Perturbative Quadruple Research Articles

Quantum chemical calculations of electron affinities of alkaline earth metal atoms (Ca, Sr, Ba, and Ra)

We performed high-level ab initio quantum chemical calculations, incorporating higher-order excitations, spin–orbit coupling (SOC), and the Gaunt interaction, to calculate the electron affinities (EAs) of alkaline earth (AE) metal atoms (Ca, Sr, Ba, and Ra), which are notably small. The coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method is insufficient to accurately calculate the EAs of AE metal atoms. Higher-order excitations proved crucial, with the coupled-cluster singles, doubles, and triples with perturbative quadruples [CCSDT(2)Q] method effectively capturing dynamic electron correlation effects. The contributions of SOC (ΔESOs) to the EAs calculated using the multireference configuration interaction method with the Davidson correction, including SOC, positively enhance the EAs; however, these contributions are overestimated. The Dirac–Hartree–Fock (DHF)-CCSD(T) method addresses this overestimation and provides reasonable values for ΔESO (ΔESO−D). Employing additional sets of diffuse and core–valence correlation basis sets is critical for accurately calculating the EAs of AE metal atoms. The contributions of the Gaunt interaction (ΔEGaunt) to the EAs of AE metal atoms are negligible. Notably, the CCSDT(2)Q with the complete basis set limit + ΔESO−D + ΔEGaunt produced EA values for Ca, Sr, and Ba that closely aligned with experimental data and achieved accuracy exceeding the chemical accuracy. Based on our findings, the accurately proposed EA for Ra is 9.88 kJ/mol.

Ab initio potential energy surfaces for the O2-O2 system and derived thermophysical properties.

New intermolecular potential energy surfaces (PESs) for the quintet, triplet, and singlet states of two rigid oxygen (O2) molecules in their triplet ground electronic states were developed. Quintet interaction energies were obtained for 896 O2-O2 configurations by supermolecular coupled cluster (CC) calculations at levels up to CC with single, double, triple, and perturbative quadruple excitations [CCSDT(Q)] with unrestricted Hartree-Fock (UHF) reference wave functions. Corrections for scalar relativistic effects were calculated as well. Triplet interaction energies were obtained by combining the quintet interaction energies with accurate estimates for the differences between the quintet and triplet energies obtained at the UHF-CCSD(T) level of theory. Here, we exploited the fact that the triplet state is almost identical to the readily accessible "broken-symmetry" state, as shown by Valentin-Rodríguez et al. [J. Chem. Phys. 152, 184304 (2020)]. The singlet interaction energies were estimated from the quintet and triplet interaction energies by employing the Heisenberg Hamiltonian description of the spin splittings. The three PESs are represented analytically by site-site models with five sites per molecule and anisotropic site-site interactions. To validate the PESs, we calculated at temperatures from 55 to 2000K the second virial coefficient using statistical thermodynamics and the shear viscosity, thermal conductivity, and self-diffusion coefficient in the dilute gas phase using the kinetic theory of molecular gases. The calculated property values are in excellent agreement with the most accurate experimental data from the literature. Therefore, we also propose new reference correlations for the investigated properties based solely on the calculated values.

Cross Second Virial Coefficients of the H2O-H2 and H2S-H2 Systems from First-Principles.

The cross second virial coefficients B12 for the interactions of water (H2O) with molecular hydrogen (H2) and of hydrogen sulfide (H2S) with H2 were obtained at temperatures in the range from 150 to 2000 K from new intermolecular potential energy surfaces (PESs) for the respective molecule pairs. The PESs are based on interaction energies determined for about 12 000 configurations of each molecule pair employing different high-level quantum-chemical ab initio methods up to coupled cluster with single, double, triple, and perturbative quadruple excitations [CCSDT(Q)]. Furthermore, the interaction energies were corrected for scalar relativistic effects. Both classical and semiclassical values for B12 were extracted from the PESs using the Mayer-sampling Monte Carlo approach. While our results for the H2O-H2 system validate the older first-principles results of Hodges et al. [J. Chem. Phys. 2004, 120, 710-720], B12 for the H2S-H2 system was, to the best of our knowledge, hitherto neither measured experimentally nor predicted from first principles.

Enthalpies of formation for Criegee intermediates: A correlation energy convergence study.

Criegee intermediates, formed from the ozonolysis of alkenes, are known to have a role in atmospheric chemistry, including the modulation of the oxidizing capacity of the troposphere. Although studies have been conducted since their discovery, the synthesis of these species in the laboratory has ushered in a new wave of investigations of these structures, both theoretically and experimentally. In some of these theoretical studies, high-order corrections for correlation energy are included to account for the mid multi-reference character found in these systems. Many of these studies include a focus on kinetics; therefore, the calculated energies should be accurate (<1 kcal/mol in error). In this research, we compute the enthalpies of formation for a small set of Criegee intermediates, including higher-order coupled cluster corrections for correlation energy up to coupled cluster with perturbative quintuple excitations. The enthalpies of formation for formaldehyde oxide, anti-acetaldehyde oxide, syn-acetaldehyde oxide, and acetone oxide are presented at 0K as 26.5, 15.6, 12.2, and 0.1kcal mol-1, respectively. Additionally, we do not recommend the coupled cluster with perturbative quadruple excitations [CCSDT(Q)] energy correction, as it is approximately twice as large as that of the coupled cluster with full quadruple excitations (CCSDTQ). Half of the CCSDT(Q) energy correction may be included as a reliable, cost-effective estimation of CCSDTQ energies for Criegee intermediates.

Ab initio potential energy functions, spectroscopy and thermal physics for krypton-contained rare gas dimers

Three state-of-the-art ab initio interatomic potential energy functions (PEFs) for the Kr-Ne, Kr-Ar, Kr-Xe rare gas dimers are presented. These PEFs are based upon extrapolation to complete basis set (CBS) limit results of supermolecular computations at the coupled-cluster level with single, double, and perturbative triple excitations (CCSD(T)) and correlation-consistent basis sets up to sextuple-zeta quality, augmented with mid-bond functions. Core-core and core-valence electron correlation, higher-order coupled-cluster excitations up to perturbative quadruple excitations, CCSDT(Q), and scalar relativistic corrections have also been taken into account. We have employed Morse/Long Range (MLR) potential energy functions (PEFs) to fit the total interaction energies as a function of the internuclear separation, followed by the calculation of spectroscopic parameters, vibrational and rotational energy levels, absorption spectra, and thermophysical properties over an extensive temperature range. Good agreement with experimental data and an empirical potential energy function shows that our ab initio MLR PEFs are superior not only to previous PEFs, but also to most empirical PEFs.

Substituent Effects on Aluminyl Anions and Derived Systems: A High-Level Theory.

Aluminyl anions are low-valent aluminum species bearing a lone pair of electrons and a negative charge. These systems have drawn recent synthetic interest for their nucleophilic nature, allowing for the activation of σ-bonds, and have been proposed as a pathway to hydrogen energy storage. In this research, we provide high-level ab initio geometries and energies for both the simplest aluminyl anion (AlH2-) and several substituted derivatives. Geometries are reported using the gold-standard CCSD(T)/aug-cc-pV(T+d)Z level of theory. Energies were extrapolated to the complete basis set limit through the focal point approach, utilizing coupled-cluster methods through perturbative quadruples and basis sets up to five-ζ quality. Geometries were rationalized using electrostatic, steric, and orbital donation effects. The donation from substituents to Al is accompanied by back-donation effects, a property traditionally thought of in transition-metal systems. Stereoelectronic effects through the secondary orbital interaction play a fundamental role in stabilizing these low-valent aluminum compounds and would likely also affect the feasibility of their use within several industrial applications. The energetic analysis of the formation of each substituted anion is rationalized as the result of three energetic schemes. The effectiveness of these schemes for determining the relative formation energies is discussed.

On the role of coupled-clusters' full triple and perturbative quadruple excitations on rovibrational spectra of van der Waals complexes

The importance of coupled clusters iterative triple and noniterative quadruple, , electron excitations on the potential energy surfaces (PESs) of van der Waals molecules is examined for H–CO. The evaluation of this importance is performed by comparing theoretical spectra with experiment. Somewhat surprisingly, although the contributions to interaction energies are below 3%, the inclusion of them reduces the error of theory with respect to experiment by an order of magnitude and qualitative agreement of the spectra in some regions is achieved only when they are included. The main reason for these observations is that the effects significantly change the anisotropy of the PES.

Platinum, gold, and silver standards of intermolecular interaction energy calculations

High-accuracy noncovalent interaction energies are indispensable as data points for potential energy surfaces and as benchmark values for improving and testing more approximate approaches. The preferred algorithm (the gold standard) for computing these energies has been the coupled-cluster method with singles, doubles, and perturbative triples [CCSD(T)] converged to the complete basis set (CBS) limit. However, gold-standard calculations are expensive as correlated interaction energies converge slowly with the basis set size, and establishing the CBS limit to better than 0.05 kcal/mol typically requires a CCSD(T) calculation in a basis set of at least triple-zeta quality. If an even higher accuracy is required (for example, for the assignment of complicated high-resolution spectra), establishing a superior platinum standard requires both a precisely converged CCSD(T)/CBS limit and the corrections for the core correlation, relativistic effects, and higher-order coupled-cluster terms at least through the perturbative quadruple excitations. On the other hand, if a triple-zeta CCSD(T) calculation is not feasible but a double-zeta one is, it is worthwhile to look for a silver standard that provides the most accurate and consistent approximation to the gold standard at a reduced computational cost. We review the recent developments aimed at (i) increasing the breadth and diversity of the available collection of gold-standard benchmark interaction energies, (ii) evaluating the best computational strategies for platinum-standard calculations and producing beyond-CCSD(T) potential energy surfaces for spectroscopic and scattering applications of the highest precision, and (iii) improving the accuracy of the silver-standard, double-zeta-level CCSD(T)/CBS estimates through the use of explicit correlation and midbond basis functions. We also outline the remaining challenges in the accurate ab initio calculations of noncovalent interaction energies.

Gas-Phase Ozone Reactions with a Structurally Diverse Set of Molecules: Barrier Heights and Reaction Energies Evaluated by Coupled Cluster and Density Functional Theory Calculations.

Reactions with ozone transform organic and inorganic molecules in water treatment systems as well as in atmospheric chemistry, either in the aqueous phase, at gas/particle interfaces, or in the gas phase. Computed thermokinetic data can be used to estimate the reactivities of molecules toward ozone in cases where no experimental data are available. Although the gas-phase reactivity of olefins with ozone has been characterized extensively in the literature, this is not the case for the richer chemistry of ozone with polar molecules, which occurs in the aqueous phase or in microhydrated environments. Here, we selected a number of model reactions with small molecules (ethene, ethyne, hydrogen cyanide, hydrogen chloride, ammonia, bromide, and trimethylamine) to study the accuracy of different quantum chemical methods for describing the reactivities of these molecules with ozone. We calculated benchmark electronic energies of gas-phase reactions of these systems with single-reference coupled cluster (CC) theory. These benchmark results for the binding energy in the van der Waals complex, the energy of the transition structure, and the reaction energy were estimated to be accurate within 1-2 kcal mol-1. Singlet oxygen (1O2) is a common product of ozone reactions. Coupled cluster calculations with up to perturbative quadruples (CCSDT( Q)) were needed to obtain reaction energies accurate within 1 kcal mol-1 when this species was involved. In (micro)hydrated environments or at interfaces, coupled cluster methods are prohibitively expensive in most cases. We tested the suitability of some contemporary density functional theory (DFT) methods to reproduce the benchmark electronic energy differences. Range-separated functionals were found to be promising candidates to estimate forward barrier heights, with LC-ωPBE rivaling the accuracy of CCSD( T). For energies of reaction, however, DFT methods exhibited large systematic errors, depending on their fraction of orbital exchange. This was found to worsen when 1O2 is a product, and no safe recommendation can be given for DFT reaction energies in such cases.

The multichannel n-propyl + O2 reaction surface: Definitive theory on a model hydrocarbon oxidation mechanism

The n-propyl + O2 reaction is an important model of chain branching reactions in larger combustion systems. In this work, focal point analyses (FPAs) extrapolating to the ab initio limit were performed on the n-propyl + O2 system based on explicit quantum chemical computations with electron correlation treatments through coupled cluster single, double, triple, and perturbative quadruple excitations [CCSDT(Q)] and basis sets up to cc-pV5Z. All reaction species and transition states were fully optimized at the rigorous CCSD(T)/cc-pVTZ level of theory, revealing some substantial differences in comparison to the density functional theory geometries existing in the literature. A mixed Hessian methodology was implemented and benchmarked that essentially makes the computations of CCSD(T)/cc-pVTZ vibrational frequencies feasible and thus provides critical improvements to zero-point vibrational energies for the n-propyl + O2 system. Two key stationary points, n-propylperoxy radical (MIN1) and its concerted elimination transition state (TS1), were located 32.7 kcal mol−1 and 2.4 kcal mol−1 below the reactants, respectively. Two competitive β-hydrogen transfer transition states (TS2 and TS2′) were found separated by only 0.16 kcal mol−1, a fact unrecognized in the current combustion literature. Incorporating TS2′ in master equation (ME) kinetic models might reduce the large discrepancy of 2.5 kcal mol−1 between FPA and ME barrier heights for TS2. TS2 exhibits an anomalously large diagonal Born-Oppenheimer correction (ΔDBOC = 1.71 kcal mol−1), which is indicative of a nearby surface crossing and possible nonadiabatic reaction dynamics. The first systematic conformational search of three hydroperoxypropyl (QOOH) intermediates was completed, uncovering a total of 32 rotamers lying within 1.6 kcal mol−1 of their respective lowest-energy minima. Our definitive energetics for stationary points on the n-propyl + O2 potential energy surface provide key benchmarks for future studies of hydrocarbon oxidation.

The Structure and Cl-O Dissociation Energy of the ClOO Radical: Finally, the Right Answers for the Right Reason.

The chlorine peroxy radical (ClOO) has historically been a highly problematic system for theoretical studies. In particular, the erratic ab initio predictions of the Cl-O bond length reported in the literature thus far exhibit unacceptable errors with respect to the experimental structure. In light of the widespread disagreement observed, we present a careful and systematic investigation of the ClOO geometry toward the basis set and correlation limits of single reference ab initio theory, employing the cc-pVXZ (X = D, T, Q, 5, 6) basis sets extrapolated to the complete basis set limit and coupled cluster theory through single, double, triple, and perturbative quadruple excitations [CCSDT(Q)]. We demonstrate a considerable sensitivity of the Cl-O bond length to both electron correlation and basis set size. The CCSDT(Q)/CBS structure is found to be re(ClO) = 2.082, re(OO) = 1.208, and θe(ClOO) = 115.4°, in remarkable agreement with Endo's semi-experimentally determined values re(ClO) = 2.084(1), re(OO) = 1.206(2), and θe(ClOO) = 115.4(1)°. Moreover, we compute a Cl-O bond dissociation energy of 4.77 kcal mol-1, which is likewise in excellent agreement with the most recent experimental value of 4.69 ± 0.10 kcal mol-1.

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

Stabilized Criegee intermediates (SCI) are formed during the ozonolysis of unsaturated hydrocarbons and have been implicated in the formation of hydroxyl radicals and aerosols. Previous theoretical research [S. Jørgenson and A. Gross, J. Phys. Chem. A, 2009, 113, 10284-10290] computed the rate constants for addition of ammonia to simple SCIs, but reported a wide distribution of quantum chemical energies, depending on the basis set used. We report optimized geometries for these reactions at the CCSD(T)/ANO2 and CCSD(T)/ANO1 levels, and CCSD(T)/CBS energies with perturbative quadruples corrections. We find the inclusion of perturbative quadruples corrections elevates the energy of the transition state by 0.76-0.88 kcal mol-1 relative to the reactants, which qualitatively changes the reaction surface. We calculate rate constants and find that Jørgenson and Gross previously overestimated the rate constants for ammonia addition to SCIs, but were within an order of magnitude. This supports the previous conclusion of Vereecken et al. [L. Vereecken, H. Harder and A. Novelli, Phys. Chem. Chem. Phys., 2012, 14, 14682-14695] that ammonia addition to SCIs is a negligible sink of Criegee intermediates.

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.

Moderate-Cost Ab Initio Thermochemistry with Chemical Accuracy.

A moderate-cost ab initio composite model chemistry including the explicitly correlated CCSD(T*)(F12) and conventional coupled-cluster methods up to perturbative quadruple excitations along with correlation consistent basis sets is developed. The model, named diet-HEAT-F12, is also augmented with diagonal Born-Oppenheimer and scalar relativistic corrections. The methods and basis sets used for the calculation of the individual components are selected to reproduce, as close as possible, without using any fitted parameters, the benchmark HEAT contributions. A well-defined recipe for calculating size-dependent 95% confidence intervals was also worked out for the model. The reliability of the protocol was checked using the W4-11 data set as well as a disjoint set of 23 accurate atomization energies collected from the literature and obtained by the procedure of Feller, Peterson, and Dixon. The best error statistics for the test set was yielded by the diet-HEAT-F12 protocol among the models W3X, W3X-L, and W3-F12 considered.

Structural Distortions Accompanying Noncovalent Interactions: Methane-Water, the Simplest C-H Hydrogen Bond.

Neglect of fragment structural distortions resulting from noncovalent interactions is a common practice when examining a potential energy surface (PES). Herein, we make quantitative predictions concerning the magnitude of such distortions in the methane-water system. Coupled cluster methods up to perturbative quadruples [CCSDT(Q)] were used in the structural optimizations to the complete basis set limit (using up to cc-pV6Z basis sets). Our results show that the interaction energy differences between the fully optimized and nonoptimized structures are on the order of 0.02 kcal mol-1. These findings imply that scanning the PES of a very weakly bound noncovalent system, while neglecting intramolecular distortions, is a reasonable approximation for points other than the minima.

Accurate Theoretical Thermochemistry for Fluoroethyl Radicals.

An accurate coupled-cluster (CC) based model chemistry was applied to calculate reliable thermochemical quantities for hydrofluorocarbon derivatives including radicals 1-fluoroethyl (CH3-CHF), 1,1-difluoroethyl (CH3-CF2), 2-fluoroethyl (CH2F-CH2), 1,2-difluoroethyl (CH2F-CHF), 2,2-difluoroethyl (CHF2-CH2), 2,2,2-trifluoroethyl (CF3-CH2), 1,2,2,2-tetrafluoroethyl (CF3-CHF), and pentafluoroethyl (CF3-CF2). The model chemistry used contains iterative triple and perturbative quadruple excitations in CC theory, as well as scalar relativistic and diagonal Born-Oppenheimer corrections. To obtain heat of formation values with better than chemical accuracy perturbative quadruple excitations and scalar relativistic corrections were inevitable. Their contributions to the heats of formation steadily increase with the number of fluorine atoms in the radical reaching 10 kJ/mol for CF3-CF2. When discrepancies were found between the experimental and our values it was always possible to resolve the issue by recalculating the experimental result with currently recommended auxiliary data. For each radical studied here this study delivers the best heat of formation as well as entropy data.

Radicals derived from acetaldehyde and vinyl alcohol.

Vinyl alcohol and acetaldehyde are isoelectronic products of incomplete butanol combustion. Along with the radicals resulting from the removal of atomic hydrogen or the hydroxyl radical, these species are studied here using ab initio methods as complete as coupled cluster theory with single, double, triple, and perturbative quadruple excitations [CCSDT(Q)], with basis sets as large as cc-pV5Z. The relative energies provided herein are further refined by including corrections for relativistic effects, the frozen core approximation, and the Born-Oppenheimer approximation. The effects of anharmonic zero-point vibrational energies are also treated. The syn conformer of vinyl alcohol is predicted to be lower in energy than the anti conformer by 1.1 kcal mol-1. The alcoholic hydrogen of syn-vinyl alcohol is found to be the easiest to remove, requiring 84.4 kcal mol-1. Five other radicals are also carefully considered, with four conformers investigated for the 1-hydroxyvinyl radical. Beyond energetics, we have conducted an overhaul of the spectroscopic literature for these species. Our results also provide predictions for fundamental modes yet to be reported experimentally. To our knowledge, the ν3 (3076 cm-1) and ν4 (2999 cm-1) C-H stretches for syn-vinyl alcohol and all but one of the vibrational modes for anti-vinyl alcohol (ν1-ν14) are yet to be observed experimentally. For the acetyl radical, ν6 (1035 cm-1), ν11 (944 cm-1), ν12 (97 cm-1), and accounting for our changes to the assignment of the 1419.9 cm-1 experimental mode, ν10 (1441 cm-1), are yet to be observed. We have predicted these unobserved fundamentals and reassigned the experimental 1419.9 cm-1 frequency in the acetyl radical to ν4 rather than to ν10. Our work also strongly supports reassignment of the ν10 and ν11 fundamentals of the vinoxy radical. We suggest that the bands assigned to the overtones of these fundamentals were in fact combination bands. Our findings may be useful in constructing improved combustion models of butanol and in spectroscopically characterizing these molecules further.

Enthalpy Differences of the n-Pentane Conformers.

The energy and enthalpy differences of alkane conformers in various temperature ranges have been the subject for both experimental and theoretical studies over the last few decades. It was shown previously for the conformers of butane [G. Tasi et al., J. Chem. Theory Comput. 2012, 8, 479-486] that quantum chemical results can compete with spectroscopic techniques and results obtained even from the most carefully performed experiments could be biased due to the improper statistical model utilized to evaluate the raw experimental data. In the current study, on one hand, the experimental values and their uncertainties for the enthalpy differences for pentane conformers are re-evaluated using the appropriate statistical model. On the other hand, a coupled-cluster-based focal-point analysis has been performed to calculate energy and enthalpy differences for the conformers of pentane. The model chemistry defined in this study includes contributions up to the perturbative quadruple excitations augmented with further small correction terms beyond the Born-Oppenheimer and nonrelativistic approximations. Benchmark quality energy and enthalpy differences for the pentane conformers are given at temperatures 0 and 298.15 K as well as for the various temperature ranges used in the gas-phase experimental measurements. Furthermore, a slight positive shift for the experimental enthalpy differences is also predicted due to an additional Raman active band belonging to the gauche-gauche conformer.

1,1-Dilithioethylene: Toward Spectroscopic Identification of the Definitive Singlet Ground Electronic State of a Peculiar Structure.

1,1-Dilithioethylene is a prototypical carbon-lithium compound that is not known experimentally. All low-lying singlet and triplet structures of interest were investigated by using high-level theoretical methods with correlation-consistent basis sets up to pentuple ζ. The coupled cluster methods adopted included up to full triple excitations and perturbative quadruples. In contrast to earlier studies that predicted the twisted C2v triplet to be the ground state, we found a peculiar planar Cs singlet ground state in the present research. The lowest excited electronic state of 1,1-dilithioethylene, the twisted Cs triplet, was found to lie 9.0 kcal mol(-1) above the ground state by using energy extrapolation to the complete basis set limit. For the planar Cs singlet and twisted Cs triplet states of 1,1-dilithioethylene, anharmonic vibrational frequencies were reported on the basis of second-order vibrational perturbation theory. The remarkably low (2050 cm(-1) ) C-H stretching fundamental (the C-H bond near the bridging lithium) of the singlet state was found to have very strong infrared intensity. These highly reliable theoretical findings may assist in the long-sought experimental identification of 1,1-dilithioethylene. Using natural bond orbital analysis, we found that lithium bridging structures were strongly influenced by electrostatic effects. All carbon-carbon linkages corresponded to conventional double bonds.

High precision quantum-chemical treatment of adsorption: Benchmarking physisorption of molecular hydrogen on graphane.

A multilevel hierarchical ab initio protocol for calculating adsorption on non-conducting surfaces is presented. It employs fully periodic treatment, which reaches local Møller-Plesset perturbation theory of second order (MP2) with correction for the basis set incompleteness via the local F12 technique. Post-MP2 corrections are calculated using finite clusters. That includes the coupled cluster treatment in the local and canonical frameworks (up to perturbative quadruples) and correlated core (with MP2). Using this protocol, the potential surface of hydrogen molecules adsorbed on graphane was computed. According to the calculations, hydrogen molecules are adsorbed on graphane in a perpendicular to the surface orientation with the minimum of the potential surface of around -3.6 kJ/mol located at the distance of 3.85 Å between the bond center of the hydrogen molecule and the mid-plane of graphane. The adsorption sites along the path from the downward-pointing carbon to the ring center of the graphane are energetically virtually equally preferable, which can enable nearly free translations of hydrogen molecules along these paths. Consequently, the hydrogen molecules on graphane most likely form a non-commensurate monolayer. The analysis of the remaining errors reveals a very high accuracy of the computed potential surface with an error bar of a few tenths of a kJ/mol. The obtained results are a high-precision benchmark for further theoretical and experimental studies of hydrogen molecules interacting with graphane.