PESPIP: Software to fit complex molecular and many-body potential energy surfaces with permutationally invariant polynomials

Quantum Monte Carlo Simulations of the Vibrational Wavefunction of the Aromatic Cyclo[10]carbon Using a Full Dimensional Permutationally Invariant Potential Energy Surface

New experimental measurements [Sun et al., Nature 2023, 623, 972] of the cyclic C10 reveal a cumulenic pentagon-like D5h structure at ∼5 K. However, the long-standing presumption that a large zero-point vibrational energy combined with an extremely flat D5h ↔ D10h ↔ D5h isomerization pathway washes out the pentagonal D5h structure and yields a symmetric D10h decagon remains at odds with the experiment. We resolve this issue with our fitting approach based on a bond-order charge-density matrix expressed in permutationally invariant polynomials. We train the model on τHCTH/cc-pVQZ data morphed to reproduce a relativistic all-electron CCSDT(Q)/CBS D5h-D10h potential energy barrier (benchmarked previously by others). Large scale diffusion Monte Carlo simulations in full dimensionality show that the vibrational ground state of C10 has compositional character of more than 96% D5h, fully reflecting the experimental imaging data. Quantum mechanical variational calculations in 1-D further suggest persistence of the D5h symmetry structure at higher temperatures.

Assessing Permutationally Invariant Polynomial and Symmetric Gradient Domain Machine Learning Potential Energy Surfaces for H3O2. J Phys Chem A 2024;128:3212-3219. [PMID: 38624168 PMCID: PMC11056970 DOI: 10.1021/acs.jpca.4c01044] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

The singly hydrated hydroxide anion OH-(H2O) is of central importance to a detailed molecular understanding of water; therefore, there is strong motivation to develop a highly accurate potential to describe this anion. While this is a small molecule, it is necessary to have an extensive data set of energies and, if possible, forces to span several important stationary points. Here, we assess two machine-learned potentials, one using the symmetric gradient domain machine learning (sGDML) method and one based on permutationally invariant polynomials (PIPs). These are successors to a PIP potential energy surface (PES) reported in 2004. We describe the details of both fitting methods and then compare the two PESs with respect to precision, properties, and speed of evaluation. While the precision of the potentials is similar, the PIP PES is much faster to evaluate for energies and energies plus gradient than the sGDML one. Diffusion Monte Carlo calculations of the ground vibrational state, using both potentials, produce similar large anharmonic downshift of the zero-point energy compared to the harmonic approximation of the PIP and sGDML potentials. The computational time for these calculations using the sGDML PES is roughly 300 times greater than using the PIP one.

Tell Machine Learning Potentials What They Are Needed For: Simulation-Oriented Training Exemplified for Glycine

Machine learning potentials (MLPs) are widely applied as an efficient alternative way to represent potential energy surfaces (PESs) in many chemical simulations. The MLPs are often evaluated with the root-mean-square errors on the test set drawn from the same distribution as the training data. Here, we systematically investigate the relationship between such test errors and the simulation accuracy with MLPs on an example of a full-dimensional, global PES for the glycine amino acid. Our results show that the errors in the test set do not unambiguously reflect the MLP performance in different simulation tasks, such as relative conformer energies, barriers, vibrational levels, and zero-point vibrational energies. We also offer an easily accessible solution for improving the MLP quality in a simulation-oriented manner, yielding the most precise relative conformer energies and barriers. This solution also passed the stringent test by diffusion Monte Carlo simulations.

No Headache for PIPs: A PIP Potential for Aspirin Runs Much Faster and with Similar Precision Than Other Machine-Learned Potentials

Assessments of machine-learning (ML) potentials are an important aspect of the rapid development of this field. We recently reported an assessment of the linear-regression permutationally invariant polynomial (PIP) method for ethanol, using the widely used (revised) rMD17 data set. We demonstrated that the PIP approach outperformed numerous other methods, e.g., ANI, PhysNet, sGDML, and p-KRR, with respect to precision and notably with respect to speed [Houston et al., J. Chem. Phys. 2022, 156, 044120]. Here, we extend this assessment to the 21-atom aspirin molecule, using the rMD17 data set, with a focus on the speed of evaluation. Both energies and forces are used for training, and the precision of several PIPs is examined for both. Normal mode frequencies, the methyl torsional potential, and 1d vibrational energies for an OH stretch are presented. We show that the PIP approach achieves the level of precision obtained from other ML methods, e.g., atom-centered neural network methods, linear regression ACE, and kernel methods, as reported by Kovács et al. in J. Chem. Theory Comput. 2021, 17, 7696-7711. More significantly, we show that the PIP PESs run much faster than all other ML methods, whose timings were evaluated in that paper. We also show that the PIP PES extrapolates well enough to describe several internal motions of aspirin, including an OH stretch.

Formic Acid-Ammonia Heterodimer: A New Δ-Machine Learning CCSD(T)-Level Potential Energy Surface Allows Investigation of the Double Proton Transfer

The formic acid-ammonia dimer is an important example of a hydrogen-bonded complex in which a double proton transfer can occur. Its microwave spectrum has recently been reported and rotational constants and quadrupole coupling constants were determined. Calculated estimates of the double-well barrier and the internal barriers to rotation were also reported. Here, we report a full-dimensional potential energy surface (PES) for this complex, using two closely related Δ-machine learning methods to bring it to the CCSD(T) level of accuracy. The PES dissociates smoothly and accurately. Using a 2d quantum model the ground vibrational-state tunneling splitting is estimated to be less than 10-4 cm-1. The dipole moment along the intrinsic reaction coordinate is calculated along with a Mullikan charge analysis and supports the mildly ionic character of the minimum and strongly ionic character at the double-well barrier.

MLatom 3: A Platform for Machine Learning-Enhanced Computational Chemistry Simulations and Workflows

Machine learning (ML) is increasingly becoming a common tool in computational chemistry. At the same time, the rapid development of ML methods requires a flexible software framework for designing custom workflows. MLatom 3 is a program package designed to leverage the power of ML to enhance typical computational chemistry simulations and to create complex workflows. This open-source package provides plenty of choice to the users who can run simulations with the command-line options, input files, or with scripts using MLatom as a Python package, both on their computers and on the online XACS cloud computing service at XACScloud.com. Computational chemists can calculate energies and thermochemical properties, optimize geometries, run molecular and quantum dynamics, and simulate (ro)vibrational, one-photon UV/vis absorption, and two-photon absorption spectra with ML, quantum mechanical, and combined models. The users can choose from an extensive library of methods containing pretrained ML models and quantum mechanical approximations such as AIQM1 approaching coupled-cluster accuracy. The developers can build their own models using various ML algorithms. The great flexibility of MLatom is largely due to the extensive use of the interfaces to many state-of-the-art software packages and libraries.

Ab Initio Potential Energy Surface for NaCl-H2 with Correct Long-Range Behavior

We report a full dimensional ab initio potential energy surface for NaCl-H2 based on precise fitting of a large data set of CCSD(T)/aug-cc-pVTZ energies. A major goal of this fit is to describe the very long-range interaction accurately. This is done in this instance via the dipole-quadrupole interaction. The NaCl dipole and the H2 quadrupole are available through previous works over a large range of internuclear distances. We use these to obtain exact effect charges on each atom. Diffusion Monte Carlo calculations are done for the ground vibrational state using the new potential.

Accurate fundamental invariant-neural network representation of ab initio potential energy surfaces

Highly accurate potential energy surfaces are critically important for chemical reaction dynamics. The large number of degrees of freedom and the intricate symmetry adaption pose a big challenge to accurately representing potential energy surfaces (PESs) for polyatomic reactions. Recently, our group has made substantial progress in this direction by developing the fundamental invariant-neural network (FI-NN) approach. Here, we review these advances, demonstrating that the FI-NN approach can represent highly accurate, global, full-dimensional PESs for reactive systems with even more than 10 atoms. These multi-channel reactions typically involve many intermediates, transition states, and products. The complexity and ruggedness of this potential energy landscape present even greater challenges for full-dimensional PES representation. These PESs exhibit a high level of complexity, molecular size, and accuracy of fit. Dynamics simulations based on these PESs have unveiled intriguing and novel reaction mechanisms, providing deep insights into the intricate dynamics involved in combustion, atmospheric, and organic chemistry.

ChemPotPy: A Python Library for Analytic Representations of Potential Energy Surfaces and Diabatic Potential Energy Matrices

Constructing analytic representations of global and semiglobal potential energy surfaces is difficult and can be laborious, and it is even harder when one needs coupled potential energy surfaces and their electronically nonadiabatic couplings. When accomplished, however, the resulting potential functions are a valuable resource. To facilitate the convenient use of potentials that have been developed, we provide a collection of existing surfaces in a library with consistent units and formats. A potential energy surface library of this type, namely PotLib, was built more than 20 years ago. However, that library only provided pristine Fortran subroutines for each potential energy surface, and therefore, it is not as user-friendly as would be desirable. Here, we report the creation of ChemPotPy, a CHEMical library of POTential energy surfaces in PYthon. ChemPotPy is a user-friendly library for analytic representation of single-state and multistate potential energy surfaces and couplings. A given entry in the library contains an analytic potential energy function or analytic functions for a set of coupled potential energy surfaces, and depending on the case, it may also include analytic or numerical gradients, nonadiabatic coupling vectors, and/or diabatic potential energy matrices and their gradients. Only three inputs, namely, the chemical formula of the system, the name of the potential energy surface or surface set, and the Cartesian geometry, are required. ChemPotPy uses the same units for input and output quantities of all surfaces and surface sets to facilitate general interfaces with the dynamics programs. The initial version of the library contains 338 entries, and we anticipate that more will be added in the future.

Fitting Potential Energy Surfaces by Learning the Charge Density Matrix with Permutationally Invariant Polynomials

The electronic energy in the Hartree-Fock (HF) theory is the trace of the product of the charge density matrix (CDM) with the one-electron and two-electron matrices represented in an atomic orbital basis, where the two-electron matrix is also a function of the same CDM. In this work, we examine a formalism of analytic representation of a generic molecular potential energy surface (PES) as a sum of a linearly parameterized HF and a correction term, the latter formally representing the electron correlation energy, also linearly parameterized, by expressing the elements of CDM using permutationally invariant polynomials (PIPs). We show on a variety of numerical examples, ranging from exemplary two-electron systems HeH+ and H3+ to the more challenging cases of methanium (CH5+) fragmentation and high-energy tautomerization of formamide to formimidic acid that such a formulation requires significantly fewer, 10-20% of PIPs, to accomplish the same accuracy of the fit as the conventional representation at practically the same computational cost.

Manipulating hydrogen bond dissociation rates and mechanisms in water dimer through vibrational strong coupling

The vibrational strong coupling (VSC) between molecular vibrations and cavity photon modes has recently emerged as a promising tool for influencing chemical reactivities. Despite numerous experimental and theoretical efforts, the underlying mechanism of VSC effects remains elusive. In this study, we combine state-of-art quantum cavity vibrational self-consistent field/configuration interaction theory (cav-VSCF/VCI), quasi-classical trajectory method, along with the quantum-chemical CCSD(T)-level machine learning potential, to simulate the hydrogen bond dissociation dynamics of water dimer under VSC. We observe that manipulating the light-matter coupling strength and cavity frequencies can either inhibit or accelerate the dissociation rate. Furthermore, we discover that the cavity surprisingly modifies the vibrational dissociation channels, with a pathway involving both water fragments in their ground vibrational states becoming the major channel, which is a minor one when the water dimer is outside the cavity. We elucidate the mechanisms behind these effects by investigating the critical role of the optical cavity in modifying the intramolecular and intermolecular coupling patterns. While our work focuses on single water dimer system, it provides direct and statistically significant evidence of VSC effects on molecular reaction dynamics.