The insights from computational chemistry into noncovalently interacting systems go far beyond a single number that is the interaction energy. Quantum chemistry methods that provide a decomposition of this number in terms of both physical modes of interaction (such as electrostatics and dispersion) and specific molecular fragments provide a wealth of useful data for understanding and rationally designing weakly bound complexes. Symmetry-adapted perturbation theory (SAPT) is a well-grounded and robust approach that can provide such a dual interaction energy decomposition. This review describes novel variants of SAPT that can elucidate noncovalent interactions involving fragments on different molecules, fragments on the same molecule, complexes embedded in an environment, and complexes of three or more interacting subsystems.

In symmetry-adapted perturbation theory (SAPT), the exchange corrections are often calculated utilizing the so-called single-exchange or S2 approximation, that is, by approximating the antisymmetrizer of the whole system by permutations of a single pair of electrons between weakly interacting subsystems. The error introduced in this approximation is typically tolerable; however, it is the reason for qualitatively wrong results of selected S2 SAPT corrections for some ionic systems. This work presents the third-order exchange-induction-dispersion correction (Eexch-ind-disp(30)) of SAPT, describing the quenching of the mixed induction-dispersion attractive energy by intermolecular exchange tunneling, derived without the single-exchange approximation in the second-quantization formalism. To obtain the explicit orbital expression for the Eexch-ind-disp(30) energy, the approach that was developed earlier by two of us [B. Tyrcha, F. Brzęk, and P. S. Żuchowski, J. Chem. Phys. 160, 044118 (2024)] was extended to the third order of SAPT. The quality of the S2 approximation to all available second- and third-order exchange corrections (including the newly developed Eexch-ind-disp(30) energy) has been studied on a selection of benchmark noncovalent interaction databases, including some ionic datasets.

The induction part of intermolecular interaction energy describes the effect of the mutual polarization of subsystems. Low-order induction effects can be reasonably described by symmetry-adapted perturbation theory (SAPT), but the capture of important higher-order polarization effects requires the use of an external correction from supermolecular Hartree-Fock (HF) theory, which is not free from artifacts. When one describes induction through a response to an embedding potential representing the other molecule(s) (which is the case in a number of existing approaches such as the electrostatic embedding, Hartree-Hartree-Fock, and explicit polarization methods), it is easy to succumb to overpolarization unless the embedding potential fully accounts for the exchange effects, enforcing the Pauli exclusion principle and preventing a variational collapse to a Pauli-forbidden state. Here, we propose a new embedding framework that accounts for both electrostatic polarization and exchange effects in many-body systems. As a proof of principle, we apply the novel embedding potentials in a variational approach called symmetry-adapted relaxation theory (SART) that succeeds in recovering infinite-order induction energy from the HF method without a need to compute the HF wave function or energy of the entire complex. SART is expected to be the foundation for a new class of intermolecular perturbation theories, while the newly proposed potentials can also be applied to incorporate complete exchange into various embedding algorithms.

Although the collision-induced absorption spectrum of the nitrogen gas is known in considerable detail, little has been learned experimentally about the structural, dynamical, and rovibrational characteristics of the nitrogen dimer itself. This study explores all these properties of this prototypical van der Waals (vdW) dimer and provides definitive quantum chemical results, mostly with attached conservative uncertainty estimates, particularly for the parent isotopologue, 14N2⋅14N2. The results obtained are based on three analytical representations of the dimer’s ground-state potential energy surface (PES), including two full-dimensional models of spectroscopic accuracy, constructed during the present study. The structural and focal-point analyses confirm that the global minimum of (N2)2 is planar and has a tilted, Z-shaped form, with an electronic dissociation energy of 109.3(26) cm−1. After considering zero-point vibrational effects variationally, the first dissociation limit of 14N2⋅14N2 is estimated to be 72.2(15) cm−1. The full- and reduced-dimensional variational nuclear-motion computations performed result in almost 6000 bound rovibrational states for 14N2⋅14N2, including over 100 purely vibrational modes. Effects arising from isotopic substitutions, as well as the shifts and splittings of the two quasi-bound N ≡ N stretch fundamentals, are also examined. An in-depth analysis of the rovibrational eigenstates indicates that N2⋅N2 is a quasistructural molecular complex. Although the collision-induced absorption spectrum of molecular nitrogen has been studied in detail, rovibrational dynamics studies of the dimer remain scarce at best. Here, the authors report on the structure, rovibrational energy levels and nuclear dynamics of N2⋅N2, using newly developed 4D and 6D potential energy surfaces, resulting in a large number of bound rovibrational states and accurate shift and splitting values for the intramonomer (quasi-bound) stretch fundamentals.

We construct a new noncovalent benchmark dataset 3BXB that combines halogen-bonded bimolecular complexes from the SH250 dataset [K. Kříž and J. Řezáč, Phys. Chem. Chem. Phys., 2022, 24, 14794-14804] with a third interacting partner, either H2O or CH4. The reference total and three-body interaction energies are computed at the CCSD(T) level. To shed light on the physical origins of binding and cooperativity in complexes of this kind, several symmetry-adapted perturbation theory (SAPT)-based energy decompositions were performed for both pairwise additive and nonadditive terms. We found that the two-body attractions in the 3BXB complexes are dominated by either electrostatics or dispersion, while the three-body effect is dominated by induction and can be either attractive or repulsive. An accurate recovery of reference interaction energies is attained by the wavefunction-based two-body SAPT variants including the δMP2 correction, combined with the SAPT(DFT) estimates of nonadditive induction and first-order exchange and any estimate of nonadditive dispersion. The values for the latter term are sometimes quite inconsistent between different approaches; fortunately, nonadditive dispersion is a relatively minor effect for complexes studied here, and all reasonable estimates lead to total interaction energies of similar accuracy.

We present a comprehensive quantum mechanical study of stereodynamic control of HD + He and D2 + He collisions that have been probed experimentally by Perreault et al. [J. Phys. Chem. Lett. 13, 10912 (2022)] using Stark-induced adiabatic Raman passage (SARP) techniques. Our calculations utilize a highly accurate full-dimensional H2 + He interaction potential with diagonal Born–Oppenheimer correction appropriate for HD and D2 isotopomers. The results show that rotational quenching of HD from j = 2 → j′ = 0 in v = 2, j = 2 → j′ = 1 in v = 2 and v = 4, and j = 4 → j′ = 3 in v = 4 is dominated by an l = 1 shape resonance located between 0.1 and 1.0 cm−1. For collision energies less than 0.1 cm−1, isotropic scattering prevails. An l = 1 resonance centered around 0.02 cm−1 is also found to dominate the j = 2 → j′ = 0 and j = 4 → j′ = 2 transitions in v = 4 for He–D2 collisions consistent with our prior studies of Δj = −2 transition in He + D2(v = 2, j = 2) collisions. Our analysis does not support the hypothesis of Perreault et al. [J. Phys. Chem. Lett. 13, 10912 (2022)] that a strong l = 2 resonance controls the angular distribution for Δj = −2 transition for both systems. Despite improvements in the development of the potential energy surface, a good agreement with SARP experiments for v = 2 is achieved only when contributions from collision energies less than 1.0 cm−1 were excluded in the computation of velocity averaged differential rate coefficients for both systems. This could be due to some uncertainties in the velocity spread in the experiment that employs co-propagation of the collision partners and possibly, the neglect of transverse velocities in the simulation of the experiment.

A new approach that allows for the calculation of interaction-induced properties exclusively from the properties of monomers is presented. The method is derived in the spirit of the symmetry-adapted perturbation theory (SAPT). The interaction-induced property is presented in the first order of the molecular interaction operator, including the exchange effects. Test calculations of the interaction-induced dipole moment were carried out for a number of small nonpolar and polar atomic and molecular dimers. The numerical results show that the analytical first-order corrections proposed in this paper reproduce the finite-field treatment of the first-order corrections of SAPT. Compared to supermolecular approaches, the performance of the finite-field SAPT (up to the second order) constitutes an insightful alternative for calculations of interaction-induced properties.

Psi4NumPy demonstrates the use of efficient computational kernels from the open- source Psi4 program through the popular NumPy library for linear algebra in Python to facilitate the rapid development of clear, understandable Python computer code for new quantum chemical methods, while maintaining a relatively low execution time. Using these tools, reference implementations have been created for a number of methods, including self-consistent field (SCF), SCF response, many-body perturbation theory, coupled-cluster theory, configuration interaction, and symmetry-adapted perturbation theory. Further, several reference codes have been integrated into Jupyter notebooks, allowing background and explanatory information to be associated with the imple- mentation. Psi4NumPy tools and associated reference implementations can lower the barrier for future development of quantum chemistry methods. These implementa- tions also demonstrate the power of the hybrid C++/Python programming approach employed by the Psi4 program.

Symmetry-adapted perturbation theory (SAPT) is a popular and versatile tool to compute and decompose noncovalent interaction energies between molecules. The intramolecular SAPT (ISAPT) variant provides a similar energy decomposition between two nonbonded fragments of the same molecule, covalently connected by a third fragment. In this work, we explore an alternative approach where the noncovalent interaction is singled out by a range separation of the Coulomb potential. We investigate two common splittings of the 1/r potential into long-range and short-range parts based on the Gaussian and error functions, and approximate either the entire intermolecular/interfragment interaction or only its attractive terms by the long-range contribution. These range separation schemes are tested for a number of intermolecular and intramolecular complexes. We find that the energy corrections from range-separated SAPT or ISAPT are in reasonable agreement with complete SAPT/ISAPT data. This result should be contrasted with the inability of the long-range multipole expansion to describe crucial short-range charge penetration and exchange effects; it shows that the long-range interaction potential does not just recover the asymptotic interaction energy but also provides a useful account of short-range terms. The best consistency is attained for the error-function separation applied to all interaction terms, both attractive and repulsive. This study is the first step toward a fragmentation-free decomposition of intramolecular nonbonded energy.

The hydrogen deuteride (HD) molecule is an important deuterium tracer in astrophysical studies. The atmospheres of gas giants are dominated by molecular hydrogen, and simultaneous observation of H$_2$ and HD lines provides reliable information on the D/H ratios on these planets. The reference spectroscopic parameters play a crucial role in such studies. Under thermodynamic conditions encountered in these atmospheres, the spectroscopic studies of HD require not only the knowledge of line intensities and positions but also accurate reference data on pressure-induced line shapes and shifts. Our aim is to provide accurate collision-induced line-shape parameters for HD lines that cover any thermodynamic conditions relevant to the atmospheres of giant planets, i.e., any relevant temperature, pressure, and perturbing gas (the H$_2$/He mixture) composition. We perform quantum-scattering calculations on a new highly accurate ab initio potential energy surface, and we use scattering S-matrices obtained this way to determine the collision-induced line-shape parameters. We use the cavity ring-down spectroscopy for validation of our theoretical methodology. We report accurate collision-induced line-shape parameters for the pure rotational R(0), R(1), and R(2) lines, the most relevant HD lines for the investigations of atmospheres of the giant planets. Besides the basic Voigt-profile collisional parameters (i.e. the broadening and shift parameters), we also report their speed dependences and the complex Dicke parameter, which can influence the effective width and height of the HD lines up to almost a factor of 2 for giant planet conditions. The sub-percent-level accuracy, reached in this work, considerably improves the previously available data. All the reported parameters are consistent with the HITRAN database format, hence allowing for the use of HAPI for generating the beyond-Voigt spectra of HD.

An impressive collection of accurate two-body interaction energies for small complexes has been assembled into benchmark databases and used to improve the performance of multiple density functional, semiempirical, and machine learning methods. Similar benchmark data on nonadditive three-body energies in molecular trimers are comparatively scarce, and the existing ones are practically limited to homotrimers. In this work, we present a benchmark dataset of 20 equilibrium noncovalent interaction energies for a small but diverse selection of 10 heteromolecular trimers. The new 3BHET dataset presents complexes that combine different interactions including π-π, anion-π, cation-π, and various motifs of hydrogen and halogen bonding in each trimer. A detailed symmetry-adapted perturbation theory (SAPT)-based energy decomposition of the two- and three-body interaction energies shows that 3BHET consists of electrostatics- and dispersion-dominated complexes. The nonadditive three-body contribution is dominated by induction, but its influence on the overall bonding type in the complex (as exemplified by its position on the ternary diagram) is quite small. We also tested the extended SAPT (XSAPT) approach which is capable of including some nonadditive interactions in clusters of any size. The resulting three-body dispersion term (obtained from the many-body dispersion formalism) is mostly in good agreement with the supermolecular CCSD(T)-MP2 values and the nonadditive induction term is similar to the three-body SAPT(DFT) data, but the overall three-body XSAPT energies are not very accurate as they are missing the first-order exchange terms.

Intramolecular symmetry-adapted perturbation theory (ISAPT) is a method to compute and decompose the noncovalent interaction energy between two molecular fragments A and B covalently connected via a linker C. However, the existing ISAPT algorithm displays several issues for many fragmentation patterns (that is, specific assignments of atoms to the A/B/C subsystems), including an artificially repulsive electrostatic energy (even when the fragments are hydrogen-bonded) and very large and mutually cancelling induction and exchange-induction terms. We attribute those issues to the presence of artificial dipole moments at the interfragment boundary, as the atoms of A and B directly connected to C are missing electrons on one of their hybrid orbitals. Therefore, we propose several new partitioning algorithms which reassign one electron, on a singly occupied link hybrid orbital, from C to each of A/B. Once the contributions from these link orbitals are added to fragment density matrices, the computation of ISAPT electrostatic, induction, and dispersion energies proceeds exactly as normal, and the exchange energy expressions need only minor modifications. Among the link partitioning algorithms introduced, the so-called ISAPT(SIAO1) approach (in which the link orbital is obtained by a projection onto the intrinsic atomic orbitals (IAOs) of a given fragment followed by orthogonalization to this fragment's occupied space) leads to reasonable values of all ISAPT corrections for all fragmentation patterns, and exhibits a fast and systematic basis set convergence. This improvement is made possible by a significant reduction in magnitude (even though not a complete elimination) of the unphysical dipole moments at the interfragment boundaries. We demonstrate the utility of the improved ISAPT partitioning by examining intramolecular interactions in several pentanediol isomers, examples of linear and branched alkanes, and the open and closed conformations of a family of N-arylimide molecular torsion balances.

We investigate collisional line-shape effects that are present in highly accurate experimental spectra of the 3-0 S(1) and 2-0 Q(1) molecular hydrogen absorption lines perturbed by helium. We clearly distin-guish the influence of six different collisional effects (i.e.: collisional broadening and shift, their speed dependencies and the complex Dicke effect) on the shapes of H-2 lines. We demonstrate that only a very specific combination of these six contributions, determined from our ab initio calculations, gives unprece-dentedly good agreement with experimental spectra. If any of the six contributions is neglected, then the experiment-theory comparison deteriorates at least several times. We also analyze the influence of the centrifugal distortion on our ab initio calculations and we demonstrate that the inclusion of this effect slightly improves the agreement with the experimental spectra. (C) 2021 The Author(s). Published by Elsevier Ltd.

We demonstrate a new method for populating line-by-line spectroscopic databases with beyond-Voigt line-shape parameters, which is based on ab initio quantum scattering calculations. We report a comprehensive dataset for the benchmark system of He-perturbed H-2 (we cover all the rovibrational bands that are present in the HITRAN spectroscopic database). We generate the entire dataset of the line-shape parameters (broadening and shift, their speed dependence, and the complex Dicke parameter) from fully ab initio quantum-scattering calculations. We extend the previous calculations by taking into account the centrifugal distortion for all the bands and by including the hot bands. The results are projected on a simple structure of the quadratic speed-dependent hard-collision profile. We report a simple and compact formula that allows the speed-dependence parameters to be calculated directly from the generalized spectroscopic cross sections. For each line and each line-shape parameter, we provide a full temperature dependence within the double-power-law (DPL) representation, which makes the dataset compatible with the HITRAN database. The temperature dependences cover the range from 20 to 1000 K, which includes the low temperatures relevant for the studies of the atmospheres of giant planets. The final outcome from our dataset is validated on highly accurate experimental spectra collected with cavity ring-down spectrometers. The methodology can be applied to many other molecular species important for atmospheric and planetary studies. (C) 2020 Elsevier Ltd. All rights reserved.

The exchange terms in symmetry-adapted perturbation theory (SAPT) are normally calculated within the so-called S2 or single exchange approximation, which approximates the all-electron antisymmetrizer by interchanges of at most one electron pair between the interacting molecules. This approximation is typically very accurate at the van der Waals minimum separation and at larger intermolecular distances but begins to deteriorate at short range. Nonapproximated expressions for the second-order SAPT exchange corrections have been derived some time ago by Schäffer and Jansen [Mol. Phys. 111, 2570 (2013)]. In this work, we extend Schäffer and Jansen's formalism to derive and implement a nonapproximated expression for the third-order exchange-induction correction. Numerical tests on several representative noncovalent databases show that the S2 approximation underestimates the exchange-induction contributions in both second and third orders. This underestimation is very similar in relative terms, but the larger absolute values of the third-order exchange-induction effects, and their near complete cancellation with the corresponding induction energies, make the third-order errors more severe. In the worst-case scenario of interactions involving ions, the breakdown of the S2 approximation can result in a qualitatively wrong, attractive character of SAPT total energies at short range {as first observed by Lao and Herbert [J. Phys. Chem. A 116, 3042 (2012)]}. As expected, the inclusion of the full third-order exchange-induction energy in place of its S2-approximated counterpart restores the correct, repulsive short-range behavior of the SAPT potential energy curves computed through the third order.