The Quasi-Diabatic Hamiltonian Approach to Accurate and Efficient Nonadiabatic Dynamics with Correct Treatment of Conical Intersection Seams
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A method to simulate photoelectron spectra using quadratic local quasi-diabatic Hamiltonians (Hd) is generalized and augmented to enable high accuracy dynamics simulations of nonadiabatic processes that involve large amplitude motions, including dissociation. The improvement is achieved by using a flexible symmetry adapted analytical expansion to approximate the representation of electronic Hamiltonian operator in a quasi-diabatic basis, the diabaticity of which is achieved by minimization of residual coupling between quasi-diabatic states. Although previous theoretical treatments have been used to treat adiabatic dissociation and rearrangement processes with success, difficulties have been encountered in systems complicated by seams of conical intersections. Existing methods are either too expensive to be applied, or could not provide sufficient accuracy. Even for nonadiabatic reactions of very small systems, such as photodissociation of NH3, all previous theoretical treatments have been unable to accurately reproduce experimental measurements. In this work, inspired by the success of bound-state Hd approach, a rigorous and flexible framework is established to create a more robust method for accurate and efficient nonadiabatic dynamics simulations, through the construction of quasi-diabatic Hamiltonians(Hd) that correctly describes reactions. This new method requires no assumption on the properties of individual systems. The application of local intersection adapted representations and partially diagonalized representations enabled entire seams of conical intersections as well as the nearby regions to be accurately described. No ad hoc approximation is made in the diabatization procedure, and the residual coupling of the underlying quasi-diabatic representation is minimized in a least squares sense and can be exactly quantified. Polynomials of arbitrary functions of internal coordinates are used to construct an extremely flexible basis for Hd, and generic symmetry treatment allows incorporation of arbitrary point group or Complete Nuclear Permutation Inversion (CNPI) group symmetry . With the Hd constructed from the new approach, the Ã←X̃ photodissociation process of NH3 was simulated. New results, obtained using Hd constructed with the method described in this work, accurately reproduce experimental measurements, illustrating its promising potential. The method is then further enhanced to allow application to much larger systems, with the coupled potential energy surfaces of the 1,2,31A states for the photodissociation of phenol used as an example. A partially diagonalized representation approach is developed to accurately treat near degenerate points, and a null-space analysis procedure is added to guide the selection of monomial basis and to remove linear dependencies in the fitting procedure. Coupled potential energy surfaces that fully incorporate all 33 degrees of freedom, many different large amplitude motions, and multiple seams of conical intersections, are successfully constructed from ab initio data.