Cartesian and Curvilinear Anharmonic Frequencies and Intensities: Perturb-then-Diagonalize Polyad Transport and Adiabatic Discrete-Variable Representation
Abstract
Anharmonic intensities reveal vibrational coupling that band positions alone cannot determine. We derive explicit second-order infrared transition moments in curvilinear normal coordinates, including kinetic metric derivatives and transport through variational resonance polyads. The vibrational perturbation-to-second-order-then-diagonalization (VP2TD) treatment covers fundamentals, overtones, three-quantum transitions, and hot bands. A general computational platform combines Extended Symmetry-Adapted Local Coordinates (ESALCs), using Cartesian (ESALC-C) or internal (ESALC-I) primitives, with interchangeable quantum-chemical programs and parallel finite differences. Independent oscillator matrices verify the intensity equations; a molecular water check reproduces second-order amplitudes within 8.4×10−8 atomic units. Comparisons with established tools reproduce a formaldehyde Fermi polyad within 0.163 cm−1 and 0.061 km mol−1 and water Raman activities within 10−7 Angstrom6. For 29 matched formaldehyde rotational line pairs, the predicted hot-to-fundamental intensity ratio, using the measured lower-state energy, is consistent with the nuclear-spin-corrected median: the differences are 3.9% (ESALC-I) and 3.8% (ESALC-C), compared with a 15% uncertainty estimate for individual measured line intensities. Common analytic reference derivatives ensure identical harmonic observables, while internal coordinates reduce and localize intermode anharmonic couplings. Rotation-vibration constants extend the same tensor treatment. An integrated adiabatic discrete-variable representation treats large-amplitude motions, and finite-level partition functions provide anharmonic thermochemistry.
Related
- Semiclassical initial value representation in curvilinear coordinates
- Anharmonic Vibrational Structure and Bound States of the He-CO2 van der Waals Complex
- Correlation between normal character and Raman intensities of isotopologues of carbon dioxide
- Visualizing and Quantifying Atomic Contributions to Raman Intensities governed by Spatially-Resolved Atomic Interferences
- An anharmonic liquid-entropy functional from the Mori-Zwanzig memory kernel
BibTeX
@misc{barone2026cartesian,
title = {{Cartesian and Curvilinear Anharmonic Frequencies and Intensities: Perturb-then-Diagonalize Polyad Transport and Adiabatic Discrete-Variable Representation}},
author = {Vincenzo Barone},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20488},
eprint = {2610.20488},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20488},
}
RIS
TY - UNPB
TI - Cartesian and Curvilinear Anharmonic Frequencies and Intensities: Perturb-then-Diagonalize Polyad Transport and Adiabatic Discrete-Variable Representation
AU - Vincenzo Barone
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20488
UR - https://arxiv.org/abs/2610.20488
AB - Anharmonic intensities reveal vibrational coupling that band positions alone cannot determine. We derive explicit second-order infrared transition moments in curvilinear normal coordinates, including kinetic metric derivatives and transport through variational resonance polyads. The vibrational perturbation-to-second-order-then-diagonalization (VP2TD) treatment covers fundamentals, overtones, three-quantum transitions, and hot bands. A general computational platform combines Extended Symmetry-Adapted Local Coordinates (ESALCs), using Cartesian (ESALC-C) or internal (ESALC-I) primitives, with interchangeable quantum-chemical programs and parallel finite differences. Independent oscillator matrices verify the intensity equations; a molecular water check reproduces second-order amplitudes within 8.4×10^−8 atomic units. Comparisons with established tools reproduce a formaldehyde Fermi polyad within 0.163 cm^−1 and 0.061 km mol^−1 and water Raman activities within 10^−7 Angstrom^6. For 29 matched formaldehyde rotational line pairs, the predicted hot-to-fundamental intensity ratio, using the measured lower-state energy, is consistent with the nuclear-spin-corrected median: the differences are 3.9% (ESALC-I) and 3.8% (ESALC-C), compared with a 15% uncertainty estimate for individual measured line intensities. Common analytic reference derivatives ensure identical harmonic observables, while internal coordinates reduce and localize intermode anharmonic couplings. Rotation-vibration constants extend the same tensor treatment. An integrated adiabatic discrete-variable representation treats large-amplitude motions, and finite-level partition functions provide anharmonic thermochemistry.
ER -