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Permutation invariant polynomial neural network approach to fitting potential energy surfaces. IV. Coupled diabatic potential energy matrices
A machine learning method is proposed for representing the elements of diabatic potential energy matrices (PEMs) with high fidelity. This is an extension of the so-called permutation invariant polynomial-neural network (PIP-NN) method for representing adiabatic potential energy surfaces. While for one-dimensional irreducible representations the diagonal elements of a diabatic PEM are invariant under exchange of identical nuclei in a molecular system, the off-diagonal elements require special symmetry consideration, particularly in the presence of a conical intersection. A multiplicative factor is introduced to take into consideration the particular symmetry properties while maintaining the PIP-NN framework. Here, we demonstrate here that the extended PIP-NN approach is accurate in representing diabatic PEMs, as evidenced by small fitting errors and by the reproduction of absorption spectra and product branching ratios in both H 2 O$(\tilde{X} / \tilde{B})$ and NH 3 $(\tilde{X} $/Ã) non-adiabatic photodissociation.
A generalized force-modified potential energy surface for mechanochemical simulations
We describe the modifications that a spatially varying external load produces on a Born-Oppenheimer potential energy surface (PES) by calculating static quantities of interest. The effects of the external loads are exemplified using electronic structure calculations (at the HF/6-31G{sup ∗∗} level) of two different molecules: ethane and hexahydro-1,3,5-trinitro-s-triazine (RDX). The calculated transition states and Hessian matrices of stationary points show that spatially varying external loads shift the stationary points and modify the curvature of the PES, thereby affecting the harmonic transition rates by altering both the energy barrier as well as the prefactor. The harmonic spectra of both molecules are blueshifted with increasing compressive “pressure.” Some stationary points on the RDX-PES disappear under application of the external load, indicating the merging of an energy minimum with a saddle point.
A permutationally invariant full-dimensional ab initio potential energy surface for the abstraction and exchange channels of the H + CH{sub 4} system
We report a permutationally invariant global potential energy surface (PES) for the H + CH{sub 4} system based on ∼63 000 data points calculated at a high ab initio level (UCCSD(T)-F12a/AVTZ) using the recently proposed permutation invariant polynomial-neural network method. The small fitting error (5.1 meV) indicates a faithful representation of the ab initio points over a large configuration space. The rate coefficients calculated on the PES using tunneling corrected transition-state theory and quasi-classical trajectory are found to agree well with the available experimental and previous quantum dynamical results. The calculated total reaction probabilities (J{sub tot} = 0) including the abstraction and exchange channels using the new potential by a reduced dimensional quantum dynamic method are essentially the same as those on the Xu-Chen-Zhang PES [Chin. J. Chem. Phys. 27, 373 (2014)].
Imaging a multidimensional multichannel potential energy surface: Photodetachment of H{sup −}(NH{sub 3}) and NH{sub 4}{sup −}
Probes of the Born-Oppenheimer potential energy surfaces governing polyatomic molecules often rely on spectroscopy for the bound regions or collision experiments in the continuum. A combined spectroscopic and half-collision approach to image nuclear dynamics in a multidimensional and multichannel system is reported here. The Rydberg radical NH{sub 4} and the double Rydberg anion NH{sub 4}{sup −} represent a polyatomic system for benchmarking electronic structure and nine-dimensional quantum dynamics calculations. Photodetachment of the H{sup −}(NH{sub 3}) ion-dipole complex and the NH{sub 4}{sup −} DRA probes different regions on the neutral NH{sub 4} PES. Photoelectron energy and angular distributions at photon energies of 1.17, 1.60, and 2.33 eV compare well with quantum dynamics. Photoelectron-photofragment coincidence experiments indicate dissociation of the nascent NH{sub 4} Rydberg radical occurs to H + NH{sub 3} with a peak kinetic energy of 0.13 eV, showing the ground state of NH{sub 4} to be unstable, decaying by tunneling-induced dissociation on a time scale beyond the present scope of multidimensional quantum dynamics.
New XDM-corrected potential energy surfaces for Ar–NO(X{sup 2}Π): A comparison with CCSD(T) calculations and experiments
We report new potential energy surfaces for the ground state Ar–NO(X{sup 2}Π) van der Waals system calculated using the unrestricted Hartree-Fock (UHF) method with the addition of the Becke-Roussel correlation functional and exchange-hole dipole moment dispersion correction (XDM). We compare UHFBR-XDM surfaces and those previously reported by Alexander from coupled cluster CCSD(T) calculations [J. Chem. Phys. 111, 7426 (1999)]. The bound states of Ar–NO have been investigated with these new UHFBR-XDM surfaces, including relative energy-level spacing, adiabatic bender states and wave functions, and spectroscopic data. These results have been found to be in good agreement with calculations based on the CCSD(T) PESs. These new PESs are used to investigate the inelastic scattering of NO(X) by Ar. Full close-coupling integral cross sections at collision energies of 442 cm{sup −1}, 1774 cm{sup −1} and differential cross sections at collision energy of 530 cm{sup −1} were determined for transitions out of the lowest NO(X) rotational level (j = ω = 1/2,f). These cross sections are in good agreement with those calculated with CCSD(T) and accordingly in good agreement with the most recent initial and final state resolved experimental data. The UHFBR-XDM scheme yields high-quality potential surfaces with computational cost comparable to the Hartree-Fock method and our results may serve as a benchmark for application of this scheme to collisions between larger molecules.
Direct molecular simulation of nitrogen dissociation based on an ab initio potential energy surface
Not Available
Toward spectroscopically accurate global ab initio potential energy surface for the acetylene-vinylidene isomerization
A new full-dimensional global potential energy surface (PES) for the acetylene-vinylidene isomerization on the ground (S{sub 0}) electronic state has been constructed by fitting ∼37 000 high-level ab initio points using the permutation invariant polynomial-neural network method with a root mean square error of 9.54 cm{sup −1}. The geometries and harmonic vibrational frequencies of acetylene, vinylidene, and all other stationary points (two distinct transition states and one secondary minimum in between) have been determined on this PES. Furthermore, acetylene vibrational energy levels have been calculated using the Lanczos algorithm with an exact (J = 0) Hamiltonian. The vibrational energies up to 12 700 cm{sup −1} above the zero-point energy are in excellent agreement with the experimentally derived effective Hamiltonians, suggesting that the PES is approaching spectroscopic accuracy. In addition, analyses of the wavefunctions confirm the experimentally observed emergence of the local bending and counter-rotational modes in the highly excited bending vibrational states. The reproduction of the experimentally derived effective Hamiltonians for highly excited bending states signals the coming of age for the ab initio based PES, which can now be trusted for studying the isomerization reaction.
An adaptive interpolation scheme for molecular potential energy surfaces
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task—especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm based on polyharmonic splines combined with a partition of unity approach. The adaptive node refinement allows to greatly reduce the number of sample points by employing a local error estimate. The algorithm and its scaling behavior are evaluated for a model function in 2, 3, and 4 dimensions. The developed algorithm allows for a more rapid and reliable interpolation of a potential energy surface within a given accuracy compared to the non-adaptive version.
Theoretical characterization of the potential energy surface for the reversible reaction H + O2 yields HO2(asterisk) yields OH + O. III - Computed points to define a global potential energy surface
Computed energies and geometries are reported which, combined with previously published calculations, permit a global representation of the potential energy surface for the reaction H + O2 yields HO2(asterisk) yields OH + O. These new calculations characterize the potential energy surface (PES) for all H atom angles of approach to O2 and for the region of the inner repulsive wall. The region of the T-shaped H-O2 exchange saddle point is connected with the constrained energy minimum (CEM) path, and a new collinear H-O2 exchange saddle point is characterized which lies only 9 kcal/mol above the H + O2 asymptote. A vibrational analysis which utilizes local cubic and quartic polynomial representations of the PES along the CEM path has been carried out. Optimal geometries, energies, and harmonic frequencies are reported along with anharmonic analyses for the O2 and OH asymptotes and for the HO2 minimum region of the PES.
Mode specificity in the OH + CHD{sub 3} reaction: Reduced-dimensional quantum and quasi-classical studies on an ab initio based full-dimensional potential energy surface
An initial state selected time-dependent wave packet method is applied to study the dynamics of the OH + CHD{sub 3} reaction with a six-dimensional model on a newly developed full-dimensional ab initio potential energy surface (PES). This quantum dynamical (QD) study is complemented by full-dimensional quasi-classical trajectory (QCT) calculations on the same PES. The QD results indicate that both translational energy and the excitation of the CH stretching mode significantly promote the reaction while the excitation of the umbrella mode has a negligible effect on the reactivity. For this early barrier reaction, interestingly, the CH stretching mode is more effective than translational energy in promoting the reaction except at very low collision energies. These QD observations are supported by QCT results. The higher efficacy of the CH stretching model in promoting this early barrier reaction is inconsistent with the prediction of the naively extended Polanyi’s rules, but can be rationalized by the recently proposed sudden vector projection model.
Quantum and quasi-classical dynamics of the OH + CO → H + CO{sub 2} reaction on a new permutationally invariant neural network potential energy surface
A permutationally invariant global potential energy surface for the HOCO system is reported by fitting a larger number of high-level ab initio points using the newly proposed permutation invariant polynomial-neural network method. The small fitting error (∼5 meV) indicates a faithful representation of the potential energy surface over a large configuration space. Full-dimensional quantum and quasi-classical trajectory studies of the title reaction were performed on this potential energy surface. While the results suggest that the differences between this and an earlier neural network fits are small, discrepancies with state-to-state experimental data remain significant.
Full-dimensional, high-level ab initio potential energy surfaces for H{sub 2}(H{sub 2}O) and H{sub 2}(H{sub 2}O){sub 2} with application to hydrogen clathrate hydrates
New, full-dimensional potential energy surfaces (PESs), obtained using precise least-squares fitting of high-level electronic energy databases, are reported for intrinsic H{sub 2}(H{sub 2}O) two-body and H{sub 2}(H{sub 2}O){sub 2} three-body potentials. The database for H{sub 2}(H{sub 2}O) consists of approximately 44 000 energies at the coupled cluster singles and doubles plus perturbative triples (CCSD(T))-F12a/haQZ (aug-cc-pVQZ for O and cc-pVQZ for H) level of theory, while the database for the three-body interaction consists of more than 36 000 energies at the CCSD(T)-F12a/haTZ (aug-cc-pVTZ for O, cc-pVTZ for H) level of theory. Two precise potentials are based on the invariant-polynomial technique and are compared to computationally faster ones obtained via “purified” symmetrization. All fits use reduced permutational symmetry appropriate for these non-covalent interactions. These intrinsic potentials are employed together with existing ones for H{sub 2}, H{sub 2}O, and (H{sub 2}O){sub 2}, to obtain full PESs for H{sub 2}(H{sub 2}O) and H{sub 2}(H{sub 2}O){sub 2}. Properties of these full PESs are presented, including a diffusion Monte Carlo calculation of the zero-point energy and wavefunction, and dissociation energy of the H{sub 2}(H{sub 2}O) dimer. These PESs together with an existing one for water clusters are used in a many-body representation of the PES of hydrogen clathrate hydrates, illustrated for H{sub 2}@(H{sub 2}O){sub 20}. An analysis of this hydrate is presented, including the electronic dissociation energy to remove H{sub 2} from the calculated equilibrium structure.
An improved quasi-diabatic representation of the 1, 2, 3 1 A coupled adiabatic potential energy surfaces of phenol in the full 33 internal coordinates
In a previous project we constructed a quasi-diabatic representation, H d , of the 1, 2, 3 1 A adiabatic states of phenol from high level multireference single and double excitation configuration interaction electronic structure data, energies, energy gradients, and derivative couplings. That H d accurately describes surface minima, saddle points, and also regions of strong nonadiabatic interactions, reproducing the locus of conical intersection seams and the coordinate dependence of the derivative couplings. The present work determines the accuracy of H d for describing phenol photodissociation. Additionally, we demonstrate that a modest energetic shift of two diabats yields a quantifiably more accurate H d compared with experimental energetics. The analysis shows that in favorable circumstances it is possible to use single point energies obtained from the most reliable electronic structure methods available, including methods for which the energy gradients and derivative couplings are not available, to improve the quality of a global representation of several coupled potential energy surfaces. Our data indicate an alternative interpretation of kinetic energy release measurements near λ phot ~ 248 nm.