arXiv subjects

Apurba Nandi

Publications and source records attributed to Apurba Nandi.

18 recordsLinked to original sources

arXiv2026

VPT2 Calculations of Vibrational Energies of CH3COOC6H4COOH Done in Seconds on a Laptop Using a Machine Learned Potential

The determination of quartic force fields for use in vibrational second-order perturbation (VPT2) calculations, currently available in numerous electronic structure packages, becomes very expensive as the size of the molecule increases, especially if high-level coupled cluster theory is used. Machine-learned potentials (MLPs) for large molecules and clusters offer a viable alternative to obtain the quartic force field (QFF). Here, we report Fortran and Python software to determine the QFF and perform VPT2 calculations of energies from MLPs. We describe this software briefly and then apply it to \ce{H2O} and protonated oxalate as test cases. The Fortran software is applied to 21-atom aspirin, using a fast MLP reported by us. Despite the fact that there are 32,509 unique cubic force constants for aspirin, the computer time to calculate them using this MLP is trivial, i.e., around one minute. These results are the first quantum anharmonic ones for such a large molecule. The present protocol offers an efficient way to study quantum anharmonic effects for vibrational energies in large molecules. Currently, these are obtained overwhelmingly from classical molecular dynamics simulations, which cannot describe strong anharmonicity.

physics.chem-ph↗

arXiv2026

Fidelity of Machine Learned Potentials: Quantitative Assessment for Protonated Oxalate

There has been a veritable explosion of methods and software to perform machine-learned regression on datasets of electronic energies and forces to develop high-dimensional machine learned potential energy surfaces (ML-PESs). A major, but not deeply-studied aspect is how well different ML-PESs represent the same dataset on which they are trained, beyond the standard fitting precision metrics. Here, this is examined in detail using several ''stress tests'', for two widely applied machine-learned potential approaches. One is based on permutationally invariant polynomial (PIP) linear least square regression and the other is the message-passing neural network PhysNet approach. These potentials and dipole moment surfaces are used in VSCF/VCI calculations of vibrational energies and wavefunctions. The energies from the two PESs are directly compared as are the IR spectra. In addition, tunneling splittings for the hydrogen transfer between two equivalent structures are reported from using three methods: ring polymer instanton theory, diffusion Monte Carlo simulations, and the $Q_{im}$ path method. These calculations require the evaluation of on the order of one billion energies that are widely dispersed in the 15-dimensional configurational space. The two PESs yield results for these quantities in excellent agreement with each other.

physics.chem-ph↗

arXiv2025

"Gold-Standard" $\Delta$-Machine Learned and Transferable Potential for Linear Alkanes

The conformational properties of linear alkanes, C$_n$H$_{2n+2}$, have been of intense interest for many years. Experiments and corresponding electronic structure calculations were first reported in the mid-2000s and continue to the present time. These focus on the minimum chain length where the transition from the linear minimum to the hairpin minimum occurs. We recently reported a transferable many-body permutationally invariant polynomial (MB-PIP) for linear alkanes using B3LYP electronic energies, which do not account for dispersion. Here we report a $\Delta$-ML approach to elevate this B3LYP-based and new PBE0+MBD MB-PIP potentials using PNO-LCCSD(T)-F12 energies. The new $\Delta$-corrected potentials predict the difference in these minima accurately, compared to benchmark CCSD(T) results, over the range C$_{12}$H$_{28}$ to C$_{28}$H$_{58}$. Vibrational power spectra are also reported for C$_{14}$H$_{30}$ and C$_{30}$H$_{62}$ using the uncorrected and $\Delta$-ML B3LYP. These new PIP-MB potentials for linear alkanes are the most accurate ones currently available and can be used in studies of properties of linear alkanes.

physics.chem-ph↗

arXiv2025

The quantum nature of ubiquitous vibrational features revealed for ethylene glycol

Vibrational properties of molecules are of widespread interest and importance in chemistry and biochemistry. The reliability of widely employed approximate computational methods is questioned here against the complex experimental spectrum of ethylene glycol. Comparisons between quantum vibrational self-consistent field and virtual-state configuration interaction (VSCF/VCI), adiabatically switched semiclassical initial value representation (AS SCIVR), and thermostatted ring polymer molecular dynamics (TRPMD) calculations are made using a full-dimensional machine-learned potential energy surface. Calculations are done for five low-lying conformers and compared with the experiment, with a focus on the high-frequency, OH-stretches, and CH-stretches, part of the spectrum. Fermi resonances are found in the analysis of VSCF/VCI eigenstates belonging to the CH-stretching band. Results of comparable accuracy, quality, and level of detail are obtained by means of AS SCIVR. The current VSCF/VCI and AS-SCIVR power spectra largely close the gaps between the experiment and TRPMD and classical MD calculations. Analysis of these results provide guidance on what level of accuracy to expect from TRPMD and classical MD calculations of the vibrational spectra for ubiquitous CH and OH-stretches bands. This work shows that even general vibrational features require a proper quantum treatment usually not achievable by the most popular theoretical approaches.

physics.chem-ph↗

arXiv2024

Extending the atomic decomposition and many-body representation, a chemistry-motivated monomer-centered approach for machine learning potentials

Most widely used machine learned (ML) potentials for condensed phase applications rely on many-body permutationally invariant polynomial (PIP) or atom-centered neural networks (NN). However, these approaches often lack chemical interpretability in atomistic energy decomposition and the computational efficiency of traditional force fields has not been fully achieved. Here, we present a novel method that combines aspects of both approaches, and achieves state-of-the-art balance of accuracy and force field-level speed. This method utilizes a monomer-centered representation, where the potential energy is decomposed into the sum of chemically meaningful monomeric energies. Without sophisticated neural network design, the structural descriptors of monomers are described by 1-body and 2-body effective interactions, enforced by appropriate sets of PIPs as inputs to the feed forward NN. We demonstrate the performance of this method through systematic assessments of models for gas-phase water trimer, liquid water, and also liquid CO2. The high accuracy, fast speed, and flexibility of this method provide a new route for constructing accurate ML potentials and enabling large-scale quantum and classical simulations for complex molecular systems.

physics.chem-ph↗

arXiv2024

$\Delta$-Machine Learning to Elevate DFT-based Potentials and a Force Field to the CCSD(T) Level Illustrated for Ethanol

Progress in machine learning has facilitated the development of potentials that offer both the accuracy of first-principles techniques and vast increases in the speed of evaluation. Recently,"$\Delta$-machine learning" has been used to elevate the quality of a potential energy surface (PES) based on low-level, e.g., density functional theory (DFT) energies and gradients to close to the gold-standard coupled cluster level of accuracy. We have demonstrated the success of this approach for molecules, ranging in size from H$_3$O$^+$ to 15-atom acetyl-acetone and tropolone. These were all done using the B3LYP functional. Here we investigate the generality of this approach for the PBE, M06, M06-2X, and PBE0+MBD functionals, using ethanol as the example molecule. Linear regression with permutationally invariant polynomials is used to fit both low-level and correction PESs. These PESs are employed for standard RMSE analysis for training and test datasets, and then general fidelity tests such as energetics of stationary points, normal mode frequencies, and torsional potentials are examined. We achieve similar improvements in all cases. Interestingly, we obtained significant improvement over DFT gradients where coupled cluster gradients were not used to correct the low-level PES. Finally, we present some results for correcting a recent molecular mechanics force field for ethanol and comment on the possible generality of this approach.

physics.chem-ph↗

arXiv2024

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 (PES) 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 the diffusion Monte Carlo simulations.

physics.chem-ph↗

arXiv2024

No Headache for PIPs: A PIP Potential for Aspirin Outperforms Other Machine-Learned Potentials

Assessments of machine-learned (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) MD17 dataset. We demonstrated that the PIP approach outperformed numerous other methods, e.g., ANI, PhysNet, sGDML, 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 dataset. 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. Overall, we show that the PIPs approach outperforms other ML methods, including sGDML, ANI, GAP, PhysNet, and ACE, as reported by Kov\'acs $et$ $al.$ in $J. Chem. Theory$ $Comput.$ 2021, 17, 7696-7711.

physics.chem-ph↗

arXiv2022

A Machine Learning Approach for Rate Constants III: Application to the Cl($^2$P) + CH$_4$ $\rightarrow$ CH$_3$ + HCl Reaction

The temperature dependence of the thermal rate constant for the reaction Cl($^2$P) + CH$_4$ $\rightarrow$ CH$_3$ + HCl is calculated using a Gaussian Process machine learning (ML) approach to train on and predict thermal rate constants over a large temperature range. Following procedures developed in two previous reports, we use a training dataset of approximately 40 reaction/potential surface combinations, each of which is used to calculate the corresponding data base of rate constant at approximately eight temperatures. For the current application, we train on the entire dataset and then predict the temperature dependence of the title reaction employing a "split" dataset for correction at low and high temperatures to capture both tunneling and recrossing. The results are an improvement on recent RPMD calculations compared to accurate quantum ones, using the same high-level ab initio potential energy surface. Both tunneling at low temperatures and recrossing at high temperatures are observed to influence the rate constants. Recrossing effects, which are not described by TST and even sophisticated tunneling corrections, do appear in experiment at temperatures above around 600 K. The ML results describe these effects and in fact, merge at 600 K with RPMD results (which can describe recrossing), and both are close to experiment at the highest experimental temperatures.

physics.chem-ph↗

arXiv2022

A $\Delta$-Machine Learning Approach for Force Fields, Illustrated by a CCSD(T) 4-body Correction to the MB-pol Water Potential

$\Delta$-Machine Learning ($\Delta$-ML) has been shown to effectively and efficiently bring a low-level ML potential energy surface to CCSD(T) quality. Here we propose extending this approach to general force fields, which implicitly or explicitly contain many-body effects. After describing this general approach, we illustrate it for the MB-pol water potential which contains CCSD(T) 2-body and 3-body interactions but relies on the TTM4-F 4-body and higher body interactions. The 4-body MB-pol (TTM4-F) interaction fails at a very short range and for the water hexamer errors up to 0.84 kcal/mol are seen for some isomers, owing mainly to 4-body errors. We apply $\Delta$-ML for the 4-body interaction, using a recent dataset of CCSD(T) 4-body energies that we used to develop a new water potential, q-AQUA. This 4-body correction is shown to improve the accuracy of the MB-pol potential for the relative energies of 8 isomers of the water hexamer as well as the harmonic frequencies. The new potential is robust in the very short range and so should be reliable for simulations at high pressure and/or high temperature.

physics.chem-ph↗

arXiv2022

Quantum calculations on a new CCSD(T) machine-learned PES reveal the leaky nature of gas-phase $trans$ and $gauche$ ethanol conformers

Ethanol is a molecule of fundamental interest in combustion, astrochemistry, and condensed phase as a solvent. It is characterized by two methyl rotors and $trans$ ($anti$) and $gauche$ conformers, which are known to be very close in energy. Here we show that based on rigorous quantum calculations of the vibrational zero-point state, using a new ab initio potential energy surface (PES), the ground state resembles the $trans$ conformer but substantial delocalization to the $gauche$ conformer is present. This explains experimental issues about the identification and isolation of the two conformers. This "leak" effect is partially quenched when deuterating the OH group, which further demonstrates the need for a quantum mechanical approach. Diffusion Monte Carlo (DMC) and full-dimensional semiclassical dynamics calculations are employed. The new PES is obtained by means of a $\Delta$-Machine learning approach starting from a pre-existing low level (LL) density functional theory (DFT) surface. This surface is brought to the CCSD(T) level of theory using a relatively small number of $ab$ $initio$ CCSD(T) energies. Agreement between the corrected PES and direct $ab$ $initio$ results for standard fidelity tests is excellent. One- and two-dimensional discrete variable representation calculations focusing on the $trans$-$gauche$ torsional motion are also reported, in reasonable agreement with the experiment.

physics.chem-ph↗

arXiv2022

The MD17 Datasets from the Perspective of Datasets for Gas-Phase "Small" Molecule Potentials

There has been great progress in developing methods for machine-learned potential energy surfaces. There have also been important assessments of these methods by comparing so-called learning curves on datasets of electronic energies and forces, notably the MD17 database. The dataset for each molecule in this database generally consists of tens of thousands of energies and forces obtained from DFT direct dynamics at 500 K. We contrast the datasets from this database for three "small" molecules, ethanol, malonaldehyde, and glycine, with datasets we have generated with specific targets for the PESs in mind: a rigorous calculation of the zero-point energy and wavefunction, the tunneling splitting in malonaldehyde and in the case of glycine a description of all eight low-lying conformers. We found that the MD17 datasets are too limited for these targets. We also examine recent datasets for several PESs that describe small-molecule but complex chemical reactions. Finally, we introduce a new database, "QM-22", which contains datasets of molecules ranging from 4 to 15 atoms that extend to high energies and a large span of configurations.

physics.chem-ph↗

arXiv2022

q-AQUA: a many-body CCSD(T) water potential, including 4-body interactions, demonstrates the quantum nature of water from clusters to the liquid phase

Many model potential energy surfaces (PESs) have been reported for water; however, none are strictly from "first principles". Here we report such a potential, based on a many-body representation at the CCSD(T) level of theory up to the ultimate 4-body interaction. The new PES is benchmarked for the isomers of the water hexamer for dissociation energies, harmonic frequencies, and unrestricted diffusion Monte Carlo (DMC) calculations of the zero-point energies of the Prism, Book, and Cage isomers. Dissociation energies of several isomers of the 20-mer agree well with recent benchmark energies. Exploratory DMC calculations on this cluster verify the robustness of the new PES for quantum simulations. The accuracy and speed of the new PES are demonstrated for standard condensed phase properties, i.e., the radial distribution function and the self-diffusion constant. Quantum effects are shown to be substantial for these observables and also needed to bring theory into an excellent agreement with experiment.

physics.chem-ph↗

arXiv2021

Permutationally invariant polynomial regression for energies and gradients, using reverse differentiation, achieves orders of magnitude speed-up with high precision compared to other machine learning methods

Permutationally invariant polynomial (PIP) regression has been used to obtain machine-learned (ML) potential energy surfaces, including analytical gradients, for many molecules and chemical reactions. Recently, the approach has been extended to moderate size molecules and applied to systems up to 15 atoms. The algorithm, including "purification of the basis", is computationally efficient for energies; however, we found that the recent extension to obtain analytical gradients, despite being a remarkable advance over previous methods, could be further improved. Here we report developments to compact further a purified basis and, more significantly, to use the reverse gradient approach to greatly speed up gradient evaluation. We demonstrate this for our recent 4-body water interaction potential. Comparisons of training and testing precision on the MD17 database of energies and gradients (forces) for ethanol against GP-SOAP, ANI, sGDML, PhysNet, pKREG, KRR, and other methods, which were recently assessed by Dral and co-workers, are given. The PIP fits are as precise as those using these methods, but the PIP computation time for energy and force evaluation is shown to be 10 to 1000 times faster. Finally, a new PIP PES is reported for ethanol based on a more extensive dataset of energies and gradients than in the MD17 database. Diffusion Monte Carlo calculations which fail on MD17-based PESs are successful using the new PES.

physics.chem-ph↗

arXiv2021

Enabling rapid and accurate construction of CCSD(T)-level potential energy surface of large molecules using molecular tailoring approach

The construction of the potential energy surface (PES) of even a medium-sized molecule employing correlated theory, such as CCSD(T), is an arduous task due to the high computational cost. In this Letter, we report the possibility of efficient construction of such a PES employing the molecular tailoring approach (MTA) on off-the-shelf hardware. The full calculation (FC) as well as MTA energies at CCSD(T)/aug-cc-pVTZ level for three test molecules, viz. acetylacetone, N-methyacetamide, and tropolone are reported. All the MTA energies are in excellent agreement with their FC counterparts (typical error being sub-millihartree) with a time advantage factor of 3 to 5. The energy barrier from the ground- to transition-state is accurately captured. Further, the accuracy and efficiency of the MTA method for estimating energy gradients at CCSD(T) level are demonstrated. This work brings out the possibility of the construction of PES for large molecules using MTA with the computational economy at a high level of theory and/or basis set.

physics.chem-ph↗

arXiv2021

A CCSD(T)-based permutationally invariant polynomial 4-body potential for water

We report a permutationally invariant polynomial (PIP) potential energy surface for the water 4-body interaction. This 12-atom PES is a fit to 2119, symmetry-unique, CCSD(T)-F12a/haTZ (aug-cc-pVTZ basis for 'O' atom and cc-pVTZ basis for 'H' atom) 4-b interaction energies. These come from low-level, direct-dynamics calculations, tetramer fragments from an MD water simulation at 300 K, and from the water hexamer, heptamer, decamer, and 13-mer clusters. The PIP basis is purified to ensure that the 4-b potential goes rigorously to zero in monomer+trimer and dimer+dimer dissociations for all possible such fragments. The 4-b energies of isomers of the hexamer calculated with the new surface are shown to be in better agreement with benchmark CCSD(T) results than those from the MB-pol potential. Other tests validate the high-fidelity of the PES.

physics.chem-ph↗

arXiv2021

Breaking the Coupled Cluster Barrier for Machine Learned Potentials of Large Molecules: The Case of 15-atom Acetylacetone

Machine-learned potential energy surfaces (PESs) for molecules with more than 10 atoms are typically forced to use lower-level electronic structure methods such as density functional theory and second-order Moller-Plesset perturbation theory (MP2). While these are efficient and realistic, they fall short of the accuracy of the ``gold standard'' coupled-cluster method, especially with respect to reaction and isomerization barriers. We report a major step forward in applying a $\Delta$-machine learning method to the challenging case of acetylacetone, whose MP2 barrier height for H-atom transfer is low by roughly 1.5 kcal/mol relative to the benchmark CCSD(T) barrier of 3.2 kcal/mol. From a database of 2151 local CCSD(T) energies, and training with as few as 430 energies, we obtain a new PES with a barrier of 3.49 kcal/mol in agreement with the LCCSD(T) one of 3.54 kcal/mol and close to the benchmark value. Tunneling splittings due to H-atom transfer are calculated using this new PES, providing improved estimates over previous ones obtained using an MP2-based PES.

physics.chem-ph↗

arXiv2020

$\Delta$-Machine Learning for Potential Energy Surfaces: A PIP approach to bring a DFT-based PES to CCSD(T) Level of Theory

``$\Delta$-machine learning" refers to a machine learning approach to bring a property such as a potential energy surface (PES) based on low-level (LL) density functional theory (DFT) energies and gradients to close to a coupled cluster (CC) level of accuracy. Here we present such an approach that uses the permutationally invariant polynomial (PIP) method to fit high-dimensional PESs. The approach is represented by a simple equation, in obvious notation $V_{LL{\rightarrow}CC}=V_{LL}+\Delta{V_{CC-LL}}$, and demonstrated for \ce{CH4}, \ce{H3O+}, and $trans$ and $cis$-$N$-methyl acetamide (NMA), \ce{CH3CONHCH3}. For these molecules, the LL PES, $V_{LL}$, is a PIP fit to DFT/B3LYP/6-31+G(d) energies and gradients, and $\Delta{V_{CC-LL}}$ is a precise PIP fit obtained using a low-order PIP basis set and based on a relatively small number of CCSD(T) energies. For \ce{CH4} these are new calculations adopting an aug-cc-pVDZ basis, for \ce{H3O+} previous CCSD(T)-F12/aug-cc-pVQZ energies are used, while for NMA new CCSD(T)-F12/aug-cc-pVDZ calculations are performed. With as few as 200 CCSD(T) energies, the new PESs are in excellent agreement with benchmark CCSD(T) results for the small molecules, and for 12-atom NMA training is done with 4696 CCSD(T) energies.

physics.chem-ph↗