Performance of quantum Monte Carlo for calculating molecular bond lengths

Toward Compact Selected Configuration Interaction Wave Functions with Quantum Monte Carlo─A Case Study of C2

The ¹Σ_g⁺ ground state of C₂ is investigated using truncated CIPSI-Jastrow CSF wave functions with Hartree-Fock orbitals within the framework of variational and diffusion quantum Monte Carlo. The truncation is performed based on the absolute value of the CI coefficients, and the Jastrow, molecular orbitals, and CI parameters are either partially or fully reoptimized with respect to the variational energy. Excellent absolute as well as bond dissociation energies are obtained at DMC level with very compact, fully optimized wave functions. By studying the expansions in more detail, we observe a change in the CI picture when reoptimizing the antisymmetric part of the CIPSI-Jastrow wave functions. Furthermore, we demonstrate that a decrease in the VMC energy as well as an improvement of the nodal surface quality can be achieved─with the same expansion size─if the CSFs are selected in the presence of a Jastrow correlation function, laying the foundation for a Jastrow selected CI scheme with quantum Monte Carlo.

Accurate Excited-State Geometries: A CASPT2 and Coupled-Cluster Reference Database for Small Molecules

We present an investigation of the excited-state structural parameters determined for a large set of small compounds with the dual goals of defining reference values for further works and assessing the quality of the geometries obtained with relatively cheap computational approaches. In the first stage, we compare the excited-state geometries obtained with ADC(2), CC2, CCSD, CCSDR(3), CC3, and CASPT2 and large atomic basis sets. It is found that CASPT2 and CC3 results are generally in very good agreement with one another (typical differences of ca. 3 × 10^–3 Å) when all electrons are correlated and when the aug-cc-pVTZ atomic basis set is employed with both methods. In a second stage, a statistical analysis reveals that, on the one hand, the excited-state (ES) bond lengths are much more sensitive to the selected level of theory than their ground-state (GS) counterparts and, on the other hand, that CCSDR(3) is probably the most cost-effective method delivering accurate structures. Indeed, CCSD tends to provide too compact multiple bond lengths on an almost systematic basis, whereas both CC2 and ADC(2) tend to exaggerate these bond distances, with more erratic error patterns, especially for the latter method. The deviations are particularly marked for the polarized CO and CN bonds, as well as for the puckering angle in formaldehyde homologues. In the last part of this contribution, we provide a series of CCSDR(3) GS and ES geometries of medium-sized molecules to be used as references in further investigations.

Bias-Free Chemically Diverse Test Sets from Machine Learning

Current benchmarking methods in quantum chemistry rely on databases that are built using a chemist's intuition. It is not fully understood how diverse or representative these databases truly are. Multivariate statistical techniques like archetypal analysis and K-means clustering have previously been used to summarize large sets of nanoparticles however molecules are more diverse and not as easily characterized by descriptors. In this work, we compare three sets of descriptors based on the one-, two-, and three-dimensional structure of a molecule. Using data from the NIST Computational Chemistry Comparison and Benchmark Database and machine learning techniques, we demonstrate the functional relationship between these structural descriptors and the electronic energy of molecules. Archetypes and prototypes found with topological or Coulomb matrix descriptors can be used to identify smaller, statistically significant test sets that better capture the diversity of chemical space. We apply this same method to find a diverse subset of organic molecules to demonstrate how the methods can easily be reapplied to individual research projects. Finally, we use our bias-free test sets to assess the performance of density functional theory and quantum Monte Carlo methods.