Do CCSD and approximate CCSD-F12 variants converge to the same basis set limits? The case of atomization energies

While the title question is a clear 'yes' from purely theoretical arguments, the case is less clear for practical calculations with finite (one-particle) basis sets. To shed further light on this issue, the basis set limits of CCSD (coupled cluster theory with all single and double excitations) and of different approximate implementations of CCSD-F12 (explicitly correlated CCSD) have been investigated on detail for the W4-17 thermochemical benchmark. Near the CBS ([1-particle] complete basis set) limit, CCSD and CCSD(F12*) agree to within their respective uncertainties (about \pm0.04 kcal/mol) due to residual basis set incompleteness error, but a nontrivial difference remains between CCSD-F12b and CCSD(F12*), which is roughly proportional to the degree of static correlation. The observed basis set convergence behavior results from the superposition of a rapidly converging, attractive, CCSD[F12]--CCSD-F12b difference (consisting mostly of third-order terms), and a more slowly converging, repulsive, fourth-order difference between CCSD(F12*) and CCSD[F12]. For accurate thermochemistry, we recommend CCSD(F12*) over CCSD-F12b if at all possible. There are some indications that the nZaPa family of basis sets exhibits somewhat smoother convergence than the correlation consistent family.Comment: (J. Chem. Phys., revised

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

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

Coupled cluster benchmarks of water monomers and dimers extracted from DFT liquid water: the importance of monomer deformations

To understand the performance of popular density-functional theory (DFT) exchange-correlation (xc) functionals in simulations of liquid water, water monomers and dimers were extracted from a PBE simulation of liquid water and examined with coupled cluster with single and double excitations plus a perturbative correction for connected triples [CCSD(T)]. CCSD(T) reveals that most of the dimers are unbound compared to two gas phase equilibrium water monomers, largely because monomers within the liquid have distorted geometries. Of the three xc functionals tested, PBE and BLYP systematically underestimate the cost of the monomer deformations and consequently predict too large dissociation energies between monomers within the dimers. This is in marked contrast to how these functionals perform for an equilibrium water dimer and other small water clusters in the gas phase, which only have moderately deformed monomers. PBE0 reproduces the CCSD(T) monomer deformation energies very well and consequently the dimer dissociation energies much more accurately than PBE and BLYP. Although this study is limited to water monomers and dimers, the results reported here may provide an explanation for the overstructured radial distribution functions routinely observed in BLYP and PBE simulations of liquid water and are of relevance to water in other phases and to other associated molecular liquids.Comment: 10 pages, 8 figures, Submitted to Journal of Chemical Physics, Related information can be found in http://www.fhi-berlin.mpg.de/th

Theoretical studies in the molecular Platonic solids: Pure and mixed carbon, nitrogen, phosphorus, and silicon tetrahedranes

Calculations were conducted at the G4MP2 and G4 composite method levels of theory on the 35 potential carbon, nitrogen, silicon, and phosphorus tetrahedrane derivatives with the general form C~a~N~b~Si~c~P~d~H~(4-b-d)~ (where a+b+c+d=4). At both levels of theory, optimized electronic ground state neutral singlet gas phase (298.15 K, 1 atm) geometries were obtained for 24 of the 35 possible C/N/Si/P tetrahedrane derivatives. Corresponding enthalpies of formation were calculated using the atomization method. Triplet state neutral tetrahedron starting geometries for all compounds either resulted in cage opening or failed to converge. Only 9 cationic and 3 anionic forms converged to stable geometries that retained the tetrahedron cage and were absent imaginary frequencies, thereby allowing the calculation of adiabatic ionization energies and electron affinities

Gas phase enthalpies of formation, isomerization, and disproportionation of mono- through tetra-substituted tetrahedranes: A G4MP2/G4 theoretical study

Gas phase (298.15 K, 1 atm) enthalpies of formation (Δ~f~H°~(g)~), enthalpies of disproportionation to two corresponding acetylene molecules (Δ~rxn~H°~(g),Td→acet~), and enthalpies of isomerization from a tetrahedrane geometry to a 1,3-cyclobutadiene structure (Δ~isom~H°~(g),Td→CBD~) were calculated for the mono- through tetra-substituted hydro, fluoro, chloro, bromo, methyl, ethynyl, and cyano carbon tetrahedrane derivatives at the G4MP2 and G4 levels of theory. All derivatives have endothermic Δ~f~H°~(g)~ indicative of the cage strain in these systems. In all cases, Δ~rxn~H°~(g),Td→acet~ and Δ~isom~H°~(g),Td→CBD~ are predicted to be substantially exothermic. High quality linear regression fits within a homologous series were obtained between the number of substituents and the G4MP2/G4 estimated Δ~f~H°~(g)~. Via calculations on lower homolog members, this strategy was employed to allow extrapolated G4 and/or G4MP2 Δ~f~H°~(g)~ (as well as some Δ~rxn~H°~(g),Td→acet~ and Δ~isom~H°~(g),Td→CBD~) to be obtained for the mono- through tetra-substituted t-butyl, trifluoromethyl, and trimethylsilyl carbon tetrahedrane derivatives