Optical study of Te8 ring clusters: comparison with density functional theory and a step towards materials design using nanoporous zeolite space.

The Te8 ring molecule (cluster) is poorly investigated due to the lack of experimental data. Here, we report an experimental and theoretical study of a regular array of oriented Te8 rings formed in the ∼1.14 nm diameter cavities of zeolite LTA, which are arranged in a cubic lattice with a spacing of ∼1.2 nm. Single crystals of LTA with encapsulated tellurium (LTA-Te) were studied using Raman spectroscopy (RS) and optical absorption spectroscopy (OAS). The experimental LTA-Te spectra were found to be in agreement with those calculated using density functional theory (PBE0 hybrid functional and def2-TZVP basis sets) for the crown-shaped Te8 ring molecule with D4d symmetry. Using polarization-orientation RS, we show that the Te8 rings are oriented by their major axes along the 4-fold axes of cubic LTA. We also show that the site symmetry of Te8 in LTA-Te is lower than D4d. Te8 bond-bending modes are well described in the harmonic approximation, while bond-stretching modes are mixed due to the reduced ring symmetry and, probably, anharmonicity. Importantly, OAS data of LTA-Te display dependence on the Te8 concentration, implying the interaction of the rings from neighbouring LTA cavities with the generation of the valence and conduction electron bands of such a cluster crystal.

Natural determinant reference functional theory.

The natural determinant reference (NDR) or principal natural determinant is the Slater determinant comprised of the N most strongly occupied natural orbitals of an N-electron state of interest. Unlike the Kohn-Sham (KS) determinant, which yields the exact ground-state density, the NDR only yields the best idempotent approximation to the interacting one-particle reduced density matrix, but it is well-defined in common atom-centered basis sets and is representation-invariant. We show that the under-determination problem of prior attempts to define a ground-state energy functional of the NDR is overcome in a grand-canonical ensemble framework at the zero-temperature limit. The resulting grand potential functional of the NDR ensemble affords the variational determination of the ground state energy, its NDR (ensemble), and select ionization potentials and electron affinities. The NDR functional theory can be viewed as an "exactification" of orbital optimization and empirical generalized KS methods. NDR functionals depending on the noninteracting Hamiltonian do not require troublesome KS-inversion or optimized effective potentials.

A DFT perspective on organometallic lanthanide chemistry.

Computational studies of the coordination chemistry and bonding of lanthanides have grown in recent decades as the need for understanding the distinct physical, optical, and magnetic properties of these compounds increased. Density functional theory (DFT) methods offer a favorable balance of computational cost and accuracy in lanthanide chemistry and have helped to advance the discovery of novel oxidation states and electronic configurations. This Frontier article examines the scope and limitations of DFT in interpreting structural and spectroscopic data of low-valent lanthanide complexes, elucidating periodic trends, and predicting their properties and reactivity, presented through selected examples.

TURBOMOLE: Today and Tomorrow.

TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

Constructing the Mechanism of Dinoflagellate Luciferin Bioluminescence Using Computation.

Dinoflagellate luciferin bioluminescence is unique since it does not rely on decarboxylation but is poorly understood compared to that of firefly, bacteria, and coelenterata luciferins. Here we computationally investigate possible protonation states, stereoisomers, a chemical mechanism, and the dynamics of the bioluminescence intermediate that is responsible for chemiexcitation. Using semiempirical dynamics, time-dependent density functional theory static calculations, and a correlation diagram, we find that the intermediate's functional group that is likely responsible for chemiexcitation is a 4-member ring, a dioxetanol, that undergoes [2π + 2π] cycloreversion and the biolumiphore is the cleaved structure. The simulated emission spectra and luciferase-dependent absorbance spectra agree with the experimental data, giving support to our proposed mechanism and biolumiphore. We also compute circular dichroism spectra of the intermediate's four stereoisomers to guide future experiments in differentiating them.

Statistics and Bias-Free Sampling of Reaction Mechanisms from Reaction Network Models.

Selection bias is inevitable in manually curated computational reaction databases but can have a significant impact on generalizability of quantum chemical methods and machine learning models derived from these data sets. Here, we propose quasireaction subgraphs as a discrete, graph-based representation of reaction mechanisms that has a well-defined associated probability space and admits a similarity function using graph kernels. Quasireaction subgraphs are thus well suited for constructing representative or diverse data sets of reactions. Quasireaction subgraphs are defined as subgraphs of a network of formal bond breaks and bond formations (transition network) composed of all shortest paths between reactant and product nodes. However, due to their purely geometric construction, they do not guarantee that the corresponding reaction mechanisms are thermodynamically and kinetically feasible. As a result, a binary classification of feasible (reaction subgraphs) and infeasible (nonreactive subgraphs) must be applied after sampling. In this paper, we describe the construction and properties of quasireaction subgraphs and characterize the statistics of quasireaction subgraphs from CHO transition networks with up to six non-hydrogen atoms. We explore their clustering using Weisfeiler-Lehman graph kernels.

Implementation of the self-consistent phonons method with ab initio potentials (AI-SCP).

The self-consistent phonon (SCP) method allows one to include anharmonic effects when treating a many-body quantum system at thermal equilibrium. The system is then described by an effective temperature-dependent harmonic Hamiltonian, which can be used to estimate its various dynamic and static properties. In this paper, we combine SCP with ab initio (AI) potential energy evaluation in which case the numerical bottleneck of AI-SCP is the evaluation of Gaussian averages of the AI potential energy and its derivatives. These averages are computed efficiently by the quasi-Monte Carlo method utilizing low-discrepancy sequences leading to a fast convergence with respect to the number, S, of the AI energy evaluations. Moreover, a further substantial (an-order-of-magnitude) improvement in efficiency is achieved once a numerically cheap approximation of the AI potential is available. This is based on using a perturbation theory-like (the two-grid) approach in which it is the average of the difference between the AI and the approximate potential that is computed. The corresponding codes and scripts are provided.

Enzyme Substrate Prediction from Three-Dimensional Feature Representations Using Space-Filling Curves.

Compact and interpretable structural feature representations are required for accurately predicting properties and function of proteins. In this work, we construct and evaluate three-dimensional feature representations of protein structures based on space-filling curves (SFCs). We focus on the problem of enzyme substrate prediction, using two ubiquitous enzyme families as case studies: the short-chain dehydrogenase/reductases (SDRs) and the S-adenosylmethionine-dependent methyltransferases (SAM-MTases). Space-filling curves such as the Hilbert curve and the Morton curve generate a reversible mapping from discretized three-dimensional to one-dimensional representations and thus help to encode three-dimensional molecular structures in a system-independent way and with only a few adjustable parameters. Using three-dimensional structures of SDRs and SAM-MTases generated using AlphaFold2, we assess the performance of the SFC-based feature representations in predictions on a new benchmark database of enzyme classification tasks including their cofactor and substrate selectivity. Gradient-boosted tree classifiers yield binary prediction accuracy of 0.77-0.91 and area under curve (AUC) characteristics of 0.83-0.92 for the classification tasks. We investigate the effects of amino acid encoding, spatial orientation, and (the few) parameters of SFC-based encodings on the accuracy of the predictions. Our results suggest that geometry-based approaches such as SFCs are promising for generating protein structural representations and are complementary to the existing protein feature representations such as evolutionary scale modeling (ESM) sequence embeddings.

Libkrylov: A modular open-source software library for extremely large on-the-fly matrix computations.

We present the design and implementation of libkrylov, an open-source library for solving matrix-free eigenvalue, linear, and shifted linear equations using Krylov subspace methods. The primary objectives of libkrylov are flexible API design and modular structure, which enables integration with specialized matrix-vector evaluation "engines." Libkrylov features pluggable preconditioning, orthonormalization, and tunable convergence control. Diagonal (conjugate gradient, CG), Davidson, and Jacobi-Davidson preconditioners are available, along with orthonormal and nonorthonormal (nKs) schemes. All functionality of libkrylov is exposed via Fortran and C application programming interfaces (APIs). We illustrate the performance of libkrylov for eigenvalue calculations arising in time-dependent density functional theory (TDDFT) in the Tamm-Dancoff approximation (TDA) and discuss the convergence behavior as a function of preconditioning and orthonormalization methods.

Solid-State End-On to Side-On Isomerization of (N═N)2- in {[(R2N)3Nd]2N2}2- (R = SiMe3) Connects In Situ LnIII(NR2)3/K and Isolated [LnII(NR2)3]1- Dinitrogen Reduction.

Examination of the reduction chemistry of Nd(NR2)3 (R = SiMe3) under N2 has provided connections between the in situ Ln(III)-based LnIII(NR2)3/K reductions of N2 that form side-on bound neutral (N=N)2- complexes, [(R2N)2(THF)Ln]2[µ-η2:η2-N2], and the Ln(II)-based [LnII(NR2)3]1- reductions by Sc, Gd, and Tb that form end-on bound (N=N)2- complexes, {[(R2N)3Ln]2[µ-η1:η1-N2]}2-, which are dianions. The reduction of Nd(NR2)3 by KC8 under dinitrogen in Et2O in the presence of 18-crown-6 (18-c-6) forms dark yellow solutions of [K2(18-c-6)3]{[(R2N)3Nd]2N2} at low temperatures that become green as they warm up to -35 °C in a glovebox freezer. Green crystals obtained from the solution turn yellow-brown when cooled below -100 °C, and the yellow-brown compound has an end-on Nd2(µ-η1:η1-N2) structure. The yellow-brown crystals isomerize in the solid state on the diffractometer upon warming, and at -25 °C, the crystals are green and have a side-on Nd2(µ-η2:η2-N2) structure. Collection of X-ray diffraction data at 10 °C intervals from -50 to -90 °C revealed that the isomerization occurs at temperatures below -100 °C. In the presence of tetrahydrofuran (THF), the dianionic {[(R2N)3Nd]2N2}2- system can lose an amide ligand to provide the monoanionic [(R2N)3NdIII(µ-η2:η2-N2)NdIII(NR2)2(THF)]1-, characterized by X-ray crystallography. These data suggest a connection between the in situ Ln(III)/K reductions and Ln(II) reductions that depends on solvent, temperature, the presence of a chelate, and the specific rare-earth metal.

Property-optimized Gaussian basis sets for lanthanides.

Property-optimized Gaussian basis sets of split-valence, triple-zeta valence, and quadruple-zeta valence quality are developed for the lanthanides Ce-Lu for use with small-core relativistic effective core potentials. They are constructed in a systematic fashion by augmenting def2 orbital basis sets with diffuse basis functions and minimizing negative static isotropic polarizabilities of lanthanide atoms with respect to basis set exponents within the unrestricted Hartree-Fock method. The basis set quality is assessed using a test set of 70 molecules containing the lanthanides in their common oxidation states and f electron occupations. 5d orbital occupation turns out to be the determining factor for the basis set convergence of polarizabilities in lanthanide atoms and the molecular test set. Therefore, two series of property-optimized basis sets are defined. The augmented def2-SVPD, def2-TZVPPD, and def2-QZVPPD basis sets balance the accuracy of polarizabilities across lanthanide oxidation states. The relative errors in atomic and molecular polarizability calculations are ≤8% for augmented split-valence basis sets, ≤ 2.5% for augmented triple-zeta valence basis sets, and ≤1% for augmented quadruple-zeta valence basis sets. In addition, extended def2-TZVPPDD and def2-QZVPPDD are provided for accurate calculations of lanthanide atoms and neutral clusters. The property-optimized basis sets developed in this work are shown to accurately reproduce electronic absorption spectra of a series of LnCp3 '- complexes (Cp' = C5H4SiMe3, Ln = Ce-Nd, Sm) with time-dependent density functional theory.

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.

Predicting Feasible Organic Reaction Pathways Using Heuristically Aided Quantum Chemistry.

Studying organic reaction mechanisms using quantum chemical methods requires from the researcher an extensive knowledge of both organic chemistry and first-principles computation. The need for empirical knowledge arises because any reasonably complete exploration of the potential energy surfaces (PES) of organic reactions is computationally prohibitive. We have previously introduced the heuristically-aided quantum chemistry (HAQC) approach to modeling complex chemical reactions, which abstracts the empirical knowledge in terms of chemical heuristics-simple rules guiding the PES exploration-and combines them with structure optimizations using quantum chemical methods. The HAQC approach makes use of heuristic kinetic criteria for selecting reaction paths that are not only plausible, that is, consistent with the empirical rules of organic reactivity, but also feasible under the reaction conditions. In this work, we develop heuristic kinetic feasibility criteria, which correctly predict feasible reaction pathways for a wide range of simple polar (substitutions, additions, and eliminations) and pericyclic organic reactions (cyclizations, sigmatropic shifts, and cycloadditions). In contrast to knowledge-based reaction mechanism prediction methods, the same kinetic heuristics are successful in classifying reaction pathways as feasible or infeasible across this diverse set of reaction mechanisms. We discuss the energy profiles of HAQC and their potential applications in machine learning of chemical reactivity.

Charge Transport through Self-Assembled Monolayers of Monoterpenoids.

The nature of the processes at the origin of life that selected specific classes of molecules for broad incorporation into cells is controversial. Among those classes selected were polyisoprenoids and their derivatives. This paper tests the hypothesis that polyisoprenoids were early contributors to membranes in part because they (or their derivatives) could facilitate charge transport by quantum tunneling. It measures charge transport across self-assembled monolayers (SAMs) of carboxyl-terminated monoterpenoids (O2 C(C9 HX)) and alkanoates (O2 C(C7 HX)) with different degrees of unsaturation, supported on silver (AgTS ) bottom electrodes, with Ga2 O3 /EGaIn top electrodes. Measurements of current density of SAMs of linear length-matched hydrocarbons-both saturated and unsaturated-show that completely unsaturated molecules transport charge faster than those that are completely saturated by approximately a factor of ten. This increase in relative rates of charge transport correlates with the number of carbon-carbon double bonds, but not with the extent of conjugation. These results suggest that polyisoprenoids-even fully unsaturated-are not sufficiently good tunneling conductors for their conductivity to have favored them as building blocks in the prebiotic world.

Reaction Networks and the Metric Structure of Chemical Space(s).

In this paper, we develop a formal definition of chemical space as a discrete metric space of molecules and analyze its properties. To this end, we utilize the shortest path metric on reaction networks to define a distance function between molecules of the same stoichiometry (number of atoms). The distance between molecules with different stoichiometries is formalized by making use of the partial ordering of stoichiometries with respect to inclusion. Calculations of fractal dimension on metric spaces for individual stoichiometries show that they have low intrinsic dimensionality, about an order of magnitude less than the dimension of the underlying reactive potential energy surface. Our findings suggest that efficient search strategies on chemical space can be designed that take advantage of its metric structure.

Excitonics: A Set of Gates for Molecular Exciton Processing and Signaling.

Regulating energy transfer pathways through materials is a central goal of nanotechnology, as a greater degree of control is crucial for developing sensing, spectroscopy, microscopy, and computing applications. Such control necessitates a toolbox of actuation methods that can direct energy transfer based on user input. Here we introduce a proposal for a molecular exciton gate, analogous to a traditional transistor, for regulating exciton flow in chromophoric systems. The gate may be activated with an input of light or an input flow of excitons. Our proposal relies on excitation migration via the second excited singlet (S2) state of the gate molecule. It exhibits the following features, only a subset of which are present in previous exciton switching schemes: picosecond time scale actuation, amplification/gain behavior, and a lack of molecular rearrangement. We demonstrate that the device can be used to produce universal binary logic or amplification of an exciton current, providing an excitonic platform with several potential uses, including signal processing for microscopy and spectroscopy methods that implement tunable exciton flux.

Quadratic Response Properties from TDDFT: Trials and Tribulations.

We report on the efficient turbomole implementation of quadratic response properties within the time-dependent density functional theory (TDDFT) context that includes the static and dynamic dipole hyperpolarizability, ground-to-excited-state two-photon absorption amplitudes (through a single residue) and state-to-state one-photon absorption amplitudes (through a double residue). Our implementation makes full use of arbitrary (including non-Abelian) point-group symmetry as well as permutational symmetry and enables the calculation of nonlinear properties with hybrid density functionals for molecules with hundreds of atoms and thousands of basis functions at a cost that is a fixed multiple of the cost of the corresponding linear properties. Using the PBE0 hybrid density functional, we show that excited-state absorption spectra computed within the pseudowavefunction approach contain the qualitative features of transient absorption spectra tracking excimer formation in perylene diimide dimers, two-photon absorption cross sections for a series of highly twisted fused porphyrin chains are semiquantitatively reproduced, and the computed dynamic hyperpolarizability of several calix[4]arene stereoisomers yield simulated hyper-Raleigh scattering signals consistent with experiment. In addition, we show that the incorrect pole structure of adiabatic TDDFT properties can cause incorrect excited-state absorption spectra and overly resonant hyperpolarizabilities, and discuss possible remedies.

Anomalously Rapid Tunneling: Charge Transport across Self-Assembled Monolayers of Oligo(ethylene glycol).

This paper describes charge transport by tunneling across self-assembled monolayers (SAMs) of thiol-terminated derivatives of oligo(ethylene glycol) (HS(CH2CH2O)nCH3; HS(EG)nCH3); these SAMs are positioned between gold bottom electrodes and Ga2O3/EGaIn top electrodes. Comparison of the attenuation factor (ß of the simplified Simmons equation) across these SAMs with the corresponding value obtained with length-matched SAMs of oligophenyls (HS(Ph)nH) and n-alkanethiols (HS(CH2)nH) demonstrates that SAMs of oligo(ethylene glycol) have values of ß (ß(EG)n = 0.29 ± 0.02 natom-1 and ß = 0.24 ± 0.01 Å-1) indistinguishable from values for SAMs of oligophenyls (ß(Ph)n = 0.28 ± 0.03 Å-1), and significantly lower than those of SAMs of n-alkanethiolates (ß(CH2)n = 0.94 ± 0.02 natom-1 and 0.77 ± 0.03 Å-1). There are two possible origins for this low value of ß. The more probable involves hole tunneling by superexchange, which rationalizes the weak dependence of the rate of charge transport on the length of the molecules of HS(EG)nCH3 using interactions among the high-energy, occupied orbitals associated with the lone-pair electrons on oxygen. Based on this mechanism, SAMs of oligo(ethylene glycol)s are good conductors (by hole tunneling) but good insulators (by electron and/or hole drift conduction). This observation suggests SAMs derived from these or electronically similar molecules are a new class of electronic materials. A second but less probable mechanism for this unexpectedly low value of ß for SAMs of S(EG)nCH3 rests on the possibility of disorder in the SAM and a systematic discrepancy between different estimates of the thickness of these SAMs.

Charge Tunneling along Short Oligoglycine Chains.

This work examines charge transport (CT) through self-assembled monolayers (SAMs) of oligoglycines having an N-terminal cysteine group that anchors the molecule to a gold substrate, and demonstrate that CT is rapid (relative to SAMs of n-alkanethiolates). Comparisons of rates of charge transport-using junctions with the structure Au(TS)/SAM//Ga2O3/EGaIn (across these SAMs of oligoglycines, and across SAMs of a number of structurally and electronically related molecules) established that rates of charge tunneling along SAMs of oligoglycines are comparable to that along SAMs of oligophenyl groups (of comparable length). The mechanism of tunneling in oligoglycines is compatible with superexchange, and involves interactions among high-energy occupied orbitals in multiple, consecutive amide bonds, which may by separated by one to three methylene groups. This mechanistic conclusion is supported by density functional theory (DFT).

Uncertainty of prebiotic scenarios: the case of the non-enzymatic reverse tricarboxylic acid cycle.

We consider the hypothesis of the primordial nature of the non-enzymatic reverse tricarboxylic acid (rTCA) cycle and describe a modeling approach to quantify the uncertainty of this hypothesis due to the combinatorial aspect of the constituent chemical transformations. Our results suggest that a) rTCA cycle belongs to a degenerate optimum of auto-catalytic cycles, and b) the set of targets for investigations of the origin of the common metabolic core should be significantly extended.