Optimal Mode Combination in the Multiconfiguration Time-Dependent Hartree Method through Multivariate Statistics: Factor Analysis and Hierarchical Clustering

Mendive-Tapia, David; Meyer, Hans‐Dieter; Vendrell, Oriol

doi:10.1021/acs.jctc.2c01089

Cited by 7 publications

(5 citation statements)

References 85 publications

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“…In order to explore the spatiotemporal evolution characteristics of the high-quality economic development in the counties along the Yellow River in Ningxia from 2014 to 2020, a traditional factor analysis is obviously not applicable, so a multi-indicator panel data factor analysis is used for this research [26]. Due to the differences in data among different indicator units in the indicator system, which do not have comparability and uniformity, in order to avoid bias in the evaluation results, data standardization is carried out before analyzing the data.…”

Section: Multi-indicator Panel Data Factor Analysismentioning

confidence: 99%

Comprehensive Evaluation of the High-Quality Development of the Ecological and Economic Belt along the Yellow River in Ningxia

Peng

Shen

et al. 2023

Sustainability

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The measurement of high-quality economic development and regional research plays a crucial role in achieving ecologically led high-quality development. This paper aims to establish a comprehensive evaluation index system for the high-quality level of development in Ningxia’s Yellow River ecological and economic zone, focusing on five dimensions: innovation, coordination, green, openness, and shared. By employing a factor analysis, this study estimates the level of high-quality development along the Yellow River Ecological Economic Belt in Ningxia for the year 2020. A multi-index panel data factor analysis and entropy weight TOPSIS method are employed to analyze the spatiotemporal evolution characteristics of high-quality development across 10 counties from 2014 to 2020. The empirical findings reveal that, in 2020, the overall level of high-quality development in the region remained relatively low. Among the contributing factors, shared and coordinated development demonstrated the highest impact on high-quality development, while open, green, and innovative development showed limited influence. Only Xingqing District, Litong District, and Helan County in the 10 counties have a composite factor score of greater than 0 on the level of economic development, while the other 7 counties have a composite score of less than 0. The study also identified a significant spatial heterogeneity in the quality of high-quality development along Ningxia’s Yellow River Ecological Economic Belt. Through a cluster analysis, the regions along the Yellow River Ecological Economic Belt in Ningxia are classified into categories of high, medium, and low levels of quality development. Over the period from 2014 to 2020, each county exhibited a steady increase in high-quality development, while the differences in development levels among the 10 counties gradually diminished. Based on these findings, practical suggestions are provided to guide Ningxia in leading the path of high-quality development through ecological civilization construction along the Yellow River ecological economy.

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Section: Multi-indicator Panel Data Factor Analysismentioning

confidence: 99%

Comprehensive Evaluation of the High-Quality Development of the Ecological and Economic Belt along the Yellow River in Ningxia

Peng

Shen

et al. 2023

Sustainability

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“…16,[74][75][76][77][78][79][80][81][82][83][84][85] It has further become increasingly important to combine different coordinates, e.g., in multi-layer multiconfiguration time-dependent Hartree, as illustrated by combined Jacobi and Cartesian coordinates in the description of the Zundel cation. 86 Although curvilinear coordinates solve some issues rectilinear NCs pose, their applicability is limited as they complicate the expression of the nuclear KEO. The main issues arise from kinetic coupling terms, as the nuclear KEO is not separable in curvilinear coordinates, in contrast to the KEO in rectilinear NCs.…”

Section: Introduction a Coordinate Systemsmentioning

confidence: 99%

Determining internal coordinate sets for optimal representation of molecular vibration

Oenen,

Dinu,

Liedl

2024

The Journal of Chemical Physics

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Arising from the harmonic approximation in solving the vibrational Schrödinger equation, normal modes dissect molecular vibrations into distinct degrees of freedom. Normal modes are widely used as they give rise to descriptive vibrational notations and are convenient for expanding anharmonic potential energy surfaces as an alternative to higher-order Taylor series representations. Usually, normal modes are expressed in Cartesian coordinates, which bears drawbacks that can be overcome by switching to internal coordinates. Considering vibrational notations, normal modes with delocalized characters are difficult to denote, but internal coordinates offer a route to clearer notations. Based on the Hessian, normal mode decomposition schemes for a given set of internal coordinates can describe a normal mode by its contributions from internal coordinates. However, choosing a set of internal coordinates is not straightforward. While the Hessian provides unique sets of normal modes, various internal coordinate sets are possible for a given system. In the present work, we employ a normal mode decomposition scheme to choose an optimal set. Therefore, we screen reasonable sets based on topology and symmetry considerations and rely on a metric that minimizes coupling between internal coordinates. Ultimately, the Nomodeco toolkit presented here generates internal coordinate sets to find an optimal set for representing molecular vibrations. The resulting contribution tables can be used to clarify vibrational notations. We test our scheme on small to mid-sized molecules, showing how the space of definable internal coordinate sets can significantly be reduced.

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“…The correlated/coupled motion of the nuclei in a molecular system is an ultrafast phenomenon, and, as such, it must be studied using either experimental ultrafast techniques, which include pulse probe methods, or computer simulation methods aimed at the interpretation and simulation of two-dimensional spectra. ,− In theoretical chemistry, the identification of the uncoupled degrees of freedom is useful for computational methodologies that calculate the vibrational spectrum in reduced dimensionality, such as, for instance, semiclassical approaches, − QM/MM calculations, tensor-trains and sum of products of basis functions methods − and also the Multi-Configuration Time-Dependent Hartree method (MCTDH) − and methods based on MCTDH-like ansatz . Applications of all the aforementioned methods imply either that part of a system is partially independent of another or that the two parts have an artificial interaction.…”

Section: Introductionmentioning

confidence: 99%

Molecular Dynamics of Artificially Pair-Decoupled Systems: An Accurate Tool for Investigating the Importance of Intramolecular Couplings

Gandolfi,

Ceotto

2023

J. Chem. Theory Comput.

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We propose a numerical technique to accurately simulate the vibrations of organic molecules in the gas phase, when pairs of atoms (or, in general, groups of degrees of freedom) are artificially decoupled, so that their motion is instantaneously decorrelated. The numerical technique we have developed is a symplectic integration algorithm that never requires computation of the force but requires estimates of the Hessian matrix. The theory we present to support our technique postulates a pair-decoupling Hamiltonian function, which parametrically depends on a decoupling coefficient α ∈ [0, 1]. The closer α is to 0, the more decoupled the selected atoms. We test the correctness of our numerical method on small molecular systems, and we apply it to study the vibrational spectroscopic features of salicylic acid at the Density Functional Theory ab initio level on a fitted potential. Our pair-decoupled simulations of salicylic acid show that decoupling hydrogen-bonded atoms do not significantly influence the frequencies of stretching modes, but enhance enormously the out-of-plane wagging and twisting motions of the hydroxyl and carboxyl groups to the point that the carboxyl and hydroxyl groups may overcome high potential energy barriers and change the salicylic acid conformation after a short simulation time. In addition, we found that the acidity of salicylic acid is more influenced by the dynamical couplings of the proton of the carboxylic group with the carbon ring than with the hydroxyl group.

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Optimal Mode Combination in the Multiconfiguration Time-Dependent Hartree Method through Multivariate Statistics: Factor Analysis and Hierarchical Clustering

Cited by 7 publications

References 85 publications

Comprehensive Evaluation of the High-Quality Development of the Ecological and Economic Belt along the Yellow River in Ningxia

Comprehensive Evaluation of the High-Quality Development of the Ecological and Economic Belt along the Yellow River in Ningxia

Determining internal coordinate sets for optimal representation of molecular vibration

Molecular Dynamics of Artificially Pair-Decoupled Systems: An Accurate Tool for Investigating the Importance of Intramolecular Couplings

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