A systematic study of the leading isotropic van der Waals coefficients for the alkali-metal atom + molecule and molecule + molecule systems is presented. Dipole moments and static and dynamic dipole polarizabilities are calculated employing high-level quantum chemistry calculations. The dispersion, induction, and rotational parts of the isotropic van der Waals coefficient are evaluated. The known van der Waals coefficients are then used to derive characteristics essential for simple models of the collisions involving the corresponding ultracold polar molecules.

High-accuracy noncovalent interaction energies are indispensable as data points for potential energy surfaces and as benchmark values for improving and testing more approximate approaches. The preferred algorithm (the gold standard) for computing these energies has been the coupled-cluster method with singles, doubles, and perturbative triples [CCSD(T)] converged to the complete basis set (CBS) limit. However, gold-standard calculations are expensive as correlated interaction energies converge slowly with the basis set size, and establishing the CBS limit to better than 0.05 kcal/mol typically requires a CCSD(T) calculation in a basis set of at least triple-zeta quality. If an even higher accuracy is required (for example, for the assignment of complicated high-resolution spectra), establishing a superior platinum standard requires both a precisely converged CCSD(T)/CBS limit and the corrections for the core correlation, relativistic effects, and higher-order coupled-cluster terms at least through the perturbative quadruple excitations. On the other hand, if a triple-zeta CCSD(T) calculation is not feasible but a double-zeta one is, it is worthwhile to look for a silver standard that provides the most accurate and consistent approximation to the gold standard at a reduced computational cost. We review the recent developments aimed at (i) increasing the breadth and diversity of the available collection of gold-standard benchmark interaction energies, (ii) evaluating the best computational strategies for platinum-standard calculations and producing beyond-CCSD(T) potential energy surfaces for spectroscopic and scattering applications of the highest precision, and (iii) improving the accuracy of the silver-standard, double-zeta-level CCSD(T)/CBS estimates through the use of explicit correlation and midbond basis functions. We also outline the remaining challenges in the accurate ab initio calculations of noncovalent interaction energies.

The individual interaction energy terms in symmetry-adapted perturbation theory (SAPT) not only have different physical interpretations but also converge to their complete basis set (CBS) limit values at quite different rates. Dispersion energy is notoriously the slowest converging interaction energy contribution, and exchange dispersion energy, while smaller in absolute value, converges just as poorly in relative terms. To speed up the basis set convergence of the lowest-order SAPT dispersion and exchange dispersion energies, we borrow the techniques from explicitly correlated (F12) electronic structure theory and develop practical expressions for the closed-shell E disp (20)-F12 and E exch–disp (20)-F12 contributions. While the latter term has been derived and implemented for the first time, the former correction was recently proposed by Przybytek [J. Chem. Theory Comput.20181451055117] using an Ansatz with a full optimization of the explicitly correlated amplitudes. In addition to reimplementing the fully optimized variant of E disp (20)-F12, we propose three approximate Ansätze that substantially improve the scaling of the method and at the same time avoid the numerical instabilities of the unrestricted optimization. The performance of all four resulting flavors of E disp (20)-F12 and E exch–disp (20)-F12 is first tested on helium, neon, argon, water, and methane dimers, with orbital and auxiliary basis sets up to aug-cc-pV5Z and aug-cc-pV5Z-RI, respectively. The double- and triple-ζ basis set calculations are then extended to the entire A24 database of noncovalent interaction energies and compared with CBS estimates for E disp (20) and E exch–disp (20) computed using conventional SAPT with basis sets up to aug-cc-pV6Z with midbond functions. It is shown that the F12 treatment is highly successful in improving the basis set convergence of the SAPT terms, with the F12 calculations in an X-tuple ζ basis about as accurate as conventional calculations in bases with cardinal numbers (X + 2) for E disp (20) and either (X + 1) or (X + 2) for E exch–disp (20). While the full amplitude optimization affords the highest accuracy for both corrections, the much simpler and numerically stable optimized diagonal Ansatz is a very close second. We have also tested the performance of the simple F12 correction based on the second-order Møller–Plesset perturbation theory, SAPT-F12­(MP2) [FreyJ. A. Frey, J. A. Chem. Rev.201611656145641] and observed that it is also quite successful in speeding up the basis set convergence of conventional E disp (20) + E exch–disp (20), albeit with some outliers.

No abstract

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 (KodryckaM. M., Kodrycka J. Chem. Theory Comput.20191559655986), 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.