| 研究課題/領域番号 |
15K17805
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| 研究機関 | 東京大学 |
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研究代表者 |
LOETSTEDT ERIK 東京大学, 大学院理学系研究科(理学部), 助教 (80632984)
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| 研究期間 (年度) |
2015-04-01 – 2018-03-31
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| キーワード | Schrodinger equation / laser-matter interaction / quantum chemistry |
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| 研究実績の概要 |
The research performed within the current grant concerns the efficient numerical solution of the time-dependent many-electron Schrodinger equation, and the physical interpretation of the numerically obtained solution. The numerical solution of the many-electron Schrodinger equation is important for the interpretation of gas-phase experiments on atoms and molecules performed with ultrashort, intense laser pulses.
The current research is based on the Multi-Configuration Time-Dependent Hartree-Fock (MCTDHF) method, where the time-dependent wave function is written as a sum of products of time-dependent determinants and time-dependent configuration-interaction (CI) coefficients. The aim is to simplify the MCTDHF method to make it more efficient, enabling the application to larger many-electron systems. In addition, I also aim to clarify the structure of the many-electron wave function by making approximations that have a transparent physical meaning.
The main approach to simplifying the MCTDHF method is to make a product approximation for the CI coefficients. This approach has the possibility of largely reducing the computational effort for the solution of the MCTDHF equations, while at the same time providing an insight into the structure of the many-electron time-dependent wave function. To date, two different factorization schemes have been proposed, the Factorized CI method, and the Time-Dependent Geminal Method. Both methods have been confirmed by application to laser-driven atoms and model molecules.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
In FY 2015, I proposed a new way of simplifying the MCTDHF method: The Factorized CI method, in which the large CI-matrix is factorized into a product of three smaller matrices. The Factorized CI method was tested on one-dimensional model systems, with the results published in [E. Lotstedt, T. Kato, K. Yamanouchi, J. Chem. Phys. 144, 154111 (2016)].
The efforts during the fiscal year FY 2016 were concentrated on the following two (related) projects:
(i) Implementation of the MCTDHF equations for three-dimensional atomic systems. In order to efficiently calculate the two-electron integrals, a program code for the solution of the Poisson equation was developed. The time-dependent response of a beryllium atom to an intense, short laser pulse was calculated, and the method was confirmed to work correctly.
(ii) Development of a simplification scheme called the Time-Dependent Geminal method. A geminal is a two-electron orbital. The Time-Dependent Geminal approach can be viewed as a particular scheme for CI-matrix factorization. I demonstrated that the Time-Dependent Geminal method can be used to obtain insight into the time-dependent correlation between pairs of electrons.
A manuscript describing the accomplishments (i) and (ii) is being written up for submission to a scientific journal.
Furthermore, a review about time-dependent many-particle methods in general and the Factorized CI method in particular has been accepted for publication in “Progress in Ultrafast Intense Laser Science XIII” (Springer publications, to appear in 2017).
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| 今後の研究の推進方策 |
During the final year (FY 2017) of the present grant, I plan to (i) apply the two newly introduced factorization schemes (the Factorized CI method and the Time-Dependent Geminal method) to diatomic molecules, and (ii) develop a hybrid grid for the application to molecules of arbitrary symmetry.
The main effort will be put into the completion of part (i). For the application of the MCTDHF method combined with the Factorized CI or the Time-Dependent Geminal method, it is necessary to implement a method for solving the Poisson equation for systems with cylindrical symmetry. After completion of such a code, interesting systems which could be studied are acetylene (C2H2) and nitrogen (N2). Acetylene is interesting because of the finding of enhanced ionization at stretched C-H internuclear distance [see e.g. Gong et al., Phys. Rev. Lett. 112, 243001 (2014)], and N2 is interesting because of the possibility of inducing lasing in the molecular ion N2+ created by strong-field ionization [see Xu et al., Nat. Commun. 6, 8347 (2015)].
If time allows, project (ii) will be started. As a first application of the method, the ionization yield of small molecules without any symmetry (e.g. H3+ with a distorted molecular geometry) will be calculated, employing the single-active electron approximation.
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| 備考 |
Research results will be posted on the webpage of the Yamanouchi lab at The University of Tokyo.
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