Historical perspective on: A fifth-order perturbation comparison of electron correlation theories [Volume 157, Issue 6, 26 May 1989, Pages 479–483]

Studying the adsorption of emerging organic contaminants in zeolites with dispersion-corrected density functional theory calculations: From numbers to recommendations

Adsorption energies obtained from dispersion-corrected density functional theory (DFT) calculations show a considerable dependence on the choice of exchange-correlation functional and dispersion correction. A number of investigations have employed different approaches to compute adsorption energies of small molecules in zeolites, using reference values from high-level calculations and/or experiments. Such comparative studies are lacking for larger functional organic molecules such as pharmaceuticals or personal care products, despite their potential relevance for applications, e. g., in contaminant removal or drug delivery. The present study aims to fill this gap by comparing adsorption energies and, for selected cases, equilibrium structures of emerging organic contaminants adsorbed in MOR- and FAU-type all-silica zeolites. A total of 13 dispersion-corrected DFT approaches are compared, including methods using a pairwise dispersion correction as well as non-local van der Waals density functionals. While absolute values of adsorption energies vary widely, qualitative trends across the set of zeolite-guest combinations are not strongly dependent on the choice of functional. For selected cluster models, DFT adsorption energies are compared to reference values from coupled cluster (DLPNO-CCSD(T)) calculations. Although all DFT approaches deliver systematically more negative adsorption energies than the coupled cluster reference, this tendency is least pronounced for the rev-vdW-DF2 functional.

Big data benchmarking: how do DFT methods across the rungs of Jacob's ladder perform for a dataset of 122k CCSD(T) total atomization energies?

Total atomization energies (TAEs) are a central quantity in density functional theory (DFT) benchmark studies. However, so far TAE databases obtained from experiment or high-level ab initio wavefunction theory included up to hundreds of TAEs. Here, we use the GDB-9 database of 133k CCSD(T) TAEs generated by Curtiss and co-workers [B. Narayanan, P. C. Redfern, R. S. Assary and L. A. Curtiss, Chem. Sci., 2019, 10, 7449] to evaluate the performance of 14 representative DFT methods across the rungs of Jacob's ladder (namely, PBE, BLYP, B97-D, M06-L, τ-HCTH, PBE0, B3LYP, B3PW91, ωB97X-D, τ-HCTHh, PW6B95, M06, M06-2X, and MN15). We first use the A25[PBE] diagnostic for nondynamical correlation to eliminate systems that potentially include significant multireference effects, for which the CCSD(T) TAEs might not be sufficiently reliable. The resulting database (denoted by GDB9-nonMR) includes 122k species. Of the considered functionals, B3LYP attains the best performance relative to the G4(MP2) reference TAEs, with a mean absolute deviation (MAD) of 4.09 kcal mol-1. This first-generation hybrid functional, in which the three mixing coefficients were fitted against a small set of TAEs, is one of the few functionals that are not systematically biased towards overestimating the G4(MP2) TAEs, as demonstrated by a mean-signed deviation (MSD) of 0.45 kcal mol-1. The relatively good performance of B3LYP is followed by the heavily parameterized M06-L meta-GGA functional, which attains a MAD of 6.24 kcal mol-1. The PW6B95, M06, M06-2X, and MN15 functionals tend to systematically overestimate the G4(MP2) TAEs and attain MADs ranging between 18.69 (M06) and 28.54 (MN15) kcal mol-1. However, PW6B95 and M06-2X exhibit particularly narrow error distributions. Thus, scaling their TAEs by an empirical scaling factor reduces their MADs to merely 3.38 (PW6B95) and 2.85 (M06-2X) kcal mol-1. Empirical dispersion corrections (e.g., D3 and D4) are attractive, and therefore, their inclusion worsens the performance of methods that systematically overestimate the TAEs.

CCSD(T) Rotational Constants for Highly Challenging C5H2 Isomers-A Comparison between Theory and Experiment

We evaluate the accuracy of CCSD(T) and density functional theory (DFT) methods for the calculation of equilibrium rotational constants (Ae, Be, and Ce) for four experimentally detected low-lying C5H2 isomers (ethynylcyclopropenylidene (2), pentatetraenylidene (3), ethynylpropadienylidene (5), and 2-cyclopropen-1-ylidenethenylidene (8)). The calculated rotational constants are compared to semi-experimental rotational constants obtained by converting the vibrationally averaged experimental rotational constants (A0, B0, and C0) to equilibrium values by subtracting the vibrational contributions (calculated at the B3LYP/jun-cc-pVTZ level of the theory). The considered isomers are closed-shell carbenes, with cumulene, acetylene, or strained cyclopropene moieties, and are therefore highly challenging from an electronic structure point of view. We consider both frozen-core and all-electron CCSD(T) calculations, as well as a range of DFT methods. We find that calculating the equilibrium rotational constants of these C5H2 isomers is a difficult task, even at the CCSD(T) level. For example, at the all-electron CCSD(T)/cc-pwCVTZ level of the theory, we obtain percentage errors ≤0.4% (Ce of isomer 3, Be and Ce of isomer 5, and Be of isomer 8) and 0.9-1.5% (Be and Ce of isomer 2, Ae of isomer 5, and Ce of isomer 8), whereas for the Ae rotational constant of isomers 2 and 8 and Be rotational constant of isomer 3, high percentage errors above 3% are obtained. These results highlight the challenges associated with calculating accurate rotational constants for isomers with highly challenging electronic structures, which is further complicated by the need to convert vibrationally averaged experimental rotational constants to equilibrium values. We use our best CCSD(T) rotational constants (namely, ae-CCSD(T)/cc-pwCVTZ for isomers 2 and 5, and ae-CCSD(T)/cc-pCVQZ for isomers 3 and 8) to evaluate the performance of DFT methods across the rungs of Jacob's Ladder. We find that the considered pure functionals (BLYP-D3BJ, PBE-D3BJ, and TPSS-D3BJ) perform significantly better than the global and range-separated hybrid functionals. The double-hybrid DSD-PBEP86-D3BJ method shows the best overall performance, with percentage errors below 0.5% in nearly all cases.

6-Endo-dig versus 5-exo-dig: Exploring Radical Cyclization Preference with First-, Second-, and Third-row Linkers using High-level Quantum Chemical Methods

As an expansion upon Baldwin rules, the cyclization reactions of hex-5-yn-1-yl radical systems with different first-, second-, and third-row linkers are explored at the CCSD(T) level via means of the SMD(benzene)-G4(MP2) thermochemical protocol. Unlike C, O, and N linkers, systems with B, Si, P, S, Ge, As, and Se linkers are shown to favor 6-endo-dig cyclization. This offers fundamental insights into the rational synthetic design of cyclic compounds. A thorough analysis of stereoelectronic effects, cyclization barriers, and intrinsic barriers illustrates that structural changes alter the cyclization preference by mainly impacting 5-exo-dig reaction barriers. Based on the high-level computational modeling, we proceed to develop a new tool for cyclization preference prediction from the correlation between cyclization barriers and radical structural parameters (e. g., linker bond length and bond angle). A strong correlation is found between the radical attack trajectory angle and the reaction barrier heights, i. e., cyclization preference. Finally, the influence of stereoelectronic effects on the two radical cyclization pathways is further investigated in stereoisomers of hypervalent silicon system, which provides novel insight into cyclization control.

Intramolecular Proton-Coupled Hydride Transfers with Relatively Low Activation Barriers

We report that bifunctional molecules containing hydroxyl and carbonyl functional groups can undergo an effective transfer hydrogenation via an intramolecular proton-coupled hydride transfer (PCHT) mechanism. In this reaction mechanism, a hydride transfer between two carbon atoms is coupled with a proton transfer between two oxygen atoms via a cyclic bond rearrangement transition structure. The coupled transfer of the two hydrogens as H^δ+ and H^δ- is supported by atomic polar tensor charges. The activation energy for the PCHT reaction is strongly dependent on the length of the alkyl chain between the hydroxyl and carbonyl functional groups but relatively weakly dependent on the functional groups attached to the hydroxyl and carbonyl carbons. We investigate the PCHT reaction mechanism using the Gaussian-4 thermochemical protocol and obtain high activation energy barriers (ΔH^‡₂₉₈) of 210.5-228.3 kJ mol^-1 for chain lengths of one carbon atom and 160.2-163.9 kJ mol^-1 for chain lengths of two carbon atoms. However, for longer chain lengths containing 3-4 carbon atoms, we obtain ΔH^‡₂₉₈ values as low as 101.9 kJ mol^-1. Importantly, the hydride transfer between two carbon atoms proceeds without the need for a catalyst or hydride transfer activating agent. These results indicate that the intramolecular PCHT reaction provides an effective avenue for uncatalyzed, metal-free hydride transfers at ambient temperatures.

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 0 K as 26.5, 15.6, 12.2, and 0.1 kcal 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.

Structural and Vibrational Properties of Amino Acids from Composite Schemes and Double-Hybrid DFT: Hydrogen Bonding in Serine as a Test Case

The structures, relative stabilities, and vibrational wavenumbers of the two most stable conformers of serine, stabilized by the O-H···N, O-H···O═C and N-H···O-H intramolecular hydrogen bonds, have been evaluated by means of state-of-the-art composite schemes based on coupled-cluster (CC) theory. The so-called "cheap" composite approach (CCSD(T)/(CBS+CV)^MP2) allowed determination of accurate equilibrium structures and harmonic vibrational wavenumbers, also pointing out significant corrections beyond the CCSD(T)/cc-pVTZ level. These accurate results stand as a reference for benchmarking selected hybrid and double-hybrid, dispersion-corrected DFT functionals. B2PLYP-D3 and DSDPBEP86 in conjunction with a triple-ζ basis set have been confirmed as effective methodologies for structural and spectroscopic studies of medium-sized flexible biomolecules, also showing intramolecular hydrogen bonding. These best performing double-hybrid functionals have been employed to simulate IR spectra by means of vibrational perturbation theory, also considering hybrid CC/DFT schemes. The best overall agreement with experiment, with mean absolute error of 8 cm^-1, has been obtained by combining CCSD(T)/(CBS+CV)^MP2 harmonic wavenumbers with B2PLYP-D3/maug-cc-pVTZ anharmonic corrections. Finally, a composite scheme entirely based on CCSD(T) calculations (CCSD(T)/CBS+CV) has been employed for energetics, further confirming that serine II is the most stable conformer, also when zero-point vibrational energy corrections are included.

Approximate equation-of-motion coupled-cluster methods for electron affinities of closed-shell molecules

We investigate performance of the equation-of-motion coupled-cluster method at the single and doubles level (EOM-CCSD) and a series of approximate methods based on EOM-CCSD on electron affinities (EA) of closed-shell cations and neutral molecules with positive and negative EAs in this work. Our results confirm that P-EOM-MBPT2 can provide reasonable EAs when molecules with significant multireference character are not considered and its mean absolute error on EAs of these molecules is around or less than 0.2 eV. Its accuracy is comparable to that of the more expensive EOM-CCSD(2) method. Results of EOM-CCSD(2), P-EOM-MBPT2, and CIS(D_∞) indicate that the [[H, a_c ⁺], T₂] term in the 1h2p-1h block is more important on EAs than the term neglected in the 1h2p-1h2p block in P-EOM-MBPT2. We proposed an economical method where EAs from CIS(D_∞) are corrected by treating this [[H, a_c ⁺], T₂] term in the 1h2p-1h block perturbatively [corr-CIS(D_∞)]. EAs with corr-CIS(D_∞) agree very well with those of P-EOM-MBPT2 with a difference of less than 0.02 eV. Computational scaling of this method is N⁴ for the iterative part and N⁵ for some non-iterative steps. Its storage requirement is only of OV³. Corr-CIS(D_∞) is an economical and reliable method on EAs, and it can be applied to EAs of large molecules.