2015 Fiscal Year Research-status Report
Simulation of laser-driven many-electron atoms and molecules
| Project/Area Number |
15K17805
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| Research Institution | The University of Tokyo |
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Principal Investigator |
LOETSTEDT ERIK 東京大学, 理学(系)研究科(研究院), 助教 (80632984)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | TDSE / laser-matter interaction / computational chemistry / Hartree-Fock |
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| Outline of Annual Research Achievements |
The aim of the present research is to develop an efficient method to solve the time-dependent Schrodinger equation for many-electron atoms and molecules exposed to intense laser pulses. Presently, sophisticated laser systems make it possible to perform very detailed experiments on intense laser-atom and laser-molecule interaction. However, to interpret the experimental results, efficient simulation algorithms are necessary. Standard quantum chemistry software cannot be directly used, since these programs were developed for problems which do not depend on time. Methods that can be used to simulate the real-time motion of electrons in atoms and molecules are crucial to approach the goal of a complete understanding of the correlated motion of laser-driven electrons.
By using the well-established Multi-Configuration Time-Dependent Hartree-Fock (MCTDHF) method as a starting point, I aim to develop a new approximation scheme. In the MCTDHF method, the wave function is written as a sum of time-dependent determinants multiplied with time-dependent CI coefficients. My proposal is to further simplify the wave function by decomposing the array of the CI coefficients into a product form. In this way, much fewer parameters are needed to construct the time-dependent wave function.
During FY2015, I have investigated one particular ansatz for the decomposition of the array of CI coefficients. By applying the method to several model systems, I confirmed the efficiency and usefulness of the method.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
During FY2015, I have investigated one particular form of product ansatz for the array of CI coefficients. In the adopted ansatz, the array of CI coefficients is labelled by two indices: one index for the spin-up electrons, and one index for the spin-down electrons. The CI two-index array (a matrix) is then factorized into three matrices of much smaller dimension than the original CI matrix. I call the method the “Factorized CI” method.
The Factorized CI method was implemented and applied to three model systems (a 1D carbon atom, a 1D beryllium atom, and a 1D chain of four hydrogen atoms), where all electrons are restricted to move in one dimension. I confirmed that the results obtained by the Factorized CI method converge to the results obtained by the reference MCTDHF method, provided that a certain expansion length parameter is large enough. A manuscript containing the above results was published in the Journal of Chemical Physics (AIP) in April 2016.
A drawback of the Factorized CI method in its present form is that the spin quantum number is not exactly conserved. A small amount of spin contamination may be present in the wave function. This issue will be addressed in the ensuing two years of the present project.
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| Strategy for Future Research Activity |
During the present fiscal year (FY2016), I will concentrate my research around two major directions:
1. Development of a more efficient CI matrix factorization scheme. Efforts will be made to find a factorization scheme where the spin quantum number is conserved by construction. Other factorization schemes, where the number of parameters required for the construction of the CI matrix is further reduced, will also be investigated.
2. Implementation of the Factorized CI method for three-dimensional systems. At first, systems with spherical symmetry (atoms) will be investigated. Following a successful demonstration on atomic systems, I will continue with the development of a hybrid grid consisting of a combination of a Cartesian grid and a radial grid. The hybrid grid should allow the treatment of molecular systems with arbitrary symmetry.
I plan to delay the parallelization of the code for supercomputer calculations until the following fiscal year.
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| Remarks |
Research results are posted on the webpage of the Yamanouchi lab at The University of Tokyo.
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