Computational fitting of AB initio potential energy surfaces

Quantum rotational dynamics of linear C5 at low interstellar temperatures for H2 collision

The quantum dynamics of carbon chains through H2 and He collisions in the interstellar medium (ISM) is an important step toward accurate modeling of their abundance in non-local thermodynamic equilibrium conditions. The C5(Σg+1) molecule is the longest pure carbon chain detected in the ISM to date. While He collisions are computationally easy to perform, the collision with much more abundant H2 is both complicated and computationally demanding. Using templates for approximating p-H2 collisional rates, such as scaling He rates and using a reduced 4D → 2D potential energy surface (PES), has limited applicability. On the other hand, any such approximation does not exist for o-H2. Therefore, a full rotational dynamics of C5 with both p- and o-H2 is performed considering both molecules as rigid-rotors. The PES is calculated using CCSD(T)-F12a/AVTZ, and a neural network fitting model has been carefully chosen to strictly obey spectroscopic accuracy and augment the PES. The augmented PES is then expanded into radial terms using the bispherical harmonics function, and close coupling calculations have been done to get the cross sections and, subsequently, rate coefficients for various rotational transitions of C5.

Rotational dynamics of CNCN by p-H2 and o-H2 collision at interstellar temperatures

The rotational dynamics of isocyanogen (CNCN) is studied for its collision with para (p-) and ortho (o-) hydrogen (H2) in the temperature range of 1-100 K. These temperatures correspond to the cold dense molecular clouds in the interstellar medium where molecular hydrogen is the primary collider. An ab initio 4D potential energy surface (PES) is constructed keeping the two molecules under rigid rotor approximation. The PES is generated using the CCSD(T)-F12b/AVTZ level of theory. The 4D PES is further fitted into a neural network (NN) model, which can augment the surface and account for missing data points within spectroscopic accuracy. This NN-fitted PES is then expanded over a bispherical harmonics function to get radial terms, which are expressed into analytic functions. Thereafter, the cross sections (σ) are computed for rotational transitions of CNCN (j → j') using the close-coupling and centrifugal sudden methods for both p-H2 (jc = 0) and o-H2 (jc = 1) collision till 194 cm-1. In addition, p-H2 (jc = 0, 2) cross sections are also computed using the centrifugal sudden approximation method. The collisional rates are achieved by taking the Boltzmann distribution of σ over the translational energy of H2 till 100 K. Finally, the CNCN-H2 rates are compared to CNCN-He and NCCN-H2 collisional rates. Comparing even and odd transitions for the CNCN-H2 rates show a propensity toward higher rates for even transitions especially for o-H2 collisions considering low-order transitions.

Quantum rotational dynamics of l-C4(3Σ-g) by H2 at low temperatures employing a machine learning augmented potential energy surface

A new four dimensional (4D) ab initio potential energy surface (PES) is generated for the collision of C4(3Σg-) with H2(1Σg), considering both molecules as rigid rotors. A supervised neural network model is created to augment the ab initio PES and to get the missing data points. Furthermore, space fixed expansion of the augmented PES is carried out using a least squares fit over two spherical harmonics terms, resulting in radial coefficients (λ1, λ2, and λ). The centre of symmetry in both C4 and H2 forces λ1 and λ2 to have even values, respectively. Moreover, the rotational states of C4 are only populated by odd levels due to its ground state triplet symmetry and the nuclear spin (I = 0) of 12C. The cross-sections and rate coefficients with para and ortho H2 partners are studied for various odd state transitions, where the rate coefficients of the ortho are 10-20% higher than those of the latter. The de-excitation rates obtained by the para H2 collisions are also compared to those of He and are found to be ∼1.7-2.8 times the He rates, across various order transitions. The simple scaling of He rates using a factor of 1.38 proves insufficient to describe para H2 rates. Therefore, these results show the importance of explicitly studying H2 as an important colliding partner, governing the kinetics of various rotational processes in the interstellar space.

4D potential energy surface of NCCN-H2 collision: Rotational dynamics by p-H2 and o-H2 at interstellar temperatures

The rotational excitation rates of NCCN species are studied for its collision with hydrogen (H2) in temperatures ranging from 1 to 100 K. Such collisions can occur in the interstellar medium with H2 in either para (p-) or ortho (o-) state, of which the p-H2 state can be approximated via its collision with He (using a scaling factor) or with a reduced rigid rotor-H2 surface (by averaging over various orientations of H2). In the current work, a four-dimensional (4D) ab initio potential energy surface (PES) is considered to study the collision dynamics of H2 in both p- and o-states and the results are compared with previous approximations. The 4D surface is constructed using the explicitly correlated coupled-cluster method CCSD(T)-F12b with the augmented triple zeta basis AVTZ and then fitted into an artificial neural networks (NN) model to augment the surface and account for missing data points. The radial coefficients are obtained from this NN fitted 4D PES via a least square fit over two spherical harmonics functions. The cross sections (σ) are computed using the close-coupling (CC) method (until 230 cm-1) for both p- and o-H2 collisions, and the rates are obtained by Boltzmann distribution over the translational energy of H2 until 100 K. The o-H2 rates are found to be higher by 25%-30% and 10%-20% compared to the p-H2 rates for Δj = 2 and higher order transitions, respectively. The coupled-state/centrifugal sudden approximated rates are also computed and found to have deviations as large as 40% when compared to CC rates, thus making quantitative descriptions unreliable.

Time-dependent quantum mechanical wave packet dynamics

Starting from a model study of the collinear (H, H₂) exchange reaction in 1959, the time-dependent quantum mechanical wave packet (TDQMWP) method has come a long way in dealing with systems as large as Cl + CH₄. The fast Fourier transform method for evaluating the second order spatial derivative of the wave function and split-operator method or Chebyshev polynomial expansion for determining the time evolution of the wave function for the system have made the approach highly accurate from a practical point of view. The TDQMWP methodology has been able to predict state-to-state differential and integral reaction cross sections accurately, in agreement with available experimental results for three dimensional (H, H₂) collisions, and identify reactive scattering resonances too. It has become a practical computational tool in predicting the observables for many A + BC exchange reactions in three dimensions and a number of larger systems. It is equally amenable to determining the bound and quasi-bound states for a variety of molecular systems. Just as it is able to deal with dissociative processes (without involving basis set expansion), it is able to deal with multi-mode nonadiabatic dynamics in multiple electronic states with equal ease. We present an overview of the method and its strength and limitations, citing examples largely from our own research groups.

A high order predictor–corrector integration algorithm for first principle chemical dynamics simulations

H. Wu submitted the paper without having obtained permissions for submission from some of the co-authors or some of the major contributors, and hereby requested to retract the publication.

Coping with the anisotropy in the analytical representation of an ab initio potential energy surface for the Cl2 dimer

The intermolecular potential energy surface (PES) of the Cl2 dimer is calculated at the MP2/aTZ + b level of ab initio theory. A quantitative measure is proposed for comparison of the anisotropy of PESs of different systems at different intermolecular distances. A high degree of anisotropy at short and intermediate distances results in the failure of fitting strategies that are based on the angular expansion of the potential energy. To tackle this problem, a step-by-step fitting strategy is designed for analytical representation of the PES. The global minimum energy configuration of the dimer is found to be a distorted L-shape structure with a well depth of around 615 cm(-1). The PES is finally scaled to minimize deviations between calculated and experimental second virial coefficients.

Accurate ab initio potential energy curve of F2. III. The vibration rotation spectrum

An analytical expression is found for the accurate ab initio potential energy curve of the fluorine molecule that has been determined in the preceding two papers. With it, the vibrational and rotational energy levels of F(2) are calculated using the discrete variable representation. The comparison of this theoretical spectrum with the experimental spectrum, which had been measured earlier using high-resolution electronic spectroscopy, yields a mean absolute deviation of about 5 cm(-1) over the 22 levels. The dissociation energy with respect to the lowest vibrational energy is calculated within 30 cm(-1) of the experimental value of 12 953+/-8 cm(-1). The reported agreement of the theoretical spectrum and dissociation energy with experiment is contingent upon the inclusion of the effects of core-generated electron correlation, spin-orbit coupling, and scalar relativity. The Dunham analysis [Phys. Rev. 41, 721 (1932)] of the spectrum is found to be very accurate. New values are given for the spectroscopic constants.

Direct dynamics simulations using Hessian-based predictor-corrector integration algorithms

In previous research [J. Chem. Phys. 111, 3800 (1999)] a Hessian-based integration algorithm was derived for performing direct dynamics simulations. In the work presented here, improvements to this algorithm are described. The algorithm has a predictor step based on a local second-order Taylor expansion of the potential in Cartesian coordinates, within a trust radius, and a fifth-order correction to this predicted trajectory. The current algorithm determines the predicted trajectory in Cartesian coordinates, instead of the instantaneous normal mode coordinates used previously, to ensure angular momentum conservation. For the previous algorithm the corrected step was evaluated in rotated Cartesian coordinates. Since the local potential expanded in Cartesian coordinates is not invariant to rotation, the constants of motion are not necessarily conserved during the corrector step. An approximate correction to this shortcoming was made by projecting translation and rotation out of the rotated coordinates. For the current algorithm unrotated Cartesian coordinates are used for the corrected step to assure the constants of motion are conserved. An algorithm is proposed for updating the trust radius to enhance the accuracy and efficiency of the numerical integration. This modified Hessian-based integration algorithm, with its new components, has been implemented into the VENUS/NWChem software package and compared with the velocity-Verlet algorithm for the H(2)CO-->H(2)+CO, O(3)+C(3)H(6), and F(-)+CH(3)OOH chemical reactions.