Scalable Synthesis and Characterization of Multilayer γ-Graphyne, New Carbon Crystals with a Small Direct Band Gap.

γ-Graphyne is the most symmetric sp2/sp1 allotrope of carbon, which can be viewed as graphene uniformly expanded through the insertion of two-carbon acetylenic units between all the aromatic rings. To date, synthesis of bulk γ-graphyne has remained a challenge. We here report the synthesis of multilayer γ-graphyne through crystallization-assisted irreversible cross-coupling polymerization. A comprehensive characterization of this new carbon phase is described, including synchrotron powder X-ray diffraction, electron diffraction, lateral force microscopy, Raman spectroscopy, infrared spectroscopy, and cyclic voltammetry. Experiments indicate that γ-graphyne is a 0.48 eV band gap semiconductor, with a hexagonal a-axis spacing of 6.88 Å and an interlayer spacing of 3.48 Å, which is consistent with theoretical predictions. The observed crystal structure has an aperiodic sheet stacking. The material is thermally stable up to 240 °C but undergoes transformation at higher temperatures. While conventional 2D polymerization and reticular chemistry rely on error correction through reversibility, we demonstrate that a periodic covalent lattice can be synthesized under purely kinetic control. The reported methodology is scalable and inspires extension to other allotropes of the graphyne family.

Tuning the Properties of Azadipyrromethene-Based Near-Infrared Dyes Using Intramolecular BO Chelation and Peripheral Substitutions.

Tetraphenylazadipyrromethenes (ADPs) are attractive near-infrared (NIR) dyes because of their simple synthesis and exceptional optical and electronic properties. The typical BF2 and less explored intramolecular BO coordination planarize the molecule, making them promising π-conjugated materials for organic electronic applications. However, their use has been mostly limited to vacuum-deposited devices. To improve the properties, we synthesized and characterized a series of ADP complexes and used density functional theory calculations to further explain the properties. Hexyloxy solubilizing groups increase the complexes' solubility in organic solvents and enable film formation from solution. Phenylethynyls at the pyrrolic positions extend π conjugation, red-shift absorption and emission peaks, and increase the ionization potential (IP) and electron affinity. When the properties of complexes with hexyloxy and phenyethynyl substitutions are compared, the BO complex is more planar and has a smaller IP than the corresponding BF2 complex because of increased electron density on the proximal phenyls. The BO complex has an unusual combination of properties: a solution λmax of 781 nm, emission at 805 nm, a small Stokes shift, and a quantum yield of 6%. It forms transparent films with a low optical gap of 1.22 eV. This new complex is a promising candidate for transparent solar cells and NIR photodetectors.

Accelerating molecular property calculations with semiempirical preconditioning.

Computing ab initio molecular linear response properties, e.g., electronic excitation energies and transition dipole moments, requires the solution of large eigenvalue problems or large systems of equations. These large eigenvalue problems or large systems of equations are commonly solved iteratively using Krylov space algorithms, such as the Davidson algorithm for eigenvalue problems. A critical ingredient in Krylov space algorithms is the preconditioner, which is used to generate optimal update vectors in each iteration. We propose to use semiempirical approximations as preconditioners to accelerate the calculation of ab initio properties. The crucial advantage to improving the preconditioner is that the converged result is unchanged, so there is no trade-off between accuracy and speedup. We demonstrate our approach by accelerating the calculation of electronic excitation energies and electric polarizabilities from linear response time-dependent density functional theory using the simplified time-dependent density functional theory semiempirical model. For excitation energies, the semiempirical preconditioner reduces the number of iterations on average by 37% and up to 70%. The semiempirical preconditioner reduces the number of iterations for computing the polarizability by 15% on average and up to 33%. Moreover, we show that the preconditioner can be further improved by tuning the empirical parameters that define the semiempirical model, leading to an additional reduction in the number of iterations by about 20%. Our approach bridges the gap between semiempirical models and ab initio methods and charts a path toward combining the speed of semiempirical models with the accuracy of ab initio methods.

Surface hopping with cumulative probabilities: Even sampling and improved reproducibility.

Trajectory surface hopping simulations of photochemical reactions are a powerful and increasingly important tool to unravel complex photochemical reactivity. Within surface hopping, electronic transitions are mimicked by stochastic hops between electronic potential surfaces. Thus, statistical sampling is an inescapable component of trajectory-surface-hopping-based nonadiabatic molecular dynamics methods. However, the standard sampling strategy inhibits computational reproducibility, limits predictability, and results in trajectories that are overly sensitive to numerical parameters like the time step. We describe an equivalent approach to sampling electronic transitions within fewest switches surface hopping (FSSH) in which hops are decided in terms of the cumulative probability (FSSH-c) as opposed to the usual prescription, which is in terms of the instantaneous conditional probability (FSSH-i). FSSH-c is statistically equivalent to FSSH-i and can be implemented from trivial modifications to an existing surface hopping algorithm but has several key advantages: (i) a single trajectory is fully specified by just a handful of random numbers, (ii) all hopping decisions are independent of the time step such that the convergence behavior of individual trajectories can be explored, and (iii) alternative integral-based sampling schemes are enabled. In addition, we show that the conventional hopping probability overestimates the hopping rate and propose a simple scaling correction as a fix. Finally, we demonstrate these advantages numerically on model scattering problems.

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.

Multistate hybrid time-dependent density functional theory with surface hopping accurately captures ultrafast thymine photodeactivation.

We report an efficient analytical implementation of first-order nonadiabatic derivative couplings between arbitrary Born-Oppenheimer states in the hybrid time-dependent density functional theory (TDDFT) framework using atom-centered basis functions. Our scheme is based on quadratic response theory and includes orbital relaxation terms neglected in previous approaches. Simultaneous computation of multiple derivative couplings and energy gradients enables efficient multistate nonadiabatic molecular dynamics simulations in conjunction with Tully's fewest switches surface hopping (SH) method. We benchmark the thus obtained multistate TDDFT-SH scheme by simulating ultrafast decay of UV-photoexcited thymine, for which accurate gas-phase data from ultrafast spectroscopy experiments are available. The calculations predict a fast 153 fs decay from the bright S2 to the dark S1 excited state, followed by a much slower 14 ps S1 deactivation to the ground state; statistical uncertainties were estimated using bootstrap sampling. These results agree well with the experimentally observed time constants of 100-200 fs and 5-7 ps, respectively, unlike previous multiconfigurational self-consistent field and second-order algebraic diagrammatic construction calculations. Furthermore, our results support the S1-trapping hypothesis [J. J. Szymczak et al., J. Phys. Chem. A, 2009, 113, 12686-12693]. For thymine, the computational cost of a single TDDFT-SH time-step including the lowest 3 states, all couplings and gradients, is ∼5 times larger than the cost of a single Born-Oppenheimer dynamics time step for the ground state in our implementation. Thus, ps nonadiabatic dynamics simulations using multistate hybrid TDDFT-SH for systems with up to ∼100 atoms are possible without drastic approximations on single workstation nodes. Our implementation will be made available through Turbomole.

Unphysical divergences in response theory.

Transition densities between excited states are key for nonlinear theoretical spectroscopy and multi-state non-adiabatic molecular dynamics (NAMD) simulations. In the framework of response theory, these transition densities are accessible from poles of the quadratic response function. It was shown recently that the thus obtained transition densities within time-dependent Hartree-Fock (TDHF) and adiabatic time-dependent density functional theory (TDDFT) exhibit unphysical divergences when the difference in excitation energy of the two states of interest matches another excitation energy. This unphysical behavior is a consequence of spurious poles in the quadratic response function. We show that the incorrect pole structure of the quadratic response is not limited to TDHF and adiabatic TDDFT, but is also present in many other approximate many-electron response functions, including those from coupled cluster and multiconfigurational self-consistent field response theory. The divergences appear in regions of the potential energy surface where the ground state is perfectly well behaved, and they are frequently encountered in NAMD simulations of photochemical reactions. The origin of the divergences is traced to an incorrect instantaneous time-dependence of the effective Hamiltonian. The implications for computations of frequency-dependent response properties are considerable and call into question the validity of conventional approximate many-electron response theories beyond linear response.

Molecular junctions: can pulling influence optical controllability?

We suggest the combination of single molecule pulling and optical control as a way to enhance control over the electron transport characteristics of a molecular junction. We demonstrate using a model junction consisting of biphenyl-dithiol coupled to gold contacts. The junction is pulled while optically manipulating the dihedral angle between the two rings. Quantum dynamics simulations show that molecular pulling enhances the degree of control over the dihedral angle and hence over the transport properties.

Communication: Active space decomposition with multiple sites: density matrix renormalization group algorithm.

We extend the active space decomposition method, recently developed by us, to more than two active sites using the density matrix renormalization group algorithm. The fragment wave functions are described by complete or restricted active-space wave functions. Numerical results are shown on a benzene pentamer and a perylene diimide trimer. It is found that the truncation errors in our method decrease almost exponentially with respect to the number of renormalization states M, allowing for numerically exact calculations (to a few µE(h) or less) with M = 128 in both cases. This rapid convergence is because the renormalization steps are used only for the interfragment electron correlation.

Communication: Active-space decomposition for molecular dimers.

We have developed an active-space decomposition strategy for molecular dimers that allows for the efficient computation of the dimer's complete-active-space wavefunction while only constructing the monomers' active-space wavefunctions. Dimer states are formed from linear combinations of direct products of localized orthogonal monomer states and Hamiltonian matrix elements are computed directly without explicitly constructing the product space. This decomposition is potentially exact in the limit where a full set of monomer states is included. The adiabatic states are then found by diagonalizing the dimer Hamiltonian matrix. We demonstrate the convergence of our method to a complete-active-space calculation of the full dimer with two test cases: the benzene and naphthalene dimers.

Minimal Auxiliary Basis Set Approach for the Electronic Excitation Spectra of Organic Molecules.

We report a minimal auxiliary basis model for time-dependent density functional theory (TDDFT) with hybrid density functionals that can accurately reproduce excitation energies and absorption spectra from TDDFT while reducing cost by about 2 orders of magnitude. Our method, dubbed TDDFT-ris, employs the resolution-of-the-identity technique with just one s-type auxiliary basis function per atom for the linear response operator, where the Gaussian exponents are parametrized across the periodic table using tabulated atomic radii with a single global scaling factor. By tuning on a small test set, we determine a single functional-independent scale factor that balances errors in excitation energies and absorption spectra. Benchmarked on organic molecules and compared to standard TDDFT, TDDFT-ris has an average energy error of only 0.06 eV and yields absorption spectra in close agreement with TDDFT. Thus, TDDFT-ris enables simulation of realistic absorption spectra in large molecules that would be inaccessible from standard TDDFT.

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.

Coherent control of molecular torsion.

We propose a coherent, strong-field approach to control the torsional modes of biphenyl derivatives, and develop a numerical scheme to simulate the torsional dynamics. By choice of the field parameters, the method can be applied either to drive the torsion angle to an arbitrary configuration or to induce free internal rotation. Transient absorption spectroscopy is suggested as a probe of torsional control and the usefulness of this approach is numerically explored. Several consequences of our ability to manipulate molecular torsional motions are considered. These include a method for the inversion of molecular chirality and an ultrafast chiral switch.

Mutually Orthogonal Bioconjugation of Vinyl Nucleosides for RNA Metabolic Labeling.

We report a strategy for the orthogonal conjugation of the vinyl nucleosides, 5-vinyluridine (5-VU) and 2-vinyladenosine (2-VA), via selective reactivity with maleimide and tris(2-carboxyethyl)phosphine (TCEP), respectively. The orthogonality was investigated using density functional theory (DFT) and confirmed by reactions with vinyl nucleosides. Further, these chemistries were used to modify RNA for fluorescent cell imaging. These reactions allow for the expanded use of RNA metabolic labeling to study nascent RNA expression within different RNA populations.

Expanding the Scope of RNA Metabolic Labeling with Vinyl Nucleosides and Inverse Electron-Demand Diels-Alder Chemistry.

Optimized and stringent chemical methods to profile nascent RNA expression are still in demand. Herein, we expand the toolkit for metabolic labeling of RNA through application of inverse electron demand Diels-Alder (IEDDA) chemistry. Structural examination of metabolic enzymes guided the design and synthesis of vinyl-modified nucleosides, which we systematically tested for their ability to be installed through cellular machinery. Further, we tested these nucleosides against a panel of tetrazines to identify those which are able to react with a terminal alkene, but are stable enough for selective conjugation. The selected pairings then facilitated RNA functionalization with biotin and fluorophores. We found that this chemistry not only is amenable to preserving RNA integrity but also endows the ability to both tag and image RNA in cells. These key findings represent a significant advancement in methods to profile the nascent transcriptome using chemical approaches.

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.

Mechanism of photocatalytic water oxidation on small TiO2 nanoparticles.

We present the first unconstrained nonadiabatic molecular dynamics (NAMD) simulations of photocatalytic water oxidation by small hydrated TiO2 nanoparticles using Tully surface hopping and time-dependent density functional theory. The results indicate that ultrafast electron-proton transfer from physisorbed water to the photohole initiates the photo-oxidation on the S1 potential energy surface. The new mechanism readily explains the observation of mobile hydroxyl radicals in recent experiments. Two key driving forces for the photo-oxidation reaction are identified: localization of the electron-hole pair and stabilization of the photohole by hydrogen bonding interaction. Our findings illustrate the scope of recent advances in NAMD methods and emphasize the importance of explicit simulation of electronic excitations.

Orbital Optimization in the Active Space Decomposition Model.

We report the derivation and implementation of orbital optimization algorithms for the active space decomposition (ASD) model, which are extensions of complete active space self-consistent field (CASSCF) and its occupation-restricted variants in the conventional multiconfiguration electronic-structure theory. Orbital rotations between active subspaces are included in the optimization, which allows us to unambiguously partition the active space into subspaces, enabling application of ASD to electron and exciton dynamics in covalently linked chromophores. One- and two-particle reduced density matrices, which are required for evaluation of orbital gradient and approximate Hessian elements, are computed from the intermediate tensors in the ASD energy evaluation. Numerical results on 4-(2-naphthylmethyl)-benzaldehyde and [36]cyclophane and model Hamiltonian analyses of triplet energy transfer processes in the Closs systems are presented. Furthermore, model Hamiltonians for hole and electron transfer processes in anti-[2.2](1,4)pentacenophane are studied using an occupation-restricted variant.

Quasi-diabatic States from Active Space Decomposition.

We present ab initio theory and efficient algorithms for computing model Hamiltonians of excited-state dynamics in the quasi-diabatic representation. The method is based on a recently developed multiconfiguration electronic structure method, called the active space decomposition method (ASD), in which quasi-diabatic basis states are constructed from physical fragment states. An efficient tree-based algorithm is presented for computing and reusing intermediate tensors appearing in the ASD model. Parallel scalability and wall times are reported to attest the efficiency of our program. Applications to electron, hole, and triplet energy transfers in molecular dimers are presented, demonstrating its versatility.