HN2(2A‘) Electronic Manifold. II. Ab Initio Based Double-Sheeted DMBE Potential Energy Surface via a Global Diabatization Angle

Accurate Potential Energy Surface for Quartet State HN2 and Interplay of N(4S) + NH(X̃3Σ-) versus H + N2(A3Σu+) Reactions

A global potential energy surface for the lowest quartet state of HN₂ is reported for the first time from accurate multireference ab initio calculations extrapolated to the complete basis set limit using the double many-body expansion method. All its stationary points are characterized, with the lowest quartet of HN₂ predicted to have a bent global minimum 36 kcal mol^-1 below the N(⁴S) + NH(X̃³Σ^-) asymptote, from which it is barrierlessly achievable. The entire set of calculated ab initio points has been fitted for energies up to 1000 kcal mol^-1 above the global minimum with an RMSD of 0.89 kcal mol^-1, a gap comprising all identified stationary points. Special care is taken in modeling the involved long-range forces and cusps caused by crossing seams. The novel PES prompts for the calculation of rate constants for several unexplored reactions that are relevant for combustion, plasma, and atmospheric chemistry.

Accurate CHIPR Potential Energy Surface for the Lowest Triplet State of C3

We report the first global ab initio-based potential energy surface (PES) for ground-state triplet C₃(³A') based on accurate energies extrapolated to the complete basis set (CBS) limit, and using the combined-hyperbolic-inverse-power-representation method for the analytical modeling. By relying on a cost-effective CBS(D,T) protocol, we ensure that the final form reproduces all topographical features of the PES, including its cyclic-linear isomerization barrier, with CBS(5,6)-quality. To partially account for the incompleteness of the N-electron basis and other minor effects, the available accurate experimental data on the relevant diatomics were used to obtain direct-fit curves that replace the theoretical ones in the many-body expansion. Besides describing properly long-range interactions at all asymptotic channels and permutational symmetry by built-in construction, the PES reported here reproduces the proper exothermicities at dissociation regions as well as the spectroscopy of the diatomic fragments. Bound vibrational state calculations in both linear and cyclic isomers have also been carried out, unveiling a good match of the available data on C₃(ã ³Π_u), while assisting with IR band positions for C₃(³A₂^') that may serve as a guide for its laboratory and astronomical detection.

A discontinuous basis enables numerically exact solution of the Schrödinger equation around conical intersections in the adiabatic representation

Solving the vibrational Schrödinger equation in the neighborhood of conical intersections in the adiabatic representation is a challenge. At the intersection point, first- and second-derivative nonadiabatic coupling matrix elements become singular, with the singularity in the second-derivative coupling (diagonal Born-Oppenheimer correction) being non-integrable. These singularities result from discontinuities in the vibronic functions associated with the individual adiabatic states, and our group has recently argued that these divergent matrix elements cancel when discontinuous adiabatic vibronic functions sum to a continuous total nonadiabatic wave function. Here we describe the realization of this concept: a novel scheme for the numerically exact solution of the Schrödinger equation in the adiabatic representation. Our approach is based on a basis containing functions that are discontinuous at the intersection point. We demonstrate that the individual adiabatic nuclear wave functions are themselves discontinuous at the intersection point. This proves that discontinuous basis functions are essential to any tractable method that solves the Schrödinger equation around conical intersections in the adiabatic representation with high numerical precision. We establish that our method provides numerically exact results by comparison to reference calculations performed in the diabatic representation. In addition, we quantify the energetic error associated with constraining the density to be zero at the intersection point, a natural approximation. Prospects for extending the present treatment of a two-dimensional model to systems of higher dimensionality are discussed.

Diabatic States at Construction (DAC) through Generalized Singular Value Decomposition

A procedure, called generalized diabatic-at-construction (GDAC), is presented to transform adiabatic potential energy surfaces into a diabatic representation by generalized singular value decomposition. First, we use a set of localized, valence bond-like configuration state functions, called DAC, as the basis states. Then, the adiabatic ground and relevant excited states are determined using multistate density functional theory (MSDFT). GDAC differs in the opposite direction from traditional approaches based on adiabatic-to-diabatic transformation with certain property restraints. The method is illustrated with applications to a model first-order bond dissociation reaction of CH₃OCH₂Cl polarized by a solvent molecule, the ground- and first-excited-state potential energy surfaces near the minimum conical intersection for the ammonia dimer photodissociation, and the multiple avoided curve crossings in the dissociation of lithium hydride. The GDAC diabatization method may be useful for defining charge-localized states in studies of electron transfer and proton-coupled electron transfer reactions in proteins.

Multiple conical intersections in small linear parameter Jahn-Teller systems: the DMBE potential energy surface of ground-state C3 revisited

A new single-sheeted DMBE potential energy surface for ground-state C3 is reported. The novel analytical form accurately describes the three symmetry-equivalent C2v disjoint seams, in addition to the symmetry-required D3h one, over the entire configuration space. The present formalism warrants by built-in construction the confluence of the above crossings, and the rotation-in-plane of the C2v seams when the perimeter of the molecule fluctuates. Up to 1050 ab initio energies have been employed in the calibration procedure, of which 421 map the loci of intersection. The calculated energies have been scaled to account for the incompleteness of the basis set and truncation of the MRCI expansion, and fitted analytically with chemical accuracy. The novel form is shown to accurately mimic the region defined by the 4 conical intersections, while exhibiting similar attributes to the previously reported one [J. Chem. Phys., 2015, 143, 074302] at the regions of configuration space away from the crossing seams. Despite being mainly addressed to C3, the present approach should be applicable to adiabatic PESs of any X3 system experiencing similar topological attributes, in particular the small-linear-parameter Jahn-Teller molecules.

Diabatic-At-Construction Method for Diabatic and Adiabatic Ground and Excited States Based on Multistate Density Functional Theory

We describe a diabatic-at-construction (DAC) strategy for defining diabatic states to determine the adiabatic ground and excited electronic states and their potential energy surfaces using the multistate density functional theory (MSDFT). The DAC approach differs in two fundamental ways from the adiabatic-to-diabatic (ATD) procedures that transform a set of preselected adiabatic electronic states to a new representation. (1) The DAC states are defined in the first computation step to form an active space, whose configuration interaction produces the adiabatic ground and excited states in the second step of MSDFT. Thus, they do not result from a similarity transformation of the adiabatic states as in the ATD procedure; they are the basis for producing the adiabatic states. The appropriateness and completeness of the DAC active space can be validated by comparison with experimental observables of the ground and excited states. (2) The DAC diabatic states are defined using the valence bond characters of the asymptotic dissociation limits of the adiabatic states of interest, and they are strictly maintained at all molecular geometries. Consequently, DAC diabatic states have specific and well-defined physical and chemical meanings that can be used for understanding the nature of the adiabatic states and their energetic components. Here we present results for the four lowest singlet states of LiH and compare them to a well-tested ATD diabatization method, namely the 3-fold way; the comparison reveals both similarities and differences between the ATD diabatic states and the orthogonalized DAC diabatic states. Furthermore, MSDFT can provide a quantitative description of the ground and excited states for LiH with multiple strongly and weakly avoided curve crossings spanning over 10 Å of interatomic separation.

Modeling cusps in adiabatic potential energy surfaces

A method for modeling cusps on adiabatic potential energy surfaces without the need for any adiabatic-to-diabatic transformation is presented and shown to be successfully applied to the (2)A″ state of NO2. The more complicated case of a system with permutationally equivalent crossing seams is also examined and illustrated by considering the two first (2)A' states of the nitrogen trimer.

VECTOR CORRELATIONS AND PRODUCT POLARIZATIONS IN THE N(2D) + D2 → ND + D REACTIVE SYSTEM

The vector correlations between products and reagents of the N (2D) + D 2 reaction are investigated by employing quasi-classical trajectory (QCT) calculation on the accurate DMBE potential energy surface (PES) of the 2A″ state. Stereo-dynamic quantities, including the four generalized polarization-dependent differential cross-sections (PDDCSs), the angular distribution P(θr), the dihedral-angle distribution P(φr), as well as the product rotational angular distribution in the polar form of P(θr, φr), are calculated in the center-of-mass (CM) frame. The results indicate that the product rotational angular momentum j′ not only aligns along the y-axis, but also orients to the negative direction of the y-axis. The isotope effect in the context of chemical stereo-dynamics and influences of different versions of ground-state PESs on vector correlations are shown and discussed.

DIABATIC ELECTRONIC MANIFOLD OF HN2(2A′) AND N + NH REACTION DYNAMICS ON ITS LOWEST ADIABAT

A previously reported approach [J. Chem. Phys.97:867, (1997)] to back transform the diagonal adiabats into a 2 × 2 diabatic potential matrix has been utilized to generate a global multi-sheeted form for the title system. Global adiabatic dynamics calculations carried out on the new form using the quasi-classical trajectory method yield results that lie essentially within the statistical error of similar calculations performed on the best surface reported thus far for the title reaction. This makes it suitable for future adiabatic and nonadiabatic calculations carried out either using classical or quantum methods.

Nonadiabatic quantum dynamics calculations for the N + NH --> N(2) + H reaction

Nonadiabatic quantum dynamics calculations on the two coupled potential energy surfaces (PESs) (1(2)A' and 2(2)A') and also adiabatic quantum calculations on the lowest adiabatic PES are reported for the title reaction. Reaction probabilities for total angular momenta, J, varying from 0 to 160, are calculated to obtain the integral cross section (ICS) for collision energies ranging from 0.05 to 1.0 eV. Calculations using both the close coupling and the Centrifugal Sudden (CS) approximation are carried out to evaluate the role of Coriolis coupling effects for this reaction. The results of the nonadiabatic calculations show that the nonadiabatic effects in the title reaction for the initial state of NH (v = 0, j = 0) could be neglected, at least in the collision energy range considered in this study.