Combining low-cost electronic structure theory and low-cost parallel computing architecture.

The computational efficiency of low-cost electronic structure methods can be further improved by leveraging heterogenous computing architectures. The software package TeraChem has been developed since 2008 to make use of graphical processing units (GPUs), particularly their strong single-precision performance, for the acceleration of quantum chemical calculations. Here, we present the implementation of three low-cost methods, namely HF-3c, PBEh-3c, and the recently introduced ωB97X-3c. We show that these can benefit in terms of performance when combined with "consumer grade" GPUs by leveraging the mixed precision integral handling in TeraChem. The current limitation of the latter's GPU integral library is that Gaussian integrals only for functions with angular momentum l < 3 can be computed, which generally restricts the achievable accuracy in terms of the one-particle basis set. Particularly, the implementation of the ωB97X-3c method now enables higher accuracy with this setting which, in turn, provides the most efficient implementation accessible with consumer-grade hardware. We furthermore show that the implemented 3c methods can be combined with the hh-TDA formalism. This gives new and efficient low-cost multi-configurational excited states methods, which are benchmarked for the description of lowest vertical excitation energies in this work. All in all, the combination of these efficient electronic structure theory methods with affordable highly parallelized computing hardware provides an optimal computational and monetary cost to accuracy ratio.

CREST-A program for the exploration of low-energy molecular chemical space.

Conformer-rotamer sampling tool (CREST) is an open-source program for the efficient and automated exploration of molecular chemical space. Originally developed in Pracht et al. [Phys. Chem. Chem. Phys. 22, 7169 (2020)] as an automated driver for calculations at the extended tight-binding level (xTB), it offers a variety of molecular- and metadynamics simulations, geometry optimization, and molecular structure analysis capabilities. Implemented algorithms include automated procedures for conformational sampling, explicit solvation studies, the calculation of absolute molecular entropy, and the identification of molecular protonation and deprotonation sites. Calculations are set up to run concurrently, providing efficient single-node parallelization. CREST is designed to require minimal user input and comes with an implementation of the GFNn-xTB Hamiltonians and the GFN-FF force-field. Furthermore, interfaces to any quantum chemistry and force-field software can easily be created. In this article, we present recent developments in the CREST code and show a selection of applications for the most important features of the program. An important novelty is the refactored calculation backend, which provides significant speed-up for sampling of small or medium-sized drug molecules and allows for more sophisticated setups, for example, quantum mechanics/molecular mechanics and minimum energy crossing point calculations.

Photoswitchable Quadruple Hydrogen-Bonding Motif.

Multiple hydrogen-bonding motifs serve as important building blocks for molecular recognition and self-assembly. Herein, a photoswitchable quadruple hydrogen-bonding motif featuring near-complete, reversible, and thermostable conversion between DADA and AADD arrays associated with an alteration of their dimerization constants by over 3 orders of magnitude is reported. The system is based on a diarylethene featuring a ureidopyrimidin-4-ol moiety, which upon photoinduced ring closure and associated loss of aromaticity undergoes enol-keto tautomerization to a ureidopyrimidinone moiety. The latter causes a transformation of the hydrogen-bonding arrays and significantly weakens the free energy of dimerization in the case of the closed isomer. This photoswitchable quadruple hydrogen-bonding motif should allow us to spatially and temporarily direct self-assembly and supramolecular polymerization processes by light.

Diaryltriazolium Photoswitch: Reaching a Millisecond Cycloreversion with High Stability and NIR Absorption.

The exceptional thermal stability of diarylethene closed isomers enabled many applications but also prevented utilization in photochromic systems that require rapid thermal reversibility. Herein, we report the diaryltriazolium (DAT+ ) photoswitch undergoing thermal cycloreversion within a few milliseconds and absorption of the closed form in the near-infrared region above 900 nm. Click chemistry followed by alkylation offers modular and fast access to the electron-deficient DAT+ scaffold. In addition to excellent fatigue resistance, the introduced charge increases water solubility, rendering this photoswitch an ideal candidate for exploring biological applications.

Finding Excited-State Minimum Energy Crossing Points on a Budget: Non-Self-Consistent Tight-Binding Methods.

The automated exploration and identification of minimum energy conical intersections (MECIs) is a valuable computational strategy for the study of photochemical processes. Due to the immense computational effort involved in calculating non-adiabatic derivative coupling vectors, simplifications have been introduced focusing instead on minimum energy crossing points (MECPs), where promising attempts were made with semiempirical quantum mechanical methods. A simplified treatment for describing crossing points between almost arbitrary diabatic states based on a non-self-consistent extended tight-binding method, GFN0-xTB, is presented. Involving only a single diagonalization of the Hamiltonian, the method can provide energies and gradients for multiple electronic states, which can be used in a derivative coupling-vector-free scheme to calculate MECPs. By comparison with high-lying MECIs of benchmark systems, it is demonstrated that the identified geometries are good starting points for further MECI refinement with ab initio methods.

SQMBox: Interfacing a semiempirical integral library to modular ab initio electronic structure enables new semiempirical methods.

Ab initio and semiempirical electronic structure methods are usually implemented in separate software packages or use entirely different code paths. As a result, it can be time-consuming to transfer an established ab initio electronic structure scheme to a semiempirical Hamiltonian. We present an approach to unify ab initio and semiempirical electronic structure code paths based on a separation of the wavefunction ansatz and the needed matrix representations of operators. With this separation, the Hamiltonian can refer to either an ab initio or semiempirical treatment of the resulting integrals. We built a semiempirical integral library and interfaced it to the GPU-accelerated electronic structure code TeraChem. Equivalency between ab initio and semiempirical tight-binding Hamiltonian terms is assigned according to their dependence on the one-electron density matrix. The new library provides semiempirical equivalents of the Hamiltonian matrix and gradient intermediates, corresponding to those provided by the ab initio integral library. This enables the straightforward combination of semiempirical Hamiltonians with the full pre-existing ground and excited state functionality of the ab initio electronic structure code. We demonstrate the capability of this approach by combining the extended tight-binding method GFN1-xTB with both spin-restricted ensemble-referenced Kohn-Sham and complete active space methods. We also present a highly efficient GPU implementation of the semiempirical Mulliken-approximated Fock exchange. The additional computational cost for this term becomes negligible even on consumer-grade GPUs, enabling Mulliken-approximated exchange in tight-binding methods for essentially no additional cost.

Multifaceted View on the Mechanism of a Photochemical Deracemization Reaction.

Upon irradiation in the presence of a chiral benzophenone catalyst (5 mol %), a racemic mixture of a given chiral imidazolidine-2,4-dione (hydantoin) can be converted almost quantitatively into the same compound with high enantiomeric excess (80-99% ee). The mechanism of this photochemical deracemization reaction was elucidated by a suite of mechanistic experiments. It was corroborated by nuclear magnetic resonance titration that the catalyst binds the two enantiomers by two-point hydrogen bonding. In one of the diastereomeric complexes, the hydrogen atom at the stereogenic carbon atom is ideally positioned for hydrogen atom transfer (HAT) to the photoexcited benzophenone. Detection of the protonated ketyl radical by transient absorption revealed hydrogen abstraction to occur from only one but not from the other hydantoin enantiomer. Quantum chemical calculations allowed us to visualize the HAT within this complex and, more importantly, showed that the back HAT does not occur to the carbon atom of the hydantoin radical but to its oxygen atom. The achiral enol formed in this process could be directly monitored by its characteristic transient absorption signal at λ ≅ 330 nm. Subsequent tautomerization leads to both hydantoin enantiomers, but only one of them returns to the catalytic cycle, thus leading to an enrichment of the other enantiomer. The data are fully consistent with deuterium labeling experiments and deliver a detailed picture of a synthetically useful photochemical deracemization reaction.

Fast Screening of Minimum Energy Crossing Points with Semiempirical Tight-Binding Methods.

The investigation of photochemical processes is a highly active field in computational chemistry. One research direction is the automated exploration and identification of minimum energy conical intersection (MECI) geometries. However, due to the immense technical effort required to calculate nonadiabatic potential energy landscapes, the routine application of such computational protocols is severely limited. In this study, we will discuss the prospect of combining adiabatic potential energy surfaces from semiempirical quantum mechanical calculations with specialized confinement potential and metadynamics simulations to identify S0/T1 minimum energy crossing point (MECP) geometries. It is shown that MECPs calculated at the GFN2-xTB level can provide suitable approximations to high-level S0/S1ab initio conical intersection geometries at a fraction of the computational cost. Reference MECIs of benzene are studied to illustrate the basic concept. An example application of the presented protocol is demonstrated for a set of photoswitch molecules.

Photochemical Deracemization of Chiral Alkenes via Triplet Energy Transfer.

A visible-light-mediated, enantioselective approach to axially chiral alkenes is described. Starting from a racemic mixture, a major alkene enantiomer is formed due to selective triplet energy transfer from a catalytically active chiral sensitizer. A catalyst loading of 2 mol % was sufficient to guarantee consistently high enantioselectivities and yields (16 examples, 51%-quant., 81-96% ee). NMR studies and DFT computations revealed that triplet energy transfer is more rapid within the substrate-catalyst complex of the minor alkene enantiomer. Since this enantiomer is continuously racemized, the major enantiomer is enriched in the photostationary state.

Chiral photochemistry of achiral molecules.

Chirality is a molecular property governed by the topography of the potential energy surface (PES). Thermally achiral molecules interconvert rapidly when the interconversion barrier between the two enantiomers is comparable to or lower than the thermal energy, in contrast to thermally stable chiral configurations. In principle, a change in the PES topography on the excited electronic state may diminish interconversion, leading to electronically prochiral molecules that can be converted from achiral to chiral by electronic excitation. Here we report that this is the case for two prototypical examples - cis-stilbene and cis-stiff stilbene. Both systems exhibit unidirectional photoisomerization for each enantiomer as a result of their electronic prochirality. We simulate an experiment to demonstrate this effect in cis-stilbene based on its interaction with circularly polarized light. Our results highlight the drastic change in chiral behavior upon electronic excitation, opening up the possibility for asymmetric photochemistry from an effectively nonchiral starting point.

Predictions of Pre-edge Features in Time-Resolved Near-Edge X-ray Absorption Fine Structure Spectroscopy from Hole-Hole Tamm-Dancoff-Approximated Density Functional Theory.

Time-resolved near-edge X-ray absorption fine structure (TR-NEXAFS) spectroscopy is a powerful technique for studying photochemical reaction dynamics with femtosecond time resolution. In order to avoid ambiguity in TR-NEXAFS spectra from nonadiabatic dynamics simulations, core- and valence-excited states must be evaluated on equal footing and those valence states must also define the potential energy surfaces used in the nonadiabatic dynamics simulation. In this work, we demonstrate that hole-hole Tamm-Dancoff-approximated density functional theory (hh-TDA) is capable of directly simulating TR-NEXAFS spectroscopies. We apply hh-TDA to the excited-state dynamics of acrolein. We identify two pre-edge features in the oxygen K-edge TR-NEXAFS spectrum associated with the S2 (ππ*) and S1 (nπ*) excited states. We show that these features can be used to follow the internal conversion dynamics between the lowest three electronic states of acrolein. Due to the low, O(N2) apparent computational complexity of hh-TDA and our GPU-accelerated implementation, this method is promising for the simulation of pre-edge features in TR-NEXAFS spectra of large molecules and molecules in the condensed phase.

Hot exciplexes in U-shaped TADF molecules with emission from locally excited states.

Fast emission and high color purity are essential characteristics of modern opto-electronic devices, such as organic light emitting diodes (OLEDs). These properties are currently not met by the latest generation of thermally activated delayed fluorescence (TADF) emitters. Here, we present an approach, called "hot exciplexes" that enables access to both attributes at the same time. Hot exciplexes are produced by coupling facing donor and acceptor moieties to an anthracene bridge, yielding an exciplex with large T1 to T2 spacing. The hot exciplex model is investigated using optical spectroscopy and quantum chemical simulations. Reverse intersystem crossing is found to occur preferentially from the T3 to the S1 state within only a few nanoseconds. Application and practicality of the model are shown by fabrication of organic light-emitting diodes with up to 32 % hot exciplex contribution and low efficiency roll-off.

Cycloadditions of Donor-Acceptor Cyclopropanes and -butanes using S=N-Containing Reagents: Access to Cyclic Sulfinamides, Sulfonamides, and Sulfinamidines.

We present (3+2)- and (4+2)-cycloadditions of donor-acceptor (D-A) cyclopropanes and cyclobutanes with N-sulfinylamines and a sulfur diimide, along with a one-pot, two-step strategy for the formal insertion of HNSO2 into D-A cyclopropanes. These are rare examples of cycloadditions with D-A cyclopropanes and cyclobutanes whereby the 2π component consists of two different heteroatoms, thus leading to five- and six-membered rings containing adjacent heteroatoms.

Photochemical Deracemization of Primary Allene Amides by Triplet Energy Transfer: A Combined Synthetic and Theoretical Study.

The photochemical deracemization of 2,4-disubstituted 2,3-butadienamides (allene amides) was investigated both experimentally and theoretically. The reaction was catalyzed by a thioxanthone which is covalently linked to a chiral 1,5,7-trimethyl-3-azabicyclo[3.3.1]nonan-2-one skeleton providing a U-shaped arrangement of the sensitizing unit relative to a potential hydrogen-bonding site. Upon irradiation at λ = 420 nm in the presence of the sensitizer (2.5 mol %), the amides reached at -10 °C a photostationary state in which one enantiomer prevailed. The enantioenriched allene amides (70-93% ee) were isolated in 74% to quantitative yield (19 examples). Based on luminescence data and DFT calculations, energy transfer from the thioxanthone to the allene amides is thermodynamically feasible, and the achiral triplet allene intermediate was structurally characterized. Hydrogen bonding of the amide enantiomers to the sensitizer was monitored by NMR titration. The experimental association constants (Ka) were similar (59.8 vs 25.7 L·mol-1). DFT calculations, however, revealed a significant difference in the binding properties of the two enantiomers. The major product enantiomer exhibits a noncovalent dispersion interaction of its arylmethyl group to the external benzene ring of the thioxanthone, thus moving away the allene from the carbonyl chromophore. The minor enantiomer displays a CH-π interaction of the hydrogen atom at the terminal allene carbon atom to the same benzene ring, thus forcing the allene into close proximity to the chromophore. The binding behavior explains the observed enantioselectivity which, as corroborated by additional calculations, is due to a rapid triplet energy transfer within the substrate-catalyst complex of the minor enantiomer.

Nonadiabatic Dynamics Simulation of the Wavelength-Dependent Photochemistry of Azobenzene Excited to the nπ* and ππ* Excited States.

Azobenzene is one of the most ubiquitous photoswitches in photochemistry and a prototypical model for photoisomerizing systems. Despite this, its wavelength-dependent photochemistry has puzzled researchers for decades. Upon excitation to the higher energy ππ* excited state instead of the dipole-forbidden nπ* state, the quantum yield of isomerization from trans- to cis-azobenzene is halved. The difficulties associated with unambiguously resolving this effect both experimentally and theoretically have contributed to lasting controversies regarding the photochemistry of azobenzene. Here, we systematically characterize the dynamic photoreaction pathways of azobenzene by performing first-principles simulations of the nonadiabatic dynamics following excitation to both the ππ* and the nπ* states. We demonstrate that ground-state recovery is mediated by two distinct S1 decay pathways: a reactive twisting pathway and an unreactive planar pathway. Increased preference for the unreactive pathway upon ππ* excitation largely accounts for the wavelength-dependent behavior observed in azobenzene.

Ab Initio Nonadiabatic Molecular Dynamics with Hole-Hole Tamm-Dancoff Approximated Density Functional Theory.

The study of photoinduced dynamics in chemical systems necessitates accurate and computationally efficient electronic structure methods, especially as the systems of interest grow larger. The linear response hole-hole Tamm-Dancoff approximated (hh-TDA) density functional theory method was recently proposed to satisfy such demands. The N-electron electronic states are obtained by means of double annihilations on a doubly anionic (N + 2)-electron reference state, allowing for the ground and excited states to be formed on the same footing and thus enabling the correct description of conical intersections. Dynamic electron correlation effects are incorporated by means of the exchange-correlation functional. The accuracy afforded by the simultaneous treatment of static and dynamic correlation in addition to the relatively low computational cost, comparable to that of time-dependent density functional theory (TDDFT), makes it a promising ab initio electronic structure method for on-the-fly generation of potential energy surfaces in nonadiabatic dynamics simulations of photochemical systems, particularly those for which the nπ* and ππ* electronic excitations are most relevant. Here, we apply the hh-TDA method to nonadiabatic dynamics simulations of prototypical photochemical processes. First, we demonstrate the ability of hh-TDA to adequately describe conical intersection geometries. We next examine its ability to describe the ultrafast excited state dynamics of photoexcited ethylene through an ab initio multiple spawning (AIMS) dynamics simulation. Finally, we present an alternative variant of the hh-TDA method, which uses orbitals from a fractional occupation number Kohn-Sham (FON-KS) calculation applied to an ensemble with N-electrons. The resulting method is termed floating occupation molecular orbital hh-TDA (FOMO-hh-TDA). This scheme allows us to combine hh-TDA with global hybrid functionals and allows us to avoid unbound valence orbitals that may result from an (N + 2)-electron self-consistent field (SCF) procedure. FOMO-hh-TDA-BHLYP faithfully reproduces the nonadiabatic dynamics of trans-azobenzene (TAB) and is used to characterize the excited state decay pathways from the first (nπ*) excited state.

Hole-hole Tamm-Dancoff-approximated density functional theory: A highly efficient electronic structure method incorporating dynamic and static correlation.

The study of photochemical reaction dynamics requires accurate as well as computationally efficient electronic structure methods for the ground and excited states. While time-dependent density functional theory (TDDFT) is not able to capture static correlation, complete active space self-consistent field methods neglect much of the dynamic correlation. Hence, inexpensive methods that encompass both static and dynamic electron correlation effects are of high interest. Here, we revisit hole-hole Tamm-Dancoff approximated (hh-TDA) density functional theory for this purpose. The hh-TDA method is the hole-hole counterpart to the more established particle-particle TDA (pp-TDA) method, both of which are derived from the particle-particle random phase approximation (pp-RPA). In hh-TDA, the N-electron electronic states are obtained through double annihilations starting from a doubly anionic (N+2 electron) reference state. In this way, hh-TDA treats ground and excited states on equal footing, thus allowing for conical intersections to be correctly described. The treatment of dynamic correlation is introduced through the use of commonly employed density functional approximations to the exchange-correlation potential. We show that hh-TDA is a promising candidate to efficiently treat the photochemistry of organic and biochemical systems that involve several low-lying excited states-particularly those with both low-lying ππ* and nπ* states where inclusion of dynamic correlation is essential to describe the relative energetics. In contrast to the existing literature on pp-TDA and pp-RPA, we employ a functional-dependent choice for the response kernel in pp- and hh-TDA, which closely resembles the response kernels occurring in linear response and collinear spin-flip TDDFT.

TeraChem: Accelerating electronic structure and ab initio molecular dynamics with graphical processing units.

Developed over the past decade, TeraChem is an electronic structure and ab initio molecular dynamics software package designed from the ground up to leverage graphics processing units (GPUs) to perform large-scale ground and excited state quantum chemistry calculations in the gas and the condensed phase. TeraChem's speed stems from the reformulation of conventional electronic structure theories in terms of a set of individually optimized high-performance electronic structure operations (e.g., Coulomb and exchange matrix builds, one- and two-particle density matrix builds) and rank-reduction techniques (e.g., tensor hypercontraction). Recent efforts have encapsulated these core operations and provided language-agnostic interfaces. This greatly increases the accessibility and flexibility of TeraChem as a platform to develop new electronic structure methods on GPUs and provides clear optimization targets for emerging parallel computing architectures.

A Simplified Spin-Flip Time-Dependent Density Functional Theory Approach for the Electronic Excitation Spectra of Very Large Diradicals.

Experimentalists working with diradicals are often facing the question of what kind of species among singlet or triplet diradicals or closed-shell molecules are observed. To treat large diradicals with a high density of electronic states, we propose a simplified version of the spin-flip time-dependent density functional theory (SF-TD-DFT) method for a fast computation of their state energies and absorption spectra with an accuracy similar to the nonsimplified scheme. An ultrafast tight-binding variant called SF-sTD-DFT-xTB is also developed to treat even larger systems. For a benchmark set of nine diradicals, good agreement between simplified and conventional SF excitation energies for standard functionals is found. This shows that the proposed parameterization is robust for a wide range of Fock exchange mixing values. With the asymptotically correct response integrals used in SF-sTD-DFT and a correction factor of 2 for the transition moments, the SF-sTD-DFT/B5050LYP/cc-pVDZ method even outperforms the nonsimplified scheme at drastically reduced computational effort when comparing to the experimental absorption spectra for this set of diradicals. To showcase the actual performance of the method, absorption spectra of two µ-hydroxo-bridged dimers of corrole tape Ga(III) complex derivatives were computed and compared to the experiment, providing good qualitative agreement. Finally, a comparison with the high-spin triplet spectrum of a perylene bisimide biradical and the one determined at the SF-sTD-DFT level showed that at room temperature, mostly triplet diradicals are present in solution.

A generally applicable atomic-charge dependent London dispersion correction.

The so-called D4 model is presented for the accurate computation of London dispersion interactions in density functional theory approximations (DFT-D4) and generally for atomistic modeling methods. In this successor to the DFT-D3 model, the atomic coordination-dependent dipole polarizabilities are scaled based on atomic partial charges which can be taken from various sources. For this purpose, a new charge-dependent parameter-economic scaling function is designed. Classical charges are obtained from an atomic electronegativity equilibration procedure for which efficient analytical derivatives with respect to nuclear positions are developed. A numerical Casimir-Polder integration of the atom-in-molecule dynamic polarizabilities then yields charge- and geometry-dependent dipole-dipole dispersion coefficients. Similar to the D3 model, the dynamic polarizabilities are precomputed by time-dependent DFT and all elements up to radon (Z = 86) are covered. The two-body dispersion energy expression has the usual sum-over-atom-pairs form and includes dipole-dipole as well as dipole-quadrupole interactions. For a benchmark set of 1225 molecular dipole-dipole dispersion coefficients, the D4 model achieves an unprecedented accuracy with a mean relative deviation of 3.8% compared to 4.7% for D3. In addition to the two-body part, three-body effects are described by an Axilrod-Teller-Muto term. A common many-body dispersion expansion was extensively tested, and an energy correction based on D4 polarizabilities is found to be advantageous for larger systems. Becke-Johnson-type damping parameters for DFT-D4 are determined for more than 60 common density functionals. For various standard energy benchmark sets, DFT-D4 slightly but consistently outperforms DFT-D3. Especially for metal containing systems, the introduced charge dependence of the dispersion coefficients improves thermochemical properties. We suggest (DFT-)D4 as a physically improved and more sophisticated dispersion model in place of DFT-D3 for DFT calculations as well as other low-cost approaches like semi-empirical models.