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Hagedorn wavepackets have been used with local harmonic approximation to partially capture the anharmonic effects on single vibronic level (SVL) spectra in model potentials. To make the Hagedorn approach practical for realistic anharmonic polyatomic molecules, 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 CF$_2$, the spectra computed with the on-the-fly local harmonic Hagedorn wavepacket dynamics agree well with experimental data, especially for low initial excitations.

Hagedorn wavepacket dynamics yields exact single vibronic level (SVL) fluorescence spectra from any initial vibrational level in displaced, squeezed, and Duschinsky-rotated global harmonic models. Real molecules, however, have anharmonic potential energy surfaces. To partially describe effects of anharmonicity on the spectra, we combine the Hagedorn approach to spectroscopy with the local harmonic approximation of the potential. We compute the SVL spectra for several anharmonic Morse-type potentials in one, two, and twenty dimensions and compare them to the results of global harmonic approximations and, where possible, of exact quantum calculations. We show that the local harmonic approach yields more accurate results than global harmonic approximations, especially for the emission spectra from higher initial vibrational levels., Comment: 7 pages, 5 figures

With the rapid development of natural language processing (NLP) technology, large-scale pre-trained language models such as GPT-3 have become a popular research object in NLP field. This paper aims to explore sentiment analysis optimization techniques based on large pre-trained language models such as GPT-3 to improve model performance and effect and further promote the development of natural language processing (NLP). By introducing the importance of sentiment analysis and the limitations of traditional methods, GPT-3 and Fine-tuning techniques are introduced in this paper, and their applications in sentiment analysis are explained in detail. The experimental results show that the Fine-tuning technique can optimize GPT-3 model and obtain good performance in sentiment analysis task. This study provides an important reference for future sentiment analysis using large-scale language models.

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; corrected the prefactor in eqs. 43, 65 and 66

The Human Genome Project has led to an exponential increase in data related to the sequence, structure, and function of biomolecules. Bioinformatics is an interdisciplinary research field that primarily uses computational methods to analyze large amounts of biological macromolecule data. Its goal is to discover hidden biological patterns and related information. Furthermore, analysing additional relevant information can enhance the study of biological operating mechanisms. This paper discusses the fundamental concepts of RNA, RNA secondary structure, and its prediction.Subsequently, the application of machine learning technologies in predicting the structure of biological macromolecules is explored. This chapter describes the relevant knowledge of algorithms and computational complexity and presents a RNA tertiary structure prediction algorithm based on ResNet. To address the issue of the current scoring function's unsuitability for long RNA, a scoring model based on ResNet is proposed, and a structure prediction algorithm is designed. The chapter concludes by presenting some open and interesting challenges in the field of RNA tertiary structure prediction.

The integration of LLMOps into personalized recommendation systems marks a significant advancement in managing LLM-driven applications. This innovation presents both opportunities and challenges for enterprises, requiring specialized teams to navigate the complexity of engineering technology while prioritizing data security and model interpretability. By leveraging LLMOps, enterprises can enhance the efficiency and reliability of large-scale machine learning models, driving personalized recommendations aligned with user preferences. Despite ethical considerations, LLMOps is poised for widespread adoption, promising more efficient and secure machine learning services that elevate user experience and shape the future of personalized recommendation systems.

This paper explores the application of deep learning techniques, particularly focusing on BERT models, in sentiment analysis. It begins by introducing the fundamental concept of sentiment analysis and how deep learning methods are utilized in this domain. Subsequently, it delves into the architecture and characteristics of BERT models. Through detailed explanation, it elucidates the application effects and optimization strategies of BERT models in sentiment analysis, supported by experimental validation. The experimental findings indicate that BERT models exhibit robust performance in sentiment analysis tasks, with notable enhancements post fine-tuning. Lastly, the paper concludes by summarizing the potential applications of BERT models in sentiment analysis and suggests directions for future research and practical implementations.

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

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

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

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