Geometric Energy Derivatives at the Complete Basis Set Limit: Application to the Equilibrium Structure and Molecular Force Field of Formaldehyde

Abstract

Geometric energy derivatives which rely on core-corrected focal-point energies extrapolated to the complete basis set (CBS) limit of coupled cluster theory with iterative and noniterative quadruple excitations, CCSDTQ and CCSDT(Q), are used as elements of molecular gradients and, in the case of CCSDT(Q), expansion coefficients of an anharmonic force field. These gradients are used to determine the CCSDTQ/CBS and CCSDT(Q)/CBS equilibrium structure of the S ground state of HCO where excellent agreement is observed with previous work and experimentally derived results. A fourth-order expansion about this CCSDT(Q)/CBS reference geometry using the same level of theory produces an exceptional level of agreement to spectroscopically observed vibrational band origins with a MAE of 0.57 cm. Second-order vibrational perturbation theory (VPT2) and variational discrete variable representation (DVR) results are contrasted and discussed. Vibration-rotation, anharmonicity, and centrifugal distortion constants from the VPT2 analysis are reported and compared to previous work. Additionally, an initial application of a sum-over-states fourth-order vibrational perturbation theory (VPT4) formalism is employed herein, utilizing quintic and sextic derivatives obtained with a recursive algorithmic approach for response theory.

Vibrational levels of formaldehyde: Calculations from new high precision potential energy surfaces and comparison with experimental band origins

“…Previous experience with some 4-5 atomic molecules [7] [8] [9] [10] [11] have shown that ab initio based approaches could be useful for better modelling and assignments of high-resolution spectra. In the present work, we report theoretical vibrational levels of formaldehyde computed from new accurate ab initio PES using the algorithms similar to one recently applied for the methane molecule [12] and compare our results with other recent calculations [13] [14].…”

“…A detailed review of earlier works refs [17] [15] [16] [18] [19] [20] that reported calculations of the formaldehyde PES and energy levels can be found refs. [13] [14].…”

Coupled-cluster techniques for computational chemistry: The CFOUR program package

“…The xcubic module calculates anharmonic contributions based on secondorder vibrational perturbation theory (VPT2) [380][381][382][383][384]. While VPT2, when paired with a sufficient level of electron correlation and basis set completeness, can provide highly-accurate frequencies and intensities compared to gas-phase experiments,[385][386][387][388][389][390] the presence of near-degeneracies in the harmonic frequencies can lead to a breakdown in the perturbation theory. Most commonly, VPT2 is affected by Fermi 391 and Darling-Dennison 392 resonances (although the latter is better described as a missing vibrational interaction rather than a PT breakdown).…”

State‐of‐the‐art computations of dipole moments using analytic gradients of high‐level density‐fitted coupled‐cluster methods with focal‐point approximations

“…However, the coefficients A and B will be different for each property. Therefore, we do not need to obtain new CBS formulas for properties, as one presented by Schaefer and coworkers for energy gradients with respect to nuclear displacements. We also implement their formulas and obtain the same results with the one obtained from eqs.…”