A transferable sum-of-products Hamiltonian formalism for variational rovibrational calculations of polyatomic molecules

Sum-of-products (SOP) operator representations and extensible libraries of one-dimensional functions provide a well-established formalism in nuclear-motion methods and programs. Building on this design philosophy, we present Summed Product Analytic Representation (SPAR), a transferable interface for representing kinetic energy operators (KEOs), potential energy functions (PEFs), and dipole moment functions (DMFs) of polyatomic molecules that possess an analytic SOP form. Each operator is specified through a finite library of one-dimensional basic functions, each depending on a single vibrational coordinate, and a mapping that reconstructs the multidimensional expression. SPAR supports any SOP representations of the molecular Hamiltonian, whether exact, approximate, or hybrid. The distinctive features of the present implementation are the use of a common structure for all three classes of molecular property and explicit support for mass-dependent KEOs and coordinate singularities. We demonstrate the representation for exact analytic KEOs from triatomic to octatomic molecules, including operators derived with symmetry-adapted frame embeddings, and provide associated KEO expansions as well as illustrative PEF and DMF examples. SPAR is implemented in the nuclear-motion program trove; the resulting operator files are intended both for molecule-independent evaluation within trove and, more broadly, as a portable format through which the same analytic molecular model can be communicated to and compared across different nuclear-motion codes. Examples of automated procedures that identify the required one-dimensional basic functions and construct the SPAR mapping for algebraically complicated exact or hybrid SOP KEOs derived symbolically are provided.