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

Active learning approach to simulations of strongly correlated matter with the ghost Gutzwiller approximation

Quantum embedding (QE) methods such as the ghost Gutzwiller approximation (gGA) offer a powerful approach to simulating strongly correlated systems, but come with the computational bottleneck of computing the ground state of an auxiliary embedding Hamiltonian (EH) iteratively. In this work, we introduce an active learning (AL) framework integrated within the gGA to address this challenge. The methodology is applied to the single-band Hubbard model and results in a significant reduction in the number of instances where the EH must be solved. Through a principal component analysis (PCA), we find that the EH parameters form a low-dimensional structure that is largely independent of the geometric specifics of the systems, especially in the strongly correlated regime. Our AL strategy enables us to discover this low-dimensionality structure on the fly, while leveraging it for reducing the computational cost of gGA, laying the groundwork for more efficient simulations of complex strongly correlated materials

Electric properties of the Cu

The lowest-order electric properties of the coinage metal cations Cu+, Ag+ and Au+ are calculated ab initio. For the ground states, accurate coupled cluster estimations are presented for the static and dynamic dipole and quadrupole polarizabilities. Results of the similar quality are obtained for the static dipole polarizabilities and permanent quadrupole moments of the lowest excited triplet 3D states, whereas the first excited singlet 1D states are characterized at the lower level of correlation treatment. Effect of vectorial spin-orbit coupling is assessed using the spin-orbit configuration interaction method

Computational Investigation of the Spin-Density Asymmetry in Photosynthetic Reaction Center Models from First Principles

We present a computational analysis of the spin-density asymmetry in cation radical states of reaction center models from photosystem I, photosystem II, and bacteria from Synechococcus elongatus, Thermococcus vulcanus, and Rhodobacter sphaeroides, respectively. The recently developed FDE-diab methodology [J. Chem. Phys., 148 (2018), 214104] allowed us to effectively avoid the spin-density overdelocalization error characteristic for standard Kohn–Sham Density Functional Theory and to reliably calculate spin-density distributions and electronic couplings for a number of molecular systems ranging from inner pairs of (bacterio)chlorophyll a molecules in vacuum to large protein including up to about 2000 atoms. The calculated spin densities show a good agreement with available experimental results and were used to validate reaction center models reported in the literature. Here we demonstrate that the applied theoretical approach is very sensitive to changes in molecular structures and relative orientation of molecules. This makes FDE-diab a valuable tool for electronic structure calculations of large photosynthetic models effectively complementing the existing experimental techniques.<br /

Interaction of the Beryllium Cation with Molecular Hydrogen and Deuterium

The structural and spectroscopic properties of the Be(+)-H2 and Be(+)-D2 electrostatic complexes are investigated theoretically. A three-dimensional ground-state potential energy surface is generated ab initio at the CCSD(T) level and used for calculating the lower rovibrational energy levels variationally. The minimum of the potential energy surface corresponds to a well depth of 3168 cm(-1), an intermolecular separation of 1.776 Å, with the bond of the H2 subunit being 0.027 Å longer than for the free molecule. Taking vibrational zero point energy into account, the complexes containing para H2 and ortho D2 are predicted to have dissociation energies of 2678 and 2786 cm(-1), respectively. The νHH band of Be(+)-H2 is predicted to be red-shifted from the free dihydrogen transition by -323 cm(-1), whereas the corresponding shift for Be(+)-D2 is predicted to be -229 cm(-1). The dissociation energy of the Be(+)-D2 complex is calculated to be slightly higher than the energy required to vibrationally excite the D2 subunit, raising the possibility that the onset of dissociation can be observed in the infrared predissociation spectrum at a particular rotational energy level in the νDD manifold

Theoretical Assessment of Hinge-Type Models for Electron Donors in Reaction Centers of Photosystems I and II as Well as of Purple Bacteria

Hinge-type molecular models for electron donors in reaction centers of Photosystem I, II, and purple bacteria were investigated using a two-state computational approach based on Frozen-Density Embedding. This methodology, dubbed FDE-diab, is known to avoid consequences of the self-interaction error as far as intermolecular phenomena are concerned, which allows to predict qualitatively correct spin densities for large bio-molecular systems. The calculated spin density distributions are in a good agreement with available experimental results and demonstrated a very high sensitivity to changes in relative orientiation of co-factors and amino-acid protonation states. This allows to validate the previously proposed hinge-type models and make predictions on protonation states of axial histidine molecules. Contrary to the reaction centers in Photosystem I and purple bacteria, the axial histidines from Photosystem II were found to be deprotonated. This fact might shed some light on remarkable properties of Photosystem II reaction centers

Ab Initio Characterization of the Electrostatic Complexes Formed by H₂ Molecule and Cr⁺, Mn⁺, Cu⁺, and Zn⁺ Cations

Equilibrium structures, dissociation energies, and rovibrational energy levels of the electrostatic complexes formed by molecular hydrogen and first-row S-state transition metal cations Cr⁺, Mn⁺, Cu⁺, and Zn⁺ are investigated ab initio. Extensive testing of the CCSD­(T)-based approaches for equilibrium structures provides an optimal scheme for the potential energy surface calculations. These surfaces are calculated in two dimensions by keeping the H–H internuclear distance fixed at its equilibrium value in the complex. Subsequent variational calculations of the rovibrational energy levels permits direct comparison with data obtained from equilibrium thermochemical and spectroscopic measurements. Overall accuracy within 2–3% is achieved. Theoretical results are used to examine trends in hydrogen activation, vibrational anharmonicity, and rotational structure along the sequence of four electrostatic complexes covering the range from a relatively floppy van der Waals system (Mn⁺···H₂) to an almost a rigid molecular ion (Cu⁺···H₂)