المؤلفون: Vaníček, Jiří J. L., Zhang, Zhan Tong

مصطلحات موضوعية: Quantum Physics, Mathematical Physics, Physics - Chemical Physics

الوصف: 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 Schr\"{o}dinger 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.
Comment: 26 pages, 2 figures; minor textual revisions, correction of two entries in Table 2

الوصول الحر: http://arxiv.org/abs/2405.07880Test

المؤلفون: Zhang, Zhan Tong, Vaníček, Jiří J. L.

مصطلحات موضوعية: Physics - Chemical Physics, Quantum Physics

الوصف: Single vibronic level (SVL) fluorescence spectroscopy contributes to the understanding of molecular vibrational structures and relaxation processes. Here, we present a practical method for computing SVL fluorescence spectra of polyatomic molecules from arbitrary initial vibrational levels. This method, which combines a time-dependent approach using Hagedorn wavepackets with accurate evaluation of electronic structure, captures both mode distortion and Duschinsky rotation. 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. With the Hagedorn approach, we not only reproduce the previously reported simulation results for singly excited $12^{1}$ and $\overline{11}^{1}$ levels, but also are able to compute SVL spectra from multiply excited levels in good agreement with experiments. All spectra were obtained from the same wavepacket trajectory without any additional propagation beyond what is required for ground-state emission spectra.
Comment: 12 pages, 3 figures; v3: text revisions

الوصول الحر: http://arxiv.org/abs/2403.00702Test

المؤلفون: Zhang, Zhan Tong, Vaníček, Jiří J. L.

مصطلحات موضوعية: Physics - Chemical Physics, Quantum Physics

الوصف: 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 Schr\"{o}dinger 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.
Comment: 8 pages, 5 figures

الوصول الحر: http://arxiv.org/abs/2403.00577Test

المؤلفون: Zhang, Zhan Tong, Vaníček, Jiří J. L.

المصدر: J. Chem. Phys. 160, 084103 (2024)

مصطلحات موضوعية: Physics - Chemical Physics, Physics - Computational Physics, Quantum Physics

الوصف: 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 Schr\"odinger 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.
Comment: 5 pages, 4 figures

الوصول الحر: http://arxiv.org/abs/2311.10004Test

المؤلفون: Zhang, Zhan Tong¹ (AUTHOR), Vaníček, Jiří J. L.¹ (AUTHOR) jiri.vanicek@epfl.ch

المصدر: Journal of Chemical Physics. 2/28/2024, Vol. 160 Issue 8, p1-6. 6p.

مصطلحات موضوعية: *SEPARATION of variables, *ELECTRONIC spectra, *VIBRATIONAL spectra, *SCHRODINGER equation, *MORSE theory, *COHERENCE (Physics), *VON Neumann algebras

مستخلص: 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. [ABSTRACT FROM AUTHOR]

المؤلفون: Prlj, Antonio, Begušić, Tomislav, Zhang, Zhan Tong, Fish, George Cameron, Wehrle, Marius, Zimmermann, Tomáš, Choi, Seonghoon, Roulet, Julien, Moser, Jacques-Edouard, Vaníček, Jiří

مصطلحات موضوعية: Physics - Chemical Physics, Physics - Computational Physics, Quantum Physics

الوصف: 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.
Comment: Added Fig. 1 and Eq. (5), modified figure captions. Last 15 pages contain the Supporting Information

الوصول الحر: http://arxiv.org/abs/2001.08414Test

المؤلفون: Zhang, Zhan Tong, Vaníček, Jiří

مصطلحات موضوعية: Physics - Chemical Physics, Physics - Computational Physics, Quantum Physics

الوصف: The inclusion of temperature effects is important to properly simulate and interpret experimentally observed vibrationally resolved electronic spectra. We present a numerically exact approach for evaluating these spectra at finite temperature using the thermofield coherence dynamics. In this method, which avoids implementing an algorithm for solving the von Neumann equation for the 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 Schr\"{o}dinger equation with the split-operator Fourier method. We show that the finite-temperature spectra obtained with the thermofield coherence 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. ; Comment: 5 pages, 4 figures

العلاقة: http://arxiv.org/abs/2311.10004Test

الإتاحة: http://arxiv.org/abs/2311.10004Test

المؤلفون: Prlj, Antonio, Begušić, Tomislav, Zhang, Zhan Tong, Fish, George Cameron, Wehrle, Marius, Zimmermann, Tomáš, Choi, Seonghoon, Roulet, Julien, Moser, Jacques-Edouard, Vaníček, Jiří

الوصف: Data for publication: A. Prlj, T. Begušić, Z. T. Zhang, G. C. Fish, M. Wehrle, T. Zimmermann, S. Choi, J. Roulet, J.-E. Moser, and J. Vaníček, J. Chem. Theory Comput. 16 (4), 2617–2626 (2020). Contains simulated linear absorption and emission spectra of azulene, excited-state and ground-state ab initio trajectories and single-point calculations, and results of nonadiabatic mixed quantum-classical simulations.

العلاقة: info:eu-repo/grantAgreement/SNSF/Programmes/51NF40-157956/; info:eu-repo/grantAgreement/EC/H2020/683069/; https://zenodo.org/communities/epflTest; https://zenodo.org/record/5046051Test; https://doi.org/10.5281/zenodo.5046051Test; oai:zenodo.org:5046051

الإتاحة: https://doi.org/10.5281/zenodo.5046051Test
https://doi.org/10.1021/acs.jctc.0c00079Test
https://doi.org/10.5281/zenodo.5046050Test
https://zenodo.org/record/5046051Test