Analytic Morse/long-range potential energy surfaces and "adiabatic-hindered-rotor" treatment for a symmetric top-linear molecule dimer: A case study of CH3F-H2

An intramolecular vibrationally excited intermolecular potential energy surface and predicted 2OH overtone spectroscopy of H2O-Kr

A new five-dimensional potential energy surface (PES) for H2O-Kr which explicitly includes the intramolecular 2OH overtone state of the H2O monomer is presented. The intermolecular potential energies were evaluated using explicitly correlated coupled cluster theory [CCSD(T)-F12] with a large basis set. Four vibrationally averaged analytical intermolecular PESs for H2O-Kr with H2O molecules in its |00+〉, |02+〉, |02-〉, and |11+〉 states are obtained by fitting to the multi-dimensional Morse/Long-Range potential function form. Each vibrationally averaged PES fitted to 578 points has root-mean-square (RMS) deviations smaller than 0.14 cm-1 and requires only 58 parameters. The combined radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm were employed to calculate the rovibrational energy levels for |00+〉, |02+〉, |02-〉, and |11+〉 states of the H2O-Kr complexes. The calculated |02-〉Πf/e(101) ← |00+〉Σe(000) and |02+〉Πf/e(110) ← |00+〉Σe(101) infrared transitions are in excellent agreement with the experimental values with RMS discrepancies being only 0.007 and 0.016 cm-1, respectively. These analytical PESs can be used to provide reliable theoretical guidance for future infrared overtone spectroscopy of H2O-Kr.

MLRNet: Combining the Physics-Motivated Potential Models with Neural Networks for Intermolecular Potential Energy Surface Construction

A physics-based machine learning model called MLRNet has been developed to construct the high-accuracy two-body intermolecular potential energy surface (IPES). The outputs of the neural network are integrated into the physically realistic Morse/long-range (MLR) function, which ensures that the MLRNet has meaningful extrapolation at both short and long ranges and solves the asymptotic problem in common neural network potential (NNP) models. The neural network representation of the MLR parameters is more flexible and more efficient than the polynomial expansion in the conventional mdMLR model, especially for systems containing nonrigid monomer(s). The present work illustrates the basic framework of the current MLRNet model, including (i) how to combine the physically meaningful MLR function with different possible NN structures, (ii) the preservation of permutation symmetry, and (iii) the predetermination of the long-range function u_LR. We choose two realistic systems to demonstrate the performance of MLRNet: the three-dimensional IPES of CO₂-He including the CO₂ antisymmetric vibration Q₃ and the six-dimensional IPES of the H₂O-Ar system. In both cases, the fitting errors of the MLRNet are several times smaller than those of the conventional mdMLR model. Both short-range and long-range extrapolation tests were performed to illustrate the extrapolation ability of the MLRNet and its damping function version. Moreover, for the 6-D H₂O-Ar system, the MLRNet only needs 1596 trainable parameters, which is almost equal to the number needed for the 5-D mdMLR model (1509) and half that needed for the PIP-NN model (3501) within similar accuracy, which illustrates the model efficiency in high-dimensional IPES fitting.

Neural network interaction potentials for para-hydrogen with flexible molecules

The study of molecular impurities in para-hydrogen ( pH2) clusters is key to push forward our understanding of intra- and intermolecular interactions, including their impact on the superfluid response of this bosonic quantum solvent. This includes tagging with only one or very few pH2, the microsolvation regime for intermediate particle numbers, and matrix isolation with many solvent molecules. However, the fundamental coupling between the bosonic pH2 environment and the (ro-)vibrational motion of molecular impurities remains poorly understood. Quantum simulations can, in principle, provide the necessary atomistic insight, but they require very accurate descriptions of the involved interactions. Here, we present a data-driven approach for the generation of impurity⋯ pH2 interaction potentials based on machine learning techniques, which retain the full flexibility of the dopant species. We employ the well-established adiabatic hindered rotor (AHR) averaging technique to include the impact of the nuclear spin statistics on the symmetry-allowed rotational quantum numbers of pH2. Embedding this averaging procedure within the high-dimensional neural network potential (NNP) framework enables the generation of highly accurate AHR-averaged NNPs at coupled cluster accuracy, namely, explicitly correlated coupled cluster single, double, and scaled perturbative triples, CCSD(T*)-F12a/aVTZcp, in an automated manner. We apply this methodology to the water and protonated water molecules as representative cases for quasi-rigid and highly flexible molecules, respectively, and obtain AHR-averaged NNPs that reliably describe the corresponding H2O⋯ pH2 and H3O+⋯ pH2 interactions. Using path integral simulations, we show for the hydronium cation, H3O+, that umbrella-like tunneling inversion has a strong impact on the first and second pH2 microsolvation shells. The automated and data-driven nature of our protocol opens the door to the study of bosonic pH2 quantum solvation for a wide range of embedded impurities.

Calculating Entropies of Large Molecules in Aqueous Phase

Entropy benchmarking of different sized molecules in aqueous phase is carried out for known solvation models, where we compare geometry and solvation cavity packing parameters, which allows us to improve the accuracy of the obtained entropy values using empirical corrections. A comparison of solvation entropy models is conducted for a benchmarking set of 56 molecules, showing how an accurate description of cavitation entropy and its hindrance on other entropy values is important for large-sized solute molecules. Finally, we compare reaction free energies with entropies calculated using the most accurate solvation model considered, where we demonstrate a significant improvement in the accuracy relative to experimental values.

Vibrational Raman Shifts of Spin Isomer Combinations of Hydrogen Dimers and Isotopologues

Binding energies for para-para, ortho-para, and ortho-ortho hydrogen dimers (H₂)₂ are calculated using the six-dimensional (6D) interaction potential developed by Hinde [ J. Chem. Phys. 2008, 128, 154308]. The eigenstates of the dimers are computed by diagonalization using, as a basis, products of the rovibrational states of the monomers, a radial grid for the distance between the monomers, and spherical harmonics for the end-over-end rotation of the dimer. We describe the overall nuclear spin symmetry and use these properties to determine the relative population of various states, making use of a Boltzmann factor for each spin isomer to assess the effect of temperature. A predicted Raman spectrum in the Q(0) and Q(1) region of the hydrogen dimer is produced. To assess the accuracy of our model, we verify our produced shifts with experimental results obtained previously by Montero et al. [ Eur. Phys. J. D 2009, 52, 31-34] and find good agreement. These results are extended to other cases involving the deuterium (D₂)₂ and tritium dimer (T₂)₂ isotopologues, to predict Raman shifts.

Explicitly correlated ab initio potential energy surface and predicted rovibrational spectra for H2O-N2 and D2O-N2 complexes

An ab initio intermolecular potential energy surface (PES) for the van der Waals complex of H₂O-N₂ that explicitly incorporates the intramolecular Q₂ bending normal mode of the H₂O monomer is presented. The electronic structure computations have been carried out at the explicitly correlated coupled cluster theory [CCSD(T)-F12] with an augmented correlation-consistent triple zeta basis set and an additional bond function. Analytic five-dimensional intermolecular PESs for ν₂(H₂O) = 0 and 1 are obtained by fitting to the multi-dimensional Morse/long-range potential function form. These fits to 40 890 points have the root-mean-square (rms) discrepancy of 0.88 cm^-1 for interaction energies less than 2000.0 cm^-1. The resulting vibrationally averaged PESs provide good representations of the experimental microwave and infrared data: for microwave transitions of H₂O-N₂, the rms discrepancy is only 0.0003 cm^-1, and for infrared transitions of the A₁ symmetry of the H₂O(ν₂ = 1 ← 0)-N₂, the rms discrepancy is 0.001 cm^-1. The calculated infrared band origin shifts associated with the ν₂ bending vibration of water are 2.210 cm^-1 and 1.323 cm^-1 for H₂O-N₂ and D₂O-N₂, respectively, in good agreement with the experimental values of 2.254 cm^-1 and 1.266 cm^-1. The benchmark tests and comparisons of the predicted spectral properties are carried out between CCSD(T)-F12a and CCSD(T)-F12b approaches.

Analytic intermolecular potential energy surface and first-principles prediction of the rotational profiles for a symmetric top ion-atom complex: A case study of H3O+-Ar

We presented the first three-dimensional (3D) ab initio intermolecular potential energy surface (PES) for the H₃O⁺-Ar complex. The electronic structure computations were carried out at the explicitly correlated coupled cluster theory-F12 with an augmented correlation-consistent triple zeta basis set. Analytic 3D PES was obtained by least-squares fitting the multi-dimensional Morse/Long-Range (mdMLR) potential model to interaction energies, where the mdMLR function form was applied to the nonlinear ion-atom case for the first time. The 3D PES fitting to 1708 points has root-mean-square deviations of 0.19 cm^-1 with only 108 parameters for interaction energies less than 500 cm^-1. With the 3D PES of the H₃O⁺-Ar complex, we employed the combined radial discrete variable representation/angular finite basis representation method and Lanczos algorithm to calculate rovibrational energy levels. The rotational profiles of the O-H anti-stretching vibrational bands of v₃ ⁺(S)←0⁺ and v₃ ^-(A)←0^- for the H₃O⁺-Ar complex were predicted and were in good agreement with the experimental results.

Full quantum calculation of the rovibrational states and intensities for a symmetric top-linear molecule dimer: Hamiltonian, basis set, and matrix elements

The rovibrational energy levels and intensities of the CH₃F-H₂ dimer have been obtained using our recent global intermolecular potential energy surface [X.-L. Zhang et al., J. Chem. Phys. 148, 124302 (2018)]. The Hamiltonian, basis set, and matrix elements are derived and given for a symmetric top-linear molecule complex. This approach to the generation of energy levels and wavefunctions can readily be utilized for studying the rovibrational spectra of other van der Waals complexes composed of a symmetric top molecule and a linear molecule, and may readily be extended to other complexes of nonlinear molecules and linear molecules. To confirm our method, the rovibrational levels of the H₂O-H₂ dimer have been computed and shown to be in good agreement with experiment and with previous theoretical results. The rovibrational Schrödinger equation has been solved using a Lanczos algorithm together with an uncoupled product basis set. As expected, dimers containing ortho-H₂ are more strongly bound than dimers containing para-H₂. Energies and wavefunctions of the discrete rovibrational levels of CH₃F-paraH₂ complexes obtained from the direct vibrationally averaged 5-dimensional potentials are in good agreement with the results of the reduced 3-dimensional adiabatic-hindered-rotor (AHR) approximation. Accurate calculations of the transition line strengths for the orthoCH₃F-paraH₂ complex are also carried out, and are consistent with results obtained using the AHR approximation. The microwave spectrum associated with the orthoCH₃F-orthoH₂ dimer has been predicted for the first time.