# Characterization of multielectron dynamics in molecules: A multiconfiguration time-dependent Hartree-Fock picture

## Abstract

Using the framework of multiconfiguration theory, where the wavefunction Φ(t) of a many-electron system at time t is expanded as Φ(t)=∑{sub I}C{sub I}(t)Φ{sub I}(t) in terms of electron configurations (Φ{sub I}(t)), we divided the total electronic energy E(t) as E(t)=∑{sub I}|C{sub I}(t)|{sup 2}E{sub I}(t) . Here E{sub I}(t) is the instantaneous phase changes of C{sub I}(t) regarded as a configurational energy associated with Φ{sub I}(t). We then newly defined two types of time-dependent states: (i) a state at which the rates of population transfer among configurations are all zero; (ii) a state at which (E{sub I}(t)) associated with the quantum phases of C{sub I}(t) are all the same. We call the former time-dependent state a classical stationary state by analogy with the stationary (steady) states of classical reaction rate equations and the latter one a quantum stationary state. The conditions (i) and (ii) are satisfied simultaneously for the conventional stationary state in quantum mechanics. We numerically found for a LiH molecule interacting with a near-infrared (IR) field ε(t) that the condition (i) is satisfied whenever the average velocity of electrons is zero and the condition (ii) is satisfied whenever the average acceleration is zero. We also derived the chemical potentialsmore »

- Authors:

- Department of Chemistry, Graduate School of Science, Tohoku University, Sendai 980-8578 (Japan)
- Graduate School of Nanobioscience, Yokohama City University, 22-2 Seto, Kanazawa-ku, Yokohama 236-0027 (Japan)
- Department of Chemistry, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan)
- Department of Chemistry, Graduate School of Science, Osaka Prefecture University, Osaka 599-8531 (Japan)

- Publication Date:

- OSTI Identifier:
- 22308397

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 141; Journal Issue: 11; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; COMPARATIVE EVALUATIONS; DIPOLE MOMENTS; ELECTRON-ELECTRON INTERACTIONS; ELECTRONS; HARTREE-FOCK METHOD; HYDROGEN; LITHIUM HYDRIDES; MOLECULES; REACTION KINETICS; TIME DEPENDENCE; WAVE FUNCTIONS

### Citation Formats

```
Ohmura, Shu, Kono, Hirohiko, E-mail: hirohiko-kono@m.tohoku.ac.jp, Oyamada, Takayuki, Kato, Tsuyoshi, Nakai, Katsunori, and Koseki, Shiro.
```*Characterization of multielectron dynamics in molecules: A multiconfiguration time-dependent Hartree-Fock picture*. United States: N. p., 2014.
Web. doi:10.1063/1.4894505.

```
Ohmura, Shu, Kono, Hirohiko, E-mail: hirohiko-kono@m.tohoku.ac.jp, Oyamada, Takayuki, Kato, Tsuyoshi, Nakai, Katsunori, & Koseki, Shiro.
```*Characterization of multielectron dynamics in molecules: A multiconfiguration time-dependent Hartree-Fock picture*. United States. doi:10.1063/1.4894505.

```
Ohmura, Shu, Kono, Hirohiko, E-mail: hirohiko-kono@m.tohoku.ac.jp, Oyamada, Takayuki, Kato, Tsuyoshi, Nakai, Katsunori, and Koseki, Shiro. Sun .
"Characterization of multielectron dynamics in molecules: A multiconfiguration time-dependent Hartree-Fock picture". United States. doi:10.1063/1.4894505.
```

```
@article{osti_22308397,
```

title = {Characterization of multielectron dynamics in molecules: A multiconfiguration time-dependent Hartree-Fock picture},

author = {Ohmura, Shu and Kono, Hirohiko, E-mail: hirohiko-kono@m.tohoku.ac.jp and Oyamada, Takayuki and Kato, Tsuyoshi and Nakai, Katsunori and Koseki, Shiro},

abstractNote = {Using the framework of multiconfiguration theory, where the wavefunction Φ(t) of a many-electron system at time t is expanded as Φ(t)=∑{sub I}C{sub I}(t)Φ{sub I}(t) in terms of electron configurations (Φ{sub I}(t)), we divided the total electronic energy E(t) as E(t)=∑{sub I}|C{sub I}(t)|{sup 2}E{sub I}(t) . Here E{sub I}(t) is the instantaneous phase changes of C{sub I}(t) regarded as a configurational energy associated with Φ{sub I}(t). We then newly defined two types of time-dependent states: (i) a state at which the rates of population transfer among configurations are all zero; (ii) a state at which (E{sub I}(t)) associated with the quantum phases of C{sub I}(t) are all the same. We call the former time-dependent state a classical stationary state by analogy with the stationary (steady) states of classical reaction rate equations and the latter one a quantum stationary state. The conditions (i) and (ii) are satisfied simultaneously for the conventional stationary state in quantum mechanics. We numerically found for a LiH molecule interacting with a near-infrared (IR) field ε(t) that the condition (i) is satisfied whenever the average velocity of electrons is zero and the condition (ii) is satisfied whenever the average acceleration is zero. We also derived the chemical potentials μ{sub j}(t) for time-dependent natural orbitals ϕ{sub j}(t) of a many-electron system. The analysis of the electron dynamics of LiH indicated that the temporal change in Δμ{sub j}(t) ≡ μ{sub j}(t) + ε(t) · d{sub j}(t) − μ{sub j}(0) correlates with the motion of the dipole moment of ϕ{sub j}(t), d{sub j}(t). The values Δμ{sub j}(t) are much larger than the energy ζ{sub j}(t) directly supplied to ϕ{sub j}(t) by the field, suggesting that valence electrons exchange energy with inner shell electrons. For H{sub 2} in an intense near-IR field, the ionization efficiency of ϕ{sub j}(t) is correlated with Δμ{sub j}(t). Comparing Δμ{sub j}(t) to ζ{sub j}(t), we found that energy accepting orbitals of Δμ{sub j}(t) > ζ{sub j}(t) indicate high ionization efficiency. The difference between Δμ{sub j}(t) and ζ{sub j}(t) is significantly affected by electron-electron interactions in real time.},

doi = {10.1063/1.4894505},

journal = {Journal of Chemical Physics},

issn = {0021-9606},

number = 11,

volume = 141,

place = {United States},

year = {2014},

month = {9}

}