On the representation of coupled adiabatic potential energy surfaces using quasi-diabatic Hamiltonians: A distributed origins expansion approach

Abstract

In two previous papers we have introduced a method to generate coupled quasi-diabatic Hamiltonians (H(d)) that are capable of representing adiabatic energies, energy gradients, and derivative couplings over a wide range of geometries including seams of conical intersection. In this work, two new synergistic features are introduced. Firstly, the functional form of H(d) is generalized. Rather than requiring there to be a low energy point of high symmetry to serve as the unique origin, functions centered on points distributed in nuclear coordinate space are used in the polynomials that comprise the matrix elements in H(d). The use of functions with distributed origins, allows reproduction of the ab initio data with lower order expansions, and offers the possibility of describing multichannel dissociation. The fitting algorithm is combined with a three-step procedure in which the domain of H(d) is extended from a core set of nuclear configurations to a region of nuclear coordinate space appropriate for nuclear dynamics, with a prescribed accuracy. This significant extension of the domain of definition compared to our original work, which is facilitated by the distributed origin approach, is achieved largely through the use of surface hopping trajectories. The 1,2(1)A states of NH(3), which provide an archetypical example of nonadiabatic dynamics, are used to demonstrate the utility of this approach. The representation describes 21 points on the 1(1)A-2(1)A seam of conical intersection and their local topography flawlessly and on the entire domain, the electronic structure data is represented to an accuracy of 77.00 (46.90) cm(-1), as measured by the root mean square (mean unsigned) error for energies lower than 50 000 cm(-1). This error is a factor of 10 lower than that of the most accurate representation of high quality ab initio data, on a comparable domain, previously reported for this system.

First principles determination of the NH2/ND2($\skew4\tilde A, \skew3\tilde X$Ã,X̃) branching ratios for photodissociation of NH3/ND3 via full-dimensional quantum dynamics based on a new quasi-diabatic representation of coupled ab initio potential energy surfaces

“…Compared to reciprocally scaled triple product coordinate used previously, 47 the new coordinate scales more subtly in the interaction region but dissipates much more rapidly upon dissociation. Second, in constructing H d,prev , data points with energies greater than E thres = 50 000 cm −1 were deemed to be less important, and given lower weights in the construction.…”

“…The g l (R) currently in use are described in Ref. 47. The p (n) (R) are given by p (n) (R) = P u(n) g l(n) (R), where P u(n) is the appropriate group theoretical projection operator.…”

“…For the remaining points the data are described in a least squares sense. 47,58 Two methods for obtaining the optimal V (and γ , under development) are currently in use. Both determine extrema of the Lagrangian, (V, γ , λ), that is, the parameters satisfy…”

“…H d,prev was shown to provide an excellent representation of the ab initio data from which it was constructed. 47 The utility of H d,prev for describing ammonia photodissociation was validated using the fully quantum mechanical, six-dimensional method described below to simulate the ν 2 progression in theà ←X absorption spectra of both NH 3 and ND 3 , including the line positions, intensities, and line widths. 44 Although these spectra had proven difficult to reproduce previously, 56 excellent agreement with the experimental results was found.…”

“…In this regard, we have recently reported accurate global PESs for the NH 3 (Ã/X) system in a quasi-diabatic representation, 44 using a newly developed fitting scheme. [45][46][47] A unique feature of this representation is an accurate description of the ab initio seam of conical intersections.…”