (planar) and Au20 (pyramidal) are experimentally determined clusters having structures of increasing complexity. Results are analysed both in terms of the energetics of the complexes and of the electron charge rearrangement accompanying their formation. In line with the available experimental data, Cn and more markedly Fl are found to be less reactive than their lighter homologues. On the contrary, Uuo is found to be more reactive than Rn and Xe. Cn forms the weakest bond with the gold atom, compared to Fl and Uuo. The reactivity of Fl decreases with increasing gold-fragment size more rapidly than that of Cn and, as a consequence, the order of the reactivity of these two elements is inverted upon reaching the Au20-cluster adduct. Density difference maps between adducts and fragments reveal similarities in the behaviour of Cn and Xe, and in that of Uuo and the more reactive species Hg and Pb. These findings are given a quantitative ground via charge-displacement analysis.

Improved Quantum-Classical Treatment of N2-N2 Inelastic Collisions: Effect of the Potentials and Complete Rate Coefficient Data Sets.

In this study, complete (i.e., including all vibrational quantum numbers in an N2 vibrational ladder) data sets of vibration-to-vibration and vibration-to-translation rate coefficients for N2-N2 collisions are explicitly computed along with transport properties (shear and bulk viscosity, thermal conductivity, and self-diffusion) in the temperature range 100-9000 K. To reach this goal, we improved a mixed quantum-classical (MQC) dynamics approach by lifting the constraint of a Morse treatment of the vibrational wave function and intramolecular potential and permitting the use of more realistic and flexible representations. The new formulation has also allowed us to separately analyze the role of intra- and intermolecular potentials on the calculated rates and properties. Ab initio intramolecular potentials are indispensable for highly excited vibrational states, though the Morse potential still gives reasonable values up to v = 20. An accurate description of the long-range interaction and the van der Waals well is a requisite for the correct reproduction of qualitative and quantitative rate coefficients, particularly at low temperatures, making physically meaningful analytical representations still the best choice compared to currently available ab initio potential energy surfaces. These settings were used to directly compute the MQC rates corresponding to a large number of initial vibrational quantum numbers, and the missing intermediate values were predicted using a machine learning technique (i.e., the Gaussian process regression approach). The obtained values are reliable in the wide temperature range employed and are therefore valuable data for many communities dealing with nonlocal thermal equilibrium conditions in different environments.

Homodimeric complexes of the 90-231 human prion: a multilayered computational study based on FMO/GRID-DRY approach.

The molecular interaction properties and aggregation capabilities disclosed by PrP-E200K, a pathogenic mutant of the human prion protein, were investigated in detail using multilayered computational approaches. In a previous work, we reported that the electrostatic complementarity between region1 (negative) and region3 (positive) has been assumed to lead to a head-to tail interaction between 120 and 231 PrP-E200K units and to initiation of the aggregation process. In this work, we extended the PrP-E200K structure by including the unstructured 90-120 segment which was found to assume different conformations. Plausible models of 90-231 PrP-E200K dimers were calculated and analyzed in depth to identify the nature of the involved protein-protein interactions. The unstructured 90-120 segment was found to extend the positively charged region3 involved in the association of PrP-E200K units which resulted to be driven by hydrophobic interactions. The combination of molecular dynamics, protein-protein docking, grid-based mapping, and fragment molecular orbital approaches allowed us to provide a plausible mechanism of the early state of 90-231 PrP-E200K aggregation, considered a preliminary step of amyloid conversion.

Frozen-Density Embedding for Including Environmental Effects in the Dirac-Kohn-Sham Theory: An Implementation Based on Density Fitting and Prototyping Techniques.

Frozen density embedding (FDE) represents an embedding scheme in which environmental effects are included from first-principles calculations by considering the surrounding system explicitly by means of its electron density. In the present paper, we extend the full four-component relativistic Dirac-Kohn-Sham (DKS) method, as implemented in the BERTHA code, to include environmental and confinement effects with the FDE scheme (DKS-in-DFT FDE). The implementation, based on the auxiliary density fitting techniques, has been enormously facilitated by BERTHA's python API (PyBERTHA), which facilitates the interoperability with other FDE implementations available through the PyADF framework. The accuracy and numerical stability of this new implementation, also using different auxiliary fitting basis sets, has been demonstrated on the simple NH3-H2O system, in comparison with a reference nonrelativistic implementation. The computational performance has been evaluated on a series of gold clusters (Aun, with n = 2, 4, 8) embedded into an increasing number of water molecules (5, 10, 20, 40, and 80 water molecules). We found that the procedure scales approximately linearly both with the size of the frozen surrounding environment (consistent with the underpinnings of the FDE approach) and with the size of the active system (in line with the use of density fitting). Finally, we applied the code to a series of heavy (Rn) and super-heavy elements (Cn, Fl, Og) embedded in a C60 cage to explore the confinement effect induced by C60 on their electronic structure. We compare the results from our simulations, with respect to more-approximate models employed in the atomic physics literature. Our results indicate that the specific interactions described by FDE are able to improve upon the cruder approximations currently employed, and, thus, they provide a basis from which to generate more-realistic radial potentials for confined atoms.

Recent advances and perspectives in four-component Dirac-Kohn-Sham calculations.

We review recent theoretical and computational advances in the full relativistic four-component Dirac-Kohn-Sham (DKS) approach and its application to the calculation of the electronic structure of chemical systems containing many heavy atoms. We describe our implementation of an all-electron DKS approach based on the use of G-spinor basis sets, Hermite Gaussian functions, state-of-the-art density-fitting techniques and memory distributed parallelism. This approach has enormously extended the applicability of the DKS method, including for example large clusters of heavy atoms, and opens the way for future key developments. We examine the current limitations and future possible applications of the DKS approach, including the implementation of four-current density functionals and real-time propagation schemes. This would make possible to describe molecules in strong fields, accurately accounting for relativistic kinematic effects and spin-orbit coupling.

Reactivity of antitumor coinage metal-based N-heterocyclic carbene complexes with cysteine and selenocysteine protein sites.

The reaction of the antitumor M(I)-bis-N-heterocyclic carbene (M(I)-NHC) complexes, M = Cu, Ag, and Au, with their potential protein binding sites, i.e. cysteine and selenocysteine, was investigated by means of density functional theory approaches. Capped cysteine and selenocysteine were employed to better model the corresponding residues environment within peptide structures. By assuming the neutral or deprotonated form of the side chains of these amino acids and by considering the possible assistance of an external proton donor such as an adjacent acidic residue or the acidic component of the surrounding buffer environment, we devised five possible routes leading to the binding of the investigated M(I)-NHC scaffolds to these protein sites, reflecting their different location in the protein structure and exposure to the bulk. The targeting of either cysteine or selenocysteine in their neutral forms is a kinetically unfavored process, expected to be quite slow if observable at all at physiological temperature. On the other hand, the reaction with the deprotonated forms is much more favored, even though an external proton source is required to assist the protonation of the leaving carbene. Our calculations also show that all coinage metals are characterized by a similar reactivity toward the binding of cysteine and selenocysteine sites, although the Au(I) complex has significantly higher reaction and activation free energies compared to Cu(I) and Ag(I).

PyBERTHART: A Relativistic Real-Time Four-Component TDDFT Implementation Using Prototyping Techniques Based on Python.

We present a real-time time-dependent four-component Dirac-Kohn-Sham (RT-TDDKS) implementation based on the BERTHA code. This new implementation takes advantage of modern software engineering, including the prototyping techniques. The software design follows a three step approach: (i) the prototype implementation of a time-propagation algorithm in nonrelativistic real-time TDDFT within the Psi4NumPy framework, which provides a suitable environment for the creation of a clear, readable, and easy to test reference code in Python, (ii) the design of an original Python application programming interface for the relativistic four-component code BERTHA (PyBERTHA), which has an efficient computational kernel for relativistic integrals written in FORTRAN, and (iii) the porting of the time-propagation scheme enveloped within the Psi4NumPy framework to PyBERTHA. The propagation scheme consequently resides in a single readable Python computer code that is easy to maintain and in which the key quantities, such as the Dirac-Kohn-Sham and dipole matrices, can be accessed directly from the PyBERTHA module. For linear algebra operations (matrix-matrix multiplications and diagonalization) we use the highly optimized procedures implemented in the popular NumPy library. The overhead introduced by the Python interface to BERTHA is almost negligible (less than 1% evaluated on the SCF procedure), and the interoperability between different programming languages (FORTRAN, C, and Python) does not affect the numerical stability of the time-propagation scheme. Our new RT-TDDKS implementation has been employed to investigate the stability of the time-propagation procedure in combination with a density-fitting algorithm (both for the Coulomb and for the exchange-correlation matrix construction), which are employed in BERTHA to speed up the Dirac-Kohn-Sham matrix evaluation. On the basis of systematic calculations, employing several density-fitting basis sets of increasing accuracy, we showed that quantitative agreement can be achieved in combination with extended-fitting basis sets, with an error in the Coulomb energy below 1 µ-hartree. Convergence of the transition energies increasing of quality of the fitting basis sets has been also observed. Our data suggest that the error in the Coulomb energy may also represent a good estimate of the fitting basis set quality for real-time electron dynamics simulations. Further, we study the applicability of the RT-TDDKS method in combination with both weak- and extreme strong-field regime. Numerical results of excited-state transitions for the Group 12 atoms are reported and compared with a previous real-time Dirac-Kohn-Sham implementation (Repisky et al. J. Chem. Theory Comput. 2015, 11, 980-991). Finally, calculations of high harmonic generation in the hydrogen molecule and Au dimer have been also carried out. We were able to generate high harmonics with relatively well-defined peaks up to the 21st and 13th order in the case of H2 and Au2, respectively. Our findings show that the four-component structure of the Dirac-Kohn-Sham Hamiltonian provides a suitable theoretical framework, with no intrinsic unfavorable features, to study molecules in the strong-field regime.

The Role of APOSTART in Switching between Sexuality and Apomixis in Poa pratensis.

The production of seeds without sex is considered the holy grail of plant biology. The transfer of apomixis to various crop species has the potential to transform plant breeding, since it will allow new varieties to retain valuable traits thorough asexual reproduction. Therefore, a greater molecular understanding of apomixis is fundamental. In a previous work we identified a gene, namely APOSTART, that seemed to be involved in this asexual mode of reproduction, which is very common in Poa pratensis L., and here we present a detailed work aimed at clarifying its role in apomixis. In situ hybridization showed that PpAPOSTART is expressed in reproductive tissues from pre-meiosis to embryo development. Interestingly, it is expressed early in few nucellar cells of apomictic individuals possibly switching from a somatic to a reproductive cell as in aposporic apomixis. Moreover, out of 13 APOSTART members, we identified one, APOSTART_6, as specifically expressed in flower tissue. APOSTART_6 also exhibited delayed expression in apomictic genotypes when compared with sexual types. Most importantly, the SCAR (Sequence Characterized Amplified Region) derived from the APOSTART_6 sequence completely co-segregated with apomixis.

Environmental Effects with Frozen-Density Embedding in Real-Time Time-Dependent Density Functional Theory Using Localized Basis Functions.

Frozen-density embedding (FDE) represents a versatile embedding scheme to describe the environmental effect on electron dynamics in molecular systems. The extension of the general theory of FDE to the real-time time-dependent Kohn-Sham method has previously been presented and implemented in plane waves and periodic boundary conditions [Pavanello, M.; J. Chem. Phys. 2015, 142, 154116]. In the current paper, we extend our recent formulation of the real-time time-dependent Kohn-Sham method based on localized basis set functions and developed within the Psi4NumPy framework to the FDE scheme. The latter has been implemented in its "uncoupled" flavor (in which the time evolution is only carried out for the active subsystem, while the environment subsystems remain at their ground state), using and adapting the FDE implementation already available in the PyEmbed module of the scripting framework PyADF. The implementation was facilitated by the fact that both Psi4NumPy and PyADF, being native Python API, provided an ideal framework of development using the Python advantages in terms of code readability and reusability. We employed this new implementation to investigate the stability of the time-propagation procedure, which is based on an efficient predictor/corrector second-order midpoint Magnus propagator employing an exact diagonalization, in combination with the FDE scheme. We demonstrate that the inclusion of the FDE potential does not introduce any numerical instability in time propagation of the density matrix of the active subsystem, and in the limit of the weak external field, the numerical results for low-lying transition energies are consistent with those obtained using the reference FDE calculations based on the linear-response TDDFT. The method is found to give stable numerical results also in the presence of a strong external field inducing nonlinear effects. Preliminary results are reported for high harmonic generation (HHG) of a water molecule embedded in a small water cluster. The effect of the embedding potential is evident in the HHG spectrum reducing the number of the well-resolved high harmonics at high energy with respect to the free water. This is consistent with a shift toward lower ionization energy passing from an isolated water molecule to a small water cluster. The computational burden for the propagation step increases approximately linearly with the size of the surrounding frozen environment. Furthermore, we have also shown that the updating frequency of the embedding potential may be significantly reduced, much less than one per time step, without jeopardizing the accuracy of the transition energies.