arXiv subjects

Zhan Tong Zhang

Publications and source records attributed to Zhan Tong Zhang.

7 recordsLinked to original sources

arXiv2025

Capturing anharmonic effects in single vibronic level fluorescence spectra using local harmonic Hagedorn wavepacket dynamics

Hagedorn wavepacket dynamics yields exact single vibronic level (SVL) fluorescence spectra in global harmonic models. To partially describe the effects of anharmonicity, important in the spectra of real molecules, we describe a combination of the Hagedorn wavepacket approach to SVL spectroscopy with the local harmonic approximation. In a proof-of-principle study [Phys. Rev. A 111, L010801 (2025)], we successfully demonstrated the utility of this method by computing the SVL spectra of difluorocarbene, a floppy molecule with moderately anharmonic potential. Here, we describe the theory in detail and analyse the method more thoroughly. To assess the accuracy of the method independently of electronic structure errors, we use a two-dimensional Morse-type potential for which exact quantum benchmarks are available, and show that the local harmonic approach yields more accurate results than global harmonic approximations, especially for the emission spectra from higher initial vibrational levels. Next, we compare the global and local harmonic SVL spectra of anthracene, where the more expensive local harmonic corrections turn out to be less important as long as the correct global harmonic model is used. We also present additional local harmonic results for difluorocarbene, where treating anharmonicity is essential for accurate evaluation of the spectra. Yet, we also show that the structure of the difluorocarbene spectra can be explained qualitatively (but not quantitatively) with a reduced-dimensional harmonic model, for which the spectral intensities can be evaluated analytically.

physics.chem-ph↗

arXiv2025

Simulating Molecular Single Vibronic Level Fluorescence Spectra with ab initio Hagedorn Wavepacket Dynamics

We present a practical, ab initio time-dependent method using Hagedorn wavepackets to efficiently simulate single vibronic level (SVL) fluorescence spectra of polyatomic molecules from arbitrary initial vibrational levels. We apply the method to compute SVL spectra of anthracene by performing wavepacket dynamics on a 66-dimensional harmonic potential energy surface constructed from density functional theory calculations. The Hagedorn approach captures both mode distortion (frequency changes) and mode mixing (Duschinsky rotation) within the harmonic approximation. We not only reproduce the previously reported simulation results for singly excited $12^1$ and $\overline{11}^1$ levels, but are also able to compute SVL spectra from multiply excited levels in good agreement with experiments. Notably, all spectra were obtained from the same wavepacket trajectory without any additional propagation beyond what is required for the emission spectrum from the ground vibrational level of the electronically excited state.

physics.chem-ph↗

arXiv2024

On-the-Fly Ab Initio Hagedorn Wavepacket Dynamics: Single Vibronic Level Fluorescence Spectra of Difluorocarbene

Hagedorn wavepackets have been used to compute single vibronic level (SVL) spectra efficiently in model harmonic potentials. To make the Hagedorn approach practical for realistic polyatomic molecules with anharmonicity, here we combine local harmonic Hagedorn wavepacket dynamics with on-the-fly ab initio dynamics. We then test this method by computing the SVL fluorescence spectra of difluorocarbene, a small, floppy molecule with a very anharmonic potential energy surface. Our time-dependent approach obtains the emission spectra of all initial vibrational levels from a single anharmonic semiclassical wavepacket trajectory without the need to fit individual anharmonic vibrational wavefunctions and to calculate the Franck-Condon factors for all vibronic transitions. We show that, whereas global harmonic models are inadequate for CF2, the spectra computed with the on-the-fly local harmonic Hagedorn wavepacket dynamics agree well with experimental data, especially for low initial excitations.

physics.chem-ph↗

arXiv2024

Single vibronic level fluorescence spectra from Hagedorn wavepacket dynamics

In single vibronic level (SVL) fluorescence experiments, the electronically excited initial state is also excited in one or several vibrational modes. Whereas computing all contributing Franck-Condon factors individually becomes impractical in large systems, a time-dependent formalism has not been applied to simulate emission from arbitrary initial vibrational levels. Here, we use Hagedorn functions, which are products of a Gaussian and carefully generated polynomials, to represent SVL initial states. In systems where the potential is at most quadratic, the Hagedorn functions are exact solutions to the time-dependent Schrödinger equation and can be propagated with the same equations of motion as a simple Gaussian wavepacket. Having developed an efficient recursive algorithm to compute the overlaps between two Hagedorn wavepackets, we can now evaluate emission spectra from arbitrary vibronic levels using a single trajectory. We validate the method in two-dimensional global harmonic models by comparing it with quantum split-operator calculations. Additionally, we study the effects of displacement, distortion (squeezing), and Duschinsky rotation on SVL spectra. Finally, we demonstrate the applicability of the Hagedorn approach to high-dimensional systems on an example of displaced, distorted, and Duschinsky-rotated harmonic model with 100 degrees of freedom.

physics.chem-ph↗

arXiv2024

On Hagedorn wavepackets associated with different Gaussians

Hagedorn functions are carefully constructed generalizations of Hermite functions to the setting of many-dimensional squeezed and coupled harmonic systems. Wavepackets formed by superpositions of Hagedorn functions have been successfully used to solve the time-dependent Schrödinger equation exactly in harmonic systems and variationally in anharmonic systems. For evaluating typical observables, such as position or kinetic energy, it is sufficient to consider orthonormal Hagedorn functions with a single Gaussian center. Here, we instead derive various relations between Hagedorn bases associated with different Gaussians, including their overlaps, which are necessary for evaluating quantities nonlocal in time, such as time correlation functions needed for computing spectra. First, we use the Bogoliubov transformation to obtain commutation relations between the ladder operators associated with different Gaussians. Then, instead of using numerical quadrature, we employ these commutation relations to derive exact recurrence relations for the overlap integrals between Hagedorn functions with different Gaussian centers. Finally, we present numerical experiments that demonstrate the accuracy and efficiency of our algebraic method as well as its suitability to treat problems in spectroscopy and chemical dynamics.

quant-ph↗

arXiv2024

Finite-temperature vibronic spectra from the split-operator coherence thermofield dynamics

We present a numerically exact approach for evaluating vibrationally resolved electronic spectra at finite temperatures using the coherence thermofield dynamics. In this method, which avoids implementing an algorithm for solving the von Neumann equation for coherence, the thermal vibrational ensemble is first mapped to a pure-state wavepacket in an augmented space, and this wavepacket is then propagated by solving the standard, zero-temperature Schrödinger equation with the split-operator Fourier method. We show that the finite-temperature spectra obtained with the coherence thermofield dynamics in a Morse potential agree exactly with those computed by Boltzmann-averaging the spectra of individual vibrational levels. Because the split-operator thermofield dynamics on a full tensor-product grid is restricted to low-dimensional systems, we briefly discuss how the accessible dimensionality can be increased by various techniques developed for the zero-temperature split-operator Fourier method.

physics.chem-ph↗

arXiv2020

Semiclassical Approach to Photophysics Beyond Kasha's Rule and Vibronic Spectroscopy Beyond the Condon Approximation. The Case of Azulene

Azulene is a prototypical molecule with an anomalous fluorescence from the second excited electronic state, thus violating Kasha's rule, and with an emission spectrum that cannot be understood within the Condon approximation. To better understand photophysics and spectroscopy of azulene and other non-conventional molecules, we develop a systematic, general, and efficient computational approach combining semiclassical dynamics of nuclei with ab initio electronic structure. First, to analyze the nonadiabatic effects, we complement the standard population dynamics by a rigorous measure of adiabaticity, estimated with the multiple-surface dephasing representation. Second, we propose a new semiclassical method for simulating non-Condon spectra, which combines the extended thawed Gaussian approximation with the efficient single-Hessian approach. S$_{1} \leftarrow$ S$_0$ and S$_{2} \leftarrow$ S$_0$ absorption and S$_{2} \rightarrow$ S$_0$ emission spectra of azulene, recorded in a new set of experiments, agree very well with our calculations. We find that accuracy of the evaluated spectra requires the treatment of anharmonicity, Herzberg--Teller, and mode-mixing effects.

physics.chem-ph↗