Toward eliminating the electronic structure bottleneck in nonadiabatic dynamics on the fly: An algorithm to fit nonlocal, quasidiabatic, coupled electronic state Hamiltonians based on ab initio electronic structure data

An algorithm for constructing a quasidiabatic, coupled electronic state Hamiltonian, in a localized region of nuclear coordinate space, suitable for determining bound state spectra, is generalized to determine a nonlocal Hamiltonian capable of describing, for example, multichannel nonadiabatic photodissociation. For N-state coupled electronic states, the Hamiltonian, H-d, is a symmetric N(state)xN(state) matrix whose elements are polynomials involving: decaying exponentials exp(-ar(i,j)(n)) n=1,2, where r(i,j)=R-i-R-j, r(i,j)=vertical bar r(i,j)vertical bar, R-j locates the jth nucleus; and scaled dot-cross product coordinates, proportional to r(i,j)xr(i,k)center dot r(i,l). The constructed Hamiltonian is constrained to reproduce, exactly, the ab initio data, energies, gradients, and derivative coupling at selected points, or nodes, in nuclear coordinate space. The remainder of the ab initio data is approximated in a least-squares sense using a normal equations approach. The fitting procedure includes a damping term that precludes oscillations due to the nodal constraints or local excesses of parameters. To illustrate the potential of the fitting procedure an H-d is constructed, with the full nuclear permutation-inversion symmetry, which describes portions of the 1,2 (1)A potential energy surfaces of NH3, including the minimum energy point on the 1,2 (1)A seam of conical intersection and the NH2+H asymptote. Ab initio data at 239 nuclear configurations was used in the construction which was tested at 48 additional nuclear configurations. While the energy range on the ground and excited potential energy surface is each individually similar to 45 000 cm(-1), the root mean square error for the energies at all points is only 93.6 cm(-1). The location and local conical topography of the minimum energy conical intersection is exactly reproduced. The derivative couplings are shown to be well reproduced, justifying the attribute quasidiabatic.