Analyzing the errors of DFT approximations for compressed water systems

Fine Tuning the Intermolecular Interactions of Water Clusters Using the Dispersion-Corrected Density Functional Theory

Dispersion-inclusive density functional theory (DFT) methods have unequivocally demonstrated improved performances with respect to standard DFT approximations for modeling large and extended molecular systems at the quantum mechanical level. Yet, in some cases, disagreements with highly accurate reference calculations, such as CCSD(T) and quantum Monte Carlo (MC) calculations, still remain. Furthermore, the application of general-purpose corrections, such as the popular Grimme's semi-classical models (DFT-D), to different Kohn-Sham exchange-correlation functionals sometimes leads to variable and inconsistent results, which recommend a careful prior evaluation. In a recent study, we proposed a simple optimization protocol for enhancing the accuracy of these DFT-D methods by following an alternative and system-specific approach. Here, adopting the same computational strategy, we show how the accurate MC intermolecular interactions of a large set of water clusters of variable sizes (i.e., 300 (H₂O)_n structures, n = 9, 15, 27) can be reproduced remarkably well by dispersion-corrected DFT models (i.e., B3LYP-D4, PBE-D4, revPBE(0)-D4) upon re-optimization, reaching a mean absolute error per monomer of ~0.1 kcal/mol. Hence, the obtained results support the use of this procedure for fine-tuning tailored DFT-D models for the accurate description of targeted molecular systems.

Static and Dynamic Correlations in Water: Comparison of Classical Ab Initio Molecular Dynamics at Elevated Temperature with Path Integral Simulations at Ambient Temperature

It is a common practice in ab initio molecular dynamics (AIMD) simulations of water to use an elevated temperature to overcome the overstructuring and slow diffusion predicted by most current density functional theory (DFT) models. The simulation results obtained in this distinct thermodynamic state are then compared with experimental data at ambient temperature based on the rationale that a higher temperature effectively recovers nuclear quantum effects (NQEs) that are missing in the classical AIMD simulations. In this work, we systematically examine the foundation of this assumption for several DFT models as well as for the many-body MB-pol model. We find for the cases studied that a higher temperature does not correctly mimic NQEs at room temperature, which is especially manifest in significantly different three-molecule correlations as well as hydrogen bond dynamics. In many of these cases, the effects of NQEs are the opposite of the effects of carrying out the simulations at an elevated temperature.

Chemical accuracy from quantum Monte Carlo for the benzene dimer

We report an accurate study of interactions between benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory using different van der Waals functionals. In our quantum Monte Carlo (QMC) calculations, we use accurate correlated trial wave functions including three-body Jastrow factors and backflow transformations. We consider two benzene molecules in the parallel displaced geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimal VMC and DMC binding energies of -2.3(4) and -2.7(3) kcal/mol, respectively. The best estimate of the coupled-cluster theory through perturbative triplets/complete basis set limit is -2.65(2) kcal/mol [Miliordos et al., J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, comparable to results from the best quantum chemistry methods.

Energy benchmarks for methane-water systems from quantum Monte Carlo and second-order Møller-Plesset calculations

The quantum Monte Carlo (QMC) technique is used to generate accurate energy benchmarks for methane-water clusters containing a single methane monomer and up to 20 water monomers. The benchmarks for each type of cluster are computed for a set of geometries drawn from molecular dynamics simulations. The accuracy of QMC is expected to be comparable with that of coupled-cluster calculations, and this is confirmed by comparisons for the CH4-H2O dimer. The benchmarks are used to assess the accuracy of the second-order Møller-Plesset (MP2) approximation close to the complete basis-set limit. A recently developed embedded many-body technique is shown to give an efficient procedure for computing basis-set converged MP2 energies for the large clusters. It is found that MP2 values for the methane binding energies and the cohesive energies of the water clusters without methane are in close agreement with the QMC benchmarks, but the agreement is aided by partial cancelation between 2-body and beyond-2-body errors of MP2. The embedding approach allows MP2 to be applied without loss of accuracy to the methane hydrate crystal, and it is shown that the resulting methane binding energy and the cohesive energy of the water lattice agree almost exactly with recently reported QMC values.