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arXiv:2608.20075

Nonzero-temperature vibronic spectra of polyatomic molecules from a zero-temperature classical trajectory

Davide Barbiero, Jiří J. L. Vaníček

physics.chem-phphysics.comp-phquant-phSubmitted Aug 20, 2026• Announced Aug 21, 2026
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Abstract

By combining coherence thermofield dynamics with the single-Hessian approximation, we enable simulations of low- to medium-resolution vibronic spectra of weakly anharmonic systems at nonzero temperatures, at negligible additional cost relative to zero-temperature calculations. Single-Hessian coherence thermofield Gaussian wavepacket dynamics is exact in any harmonic potential, provided that the reference Hessian is that of the final surface. When applied to Morse systems of increasing anharmonicity and varying temperature, this method successfully captures excited-state anharmonicity and key temperature-dependent spectral features, including hot bands and broadening. By combining the method with on-the-fly ab initio dynamics, we demonstrate its utility by computing the absorption spectra of naphthalene, aminocoumarin C450, and phenyl radical, and the photoelectron spectrum of SeO$_{2}^{-}$ . Within the ab initio single-Hessian approximation, after the zero-temperature spectrum is obtained at the cost of classical molecular dynamics (on the order of hours), all nonzero-temperature spectra are computed in seconds.

Related papers

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Single-Hessian Gaussian wavepacket dynamics (GWD) significantly reduces the computational burden of Heller's local harmonic GWD, while maintaining comparable accuracy in approximating vibronic spectra. Here, we provide a new, symplectic derivation of the equations of motion of single-Hessian GWD and show that, unlike the local harmonic version, this method conserves the non-canonical symplectic structure on the manifold of Gaussian wavepackets and$-$for bounded dynamics in smooth potentials$-$avoids the drift of energy. Our numerical results suggest that, despite being much more efficient than the local harmonic variant, the single-Hessian GWD exhibits the same $\mathcal{O}(\hbar)$ asymptotic error in averages of observables. To further accelerate numerical simulations, we implement high-order time-stepping geometric integrators that are time-reversible and conserve the norm and symplectic structure exactly, regardless of the time step. In addition, we present explicit expressions for the exact evolution of the width of a single-Hessian Gaussian wavepacket in a general potential, as well as for the exact evolution of the whole wavepacket in a global harmonic potential. Using on-the-fly ab initio Gaussian wavepacket dynamics on the first excited-state surface of ammonia, we numerically confirm the conservation of geometric properties by these integrators and demonstrate that high-order integrators can enhance both accuracy and computational efficiency. We also compute the photoelectron spectrum of the difluorocarbene anion and the absorption spectrum of methylamine, and find that, in comparison with experiment, single-Hessian GWD outperforms global harmonic models and matches the accuracy of local harmonic GWD. Finally, we identify which spectral features are sensitive to the choice of reference Hessian.

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We introduce two non-adiabatic semiclassical methods that employ two coupled Gaussian wavepackets, each one traveling on a separate diabatic potential energy surface. The wavepackets take the form of thawed Gaussians and are driven by classical equations of motion which account for the diabatic coupling. The classical equations of motion are derived in one case by enforcing the thawed Gaussian ansatz, while in the other the time-dependent variational principles to the thawed Gaussian ansatz. After a sanity check where both approximations reproduce Rabi oscillations, the methods are applied to two non-adiabatic potential energy scenarios. The first one involves two coupled displaced harmonic oscillators, as in a typical electron transfer reaction. The second one comprises a Morse potential coupled to an upper dissociative state, modeling a photo-dissociation process. In both scenarios, the variational thawed Gaussian approach is quite accurate, while the standard thawed Gaussian one fails to fully capture the non-adiabatic effects. Ultimately, non-adiabatic molecular dynamics is reproduced by means of two classical trajectories without introducing any artificial jump or other ad-hoc non-classical effects.

physics.chem-phCross-listedarXiv:2607.09592•Jul 13, 2026
By combining coherence thermofield dynamics with the single-Hessian approximation, we enable simulations of low- to medium-resolution vibronic spectra of weakly anharmonic systems at nonzero temperatures, at negligible additional cost relative to zero-temperature calculations. Single-Hessian coherence thermofield Gaussian wavepacket dynamics is exact in any harmonic potential, provided that the reference Hessian is that of the final surface. When applied to Morse systems of increasing anharmonicity and varying temperature, this method successfully captures excited-state anharmonicity and key temperature-dependent spectral features, including hot bands and broadening. By combining the method with on-the-fly ab initio dynamics, we demonstrate its utility by computing the absorption spectra of naphthalene, aminocoumarin C450, and phenyl radical, and the photoelectron spectrum of SeO2−_{2}^{-}2−​ . Within the ab initio single-Hessian approximation, after the zero-temperature spectrum is obtained at the cost of classical molecular dynamics (on the order of hours), all nonzero-temperature spectra are computed in seconds.
Single-Hessian Gaussian wavepacket dynamics (GWD) significantly reduces the computational burden of Heller's local harmonic GWD, while maintaining comparable accuracy in approximating vibronic spectra. Here, we provide a new, symplectic derivation of the equations of motion of single-Hessian GWD and show that, unlike the local harmonic version, this method conserves the non-canonical symplectic structure on the manifold of Gaussian wavepackets and−-−for bounded dynamics in smooth potentials−-−avoids the drift of energy. Our numerical results suggest that, despite being much more efficient than the local harmonic variant, the single-Hessian GWD exhibits the same O(ℏ)\mathcal{O}(\hbar)O(ℏ) asymptotic error in averages of observables. To further accelerate numerical simulations, we implement high-order time-stepping geometric integrators that are time-reversible and conserve the norm and symplectic structure exactly, regardless of the time step. In addition, we present explicit expressions for the exact evolution of the width of a single-Hessian Gaussian wavepacket in a general potential, as well as for the exact evolution of the whole wavepacket in a global harmonic potential. Using on-the-fly ab initio Gaussian wavepacket dynamics on the first excited-state surface of ammonia, we numerically confirm the conservation of geometric properties by these integrators and demonstrate that high-order integrators can enhance both accuracy and computational efficiency. We also compute the photoelectron spectrum of the difluorocarbene anion and the absorption spectrum of methylamine, and find that, in comparison with experiment, single-Hessian GWD outperforms global harmonic models and matches the accuracy of local harmonic GWD. Finally, we identify which spectral features are sensitive to the choice of reference Hessian.
We present a practical, ab initio time-dependent method using Hagedorn wavepackets to simulate resonance Raman (RR) spectra of polyatomic molecules. Hagedorn functions---Gaussians multiplied by specific polynomials---are used to represent RR initial and final states because these functions are exact solutions to the time-dependent Schrödinger equation for at-most-quadratic potentials and can be propagated at zero cost beyond that of propagating the guiding Gaussian. Using efficient recursive formulae to compute overlaps between Hagedorn wavepackets, we can evaluate RR excitation profiles for arbitrary spectral signals, such as fundamental, overtone, combination, and hot bands. We then construct the Stokes and anti-Stokes RR spectra from these profiles. We first validate the method in a two-dimensional displaced, distorted, and Duschinsky-rotated harmonic model against numerically exact split-operator calculations. Then, we apply the method to compute RR spectra of anthracene by performing dynamics on a 66-dimensional harmonic potential energy surface constructed from density functional theory calculations.
We present a quantum algorithm for calculating the vibronic spectrum of a molecule, a useful but classically hard problem in chemistry. We show several advantages over previous quantum approaches: vibrational anharmonicity is naturally included; after measurement, some state information is preserved for further analysis; and there are potential error-related benefits. Considering four triatomic molecules, we numerically study truncation errors in the harmonic approximation. Further, in order to highlight the fact that our quantum algorithm's primary advantage over classical algorithms is in simulating anharmonic spectra, we consider the anharmonic vibronic spectrum of sulfur dioxide. In the future, our approach could aid in the design of materials with specific light-harvesting and energy transfer properties, and the general strategy is applicable to other spectral calculations in chemistry and condensed matter physics.
Measuring vibronic spectra probes dynamical processes in molecular systems. When interpreted via suitable theoretical tools, the experimental data provides comprehensive information about the system in question. For complex many-body problems, such an approach usually requires the formulation of proper classical-like approximations, which is particularly challenging if multiple electronic states are involved. In this work, we express the imaginary-time shifted time correlation function and, thus, the vibronic spectrum in terms of the so-called Matsubara dynamics, which combines quantum statistics and classical-like dynamics. By applying the Matsubara approximation in the adiabatic limit, we derive a formal generalization of the existing Matsubara dynamics formalism to multiple potential energy surfaces (PESs), which, however, does not feature all the defining properties of its single-PES counterpart though suffering equally from the sign problem. The mathematical analysis for two shifted harmonic oscillators suggests a new modified method to practically simulate the standard correlation function via Matsubara-like dynamics. Importantly, this modified method samples the thermal Wigner function without suffering from the sign problem and yields an accurate approximation to the vibronic absorption spectrum, not only for the harmonic system but also for the anharmonic one.
Chemical systems normally possess strong nonlinear vibronic couplings at both zero and finite temperature. For the lowest-order quadratic couplings, here, we introduce a squeezing operator into a variational coherent-state-based method, Davydov ansatz, to simulate the quantum dynamics and the respective spectroscopy. Two molecular systems, pyrazine and the 2-pyridone dimer, are taken as calculated model systems, both of which involve nontrivial quadratic vibronic couplings in high- and low-frequency regions, respectively. Upon a comparison with the benchmarks, the method manifests its advantage for nonlinear couplings. The squeezed bases are also proven to be applicable for the finite temperature by adapting with the thermofield dynamics.
We introduce two non-adiabatic semiclassical methods that employ two coupled Gaussian wavepackets, each one traveling on a separate diabatic potential energy surface. The wavepackets take the form of thawed Gaussians and are driven by classical equations of motion which account for the diabatic coupling. The classical equations of motion are derived in one case by enforcing the thawed Gaussian ansatz, while in the other the time-dependent variational principles to the thawed Gaussian ansatz. After a sanity check where both approximations reproduce Rabi oscillations, the methods are applied to two non-adiabatic potential energy scenarios. The first one involves two coupled displaced harmonic oscillators, as in a typical electron transfer reaction. The second one comprises a Morse potential coupled to an upper dissociative state, modeling a photo-dissociation process. In both scenarios, the variational thawed Gaussian approach is quite accurate, while the standard thawed Gaussian one fails to fully capture the non-adiabatic effects. Ultimately, non-adiabatic molecular dynamics is reproduced by means of two classical trajectories without introducing any artificial jump or other ad-hoc non-classical effects.