Coupled-perturbed extended tight-binding for analytic Hessians, infrared and Raman spectra
Year: 2026
Type: preprint
Abstract: We present an analytic response formalism for harmonic vibrational spectroscopy with the extended tight-binding (xTB) family of electronic-structure methods. A fieldspace coupled-perturbed self-consistent-charge treatment delivers molecular polarizabilities and, via the interchange theorem, analytic dipole derivatives (atomic polar tensors). Carrying the same formalism to nuclear perturbations yields closed-form analytic nuclear Hessians, which combine a metric-perturbed coupled-perturbed solve with explicit second-derivative terms built on dedicated integral kernels, and whose response weights carry the occupation and Fermi-level response of a Fermi-smeared reference, so that fractionally occupied and restricted odd-electron systems are treated in the same theory as closed shells. Combining the two first-order response sets in a mixed field–nuclear treatment then gives analytic polarizability derivatives (Raman tensors) without any second-order response solve. The formulation covers the GFN{0/1/2}xTB family, from the non-self-consistent GFN0-xTB to the anisotropic multipole electrostatics and self-consistent dispersion of GFN2-xTB, and is implemented on top of the public interfaces of the tblite library. All properties are validated against finitedifference references at their noise floor, and the response solves add only a small, diagonalization-free overhead to a converged calculation, so all three tensors of the double-harmonic infrared and Raman spectrum become available analytically at tightbinding cost.
Source: ChemRxiv
Authors: Philipp Pracht, Lukas S. Rindt
Institution: Heidelberg University
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208784846