Explicit correlation and basis set superposition error: The structure and energy of carbon dioxide dimer

We have investigated the slipped parallel and t-shaped structures of carbon dioxide dimer [(CO₂)₂] using both conventional and explicitly correlated coupled cluster methods, inclusive and exclusive of counterpoise (CP) correction. We have determined the geometry of both structures with conventional coupled cluster singles doubles and perturbative triples theory [CCSD(T)] and explicitly correlated cluster singles doubles and perturbative triples theory [CCSD(T)-F12b] at the complete basis set (CBS) limits using custom optimization routines. Consistent with previous investigations, we find that the slipped parallel structure corresponds to the global minimum and is 1.09 kJ mol⁻¹ lower in energy. For a given cardinal number, the optimized geometries and interaction energies of (CO₂)₂ obtained with the explicitly correlated CCSD(T)-F12b method are closer to the CBS limit than the corresponding conventional CCSD(T) results. Furthermore, the magnitude of basis set superposition error (BSSE) in the CCSD(T)-F12b optimized geometries and interaction energies is appreciably smaller than the magnitude of BSSE in the conventional CCSD(T) results. We decompose the CCSD(T) and CCSD(T)-F12b interaction energies into the constituent HF or HF CABS, CCSD or CCSD-F12b, and (T) contributions. We find that the complementary auxiliary basis set (CABS) singles correction and the F12b approximation significantly reduce the magnitude of BSSE at the HF and CCSD levels of theory, respectively. For a given cardinal number, we find that non-CP corrected, unscaled triples CCSD(T)-F12b/VXZ-F12 interaction energies are in overall best agreement with the CBS limit

Explicit correlation and intermolecular interactions: Investigating carbon dioxide complexes with the CCSD(T)-F12 method

We have optimized the lowest energy structures and calculated interaction energies for the CO₂–Ar, CO₂–N₂, CO₂–CO, CO₂–H₂O, and CO₂–NH₃ dimers with the recently developed explicitly correlated coupled cluster singles doubles and perturbative triples [CCSD(T)]-F12 methods and the associated VXZ-F12 (where X = D,T,Q) basis sets. For a given cardinal number, we find that results obtained with the CCSD(T)-F12 methods are much closer to the CCSD(T) complete basis set limit than the conventional CCSD(T) results. The relatively modest increase in the computational cost between explicit and conventional CCSD(T) is more than compensated for by the impressive accuracy of the CCSD(T)-F12 method. We recommend use of the CCSD(T)-F12 methods in combination with the VXZ-F12 basis sets for the accurate determination of equilibrium geometries and interaction energies of weakly bound electron donor acceptor complexes

Extension of coupled-cluster theory with a non-iterative treatment of connected triply excited clusters to three-body Hamiltonians

We generalize the coupled-cluster (CC) approach with singles, doubles, and the non-iterative treatment of triples termed $\Lambda$CCSD(T) to Hamiltonians containing three-body interactions. The resulting method and the underlying CC approach with singles and doubles only (CCSD) are applied to the medium-mass closed-shell nuclei O16, O24, and Ca40. By comparing the results of CCSD and $\Lambda$CCSD(T) calculations with explicit treatment of three-nucleon interactions to those obtained using an approximate treatment in which they are included effectively via the zero-, one-, and two-body components of the Hamiltonian in normal-ordered form, we quantify the contributions of the residual three-body interactions neglected in the approximate treatment. We find these residual normal-ordered three-body contributions negligible for the $\Lambda$CCSD(T) method, although they can become significant in the lower-level CCSD approach, particularly when the nucleon-nucleon interactions are soft.Comment: 21 pages, 3 figure

Explicitly correlated intermolecular distances and interaction energies of hydrogen bonded complexes

We have optimized the lowest energy structures and calculated interaction energies for the H2O–H2O, H2O–H2S, H2O–NH3, and H2O–PH3 dimers with the recently developed explicitly correlated CCSD(T)-F12 methods and the associated VXZ-F12 (where X=D,T,Q) basis sets. For a given cardinal number, we find that the results obtained with the CCSD(T)-F12 methods are much closer to the CCSD(T) complete basis set limit than the conventional CCSD(T) results. In general we find that CCSD(T)-F12 results obtained with the VTZ-F12 basis set are better than the conventional CCSD(T) results obtained with an aug-cc-pV5Z basis set. We also investigate two ways to reduce the effects of basis set superposition error with conventional CCSD(T), namely, the popular counterpoise correction and limiting diffuse basis functions to the heavy atoms only. We find that for a given cardinal number, these selectively augmented correlation consistent basis sets yield results that are closer to the complete basis set limit than the corresponding fully augmented basis sets. Furthermore, we find that the difference between standard and counterpoise corrected interaction energies and intermolecular distances is reduced with the selectively augmented basis sets

XH-stretching overtone transitions calculated using explicitly correlated coupled cluster methods

We have calculated XH-stretching (where X=O, C, F, Cl) fundamental and overtone transitions for three diatomics and a few small molecules using a local mode model. The potential energy curves and dipole moment functions are calculated using the recently developed explicitly correlated coupled cluster with single doubles and perturbative triples theory [CCSD_T_-F12] with the associated VXZ-F12 (where X=D, T, Q) basis sets. We find that the basis set convergence of calculated frequencies and oscillator strengths obtained with the explicitly correlated method is much more rapid than with conventional CCSD(T) and the Dunning type correlation consistent basis sets. Furthermore, CCSD(T)-F12 frequencies and oscillator strengths obtained with the VTZ-F12 and VQZ-F12 basis sets are found to be in excellent agreement with the CCSD(T) complete basis set limit. We find that comparison of CCSD(T)-F12 frequencies with experiment is less good. The inclusion of explicit correlation exposes the inherent error of the CCSD(T) method to overestimate vibrational frequencies, which is normally compensated by basis set incompleteness error. As a consequence, we suggest that conventional CCSD(T) in combination with the aug-cc-pVTZ or aug-cc-pVQZ basis sets is likely to yield calculated XH-stretching frequencies in closest agreement with experiment

Impact of functional studies on exome sequence variant interpretation in early-onset cardiac conduction system diseases

Aims The genetic cause of cardiac conduction system disease (CCSD) has not been fully elucidated. Whole-exome sequencing (WES) can detect various genetic variants; however, the identification of pathogenic variants remains a challenge. We aimed to identify pathogenic or likely pathogenic variants in CCSD patients by using WES and 2015 American College of Medical Genetics and Genomics (ACMG) standards and guidelines as well as evaluating the usefulness of functional studies for determining them. Methods and Results We performed WES of 23 probands diagnosed with early-onset (<65 years) CCSD and analyzed 117 genes linked to arrhythmogenic diseases or cardiomyopathies. We focused on rare variants (minor allele frequency < 0.1%) that were absent from population databases. Five probands had protein truncating variants in EMD and LMNA which were classified as “pathogenic” by 2015 ACMG standards and guidelines. To evaluate the functional changes brought about by these variants, we generated a knock-out zebrafish with CRISPR-mediated insertions or deletions of the EMD or LMNA homologs in zebrafish. The mean heart rate and conduction velocities in the CRISPR/Cas9-injected embryos and F2 generation embryos with homozygous deletions were significantly decreased. Twenty-one variants of uncertain significance were identified in 11 probands. Cellular electrophysiological study and in vivo zebrafish cardiac assay showed that 2 variants in KCNH2 and SCN5A, 4 variants in SCN10A, and 1 variant in MYH6 damaged each gene, which resulted in the change of the clinical significance of them from “Uncertain significance” to “Likely pathogenic” in 6 probands. Conclusions Of 23 CCSD probands, we successfully identified pathogenic or likely pathogenic variants in 11 probands (48%). Functional analyses of a cellular electrophysiological study and in vivo zebrafish cardiac assay might be useful for determining the pathogenicity of rare variants in patients with CCSD. SCN10A may be one of the major genes responsible for CCSD. Translational Perspective Whole-exome sequencing (WES) may be helpful in determining the causes of cardiac conduction system disease (CCSD), however, the identification of pathogenic variants remains a challenge. We performed WES of 23 probands diagnosed with early-onset CCSD, and identified 12 pathogenic or likely pathogenic variants in 11 of these probands (48%) according to the 2015 ACMG standards and guidelines. In this context, functional analyses of a cellular electrophysiological study and in vivo zebrafish cardiac assay might be useful for determining the pathogenicity of rare variants, and SCN10A may be one of the major development factors in CCSD