Gaussian process regression adaptive density-guided approach: Toward calculations of potential energy surfaces for larger molecules

We present a new program implementation of the Gaussian process regression adaptive density-guided approach [Schmitz et al., J. Chem. Phys. 153, 064105 (2020)] for automatic and cost-efficient potential energy surface construction in the MidasCpp program. A number of technical and methodological improvements made allowed us to extend this approach toward calculations of larger molecular systems than those previously accessible and maintain the very high accuracy of constructed potential energy surfaces. On the methodological side, improvements were made by using a Δ-learning approach, predicting the difference against a fully harmonic potential, and employing a computationally more efficient hyperparameter optimization procedure. We demonstrate the performance of this method on a test set of molecules of growing size and show that up to 80% of single point calculations could be avoided, introducing a root mean square deviation in fundamental excitations of about 3 cm−1. A much higher accuracy with errors below 1 cm−1 could be achieved with tighter convergence thresholds still reducing the number of single point computations by up to 68%. We further support our findings with a detailed analysis of wall times measured while employing different electronic structure methods. Our results demonstrate that GPR-ADGA is an effective tool, which could be applied for cost-efficient calculations of potential energy surfaces suitable for highly accurate vibrational spectra simulations

Gaussian Process Regression Adaptive Density-Guided Approach: Towards Calculations of Potential Energy Surfaces for Larger Molecules

We present a new program implementation of the gaussian process regression adaptive density-guided approach [J. Chem. Phys. 153 (2020) 064105] in the MidasCpp program. A number of technical and methodological improvements made allowed us to extend this approach towards calculations of larger molecular systems than those accessible previously and maintain the very high accuracy of constructed potential energy surfaces. We demonstrate the performance of this method on a test set of molecules of growing size and show that up to 80 % of single point calculations could be avoided introducing a root mean square deviation in fundamental excitations of about 3 cm$^{-1}$. A much higher accuracy with errors below 1 cm$^{-1}$ could be achieved with tighter convergence thresholds still reducing the number of single point computations by up to 68 %. We further support our findings with a detailed analysis of wall times measured while employing different electronic structure methods. Our results demonstrate that GPR-ADGA is an effective tool, which could be applied for cost-efficient calculations of potential energy surfaces suitable for highly-accurate vibrational spectra simulations

Tensor Decomposition and Vibrational Coupled Cluster Theory

The use of tensor decomposition in the calculation of anharmonic vibrational wave functions is discussed. The correlation amplitudes of vibrational coupled cluster (VCC) and vibrational configuration interaction (VCI) theories are considered as tensors and decomposed. A pilot code is implemented allowing a numerical study of the performance of the canonical decomposition/parallel factors (CP) for three and higher mode couplings in computations on water, formaldehyde, and 1,2,5-thiadiazole. The results show that there is a significant perspective in applying tensor decomposition in the context of anharmonic vibrational wave functions, with the CP tensor decomposition providing compression of data and a computational convenient representation. The calculations also illustrate how the multiplicative separability of the VCC ansatz with respect to noninteracting degrees of freedom goes well together with a tensor decomposition approach. Tensor decomposition opens for adjusting the computational effort spent on a particular mode-coupling according to the significance of that particular coupling, which is guaranteed to decrease to zero in the case of VCC in the limit of noninteracting subsystems