Basis-set extrapolation techniques for the accurate calculation of molecular equilibrium geometries using coupled-cluster theory

Abstract

To reduce remaining basis-set errors in the determination of molecular equilibrium geometries, a basis-set extrapolation (BSE) scheme is suggested for the forces used in geometry optimizations. The proposed BSE scheme is based on separating the Hartree-Fock and electron-correlation contributions and uses expressions obtained by straightforward differentiation of well established extrapolation formulas for energies when using basis sets from Dunning's hierarchy of correlation-consistent basis sets. Comparison with reference data obtained at the R12 coupled-cluster level [CCSD(T)-R12] demonstrates that BSE significantly accelerates the convergence to the basis-set limit, thus leading to improvements comparable to or even better than those obtained by increasing the cardinal number in the used basis set by one. However, BSE alone is insufficient to improve agreement with experiment, even after additional consideration of inner-shell correlation and quadruple-excitation effects (mean error and standard deviation with extrapolation are -0.014 and 0.047 pm in comparison with mean error and standard deviation of -0.002 and 0.036 pm without extrapolation). Improvement is obtained only when other contributions of similar magnitude as the BSE contributions (e.g., pentuple-excitation effects and relativistic effects) are also considered. A rather large discrepancy (of the order of a few tenths of a picometer) is observed for the F(2) molecule indicating an enhanced basis-set requirement for the various contributions in this case.

Accurate ab initio potential energy curve of F2. III. The vibration rotation spectrum

“…From this local part of the potential energy curve, the spectroscopic constants R e and e are then determined. Thus, Ruden et al 58 reported accurate ab initio values for R e and e , and Heckert et al 59 reported an accurate R e value. These calculations offer an improvement over other, mostly earlier results.…”

Rotational spectra of CF+and13CF+: accurate rest frequencies and spectroscopic parameters

“…The starting level in this scheme is CCSD(T) in conjunction with basis sets up to sextuple-zeta quality. To estimate the CCSD(T) basis-set limit, extrapolation techniques (Feller 1993;Helgaker et al 1997) are applied at the gradient level within the geometry optimization (Heckert et al 2006). Core-correlation effects are already included at this level by basing this step on all-electron CCSD(T) calculations and the core-polarized cc-pCVnZ sets.…”

Performance of W4 theory for spectroscopic constants and electrical properties of small molecules

“…[4][5][6][7]11 Recently, Mintz et al 12 have applied the multireference ccCA method 13 to compute the potential energy curves of N 2 and C 2 ; they obtained errors of ∼0.06 pm for the bond lengths and ∼2 cm −1 for the harmonic frequencies.…”

“…As for (ii), for systems with mild to moderate nondynamical correlation effects, the accuracy of CCSD(T) basis set limit results is on the order of 5-10 cm −1 for harmonic frequencies [1][2][3][4][5] and 0.1-0.5 pm for bond lengths. 1,2,6,7 To surpass this level of accuracy (or when considering molecules with more pronounced multireference character such as C 2 , BN, BeO, and O 3 ) one should consider multireference methods [8][9][10] or post-CCSD(T)…”