Sources of error in electronic structure calculations on small chemical systems

"Best" Iterative Coupled-Cluster Triples Model? More Evidence for 3CC

To follow up on the unexpectedly good performance of several coupled-cluster models with approximate inclusion of 3-body clusters [Rishi, V.; Valeev, E. F. J. Chem. Phys. 2019, 151, 064102.] we performed a more complete assessment of the 3CC method [Feller, D. . J. Chem. Phys. 2008, 129, 204105.] for accurate computational thermochemistry in the standard HEAT framework. New spin-integrated implementation of the 3CC method applicable to closed- and open-shell systems utilizes a new automated toolchain for derivation, optimization, and evaluation of operator algebra in many-body electronic structure. We found that with a double-ζ basis set the 3CC correlation energies and their atomization energy contributions are almost always more accurate (with respect to the CCSDTQ reference) than the CCSDT model as well as the standard CCSD(T) model. The mean absolute errors in cc-pVDZ {3CC, CCSDT, and CCSD(T)} electronic (per valence electron) and atomization energies relative to the CCSDTQ reference for the HEAT data set [Tajti, A. . J. Chem. Phys. 2004, 121, 11599-11613.], were {24, 70, 122} μEh/e and {0.46, 2.00, 2.58} kJ/mol, respectively. The mean absolute errors in the complete-basis-set limit {3CC, CCSDT, and CCSD(T)} atomization energies relative to the HEAT model reference, were {0.52, 2.00, and 1.07} kJ/mol, The significant and systematic reduction of the error by the 3CC method and its lower cost than CCSDT suggests it as a viable candidate for post-CCSD(T) thermochemistry applications, as well as the preferred alternative to CCSDT in general.

Basis Set Extrapolation from the Vanishing Counterpoise Correction Condition

Basis set extrapolations are typically rationalized either from analytical arguments involving the partial-wave or principal expansions of the correlation energy in helium-like systems or from fitting extrapolation parameters to reference energetics for a small(ish) training set. Seeking to avoid both, we explore a third alternative: extracting extrapolation parameters from the requirement that the BSSE (basis set superposition error) should vanish at the complete basis set limit. We find this to be a viable approach provided that the underlying basis sets are not too small and reasonably well balanced. For basis sets not augmented by diffuse functions, BSSE minimization and energy fitting yield quite similar parameters.

Comparative Study of Neutral and Cationic Sn2H2: Toward Laboratory Detection of the Cation

Group 14 M2H2 isomers (M = Si, Ge, Sn, and Pb) have attracted interest due to their radically differing electronic structures from acetylene. To better understand the Sn-H interactions of the neutral and cationic Sn2H2 structures, we present the most rigorous study of these systems to date. CCSD(T)/cc-pwCVTZ harmonic frequencies are presented as the first predictions for the neutral and cationic species to date. CCSDT(Q)/CBS relative energies are reported using the focal point approach, confirming the butterfly isomer as the global minimum on the potential energy surface for both the neutral and cationic species. In all, there exist 7 minima and 15 transition states. NBO analysis is also performed to elucidate the changes in bond order going from neutral to cation across all isomers of Sn2H2. Our results provide insights into the important Sn-H interaction and provide guidance for future work that may detect S n 2 H 2 + in the laboratory for the first time.

Robust fragment-based method of calculating hydrogen atom transfer activation barrier in complex molecules

Dynamic processes driven by non-covalent interactions (NCI), such as conformational exchange, molecular binding, and solvation, can strongly influence the rate constants of reactions with low activation barriers, especially at low temperatures. Examples of this may include hydrogen-atom-transfer (HAT) reactions involved in the oxidative stress of an active pharmaceutical ingredient (API). Here, we develop an automated workflow to generate HAT transition-state (TS) geometries for complex and flexible APIs and then systematically evaluate the influences of NCI on the free activation energies, based on the multi-conformational transition-state theory (MC-TST) within the framework of a multi-step reaction path. The two APIs studied: fesoterodine and imipramine, display considerable conformational complexity and have multiple ways of forming hydrogen bonds with the abstracting radical-a hydroxymethyl peroxyl radical. Our results underscore the significance of considering conformational exchange and multiple activation pathways in activation calculations. We also show that structural elements and NCIs outside the reaction site minimally influence TS core geometry and covalent activation barrier, although they more strongly affect reactant binding and consequently the overall activation barrier. We further propose a robust and economical fragment-based method to obtain overall activation barriers, by combining the covalent activation barrier calculated for a small molecular fragment with the binding free energy calculated for the whole molecule.

Ab initio quantum scattering calculations and a new potential energy surface for the HCl(X1Σ+)-O2(X3Σg-) system: Collision-induced line shape parameters for O2-perturbed R(0) 0-0 line in H35Cl

The remote sensing of abundance and properties of HCl-the main atmospheric reservoir of Cl atoms that directly participate in ozone depletion-is important for monitoring the partitioning of chlorine between "ozone-depleting" and "reservoir" species. Such remote studies require knowledge of the shapes of molecular resonances of HCl, which are perturbed by collisions with the molecules of the surrounding air. In this work, we report the first fully quantum calculations of collisional perturbations of the shape of a pure rotational line in H35Cl perturbed by an air-relevant molecule [as the first model system we choose the R(0) line in HCl perturbed by O2]. The calculations are performed on our new highly accurate HCl(X1Σ+)-O2(X3Σg-) potential energy surface. In addition to pressure broadening and shift, we also determine their speed dependencies and the complex Dicke parameter. This gives important input to the community discussion on the physical meaning of the complex Dicke parameter and its relevance for atmospheric spectra (previously, the complex Dicke parameter for such systems was mainly determined from phenomenological fits to experimental spectra and the physical meaning of its value in that context is questionable). We also calculate the temperature dependence of the line shape parameters and obtain agreement with the available experimental data. We estimate the total combined uncertainties of our calculations at 2% relative root-mean-square error in the simulated line shape at 296 K. This result constitutes an important step toward computational population of spectroscopic databases with accurate ab initio line shape parameters for molecular systems of terrestrial atmospheric importance.

Transfer learning for chemically accurate interatomic neural network potentials

Developing machine learning-based interatomic potentials from ab initio electronic structure methods remains a challenging task for computational chemistry and materials science. This work studies the capability of transfer learning, in particular discriminative fine-tuning, for efficiently generating chemically accurate interatomic neural network potentials on organic molecules from the MD17 and ANI data sets. We show that pre-training the network parameters on data obtained from density functional calculations considerably improves the sample efficiency of models trained on more accurate ab initio data. Additionally, we show that fine-tuning with energy labels alone can suffice to obtain accurate atomic forces and run large-scale atomistic simulations, provided a well-designed fine-tuning data set. We also investigate possible limitations of transfer learning, especially regarding the design and size of the pre-training and fine-tuning data sets. Finally, we provide GM-NN potentials pre-trained and fine-tuned on the ANI-1x and ANI-1ccx data sets, which can easily be fine-tuned on and applied to organic molecules.

High-Level Coupled-Cluster Study on Substituent Effects in H2 Activation by Low-Valent Aluminyl Anions

The synthesis of novel aluminyl anion complexes has been well exploited in recent years. Moreover, the elucidation of the structure and reactivity of these complexes opens the path toward a new understanding of low-valent aluminum complexes and their chemistry. This work computationally treats the substituent effect on aluminyl anions to discover suitable alternatives for H₂ activation at a high level of theory utilizing coupled-cluster techniques extrapolated to the complete basis set. The results reveal that the simplest AlH₂^- system is the most reactive toward the activation of H₂, but due to the low steric demand, severe difficulty in the stabilization of this system makes its use nonviable. However, the results indicate that, in principle, aluminyl systems with -C, -CN, -NC, and -N chelating centers would be the best choices of ligand toward the activation of molecular hydrogen by taking care of suitable steric demand to prevent dimerization of the catalysts. Furthermore, computations show that monosubstitution (besides -H) in aluminyl anions is preferred over disubstitution. So our predictions show that bidentate ligands may yield less reactive aluminyl anions to activate H₂ than monodentate ones.

Toward the Observation of the Tin and Lead Analogs of Formaldehyde

Heavy aldehyde and ketone analogues, R₂X═O (X = Si, Ge, Sn, or Pb), differ from their R₂C═O counterparts due to their greater tendency to oligeramize as the X═O bond polarity increases as one goes down the periodic table. To date, H₂Sn═O and H₂Pb═O have eluded experimental detection. Herein we present the most rigorous theoretical study to date on these structures, providing CCSD(T)/pwCVTZ fundamental frequencies computed on CCSD(T)/CBS optimized structures for the H₂X═O (X = Sn, Pb) potential energy surface. The focal point approach is employed to produce the CCSDTQ/CBS relative energies. For the Sn and Pb structures, the carbene-like cis-HXOH was the global minima, with the trans species being less than 0.6 and 1.1 kcal mol^-1 above the cis structures, respectively. The formaldehyde-like H₂X═O structure is in an energy well of at least 34.8 and 25.4 kcal mol^-1 for Sn and Pb, respectively. Our results provide guidance for future work that may detect H₂Sn═O or H₂Pb═O for the first time.

Estimation of Excited-State Geometries of Benzene and Fluorobenzene through Vibronic Analyses of Absorption Spectra

The parameters used in theoretical modeling of vibrational patterns within Franck-Condon (FC) approximation can be adjusted to match the vibrationally well-resolved experimental absorption spectrum of molecules. These simulation parameters can then be used to reveal the structural changes occurring between the initial and final states assuming the harmonic oscillator approximation holds for both states. Such a theoretical approach has been applied to benzene and fluorobenzene to disclose the first excited-state geometries of both compounds. The carbon-carbon bond length of benzene in the ¹B_2u state has been calculated as 1.430 Å, which is in very good agreement with the experimental bond length of 1.432 Å. The FC spectral fit method has been exploited to reveal the ¹B₂ state of fluorobenzene as well. Commonly employed density functional theory (DFT) and time-dependent DFT methods have been used to calculate the ground- and excited-state geometries of both compounds, respectively. The comparison of geometrical parameters and vibrational frequencies at the relevant states shows that frequently used hybrid functionals perform quite well in the ground state, whereas their performances drop considerably while predicting the excited-state properties. Among the hybrid functionals studied, TD-B3LYP with 6-31+G(d) basis set can be chosen to calculate the excited-state properties of molecules, albeit with much less anticipation of accuracy from the performance that B3LYP usually shows at the ground state.

The long road to calibrated prediction uncertainty in computational chemistry

Uncertainty quantification (UQ) in computational chemistry (CC) is still in its infancy. Very few CC methods are designed to provide a confidence level on their predictions, and most users still rely improperly on the mean absolute error as an accuracy metric. The development of reliable UQ methods is essential, notably for CC to be used confidently in industrial processes. A review of the CC-UQ literature shows that there is no common standard procedure to report or validate prediction uncertainty. I consider here analysis tools using concepts (calibration and sharpness) developed in meteorology and machine learning for the validation of probabilistic forecasters. These tools are adapted to CC-UQ and applied to datasets of prediction uncertainties provided by composite methods, Bayesian ensembles methods, and machine learning and a posteriori statistical methods.

Investigation of Product Formation in the O(1D, 3P) + N2O Reactions: Comparison of Experimental and Theoretical Kinetics

The spin-forbidden and spin-allowed reactions of the excited and ground electronic state O(¹D, ³P) + N₂O(X¹Σ⁺) systems have been studied theoretically. Quantum calculations at the UCCSD(T)/CBS(T, Q, 5)//CCSD/aug-cc-pVTZ level have located two crossing points, MSX1 and MSX2, with energies of 11.2 and 22.7 kcal mol^-1 above O(³P) + N₂O, respectively. The second-order P-independent rate constants for the adiabatic and non-adiabatic thermal reactions predicted by adiabatic TST/VTST and non-adiabatic TST, respectively, agree closely with the available literature results. The second-order rate constant, k_2a = 9.55 × 10^-11 exp(-26.09 kcal mol^-1/RT) cm³ molecule^-1 s^-1, for the O(³P) + N₂O → 2NO reaction, contributed by both the dominant MSX2 and the minor TS1-a channels, is in reasonable accord with prior experiments and recommendations, covering the temperature range of 1200-4100 K. The calculated rate constant, k_2b = 4.47 × 10^-12 exp(-12.9 kcal mol^-1/RT) cm³ molecule^-1 s^-1, for the O(³P) + N₂O → N₂ + O₂(a¹Δ_g) reaction, occurring exclusively via MSX1, is also in good agreement with the combined experimental data measured in a shock tube study at T = 1940-3340 K (ref 16) and the result measured by Fourier transform infrared spectroscopy in the temperature range of 988-1083 K (ref 17). Moreover, the spin-allowed rate constants predicted for the singlet-state reactions, k_1a = (7.06-7.46) × 10^-11 cm³ molecule^-1 s^-1 for O(¹D) + N₂O → 2NO and k_1b = (4.36-4.66) × 10^-11 cm³ molecule^-1 s^-1 for O(¹D) + N₂O → N₂ + O₂(a¹Δ_g) in the temperature range of 200-350 K, agree quantitatively with the experimentally measured data, while the total rate constant k₁ = k_1a + k_1b was also found to be in excellent accordance with many reported values.

High-level ab initio quartic force fields and spectroscopic characterization of C2N. Phys Chem Chem Phys 2021;23:26227-26240. [PMID: 34787132 DOI: 10.1039/d1cp03505c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

While it is now well established that large carbon chain species and radiative electron attachment (REA) are key ingredients triggering interstellar anion chemistry, the role played by smaller molecular anions, for which REA appears to be an unlikely formation pathway, is as yet elusive. Advancing this research undoubtedly requires the knowledge (and modeling) of their astronomical abundances which, for the case of C₂N^-, is largely hindered by a lack of accurate spectroscopic signatures. In this work, we provide such data for both ground -CCN^-(³Σ^-) and low-lying c-CNC^-(¹A₁) isomers and their singly-substituted isotopologues by means of state-of-the-art rovibrational quantum chemical techniques. Their quartic force fields are herein calibrated using a high-level composite energy scheme that accounts for extrapolations to both one-particle and (approximate) -particle basis set limits, in addition to relativistic effects, with the final forms being subsequently subject to nuclear motion calculations. Besides standard spectroscopic attributes, the full set of computed properties includes fine and hyperfine interaction constants and can be readily introduced as guesses in conventional experimental data reduction analyses through effective Hamiltonians. On the basis of benchmark calculations performed anew for a minimal test set of prototypical triatomics and limited (low-resolution) experimental data for -CCN^-(³Σ^-), the target accuracies are determined to be better than 0.1% of experiment for rotational constants and 0.3% for vibrational fundamentals. Apart from laboratory investigations, the results here presented are expected to also prompt future astronomical surveys on C₂N^-. To this end and using the theoretically-predicted spectroscopic constants, the rotational spectra of both -CCN^-(³Σ^-) and c-CNC^-(¹A₁) are derived and their likely detectability in the interstellar medium is further explored in connection with working frequency ranges of powerful astronomical facilities. Our best theoretical estimate places c-CNC^-(¹A₁) at about 15.3 kcal mol^-1 above the ground-state -CCN^-(³Σ^-) species.

Quantitative Account of the Bonding Properties of a Rubredoxin Model Complex [Fe(SCH3)4]q, q = -2, -1, +2, +3

Iron-sulfur clusters play important roles in biology as parts of electron-transfer chains and catalytic cofactors. Here, we report a detailed computational analysis of a structural model of the simplest natural iron-sulfur cluster of rubredoxin and its cationic counterparts. Specifically, we investigated adiabatic reduction energies, dissociation energies, and bonding properties of the low-lying electronic states of the complexes [Fe(SCH₃)₄]^2-/1-/2+/3+ using multireference (CASSCF, MRCISD), and coupled cluster [CCSD(T)] methodologies. We show that the nature of the Fe-S chemical bond and the magnitude of the ionization potentials in the anionic and cationic [Fe(SCH₃)₄] complexes offer a physical rationale for the relative stabilization, structure, and speciation of these complexes. Anionic and cationic complexes present different types of chemical bonds: prevalently ionic in [Fe(SCH₃)₄]^2-/1- complexes and covalent in [Fe(SCH₃)₄]^2+/3+ complexes. The ionic bonds result in an energy gain for the transition [Fe(SCH₃)₄]^2- → [Fe(SCH₃)₄]^- (i.e., Fe^II → Fe^III) of 1.5 eV, while the covalent bonds result in an energy loss for the transition [Fe(SCH₃)₄]²⁺ → [Fe(SCH₃)₄]³⁺ of 16.6 eV, almost half of the ionization potential of Fe²⁺. The ionic versus covalent bond character influences the Fe-S bond strength and length, that is, ionic Fe-S bonds are longer than covalent ones by about 0.2 Å (for Fe^II) and 0.04 Å (for Fe^II). Finally, the average Fe-S heterolytic bond strength is 6.7 eV (Fe^II) and 14.6 eV (Fe^III) at the RCCSD(T) level of theory.

Assessing Density Functional Theory for Chemically Relevant Open-Shell Transition Metal Reactions

Due to the principle lack of systematic improvement possibilities of density functional theory, careful assessment of the performance of density functional approximations (DFAs) on well-designed benchmark sets, for example, for reaction energies and barrier heights, is crucial. While main-group chemistry is well covered by several available sets, benchmark data for transition metal chemistry is sparse. This is especially the case for larger, chemically relevant molecules. Addressing this issue, we recently introduced the MOR41 benchmark which covers chemically relevant reactions of closed-shell complexes. In this work, we extend these efforts to single-reference open-shell systems and introduce the "reactions of open-shell single-reference transition metal complexes" (ROST61) benchmark set. ROST61 includes accurate coupled-cluster reference values for 61 reaction energies with a mean reaction energy of -42.8 kcal mol^-1. Complexes with 13-93 atoms covering 20 d-block elements are included, but due to the restriction to single-reference open-shell systems, important elements such as iron or platinum could not be taken into account, or only to a small extent. We assess the performance of 31 DFAs in combination with three London dispersion (LD) correction schemes. Further, DFT-based composite methods, MP2, and a few semiempirical quantum chemical methods are evaluated. Consistent with the results for the MOR41 closed-shell benchmark, we find that the ordering of DFAs according to Jacob's ladder is preserved and that adding an LD correction is crucial, clearly improving almost all tested methods. The recently introduced r²SCAN-3c composite method stands out with a remarkable mean absolute deviation (MAD) of only 2.9 kcal mol^-1, which is surpassed only by hybrid DFAs with low amounts of Fock exchange (e.g., 2.3 kcal mol^-1 for TPSS0-D4/def2-QZVPP) and double-hybrid (DH) DFAs but at a significantly higher computational cost. The lowest MAD of only 1.6 kcal mol^-1 is obtained with the DH DFA PWPB95-D4 in the def2-QZVPP basis set approaching the estimated accuracy of the reference method. Overall, the ROST61 set adds important reference data to a sparsely sampled but practically relevant area of chemistry. At this point, it provides valuable orientation for the application and development of new DFAs and electronic structure methods in general.

Fully quantum calculations of O2-N2 scattering using a new potential energy surface: Collisional perturbations of the oxygen 118 GHz fine structure line

A proper description of the collisional perturbation of the shapes of molecular resonances is important for remote spectroscopic studies of the terrestrial atmosphere. Of particular relevance are the collisions between the O₂ and N₂ molecules-the two most abundant atmospheric species. In this work, we report a new highly accurate O₂(X³Σ_g ^-)-N₂(X¹Σ_g ⁺) potential energy surface and use it for performing the first quantum scattering calculations addressing line shapes for this system. We use it to model the shape of the 118 GHz fine structure line in O₂ perturbed by collisions with N₂ molecules, a benchmark system for testing our methodology in the case of an active molecule in a spin triplet state. The calculated collisional broadening of the line agrees well with the available experimental data over a wide temperature range relevant for the terrestrial atmosphere. This work constitutes a step toward populating the spectroscopic databases with ab initio line shape parameters for atmospherically relevant systems.

Catalyzed reaction of isocyanates (RNCO) with water

The reactions between substituted isocyanates (RNCO) and other small molecules (e.g. water, alcohols, and amines) are of significant industrial importance, particularly for the development of novel polyurethanes and other useful polymers. We present very high-level ab initio computations on the HNCO + H₂O reaction, with results targeting the CCSDT(Q)/CBS//CCSD(T)/cc-pVQZ level of theory. Our results affirm that hydrolysis can occur across both the N[double bond, length as m-dash]C and C[double bond, length as m-dash]O bonds of HNCO via concerted mechanisms to form carbamate or imidic acid with ΔH_0K barrier heights of 38.5 and 47.5 kcal mol^-1. A total of 24 substituted RNCO + H₂O reactions were studied. Geometries obtained with a composite method and refined with CCSD(T)/CBS single point energies determine that substituted RNCO species have a significant influence on these barrier heights, with an extreme case like fluorine lowering both barriers by close to 15 kcal mol^-1 and most common alkyl substituents lowering both by approximately 3 kcal mol^-1. Natural Bond Orbital (NBO) analysis provides evidence that the predicted barrier heights are strongly associated with the occupation of the in-plane C-O* orbital of the RNCO reactant. Key autocatalytic mechanisms are considered in the presence of excess water and RNCO species. Additional waters (one or two) are predicted to lower both barriers significantly at the CCSD(T)/aug-cc-pV(T+d)Z level of theory with strongly electron withdrawing RNCO substituents also increasing these effects, similar to the uncatalyzed case. The 298 K Gibbs energies are only marginally lowered by a second catalyst water molecule, indicating that the decreasing ΔH_0K barriers are offset by loss of translational entropy with more than one catalyst water. Two-step 2RNCO + H₂O mechanisms are characterized for the formation of carbamate and imidic acid. The second step of these two pathways exhibits the largest barrier and presents no clear pattern with respect to substituent choice. Our results indicate that an additional RNCO molecule might catalyze imidic acid formation but have less influence on the efficiency of carbamate formation. We expect that these results lay a firm foundation for the experimental study of substituted isocyanates and their relationship to the energetic pathways of related systems.

Inelastic scattering in isotopologues of O2-Ar: the effects of mass, symmetry, and density of states

The two species considered here, O2 (oxygen molecule) and Ar (argon-atom), are both abundant components of Earth's atmosphere and hence familiar collision partners in this medium. O2 is quite reactive and extensively involved in atmospheric chemistry, including Chapman's cycle of the formation and destruction of ozone; while Ar, like N2, typically plays the nevertheless crucial role of inert collider. Inert species can provide stabilization to metastable encounter-complexes through the energy transfer associated with inelastic collisions. The interplay of collision frequency and energy transfer efficiency, with state lifetimes and species concentrations, contributes to the rich and varied chemistry and dynamics found in diverse environments ranging from planetary atmospheres to the interstellar and circumstellar media. The nature and density of bound and resonance states, coupled electronic states, symmetry, and nuclear spin-statistics can all play a role. Here, we systematically investigate some of those factors by looking at the O2-Ar system, comparing rigorous quantum-scattering calculations for the 16O16O-40Ar, 18O16O-40Ar, and 18O18O-40Ar isotope combinations. A new accurate potential energy surface was constructed for this purpose holding the O2 bond distance at its vibrationally averaged distance.

Collisional excitation of interstellar PN by H2: New interaction potential and scattering calculations

Rotational excitation of interstellar PN molecules induced by collisions with H₂ is investigated. We present the first ab initio four-dimensional potential energy surface (PES) for the PN-H₂ van der Waals system. The PES was obtained using an explicitly correlated coupled cluster approach with single, double, and perturbative triple excitations [CCSD(T)-F12b]. The method of interpolating moving least squares was used to construct an analytical PES from these data. The equilibrium structure of the complex was found to be linear, with H₂ aligned at the N end of the PN molecule, at an intermolecular separation of 4.2 Å. The corresponding well-depth is 224.3 cm^-1. The dissociation energies were found to be 40.19 cm^-1 and 75.05 cm^-1 for complexes of PN with ortho-H₂ and para-H₂, respectively. Integral cross sections for rotational excitation in PN-H₂ collisions were calculated using the new PES and were found to be strongly dependent on the rotational level of the H₂ molecule. These new collisional data will be crucial to improve the estimation of PN abundance in the interstellar medium from observational spectra.

The HOX⋯SO2 (X=F, Cl, Br, I) Binary Complexes: Implications for Atmospheric Chemistry

Sulfur dioxide and hypohalous acids (HOX, X=F, Cl, Br, I) are ubiquitous molecules in the atmosphere that are central to important processes like seasonal ozone depletion, acid rain, and cloud nucleation. We present the first theoretical examination of the HOX⋯SO₂ binary complexes and the associated trends due to halogen substitution. Reliable geometries were optimized at the CCSD(T)/aug-cc-pV(T+d)Z level of theory for HOF and HOCl complexes. The HOBr and HOI complexes were optimized at the CCSD(T)/aug-cc-pV(D+d)Z level of theory with the exception of the Br and I atoms which were modeled with an aug-cc-pwCVDZ-PP pseudopotential. 27 HOX⋯SO₂ complexes were characterized and the focal point method was employed to produce CCSDT(Q)/CBS interaction energies. Natural Bond Orbital analysis and Symmetry Adapted Perturbation Theory were used to classify the nature of each principle interaction. The interaction energies of all HOX⋯SO₂ complexes in this study ranged from 1.35 to 3.81 kcal mol^-1 . The single-interaction hydrogen bonded complexes spanned a range of 2.62 to 3.07 kcal mol^-1 , while the single-interaction halogen bonded complexes were far more sensitive to halogen substitution ranging from 1.35 to 3.06 kcal mol^-1 , indicating that the two types of interactions are extremely competitive for heavier halogens. Our results provide insight into the interactions between HOX and SO₂ which may guide further research of related systems.

High level ab initio investigation of the catalytic effect of water on formic acid decomposition and isomerization

Formic acid (FA) is a ubiquitous molecule found in the atmosphere, and is relevant to many important processes. The FA molecule generally exists as the trans isomer, which can decompose into H2O and CO (dehydration). It can also exist in the less favorable cis isomer which can decompose into H2 and CO2 (decarboxylation). Our work examines the complexes formed between each isomer of FA with water. We present geometries and vibrational frequencies obtained at the reliable CCSD(T)/aug-cc-pVTZ level of theory for seven FAwater complexes. We utilize the focal point method to determine CCSDT(Q)/CBS plus corrections binding energies of 7.37, 3.36, and 2.02 kcal mol-1 plus 6.07, 3.79, 2.60, and 2.55 kcal mol-1 for the trans-FAwater and cis-FAwater complexes, respectively. Natural bond orbital analysis is used to further decompose the interactions in each complex and gain insight into their relative strengths. Furthermore, we examine the effect that a single water molecule has on the barrier heights to each decomposition pathway by optimizing the transition states and verifying their connectivity with intrinsic reaction coordinate computations as well as utilizing a kinetic model. Water lowers the barrier to dehydration by at most 15.78 kcal mol-1 and the barrier to decarboxylation by up to 15.90 kcal mol-1. Our research also examines for the first time the effect of one water molecule on the interconversion barrier and we find that the barrier from trans to cis is not catalyzed by water due to the strong FA and water interactions. Our results highlight some instances where different binary complexes result in different decomposition pathways and even a case where one binary complex can form the same decomposition products via two distinct mechanisms. Our results provide a reliable benchmark of the FAH2O system as well as provide insight into future studies of similar atmospheric systems.

Computational study of the rovibrational spectrum of CO2-N2

The CO2-N2 complex is formed from two key components of Earth's atmosphere, and as such, has received some attention from both experimental and theoretical studies. On the theory side, a potential energy surface (PES) based on high level ab initio data was reported [Nasri et al., J. Chem. Phys., 2015, 142, 174301] and then used in more recently reported rovibrational calculations [Lara-Moreno et al., Phys. Chem. Chem. Phys., 2019, 21, 3550]. Accuracy of about 1 percent was achieved for calculated rotational transitions of the ground vibrational state of the complex, compared with previously reported microwave spectra. However, a very recent measurement of the geared bending mode frequency [Barclay et al., J. Chem. Phys., 2020, 153, 014303] recorded a value of 21.4 cm-1, which is wildly different from the corresponding calculated value of 45.9 cm-1. To provide some insight into this discrepancy, we have constructed a new more accurate PES, and used it to perform highly converged variational rovibrational calculations. Our new results yield a value of 21.1 cm-1 for that bending frequency, in close agreement with the experiment. We also obtain significantly improved predicted rotational transitions. Finally, we note that a very shallow well, previously reported as a distinct second isomer, is not found on our new PES, but rather a transition structure is seen in that location.

Extrapolation in quantum chemistry: Insights on energetics and reaction dynamics

Since there is no exact solution for problems in physics and chemistry, extrapolation methods may assume a key role in quantitative quantum chemistry. Two topics where it bears considerable impact are addressed, both at the heart of computational quantum chemistry: electronic structure and reaction dynamics. In the first, the problem of extrapolating the energy obtained by solving the electronic Schrödinger equation to the limit of the complete one-electron basis set is addressed. With the uniform-singlet-and-triplet-extrapolation (USTE) scheme at the focal point, the emphasis is on recent updates covering from the energy itself to other molecular properties. The second topic refers to extrapolation of quantum mechanical reactive scattering probabilities from zero total angular momentum to any of the values that it may assume when running quasiclassical trajectories, QCT/QM-[Formula: see text]J. With the extrapolation guided in both cases by physically motivated asymptotic theories, realism is seeked by avoiding unsecure jumps into the unknown. Although, mostly review oriented, a few issues are addressed for the first time here and there. Prospects for future work conclude the overview.

Effective basis set extrapolations for CCSDT, CCSDT(Q), and CCSDTQ correlation energies

It is well established that extrapolating the coupled-cluster single double triple [CCSD and (T)] correlation energies using empirically motivated extrapolation exponents can accelerate the basis set convergence. Here, we consider the extrapolation of coupled-cluster expansion terms beyond the CCSD(T) level to the complete basis set (CBS) limit. We obtain reference CCSDT-CCSD(T) [T₃-(T)], CCSDT(Q)-CCSDT [(Q)], and CCSDTQ-CCSDT(Q) [T₄-(Q)] contributions from cc-pV{5,6}Z extrapolations for a diverse set of 16 first- and second-row systems. We use these basis-set limit results to fit extrapolation exponents in conjunction with the cc-pV{D,T}Z, cc-pV{T,Q}Z, and cc-pV{Q,5}Z basis set pairs. The optimal extrapolation exponents result in noticeable improvements in performance (relative to α = 3.0) in conjunction with the cc-pV{T,Q}Z basis set pair; however, smaller improvements are obtained for the other basis sets. These results confirm that the basis sets and basis set extrapolations used for obtaining post-CCSD(T) components in composite thermochemical theories such as Weizmann-4 and HEAT are sufficiently close to the CBS limit for attaining sub-kJ/mole accuracy. The fitted extrapolation exponents demonstrate that the T₃-(T) correlation component converges more slowly to the CBS limit than the (Q) and T₄ terms. A systematic investigation of the effect of diffuse functions shows that it diminishes (i) in the order T₃-(T) > (Q) > T₄-(Q) and (ii) with the size of the basis set. Importantly, we find that diffuse functions tend to systematically reduce the T₃-(T) contribution but systematically increases the (Q) contribution. Thus, the use of the cc-pVnZ basis sets benefits from a certain degree of error cancellation between these two components.

Characterizing structures, energetics, and spectra of species on the 1,3[H, C, As] potential energy surfaces: A high-level theoretical contribution

The ground and the low lying electronic states of structures on the ^1,3[H, C, As] potential energy surfaces were investigated with the highly correlated theoretical approaches CCSD(T), CCSD(T)-F12b, and CASSCF/MRCI along with the series of correlation consistent (aug-cc-pVnZ, n = D, T, Q, 5) basis sets. Energetic and spectroscopic parameters were obtained at the complete basis set limit, and the effect of core-valence correlation on these properties evaluated. Fundamental frequencies were also computed with the variational configuration interaction (VCI) approach. Heats of formation at 0 and 298.15 K were estimated for HCAs and CH, AsH, CAs, and HCAs, as well as the calculation of ionization potentials for HCAs. Comparisons of the present results with literature ones for the systems HCN/HNC, HCP/HPC highlight similarities and differences among these systems. Altogether, this investigation provides a very reliable characterization of the species on the surfaces and should guide future experimental studies on these systems.

Relatives of cyanomethylene: replacement of the divalent carbon by B-, N+, Al-, Si, P+, Ga-, Ge, and As. Phys Chem Chem Phys 2019;21:26438-26452. [PMID: 31774089 DOI: 10.1039/c9cp05777c]

The lowest lying singlet and triplet states of HBCN-, HCCN, HNCN+, HAlCN-, HSiCN, HPCN+, HGaCN-, HGeCN, and HAsCN+ were studied using the CCSDT(Q)/CBS//CCSD(T)/aug-cc-pVQZ level of theory. Periodic trends in geometries, singlet-triplet gaps, and barriers to linearity were established and analyzed. The first row increasingly favors the triplet state, with a singlet-triplet gap (ΔEST = Esinglet - Etriplet) of 3.5 kcal mol-1, 11.9 kcal mol-1, and 22.6 kcal mol-1, respectively, for HBCN-, HCCN, and HNCN+. The second row increasing favors the singlet state, with singlet-triplet gaps of -20.4 kcal mol-1 (HAlCN-), -26.6 kcal mol-1 (HSiCN), and -26.8 kcal mol-1 (HPCN+). The third row also favors the singlet state, with singlet-triplet gaps of -26.8 kcal mol-1 (HGaCN-), -33.5 kcal mol-1 (HGeCN), and -33.1 kcal mol-1 (HAsCN+). The HXCN species have larger absolute singlet-triplet energy gaps compared to their parent species XH2 except for the case of X = N+. The effect of the substitution of hydrogen with a cyano group was analyzed with isodesmic bond separation analysis and NBO.

Important features of the potential energy surface of the methylamine plus O(1D) reaction

This research presents an ab initio characterization of the potential energy surface for the methylamine plus ¹D oxygen atom reaction, which may be relevant to interstellar chemistry. Geometries and harmonic vibrational frequencies were determined for all stationary points at the CCSD(T)/aug-cc-pVTZ level of theory. The focal point method along with several additive corrections was used to obtain reliable CCSDT(Q)/CBS potential energy surface features. Extensive conformational analysis and intrinsic reaction coordinate computations were performed to ensure accurate chemical connectivity of the stationary points. Five minima were determined to be possible products of this reaction and three novel transition states were found that were previously unreported or mislabeled in the literature. The pathways we present can be used to guide further searches for NH₂ containing species in the interstellar medium.

Complete Basis Set Extrapolation of Electronic Correlation Energies Using the Riemann Zeta Function

In this article, we demonstrate the effectiveness of the method of complete basis set (CBS) extrapolation of correlation energies based on the application of the Riemann zeta function. Instead of fitting the results obtained with a systematic sequence of one-electron bases with a certain functional form, an analytic resummation of the missing contributions coming from higher angular momenta, l, is performed. The assumption that these contributions vanish asymptotically as an inverse power of l leads to an expression for the CBS limit given in terms of the zeta function. This result is turned into an extrapolation method that is very easy to use and requires no "empirical" parameters to be optimized. The performance of the method is assessed by comparing the results with very accurate reference data obtained with explicitly correlated theories and with results obtained with standard extrapolation schemes. On average, the errors of the zeta-function extrapolation are several times smaller compared with the conventional schemes employing the same sequence of bases. A recipe for the estimation of the residual extrapolation error is also proposed.

Approaching coupled cluster accuracy with a general-purpose neural network potential through transfer learning

Computational modeling of chemical and biological systems at atomic resolution is a crucial tool in the chemist's toolset. The use of computer simulations requires a balance between cost and accuracy: quantum-mechanical methods provide high accuracy but are computationally expensive and scale poorly to large systems, while classical force fields are cheap and scalable, but lack transferability to new systems. Machine learning can be used to achieve the best of both approaches. Here we train a general-purpose neural network potential (ANI-1ccx) that approaches CCSD(T)/CBS accuracy on benchmarks for reaction thermochemistry, isomerization, and drug-like molecular torsions. This is achieved by training a network to DFT data then using transfer learning techniques to retrain on a dataset of gold standard QM calculations (CCSD(T)/CBS) that optimally spans chemical space. The resulting potential is broadly applicable to materials science, biology, and chemistry, and billions of times faster than CCSD(T)/CBS calculations.

Development of a potential energy surface for the O3–Ar system: rovibrational states of the complex

Collisional stabilization is an important step in the process of atmospheric formation of ozone.

A comparison between hydrogen and halogen bonding: the hypohalous acid–water dimers, HOX⋯H2O (X = F, Cl, Br)

Hypohalous acids (HOX) are a class of molecules that play a key role in the atmospheric seasonal depletion of ozone and have the ability to form both hydrogen and halogen bonds.

The non-covalently bound SOH2O system, including an interpretation of the differences between SOH2O and O2H2O

Despite the interest in sulfur monoxide (SO) among astrochemists, spectroscopists, inorganic chemists, and organic chemists, its interaction with water remains largely unexplored. We report the first high level theoretical geometries for the two minimum energy complexes formed by sulfur monoxide and water, and we report energies using basis sets as large as aug-cc-pV(Q+d)Z and correlation effects through perturbative quadruple excitations. One structure of SOH2O is hydrogen bonded and the other chalcogen bonded. The hydrogen bonded complex has an electronic energy of -2.71 kcal mol-1 and a zero kelvin enthalpy of -1.67 kcal mol-1, while the chalcogen bonded complex has an electronic energy of -2.64 kcal mol-1 and a zero kelvin enthalpy of -2.00 kcal mol-1. We also report the transition state between the two structures, which lies below the SOH2O dissociation limit, with an electronic energy of -1.26 kcal mol-1 and an enthalpy of -0.81 kcal mol-1. These features are much sharper than for the isovalent complex of O2 and H2O, which only possesses one weakly bound minimum, so we further analyze the structures with open-shell SAPT0. We find that the interactions between O2 and H2O are uniformly weak, but the SOH2O complex surface is governed by the superior polarity and polarizability of SO, as well as the diffuse electron density provided by sulfur's extra valence shell.

Do CCSD and approximate CCSD-F12 variants converge to the same basis set limits? The case of atomization energies

While the title question is a clear "yes" from purely theoretical arguments, the case is less clear for practical calculations with finite (one-particle) basis sets. To shed further light on this issue, the convergence to the basis set limit of CCSD (coupled cluster theory with all single and double excitations) and of different approximate implementations of CCSD-F12 (explicitly correlated CCSD) has been investigated in detail for the W4-17 thermochemical benchmark. Near the CBS ([1-particle] complete basis set) limit, CCSD and CCSD(F12^*) agree to within their respective uncertainties (about ±0.04 kcal/mol) due to residual basis set incompleteness error, but a nontrivial difference remains between CCSD-F12b and CCSD(F12^*), which is roughly proportional to the degree of static correlation. The observed basis set convergence behavior results from the superposition of a rapidly converging, attractive, CCSD[F12]-CCSD-F12b difference (consisting mostly of third-order terms) and a more slowly converging, repulsive, fourth-order difference between CCSD(F12^*) and CCSD[F12]. For accurate thermochemistry, we recommend CCSD(F12^*) over CCSD-F12b if at all possible. There are some indications that the nZaPa family of basis sets exhibits somewhat smoother convergence than the correlation consistent family.

SAMPL6 host-guest challenge: binding free energies via a multistep approach

In this effort in the SAMPL6 host-guest binding challenge, a combination of molecular dynamics and quantum mechanical methods were used to blindly predict the host-guest binding free energies of a series of cucurbit[8]uril (CB8), octa-acid (OA), and tetramethyl octa-acid (TEMOA) hosts bound to various guest molecules in aqueous solution. Poses for host-guest systems were generated via molecular dynamics (MD) simulations and clustering analyses. The binding free energies for the structures obtained via cluster analyses of MD trajectories were calculated using the MMPBSA method and density functional theory (DFT) with the inclusion of Grimme's dispersion correction, an implicit solvation model to model the aqueous solution, and the resolution-of-the-identity (RI) approximation (MMPBSA, RI-B3PW91-D3, and RI-B3PW91, respectively). Among these three methods tested, the results for OA and TEMOA systems showed MMPBSA and RI-B3PW91-D3 methods can be used to qualitatively rank binding energies of small molecules with an overbinding by 7 and 37 kcal/mol respectively, and RI-B3PW91 gave the poorest quality results, indicating the importance of dispersion correction for the binding free energy calculations. Due to the complexity of the CB8 systems, all of the methods tested show poor correlation with the experimental results. Other quantum mechanical approaches used for the calculation of binding free energies included DFT without the RI approximation, utilizing truncated basis sets to reduce the computational cost (memory, disk space, CPU time), and a corrected dielectric constant to account for ionic strength within the implicit solvation model.

Straightening the Hierarchical Staircase for Basis Set Extrapolations: A Low-Cost Approach to High-Accuracy Computational Chemistry

Because the one-electron basis set limit is difficult to reach in correlated post-Hartree-Fock ab initio calculations, the low-cost route of using methods that extrapolate to the estimated basis set limit attracts immediate interest. The situation is somewhat more satisfactory at the Hartree-Fock level because numerical calculation of the energy is often affordable at nearly converged basis set levels. Still, extrapolation schemes for the Hartree-Fock energy are addressed here, although the focus is on the more slowly convergent and computationally demanding correlation energy. Because they are frequently based on the gold-standard coupled-cluster theory with single, double, and perturbative triple excitations [CCSD(T)], correlated calculations are often affordable only with the smallest basis sets, and hence single-level extrapolations from one raw energy could attain maximum usefulness. This possibility is examined. Whenever possible, this review uses raw data from second-order Møller-Plesset perturbation theory, as well as CCSD, CCSD(T), and multireference configuration interaction methods. Inescapably, the emphasis is on work done by the author's research group. Certain issues in need of further research or review are pinpointed.

Re-examining ammonia addition to the Criegee intermediate: converging to chemical accuracy

Theory shows ammonia is unlikely to be significant in Criegee chemistry and demonstrates the importance of perturbative quadruple excitations in Criegee chemistry.

CBS extrapolation in electronic structure pushed to the end: a revival of minimal and sub-minimal basis sets

The complete basis set (CBS) limit is secluded in calculations of electronic structure, and hence CBS extrapolation draws immediate attention.

C-H···O Hydrogen Bonding. The Prototypical Methane-Formaldehyde System: A Critical Assessment

Distinguishing the functionality of C-H···O hydrogen bonds (HBs) remains challenging, because their properties are difficult to quantify reliably. Herein, we present a study of the model methane-formaldehyde complex (MFC). Six stationary points on the MFC potential energy surface (PES) were obtained at the CCSD(T)/ANO2 level. The CCSDT(Q)/CBS interaction energies of the conformers range from only -1.12 kcal mol^-1 to -0.33 kcal mol^-1, denoting a very flat PES. Notably, only the lowest energy stationary point (MFC1) corresponds to a genuine minimum, whereas all other stationary points-including the previously studied ideal case of a_e(C-H···O) = 180°-exhibit some degree of freedom that leads to MFC1. Despite the flat PES, we clearly see that the HB properties of MFC1 align with those of the prototypical water dimer O-H···O HB. Each HB property generally becomes less prominent in the higher-energy conformers. Only the MFC1 conformer prominently exhibits (1) elongated C-H donor bonds, (2) attractive C-H···O═C interactions, (3) n(O) → σ*(C-H) hyperconjugation, (4) critical points in the electron density from Bader's method and from the noncovalent interactions method, (5) positively charged donor hydrogen, and (6) downfield NMR chemical shifts and nonzero ²J(C_M-H_M···O_F) coupling constants. Based on this research, some issues merit further study. The flat PES hinders reliable determinations of the HB-induced shifts of the C-H stretches; a similarly difficult challenge is observed for the experiment. The role of charge transfer in HBs remains an intriguing open question, although our BLW and NBO computations suggest that it is relevant to the C-H···O HB geometries. These issues notwithstanding, the prominence of the HB properties in MFC1 serves as clear evidence that the MFC is predominantly bound by a C-H···O HB.

Tautomerization of Thymine Using Ultraviolet Light

Ultraviolet-light-induced changes to the nucleobase thymine deposited onto a MoS₂ surface were studied using photoelectron spectroscopy and first-principles calculations. These measurements suggest changes in the molecular structure indicated by changes in core electron binding energies. The experimental work has been interpreted by means of ab initio calculations using coupled cluster singles and doubles (CCSD) linear response theory. Contrary to the expected behavior, i.e., the dimerization of two thymine molecules into a pyrimidine dimer, a shift between two tautomeric forms was observed upon UV-exposure. Exposure to ionizing radiation is known to induce damage in many biological molecules, and the present work gives additional insight into its effects on thymine, the interactions of the molecules, and finally how certain UV photoproducts may be avoided.