Tractability gains in symmetry-adapted perturbation theory including coupled double excitations: CCD+ST(CCD) dispersion with natural orbital truncations

Competition between Hydrogen and Chalcogen Bonding in Homodimers of Chalcogen Hydrides (H2X)2, X = O, S, Se, Te

The structural and chemical bonding motifs manifested by the competition between hydrogen and chalcogen bonding in the homodimers of chalcogen hydrides (H2X)2, where X = O, S, Se, Te have been characterized using high-level electronic structure calculations and analysis of the electron density based on Quasi-atomic orbital (QUAO) and the Symmetry-adapted perturbation theory (SAPT) methods. The QUAO analysis clearly identifies a three-center interaction responsible for either hydrogen or chalcogen bonds: in the former, the σ-bond connecting the donor and hydrogen atom participating in the hydrogen bond interacts with the lone pair on the nucleophile acceptor via the hydrogen atom, while in the latter this same σ-bond interacts with the nucleophile lone pair via the donor chalcogen. The number of minimum energy structures increase dramatically from one for (H2O)2, three for (H2S)2, four for (H2Se)2, and finally six for (H2Te)2. The emergence of the chalcogen-bonded arrangements appears for (H2S)2 with their subsequent energetic stabilization over the hydrogen-bonded minima manifesting in (H2Se)2 and (H2Te)2. In particular, one of the (H2S)2 , two of the (H2Se)2, and three of the (H2Te)2 dimers are chalcogen bonded. Induction plays a small but important role in stabilizing hydrogen over chalcogen-bonded structures, while dispersion is more important for chalcogen bonds.

Carbonless DNA

Carbonless DNA was designed by replacing all carbon atoms in the standard DNA building blocks with boron and nitrogen, ensuring isoelectronicity. Electronic structure quantum chemistry methods (DFT(ωB97XD)/aug-cc-pVDZ) were employed to study both the individual building blocks and the larger carbon-free DNA fragments. The reliability of the results was validated by comparing selected structures and binding energies using more accurate methods such as MP2, CCSD, and SAPT2+3(CCD)δMP2. Carbonless analogs of DNA components, including cytosine, thymine, guanine, adenine, and deoxyribose, were investigated, showing strong resemblance to the carbon-based versions in terms of spatial structure, polarity, and molecular interaction capabilities. Complementary base pairs of the carbonless analogs exhibited a similar number and length of hydrogen bonds as those found in their carbon-containing counterparts, with binding energies for A-T and G-C analogs remaining comparable. Carbonless DNA fragments containing two and six base pairs were studied, revealing double-helix structures analogous to natural DNA. Structural parameters such as fragment size, hydrogen bond lengths, and rise per base pair were consistent with those observed in unmodified DNA. Docking simulations with a 12 base pair fragment and netropsin as a ligand indicated a slight shift in binding preference for the carbonless DNA through the minor groove, with an approximate 25% increase in binding affinity compared to natural DNA.

Beryllium as a Base: Complexes of Be(CO)3 with HX (X=F, Cl, Br, CN, NC, CCH, OH)

Beryllium chemistry is typically governed by its electron deficient character, but in some compounds it can act as a base. In order to understand better the unusual basicity of Be, we have systematically explored the complexes of one such compound, Be(CO)3, towards several hydrogen bond donors HX (X=F, Cl, Br, CN, NC, CCH, OH). For all complexes we find three different minima, two hydrogen bonded minima (to the Be or O atoms), and one weak beryllium bonded minimum. Further characterization of the interactions using a topological analysis of the electron density and Symmetry Adapted Perturbation Theory (SAPT) provide insight into the nature of these interactions. Overall these results highlight the capability of certain beryllium compounds to act as either a weak Lewis acid or, unconventionally, a Lewis base whose basicity towards hydrogen bonding is comparable to that of π systems.

Kohn-Sham fragment energy decomposition analysis

We introduce the concept of Kohn-Sham fragment localized molecular orbitals (KS-FLMOs), which are Kohn-Sham molecular orbitals (MOs) localized in specific fragments constituting a generic molecular system. In detail, we minimize the local electronic energies of various fragments, while maximizing the repulsion between them, resulting in the effective localization of the MOs. We use the developed KS-FLMOs to propose a novel energy decomposition analysis, which we name Kohn-Sham fragment energy decomposition analysis, which allows for rationalizing the main non-covalent interactions occurring in interacting systems both in vacuo and in solution, providing physical insights into non-covalent interactions. The method is validated against state-of-the-art energy decomposition analysis techniques and with high-level calculations.

Halogen Bond via an Electrophilic π-Hole on Halogen in Molecules: Does It Exist?

This study reveals a new non-covalent interaction called a π-hole halogen bond, which is directional and potentially non-linear compared to its sister analog (σ-hole halogen bond). A π-hole is shown here to be observed on the surface of halogen in halogenated molecules, which can be tempered to display the aptness to form a π-hole halogen bond with a series of electron density-rich sites (Lewis bases) hosted individually by 32 other partner molecules. The [MP2/aug-cc-pVTZ] level characteristics of the π-hole halogen bonds in 33 binary complexes obtained from the charge density approaches (quantum theory of intramolecular atoms, molecular electrostatic surface potential, independent gradient model (IGM-δginter)), intermolecular geometries and energies, and second-order hyperconjugative charge transfer analyses are discussed, which are similar to other non-covalent interactions. That a π-hole can be observed on halogen in halogenated molecules is substantiated by experimentally reported crystals documented in the Cambridge Crystal Structure Database. The importance of the π-hole halogen bond in the design and growth of chemical systems in synthetic chemistry, crystallography, and crystal engineering is yet to be fully explicated.

Insight into the Binding of Argon to Cyclic Water Clusters from Symmetry-Adapted Perturbation Theory

This work systematically examines the interactions between a single argon atom and the edges and faces of cyclic H2O clusters containing three-five water molecules (Ar(H2O)n=3-5). Full geometry optimizations and subsequent harmonic vibrational frequency computations were performed using MP2 with a triple-ζ correlation consistent basis set augmented with diffuse functions on the heavy atoms (cc-pVTZ for H and aug-cc-pVTZ for O and Ar; denoted as haTZ). Optimized structures and harmonic vibrational frequencies were also obtained with the two-body-many-body (2b:Mb) and three-body-many-body (3b:Mb) techniques; here, high-level CCSD(T) computations capture up through the two-body or three-body contributions from the many-body expansion, respectively, while less demanding MP2 computations recover all higher-order contributions. Five unique stationary points have been identified in which Ar binds to the cyclic water trimer, along with four for (H2O)4 and three for (H2O)5. To the best of our knowledge, eleven of these twelve structures have been characterized here for the first time. Ar consistently binds more strongly to the faces than the edges of the cyclic (H2O)n clusters, by as much as a factor of two. The 3b:Mb electronic energies computed with the haTZ basis set indicate that Ar binds to the faces of the water clusters by at least 3 kJ mol-1 and by nearly 6 kJ mol-1 for one Ar(H2O)5 complex. An analysis of the interaction energies for the different binding motifs based on symmetry-adapted perturbation theory (SAPT) indicates that dispersion interactions are primarily responsible for the observed trends. The binding of a single Ar atom to a face of these cyclic water clusters can induce perturbations to the harmonic vibrational frequencies on the order of 5 cm-1 for some hydrogen-bonded OH stretching frequencies.

Isomer Stability Dependence of Hydrogen-Bonded Benzoxazole Clusters on Solvent Molecules

The structures of hydrogen-bonded benzoxazole clusters with methanol and ammonia, BO-(CH₃OH)_n (n = 1-3) and BO-(NH₃)_n (n = 1, 2), in a supersonic jet have been investigated by measuring the S₁-S₀ electronic spectra and isomer-selected vibrational spectra with the aid of quantum chemical calculations. Similar to BO-(H₂O)₁, two isomers of BO-(NH₃)₁ were observed, which form two types of hydrogen bond networks starting from the CH bond at the 2-/7-position to the nitrogen atom of BO (C2HN/C7HN). The relative stability of these isomers strongly depends on solvent molecules. Natural bond orbital analysis reveals that the OH···N hydrogen bond is dominant in BO-(H₂O)₁ and that intermolecular interaction between the CH group and the nitrogen atom of ammonia, especially C2H···N, is significantly enhanced, resulting in a more stable C2HN isomer. Symmetry-adapted perturbation theory calculations indicate that the dispersion interaction between the methyl group of methanol and π electron cloud on the BO ring is responsible for the extreme stability of the C7HN of BO-(CH₃OH)₁. Furthermore, using time-dependent density functional theory calculations, the isomer tendency of the electronic transition shifts from the monomer origin is reproduced and it is proposed that the significant blue shift in C2HN is due to the shortened C2H bond length upon electronic excitation.

Origin of the Microsolvation Effect on the Central Barriers of SN2 Reactions

We have quantitatively analyzed the microsolvation effect on the central barriers of microsolvated bimolecular nucleophilic substitution (S_N2) reactions by means of a two-step energy decomposition procedure. According to the first energy decompositions, an obvious increase in the central barrier for a microsolvated S_N2 reaction against its unsolvated counterpart can be mainly ascribed to the fact that the interaction between the solute and the conjunct solvent becomes less attractive from the reactant complex to the transition state. On the basis of the second energy decompositions with symmetry-adapted perturbation theory, this less attractive interaction in the transition state is primarily due to the interplay of the changes in the electrostatic, exchange, and induction components. However, the contribution of the change for the dispersion component is relatively small. A distinct linear correlation has also been observed between the changes of the total interaction energies and those of the corresponding electrostatic components for the microsolvated S_N2 reactions studied in this work. Moreover, the two-step energy decomposition procedure employed in this work is expected to be extensively applied to the gas phase reactions mediated by molecules or clusters.

Conformational Landscape of the Hydrogen-Bonded 1-Phenyl-2,2,2-Trilfuoroethanol···1,4-Dioxane Complex: Dispersion Interactions and Conformational Conversion

A rotational spectrum of the hydrogen-bonded complex between 1-phenyl-2,2,2-trilfuoroethanol (PhTFE), a chiral fluoroalcohol, and 1,4-dioxane, a common solvent for organic reactions, was measured using a chirped pulse Fourier transform microwave spectrometer. Initial theoretical conformational searches were carried out using CREST, a recently developed conformational searching tool. Subsequent geometry optimization and harmonic frequency calculations at the B3LYP-D3(BJ)/def2-TZVP level of theory yielded nearly 30 binary conformers of which 13 are within an energy window of ∼5 kJ mol^-1. Interestingly, while the O-H···O hydrogen bond dominates the attractive binary interactions, the complex conformational landscape is mainly controlled by subtle dispersion interactions between the phenyl and 1,4-dioxane rings. Two sets of rotational transitions were assigned in the experimental spectrum and attributed to the two most stable conformers of PhTFE···1,4-dioxane. The quantum theory of atoms in molecules (QTAIM), noncovalent interactions (NCI), and symmetry-adapted perturbation theory (SAPT) analyses were employed in order to appreciate how the phenyl ring and O-H functional groups influence the intermolecular interaction and conformational distribution of the binary complex. The main PhTFE conformation within the complex, identified experimentally, is different from that of the isolated PhTFE monomer reported previously.

Radial Potential Energy Functions of Linear Halogen-Bonded Complexes YX···ClF (YX = FB, OC, SC, N2) and the Effects of Substituting X by Second-Row Analogues: Mulliken Inner and Outer Complexes

Energies of linear, halogen-bonded complexes in the isoelectronic series YX···ClF (YX = FB, OC, or N₂) are calculated at several levels of theory as a function of the intermolecular distance r(X···Cl) to yield radial potential energy functions. When YX = OC, a secondary minimum is observed corresponding to lengthened and shortened distances r(ClF) and r(CCl), respectively, relative to the primary minimum, suggesting a significant contribution from the Mulliken inner complex structure [O=C–Cl]⁺···F^–. A conventional weak, halogen-bond complex OC···ClF occurs at the primary minimum. For YX = FB, the primary minimum corresponds to the inner complex [F=B–Cl]⁺···F^–, while the outer complex FB···ClF is at the secondary minimum. The effects on the potential energy function of systematic substitution of Y and X by second-row congeners and of reversing the order of X and Y are also investigated. Symmetry-adapted perturbation theory and natural population analyses are applied to further understand the nature of the various halogen-bond interactions.

Isotope Effects on the Vaporization of Organic Compounds from an Aqueous Solution-Insight from Experiment and Computations

An isotope fractionation analysis of organic groundwater pollutants can assess the remediation at contaminated sites yet needs to consider physical processes as potentially confounding factors. This study explores the predictability of water–air partitioning isotope effects from experiments and computational predictions for benzene and trimethylamine (both H-bond acceptors) as well as chloroform (H-bond donor). A small, but significant, isotope fractionation of different direction and magnitude was measured with ε = −0.12‰ ± 0.07‰ (benzene), ε_C = 0.49‰ ± 0.23‰ (triethylamine), and ε_H = 1.79‰ ± 0.54‰ (chloroform) demonstrating that effects do not correlate with expected hydrogen-bond functionalities. Computations revealed that the overall isotope effect arises from contributions of different nature and extent: a weakening of intramolecular vibrations in the condensed phase plus additional vibrational modes from a complexation with surrounding water molecules. Subtle changes in benzene contrast with a stronger coupling between intra- and intermolecular modes in the chloroform–water system and a very local vibrational response with few atoms involved in a specific mode of triethylamine. An energy decomposition analysis revealed that each system was affected differently by electrostatics and dispersion, where dispersion was dominant for benzene and electrostatics dominated for chloroform and triethylamine. Interestingly, overall stabilization patterns in all studied systems originated from contributions of dispersion rather than other energy terms.

Symmetry-Adapted Perturbation Theory Based on Multiconfigurational Wave Function Description of Monomers

We present a formulation of the multiconfigurational (MC) wave function symmetry-adapted perturbation theory (SAPT). The method is applicable to noncovalent interactions between monomers which require a multiconfigurational description, in particular when the interacting system is strongly correlated or in an electronically excited state. SAPT(MC) is based on one- and two-particle reduced density matrices of the monomers and assumes the single-exchange approximation for the exchange energy contributions. Second-order terms are expressed through response properties from extended random phase approximation (ERPA). The dispersion components of SAPT(MC) have been introduced in our previous works [HapkaM.J. Chem. Theory Comput.2019, 15, 1016−102730525591; HapkaM.J. Chem. Theory Comput.2019, 15, 6712–672331670950]. SAPT(MC) is applied either with generalized valence bond perfect pairing (GVB) or with complete active space self-consistent field (CASSCF) treatment of the monomers. We discuss two model multireference systems: the H₂ ··· H₂ dimer in out-of-equilibrium geometries and interaction between the argon atom and excited state of ethylene. Using the C₂H₄* ··· Ar complex as an example, we examine second-order terms arising from negative transitions in the linear response function of an excited monomer. We demonstrate that the negative-transition terms must be accounted for to ensure qualitative prediction of induction and dispersion energies and develop a procedure allowing for their computation. Factors limiting the accuracy of SAPT(MC) are discussed in comparison with other second-order SAPT schemes on a data set of small single-reference dimers.

Blue Biotechnology: Computational Screening of Sarcophyton Cembranoid Diterpenes for SARS-CoV-2 Main Protease Inhibition

The coronavirus pandemic has affected more than 150 million people, while over 3.25 million people have died from the coronavirus disease 2019 (COVID-19). As there are no established therapies for COVID-19 treatment, drugs that inhibit viral replication are a promising target; specifically, the main protease (Mpro) that process CoV-encoded polyproteins serves as an Achilles heel for assembly of replication-transcription machinery as well as down-stream viral replication. In the search for potential antiviral drugs that target Mpro, a series of cembranoid diterpenes from the biologically active soft-coral genus Sarcophyton have been examined as SARS-CoV-2 Mpro inhibitors. Over 360 metabolites from the genus were screened using molecular docking calculations. Promising diterpenes were further characterized by molecular dynamics (MD) simulations based on molecular mechanics-generalized Born surface area (MM-GBSA) binding energy calculations. According to in silico calculations, five cembranoid diterpenes manifested adequate binding affinities as Mpro inhibitors with ΔGbinding < -33.0 kcal/mol. Binding energy and structural analyses of the most potent Sarcophyton inhibitor, bislatumlide A (340), was compared to darunavir, an HIV protease inhibitor that has been recently subjected to clinical-trial as an anti-COVID-19 drug. In silico analysis indicates that 340 has a higher binding affinity against Mpro than darunavir with ΔGbinding values of -43.8 and -34.8 kcal/mol, respectively throughout 100 ns MD simulations. Drug-likeness calculations revealed robust bioavailability and protein-protein interactions were identified for 340; biochemical signaling genes included ACE, MAPK14 and ESR1 as identified based on a STRING database. Pathway enrichment analysis combined with reactome mining revealed that 340 has the capability to re-modulate the p38 MAPK pathway hijacked by SARS-CoV-2 and antagonize injurious effects. These findings justify further in vivo and in vitro testing of 340 as an antiviral agent against SARS-CoV-2.

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.

Random-Phase Approximation in Many-Body Noncovalent Systems: Methane in a Dodecahedral Water Cage

The many-body expansion (MBE) of energies of molecular clusters or solids offers a way to detect and analyze errors of theoretical methods that could go unnoticed if only the total energy of the system was considered. In this regard, the interaction between the methane molecule and its enclosing dodecahedral water cage, CH₄···(H₂O)₂₀, is a stringent test for approximate methods, including density functional theory (DFT) approximations. Hybrid and semilocal DFT approximations behave erratically for this system, with three- and four-body nonadditive terms having neither the correct sign nor magnitude. Here, we analyze to what extent these qualitative errors in different MBE contributions are conveyed to post-Kohn-Sham random-phase approximation (RPA), which uses approximate Kohn-Sham orbitals as its input. The results reveal a correlation between the quality of the DFT input states and the RPA results. Moreover, the renormalized singles energy (RSE) corrections play a crucial role in all orders of the many-body expansion. For dimers, RSE corrects the RPA underbinding for every tested Kohn-Sham model: generalized-gradient approximation (GGA), meta-GGA, (meta-)GGA hybrids, as well as the optimized effective potential at the correlated level. Remarkably, the inclusion of singles in RPA can also correct the wrong signs of three- and four-body nonadditive energies as well as mitigate the excessive higher-order contributions to the many-body expansion. The RPA errors are dominated by the contributions of compact clusters. As a workable method for large systems, we propose to replace those compact contributions with CCSD(T) energies and to sum up the remaining many-body contributions up to infinity with supermolecular or periodic RPA. As a demonstration of this approach, we show that for RPA(PBE0)+RSE it suffices to apply CCSD(T) to dimers and 30 compact, hydrogen-bonded trimers to get the methane-water cage interaction energy to within 1.6% of the reference value.

Spectroscopy, lifetime, and charge-displacement of the methanol-noble gas complexes: An integrated experimental-theoretical investigation

An integrated experimental-theoretical investigation was employed to determine rovibrational energies, spectroscopic constants, lifetime as a function of temperature in gas phase complexes of methanol with noble gas (NgHe, Ne, Ar, Kr, Xe, and Rn). Beside that, a parallel effort has been addressed to theoretically characterize the nature of intermolecular interactions determining the dissociation energy and equilibrium distance of the formed adducts. Dynamics and lifetime results reveal that, except for the CH₃OH-He aggregate, all other methanol-Ng compounds are sufficiently stable under thermal conditions. Their lifetimes are larger than 1 ps for the temperature of the bulk in the range between 200 and 500 K. In addition, the current lifetime results suggest that the aggregates formed by methanol and Ng are globally more stable than corresponding complexes formed by water with Ng. From the point of view of the CCSD(T)/aug-cc-pVTZ level calculation, in all compounds, the electron densities of Ng partners are weakly polarized in the presence of CH₃OH molecule. The charge-displacement curves and NBO analysis indicate that the charge transfer from Ng to methanol molecule, in general, plays a minor role, being appreciable only in the aggregate involving Ar. Finally, it was verified from the SAPT2 + (CCD)-δMP2/aug-cc-pVTZ calculations and NCI analysis that the dispersion is the essential long-range attractive contribution to the interaction energy for all studied complexes. This feature strongly suggests that these compounds are held bonded substantially by van der Waals forces. Then non-covalent intermolecular bonds are effectively formed in the gas phase, which is disturbed by small stabilizing charge-transfer contributions.

Cospatial σ-Hole and Lone Pair Interactions of Square-Pyramidal Pentavalent Halogen Compounds with π-Systems: A Quantum Mechanical Study

In the spirit of the mounting interest in noncovalent interactions, the present study was conducted to scrutinize a special type that simultaneously involved both σ-hole and lone pair (lp) interactions with aromatic π-systems. Square-pyramidal pentavalent halogen-containing molecules, including X-Cl-F4, F-Y-F4, and F-I-X4 compounds (where X = F, Cl, Br, and I and Y = Cl, Br, and I) were employed as σ-hole/lp donors. On the other hand, benzene (BZN) and hexafluorobenzene (HFB) were chosen as electron-rich and electron-deficient aromatic π-systems, respectively. The investigation relied upon a variety of quantum chemical calculations that complement each other. The results showed that (i) the binding energy of the X-Y-F4···BZN complexes increased (i.e., more negative) as the Y atom had a larger magnitude of σ-hole, contrary to the pattern of X-Y-F4···HFB complexes; (ii) the interaction energies of X-Y-F4···BZN complexes were dominated by both dispersion and electrostatic contributions, while dispersive interactions dominated X-Y-F4···HFB complexes; and (iii) the X4 atoms in F-I-X4···π-system complexes governed the interaction energy pattern: the larger the X4 atoms were, the greater the interaction energies were, for the same π-system. The results had illuminating facets in regard to the rarely addressed cases of the σ-hole/lp contradictory scene.

Description of Chiral Complexes within Functional-Group Symmetry-Adapted Perturbation Theory-The Case of (S/R)-Carvone with Derivatives of (-)-Menthol

Symmetry-adapted perturbation theory (SAPT) and functional-group SAPT (F-SAPT) are applied to examine differences in interaction energies of diastereoisomeric complexes of two chiral molecules of natural origin: (S/R)-carvone with (-)-menthol. The study is extended by including derivatives of menthol with its hydroxy group exchanged by another functional group, thus examining the substituent effect of the interaction and the interaction differences between diastereoisomers. The partitioning of the interaction energy into functional-group components allows one to explain this phenomenon by the mutual cancellation of attractive and repulsive interactions between functional groups. In some cases, one can identify dominant chiral interactions between groups of atoms of carvone and menthol derivatives, while in many other instances, no major interaction can be distinguished and the net chiral difference results from subtle near cancellation of several smaller terms. Our results indicate that the F-SAPT method can be faithfully utilized for such analyses.

σ-Hole and Lone-Pair Hole Interactions in Chalcogen-Containing Complexes: A Comparative Study

The potentiality of sp3-hybridized chalcogen-containing molecules to participate in lone-pair (lp) hole interactions was reported for the first time. lp hole interactions were characterized and compared to σ-hole ones for OF2 and SF2 molecules as a case study. Various quantum mechanical calculations, including molecular electrostatic potential (MEP), maximum positive electrostatic potential (V s,max), point of charge (PoC), symmetry-adapted perturbation theory (SAPT), quantum theory of atoms in molecule (QTAIM), and reduced density gradient-noncovalent interaction (RDG-NCI) calculations, were carried out. The more significant findings to emerge from this study are the following: (i) the V s,max calculation was proved to be an unreliable method to determine the precise σ-hole and lp hole locations. (ii) The maximum positive electrostatic potential of the σ hole and lp hole was found to be at the F-Chal···PoC angle (θ) of 180° and at the centroid of XYlp plane, respectively. (iii) Lewis basicity has a significant effect on the strength of σ-hole and lp hole interactions. (iv) The studied molecules more favorably interact with Lewis bases via the σ hole compared to the lp hole, and (v) stabilization of the σ-hole and lp hole interactions stems from the electrostatic and dispersion forces, respectively.

The challenge of non-covalent interactions: theory meets experiment for reconciling accuracy and interpretation

In the past decade, many gas-phase spectroscopic investigations have focused on the understanding of the nature of weak interactions in model systems. Despite the fact that non-covalent interactions play a key role in several biological and technological processes, their characterization and interpretation are still far from being satisfactory. In this connection, integrated experimental and computational investigations can play an invaluable role. Indeed, a number of different issues relevant to unraveling the properties of bulk or solvated systems can be addressed from experimental investigations on molecular complexes. Focusing on the interaction of biological model systems with solvent molecules (e.g., water), since the hydration of the biomolecules controls their structure and mechanism of action, the study of the molecular properties of hydrated systems containing a limited number of water molecules (microsolvation) is the basis for understanding the solvation process and how structure and reactivity vary from gas phase to solution. Although hydrogen bonding is probably the most widespread interaction in nature, other emerging classes, such as halogen, chalcogen and pnicogen interactions, have attracted much attention because of the role they play in different fields. Their understanding requires, first of all, the characterization of the directionality, strength, and nature of such interactions as well as a comprehensive analysis of their competition with other non-covalent bonds. In this review, it is shown how state-of-the-art quantum-chemical computations combined with rotational spectroscopy allow for fully characterizing intermolecular interactions taking place in molecular complexes from both structural and energetic points of view. The transition from bi-molecular complex to microsolvation and then to condensed phase is shortly addressed.

Psi4 1.4: Open-source software for high-throughput quantum chemistry

PSI4 is a free and open-source ab initio electronic structure program providing implementations of Hartree-Fock, density functional theory, many-body perturbation theory, configuration interaction, density cumulant theory, symmetry-adapted perturbation theory, and coupled-cluster theory. Most of the methods are quite efficient, thanks to density fitting and multi-core parallelism. The program is a hybrid of C++ and Python, and calculations may be run with very simple text files or using the Python API, facilitating post-processing and complex workflows; method developers also have access to most of PSI4's core functionalities via Python. Job specification may be passed using The Molecular Sciences Software Institute (MolSSI) QCSCHEMA data format, facilitating interoperability. A rewrite of our top-level computation driver, and concomitant adoption of the MolSSI QCARCHIVE INFRASTRUCTURE project, makes the latest version of PSI4 well suited to distributed computation of large numbers of independent tasks. The project has fostered the development of independent software components that may be reused in other quantum chemistry programs.

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.

Quantifying how step-wise fluorination tunes local solute hydrophobicity, hydration shell thermodynamics and the quantum mechanical contributions of solute–water interactions

Locally tuning solute–water interactions with fluorination.

Symmetry-Adapted Perturbation Theory Decomposition of the Reaction Force: Insights into Substituent Effects Involved in Hemiacetal Formation Mechanisms

The decomposition of the reaction force based on symmetry-adapted perturbation theory (SAPT) has been proposed. This approach was used to investigate the substituent effects along the reaction coordinate pathway for the hemiacetal formation mechanism between methanol and substituted aldehydes of the form CX₃CHO (X = H, F, Cl, and Br), providing a quantitative evaluation of the reaction-driving and reaction-retarding force components. Our results highlight the importance of more favorable electrostatic and induction effects in the reactions involving halogenated aldehydes that leads to lower activation energy barriers. These substituent effects are further elucidated by applying the functional-group partition of symmetry-adapted perturbation theory (F-SAPT). The results show that the reaction is largely driven by favorable direct noncovalent interactions between the CX₃ group on the aldehyde and the OH group on methanol.

Physical nature of silane⋯carbene dimers revealed by state-of-the-art ab initio calculations

Using the SAPT2 + 3(CCD)δMP2 method in complete basis set (CBS) limit, it is shown that the interactions in the recently studied silane⋯carbene dimers are mainly dispersive in nature. Consequently, slow convergence of dispersion energy also forces slow convergence of the interaction energy. Therefore, obtaining very accurate values requires extrapolation of the correlation part to the CBS limit. The most accurate values obtained at the CCSD(T)/CBS level of theory show that the studied silane⋯carbene dimers are rather weakly bound, with interaction energies ranging from about -1.9 to -1.3 kcal/mol. Comparing to CCSD(T)/CBS, it will be shown that SCS-MP2 and MP2C methods clearly underestimate and methods based on SAPT2+ and having some third-order corrections, as well as the MP2 method, overestimate values of interaction energies. Popular SAPT(DFT) method performs better than SCS-MP2 and MP2C; nevertheless, underestimation is still considerable. The underestimation is slightly quenched if third-order dispersion energy and its exchange counterpart is added to the SAPT(DFT). The closest value of CCSD(T)/CBS has been given by the SAPT2 + (3)(CCD)δMP2 method in quadruple-ζ basis set. © 2019 Wiley Periodicals, Inc.

ZMP-SAPT: DFT-SAPT using ab initio densities

Symmetry Adapted Perturbation Theory (SAPT) has become an important tool when predicting and analyzing intermolecular interactions. Unfortunately, Density Functional Theory (DFT)-SAPT, which uses DFT for the underlying monomers, has some arbitrariness concerning the exchange-correlation potential and the exchange-correlation kernel involved. By using ab initio Brueckner Doubles densities and constructing Kohn-Sham orbitals via the Zhao-Morrison-Parr (ZMP) method, we are able to lift the dependence of DFT-SAPT on DFT exchange-correlation potential models in first order. This way, we can compute the monomers at the coupled-cluster level of theory and utilize SAPT for the intermolecular interaction energy. The resulting ZMP-SAPT approach is tested for small dimer systems involving rare gas atoms, cations, and anions and shown to compare well with the Tang-Toennies model and coupled cluster results.

Second-Order Dispersion Energy Based on Multireference Description of Monomers

We propose a method for calculating a second-order dispersion energy for weakly interacting multireference systems in arbitrary electronic states. It is based on response properties obtained from extended random phase approximation equations. The introduced formalism is general and requires only one- and two-particle reduced density matrices of monomers. We combine the new method with either generalized valence bond perfect pairing (GVB) or complete active space (CAS) self-consistent field description of the interacting systems. In addition to a general scheme, three approximations, leading to significant reduction of the computational cost, are developed by exploiting Dyall partitioning of the monomer Hamiltonians. For model multireference systems (H₂···H₂ and Be···Be) the method is accurate, unlike its single-reference-based counterpart. Neither GVB nor CAS description of single-reference monomers improves the dispersion energy with respect to the Hartree-Fock-based results.

Dissociation Energy of the H2O···HF Dimer

Even though (H₂O)₂ and (HF)₂ are arguably the most thoroughly characterized prototypes for hydrogen bonding, their heterogeneous analogue H₂O···HF has received relatively little attention. Here we report that the experimental dissociation energy ( D₀) of this important paradigm for heterogeneous hydrogen bonding is too large by 2 kcal mol^-1 or 30% relative to our computed value of 6.3 kcal mol^-1. For reference, computational procedures similar to those employed here to compute D₀ (large basis set CCSD(T) computations with anharmonic corrections from second-order vibrational perturbation theory) provide results within 0.1 kcal mol^-1 of the experimental values for (H₂O)₂ and (HF)₂. Near the CCSD(T) complete basis set limit, the electronic dissociation energy for H₂O···HF is ∼4 kcal mol^-1 larger than those for (H₂O)₂ and (HF)₂ (∼9 kcal mol^-1 for the heterogeneous dimer vs ∼5 kcal mol^-1 for the homogeneous dimers). Results reported here from symmetry-adapted perturbation theory computations suggest that this large difference is primarily due to the induction contribution to the interaction energy.

Psi4 1.1: An Open-Source Electronic Structure Program Emphasizing Automation, Advanced Libraries, and Interoperability

Psi4 is an ab initio electronic structure program providing methods such as Hartree-Fock, density functional theory, configuration interaction, and coupled-cluster theory. The 1.1 release represents a major update meant to automate complex tasks, such as geometry optimization using complete-basis-set extrapolation or focal-point methods. Conversion of the top-level code to a Python module means that Psi4 can now be used in complex workflows alongside other Python tools. Several new features have been added with the aid of libraries providing easy access to techniques such as density fitting, Cholesky decomposition, and Laplace denominators. The build system has been completely rewritten to simplify interoperability with independent, reusable software components for quantum chemistry. Finally, a wide range of new theoretical methods and analyses have been added to the code base, including functional-group and open-shell symmetry adapted perturbation theory, density-fitted coupled cluster with frozen natural orbitals, orbital-optimized perturbation and coupled-cluster methods (e.g., OO-MP2 and OO-LCCD), density-fitted multiconfigurational self-consistent field, density cumulant functional theory, algebraic-diagrammatic construction excited states, improvements to the geometry optimizer, and the "X2C" approach to relativistic corrections, among many other improvements.

Spatial assignment of symmetry adapted perturbation theory interaction energy components: The atomic SAPT partition

We develop a physically-motivated assignment of symmetry adapted perturbation theory for intermolecular interactions (SAPT) into atom-pairwise contributions (the A-SAPT partition). The basic precept of A-SAPT is that the many-body interaction energy components are computed normally under the formalism of SAPT, following which a spatially-localized two-body quasiparticle interaction is extracted from the many-body interaction terms. For electrostatics and induction source terms, the relevant quasiparticles are atoms, which are obtained in this work through the iterative stockholder analysis (ISA) procedure. For the exchange, induction response, and dispersion terms, the relevant quasiparticles are local occupied orbitals, which are obtained in this work through the Pipek-Mezey procedure. The local orbital atomic charges obtained from ISA additionally allow the terms involving local orbitals to be assigned in an atom-pairwise manner. Further summation over the atoms of one or the other monomer allows for a chemically intuitive visualization of the contribution of each atom and interaction component to the overall noncovalent interaction strength. Herein, we present the intuitive development and mathematical form for A-SAPT applied in the SAPT0 approximation (the A-SAPT0 partition). We also provide an efficient series of algorithms for the computation of the A-SAPT0 partition with essentially the same computational cost as the corresponding SAPT0 decomposition. We probe the sensitivity of the A-SAPT0 partition to the ISA grid and convergence parameter, orbital localization metric, and induction coupling treatment, and recommend a set of practical choices which closes the definition of the A-SAPT0 partition. We demonstrate the utility and computational tractability of the A-SAPT0 partition in the context of side-on cation-π interactions and the intercalation of DNA by proflavine. A-SAPT0 clearly shows the key processes in these complicated noncovalent interactions, in systems with up to 220 atoms and 2845 basis functions.

Accurate description of intermolecular interactions involving ions using symmetry-adapted perturbation theory

Three new data sets for intermolecular interactions, AHB21 for anion-neutral dimers, CHB6 for cation-neutral dimers, and IL16 for ion pairs, are assembled here, with complete-basis CCSD(T) results for each. These benchmarks are then used to evaluate the accuracy of the single-exchange approximation that is used for exchange energies in symmetry-adapted perturbation theory (SAPT), and the accuracy of SAPT based on wave function and density-functional descriptions of the monomers is evaluated. High-level SAPT calculations afford poor results for these data sets, and this includes the recently proposed "gold", "silver", and "bronze standards" of SAPT, namely, SAPT2+(3)-δMP2/aug-cc-pVTZ, SAPT2+/aug-cc-pVDZ, and sSAPT0/jun-cc-pVDZ, respectively [ Parker , T. M. , et al. , J. Chem. Phys. 2014 , 140 , 094106 ]. Especially poor results are obtained for symmetric shared-proton systems of the form X(-)···H(+)···X(-), for X = F, Cl, or OH. For the anionic data set, the SAPT2+(CCD)-δMP2/aug-cc-pVTZ method exhibits the best performance, with a mean absolute error (MAE) of 0.3 kcal/mol and a maximum error of 0.7 kcal/mol. For the cationic data set, the highest-level SAPT method, SAPT2+3-δMP2/aug-cc-pVQZ, outperforms the rest of the SAPT methods, with a MAE of 0.2 kcal/mol and a maximum error of 0.4 kcal/mol. For the ion-pair data set, the SAPT2+3-δMP2/aug-cc-pVTZ performs the best among all SAPT methods with a MAE of 0.3 kcal/mol and a maximum error of 0.9 kcal/mol. Overall, SAPT2+3-δMP2/aug-cc-pVTZ affords a small and balanced MAE (<0.5 kcal/mol) for all three data sets, with an overall MAE of 0.4 kcal/mol. Despite the breakdown of perturbation theory for ionic systems at short-range, SAPT can still be saved given two corrections: a "δHF" correction, which requires a supermolecular Hartree-Fock calculation to incorporate polarization effects beyond second order, and a "δMP2" correction, which requires a supermolecular MP2 calculation to account for higher-order induction-dispersion coupling. These corrections serve to remove artifacts introduced by the single exchange approximation in the exchange-induction and exchange-dispersion interactions, and obviate the need for ad hoc scaling of the first- and second-order exchange energies. Finally, some density-functional and MP2-based electronic structure methods are assessed as well, and we find that the best density-functional method for computing binding energies in these data sets is B97M-V/aug-cc-pVTZ, which affords a MAE of 0.4 kcal/mol, whereas complete-basis MP2 affords an MAE of 0.3 kcal/mol.

Levels of symmetry adapted perturbation theory (SAPT). I. Efficiency and performance for interaction energies

A systematic examination of the computational expense and accuracy of Symmetry-Adapted Perturbation Theory (SAPT) for the prediction of non-covalent interaction energies is provided with respect to both method [SAPT0, DFT-SAPT, SAPT2, SAPT2+, SAPT2+(3), and SAPT2+3; with and without CCD dispersion for the last three] and basis set [Dunning cc-pVDZ through aug-cc-pV5Z wherever computationally tractable, including truncations of diffuse basis functions]. To improve accuracy for hydrogen-bonded systems, we also include two corrections based on exchange-scaling (sSAPT0) and the supermolecular MP2 interaction energy (δMP2). When considering the best error performance relative to computational effort, we recommend as the gold, silver, and bronze standard of SAPT: SAPT2+(3)δMP2/aug-cc-pVTZ, SAPT2+/aug-cc-pVDZ, and sSAPT0/jun-cc-pVDZ. Their respective mean absolute errors in interaction energy across the S22, HBC6, NBC10, and HSG databases are 0.15 (62.9), 0.30 (4.4), and 0.49 kcal mol(-1) (0.03 h for adenine·thymine complex).