Transfer Learning to CCSD(T): Accurate Anharmonic Frequencies from Machine Learning Models

Abstract

The calculation of the anharmonic modes of small- to medium-sized molecules for assigning experimentally measured frequencies to the corresponding type of molecular motions is computationally challenging at sufficiently high levels of quantum chemical theory. Here, a practical and affordable way to calculate coupled-cluster quality anharmonic frequencies using second-order vibrational perturbation theory (VPT2) from machine-learned models is presented. The approach, referenced as “NN + VPT2”, uses a high-dimensional neural network (PhysNet) to learn potential energy surfaces (PESs) at different levels of theory from which harmonic and VPT2 frequencies can be efficiently determined. The NN + VPT2 approach is applied to eight small- to medium-sized molecules (H2CO, trans-HONO, HCOOH, CH3OH, CH3CHO, CH3NO2, CH3COOH, and CH3CONH2) and frequencies are reported from NN-learned models at the MP2/aug-cc-pVTZ, CCSD­(T)/aug-cc-pVTZ, and CCSD­(T)-F12/aug-cc-pVTZ-F12 levels of theory. For the largest molecules and at the highest levels of theory, transfer learning (TL) is used to determine the necessary full-dimensional, near-equilibrium PESs. Overall, NN + VPT2 yields anharmonic frequencies to within 20 cm–1 of experimentally determined frequencies for close to 90% of the modes for the highest quality PES available and to within 10 cm–1 for more than 60% of the modes. For the MP2 PESs only ∼60% of the NN + VPT2 frequencies were within 20 cm–1 of the experiment, with outliers up to ∼150 cm–1, compared to the experiment. It is also demonstrated that the approach allows to provide correct assignments for strongly interacting modes such as the OH bending and the OH torsional modes in formic acid monomer and the CO-stretch and OH-bend mode in acetic acid.

Transfer learned potential energy surfaces: accurate anharmonic vibrational dynamics and dissociation energies for the formic acid monomer and dimer

“… 50 Interestingly, this reassignment was recently supported from second order vibrational perturbation theory (VPT2) calculations using a neural network-(NN) based PES. 23 …”

Transfer learning for affordable and high quality tunneling splittings from instanton calculations

“…To set the stage, the tunneling splittings for malonaldehyde were calculated on the Phys-Net MP2 PES using RPI theory. The tunneling splitting calculations were carried out with three different values of the imaginary time, τ , corresponding to effective 'temperatures' 25,12.5] K and with different numbers of beads N ∈ [2 5 , .., 2 12 ] to ensure convergence. Formally the instanton result is defined in the low-temperature limit, which is equivalent to infinitely-long imaginary times.…”

“…To avoid the need for calculating large ab initio data sets at high levels of theory transfer learning (TL) [18][19][20] and related ∆-ML 21 were shown to be data and cost-effective alternatives. [22][23][24][25][26][27] The combination of TL and instanton theory appears particularly appealing as the instanton path (IP) can be determined on a low-level PES, which gives a rough approximation to the true tunneling path, and can be included (and iteratively refined if needed) into the TL data set. Additionally, the IP is inherently local and, thus, allows concentrating on improving only a small part of a PES.…”

Impact of the Characteristics of Quantum Chemical Databases on Machine Learning Prediction of Tautomerization Energies

“…It is interesting to note that normal mode sampling was also found to be insufficient for generating sufficiently reliable, full-dimensional NN-based near-equilibrium potential energy surfaces for harmonic and anharmonic normal modes. 82 Another determinant property is the number of heavy atoms in molecules covered in the database (Section 4.1). Not surprisingly, better results are obtained for the range covered by the database, and if a sufficient number of samples is available, e.g., when considering the performance depending on the number of heavy atoms in SetLE9.…”

“…However, using a complementary technique such as active learning can substantially improve the results, as was found for ANI-1x. It is interesting to note that normal mode sampling was also found to be insufficient for generating sufficiently reliable, full-dimensional NN-based near-equilibrium potential energy surfaces for harmonic and anharmonic normal modes …”