Coupled-perturbed extended tight-binding for analytic Hessians, infrared and Raman spectra
- 1Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, Heidelberg, Germany, 69120
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.
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BibTeX
@misc{pracht2026coupledperturbed,
title = {{Coupled-perturbed extended tight-binding for analytic Hessians, infrared and Raman spectra}},
author = {Philipp Pracht and Lukas S. Rindt},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.15008278/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008278/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Coupled-perturbed extended tight-binding for analytic Hessians, infrared and Raman spectra
AU - Philipp Pracht
AU - Lukas S. Rindt
PY - 2026
DA - 2026/09/03
PB - ChemRxiv
DO - 10.26434/chemrxiv.15008278/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008278/v1
AB - 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.
ER -