Three-body interaction effects in heterolytic hydrogen splitting by frustrated Lewis pairs.

The reaction of heterolytic dihydrogen splitting by frustrated Lewis pairs P(R)3 and B(C6F5)3 (where R = t-butyl and 1-adamantene) is driven by strong three-body contributions which originate from the induction and charge transfer effects. The three-body effect increases dramatically as a function of inter-hydrogen distance. As predicted by the symmetry adapted perturbation theory, the "frustration" of Lewis pairs originates from the dual role of the exchange effects. First, the exchange manifests itself in the first-order Pauli repulsion by keeping the pairs away. Second, and equally important, the second-order exchange-induction almost completely cancels the effects of the second-order induction. This suppression of induction effects eases up upon the interaction of the frustrated pairs with H2. The activation of induction in this instance constitutes the three-body effect.

Reassessing the Role of σ Holes in Noncovalent Interactions: It is Pauli Repulsion that Counts.

A number of prototypical weak electron donor-electron acceptor complexes are investigated by the Symmetry Adapted Perturbation Theory, some of which belong to novel classes of weak bonds such as halogen and chalcogen bonds. Also included are complexes involving strong Lewis acids such as BeO and AuF. The common view in the literature is to associate these novel bonds with a variety of "holes", σ, π, δ, or positive areas in their electrostatic potential maps. The presumption is that these positive areas of the electrostatic potential are indicative of the electrostatic nature of these noncovalent bonds. The electrostatic view extends to the explanations of the directionality of approaches between the subsystems forming these bonds. This work demonstrates that one common feature of these electrostatic potential "holes" is the local depletion of electron density of which the best detector is the first-order Pauli repulsion. The minimization of this repulsion determines the bond directionality and its relative angular rigidity. In relatively strong complexes of BeO with rare gases, where BeO shows a clear cavity in electron density-an ultimate "σ hole"-the electrostatic effect does not control the bending potential-the exchange repulsion does. In halogen bonds, the halogen atom is nonspherical, displaying an axial "σ hole" in its electrostatic potential. However, in no examined case, from rare gas acting as an electron donor to a polar donor to an anionic donor, is the electrostatic energy responsible for the directionality of the halogen bond. In fact, it is not even maximized in the direction of the σ hole in N2-ClF and NH3-ClF. Yet, in all the cases, the exchange repulsion is minimized in the direction of the σ hole. The minimized exchange repulsion associated with the subtle and less subtle depletions of the electron density occur on the nodal planes or on the intersections thereof in the highest occupied molecular orbitals of Lewis acids, provided that the systems are closed-shell. The role of nodal planes in covalent and coordinate covalent bonds is well recognized. This work points to their similarly equal importance in certain types of donor-acceptor noncovalent interactions.

Assessment of SAPT(DFT) with meta-GGA functionals.

This work examines the suitability of meta-GGA functionals for symmetry-adapted perturbation theory (SAPT) calculations. The assessment is based on the term-by-term comparison with the benchmark SAPT variant based on coupled-cluster singles and doubles description of monomers, SAPT(CCSD). Testing systems include molecular complexes ranging from strong to weak and the He dimer. The following nonempirical meta-GGAs are examined: TPSS, revTPSS, MVS, SCAN, and SCAN0 with and without the asymptotic correction (AC) of the exchange-correlation potential. One range-separated meta-GGA functional, LC-PBETPSS, is also included. The AC-corrected pure meta-GGAs (with the exception of MVS) represent a definite progress in SAPT(DFT) compared to pure GGA, such as PBEAC, with their more consistent predictions of energy components. However, none of the meta-GGAs is better than the hybrid GGA approach SAPT(PBE0AC). The SAPT(DFT) electrostatic energy offers the most sensitive probe of the quality of the underlying DFT density. Both SCAN- and TPSS-based electrostatic energies agree with reference to within 5% or better which is an excellent result. We find that SCAN0 can be used in SAPT without the AC correction. The long-range corrected LC-PBETPSS is a reliable performer both for the components and total interaction energies.

How and Why Does Helium Permeate Nonporous Arsenolite Under High Pressure?

Investigations into the helium permeation of arsenolite, the cubic, molecular arsenic(III) oxide polymorph As4 O6 , were carried out to understand how and why arsenolite helium clathrate As4 O6 ⋅2 He is formed. High-pressure synchrotron X-ray diffraction experiments on arsenolite single crystals revealed that the permeation of helium into nonporous arsenolite depends on the time for which the crystal is subjected to high pressure and on the crystal history. The single crystal was totally transformed into As4 O6 ⋅2 He within 45 h under 5 GPa. After release of the pressure, arsenolite was recovered and a repeated increase in pressure up to 3 GPa led to practically instant As4 O6 ⋅2 He formation. However, when a pristine arsenolite single crystal was quickly subjected to a pressure of 13 GPa, no helium permeation was observed at all. No neon permeation was observed in analogous experiments. Quantum mechanical computations indicate that there are no specific attractive interactions between He atoms and As4 O6 molecules at the distances observed in the As4 O6 ⋅2 He crystal structure. Detailed analysis of As4 O6 molecular structure changes has shown that the introduction of He into the arsenolite crystal lattice significantly reduces molecular deformations by decreasing the anisotropy of stress exerted on the As4 O6 molecules. This effect and the pΔV term, rather than any specific As⋅⋅⋅He binding, are the driving forces for the formation As4 O6 ⋅2 He.

The nature of three-body interactions in DFT: Exchange and polarization effects.

We propose a physically motivated decomposition of density functional theory (DFT) 3-body nonadditive interaction energies into the exchange and density-deformation (polarization) components. The exchange component represents the effect of the Pauli exclusion in the wave function of the trimer and is found to be challenging for density functional approximations (DFAs). The remaining density-deformation nonadditivity is less dependent upon the DFAs. Numerical demonstration is carried out for rare gas atom trimers, Ar2-HX (X = F, Cl) complexes, and small hydrogen-bonded and van der Waals molecular systems. None of the tested semilocal, hybrid, and range-separated DFAs properly accounts for the nonadditive exchange in dispersion-bonded trimers. By contrast, for hydrogen-bonded systems, range-separated DFAs achieve a qualitative agreement to within 20% of the reference exchange energy. A reliable performance for all systems is obtained only when the monomers interact through the Hartree-Fock potential in the dispersion-free Pauli blockade scheme. Additionally, we identify the nonadditive second-order exchange-dispersion energy as an important but overlooked contribution in force-field-like dispersion corrections. Our results suggest that range-separated functionals do not include this component, although semilocal and global hybrid DFAs appear to imitate it in the short range.

Employing Range Separation on the meta-GGA Rung: New Functional Suitable for Both Covalent and Noncovalent Interactions.

We devise a scheme for converting an existing exchange functional into its range-separated hybrid variant. The underlying exchange hole of the Becke-Roussel type has the exact second-order expansion in the interelectron distance. The short-range part of the resulting range-separated exchange energy depends on the kinetic energy density and the Laplacian even if the base functional lacks the dependence on these variables. The most successful practical realization of the scheme, named LC-PBETPSS, combines the range-separated Perdew-Burke-Ernzerhof (PBE) exchange lifted to the hybrid meta-generalized gradient approximation rung and the Tao-Perdew-Staroverov-Scuseria (TPSS) correlation. The value of the range-separation parameter is estimated theoretically and confirmed by empirical optimization. The D3 dispersion correction is recommended for all energy computations employing the presented functional. Numerical tests show remarkably robust performance of the method for noncovalent interaction energies, barrier heights, main-group thermochemistry, and excitation energies.

Theoretical study of the buffer-gas cooling and trapping of CrH(X6Σ+) by 3He atoms.

We present a theoretical study of the Zeeman relaxation of the magnetically trappable lowest field seeking state of CrH(X6Σ+) in collisions with 3He. A two dimensional potential energy surface (PES) was calculated with the partially spin-restricted coupled cluster singles, doubles, and non-iterative triples [RCCSD(T)] method. The global minimum was found for the collinear He⋯Cr-H geometry with the well depth of 1143.84 cm-1 at Re = 4.15 a0. Since the RCCSD(T) calculations revealed a multireference character in the region of the global minimum, we performed additional calculations with the internally contracted multireference configuration interaction with the Davidson correction (ic-MRCISD+Q) method. The resulting PES is similar to the RCCSD(T) PES except for the region of the global minimum, where the well depth is 3032 cm-1 at Re = 3.8 a0. An insight into the character of the complex was gained by means of symmetry-adapted perturbation theory based on unrestricted Kohn-Sham description of the monomers. Close coupling calculations of the Zeeman relaxation show that although the ΔMJ=MJ'-MJ = -1 and -2 transitions are the dominant contributions to the collisional Zeeman relaxation, ΔMJ<-2 transitions cannot be neglected due to the large value of CrH spin-spin constant. The calculated elastic to inelastic cross section ratio is 1600 for the RCCSD(T) PES and 500 for the MRCISD+Q PES, while the estimate from the buffer-gas cooling and magnetic trapping experiment is 9000.

Noncovalent interactions determine the conformation of aurophilic complexes with 2-mercapto-4-methyl-5-thiazoleacetic acid ligands.

We report the synthesis of three gold(i) complexes [Au(H(2)-mmta)(2)]Cl·(3)H(2)O (1), Na(3)[Au(mmta)(2)]·6H(2)O (2) and Na(3)[Au(mmta)(2)]·10.5H(2)O (3) (H(2)-mmta = 2-mercapto-4-methyl-5-thiazoleacetic acid) in which the Au(i) centre is incorporated either in cationic or anionic units of the [Au(SR)(2)](+/-) type depending on the protonation state of the ligand. All structures were characterized by single crystal X-ray analysis and found to exhibit unsupported aurophilic interactions leading to the formation of dimeric [Au(2)(H(2)-mmta)(4)](2+) and [Au(2)(mmta)(4)](6-) species. By applying several ab initio interpretative techniques we examine the character of the intermolecular interactions stabilizing the eclipsed arrangement of the aurophilic dimers formed in 1-3.

Tuned range-separated hybrid functionals in the symmetry-adapted perturbation theory.

The aim of this study is to present a performance test of optimally tuned long-range corrected (LRC) functionals applied to the symmetry-adapted perturbation theory (SAPT). In the present variant, the second-order energy components are evaluated at the coupled level of theory. We demonstrate that the generalized Kohn-Sham (GKS) description of monomers with optimally tuned LRC functionals may be essential for the quality of SAPT interaction energy components. This is connected to the minimization of a many-electron self-interaction error and exemplified by two model systems: polyacetylenes of increasing length and stretching of He 3 (+). Next we provide a comparison of SAPT approaches based on Kohn-Sham and GKS description of the monomers. We show that LRC leads to results better or comparable with the hitherto prevailing asymptotically corrected functionals. Finally, we discuss the advantages and possible limitations of SAPT based on LRC functionals.

Density functional theory approach to gold-ligand interactions: separating true effects from artifacts.

Donor-acceptor interactions are notoriously difficult and unpredictable for conventional density functional theory (DFT) methodologies. This work presents a reliable computational treatment of gold-ligand interactions of the donor-acceptor type within DFT. These interactions require a proper account of the ionization potential of the electron donor and electron affinity of the electron acceptor. This is accomplished in the Generalized Kohn Sham framework that allows one to relate these properties to the frontier orbitals in DFT via the tuning of range-separated functionals. A donor and an acceptor typically require different tuning schemes. This poses a problem when the binding energies are calculated using the supermolecular method. A two-parameter tuning for the monomer properties ensures that a common functional, optimal for both the donor and the acceptor, is found. A reliable DFT approach for these interactions also takes into account the dispersion contribution. The approach is validated using the water dimer and the (HAuPH3)2 aurophilic complex. Binding energies are computed for Au4 interacting with the following ligands: SCN(-), benzenethiol, benzenethiolate anion, pyridine, and trimethylphosphine. The results agree for the right reasons with coupled-cluster reference values.

Range-Separated meta-GGA Functional Designed for Noncovalent Interactions.

The accuracy of applying density functional theory to noncovalent interactions is hindered by errors arising from low-density regions of interaction-induced change in the density gradient, error compensation between correlation and exchange functionals, and dispersion double counting. A new exchange-correlation functional designed for noncovalent interactions is proposed to address these problems. The functional consists of the range-separated PBEsol exchange considered in two variants, pure and hybrid, and the semilocal correlation functional of Modrzejewski et al. (J. Chem. Phys. 2012, 137, 204121) designed with the constraint satisfaction technique to smoothly connect with a dispersion term. Two variants of dispersion correction are appended to the correlation functional: the atom-atom pairwise additive DFT-D3 model and the density-dependent many-body dispersion with self-consistent screening (MBD-rsSCS). From these building blocks, a set of four functionals is created to systematically examine the role of pure versus hybrid exchange and the underlying models for dispersion. The new functional is extensively tested on benchmark sets with diverse nature and size. Truly outstanding performance is demonstrated for water clusters of varying size, ionic hydrogen bonds, and thermochemistry of isodesmic n-alkane fragmentation reactions. The merits of each component of the new functional are discussed.

Density-dependent onset of the long-range exchange: a key to donor-acceptor properties.

Quantum mechanical methods based on the density functional theory (DFT) offer a realistic possibility of first-principles design of organic donor-acceptor systems and engineered band gap materials. This promise is contingent upon the ability of DFT to predict one-particle states accurately. Unfortunately, approximate functionals fail to align the orbital energies with ionization potentials. We describe a new paradigm for achieving this alignment. In the proposed model, an average electron-exchange hole separation controls the onset of the orbital-dependent exchange in approximate range-separated functionals. The correct description of one-particle states is thus achieved without explicit electron removal or attachment. Extensive numerical tests show that the proposed method provides physically sound orbital gaps and leads to excellent predictions of charge-transfer excitations and other properties critically depending on the tail of the electron density.

First-principle interaction potentials for metastable He(3S) and Ne(3P) with closed-shell molecules: application to Penning-ionizing systems.

We present new interaction potential curves, calculated from first-principles, for the He((3)S, 1s(1)2s(1))···H2 and He((3)S)···Ar systems, relevant in recent Penning ionization experiments of Henson et al. [Science 338, 234 (2012)]. Two different approaches were applied: supermolecular using coupled cluster (CC) theory and perturbational within symmetry-adapted perturbation theory (SAPT). Both methods gave consistent results, and the potentials were used to study the elastic scattering and determine the positions of shape resonances for low kinetic energy (up to 1 meV). We found a good agreement with the experiment. In addition, we investigated two other dimers composed of metastable Ne ((3)P, 2p(5)3s(1)) and ground state He and Ar atoms. For the Ne((3)P)···He system, a good agreement between CC and SAPT approaches was obtained. The Ne((3)P)···Ar dimer was described only with SAPT, as CC gave divergent results. Ne* systems exhibit extremely small electronic orbital angular momentum anisotropy of the potentials. We attribute this effect to screening of an open 2p shell by a singly occupied 3s shell.

Theoretical studies of potential energy surface and bound states of the strongly bound He(1S)-BeO (1Σ+) complex.

We perform electronic structure calculations of the potential energy surface of the He···BeO((1)Σ(+)) complex. We use several different methods to characterize this unusual interaction. We apply coupled cluster singles, doubles, and noniterative triples [CCSD(T)] and the multireference configuration interaction [MRCI] levels of theory. The nature of the interaction is studied with symmetry-adapted perturbation theory (SAPT) based on DFT and CCSD description of the intramonomer electron densities. Our best estimate of the well depth is 1876.5 cm(-1) at the CCSD(T) level, while the dissociation energy, corrected for the zero-point energy, is equal to 1446.7 cm(-1). The global minimum is located for the collinear He···Be-O geometry at Re = 4.45a0. The rotational constant of the He-BeO complex in its ground state is 0.863 cm(-1). We also calculate bound states of the He···BeO complex for J = 0 and J = 1 (total angular momentum).

A first-principles-based correlation functional for harmonious connection of short-range correlation and long-range dispersion.

We present a physically motivated correlation functional belonging to the meta-generalized gradient approximation (meta-GGA) rung, which can be supplemented with long-range dispersion corrections without introducing double-counting of correlation contributions. The functional is derived by the method of constraint satisfaction, starting from an analytical expression for a real-space spin-resolved correlation hole. The model contains a position-dependent function that controls the range of the interelectronic correlations described by the semilocal functional. With minimal empiricism, this function may be adjusted so that the correlation model blends with a specific dispersion correction describing long-range contributions. For a preliminary assessment, our functional has been combined with an atom-pairwise dispersion correction and full Hartree-Fock (HF)-like exchange. Despite the HF-exchange approximation, its predictions compare favorably with reference interaction energies in an extensive set of non-covalently bound dimers.

Symmetry-adapted perturbation theory based on unrestricted Kohn-Sham orbitals for high-spin open-shell van der Waals complexes.

Two open-shell formulations of the symmetry-adapted perturbation theory are presented. They are based on the spin-unrestricted Kohn-Sham (SAPT(UKS)) and unrestricted Hartree-Fock (SAPT(UHF)) descriptions of the monomers, respectively. The key reason behind development of SAPT(UKS) is that it is more compatible with density functional theory (DFT) compared to the previous formulation of open-shell SAPT based on spin-restricted Kohn-Sham method of Zuchowski et al. [J. Chem. Phys. 129, 084101 (2008)]. The performance of SAPT(UKS) and SAPT(UHF) is tested for the following open-shell van der Waals complexes: He···NH, H(2)O···HO(2), He···OH, Ar···OH, Ar···NO. The results show an excellent agreement between SAPT(UKS) and SAPT(ROKS). Furthermore, for the first time SAPT based on DFT is shown to be suitable for the treatment of interactions involving Π-state radicals (He···OH, Ar···OH, Ar···NO). In the interactions of transition metal dimers ((3)Σ(u)(+))Au(2) and ((13)Σ(g)(+))Cr(2) we show that SAPT is incompatible with the use of effective core potentials. The interaction energies of both systems expressed instead as supermolecular UHF interaction plus dispersion from SAPT(UKS) result in reasonably accurate potential curves.

Optical absorption spectra of gold clusters Au(n) (n = 4, 6, 8,12, 20) from long-range corrected functionals with optimal tuning.

Absorption UV spectra of gold clusters Au(n) (n = 4, 6, 8, 12, 20) are investigated using the time-dependent density functional theory (TDDFT). The calculations employ several long-range corrected xc functionals: ωB97X, LC-ωPBEh, CAM-B3LYP∗ (where ∗ denotes a variant with corrected asymptote of CAM-B3LYP), and LC-ωPBE. The latter two are subject to first-principle tuning according to a prescription of Stein et al. [Phys. Rev. Lett. 105, 266802 (2010)] by varying the range separation parameter. TDDFT results are validated for Au(4) and Au(8) against the equation-of-motion coupled cluster singles and doubles results and the experiment. Both long-range correction and the inclusion of a fixed portion of the exact exchange in the short-range are essential for the proper description of the optical spectra of gold. The ωB97X functional performs well across all studied cluster sizes. LC-ωPBEh, with parameters recommended by Rohrdanz et al. [J. Chem. Phys. 130, 054112 (2009)], affords the best performance for clusters of n > 4. The optimally tuned CAM-B3LYP∗ features the range separation parameter of 0.33 for Au(4) and 0.25 for all the larger clusters. For LC-ωPBE the tuning procedure resulted in incorrect transition energies and oscillator strengths despite the fact that the optimized functional showed the accurate linear dependence on fractional electron numbers. Au(n) (n = 4, 6, 8) feature optical gaps above of 3 eV and Au(20) of ∼2.9 eV. In Au(12) this gap narrows to ∼2.1 eV. The calculated spectrum for Au(20) involves intensity being concentrated in only a few transitions with the absorption maximum at 3.5 eV. The intense 3.5 eV absorption is present in all cluster sizes of n > 4. The calculated HOMO-LUMO gaps for all cluster sizes are within 0.5 eV of the difference between the vertical ionization potential and electron affinity. The reasons for this and for the failure of conventional xc functionals for optical spectra of gold are discussed.

Dispersion-free component of non-covalent interaction via mutual polarization of fragment densities.

Comprehensive tests within a diverse set of noncovalently bonded systems are carried out to assess the performance of the recently-developed dispersion-free approach in the framework of density functional theory [L. Rajchel, P. Zuchowski, M. Szczesniak, and G. Chalasinski, Phys. Rev. Lett. 104, 163001 (2010)]. A numerical algorithm which cures the convergence problems of the previous implementation is presented.

Aurophilic Interactions from Wave Function, Symmetry-Adapted Perturbation Theory, and Rangehybrid Approaches.

The aurophilic interaction is examined in three model systems Au2((3)Σg(+)), (AuH)2, and (HAuPH3)2 which contain interactions of pairs of the Au centers in the oxidation state (I). Several methods are employed ranging from wave function theory-based (WFT) approaches to symmetry-adapted perturbation theory (SAPT) and range-separated hybrid (RSH) density functional theory (DFT) methods. The most promising and accurate approach consists of a combination of the DFT and WFT approaches in the RSH framework. In this combination the short-range DFT handles the slow convergence of the correlation cusp, whereas the long-range WFT is best suited for the long-range correlation. Of the three tested RSH DFT methods, the one which uses a short-range exchange functional based on the Ernzerhof-Perdew exchange hole model with a range-separation parameter of 0.4 bohr(-1) seems to be the best candidate for treatment of gold. In combination with the long-range coupled cluster singles, doubles, and noniterative triples [CCSD(T)] treatment it places the strength of aurophilic bonding in (HAuPH3)2 at 5.7 kcal/mol at R = 3.09 Å. This value is somewhat larger than our best purely WFT result based on CCSD(T), 4.95 kcal/mol (R = 3.1 Å), and considerably smaller than the Hartree-Fock+dispersion value of 7.4 kcal/mol (R = 2.9 Å). The 5.7 kcal/mol estimate fits reasonably well within the prediction of the empirical relationship proposed by Schwerdtfeger et al. (J. Am. Chem. Soc.1998, 120, 6587). A direct computation of dispersion energy, including exchange corrections, results in values of ca. -9 kcal/mol for Au2((3)Σg(+)) and (AuH)2 and -13 kcal/mol for (HAuPH3)2 at the distance of a typical aurophilic bond, R = 3.0 Å.

A density functional theory approach to noncovalent interactions via interacting monomer densities.

A recently proposed "DFT + dispersion" treatment (Rajchel et al., Phys. Rev. Lett., 2010, 104, 163001) is described in detail and illustrated by more examples. The formalism derives the dispersion-free density functional theory (DFT) interaction energy and combines it with the dispersion energy from separate DFT calculations. It consists of the self-consistent polarization of DFT monomers restrained by the exclusion principle via the Pauli blockade technique. Within the monomers a complete exchange-correlation potential should be used, but between them only the exact exchange operates. The application to a wide range of molecular complexes from rare-gas dimers to hydrogen-bonds to π-electron interactions shows good agreement with benchmark values.