Gaussian‐2 theory for molecular energies of first‐ and second‐row compounds

Scalable Ab Initio Electronic Structure Methods with Near Chemical Accuracy for Main Group Chemistry

This study evaluates the precision of widely recognized quantum chemical methodologies, CCSD(T), DLPNO-CCSD(T), and localized ph-AFQMC, for determining the thermochemistry of main group elements. DLPNO-CCSD(T) and localized ph-AFQMC, which offer greater scalability compared to canonical CCSD(T), have emerged over the past decade as pivotal in producing precise benchmark chemical data. Our investigation includes closed-shell, neutral molecules, focusing on their heat of formation and atomization energy sourced from four specific small molecule data sets. First, we selected molecules from the G2 and G3 data sets, noted for their reliable experimental heat of formation data. Additionally, we incorporate molecules from the W4-11 and W4-17 sets, which provide high-level theoretical reference values for atomization energy at 0 K. Our findings reveal that both DLPNO-CCSD(T) and ph-AFQMC methods are capable of achieving a root-mean-square deviation of less than 1 kcal/mol across the combined data set, aligning with the threshold for chemical accuracy. Moreover, we make efforts to confine the maximum deviations within 2 kcal/mol, a degree of precision that significantly broadens the applicability of these methods in fields such as biology and materials science.

Characterization of the fragmentation mechanisms in electrospray ionization tandem mass spectrometry of chloroquinoline derivatives with larvicidal activity against Aedes aegypti

RATIONALE

4,7-Dichloroquinoline (DCQ) represents a group of synthetic molecules inspired by natural products with important roles in biological and biomedical areas. This work aimed to characterize DCQ and its derivatives by high-resolution electrospray ionization (ESI) mass spectrometry and tandem mass spectrometry (ESI-MS/MS), supported by theoretical calculations. Biological assays were carried out with DCQ and its derivatives to determine LC50 values against Aedes aegypti larvae.

METHODS

Five DCQ derivatives were synthesized by using previously described protocols. ESI-MS/MS analyses were carried out with a quadrupole/time-of-flight and ion-trap instrument. The proposed gas-phase protonation sites and fragmentation were supported by density functional theory calculations. The larvicidal tests were performed with the Ae. aegypti Rockefeller strain, and the LC50 values were determined by employing five test concentrations. Larval mortality was determined after treatment for 48 h.

RESULTS

DCQ bromides or aldehydes (C-3 or C-8 positions), as well as the trimethylsilyl derivative (C-3 position), were prepared. Detailed ESI-MS/MS data revealed heteroatom elimination through an exception to the even-electron rule, to originate open-shell species. Computational studies were used to define the protonation sites and fragmentation pathways. High activity of DCQ and its derivatives against Ae. aegypti larvae was demonstrated.

CONCLUSION

Our results provided a well-founded characterization of the fragmentation reactions of DCQ and its derivatives, which can be useful for complementary studies of the development of a larvicidal product against Ae. aegypti.

Reference Energies for Valence Ionizations and Satellite Transitions

Upon ionization of an atom or a molecule, another electron (or more) can be simultaneously excited. These concurrently generated states are called "satellites" (or shakeup transitions) as they appear in ionization spectra as higher-energy peaks with weaker intensity and larger width than the main peaks associated with single-particle ionizations. Satellites, which correspond to electronically excited states of the cationic species, are notoriously challenging to model using conventional single-reference methods due to their high excitation degree compared to the neutral reference state. This work reports 42 satellite transition energies and 58 valence ionization potentials (IPs) of full configuration interaction quality computed in small molecular systems. Following the protocol developed for the quest database [Véril, M.; Scemama, A.; Caffarel, M.; Lipparini, F.; Boggio-Pasqua, M.; Jacquemin, D.; and Loos, P.-F. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517], these reference energies are computed using the configuration interaction using a perturbative selection made iteratively (CIPSI) method. In addition, the accuracy of the well-known coupled-cluster (CC) hierarchy (CC2, CCSD, CC3, CCSDT, CC4, and CCSDTQ) is gauged against these new accurate references. The performances of various approximations based on many-body Green's functions (GW, GF2, and T-matrix) for IPs are also analyzed. Their limitations in correctly modeling satellite transitions are discussed.

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.

Achieving Accuracy and Economy for Calculating Vertical Detachment Energies of Molecular Anions: A Model Chemistry Composite Methods

The vertical detachment energy (VDE) is a vital factor for predicting the stability of anions that have important applications in the atom, molecule and cluster science. Due to the synthetic or characterization difficulty of anions, accurate and efficient predictions of VDE independent of laboratory data have always been an appealing task to remedy the experimental deficiencies. Unfortunately, the generally adopted CCSD(T) and electron propagator theory (EPT) methods have respectively been proven to be reliable but very cost-expensive, and cost-effective but sometimes problematic when Koopman's theorem is invalid. Here, we for the first time introduced and benchmarked a series of model chemistry composite methods (e. g., CBS-QB3, G4 and W1BD) on calculating VDE for 57 molecular anions. Notably, CBS-QB3 exceeds the accuracy of CCSD(T) while approaching the economy of EPT. Therefore, we highly recommend the composite method CBS-QB3 to compute VDEs for molecular anions in the attractive "killing two birds with one stone" manner.

Fermionic Reduced Density Low-Rank Matrix Completion, Noise Filtering, and Measurement Reduction in Quantum Simulations

Fermionic reduced density matrices summarize the key observables in Fermionic systems. In electronic systems, the two-particle reduced density matrix (2-RDM) is sufficient to determine the energy and most physical observables of interest. Here, we consider the possibility of using matrix completion to reconstruct the two-particle reduced density matrix to chemical accuracy from partial information. We consider the case of noiseless matrix completion, where the partial information corresponds to a subset of the 2-RDM elements, as well as noisy completion, where the partial information corresponds to both a subset of elements and statistical noise in their values. Through experiments on a set of 24 molecular systems, we find that 2-RDM can be efficiently reconstructed from a reduced amount of information. In the case of noisy completion, this results in a multiple orders of magnitude reduction in the number of measurements needed to determine the 2-RDM with chemical accuracy. These techniques can be readily applied to both classical and quantum algorithms for quantum simulations.

Reference Vertical Excitation Energies for Transition Metal Compounds

To enrich and enhance the diversity of the quest database of highly accurate excitation energies [Véril, M.; et al. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517], we report vertical transition energies in transition metal compounds. Eleven diatomic molecules with a singlet or doublet ground state containing a fourth-row transition metal (CuCl, CuF, CuH, ScF, ScH, ScO, ScS, TiN, ZnH, ZnO, and ZnS) are considered, and the corresponding excitation energies are computed using high-level coupled-cluster (CC) methods, namely, CC3, CCSDT, CC4, and CCSDTQ, as well as multiconfigurational methods such as CASPT2 and NEVPT2. In many cases, to provide more comprehensive benchmark data, we also provide full configuration interaction estimates computed with the configuration interaction using a perturbative selection made iteratively (CIPSI) method. Based on these calculations, theoretical best estimates of the transition energies are established in both the aug-cc-pVDZ and aug-cc-pVTZ basis sets. This allows us to accurately assess the performance of the CC and multiconfigurational methods for this specific set of challenging transitions. Furthermore, comparisons with experimental data and previous theoretical results are also reported.

Corrected density functional theory and the random phase approximation: Improved accuracy at little extra cost

We recently introduced an efficient methodology to perform density-corrected Hartree-Fock density functional theory [DC(HF)-DFT] calculations and an extension to it we called "corrected" HF DFT [C(HF)-DFT] [Graf and Thom, J. Chem. Theory Comput. 19 5427-5438 (2023)]. In this work, we take a further step and combine C(HF)-DFT, augmented with a straightforward orbital energy correction, with the random phase approximation (RPA). We refer to the resulting methodology as corrected HF RPA [C(HF)-RPA]. We evaluate the proposed methodology across various RPA methods: direct RPA (dRPA), RPA with an approximate exchange kernel, and RPA with second-order screened exchange. C(HF)-dRPA demonstrates very promising performance; for RPA with exchange methods, on the other hand, we often find over-corrections.

On Prototropy and Bond Length Alternation in Neutral and Ionized Pyrimidine Bases and Their Model Azines in Vacuo

In this review, the complete tautomeric equilibria are derived for disubstituted pyrimidine nucleic acid bases starting from phenol, aniline, and their model compounds-monosubstituted aromatic azines. The differences in tautomeric preferences for isolated (gaseous) neutral pyrimidine bases and their model compounds are discussed in light of different functional groups, their positions within the six-membered ring, electronic effects, and intramolecular interactions. For the discussion of tautomeric preferences and for the analysis of internal effects, recent quantum-chemical results are taken into account and compared to some experimental ones. For each possible tautomer-rotamer of the title compounds, the bond length alternation, measured by means of the harmonic oscillator model of electron delocalization (HOMED) index, is examined. Significant HOMED similarities exist for mono- and disubstituted derivatives. The lack of parallelism between the geometric (HOMED) and energetic (ΔG) parameters for all possible isomers clearly shows that aromaticity is not the main factor that dictates tautomeric preferences for pyrimidine bases, particularly for uracil and thymine. The effects of one-electron loss (positive ionization) and one-electron gain (negative ionization) on prototropy and bond length alternation are also reviewed for pyrimidine bases and their models.

A larger basis set describes atomization energy core-valence correction better than a higher-order coupled-cluster method

The accuracy of coupled-cluster methods for the computation of core-valence correction to atomization energy was assessed. Truncation levels up to CCSDTQP were considered together with (aug-)cc-pwCVnZ (n = D, T, Q, 5) basis sets and three different extrapolation techniques (canonical and flexible Helgaker formula and Riemann zeta function extrapolation). With the exception of CCSD, a more accurate correction can be obtained from a larger basis set using a lower-level coupled-cluster method, and not vice versa. For the CCSD(T) level, it also implies faster computations with modern codes. We also discussed the importance of moving to higher-order or all-electron methods for geometry optimizations. The present study provides the general knowledge needed for the most accurate state-of-the-art computations.

Leveling the Mountain Range of Excited-State Benchmarking through Multistate Density Functional Theory

The performance of multistate density functional theory (MSDFT) with nonorthogonal state interaction (NOSI) is assessed for 100 vertical excitation energies against the theoretical best estimates extracted to the full configuration interaction accuracy on the database developed by Loos et al. in 2018 (Loos2018). Two optimization techniques, namely, block-localized excitation and target state optimization, are examined along with two ways of estimating the transition density functional (TDF) for the correlation energy of the Hamiltonian matrix density functional. The results from the two optimization methods are similar. It was found that MSDFT-NOSI using the spin-multiplet degeneracy constraint for the TDF of spin-coupling interaction, along with the M06-2X functional, yields a root-mean-square error (RMSE) of 0.22 eV, which performs noticeably better than time-dependent density functional theory (DFT) at an RMSE of 0.43 eV using the same functional and basis set on the Loos2018 database. In comparison with wave function theory, NOSI has smaller errors than CIS(D∞), LR-CC2, and ADC(3) all of which have an RMSE of 0.28 eV, but somewhat greater than STEOM-CCSD (RMSE of 0.14 eV) and LR-CCSD (RMSE of 0.11 eV) wave function methods. In comparison with Kohn-Sham (KS) DFT calculations, the multistate DFT approach has little double counting of correlation. Importantly, there is no noticeable difference in the performance of MSDFT-NOSI on the valence, Rydberg, singlet, triplet, and double-excitation states. Although the use of another hybrid functional PBE0 leads to a greater RMSE of 0.36 eV, the deviation is systematic with a linear regression slope of 0.994 against the results with M06-2X. The present benchmark reveals that density functional approximations developed for KS-DFT for the ground state with a noninteracting reference may be adopted in MSDFT calculations in which the state interaction is key.

Greater transferability and accuracy of norm-conserving pseudopotentials using nonlinear core corrections

We present an investigation into the transferability of pseudopotentials (PPs) with a nonlinear core correction (NLCC) using the Goedecker, Teter, and Hutter (GTH) protocol across a range of pure GGA, meta-GGA and hybrid functionals, and their impact on thermochemical and non-thermochemical properties. The GTH-NLCC PP for the PBE density functional demonstrates remarkable transferability to the PBE0 and ωB97X-V exchange-correlation functionals, and relative to no NLCC, improves agreement significantly for thermochemical benchmarks compared to all-electron calculations. On the other hand, the B97M-rV meta-GGA functional performs poorly with the PBE-derived GTH-NLCC PP, which is mitigated by reoptimizing the NLCC parameters for this specific functional. The findings reveal that atomization energies exhibit the greatest improvements from use of the NLCC, which thus provides an important correction needed for covalent interactions relevant to applications involving chemical reactivity. Finally we test the NLCC-GTH PPs when combined with medium-size TZV2P molecularly optimized (MOLOPT) basis sets which are typically utilized in condensed phase simulations, and show that they lead to consistently good results when compared to all-electron calculations for atomization energies, ionization potentials, barrier heights, and non-covalent interactions, but lead to somewhat larger errors for electron affinities.

Simple and Efficient Route toward Improved Energetics within the Framework of Density-Corrected Density Functional Theory

The crucial step in density-corrected Hartree-Fock density functional theory (DC(HF)-DFT) is to decide whether the density produced by the density functional for a specific calculation is erroneous and, hence, should be replaced by, in this case, the HF density. We introduce an indicator, based on the difference in noninteracting kinetic energies between DFT and HF calculations, to determine when the HF density is the better option. Our kinetic energy indicator directly compares the self-consistent density of the analyzed functional with the HF density, is size-intensive, reliable, and most importantly highly efficient. Moreover, we present a procedure that makes best use of the computed quantities necessary for DC(HF)-DFT by additionally evaluating a related hybrid functional and, in that way, not only "corrects" the density but also the functional itself; we call that procedure corrected Hartree-Fock density functional theory (C(HF)-DFT).

Sub 20 cm-1 computational prediction of the CH bond energy - a case of systematic error in computational thermochemistry

The bond dissociation energy of methylidyne, D0(CH), is studied using an improved version of the High-Accuracy Extrapolated ab initio Thermochemistry (HEAT) approach as well as the Feller-Peterson-Dixon (FPD) model chemistry. These calculations, which include basis sets up to nonuple (aug-cc-pCV9Z) quality, are expected to be capable of providing results substantially more accurate than the ca. 1 kJ mol-1 level that is characteristic of standard high-accuracy protocols for computational thermochemistry. The calculated 0 K CH bond energy (27 954 ± 15 cm-1 for HEAT and 27 956 ± 15 cm-1 for FPD), along with equivalent treatments of the CH ionization energy and the CH+ dissociation energy (85 829 ± 15 cm-1 and 32 946 ± 15 cm-1, respectively), were compared to the existing benchmarks from Active Thermochemical Tables (ATcT), uncovering an unexpected difference for D0(CH). This has prompted a detailed reexamination of the provenance of the corresponding ATcT benchmark, allowing the discovery and subsequent correction of a systematic error present in several published high-level calculations, ultimately yielding an amended ATcT benchmark for D0(CH). Finally, the current theoretical results were added to the ATcT Thermochemical Network, producing refined ATcT estimates of 27 957.3 ± 6.0 cm-1 for D0(CH), 32 946.7 ± 0.6 cm-1 for D0(CH+), and 85 831.0 ± 6.0 cm-1 for IE(CH).

Benchmark Phaseless Auxiliary-Field Quantum Monte Carlo Method for Small Molecules

We report a scalable Fortran implementation of the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) and demonstrate its excellent performance and beneficial scaling with respect to system size. Furthermore, we investigate modifications of the phaseless approximation that can help to reduce the overcorrelation problems common to the ph-AFQMC. We apply the method to the 26 molecules in the HEAT set, the benzene molecule, and water clusters. We observe a mean absolute deviation of the total energy of 1.15 kcal/mol for the molecules in the HEAT set, close to chemical accuracy. For the benzene molecule, the modified algorithm despite using a single-Slater-determinant trial wavefunction yields the same accuracy as the original phaseless scheme with 400 Slater determinants. Despite these improvements, we find systematic errors for the CN, CO2, and O2 molecules that need to be addressed with more accurate trial wavefunctions. For water clusters, we find that the ph-AFQMC yields excellent binding energies that differ from CCSD(T) by typically less than 0.5 kcal/mol.

Ab initio calculations on structure and stability of BN/CC isosterism in azulene

Herein, we investigated the thermodynamic stability and opto-electronic properties of a newly BN-doped azulene. The gas-phase formation enthalpies of 11 BN-doped azulene were calculated by the atomization energy method using three computational models (CBS-APNO, CBS-QB3, and G3MP2). The results suggest that AZ-1N9B exhibits the highest stability among the studied isomers. On the other hand, AZ-1B9N and AZ-9B10N display nearly equal stability with relative energies of 19.36 and 19.82 kcal/mol at CBS-QB3, respectively. These two isomers are considered the least stable among the investigated compounds. The frontier molecular orbitals (FMO), ionization energies (IE), and electron affinities (EA) of these isomers were discussed. Additionally, the electronic absorption spectra of the BN-doped azulenes were computed using the TD-B3LYP/6-31 + G(d,p) and TD-CAM-B3LYP level of theories, which using a long-range corrected hybrid functional in acetone. The computational results obtained in this research are align closely with the existing literature, thereby reinforcing the credibility and reliability of our findings.

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.

Design and synthesis of phenylene-bridged isoxazole and tetrazole-1-ol based energetic materials of low sensitivity

A variety of phenylene-bridged isoxazole and tetrazole-1-ol based green energetic materials was synthesized, for the first time, in good to excellent yields. The structures of the newly synthesized compounds were confirmed by spectroscopic techniques, elemental analysis, and single-crystal X-ray analysis. The value of the present work is that all newly synthesized compounds have good thermal stabilities ranging between 167-340 °C and acceptable densities between 1.51 g cm^-3 to 1.82 g cm^-3. Detailed computational insight into the energetic properties of the new compounds shows that they have good energetic properties (propulsive and ballistic) with excellent thermal and mechanical stabilities which makes them promising candidates for solid propulsion systems. Compounds 5, 12 and 14 are the superior candidates as melt-castable energetic materials.

The Importance of Tight f Basis Functions for Heavy p-Block Oxides and Halides: A Parallel With Tight d functions in the Second Row

It is well-known that both wave function ab initio and DFT calculations on second-row compounds exhibit anomalously slow basis set convergence unless the basis sets are augmented with additional "tight" (high-exponent) d functions, as in the cc-pV(n+d)Z and aug-cc-pV(n+d)Z basis sets. This has been rationalized as being necessary for a better description of the low-lying 3d orbital, which as the oxidation state increases sinks low enough to act as a back-donation acceptor from chalcogen and halogen lone pairs. This prompts the question whether a similar phenomenon exists for the isovalent compounds of the heavy p-block. We show that for the fourth and fifth row, this is the case, but this time for tight f functions enhancing the description of the low-lying 4f and 5f Rydberg orbitals, respectively. In the third-row heavy p block, the 4f orbitals are too far up, while the 4d orbitals are adequately covered by the basis functions already present to describe the 3d subvalence orbitals.

Thermochemistry of per- and polyfluoroalkyl substances

The determination of gas phase thermochemical properties of per- and polyfluoroalkyl substances (PFAS) is central to understanding the long-range transport behavior of PFAS in the atmosphere. Prior gas-phase studies have reported the properties of perfluorinated sulfonic acid (PFOS) and perfluorinated octanoic acid (PFOA). Here, this study reports the gas phase enthalpies of formation of short- and long-chain PFAS and their precursor molecules determined using density functional theory (DFT) and ab initio approaches. Two density functionals, two ab initio methods and an empirical method were used to compute enthalpies of formation with the total atomization approach and an isogyric reaction. The performance of the computational methods employed in this work were validated against the experimental enthalpies of linear alkanoic acids and perfluoroalkanes. The gas-phase determinations will be useful for future studies of PFAS in the atmosphere, and the methodological choices will be helpful in the study of other PFAS.

Machine Learned Composite Methods for Electronic Structure Theory

Because of the prohibitive scaling of ab initio techniques for modeling chemical species with high accuracy, they are not generally tractable for large systems. It is therefore of considerable interest to develop high-accuracy computational models with low computational cost that can afford predictions of electronic structure and properties of macromolecular species. Composite methods, as first introduced by Pople [Pople, J. A.; Head-Gordon, M.; Fox, D. J.; Raghavachari, K.; Curtiss, L. A. J. Chem. Phys.1989, 90, 5622.], are an intuitive solution to this problem as they seek to systematically increase accuracy in model chemistries by taking advantage of favorable error cancellation among reasonably low-cost models. By linearly combining a series of carefully chosen model chemistries, the result of a prohibitive-scaling correlated model chemistry with a large basis set may be approximated with relatively good fidelity. However, the full extent to which the choice of low-cost models dictates the predictive accuracy of composite methods is not known, and a full exploration of all model chemistries would be advantageous for the design and validation of a generalizable composite method for widespread application. Here, we show that remarkable accuracy can be generally achieved with composite methods that are more judiciously constructed, leading to increased accuracy with significantly reduced computational cost. By designing a systematic procedure for the automated generation and assessment of over 10 billion unique composite methods, we have extensively explored the space of modern model chemistries to elucidate important design principles in the construction of reliable composite procedures. We anticipate our work to be the starting point in the pursuit of creative approaches to modeling large chemical systems with high accuracy by using novel combinatorial modeling.

ωB97X-3c: A composite range-separated hybrid DFT method with a molecule-optimized polarized valence double-ζ basis set

A new composite density functional theory (DFT) method is presented. It is based on ωB97X-V as one of the best-performing density functionals for the GMTKN55 thermochemistry database and completes the family of "3c" methods toward range-separated hybrid DFT. This method is consistently available for all elements up to Rn (Z = 1-86). Its further key ingredients are a polarized valence double-ζ (vDZP) Gaussian basis set, which was fully optimized in molecular DFT calculations, in combination with large-core effective core potentials and a specially adapted D4 dispersion correction. Unlike most existing double-ζ atomic orbital sets, vDZP shows only small basis set superposition errors (BSSEs) and can compete with standard sets of triple-ζ quality. Small residual BSSE effects are efficiently absorbed by the D4 damping scheme, which overall eliminates the need for an explicit treatment or empirical corrections for BSSE. Thorough tests on a variety of thermochemistry benchmark sets show that the new composite method, dubbed ωB97X-3c, is on par with or even outperforms standard hybrid DFT methods in a quadruple-zeta basis set at a small fraction of the computational cost. Particular strengths of this method are the description of non-covalent interactions and barrier heights, for which it is among the best-performing density functionals overall.

When Gold Is Not Enough: Platinum Standard of Quantum Chemistry with N7 Cost

In this paper, we extend the rank-reduced coupled-cluster formalism to the calculation of non-iterative energy corrections due to quadruple excitations. There are two major components of the proposed formalism. The first is an approximate compression of the quadruple excitation amplitudes using the Tucker format. The second is a modified functional used for the evaluation of the corrections which gives exactly the same results for the exact amplitudes, but is less susceptible to errors resulting from the aforementioned compression. We show, both theoretically and numerically, that the computational cost of the proposed method scales as the seventh power of the system size. Using reference results for a set of small molecules, the method is calibrated to deliver relative accuracy of a few percent in energy corrections. To illustrate the potential of the theory, we calculate the isomerization energy of ortho/meta benzyne (C₆H₄) and the barrier height for the Cope rearrangement in bullvalene (C₁₀H₁₀). The method retains a near-black-box nature of the conventional coupled-cluster formalism and depends on only one additional parameter that controls the accuracy.

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.

Assessment of the Second-Order Statically Screened Exchange Correction to the Random Phase Approximation for Correlation Energies

With increasing interelectronic distance, the screening of the electron–electron interaction by the presence of other electrons becomes the dominant source of electron correlation. This effect is described by the random phase approximation (RPA) which is therefore a promising method for the calculation of weak interactions. The success of the RPA relies on the cancellation of errors, which can be traced back to the violation of the crossing symmetry of the 4-point vertex, leading to strongly overestimated total correlation energies. By the addition of second-order screened exchange (SOSEX) to the correlation energy, this issue is substantially reduced. In the adiabatic connection (AC) SOSEX formalism, one of the two electron–electron interaction lines in the second-order exchange term is dynamically screened (SOSEX(W, v_c)). A related SOSEX expression in which both electron–electron interaction lines are statically screened (SOSEX(W(0), W(0))) is obtained from the G3W2 contribution to the electronic self-energy. In contrast to SOSEX(W, v_c), the evaluation of this correlation energy expression does not require an expensive numerical frequency integration and is therefore advantageous from a computational perspective. We compare the accuracy of the statically screened variant to RPA and RPA+SOSEX(W, v_c) for a wide range of chemical reactions. While both methods fail for barrier heights, SOSEX(W(0), W(0)) agrees very well with SOSEX(W, v_c) for charged excitations and noncovalent interactions where they lead to major improvements over RPA.

Explicitly Correlated Double-Hybrid DFT: A Comprehensive Analysis of the Basis Set Convergence on the GMTKN55 Database

Double-hybrid density functional theory (DHDFT) offers a pathway to accuracy approaching composite wavefunction approaches such as G4 theory. However, the Görling–Levy second-order perturbation theory (GLPT2) term causes them to partially inherit the slow ∝L^–3 (with L the maximum angular momentum) basis set convergence of correlated wavefunction methods. This could potentially be remedied by introducing F12 explicit correlation: we investigate the basis set convergence of both DHDFT and DHDFT-F12 (where GLPT2 is replaced by GLPT2-F12) for the large and chemically diverse general main-group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) benchmark suite. The B2GP-PLYP-D3(BJ) and revDSD-PBEP86-D4 DHDFs are investigated as test cases, together with orbital basis sets as large as aug-cc-pV5Z and F12 basis sets as large as cc-pVQZ-F12. We show that F12 greatly accelerates basis set convergence of DHDFs, to the point that even the modest cc-pVDZ-F12 basis set is closer to the basis set limit than cc-pV(Q+d)Z or def2-QZVPPD in orbital-based approaches, and in fact comparable in quality to cc-pV(5+d)Z. Somewhat surprisingly, aug-cc-pVDZ-F12 is not required even for the anionic subsets. In conclusion, DHDF-F12/VDZ-F12 eliminates concerns about basis set convergence in both the development and applications of double-hybrid functionals. Mass storage and I/O bottlenecks for larger systems can be circumvented by localized pair natural orbital approximations, which also exhibit much gentler system size scaling.

Structural Significance of His73 in F-Actin Dynamics: Insights from Ab Initio Study

F-actin dynamics (polymerization and depolymerization) are associated with nucleotide exchange, providing the driving forces for dynamic cellular activities. As an important residue in the nucleotide state-sensing region in actin, His73 is often found to be methylated in natural actin and directly participates in F-actin dynamics by regulating nucleotide exchange. The interaction between His73 and its neighboring residue, Gly158, has significance for F-actin dynamics. However, this weak chemical interaction is difficult to characterize using classic molecular modeling methods. In this study, ab initio modeling was employed to explore the binding energy between His73 and Gly158. The results confirm that the methyl group on the His73 side chain contributes to the structural stability of atomistic networks in the nucleotide state-sensing region of actin monomers and confines the material exchange (Pi release) pathway within F-actin dynamics. Further binding energy analyses of actin structures under different nucleotide states showed that the potential model of His73/Gly158 hydrogen bond breaking in the material exchange mechanism is not obligatory within F-actin dynamics.

Determination of the standard enthalpy of formation of iodine compounds through the G2 and G3(MP2)//B3-SBK theories

The domain of application of the G3(MP2)//B3-SBK theory was expanded, and its efficiency was evaluated to determinate enthalpies of formation of forty-one iodine compounds. The results were compared to those obtained with the G2 theory for the same set of molecules. The G3(MP2)//B3-SBK theory showed a mean deviation and deviation standard equal to 3.7 kcal mol^-1 and 6.0 kcal mol^-1, respectively. The G2 theory (mean deviation = 3.1 kcal mol^-1 and standard deviation = 4.9 kcal mol^-1) presented a lower error and standard deviation, but at a significantly higher computational cost. For a more complete evaluation, as a secondary part of the work, it also used different functionals B3LYP, M06-2X, WB97XD, and MP2 method with four different basis sets 6-311G(d,p), LANL2DZ, jorge-ADZP, and CEP-31G(d). The best density functional/basis set combination was obtained with M06-2X/CEP-31G(d) among the three mentioned functionals. However, the produced mean deviation is significant and equal to 17.3 kcal mol^-1, with a standard deviation equal to 23.0 kcal mol^-1. The 6-311G(d,p) basis achieved the best performance with the MP2 method, generating an equally significant mean deviation of 12.8 kcal mol^-1 with a standard deviation equal to 18.7 kcal mol^-1.

Uniting Nonempirical and Empirical Density Functional Approximation Strategies Using Constraint-Based Regularization

In this work, we present a general framework that unites the two primary strategies for constructing density functional approximations (DFAs): nonempirical (NE) constraint satisfaction and empirical (E) data-driven optimization. The proposed method employs B-splines, bell-shaped spline functions with compact support, to construct each inhomogeneity correction factor (ICF). This choice offers several distinct advantages over traditional polynomial expansions by enabling explicit enforcement of linear and nonlinear constraints as well as ICF smoothness using Tikhonov and penalized B-splines (P-splines) regularization. As proof-of-concept, we use the so-called CASE (constrained and smoothed empirical) framework to construct a constraint-satisfying and data-driven global hybrid that exhibits enhanced performance across a diverse set of chemical properties. We argue that the CASE approach can be used to generate DFAs that maintain the physical rigor and transferability of NE-DFAs while leveraging high-quality quantum-mechanical data to remove the arbitrariness of ansatz selection and improve performance.

Informing geometric deep learning with electronic interactions to accelerate quantum chemistry

Predicting electronic energies, densities, and related chemical properties can facilitate the discovery of novel catalysts, medicines, and battery materials. However, existing machine learning techniques are challenged by the scarcity of training data when exploring unknown chemical spaces. We overcome this barrier by systematically incorporating knowledge of molecular electronic structure into deep learning. By developing a physics-inspired equivariant neural network, we introduce a method to learn molecular representations based on the electronic interactions among atomic orbitals. Our method, OrbNet-Equi, leverages efficient tight-binding simulations and learned mappings to recover high-fidelity physical quantities. OrbNet-Equi accurately models a wide spectrum of target properties while being several orders of magnitude faster than density functional theory. Despite only using training samples collected from readily available small-molecule libraries, OrbNet-Equi outperforms traditional semiempirical and machine learning-based methods on comprehensive downstream benchmarks that encompass diverse main-group chemical processes. Our method also describes interactions in challenging charge-transfer complexes and open-shell systems. We anticipate that the strategy presented here will help to expand opportunities for studies in chemistry and materials science, where the acquisition of experimental or reference training data is costly.

Ab initio composite strategies and multireference approaches for lanthanide sulfides and selenides

The f-block ab initio correlation consistent composite approach was used to predict the dissociation energies of lanthanide sulfides and selenides. Geometry optimizations were carried out using density functional theory and coupled cluster singles, doubles, and perturbative triples with one- and two-component Hamiltonians. For the two-component calculations, relativistic effects were accounted for by utilizing a third-order Douglas-Kroll-Hess Hamiltonian. Spin-orbit coupling was addressed with the Breit-Pauli Hamiltonian within a multireference configuration interaction approach. The state averaged complete active space self-consistent field wavefunctions obtained for the spin-orbit coupling energies were used to assign the ground states of diatomics, and several diagnostics were used to ascertain the multireference character of the molecules.

Improving the Accuracy of Composite Methods: A G4MP2 Method with G4-like Accuracy and Implications for Machine Learning

G4MP2 theory has proven to be a reliable and accurate quantum chemical composite method for the calculation of molecular energies using an approximation based on second-order perturbation theory to lower computational costs compared to G4 theory. However, it has been found to have significantly increased errors when applied to larger organic molecules with 10 or more nonhydrogen atoms. We report here on an investigation of the cause of the failure of G4MP2 theory for such larger molecules. One source of error is found to be the "higher-level correction (HLC)", which is meant to correct for deficiencies in correlation contributions to the calculated energies. This is because the HLC assumes that the contribution is independent of the element and the type of bonding involved, both of which become more important with larger molecules. We address this problem by adding an atom-specific correction, dependent on atom type but not bond type, to the higher-level correction. We find that a G4MP2 method that incorporates this modification of the higher-level correction, referred to as G4MP2A, becomes as accurate as G4 theory (for computing enthalpies of formation) for a test set of molecules with less than 10 nonhydrogen atoms as well as a set with 10-14 such atoms, the set of molecules considered here, with a much lower computational cost. The G4MP2A method is also found to significantly improve ionization potentials and electron affinities. Finally, we implemented the G4MP2A energies in a machine learning method to predict molecular energies.

A Mountaineering Strategy to Excited States: Revising Reference Values with EOM-CC4

In the framework of the computational determination of highly accurate vertical excitation energies in small organic compounds, we explore the possibilities offered by the equation-of-motion formalism relying on the approximate fourth-order coupled-cluster (CC) method, CC4. We demonstrate, using an extended set of more than 200 reference values based on CC including up to quadruples excitations (CCSDTQ), that CC4 is an excellent approximation to CCSDTQ for excited states with a dominant contribution from single excitations with an average deviation as small as 0.003 eV. We next assess the accuracy of several additive basis set correction schemes, in which vertical excitation energies obtained with a compact basis set and a high-order CC method are corrected with lower-order CC calculations performed in a larger basis set. Such strategies are found to be overall very beneficial, though their accuracy depends significantly on the actual scheme. Finally, CC4 is employed to improve several theoretical best estimates of the QUEST database for molecules containing between four and six (nonhydrogen) atoms, for which previous estimates were computed at the CCSDT level.

Optimization of the r2SCAN-3c Composite Electronic-Structure Method for Use with Slater-Type Orbital Basis Sets

The "Swiss army knife" composite density functional electronic-structure method r²SCAN-3c (J. Chem. Phys. 2021, 154, 064103) is extended and optimized for the use with Slater-type orbital basis sets. The meta generalized-gradient approximation (meta-GGA) functional r²SCAN by Furness et al. is combined with a tailor-made polarized triple-ζ Slater-type atomic orbital (STO) basis set (mTZ2P), the semiclassical London dispersion correction (D4), and a geometrical counterpoise (gCP) correction. Relativistic effects are treated explicitly with the scalar-relativistic zeroth-order regular approximation (SR-ZORA). The performance of the new implementation is assessed on eight geometry and 74 energy benchmark sets, including the extensive GMTKN55 database as well as recent sets such as ROST61 and IONPI19. In geometry optimizations, the STO-based r²SCAN-3c is either on par with or more accurate than the hybrid density functional approximation M06-2X-D3(0)/TZP. In energy calculations, the overall accuracy is similar to the original implementation of r²SCAN-3c with Gaussian-type atomic orbitals (GTO), but basic properties, intermolecular noncovalent interactions, and barrier heights are better described with the STO approach, resulting in a lower weighted mean absolute deviation (WTMAD-2(STO) = 7.15 vs 7.50 kcal mol^-1 with the original method) for the GMTKN55 database. The STO-optimized r²SCAN-3c outperforms many conventional hybrid/QZ approaches in most common applications at a fraction of their cost. The reliable, robust, and accurate r²SCAN-3c implementation with STOs is a promising alternative to the original implementation with GTOs and can be generally used for a broad field of quantum chemical problems.

Calculating bond dissociation energies of X-H (X=C, N, O, S) bonds of aromatic systems via density functional theory: a detailed comparison of methods

In this study, the performance of 17 different density functional theory functionals was compared for the calculation of the bond dissociation energy (BDE) values of X-H (X=C, N, O, S) bonds of aromatic compounds. The effect of the size of the basis set (expansions of 6-31(G)) was also assessed for the initial geometry and zero-point energy calculations, followed by the single-point BDE calculations with different model chemistries with the 6-311 + (3df,2p) basis set. It was found that the size of the basis set for geometry optimization has a much smaller effect on the accuracy of BDE than the choice of functional for the following single-point calculations. The M06-2X, M05-2X and M08-HX functionals yielded highly accurate BDE values compared to experimental data (with the average mean unsigned error MUE = 1.2-1.5 kcal mol^-1), performing better than any of the other functionals. The results suggest that geometry optimization may be performed with B3LYP functional and a small basis set, whereas the M06-2X, M05-2X and M08-HX density functionals with a suitably large basis set offer the best method for calculating BDEs of ArX-H (X=C, N, O, S) bonds.

Ab Initio Composite Approaches for Heavy Element Energetics: Ionization Potentials for the Actinide Series of Elements

The first, second, and third gas-phase ionization potentials have been determined for the actinide series of elements using an ab initio composite scalar and fully relativistic approach, employing the coupled cluster with single, double, and perturbative triple excitations (CCSD(T)) and Dirac Hartree-Fock (DHF) methods, extrapolated to the complete basis set (CBS) limit. The impact of electron correlation and basis set choice within this framework are examined. Additionally, the first three ionization potentials were obtained using an ab initio heavy element correlation-consistent Composite Approach (here referred to as α-ccCA). This is the first utilization of a ccCA for actinide species.

How Well Does Kohn-Sham Regularizer Work for Weakly Correlated Systems?

Kohn-Sham regularizer (KSR) is a differentiable machine learning approach to finding the exchange-correlation functional in Kohn-Sham density functional theory that works for strongly correlated systems. Here we test KSR for a weak correlation. We propose spin-adapted KSR (sKSR) with trainable local, semilocal, and nonlocal approximations found by minimizing density and total energy loss. We assess the atoms-to-molecules generalizability by training on one-dimensional (1D) H, He, Li, Be, and Be²⁺ and testing on 1D hydrogen chains, LiH, BeH₂, and helium hydride complexes. The generalization error from our semilocal approximation is comparable to other differentiable approaches, but our nonlocal functional outperforms any existing machine learning functionals, predicting ground-state energies of test systems with a mean absolute error of 2.7 mH.

Structures and Electron Affinities of Aluminum Hydride Clusters AlnH (n = 3-13)

Low-energy structures and electron affinities (EAs) for aluminum hydride clusters Al_nH (n = 3-13) have been calculated using ab initio and density functional calculations. Geometries were optimized at the PBE0/def-2-TZVPP level of theory, which has been shown to match the currently accepted lowest-energy structures for the all-aluminum clusters Al_n and their anions. Neutral hydride clusters with n = 4, 7, and 9-12 are predicted to adopt terminal structures with the hydrogen atom bound to only one aluminum atom and with only minor alterations of the aluminum atom arrangement from that of the all-aluminum cluster. Clusters with n = 3 and 13 are predicted to adopt "face-centered" geometries, and the n = 6 cluster is predicted to prefer an isomer with the hydrogen atom bridging two aluminum atoms, also with little or no distortion to the aluminum atom arrangement from the all-aluminum cluster. Addition of a hydrogen atom to clusters with n = 5 and 8 is predicted to distort the aluminum atom arrangement significantly from that of the corresponding all-aluminum cluster. In the anionic clusters, terminal clusters are preferred for all cluster sizes except for n = 6 that prefers a face-centered arrangement. Minor distortions in the aluminum scaffolding for Al₁₁ and Al₁₂ were found, while all other anionic clusters adopt structures with little or no deviation in the aluminum atom arrangement from the corresponding all-aluminum cluster. Raw adiabatic electron affinities were computed using CCSD(T)/aug-cc-pVTZ single-point energies for the anionic and neutral hydride clusters at their respective DFT geometries. Isodesmic electron affinities for the hydride clusters were computed relative to their all-aluminum counterparts and show an even-odd alternation with cluster size. Derived EAs alternate in magnitude between even- and odd-numbered clusters, with the even-numbered clusters having relatively larger EAs.

Gas-phase thermochemistry of polycyclic aromatic hydrocarbons: an approach integrating the quantum chemistry composite scheme and reaction generator

We introduce a protocol aimed at predicting the accurate gas-phase enthalpies of formation of polycyclic aromatic hydrocarbons (PAHs). Automatic generation of a dataset of equilibrated chemical reactions preserving the number of carbon atoms in each hybridization state on each side of equations is at the core of our scheme. The performed tests suggest the recommended enthalpy of formation to be derived via a two-step scheme. First, we consider the reactions with a minimal sum of the total number of particles involved, N, and the absolute difference between the total number of products and reactants, |ΔN|. Second, among these reactions, we identify the one with the smallest absolute reaction enthalpy change, . This approach has been applied to predict the gas-phase enthalpies of formation of 113 PAHs via the Feller-Peterson-Dixon approach. Our calculated values provide the mean absolute deviations of 1.7, 1.9, 4.2, 8.1, and 18.5 kJ mol^-1 with respect to the literature group-based error corrected (GBEC) G3MP2B3, ATOMIC (HC), group equivalent M06-2X, GBEC B3LYP, and G4MP2 values. Our predicted values give the mean signed and mean absolute errors of -7.5 and 12.9 kJ mol^-1 with respect to the experimental enthalpies of formation. The combination of our predicted and the experimental values provide the solid-state enthalpies of formation, , which are not available for a few species. Approaching these values as well as , producing large discrepancies from the experimental side, would be indispensable for testing and further tuning of computational chemistry approaches.

Thermodynamic Properties: Enthalpy, Entropy, Heat Capacity, and Bond Energies of Fluorinated Carboxylic Acids

Fluorinated carboxylic acids and their radicals are becoming more prevalent in environmental waters and soils as they have been produced and used for numerous commercial applications. Understanding the thermochemical properties of fluorinated carboxylic acids will provide insights into the stability and reaction paths of these molecules in the environment, in body fluids, and in biological and biochemical processes. Structures and thermodynamic properties for over 50 species related to fluorinated carboxylic acids with two and three carbons are determined with density functional computational calculations B3LYP, M06-2X, and MN15 and higher ab initio levels CBS-QB3, CBS-APNO, and G4 of theory. The lowest energy structures, moments of inertia, vibrational frequencies, and internal rotor potentials of each target species are determined. Standard enthalpies of formation, Δ_fH₂₉₈^°, from CBS-APNO calculations show the smallest standard deviation among methods used in this work. Δ_fH₂₉₈^° values are determined via several series of isodesmic and/or isogyric reactions. Enthalpies of formation are determined for fluorinated acetic and propionic acids and their respective radicals corresponding to the loss of hydrogen and fluorine atoms. Heat capacities as a function of temperature, C_p(T), and entropy at 298 K, S₂₉₈^°, are determined. Thermochemical properties for the fluorinated carbon groups used in group additivity are also developed. Bond dissociation energies (BDEs) for the carbon-hydrogen, carbon-fluorine, and oxygen-hydrogen (C-H, C-F, and O-H BDEs) in the acids are reported. The C-H, C-F, and O-H bond energies of the fluorinated carboxylic acids are in the range of 89-104, 101-125, and 109-113 kcal mol^-1, respectively. General trends show that the O-H bond energies on the acid group increase with the increase in the fluorine substitution. The strong carbon fluorine bonds in a fluorinated acid support the higher stability of the perfluorinated acids in the environment.

Use of vibrational spectroscopy to identify the formation of neptunyl-neptunyl interactions: A paired Density Functional Theory and Raman spectroscopy study

Abstract: Actinyl-Actinyl interactions (AAIs) occur in pentavalent actinide systems, particularly for Np(V), and lead to complex vibrational signals that are challenging to analyze and interpret. Previous studies have focused on...

Design and Computational Insight on Two Novel CL-20 Analogues, BNMTNIW and BNIMTNIW: High Performance Energetic Materials

In this study, a theoretical Insight into two newly designed novel CL-20-based high performance energetic compounds, namely bis(nitromethyl)-tetranitrohexaaza-isowurtzitane (BNMTNIW) and bis(nitratomethyl)-tetranitrohexaaza-isowurtzitane BNIMTNIW), is reported. The title compounds are expected to...