Medium-sized Organic Molecules Research Articles

Performance of range-separated long-range SOPPA short-range density functional theory method for vertical excitation energies.

In this paper, benchmark results are presented on the calculation of vertical electronic excitation energies using a long-range second-order polarization propagator approximation (SOPPA) description with a short-range density functional theory description based on the Perdew-Burke-Ernzerhof (PBE) functional. The excitation energies are investigated for 132 singlet states and 71 triplet states across 28 medium-sized organic molecules. The results show that overall SOPPA-srPBE always performs better than PBE and that SOPPA-srPBE performs better than SOPPA for singlet states, but slightly worse than SOPPA for triplet states when CC3 results are the reference values.

Stepping-Stone CBH: Benchmark and Application of a Multilayered Isodesmic-Based Correction Scheme.

We present a generalization of the connectivity-based hierarchy (CBH) of isodesmic-based correction schemes to a multilayered fragmentation platform for overall cost reduction while retaining high accuracy. The newly developed multilayered CBH approach, called stepping-stone CBH (SSCBH), is benchmarked on a diverse set of 959 medium-sized organic molecules. Applying SSCBH corrections to the PBEh-D3 density functional resulted in an average error of 0.76 kcal/mol for the full test set compared to accurate CCSD(T)-quality enthalpies and an even lower error of 0.44 kcal/mol on a subset containing only acyclic molecules. These results rival the traditional CBH-3 approach at a greatly reduced cost, allowing larger fragment corrections to be made at the MP2 level of theory rather than with G4. Our SSCBH approach will enable more widespread applications of CBH methods to a broader range of organic and biomolecular systems.

A Story of Three Levels of Sophistication in SCF/KS-DFT Orbital Optimization Procedures.

In this work, three versions of self-consistent field/Kohn-Sham density functional theory (SCF/KS-DFT) orbital optimization are described and benchmarked. The methods are a modified version of the geometry version of the direct inversion in the iterative subspace approach (which we call r-GDIIS), the modified restricted step rational function optimization method (RS-RFO), and the novel subspace gradient-enhanced Kriging method combined with restricted variance optimization (S-GEK/RVO). The modifications introduced are aimed at improving the robustness and computational scaling of the procedures. In particular, the subspace approach in S-GEK/RVO allows the application to SCF/KS-DFT optimization of a machine learning technique that has proven to be successful in geometry optimizations. The performance of the three methods is benchmarked for a large number of small- to medium-sized organic molecules, at equilibrium structures and close to a transition state, and a second set of molecules containing closed- and open-shell transition metals. The results indicate the importance of the resetting technique in boosting the performance of the r-GDIIS procedure. Moreover, it is demonstrated that already at the inception of the subspace version of GEK to optimize SCF wave functions, it displays superior and robust convergence properties as compared to those of the standard state-of-the-art SCF/KS-DFT optimization methods.

Performance Tests of the Second-Order Approximate Internally Contracted Multireference Coupled-Cluster Singles and Doubles Method icMRCC2.

Benchmark results are presented for the second-order approximation of the internally contracted multireference coupled-cluster method with single and double excitations, icMRCC2 [Köhn, Bargholz, J. Chem. Phys. 2019, 151, 041106], which was designed as a multireference analogue of the single-reference second-order approximate coupled-cluster method CC2 [Christiansen, Koch, Jørgensen, Chem. Phys. Lett. 1995, 243, 409-418]. Vertical excitation energies of various small to medium-sized organic molecules are investigated based on established test sets from the literature. Additionally, the spectroscopic constants of ground and excited states of diatomics and the geometric parameters of excited triatomic molecules were determined and compared to the experimental data. The results show that the method clearly extends the applicability of single-reference CC2, including doubly excited states, and also artifacts of CC2 like too low Rydberg excitations and too weak multiple bonds are eliminated. The method is computationally more demanding than standard multireference second-order perturbation theories but improves significantly in accuracy, as shown by the benchmark results. In addition, it is demonstrated that small active spaces are often sufficient to obtain accurate energies with icMRCC2. Example applications like the automerization of cyclobutadiene, the deactivation pathway of ethylene, and the excited states of an iron complex with a noninnocent nitrosyl ligand demonstrate the potential of icMRCC2 in cases with strong multireference character.

Unequivocal identification of two-bond heteronuclear correlations in natural products at nanomole scale by i-HMBC

HMBC is an essential NMR experiment for determining multiple bond heteronuclear correlations in small to medium-sized organic molecules, including natural products, yet its major limitation is the inability to differentiate two-bond from longer-range correlations. There have been several attempts to address this issue, but all reported approaches suffer various drawbacks, such as restricted utility and poor sensitivity. Here we present a sensitive and universal methodology to identify two-bond HMBC correlations using isotope shifts, referred to as i-HMBC (isotope shift detection HMBC). Experimental utility was demonstrated at the sub-milligram / nanomole scale with only a few hours of acquisition time required for structure elucidation of several complex proton-deficient natural products, which could not be fully elucidated by conventional 2D NMR experiments. Because i-HMBC overcomes the key limitation of HMBC without significant reduction in sensitivity or performance, i-HMBC can be used as a complement to HMBC when unambiguous identifications of two-bond correlations are needed.

Recent advances in transition-metal-catalyzed Büchner reaction of alkynes.

Medium-sized ring-containing organic molecules, especially seven-membered rings, are significant structural motifs. However, such frameworks are considered difficult structures to access owing to entropic effects and transannular interactions. Compared to the construction of five and six-membered rings, the synthesis of seven-membered rings can be more challenging through traditional cyclization pathways. Büchner reactions are particularly attractive and efficient synthetic strategies to construct functionalized seven-membered ring products from the benzenoid double bond with carbene. In recent years, the field of transition-metal-catalyzed Büchner ring expansion reactions of alkynes has experienced a speedy development and a diverse array of efficient synthetic procedures have been disclosed under mild experimental conditions, as the synthesis of synthetically challenging seven-membered rings is easily achieved. In this review, we will focus on the recent progress in the transition-metal-catalyzed Büchner reaction of alkynes and the mechanistic rationale is depicted where possible, with the reactions being sorted according to the type of catalyst.

Efficient Kohn–Sham density-functional theory implementation of isotropic spectroscopic observables associated with quadratic response functions

For general exchange–correlation functionals with a dependence on the local spin densities and spin-density gradients, we provide computationally tractable expressions for the tensor-averaged quadratic response functions pertinent to the experimental observables in second-harmonic generation (SHG). We demonstrate how the tensor-averaged quantities can be implemented with reference to a derived minimal number of first- and second-order perturbed Fock matrices. Our consideration has the capability of treating a situation of resonance enhancement as it is based on damped response theory and allows for the evaluation of tensor-averaged resonant-convergent quadratic response functions using only ∼25% (one-photon off-resonance regions) and ∼50% (one-photon resonance regions) of the number of auxiliary Fock matrices required when explicitly calculating all the needed individual tensor components. Numerical examples of SHG intensities in the one-photon off-resonance region are provided for a sample of makaluvamine derivatives recognized for their large nonlinear optical responses as well as a benchmark set of small- and medium-sized organic molecules.

Assessing the Performances of CASPT2 and NEVPT2 for Vertical Excitation Energies.

Methods able to simultaneously account for both static and dynamic electron correlations have often been employed, not only to model photochemical events but also to provide reference values for vertical transition energies, hence allowing benchmarking of lower-order models. In this category, both the complete-active-space second-order perturbation theory (CASPT2) and the N-electron valence state second-order perturbation theory (NEVPT2) are certainly popular, the latter presenting the advantage of not requiring the application of the empirical ionization-potential-electron-affinity (IPEA) and level shifts. However, the actual accuracy of these multiconfigurational approaches is not settled yet. In this context, to assess the performances of these approaches, the present work relies on highly accurate (±0.03 eV) aug-cc-pVTZ vertical transition energies for 284 excited states of diverse character (174 singlet, 110 triplet, 206 valence, 78 Rydberg, 78 n → π*, 119 π → π*, and 9 double excitations) determined in 35 small- to medium-sized organic molecules containing from three to six non-hydrogen atoms. The CASPT2 calculations are performed with and without IPEA shift and compared to the partially contracted (PC) and strongly contracted (SC) variants of NEVPT2. We find that both CASPT2 with IPEA shift and PC-NEVPT2 provide fairly reliable vertical transition energy estimates, with slight overestimations and mean absolute errors of 0.11 and 0.13 eV, respectively. These values are found to be rather uniform for the various subgroups of transitions. The present work completes our previous benchmarks focused on single-reference wave function methods ( J. Chem. Theory Comput. 2018, 14, 4360; J. Chem. Theory Comput. 2020, 16, 1711), hence allowing for a fair comparison between various families of electronic structure methods. In particular, we show that ADC(2), CCSD, and CASPT2 deliver similar accuracies for excited states with a dominant single-excitation character.

Teaching a neural network to attach and detach electrons from molecules

Interatomic potentials derived with Machine Learning algorithms such as Deep-Neural Networks (DNNs), achieve the accuracy of high-fidelity quantum mechanical (QM) methods in areas traditionally dominated by empirical force fields and allow performing massive simulations. Most DNN potentials were parametrized for neutral molecules or closed-shell ions due to architectural limitations. In this work, we propose an improved machine learning framework for simulating open-shell anions and cations. We introduce the AIMNet-NSE (Neural Spin Equilibration) architecture, which can predict molecular energies for an arbitrary combination of molecular charge and spin multiplicity with errors of about 2–3 kcal/mol and spin-charges with error errors ~0.01e for small and medium-sized organic molecules, compared to the reference QM simulations. The AIMNet-NSE model allows to fully bypass QM calculations and derive the ionization potential, electron affinity, and conceptual Density Functional Theory quantities like electronegativity, hardness, and condensed Fukui functions. We show that these descriptors, along with learned atomic representations, could be used to model chemical reactivity through an example of regioselectivity in electrophilic aromatic substitution reactions.

Molecular Dynamics Simulations of a Cytochrome P450 from Tepidiphilus thermophilus (P450-TT) Reveal How Its Substrate-Binding Channel Opens.

Cytochrome P450s (P450) are important enzymes in biology with useful biochemical reactions in, for instance, drug and xenobiotics metabolisms, biotechnology, and health. Recently, the crystal structure of a new member of the CYP116B family has been resolved. This enzyme is a cytochrome P450 (CYP116B46) from Tepidiphilus thermophilus (P450-TT) and has potential for the oxy-functionalization of organic molecules such as fatty acids, terpenes, steroids, and statins. However, it was thought that the opening to its hitherto identified substrate channel was too small to allow organic molecules to enter. To investigate this, we performed molecular dynamics simulations on the enzyme. The results suggest that the crystal structure is not relaxed, possibly due to crystal packing effects, and that its tunnel structure is constrained. In addition, the simulations revealed two key amino acid residues at the mouth of the channel; a glutamyl and an arginyl. The glutamyl’s side chain tightens and relaxes the opening to the channel in conjunction with the arginyl’s, though the latter’s side chain is less dramatically changed after the initial relaxation of its conformations. Additionally, it was observed that the effect of increased temperature did not considerably affect the dynamics of the enzyme fold, including the relative solvent accessibility of the amino acid residues that make up the substrate channel wall even as compared to the changes that occurred at room temperature. Interestingly, the substrate channel became distinguishable as a prominent tunnel that is likely to accommodate small- to medium-sized organic molecules for bioconversions. That is, P450-TT has the ability to pass appropriate organic substrates to its active site through its elaborate substrate channel, and notably, is able to control or gate any molecules at the opening to this channel.

Unitary coupled-cluster approach for the calculation of core-excited states and x-ray absorption spectra.

In this work, we present the core-valence separation (CVS) approximation applied to unitary coupled-cluster (UCC) theory for the calculation of core-excited states and the simulation of x-ray absorption spectroscopy (XAS). Excitation energies and oscillator strengths of small- to medium-sized organic molecules have been computed using the second-order and extended second-order UCC schemes (CVS-UCC2 and CVS-UCC2-x) as well as the third-order scheme (CVS-UCC3). All results are compared to the corresponding algebraic-diagrammatic construction methods and experimental data. The agreement between CVS-UCC and experimental data demonstrates its potential as a new approach for the calculation of XAS.

Efficient implementation of isotropic cubic response functions for two-photon absorption cross sections within the self-consistent field approximation.

Within the self-consistent field approximation, computationally tractable expressions for the isotropic second-order hyperpolarizability have been derived and implemented for the calculation of two-photon absorption cross sections. The novel tensor average formulation presented in this work allows for the evaluation of isotropic damped cubic response functions using only ∼3.3% (one-photon off-resonance regions) and ∼10% (one-photon resonance regions) of the number of auxiliary Fock matrices required when explicitly calculating all the needed individual tensor components. Numerical examples of the two-photon absorption cross section in the one-photon off-resonance and resonance regions are provided for alanine-tryptophan and 2,5-dibromo-1,4-bis(2-(4-diphenylaminophenyl)vinyl)-benzene. Furthermore, a benchmark set of 22 additional small- and medium-sized organic molecules is considered. In all these calculations, a quantitative assessment is made of the reduced and approximate forms of the cubic response function in the one-photon off-resonance regions and results demonstrate a relative error of less than ∼5% when using the reduced expression as compared to the full form of the isotropic cubic response function.

Benchmark Study of Electrochemical Redox Potentials Calculated with Semiempirical and DFT Methods

The calculation of redox potentials by semiempirical quantum mechanical (SQM) approaches is evaluated with a focus on the recently developed GFNn-xTB methods. The assessment is based on a data set comprising 313 experimental redox potentials of small to medium-sized organic and organometallic molecules in various solvents. This compilation is termed as ROP313 (reduction and oxidation potentials 313) and divided for analysis purposes into the organic subset OROP and the organometallic subset OMROP. Corresponding data for a few common density functional theory (DFT) functionals employing extended AO basis sets and small basis-set DFT composite schemes are computed for comparison. Continuum solvation models are used to calculate the important solvation free energy contribution. The results for ROP313 show that the GFNn-xTB methods provide a robust, efficient, and generally applicable workflow for the routine calculation of redox potentials. The GFNn-xTB methods outperform the PMx competitor for the OROP subset (mean absolute deviation from the experiment, MADGFN2-xTB = 0.30 V, MADGFN1-xTB = 0.31 V, PM6-D3H4 = 0.61 V, PM7 = 0.60 V), almost reaching low-cost DFT quality (MADB97-3c = 0.25 V) at drastically reduced computational cost (2-3 orders of magnitude). All SQM methods perform considerably worse for the OMROP subset. Here, the GFN2-xTB still yields semiquantitative results slightly better and more robustly than with the PMx methods (MADGFN2-xTB = 0.74 V, PM6-D3H4 = 0.78 V, PM7 = 0.82 V). The proposed workflow enables large-scale quantum chemical computations of organic and, to a lesser extent, organometallic molecule redox potentials on common laptop computers in seconds to minutes of computation time enabling, e.g., screening of extended compound libraries.

Effective Molecular Descriptors for Chemical Accuracy at DFT Cost: Fragmentation, Error-Cancellation, and Machine Learning.

Recent advances in theoretical thermochemistry have allowed the study of small organic and bio-organic molecules with high accuracy. However, applications to larger molecules are still impeded by the steep scaling problem of highly accurate quantum mechanical (QM) methods, forcing the use of approximate, more cost-effective methods at a greatly reduced accuracy. One of the most successful strategies to mitigate this error is the use of systematic error-cancellation schemes, in which highly accurate QM calculations can be performed on small portions of the molecule to construct corrections to an approximate method. Herein, we build on ideas from fragmentation and error-cancellation to introduce a new family of molecular descriptors for machine learning modeled after the Connectivity-Based Hierarchy (CBH) of generalized isodesmic reaction schemes. The best performing descriptor ML(CBH-2) is constructed from fragments preserving only the immediate connectivity of all heavy (non-H) atoms of a molecule along with overlapping regions of fragments in accordance with the inclusion-exclusion principle. Our proposed approach offers a simple, chemically intuitive grouping of atoms, tuned with an optimal amount of error-cancellation, and outperforms previous structure-based descriptors using a much smaller input vector length. For a wide variety of density functionals, DFT+ΔML(CBH-2) models, trained on a set of small- to medium-sized organic HCNOSCl-containing molecules, achieved an out-of-sample MAE within 0.5 kcal/mol and 2σ (95%) confidence interval of <1.5 kcal/mol compared to accurate G4 reference values at DFT cost.

Benchmarking doubles-corrected random-phase approximation methods for frequency dependent polarizabilities: Aromatic molecules calculated at the RPA, HRPA, RPA(D), HRPA(D), and SOPPA levels.

The performance of different polarization propagator methods, such as RPA, RPA(D), HRPA, HRPA(D), and SOPPA, have been tested against CC3 values for both static and dynamic polarizabilities. The test set consists of 14 (hetero-)aromatic medium-sized organic molecules, mostly with a high degree of symmetry. The benchmark of the methods remarkably reveals that RPA and HRPA(D) yield results comparable with the CC3 values and that they outperform SOPPA for these molecules. For a subset of the molecules, a comparison could be made to experimental values. The comparison for static polarizabilities proves that RPA and HRPA(D) as well as RPA(D) reproduce experimental values to a satisfying precision, whereas the SOPPA method compared to these three methods appears to perform only adequately. An investigation of the performance of Sadlej's polarized triple zeta basis set against Dunning's aug-cc-pVTZ basis set was also carried out. It is found that in contrast to other methods, Sadlej's basis set did not perform sufficiently compared to the larger aug-cc-pVTZ basis set for the RPA based methods.

Third-Order Unitary Coupled Cluster (UCC3) for Excited Electronic States: Efficient Implementation and Benchmarking.

The efficient implementation of the third-order unitary coupled-cluster scheme (UCC3) for the calculation of excited electronic states is reported. The UCC3 scheme and its second-order UCC2 variant have been benchmarked and compared to Jacquemin's recently introduced, as well as Thiel's well-established, benchmark sets for excitation energies and oscillator strengths. For the latter, the calculation of 134 excited singlet and 71 excited triplet states of 28 small- to medium-sized organic molecules has revealed that UCC2 exhibits a mean error and standard deviation of 0.36 ± 0.41 eV for singlet states and 0.22 ± 0.21 eV for triplet states, whereas UCC3 revealed an accuracy of 0.06 ± 0.27 eV for singlet and -0.22 ± 0.15 eV for triplet states. In addition, the oscillator strengths obtained with effective transition moments correct through second order in perturbation theory are in very good agreement with literature data.

TeraChem Cloud: A High-Performance Computing Service for Scalable Distributed GPU-Accelerated Electronic Structure Calculations.

The encapsulation and commoditization of electronic structure arise naturally as interoperability, and the use of nontraditional compute resources (e.g., new hardware accelerators, cloud computing) remains important for the computational chemistry community. We present TeraChem Cloud, a high-performance computing service (HPCS) that offers on-demand electronic structure calculations on both traditional HPC clusters and cloud-based hardware. The framework is designed using off-the-shelf web technologies and containerization to be extremely scalable and portable. Within the HPCS model, users can quickly develop new methods and algorithms in an interactive environment on their laptop while allowing TeraChem Cloud to distribute ab initio calculations across all available resources. This approach greatly increases the accessibility of hardware accelerators such as graphics processing units (GPUs) and flexibility for the development of new methods as additional electronic structure packages are integrated into the framework as alternative backends. Cost-performance analysis indicates that traditional nodes are the most cost-effective long-term solution, but commercial cloud providers offer cutting-edge hardware with competitive rates for short-term large-scale calculations. We demonstrate the power of the TeraChem Cloud framework by carrying out several showcase calculations, including the generation of 300,000 density functional theory energy and gradient evaluations on medium-sized organic molecules and reproducing 300 fs of nonadiabatic dynamics on the B800-B850 antenna complex in LH2, with the latter demonstration using over 50 Tesla V100 GPUs in a commercial cloud environment in 8 h for approximately $1250.

Hamiltonian-Reservoir Replica Exchange and Machine Learning Potentials for Computational Organic Chemistry.

This work combines a machine learning potential energy function with a modular enhanced sampling scheme to obtain statistically converged thermodynamical properties of flexible medium-size organic molecules at high ab initio level. We offer a modular environment in the python package MORESIM that allows custom design of replica exchange simulations with any level of theory including ML-based potentials. Our specific combination of Hamiltonian and reservoir replica exchange is shown to be a powerful technique to accelerate enhanced sampling simulations and explore free energy landscapes with a quantum chemical accuracy unattainable otherwise (e.g., DLPNO-CCSD(T)/CBS quality). This engine is used to demonstrate the relevance of accessing the ab initio free energy landscapes of molecules whose stability is determined by a subtle interplay between variations in the underlying potential energy and conformational entropy (i.e., a bridged asymmetrically polarized dithiacyclophane and a widely used organocatalyst) both in the gas phase and in solution (implicit solvent).

Structure of heroin in a solution revealed by chiroptical spectroscopy.

In this work, the 3-D structure of the well-known opioid drug heroin in a solution was investigated. The goal was to provide a complete and detailed description of the stable conformers with their relative abundances. This knowledge is very important from the pharmaceutical and forensic point of view as it could help significantly with deeper understanding of heroin's metabolism and the development of antagonist medicines for the case of an overdose. As heroin is a chiral compound with five stereogenic centres, the methods of chiroptical spectroscopy supplemented by density functional theory (DFT) calculations were applied to study its conformations in chloroform solution. The selected chiroptical methods, namely, electronic circular dichroism (ECD) and vibrational circular dichroism (VCD), are inherently sensitive to the 3-D structure of small- to medium-sized chiral organic molecules. A thorough conformational analysis revealed four stable conformers of heroin in chloroform solution, where the conductor-like polarizable continuum model of the solvent was used for all the calculations. The simulated ultraviolet (UV), infrared (IR), ECD, and VCD spectra were compared with the experimental ones and very good agreement was found, which enabled a detailed structure description and interpretation of the spectra. Chiroptical spectroscopy in combination with DFT calculations proved to be a very sensitive tool for the analysis of the 3-D structure of heroin in a solution in contrast with conventional spectroscopic methods. Especially, the application of VCD seems to be a promising approach for monitoring structural changes, for instance, those caused by solvents or interactions with other agents.

Is ADC(3) as Accurate as CC3 for Valence and Rydberg Transition Energies?

The search for new models rapidly delivering accurate excited-state energies and properties is one of the most active research lines of theoretical chemistry. Along with these developments, the performance of known methods is constantly reassessed on the basis of new benchmark values. In this Letter, we show that the third-order algebraic diagrammatic construction, ADC(3), does not yield transition energies of the same quality as the third-order coupled cluster method, CC3. This is demonstrated by extensive comparisons with several hundred high-quality vertical transition energies obtained with FCI, CCSDTQ, and CCSDT. Direct comparisons with experimental 0-0 energies of small- and medium-size molecules support the same conclusion, which holds for both valence and Rydberg transitions. Considering these results, we introduce a composite approach, ADC(2.5), which consists of averaging the ADC(2) and ADC(3) excitation energies. Although ADC(2.5) does not match the CC3 accuracy, it significantly improves the ADC(3) results, especially for vertical energies.