Closed-shell Molecules Research Articles

Effect of Fluorine Substitution on Magnetizabilities: Insights from Density Functional Theory and Benchmark Coupled-Cluster Calculations.

The quantitative calculation of the magnetizability tensor of fluorine-containing molecules has been a longstanding challenge for quantum chemistry. We report a benchmark study on the effect of fluorine substitution on the magnetizability (both isotropic and anisotropic) of 24 small closed-shell molecules using coupled-cluster (CCSD(T)) theory, large basis sets, and London atomic orbitals. By extrapolation to a complete basis set (CBS) result, we establish the CCSD(T)/CBS limit and take the opportunity to assess the performance of various density functional theory approximations. Correcting for zero-point vibration further allows us to directly compare theory with (gas-phase) experimental data. We revisit Flygare's hypothesis on molecular magnetizabilities, which relates the successive replacement of hydrogen by fluorine atoms to changes in the magnetizability anisotropy. Some exceptions to this hypothesis are documented, and we rationalize these observations on the basis of hybridization on carbon.

Electron Binding Energies of Open-Shell Species from Diagonal Electron-Propagator Self-Energies with Unrestricted Hartree-Fock Spin-Orbitals.

For closed-shell molecules, valence electron binding energies may be calculated accurately and efficiently with ab initio electron-propagator methods that have surpassed their predecessors. Advantageous combinations of accuracy and efficiency range from cubically scaling methods with mean errors of 0.2 eV to quintically scaling methods with mean errors of 0.1 eV or less. The diagonal self-energy approximation in the canonical Hartree-Fock basis is responsible for the enhanced efficiency of several methods. This work examines the predictive capabilities of diagonal self-energy approximations when they are generalized to the canonical spin-orbital basis of unrestricted Hartree-Fock (UHF) theory. Experimental data on atomic electron binding energies and high-level, correlated calculations in a fixed basis for a set of open-shell molecules constitute standards of comparison. A review of the underlying theory and analysis of numerical errors lead to several recommendations for the calculation of electron binding energies: (1) In calculations that employ the diagonal self-energy approximation, Koopmans's identity for UHF must be qualitatively correct. (2) Closed-shell reference states are preferable to open-shell reference states in calculations of molecular ionization energies and electron affinities. (3) For molecular electron binding energies between doublets and triplets, calculations of electron detachment energies are more accurate and efficient than calculations of electron attachment energies. When these recommendations are followed, mean absolute errors increase by approximately 0.05 eV with respect to their counterparts obtained with closed-shell reference orbitals.

Fulvenallenyl Radical (C7H5·)-Mediated Gas-Phase Synthesis of Bicyclic Aromatic C10H8 Isomers: Can Fulvenallenyl Efficiently React with Closed-Shell Hydrocarbons?

To understand the reactivity of resonantly stabilized radicals, often found in relevant concentrations in gaseous environments, it is important to determine their main reaction pathways. Here, it is investigated whether the fulvenallenyl radical (C7H5·) reacts preferentially with closed-shell molecules or radicals. Electronic structure calculations on the C10H9 potential energy surface accessed by the reactions of C7H5· with methylacetylene (CH3CCH) and allene (H2CCCH2) were combined with RRKM-ME calculations of temperature- and pressure-dependent rate constants using the automated EStokTP software suite and kinetic modeling to assess the reactivity of C7H5· with closed-shell unsaturated hydrocarbons. Experimentally, the reactions were attempted in a chemical microreactor heated to 998 ± 10 K by preparing fulvenallenyl radicals via pyrolysis of trichloromethylbenzene (C7H5Cl3) and seeding the radicals in methylacetylene or allene carrier gas, with product identification by means of photoionization mass spectrometry. The measured photoionization efficiency curve of m/z = 128 was assigned to a linear combination of the reference curves of two C10H8 isomers, azulene (minor) and naphthalene (major), presumably resulting from the C7H5· plus C3H4 reactions. However, the calculations demonstrated that these reactions are too slow, and kinetic modeling of processes in the reactor allowed us to conclude that the observation of naphthalene and azulene is due to the C7H5· plus C3H3· reaction, where propargyl is produced by direct hydrogen atom abstraction by chlorine (Cl) atoms from allene or methylacetylene and Cl stem from the pyrolysis of C7H5Cl3. Modeling results under the copyrolysis conditions of toluene and methylacetylene in high-temperature shock tube experiments confirmed the prevalence of the fulvenallenyl reaction with propargyl over its reactions with C3H4 even when the concentrations of allene and methylacetylene largely exceed that of propargyl. Overall, the reactions of fulvenallenyl with both allene and methylacetylene were found to be noncompetitive in the formation of naphthalene and azulene thus attesting the inefficiency of the fulvenallenyl radical reactions with the prototype closed-shell hydrocarbon species. In the meantime, the new reaction pathways revealed, including H-assisted isomerizations between C10H8 isomers and decomposition reactions of various C10H9 isomers, emerge as relevant and are recommended for inclusion in combustion kinetic models for naphthalene formation.

Ab Initio Electron Propagators with an Hermitian, Intermediately Normalized Superoperator Metric Applied to Vertical Electron Affinities.

New-generation ab initio electron propagator methods for calculating electron detachment energies of closed-shell molecules and anions have surpassed their predecessors' accuracy and computational efficiency. Derived from an Hermitian, intermediately normalized superoperator metric, these methods contain no adjustable parameters. To assess their versatility, a standard set (NIST-50-EA) of 50 vertical electron affinities of small closed-shell molecules based on NIST reference data has been created. Errors with respect to reference data on 23 large, conjugated organic photovoltaic (OPV23) molecules have also been analyzed. All final states are valence anions that correspond to electron affinities between 0.2 and 4.2 eV. For a given scaling of the arithmetic bottleneck, the new-generation methods obtain the lowest mean absolute errors (MAEs). The best methods with fifth-power arithmetic scaling realize MAEs below 0.1 eV. Composite models comprising cubically and quintically scaling calculations executed with large and small basis sets, respectively, produce OPV23 MAEs near 0.05 eV. The accuracy of quintically scaling methods executed with large basis sets is thereby procured with reduced computational effort. New-generation results obtained with and without the diagonal self-energy approximation in the canonical Hartree-Fock basis have been compared. These results indicate that Dyson orbitals closely resemble canonical Hartree-Fock orbitals multiplied by the square root of a probability factor above 0.85.

Study of some graph theoretical parameters for the structures of anticancer drugs

Eigenvalues have great importance in the field of mathematics, and their relevance extends beyond this area to include several other disciplines such as economics, chemistry, and numerous fields. According to our study, eigenvalues are utilized in chemistry to express a chemical compound’s numerous physical properties as well as its energy form. It is important to get a comprehensive understanding of the interrelationship underlying mathematics and chemistry. The anti-bonding phase is correlated with positive eigenvalues, whereas the bonding level is connected with negative eigenvalues. Additionally, the non-bonded level corresponds to eigenvalues of zero. This study focuses on the analysis of various structures of anticancer drugs, specifically examining their characteristic polynomials, eigenvalues of the adjacency matrix, matching number and nullity. Consequently, the selected structures of the aforementioned anticancer drugs exhibit stability since they are composed of closed-shell molecules, characterized by a nullity value of zero.

Benchmarking Correlation-Consistent Basis Sets for Frequency-Dependent Polarizabilities with Multiresolution Analysis.

This paper presents the first converged frequency-dependent HF polarizability results for general molecules, on a set of 89 closed-shell atoms and molecules. The solver employs multiresolution analysis (MRA) in a multiwavelet basis to compute both ground and response states to a guaranteed precision, which are validated against independent numerical grid calculations on atoms and linear molecules. The MRA ground-state energies and response properties are used to evaluate results in correlation-consistent basis sets up to 5Z augmented with either single or double diffuse functions and core-polarization functions. Systematic trends are revealed through consideration of chemical composition as well as the use of machine learning to cluster convergence trends, the latter suggesting the possibility of learning and correcting basis-set error.

Predicting solvation energies of free radicals and their mixtures: A robust approach coupling the Peng-Robinson and COSMO-RS models

Detailed kinetic models are valuable tools for a clear understanding of the dynamics of complex reacting systems based on radical-chain mechanisms, such as combustion and oxidation. Gas-phase automatic kinetic generators, such as EXGAS, RMG, MAMOX, NetGen, REACTION, and GENESYS can be used to establish a detailed network of reaction pathways and the rates associated with each reaction. The range of applications of these gas-phase kinetic generators can be extended to liquids through diffusional and solvation corrections directly applied to the gas-phase thermo-kinetic data. In this work, a flexible framework is proposed for the calculation of the solvation correction involving closed-shell (i.e., non-free radical) and open-shell (i.e., free radicals) molecules. This novel model relies on the Peng-Robinson cubic equation of state (EoS) combined with a quantum-based continuum solvation model (COSMO-RS) through an advanced mixing rule. Unlike most predictive equations of state, the proposed model requires only pure compound inputs: critical temperature (Tc,i), critical pressure (Pc,i), acentric factor (ωi), and the screening charge distribution (σ-profile). These inputs were obtained for C/H/O free radicals using group corrections applied to the known values of the associated closed-shell molecules (parent molecules). The resulting EoS is able to provide fast predictions of solvation quantities of closed-shell molecules and C/H/O free radicals with a mean unsigned error of around 0.30 kcal/mol. The great advantage of this method is that it allows high-throughput computation of solvation quantities in pure solvents and mixtures at any temperature (including the supercritical domain), which could enable the simulation of complex oxidation kinetics in a wide range of applications.

Subgraph Isomorphic Decision Tree to Predict Radical Thermochemistry with Bounded Uncertainty Estimation.

Detailed chemical kinetic models offer valuable mechanistic insights into industrial applications. Automatic generation of reliable kinetic models requires fast and accurate radical thermochemistry estimation. Kineticists often prefer hydrogen bond increment (HBI) corrections from a closed-shell molecule to the corresponding radical for their interpretability, physical meaning, and facilitation of error cancellation as a relative quantity. Tree estimators, used due to limited data, currently rely on expert knowledge and manual construction, posing challenges in maintenance and improvement. In this work, we extend the subgraph isomorphic decision tree (SIDT) algorithm originally developed for rate estimation to estimate HBI corrections. We introduce a physics-aware splitting criterion, explore a bounded weighted uncertainty estimation method, and evaluate aleatoric uncertainty-based and model variance reduction-based prepruning methods. Moreover, we compile a data set of thermochemical parameters for 2210 radicals involving C, O, N, and H based on quantum chemical calculations from recently published works. We leverage the collected data set to train the SIDT model. Compared to existing empirical tree estimators, the SIDT model (1) offers an automatic approach to generating and extending the tree estimator for thermochemistry, (2) has better accuracy and R2, (3) provides significantly more realistic uncertainty estimates, and (4) has a tree structure much more advantageous in descent speed. Overall, the SIDT estimator marks a great leap in kinetic modeling, offering more precise, reliable, and scalable predictions for radical thermochemistry.

Accurate Electronic and Optical Properties of Organic Doublet Radicals Using Machine Learned Range-Separated Functionals.

Luminescent organic semiconducting doublet-spin radicals are unique and emergent optical materials because their fluorescent quantum yields (Φfl) are not compromised by the spin-flipping intersystem crossing (ISC) into a dark high-spin state. The multiconfigurational nature of these radicals challenges their electronic structure calculations in the framework of single-reference density functional theory (DFT) and introduces room for method improvement. In the present study, we extended our earlier development of ML-ωPBE [J. Phys. Chem. Lett., 2021, 12, 9516-9524], a range-separated hybrid (RSH) exchange-correlation (XC) functional constructed using the stacked ensemble machine learning (SEML) algorithm, from closed-shell organic semiconducting molecules to doublet-spin organic semiconducting radicals. We assessed its performance for a new test set of 64 doublet-spin radicals from five categories while placing all previously compiled 3926 closed-shell molecules in the new training set. Interestingly, ML-ωPBE agrees with the nonempirical OT-ωPBE functional regarding the prediction of the molecule-dependent range-separation parameter (ω), with a small mean absolute error (MAE) of 0.0197 a0-1, but saves the computational cost by 2.46 orders of magnitude. This result demonstrates an outstanding domain adaptation capacity of ML-ωPBE for diverse organic semiconducting species. To further assess the predictive power of ML-ωPBE in experimental observables, we also applied it to evaluate absorption and fluorescence energies (Eabs and Efl) using linear-response time-dependent DFT (TDDFT), and we compared its behavior with nine popular XC functionals. For most radicals, ML-ωPBE reproduces experimental measurements of Eabs and Efl with small MAEs of 0.299 and 0.254 eV, only marginally different from those of OT-ωPBE. Our work illustrates a successful extension of the SEML framework from closed-shell molecules to doublet-spin radicals and will open the venue for calculating optical properties for organic semiconductors using single-reference TDDFT.

New-Generation Electron-Propagator Methods for Molecular Electron-Binding Energies.

A new generation of electron-propagator methods for the calculation of electron binding energies has surpassed its antecedents with respect to accuracy, efficiency, and interpretability. No adjustable parameters are introduced in these fully ab initio procedures. Numerical tests versus several databases of valence, vertical electron binding energies of closed-shell molecules and atoms have been performed. Easily interpreted self-energy approximations with cubic arithmetic scaling produce mean absolute errors (MAEs) of 0.2 and 0.3 eV for electron detachments and attachments, respectively. The most accurate explicitly renormalized methods with fifth-power arithmetic scaling yield MAEs below 0.1 eV for detachments and attachments. Approximate renormalization leads to more efficient fifth-power alternatives for electron detachments that achieve similar accuracy with fewer bottleneck operations. Composite protocols generate excellent predictions versus highly accurate basis-extrapolated standards and experiments. The validity of the diagonal self-energy approximation and the accuracy of the approximate renormalizations are confirmed. The success of these perturbative methods based on canonical Hartree-Fock orbitals rests on a Hermitized, intermediately normalized superoperator metric. The results of all of the new-generation calculations may be analyzed in terms of final-state orbital relaxation and differential correlation effects.

Theoretical prediction of closed-shell paramagnetism for scandium and yttrium hydride.

Following chemical intuition, one would expect that all closed-shell molecules are diamagnetic. However, it is known that this is not the case for some second-row hydrides with low-lying unoccupied orbitals due to an unquenching of the total angular momentum in the presence of an external magnetic field. In this article, the transition-metal hydrides ScH and YH are investigated, assuming a similar unquenching effect involving low-lying unoccupied and orbitals formed from the metal orbitals rather than the orbitals. We are comparing results obtained with various quantum-chemical methods (HF, CCSD, CCSD(T), CCSDT) and basis sets. The obtained positive values for the magnetizabilities clearly indicate paramagnetic behavior. Vibrational effects on the magnetizability tensor are also considered, but these effects are small and do not change the overall conclusion that both ScH and YH are further examples for closed-shell paramagnetism.

A Novel N-Type Molecular Dopant With a Closed-Shell Electronic Structure Applicable to the Vacuum-Deposition Process.

Rational design, synthesis, and characterization of a new efficient versatile n-type dopant with a closed-shell electronic structure are described. By employing the tetraphenyl-dipyranylidene (DP0) framework with two 7π-electron systems modified with N,N-dimethylamino groups as the strong electron-donating substituent, 2,2',6,6'-tetrakis[4-(dimethylamino)phenyl]-4,4'-dipyranylidene (DP7), a closed-shell molecule with an extremely high-lying energy level of the highest occupied molecular orbital, close to 4.0eV below the vacuum level, is successfully developed. Thanks to its thermal stability, DP7 is applicable to vacuum deposition, which allows utilization of DP7 in bulk doping for the development of n-type organic thermoelectric materials and contact doping for reducing contact resistance in n-type organic field-effect transistors. As vacuum-deposition processable n-type dopants are very limited, DP7 stands out as a useful n-type dopant, particularly for the latter purpose.

Luminescent Radicals.

Organic radicals are attracting increasing interest as a new class of molecular emitters. They demonstrate electronic excitation and relaxation dynamics based on their doublet or higher multiplet spin states, which are different from those based on singlet-triplet manifolds of conventional closed-shell molecules. Recent studies have disclosed luminescence properties and excited state dynamics unique to radicals, such as highly efficient electron-photon conversion in OLEDs, NIR emission, magnetoluminescence, an absence of heavy atom effect, and spin-dependent and spin-selective dynamics. These are difficult or sometimes impossible to achieve with closed-shell luminophores. This review focuses on luminescent organic radicals as an emerging photofunctional molecular system, and introduces the material developments, fundamental properties including luminescence, and photofunctions. Materials covered in this review range from monoradicals, radical oligomers, and radical polymers to metal complexes with radical ligands demonstrating radical-involved emission. In addition to stable radicals, transiently formed radicals generated in situ by external stimuli are introduced. This review shows that luminescent organic radicals have great potential to expand the chemical and spin spaces of luminescent molecular materials and thus broaden their applicability to photofunctional systems.

A comparison of QTP functionals against coupled-cluster methods for EAs of small organic molecules.

EA-EOM-CCSD electron affinities and LUMO energies of various Kohn-Sham density functional theory (DFT) methods are calculated for an a priori IP benchmark set of 64 small, closed-shell molecules. The purpose of these calculations was to investigate whether the QTP KS-DFT functionals can emulate EA-EOM-CC with only a mean-field approximation. We show that the accuracy of DFT-relative to CCSD-improves significantly when elements of correlated orbital theory are introduced into the parameterization to define the QTP family of functionals. In particular, QTP(02), which has only a single range separation parameter, provides results accurate to a MAD of <0.15eV for the whole set of 64 molecules compared to EA-EOM-CCSD, far exceeding the results from the non-QTP family of density functionals.

Generalization of One-Center Nonorthogonal Configuration Interaction Singles to Open-Shell Singlet Reference States: Theory and Application to Valence-Core Pump-Probe States in Acetylacetone.

We formulate a one-center nonorthogonal configuration interaction singles (1C-NOCIS) theory for the computation of core excited states of an initial singlet state with two unpaired electrons. This model, which we refer to as 1C-NOCIS two-electron open-shell (2eOS), is appropriate for computing the K-edge near-edge X-ray absorption spectra (NEXAS) of the valence excited states of closed-shell molecules relevant to pump-probe time-resolved (TR) NEXAS experiments. With the inclusion of core-hole relaxation effects and explicit spin adaptation, 1C-NOCIS 2eOS requires mild shifts to match experiment, is free of artifacts due to spin contamination, and can capture the high-energy region of the spectrum beyond the transitions into the singly occupied molecular orbitals (SOMOs). Calculations on water and thymine illustrate the different key features of excited-state NEXAS, namely, the core-to-SOMO transitions as well as shifts and spin-splittings in the transitions analogous to those of the ground state. Simulations of the TR-NEXAS of acetylacetone after excitation to its π → π* singlet excited state at the carbon K-edge, an experiment carried out recently, showcase the ability of 1C-NOCIS 2eOS to efficiently simulate NEXAS based on nonadiabatic molecular dynamics simulations.

Classification and quantitative characterisation of the excited states of π-conjugated diradicals.

Diradicals are of high current interest as emerging materials for next generation optoelectronic applications. To tune their excited-state properties it would be greatly beneficial to have a detailed understanding of the wave functions of the different states involved but this endeavour is hampered by formal and practical barriers. To tackle these challenges, we present a formal analysis as well as concrete results on diradical excited states. We start with a detailed investigation of the available states of a two-orbital two-electron model viewed from both the valence-bond and molecular orbital perspectives. We highlight the presence of diradical and zwitterionic states and illustrate their connections to the states found in closed-shell molecules. Subsequently, we introduce practical protocols for analysing states from realistic multireference computations applying these to the para-quinodimethane (pQDM) molecule. The analysis reveals four different categories of states - diradical, zwitterionic, HOMO-SOMO as well as biexciton - while also providing insight into their energetics and optical properties. Twisting the CH2 groups allows us to interconvert between the closed- and open-shell forms of pQDM illustrating the connection between the states in both forms. More generally, we hope that this work will lay the foundations for a more powerful rational design approach to diradicals for photophysical applications.

Experimental observation of molecular-weight growth by the reactions of o-benzyne with benzyl radicals.

The chemistry of ortho-benzyne (o-C6H4) is of fundamental importance due to its role as an essential molecular building block in molecular-weight growth reactions. Here, we report on an experimental investigation of the reaction of o-C6H4 with benzyl (C7H7) radicals in a well-controlled flash pyrolysis experiment using a resistively heated SiC microtubular reactor at temperatures of 800-1600 K and pressures near 30 torr. To this end, the reactants o-C6H4 and C7H7 were pyrolytically generated from 1,2-diiodobenzene and benzyl bromide, respectively. Using molecular-beam time-of-flight mass spectrometry, we found that o-C6H4 associates with the benzyl to form C13H11 radicals, which decompose at higher temperatures via H-loss to form closed-shell C13H10 molecules. Our experimental results agree with earlier theoretical calculations by Matsugi and Miyoshi [Phys. Chem. Chem. Phys., 2012, 14, 9722-9728], who predicted the formation of fluorene (C13H10) + H to be the dominant reaction channel. At temperatures above 1400 K, we also observed the formation of C13H9 radicals, most likely the resonance-stabilized fluorenyl π-radical. Our study confirms that molecular-mass growth via the o-C6H4 + C7H7 reaction provides a versatile pathway for introducing five-membered rings, and hence curved structures, into polycyclic aromatic hydrocarbons.

Resilience of Hund's rule in the chemical space of small organic molecules.

We embark on a quest to identify small molecules in the chemical space that can potentially violate Hund's rule. Utilizing twelve TDDFT approximations and the ADC(2) many-body method, we report the energies of S1 and T1 excited states of 12 880 closed-shell organic molecules within the bigQM7ω dataset with up to 7 CONF atoms. In this comprehensive dataset, none of the molecules, in their minimum energy geometry, exhibit a negative S1-T1 energy gap at the ADC(2) level while several molecules display values <0.1 eV. The spin-component-scaled double-hybrid method, SCS-PBE-QIDH, demonstrates the best agreement with ADC(2). Yet, at this level, a few molecules with a strained sp3-N center turn out as false-positives with the S1 state lower in energy than T1. We investigate a prototypical cage molecule with an energy gap <-0.2 eV, which a closer examination revealed as another false positive. We conclude that in the chemical space of small closed-shell organic molecules, it is possible to identify geometric and electronic structural features giving rise to S1-T1 degeneracy; still, there is no evidence of a negative gap. We share the dataset generated for this study as a module, to facilitate seamless molecular discovery through data mining.

Effects of halogen atom substitution on luminescent radicals: a case study on tris(2,4,6-trichlorophenyl)methyl radical-carbazole dyads.

A series of halogen-substitute carbazole TTM radicals was synthesized. The effect of halogen substituents on radical luminescence was systematically evaluated. It was found that the well-known heavy atom effect does not work in the emission of radicals and that halogen substitution of the donor carbazole can change the HOMO and alter the absorption and emission wavelengths. In addition, the photostability was found to be improved with respect to TTM but not significantly different from that of closed-shell fluorescent molecules.

Variational quantum eigensolver for closed-shell molecules with non-bosonic corrections.

The realization of quantum advantage with noisy-intermediate-scale quantum (NISQ) machines has become one of the major challenges in computational sciences. Maintaining coherence of a physical system with more than ten qubits is a critical challenge that motivates research on compact system representations to reduce algorithm complexity. Toward this end, the variational quantum eigensolver (VQE) used to perform quantum simulations is considered to be one of the most promising algorithms for quantum chemistry in the NISQ era. We investigate reduced mapping of one spatial orbital to a single qubit to analyze the ground state energy in a way that the Pauli operators of qubits are mapped to the creation/annihilation of singlet pairs of electrons. To include the effect of non-bosonic (or non-paired) excitations, we introduce a simple correction scheme in the electron correlation model approximated by the geometrical mean of the bosonic (or paired) terms. Employing it in a VQE algorithm, we assess ground state energies of H2O, N2, and Li2O in good agreement with full configuration interaction (FCI) models respectively, using only 6, 8, and 12 qubits with quantum gate depths proportional to the squares of the qubit counts. With the adopted seniority-zero approximation that uses only one half of the qubit counts of a conventional VQE algorithm, we find that our non-bosonic correction method reaches reliable quantum chemistry simulations at least for the tested systems.