Double-hybrid Density Functional Theory Research Articles

Monomethylation and -protonation of Lutetium Dinitrogen Complex.

Due to the highly chemically inert nature, direct activation and transformation of dinitrogen are challenging. Here, we disclose the synthesis, isolation, and derivatization of (N2)3- supported by lutetium complex. Initially, a (N2)3- radical, in [{(C5Me5){MeC(NiPr)2}Lu}2(μ2-η2:η2-N2)][K(crypt)] (crypt = 2,2,2-cryptand) complex, was generated through the reduction of neutral lutetium dinitrogen complex [{(C5Me5){MeC(NiPr)2}Lu}2(μ2-η2:η2-N2)] with potassium metal. Subsequently, the reaction of (N2)3- complex with methyl triflate (or triflic acid) led to the formation of an N-C (or N-H) bond, yielding the corresponding [{(C5Me5){MeC(NiPr)2}Lu}2(NN-R)(OTf)][K(crypt)] (R = Me, H, OTf = CF3SO3) as the product. Both electron paramagnetic resonance spectroscopy and density functional theory analyses support the radical character of the NN-Me unit. The Lu-N bonds in the (NN-Me)•2- radical complex are predominantly ionic, with 77% of the unpaired electron localized on the (NN-Me) fragment. Moreover, the geometry of the pure organic radical (NN-Me)•2-, optimized by double-hybrid density functional theory, closely matches that of the (NN-Me)•2- lutetium complex.

Chemical Aristocracy: He3 Dication and Analogous Noble-Gas-Exclusive Covalent Compounds.

Herein, we predict the first set of covalently bonded triatomic molecular compounds composed exclusively of noble gases. Using a combination of double-hybrid DFT, CCSD(T), and MRCI+Q calculations and a range of bonding analyses, we explored a set of 270 doubly charged triatomics, which included various combinations of noble gases and main group elements. This extensive exploration uncovered nine noble-gas-exclusive covalent compounds incorporating helium, neon, argon, or combinations thereof, exemplified by cases such as He32+ and related systems. This work brings to light a previously uncharted domain of noble gas chemistry, demonstrating the potential of noble gases in forming covalent molecular clusters.

Limiting factors in the accuracy of DFT calculation for redox potentials.

In the present study, we have investigated factors affecting the accuracy of computational chemistry calculation of redox potentials, namely the gas-phase ionization energy (IE) and electron affinity (EA), and the continuum solvation effect. In general, double-hybrid density functional theory methods yield IEs and EAs that are on average within ~0.1 eV of our high-level W3X-L benchmark, with the best performing method being DSD-BLYP/ma-def2-QZVPP. For lower-cost methods, the average errors are ~0.2-0.3 eV, with ωB97X-3c being the most accurate (~0.15 eV). For the solvation component, essentially all methods have an average error of ~0.3 eV, which shows the limitation of the continuum solvation model. Curiously, the directly calculated redox potentials show errors of ~0.3 eV for all methods. These errors are notably smaller than what can be expected from error propagation with the two components (IE and EA, and solvation effect). Such a discrepancy can be attributed to the cancellation of errors, with the lowest-cost GFN2-xTB method benefiting the most, and the most accurate ωB97X-3c method benefiting the least. For organometallic species, the redox potentials show large deviations exceeding ~0.5 eV even for DSD-BLYP. The large errors are attributed to those for the gas-phase IEs and EAs, which represents a major barrier to the accurate calculation of redox potentials for such systems.

Gas-Phase Phenyl Radical + O2 Reacts via a Submerged Transition State.

In the gas-phase chemistry of the atmosphere and automotive fuel combustion, peroxyl radical intermediates are formed following O2 addition to carbon-centered radicals which then initiate a complex network of radical reactions that govern the oxidative processing of hydrocarbons. The rapid association of the phenyl radical-a fundamental radical related to benzene-with O2 has hitherto been modeled as a barrierless process, a common assumption for peroxyl radical formation. Here, we provide an alternate explanation for the kinetics of this reaction by deploying double-hybrid density functional theory (DFT), at the DSD-PBEP86-D3(BJ)/aug-cc-pVTZ level of theory, and locate a submerged adiabatic transition state connected to a prereaction complex along the reaction entrance pathway. Using this potential energy scheme, experimental rate coefficients k(T) for the addition of O2 to the phenyl radical are accurately reproduced within a microcanonical kinetic model. This work highlights that purportedly barrierless radical oxidation reactions may instead be modeled using stationary points, which in turn provides insight into pressure and temperature dependence.

DLPNO-CCSD(T) and DFT study of the acetate-assisted C-H activation of benzaldimine at [RuCl2(p-cymene)]2: the relevance of ligand exchange processes at ruthenium(II) complexes in polar protic media.

To gain mechanistic insights into the acetate-assisted cyclometallations of arylimines promoted by [RuCl2(p-cymene)]2 in polar protic media, DFT geometry optimizations (with M06 and ωB97X-D3 functionals and the cc-pVDZ-PP[Ru] basis set) followed by DLPNO-CCSD(T)/CBS energy evaluations were performed using benzaldimine as a model substrate and methanol as the solvent (with CPCM or SMD models). The calculation results show that coordination of the imine to an acetate ruthenium precursor is followed by anion (chloride or acetate) dissociation as the rate-determining step of the process. H-Bonding of two explicit MeOH to the anion reduces the calculated activation energy to ca. 23 kcal mol-1, in good agreement with the experimental half-life at room temperature. Subsequent AMLA/CMD C-H activation of the intermediate cationic complexes is a faster, reversible process. Alternative reaction pathways involving neutral diacetate ruthenium complexes offer AMLA/CMD transition state structures of lower energy but are precluded due to higher energy barriers for the initial ligand exchange processes at ruthenium. Solvent assistance accelerates the final chloride/acetate exchange processes on the cycloruthenate intermediates, particularly when compression in the condensed phase is taken into consideration. The performance of six DFT functionals (with the aug-pVTZ-PP[Ru] basis set) was assessed using the DLPNO-CCSD(T)/CBS reference energies. Neutral diacetate ruthenium complexes were incorrectly predicted as being kinetically relevant when using hybrid DFT methods (PBE0-D3(BJ), M06-2X or ωB97M-V). Good agreement between the calculated barrier heights and our benchmark energy results was obtained by using double-hybrid DFT methods. PWPB95 with D3(BJ) or D4 dispersion energy corrections was found to be the most accurate (ΔG≠ MUE of ca. 1 kcal mol-1). This study may aid our understanding of and help with further experimental investigations of synthetically useful carboxylate-assisted C-H bond functionalizations involving (N,C)-cyclometallated (p-cymene)Ru(II) intermediate complexes in sustainable polar protic solvents.

Structural evolution and electronic properties of cerium doped germanium anionic nanocluster CeGen− (n = 5–17): Theoretical investigation

AbstractThe rare earth element doped germanium cluster represents a fundamental nanomaterial and exhibits potential in next‐generation industrial electronic nanodevices and applied semiconductors. Herein, the cerium‐doped germanium anionic nanocluster CeGen− (n = 5–17) has been comprehensively investigated by the double hybrid density functional theory of mPW2PLYP associated with the unbiased global searching technique of artificial bee colony algorithm. The cluster's growth pattern undergoes three stages: n = 5–9 with the replaced structure, n = 10–15 with the linked structure, and n ≥ 16 forming a Ce‐encapsulated in Ge inner cage motif. The clusters' PES, IR, and Raman spectra were simulated, and their HOMO‐LUMO gap, magnetism, charge transfer, and relative stability were predicted. These theoretical values can serve as a reference for future experiments to some extent. Moreover, the special D2d symmetry cage geometry of CeGe16− leads to a higher stability and preferred energy gap, making it an ideal candidate for further studies on its aromaticity, UV–vis spectra, and chemical bonding characteristics. In summary, CeGe16− has excellent optical activity that can be potentially employed as a building block in the development of optoelectronic functional materials.

Assessment of DLPNO-MP2 Approximations in Double-Hybrid DFT.

The unfavorable scaling (N5) of the conventional second-order Møller-Plesset theory (MP2) typically prevents the application of double-hybrid (DH) density functionals to large systems with more than 100 atoms. A prominent approach to reduce the computational demand of electron correlation methods is the domain-based local pair natural orbital (DLPNO) approximation that is successfully used in the framework of DLPNO-CCSD(T). Its extension to MP2 [Pinski P.; Riplinger, C.; Valeev, E. F.; Neese, F. J. Chem. Phys. 2015, 143, 034108.] paved the way for DLPNO-based DH (DLPNO-DH) methods. In this work, we assess the accuracy of the DLPNO-DH approximation compared to conventional DHs on a large number of 7925 data points for thermochemistry and 239 data points for structural features, including main-group and transition-metal systems. It is shown that DLPNO-DH-DFT can be applied successfully to perform energy calculations and geometry optimizations for large molecules at a drastically reduced computational cost. Furthermore, PNO space extrapolation is shown to be applicable, similar to its DLPNO-CCSD(T) counterpart, to reduce the remaining error.

Compilation of Ionic Clusters with the Rock Salt Structure: Accurate Benchmark Thermochemical Data, Assessment of Quantum Chemistry Methods, and the Convergence Behavior of Lattice Energies.

In the present study, computational quantum chemistry is used to obtain lattice energies (LEs) for a range of ionic clusters with the NaCl structure. Specifically, the compounds include NaF, NaCl, MgO, MgS, KF, CaO, and CaS clusters, (MX)n, with n = 1, 2, 4, 6, 8, 12, 16, 24, 32, 40, 50, 60, 75, 90, and 108. The highest-level W2 and W1X-2 methods are applied to the small clusters with n = 1 to 8 (the MX35 data set). The assessment with MX35 shows that, for the calculation of geometries and vibrational frequencies, the PBE0-D3(BJ) and PBE-D3(BJ) DFT methods are reasonable, but the calculation of atomization energies is more challenging. This is a result of different systematic deviations for clusters of different species. Thus, species-specific adjustments are applied for larger clusters, which are calculated with the DuT-D3 double-hybrid DFT method, the MN15 DFT method, and the PM7 semi-empirical method. They yield smoothly converging LEs to the bulk values. It is also found that, for the alkali-metal species, the LEs for a single molecule are ∼70% of the bulk values, while for the alkali-earth species, they are ∼80%. This has enabled a straightforward means to the first-principles estimation of LEs for similarly structured ionic compounds.

Protonation Isomer Specific Ion-Molecule Radical Reactions.

Through a combination of ion-mobility filtering and laser-equipped quadrupole ion-trap mass spectrometry, the gas-phase reaction kinetics of two protonation isomers of the distonic-radical quinazoline cation are independently measured with ethylene. For these radical addition reactions, protonation site variations drive significant changes in nearby radical reactivity, and this is primarily due to through-space electrostatic effects. Furthermore, quantum chemical methods specifically designed for calculating long-range interactions, such as double-hybrid density functional theory, are required to rationalize the experimentally measured difference in reactivity.

Vertical Ionization Potentials and Electron Affinities at the Double-Hybrid Density Functional Level.

The double-hybrid (DH) time-dependent density functional theory is extended to vertical ionization potentials (VIPs) and electron affinities (VEAs). Utilizing the density fitting approximation, efficient implementations are presented for the genuine DH ansatz relying on the perturbative second-order correction, while an iterative analogue is also elaborated using our second-order algebraic-diagrammatic construction [ADC(2)]-based DH approach. The favorable computational requirements of the present schemes are discussed in detail. The performance of the recently proposed spin-component-scaled and spin-opposite-scaled (SOS) range-separated (RS) and long-range corrected (LC) DH functionals is comprehensively assessed, while popular hybrid and global DH approaches are also discussed. For the benchmark calculations, up-to-date test sets are selected with high-level coupled-cluster references. Our results show that the ADC(2)-based SOS-RS-PBE-P86 approach is the most accurate and robust functional. This method consistently outperforms the excellent SOS-ADC(2) approach for VIPs, although the results are somewhat less satisfactory for VEAs. Among the genuine DH functionals, the SOS-ωPBEPP86 approach is also recommended for describing ionization processes, but its performance is even less reliable for electron-attached states. In addition, surprisingly good results are attained by the LC hybrid ωB97X-D functional, where the corresponding occupied (unoccupied) orbital energies are retrieved as VIPs (VEAs) within the present formalism.

The prospects of cation transfer to chalcogen nucleophiles

In this study, we used computational quantum chemistry to investigate the cation affinity for a range of nucleophiles to gauge the possibility of using organochalcogens as catalysts for cation transfer (reference data and geometries are provided in the repository https://github.com/armanderch/ca176 ). In general, the calculated gas-phase cation affinities decrease in the order Cl+> Br+> I+> carbon-centered cation, the anionic nucleophiles have significantly larger cation affinities than the neutral ones, sulfides have larger cation affinities than selenides, and solvation lowers the cation affinities and especially for anionic nucleophiles. These observations are consistent with general chemical intuitions. The energies for the resulting condensed-phase cation transfer reactions show that transferring a carbon-centered cation from a neutral source (e.g., Me2CO3) to a chalcogen nucleophile (e.g., Me2S) is thermochemically viable. However, they are associated with large kinetic barriers. Overall, we find that SeMeC6H5may be a suitable catalyst for transferring a carbon-centered cation from an active source such as MeCO3R or MeSO4R. In this study, we also find that double-hybrid DFT methods, e.g., DSD-PBEP86 to be reasonable for the study of these cation transfer processes.

Do Models beyond Hybrid Density Functionals Increase the Agreement with Experiment for Predicted NMR Chemical Shifts or Electric Field Gradient Tensors in Organic Solids?

Ab initio predictions of chemical shifts and electric field gradient (EFG) tensor components are frequently used to help interpret solid-state nuclear magnetic resonance (NMR) experiments. Typically, these predictions employ density functional theory (DFT) with generalized gradient approximation (GGA) functionals, though hybrid functionals have been shown to improve accuracy relative to experiment. Here, the performance of a dozen models beyond the GGA approximation are examined for the prediction of solid-state NMR observables, including meta-GGA, hybrid, and double-hybrid density functionals and second-order Møller-Plesset perturbation theory (MP2). These models are tested on organic molecular crystal data sets containing 169 experimental 13C and 15N chemical shifts and 114 17O and 14N EFG tensor components. To make these calculations affordable, gauge-including projector augmented wave (GIPAW) Perdew-Burke-Ernzerhof (PBE) calculations with periodic boundary conditions are combined with a local intramolecular correction computed at the higher level of theory. Within the context of typical NMR property calculations performed on a static, DFT-optimized crystal structure, the benchmarking finds that the double-hybrid DFT functionals produce errors versus experiment that are no smaller than those of hybrid functionals in the best cases, and they can be larger. MP2 errors versus experiment are even bigger. Overall, no practical advantages are found for using any of the tested double-hybrid functionals or MP2 to predict experimental solid-state NMR chemical shifts and EFG tensor components for routine organic crystals, especially given the higher computational cost of those methods. This finding likely reflects error cancellation benefiting the hybrid functionals. Improving the accuracy of the predicted chemical shifts and EFG tensors relative to experiment would probably require more robust treatments of the crystal structures, their dynamics, and other factors.

Estimating the Vertical Ionization Potential of Single-Stranded DNA Molecules

The electronic properties of DNA molecules, defined by the sequence-dependent ionization potentials of nucleobases, enable long-range charge transport along the DNA stacks. This has been linked to a range of key physiological processes in the cells and to the triggering of nucleobase substitutions, some of which may cause diseases. To gain molecular-level understanding of the sequence dependence of these phenomena, we estimated the vertical ionization potential (vIP) of all possible nucleobase stacks in B-conformation, containing one to four Gua, Ade, Thy, Cyt, or methylated Cyt. To do this, we used quantum chemistry calculations and more precisely the second-order Møller-Plesset perturbation theory (MP2) and three double-hybrid density functional theory methods, combined with several basis sets for describing atomic orbitals. The calculated vIP of single nucleobases were compared to experimental data and those of nucleobase pairs, triplets, and quadruplets, to observed mutability frequencies in the human genome, reported to be correlated with vIP values. This comparison selected MP2 with the 6-31G* basis set as the best of the tested calculation levels. These results were exploited to set up a recursive model, called vIPer, which estimates the vIP of all possible single-stranded DNA sequences of any length based on the calculated vIPs of overlapping quadruplets. vIPer's vIP values correlate well with oxidation potentials measured by cyclic voltammetry and activities obtained through photoinduced DNA cleavage experiments, further validating our approach. vIPer is freely available on the github.com/3BioCompBio/vIPer repository.

Double-Hybrid Density Functional Theory for Core Excitations: Theory and Benchmark Calculations.

The double-hybrid (DH) time-dependent density functional theory is extended to core excitations. Two different DH formalisms are presented utilizing the core-valence separation (CVS) approximation. First, a CVS-DH variant is introduced relying on the genuine perturbative second-order correction, while an iterative analogue is also presented using our second-order algebraic-diagrammatic construction [ADC(2)]-based DH ansatz. The performance of the new approaches is tested for the most popular DH functionals using the recently proposed XABOOM [J. Chem. Theory Comput.2021, 17, 1618] benchmark set. In order to make a careful comparison, the accuracy and precision of the methods are also inspected. Our results show that the genuine approaches are highly competitive with the more advanced CVS-ADC(2)-based methods if only excitation energies are required. In contrast, as expected, significant differences are observed in oscillator strengths; however, the precision is acceptable for the genuine functionals as well. Concerning the performance of the CVS-DH approaches, the PBE0-2/CVS-ADC(2) functional is superior, while its spin-opposite-scaled variant is also recommended as a cost-effective alternative. For these approaches, significant improvements are realized in the error measures compared with the popular CVS-ADC(2) method.

Laser Spectroscopy of Helium Solvated Clusters of Methanol and Methanol-Water in the Symmetric Methyl Stretching Band.

Mid-infrared spectra of methanol and methanol-water clusters have been investigated in the symmetric CD3 stretching band of CD3OH and CD3OD. We find that the position of this band provides a useful signature of the general type of hydrogen-bonded cluster it is associated with. Our results are consistent with those previously reported in the OH stretching region (Sulaiman, M. I.; Yang, S.; Ellis, A. M. J. Phys. Chem. A 2017, 121, 771-776) in that methanol clusters from the trimer to the pentamer are cyclic and that mixed clusters with one water molecule (and at least two methanol molecules) are also cyclic. We additionally provide evidence that the methanol trimer adopts a chair-like structure (as opposed to bowl-like), that mixed clusters with a larger number of water molecules are also cyclic, and that branched methanol clusters contribute to the depletion signal in larger methanol clusters. We performed double-hybrid DFT calculations which support these interpretations.

A deep transfer learning-based protocol accelerates full quantum mechanics calculation of protein.

Effective full quantum mechanics (FQM) calculation of protein remains a grand challenge and of great interest in computational biology with substantial applications in drug discovery, protein dynamic simulation and protein folding. However, the huge computational complexity of the existing QM methods impends their applications in large systems. Here, we design a transfer-learning-based deep learning (TDL) protocol for effective FQM calculations (TDL-FQM) on proteins. By incorporating a transfer-learning algorithm into deep neural network (DNN), the TDL-FQM protocol is capable of performing calculations at any given accuracy using models trained from small datasets with high-precision and knowledge learned from large amount of low-level calculations. The high-level double-hybrid DFT functional and high-level quality of basis set is used in this work as a case study to evaluate the performance of TDL-FQM, where the selected 15 proteins are predicted to have a mean absolute error of 0.01kcal/mol/atom for potential energy and an average root mean square error of 1.47kcal/mol/$ {\rm A^{^{ \!\!\!o}}} $ for atomic forces. The proposed TDL-FQM approach accelerates the FQM calculation more than thirty thousand times faster in average and presents more significant benefits in efficiency as the size of protein increases. The ability to learn knowledge from one task to solve related problems demonstrates that the proposed TDL-FQM overcomes the limitation of standard DNN and has a strong power to predict proteins with high precision, which solves the challenge of high precision prediction in large chemical and biological systems.

Multiscale Modeling of Phosphate···π Contacts in RNA U-Turns Exposes Differences between Quantum-Chemical and AMBER Force Field Descriptions.

Phosphate···π, also called anion···π, contacts occur between nucleobases and anionic phosphate oxygens (OP2) in r(GNRA) and r(UNNN) U-turn motifs (N = A,G,C,U; R = A,G). These contacts were investigated using state-of-the-art quantum-chemical methods (QM) to characterize their physicochemical properties and to serve as a reference to evaluate AMBER force field (AFF) performance. We found that phosphate···π interaction energies calculated with the AFF for dimethyl phosphate···nucleobase model systems are less stabilizing in comparison with double-hybrid DFT and that minimum contact distances are larger for all nucleobases. These distance stretches are also observed in large-scale AFF vs QM/MM computations and classical molecular dynamics (MD) simulations on several r(gcGNRAgc) tetraloop hairpins when compared to experimental data extracted from X-ray/cryo-EM structures (res. ≤ 2.5 Å) using the WebFR3D bioinformatic tool. MD simulations further revealed shifted OP2/nucleobase positions. We propose that discrepancies between the QM and AFF result from a combination of missing polarization in the AFF combined with too large AFF Lennard-Jones (LJ) radii of nucleobase carbon atoms in addition to an exaggerated short-range repulsion of the r-12 LJ repulsive term. We compared these results with earlier data gathered on lone pair···π contacts in CpG Z-steps occurring in r(UNCG) tetraloops. In both instances, charge transfer calculations do not support any significant n → π* donation effects. We also investigated thiophosphate···π contacts that showed reduced stabilizing interaction energies when compared to phosphate···π contacts. Thus, we challenge suggestions that the experimentally observed enhanced thermodynamic stability of phosphorothioated r(GNRA) tetraloops can be explained by larger London dispersion.

High-level quantum chemistry exploration of reduction by group-13 hydrides: insights into the rational design of bio-mimic CO2 reduction

In the present study, we have used computational quantum chemistry to explore the reduction of various types of substrates by group-13 hydrides. We use the high-level L-W1X method to obtain the energies for the constituent association and hydride transfer reactions. We find that the hydride transfer reactions are highly exothermic, while the preceding association reactions are less so. Thus, improving the thermodynamics of substrate association may improve the overall process. Among the various substrates, amine and imine show the strongest binding, while CO2 shows the weakest. Between the group-13 hydrides, alanes bind most strongly with the substrates, and they also have the most exothermic hydride transfer reactions. To facilitate CO2 binding, we have examined alanes with electron-withdrawing groups, and we indeed find CF3 groups to be effective. Drawing inspiration from the RuBisCO enzyme for CO2 fixation, we have further examined the activation of CO2 with two independent AlH(CF3)2 molecules, with the results showing an even more exothermic association. This observation may form the basis for designing an effective dialane reagent for CO2 reduction. We have also assessed a range of lower-cost computational methods for the calculation of systems in the present study. We find the DSD-PBEP86 double-hybrid DFT method to be the most suitable for the study of related medium-sized systems.

Role of Exact Exchange in Difference Projected Double-Hybrid Density Functional Theory for Treatment of Local, Charge Transfer, and Rydberg Excitations

Difference approaches to the study of excited states have undergone a renaissance in recent years, with the development of a plethora of algorithms for locating self-consistent field approximations to excited states. Density functional theory is likely to offer the best balance of cost and accuracy for difference approaches, and yet there has been little investigation of how the parametrization of density functional approximations affects performance. In this work, we aim to explore the role of the global Hartree-Fock exchange parameter in tuning accuracy of different excitation types within the framework of the recently introduced difference projected double-hybrid density functional theory approach and contrast the performance with conventional time-dependent double-hybrid density functional theory. Difference projected double-hybrid density functional theory was demonstrated to give vertical excitation energies with average error and standard deviation with respect to multireference perturbation theory comparable to more expensive linear-response coupled cluster approaches ( J. Chem. Phys.2020, 153, 074103). However, despite benchmarking of local excitations, there has been no investigation of the methods performance for charge transfer or Rydberg excitations. In this work we report a new benchmark of charge transfer, Rydberg, and local excited state vertical excitation energies and examine how the exact Hartree-Fock exchange affects the benchmark performance to provide a deeper understanding of how projection and nonlocal correlation balance differing sources of error in the ground and excited states.

Reduced-Scaling Double Hybrid Density Functional Theory with Rapid Basis Set Convergence through Localized Pair Natural Orbital F12.

Following earlier work [Mehta, N.; Martin, J. M. L. J. Chem. Theory Comput.2022, 10.1021/acs.jctc.2c00426] that showed how the slow basis set convergence of the double hybrid density functional theory can be obviated by the use of F12 explicit correlation in the GLPT2 step (second order Görling-Levy perturbation theory), we demonstrate here for the very large and chemically diverse GMTKN55 benchmark suite that the CPU time scaling of this step can be reduced (asymptotically linearized) using the localized pair natural orbital (PNO-L) approximation at negligible cost in accuracy.