Comparison of Explicitly Correlated Methods for Computing High-Accuracy Benchmark Energies for Noncovalent Interactions

Correlation Consistent Basis Sets for Explicitly Correlated Theory: The Transition Metals

We present correlation consistent basis sets for explicitly correlated (F12) calculations, denoted VnZ(-PP)-F12-wis (n = D,T), for the d-block elements. The cc-pVDZ-F12-wis basis set is contracted to [8s7p5d2f] for the 3d-block, while its ECP counterpart for the 4d and 5d-blocks, cc-pVDZ-PP-F12-wis, is contracted to [6s6p5d2f]. The corresponding contracted sizes for cc-pVTZ(-PP)-F12-wis are [9s8p6d3f2g] for the 3d-block elements and [7s7p6d3f2g] for the 4d and 5d-block elements. Our VnZ(-PP)-F12-wis basis sets are evaluated on challenging test sets for metal-organic barrier heights (MOBH35) and group-11 metal clusters (CUAGAU-2). In F12 calculations, they are found to be about as close to the complete basis set limit as the combination of standard cc-pVnZ-F12 on main-group elements with the standard aug-cc-pV(n+1)Z(-PP) basis sets on the transition metal(s). While our basis sets are somewhat more compact than aug-cc-pV(n+1)Z(-PP), the CPU time benefit is negligible for catalytic complexes that contain only one or two transition metals among dozens of main-group elements; however, it is somewhat more significant for metal clusters.

The influence of a solvent environment on direct non-covalent interactions between two molecules: A symmetry-adapted perturbation theory study of polarization tuning of π-π interactions by water

High-level quantum chemical computations have provided significant insight into the fundamental physical nature of non-covalent interactions. These studies have focused primarily on gas-phase computations of small van der Waals dimers; however, these interactions frequently take place in complex chemical environments, such as proteins, solutions, or solids. To better understand how the chemical environment affects non-covalent interactions, we have undertaken a quantum chemical study of π-π interactions in an aqueous solution, as exemplified by T-shaped benzene dimers surrounded by 28 or 50 explicit water molecules. We report interaction energies (IEs) using second-order Møller-Plesset perturbation theory, and we apply the intramolecular and functional-group partitioning extensions of symmetry-adapted perturbation theory (ISAPT and F-SAPT, respectively) to analyze how the solvent molecules tune the π-π interactions of the solute. For complexes containing neutral monomers, even 50 explicit waters (constituting a first and partial second solvation shell) change total SAPT IEs between the two solute molecules by only tenths of a kcal mol^-1, while significant changes of up to 3 kcal mol^-1 of the electrostatic component are seen for the cationic pyridinium-benzene dimer. This difference between charged and neutral solutes is attributed to large non-additive three-body interactions within solvated ion-containing complexes. Overall, except for charged solutes, our quantum computations indicate that nearby solvent molecules cause very little "tuning" of the direct solute-solute interactions. This indicates that differences in binding energies between the gas phase and solution phase are primarily indirect effects of the competition between solute-solute and solute-solvent interactions.

The effect of midbond functions on interaction energies computed using MP2 and CCSD(T)

In this article we use MP2 and CCSD(T) calculations for the A24 and S66 data sets to explore how midbond functions can be used to generate cost effective counterpoise corrected supramolecular interaction energies of noncovalent complexes. We use the A24 data set to show that the primary role of midbond functions is not to approach the complete basis set limit, but rather to ensure a balanced description of the molecules and the interaction region (unrelated to the basis set superposition error). The need for balance is a consequence of using atom centered basis sets. In the complete basis set limit, the error will disappear, but reaching the complete basis set limit is not feasible beyond small systems. For S66 we investigate the need for increasing the number of midbond centers. Results show that adding a second midbond center increases the accuracy, but the effect is secondary to changing the atom centered basis set. Further, by comparing calculations using the 3s3p2d1f1g midbond set with using aug-cc-pVDZ and aug-cc-pVTZ as midbond sets, we see that the requirements for the midbond set to be effective, is not just that it contains diffuse functions, but also that high angular momentum functions are included. By comparing two approaches for placing midbond centers we show that results are not particularly sensitive to placement as long as the placement is reasonable.

S66x8 noncovalent interactions revisited: new benchmark and performance of composite localized coupled-cluster methods

The S66x8 noncovalent interactions benchmark has been re-evaluated at the “sterling silver” level. Against this, a selection of computationally more economical alternatives has been assayed, ranging from localized CC to double hybrids and SAPT(DFT).

Methane Adsorption on Heteroatom-Modified Maquettes of Porous Carbon Surfaces

Experimental and theoretical studies disagree on the energetics of methane adsorption on carbon materials. However, this information is critical for the rational design and optimization of the structure and composition of adsorbents for natural gas storage. The delicate nature of dispersion interactions, polarization of both the adsorbent and the adsorbate, interplay between H-bonding and tetrel bonding, and induced dipole/Coulomb interactions inherent to methane physisorption require computational treatment at the highest possible level of theory. In this study, we employed the smallest reasonable computational model, a maquette of porous carbon surfaces with a central site for substitution and methane binding. The most accurate predictions of methane adsorption energetics were achieved by electron-correlated molecular orbital theory CCSD(T) and hybrid density functional theory MN15 calculations employing a saturated, all-electron basis set. The characteristic geometry of methane adsorption on a carbon surface ("lander approach") arises due to bonding interactions of the adsorbent π-system with the proximal H-C bonds of methane, in addition to tetrel bonding between the antibonding orbital of the distal C-H bond and the central atom of the maquette (C, B, or N). The polarization of the electron density, structural deformations, and the comprehensive energetic analysis clearly indicate a ∼3 kJ mol^-1 preference for methane binding on the N-substituted maquette. The B-substituted maquette showed a comparable or lower binding energy than the unsubstituted, pure C model, depending on the level of theory employed. The calculated thermodynamic results indicate a strategy for incorporating electron-enriched substitutions (e.g., N) into carbon materials as a way to increase methane storage capacity over electron-deficient (e.g., B) modifications. The thermochemical analysis was revised for establishing a conceptual agreement between the experimental isosteric heat of adsorption and the binding enthalpies from statistical thermodynamics principles.

Dataset of noncovalent intermolecular interaction energy curves for 24 small high-spin open-shell dimers

We introduce a dataset of 24 interaction energy curves of open-shell noncovalent dimers, referred to as the O24 × 5 dataset. The dataset consists of high-spin dimers up to 11 atoms selected to assure diversity with respect to interaction types: dispersion, electrostatics, and induction. The benchmark interaction energies are obtained at the restricted open-shell CCSD(T) level of theory with complete basis set extrapolation (from aug-cc-pVQZ to aug-cc-pV5Z). We have analyzed the performance of selected wave function methods MP2, CCSD, and CCSD(T) as well as the F12a and F12b variants of coupled-cluster theory. In addition, we have tested dispersion-corrected density functional theory methods based on the PBE exchange-correlation model. The O24 × 5 dataset is a challenge to approximate methods due to the wide range of interaction energy strengths it spans. For the dispersion-dominated and mixed-type subsets, any tested method that does not include the triples contribution yields errors on the order of tens of percent. The electrostatic subset is less demanding with errors that are typically an order of magnitude smaller than the mixed and dispersion-dominated subsets.

Post-complete-basis-set extrapolation of conventional and explicitly correlated coupled-cluster energies: can the convergence to the CBS limit be diagnosed?

We assess benchmark correlation energies for 130 systems in test sets A24 and TS-106 both with the canonical CCSD(T) and explicitly correlated CCSD(T)-F12 methods. Aiming at enhanced accuracy, the calculated raw energies from both sets are CBS extrapolated to the complete basis set (CBS) limit and subsequently post-CBS extrapolated. Attention is focused at total energies, since their accuracy reflects on that of the interaction energies. Using up to triple-ζ basis sets for CBS and an additional quadruple-ζ for post-CBS, the mean and standard unsigned deviations with canonical CCSD(T) theory are 0.257 ± 0.25 kcal mol^-1, while the corresponding values for CCSD(T)-F12 in its F12a and F12b variants with specialized basis sets up to VQZ-F12 are 0.170 ± 0.13 kcal mol^-1 and 0.048 ± 0.04 kcal mol^-1. Although these show gains at post-CBS level that vary from 0.08 to 0.20 kcal mol^-1 relative to their CCSD(T)/VXZ analogues, the convergence is somewhat less clear when extending the basis up to V5Z-F12, the highest-rung available: 0.220 ± 0.17 kcal mol^-1 and 0.142 ± 0.08 kcal mol^-1, in the same order. An explanation for the up to one order of magnitude smaller deviations in energy differences is detailed. Based on energy differences involving basis set pairs employed for extrapolating to the CBS limit, a convergence diagnostic is also suggested. Arising from irregularities in the basis set that directly correlate with non-dynamical correlation, the new diagnostic may complement popular ones that feature other aspects of correlation.

Prototypical π-π dimers re-examined by means of high-level CCSDT(Q) composite ab initio methods

The benzene-ethene and parallel-displaced (PD) benzene-benzene dimers are the most fundamental systems involving π-π stacking interactions. Several high-level ab initio investigations calculated the binding energies of these dimers using the coupled-cluster with singles, doubles, and quasi-perturbative triple excitations [CCSD(T)] method at the complete basis set [CBS] limit using various approaches such as reduced virtual orbital spaces and/or MP2-based basis set corrections. Here, we obtain CCSDT(Q) binding energies using a Weizmann-3-type approach. In particular, we extrapolate the self-consistent field (SCF), CCSD, and (T) components using large heavy-atom augmented Gaussian basis sets [namely, SCF/jul-cc-pV{5,6}Z, CCSD/jul-cc-pV{Q,5}Z, and (T)/jul-cc-pV{T,Q}Z]. We consider post-CCSD(T) contributions up to CCSDT(Q), inner-shell, scalar-relativistic, and Born-Oppenheimer corrections. Overall, our best relativistic, all-electron CCSDT(Q) binding energies are ∆E_e,all,rel = 1.234 (benzene-ethene) and 2.550 (benzene-benzene PD), ∆H₀ = 0.949 (benzene-ethene) and 2.310 (benzene-benzene PD), and ∆H₂₉₈ = 0.130 (benzene-ethene) and 1.461 (benzene-benzene PD) kcal mol^-1. Important conclusions are reached regarding the basis set convergence of the SCF, CCSD, (T), and post-CCSD(T) components. Explicitly correlated calculations are used as a sanity check on the conventional binding energies. Overall, post-CCSD(T) contributions are destabilizing by 0.028 (benzene-ethene) and 0.058 (benzene-benzene) kcal mol^-1, and thus, they cannot be neglected if sub-chemical accuracy is sought (i.e., errors below 0.1 kcal mol^-1). CCSD(T)/aug-cc-pwCVTZ core-valence corrections increase the binding energies by 0.018 (benzene-ethene) and 0.027 (benzene-benzene PD) kcal mol^-1. Scalar-relativistic and diagonal Born-Oppenheimer corrections are negligibly small. We use our best CCSDT(Q) binding energies to evaluate the performance of MP2-based, CCSD-based, and lower-cost composite ab initio procedures for obtaining these challenging π-π stacking binding energies.

Efficient Density-Fitted Explicitly Correlated Dispersion and Exchange Dispersion Energies

The leading-order dispersion and exchange-dispersion terms in symmetry-adapted perturbation theory (SAPT), E_disp⁽²⁰⁾ and E_exch-disp⁽²⁰⁾, suffer from slow convergence to the complete basis set limit. To alleviate this problem, explicitly correlated variants of these corrections, E_disp⁽²⁰⁾-F12 and E_exch-disp⁽²⁰⁾-F12, have been proposed recently. However, the original formalism (M., Kodrycka , J. Chem. Theory Comput. 2019, 15, 5965-5986), while highly successful in terms of improving convergence, was not competitive to conventional orbital-based SAPT in terms of computational efficiency due to the need to manipulate several kinds of two-electron integrals. In this work, we eliminate this need by decomposing all types of two-electron integrals using robust density fitting. We demonstrate that the error of the density fitting approximation is negligible when standard auxiliary bases such as aug-cc-pVXZ/MP2FIT are employed. The new implementation allowed us to study all complexes in the A24 database in basis sets up to aug-cc-pV5Z, and the E_disp⁽²⁰⁾-F12 and E_exch-disp⁽²⁰⁾-F12 values exhibit vastly improved basis set convergence over their conventional counterparts. The well-converged E_disp⁽²⁰⁾-F12 and E_exch-disp⁽²⁰⁾-F12 numbers can be substituted for conventional E_disp⁽²⁰⁾ and E_exch-disp⁽²⁰⁾ ones in a calculation of the total SAPT interaction energy at any level (SAPT0, SAPT2+3, ...). We show that the addition of F12 terms does not improve the accuracy of low-level SAPT treatments. However, when the theory errors are minimized in high-level SAPT approaches such as SAPT2+3(CCD)δMP2, the reduction of basis set incompleteness errors thanks to the F12 treatment substantially improves the accuracy of small-basis calculations.

Scalable Electron Correlation Methods. 8. Explicitly Correlated Open-Shell Coupled-Cluster with Pair Natural Orbitals PNO-RCCSD(T)-F12 and PNO-UCCSD(T)-F12

We present explicitly correlated open-shell pair natural orbital local coupled-cluster methods, PNO-RCCSD(T)-F12 and PNO-UCCSD(T)-F12. The methods are extensions of our previously reported PNO-R/UCCSD methods (J. Chem. Theory Comput., 2020, 16, 3135-3151, https://pubs.acs.org/doi/10.1021/acs.jctc.0c00192) with additions of explicit correlation and perturbative triples corrections. The explicit correlation treatment follows the spin-orbital CCSD-F12b theory using Ansatz 3*A, which is found to yield comparable or better basis set convergence than the more rigorous Ansatz 3C in computed ionization potentials and reaction energies using double- to quaduple-ζ basis sets. The perturbative triples correction is adapted from the spin-orbital (T) theory to use triples natural orbitals (TNOs). To address the coupling due to off-diagonal Fock matrix elements, the local triples amplitudes are iteratively solved using small domains of TNOs, and a semicanonical (T0) domain correction with larger domains is applied to reduce the domain errors. The performance of the methods is demonstrated through benchmark calculations on ionization potentials, radical stabilization energies, reaction energies of fragmentations and rearrangements in radical cations, and spin-state energy differences of iron complexes. For a few test sets where canonical calculations are feasible, PNO-RCCSD(T)-F12 results agree with the canonical ones to within 0.4 kcal mol^-1, and this maximum error is reduced to below 0.2 kcal mol^-1 when large local domains are used. For larger systems, results using different thresholds for the local approximations are compared to demonstrate that 1 kcal mol^-1 level of accuracy can be achieved using our default settings. For a couple of difficult cases, it is demonstrated that the errors from individual approximations are only a fraction of 1 kcal mol^-1, and the overall accuracy of the method does not rely on error compensations. In contrast to canonical calculations, the use of spin-orbitals does not lead to a significant increase of computational time and memory usage in the most expensive steps of PNO-R/UCCSD(T)-F12 calculations. The only exception is the iterative solution of the (T) amplitudes, which can be avoided without significant errors by using a perturbative treatment of the off-diagonal coupling, known as (T1) approximation. For most systems, even the semicanonical approximation (T0) leads only to small errors in relative energies. Our program is well parallelized and capable of computing accurate correlation energies for molecules with 100-200 atoms using augmented triple-ζ basis sets in less than a day of elapsed time on a small computer cluster.

Canonical and explicitly-correlated coupled cluster correlation energies of sub-kJ mol-1 accuracy via cost-effective hybrid-post-CBS extrapolation

Cost-effectiveness and accuracy are two basic pillars in electronic structure calculations. While cost-effectiveness enhances applicability, high accuracy is sustained when employing advanced computational tools. With the gold standard method of ab initio quantum chemistry at the focal point, canonical CCSD(T) and modern explicitly correlated CCSD(T)-F12 calculations are employed hand in hand to develop accurate hybrid post-CBS extrapolation schemes, which are validated using popular training sets involving a total of 130 molecules. By using raw valence-only calculations at CCSD(T)/VDZ and CCSD(T)/VQZ-F12 levels of theory, the novel scheme leads to the prediction of absolute energies that differ on average (-0.170 ± 0.224) kcal mol-1 from the highest affordable CCSD(T)-F12b/V(Q,5)Z-F12 extrapolations, but only (-0.048 ± 0.228) kcal mol-1 from the post-CBS extrapolated values based on CBS(D,T), CBS(D,Q) and CBS(T,Q) energies. From the cost-effectiveness standpoint, the approach is a kind of pseudo one-point extrapolation scheme since its cost is basically that of the highest-rung raw energy where it is based. Variants that imply no additional cost are also discussed, emerging h-pCBS(dt,dq)ab as the most effective. The approach can also be used with PNO-based local correlation methods that gained popularity due to allowing coupled-cluster calculations even for large molecules at reduced computational cost, namely local PNO-CCSD(T) and PNO-CCSD(T)-F12b. To gauge the approach performance, both the hydrogen molecule and the O-C2H5 torsion path of ethyl-methyl-ether, an extra molecule here considered with presupposed existence in astrophysical objects, are also studied. Additionally, the nonbonding interactions in the A24 test set are revisited per se. The results show that the title approach may be useful in high-accuracy quantum chemistry, with further improvements requiring the inclusion of contributions beyond the theory here employed such as the ones due to relativistic and nonadiabatic effects.

Formulation of a Dressed Coupled-Cluster Method with Implicit Triple Excitations and Benchmark Application to Hydrogen-Bonded Systems

In this paper, we present a coupled-cluster theory based on a double-exponential wave operator ansatz, which is capable of mimicking the effects of connected triple excitations in an iterative manner. The triply excited manifold is spanned via the action of a set of scattering operators on doubly excited determinants, whereas their action annihilates the Hartree-Fock reference determinant. The effect of triple excitations is included at a computational scaling slightly higher than that of conventional coupled-cluster singles and doubles. Furthermore, we demonstrate two approximate schemes, which arise naturally, and argue that both these schemes come equipped with certain renormalization terms capable of handling nonbonding interactions due to robust inclusion of the screened Coulomb interaction. We justify our claims from both a theoretical perspective and a number of numerical applications to prototypical water clusters, in a number of basis functions. Our methods show overall comparable performance to the canonical coupled-cluster theory with singles, doubles, and perturbative triples (CCSD(T)) and allied methods, however, at a lower computational scaling.

Analysis of the Proton Transfer Bands in the Infrared Spectra of Linear N2H+···OC and N2D+···OC Complexes Using Electric Field-Driven Classical Trajectories

In this work, we describe ab initio calculations and assignment of infrared (IR) spectra of hydrogen-bonded ion-molecular complexes that involve a fluxional proton: the linear N₂H⁺···OC and N₂D⁺···OC complexes. Given the challenges of describing fluxional proton dynamics and especially its IR activity, we use electric field-driven classical trajectories, i.e., the driven molecular dynamics (DMD) method that was developed by us in recent years and for similar applications, in conjunction with high-level electronic structure theory. Namely, we present a modified and a numerically efficient implementation of DMD specifically for direct (or "on the fly") calculations, which we carry out at the MP2-F12/AVDZ level of theory for the potential energy surface (PES) and MP2/AVDZ for the dipole moment surfaces (DMSs). Detailed analysis of the PES, DMS, and the time-dependence of the first derivative of the DMS, referred to as the driving force, for the highly fluxional vibrations involving H⁺/D⁺ revealed that the strongly non-harmonic PES and non-linear DMS yield remarkably complex vibrational spectra. Interestingly, the classical trajectories reveal a doublet in the proton transfer part of the spectrum with the two peaks at 1800 and 1980 cm^-1. We find that their shared intensity is due to a Fermi-like resonance interaction, within the classical limit, of the H⁺ parallel stretch fundamental and an H⁺ perpendicular bending overtone. This doublet is also observed in the deuterated species at 1360 and 1460 cm^-1.

New theoretical insights into the reaction kinetics of toluene and hydroxyl radicals

This work provides theoretical insights into the kinetics of toluene + OH, focusing on the anharmonic effect and the accuracy of barrier heights.

Explicitly Correlated Dispersion and Exchange Dispersion Energies in Symmetry-Adapted Perturbation Theory

The individual interaction energy terms in symmetry-adapted perturbation theory (SAPT) not only have different physical interpretations but also converge to their complete basis set (CBS) limit values at quite different rates. Dispersion energy is notoriously the slowest converging interaction energy contribution, and exchange dispersion energy, while smaller in absolute value, converges just as poorly in relative terms. To speed up the basis set convergence of the lowest-order SAPT dispersion and exchange dispersion energies, we borrow the techniques from explicitly correlated (F12) electronic structure theory and develop practical expressions for the closed-shell E_disp⁽²⁰⁾-F12 and E_exch-disp⁽²⁰⁾-F12 contributions. While the latter term has been derived and implemented for the first time, the former correction was recently proposed by Przybytek [ J. Chem. Theory Comput. 2018 , 14 , 5105 - 5117 ] using an Ansatz with a full optimization of the explicitly correlated amplitudes. In addition to reimplementing the fully optimized variant of E_disp⁽²⁰⁾-F12, we propose three approximate Ansätze that substantially improve the scaling of the method and at the same time avoid the numerical instabilities of the unrestricted optimization. The performance of all four resulting flavors of E_disp⁽²⁰⁾-F12 and E_exch-disp⁽²⁰⁾-F12 is first tested on helium, neon, argon, water, and methane dimers, with orbital and auxiliary basis sets up to aug-cc-pV5Z and aug-cc-pV5Z-RI, respectively. The double- and triple-ζ basis set calculations are then extended to the entire A24 database of noncovalent interaction energies and compared with CBS estimates for E_disp⁽²⁰⁾ and E_exch-disp⁽²⁰⁾ computed using conventional SAPT with basis sets up to aug-cc-pV6Z with midbond functions. It is shown that the F12 treatment is highly successful in improving the basis set convergence of the SAPT terms, with the F12 calculations in an X-tuple ζ basis about as accurate as conventional calculations in bases with cardinal numbers (X + 2) for E_disp⁽²⁰⁾ and either (X + 1) or (X + 2) for E_exch-disp⁽²⁰⁾. While the full amplitude optimization affords the highest accuracy for both corrections, the much simpler and numerically stable optimized diagonal Ansatz is a very close second. We have also tested the performance of the simple F12 correction based on the second-order Møller-Plesset perturbation theory, SAPT-F12(MP2) [ Frey , J. A. ; Chem. Rev. 2016 , 116 , 5614 - 5641 ] and observed that it is also quite successful in speeding up the basis set convergence of conventional E_disp⁽²⁰⁾ + E_exch-disp⁽²⁰⁾, albeit with some outliers.

Theoretical study of the complexes of dichlorobenzene isomers with argon. I. Global potential energy surface for all the isomers with application to intermolecular vibrations

The complexes of para- (p-), meta- (m-), and ortho- (o-)dichlorobenzene (DCB) isomers with argon are studied using an ab initio method. The interaction energy in the ground electronic state of the complexes has been calculated using the CCSD(T) method (coupled cluster method including single and double excitations with perturbative triple excitations) and Dunning's double-ζ (aug-cc-pVDZ) basis set supplemented by midbond functions. Local interaction parameters have been defined and interesting relations fulfilled by them, independent of the DCB isomer, have been revealed. This finding has allowed us to construct the accurate global analytical intermolecular potential energy surface for all the DCB-Ar complexes with the same set of parameters, except for the monomer geometries. Each complex is characterized by two symmetrically equivalent global minima, one located above and the other located below the monomer plane at distances equal to 3.497 Å, 3.494 Å, and 3.485 Å for p-, m-, and o-isomers of DCB bound to Ar, respectively. Additionally, the Ar atom is shifted from the geometrical center of the DCB monomer towards the chlorine atoms by the value x_e of 0.182 Å for m-isomer and 0.458 Å for o-isomer. The calculated binding energy D_e of 460 cm^-1, 465 cm^-1, and 478 cm^-1 for p-, m-, and o-complex, respectively, are related to x_e by simple relations. The intermolecular bending fundamentals calculated from PES depend strongly on the isomer structure. The calculated dissociation energies fit in the intervals estimated by the experiment of Gaber et al. for the S₀ state [Phys. Chem. Chem. Phys. 11, 1628 (2009)].

Understanding non-covalent interactions in larger molecular complexes from first principles

Non-covalent interactions pervade all matter and play a fundamental role in layered materials, biological systems, and large molecular complexes. Despite this, our accumulated understanding of non-covalent interactions to date has been mainly developed in the tens-of-atoms molecular regime. This falls considerably short of the scales at which we would like to understand energy trends, structural properties, and temperature dependencies in materials where non-covalent interactions have an appreciable role. However, as more reference information is obtained beyond moderately sized molecular systems, our understanding is improving and we stand to gain pertinent insights by tackling more complex systems, such as supramolecular complexes, molecular crystals, and other soft materials. In addition, accurate reference information is needed to provide the drive for extending the predictive power of more efficient workhorse methods, such as density functional approximations that also approximate van der Waals dispersion interactions. In this perspective, we discuss the first-principles approaches that have been used to obtain reference interaction energies for beyond modestly sized molecular complexes. The methods include quantum Monte Carlo, symmetry-adapted perturbation theory, non-canonical coupled cluster theory, and approaches based on the random-phase approximation. By considering the approximations that underpin each method, the most accurate theoretical references for supramolecular complexes and molecular crystals to date are ascertained. With these, we also assess a handful of widely used exchange-correlation functionals in density functional theory. The discussion culminates in a framework for putting into perspective the accuracy of high-level wavefunction-based methods and identifying future challenges.

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.

Ionization of Ammonia Nanoices with Adsorbed Methanol Molecules

Large ammonia clusters represent a model system of ices that are omnipresent throughout the space. The interaction of ammonia ices with other hydrogen-boding molecules such as methanol or water and their behavior upon an ionization are thus relevant in the astrochemical context. In this study, ammonia clusters (NH₃) _N with the mean size N̅ ≈ 230 were prepared in molecular beams and passed through a pickup cell in which methanol molecules were adsorbed. At the highest exploited pickup pressures, the average composition of (NH₃) _N(CH₃OH) _M clusters was estimated to be N: M ≈ 210:10. On the other hand, the electron ionization of these clusters yielded about 75% of methanol-containing fragments (NH₃) _n(CH₃OH) _mH⁺ compared to 25% contribution of pure ammonia (NH₃) _nH⁺ ions. On the basis of this substantial disproportion, we propose the following ionization mechanism: The prevailing ammonia is ionized in most cases, resulting in NH₄⁺ core solvated most likely with four ammonia molecules, yielding the well-known "magic number" structure (NH₃)₄NH₄⁺. The methanol molecules exhibit a strong propensity for sticking to the fragment ion. We have also considered mechanisms of intracluster reactions. In most cases, proton transfer between ammonia units take place. The theoretical calculations suggested the proton transfer either from the methyl group or from the hydroxyl group of the ionized methanol molecule to ammonia to be the energetically open channels. However, the experiments with selectively deuterated methanols did not show any evidence for the D⁺ transfer from the CD₃ group. The proton transfer from the hydroxyl group could not be excluded entirely or confirmed unambiguously by the experiment.

The S66 Non-Covalent Interactions Benchmark Reconsidered Using Explicitly Correlated Methods Near the Basis Set Limit

The S66 benchmark for non-covalent interactions has been re-evaluated using explicitly correlated methods with basis sets near the one-particle basis set limit. It is found that post-MP2 ‘high-level corrections’ are treated adequately well using a combination of CCSD(F12*) with (aug-)cc-pVTZ-F12 basis sets on the one hand, and (T) extrapolated from conventional CCSD(T)/heavy-aug-cc-pV{D,T}Z on the other hand. Implications for earlier benchmarks on the larger S66×8 problem set in particular, and for accurate calculations on non-covalent interactions in general, are discussed. At a slight cost in accuracy, (T) can be considerably accelerated by using sano-V{D,T}Z+ basis sets, whereas half-counterpoise CCSD(F12*)(T)/cc-pVDZ-F12 offers the best compromise between accuracy and computational cost.

Crystalline packing in pentacene-like organic semiconductors

Combining Hirshfeld surface analysis with single molecule electrostatic property calculations allows rationalizing crystalline packing motifs of organic semiconductors.

Development of a Flexible-Monomer Two-Body Carbon Dioxide Potential and Its Application to Clusters up to (CO2 )13

A flexible-monomer two-body potential energy function was developed that approaches the high level CCSD(T)/CBS potential energy surface (PES) of carbon dioxide (CO₂ ) systems. This function was generated by fitting the electronic energies of unique CO₂ monomers and dimers to permutationally invariant polynomials. More than 200,000 CO₂ configurations were used to train the potential function. Comparisons of the PESs of six orientations of flexible CO₂ dimers were evaluated to demonstrate the accuracy of the potential. Furthermore, the potential function was used to determine the minimum energy structures of CO₂ clusters containing as many as 13 molecules. For isomers of (CO₂ )₃ , the potential demonstrated energetic agreement with the M06-2X functional and structural agreement of the B2PLYP-D functional at substantially reduced computational costs. A separate function, fit to MP2/aug-cc-pVDZ reference energies, was developed to directly compare the two-body potential to the ab initio MP2 level of theory. © 2017 Wiley Periodicals, Inc.

Interplay among Electrostatic, Dispersion, and Steric Interactions: Spectroscopy and Quantum Chemical Calculations of π-Hydrogen Bonded Complexes

π-Hydrogen bonding interactions are ubiquitous in both materials and biology. Despite their relatively weak nature, great progress has been made in their investigation by experimental and theoretical methods, but this becomes significantly more complicated when secondary intermolecular interactions are present. In this study, the effect of successive methyl substitution on the supramolecular structure and interaction energy of indole⋅⋅⋅methylated benzene (ind⋅⋅⋅n-mb, n=1-6) complexes is probed through a combination of supersonic jet experiments and benchmark-quality quantum chemical calculations. It is demonstrated that additional secondary interactions introduce a subtle interplay among electrostatic and dispersion forces, as well as steric repulsion, which fine-tunes the overall structural motif. Resonant two-photon ionization and IR-UV double-resonance spectroscopy techniques are used to probe jet-cooled ind⋅⋅⋅n-mb (n=2, 3, 6) complexes, with redshifting of the N-H IR stretching frequency showing that increasing the degree of methyl substitution increases the strength of the primary N-H⋅⋅⋅π interaction. Ab initio harmonic frequency and binding energy calculations confirm this trend for all six complexes. Electronic spectra of the three dimers are broad and structureless, with quantum chemical calculations revealing that this is likely to be due to multiple tilted conformations of each dimer possessing similar stabilization energies.

Nucleophilicity and electrophilicity of the C(sp3)–H bond: methane and ethane binary complexes with iodine

Cooperativity is key to the ability of saturated hydrocarbons to act both as nucleophilic and electrophilic centres.