Introduction | Theoretical investigation of chemical reaction mechanism using AIMD | Development of analysis methods for AIMD simulations | Acceleration of self-consistent-field (SCF) calculation in AIMD | Toward reaction control and chemical reaction dynamics of large-scale systems | References

Molecular dynamics (MD) simulation enables to reproduce atomic/molecular motions on computer by solving Newton’s equations of motion with given initial coordinate and velocity. We have shown the availability and extension of ab initio molecular dynamics (AIMD) simulation technique (see Figure 1), possessing both advantages of MD (obtaining dynamical properties directly) and electronic structure theory (describing chemical bonds quantitatively). Several novel analysis techniques proposed in our laboratory make it possible to extract the useful information from simulation results.

**Fig. 1.**Flowchart of AIMD simulation.

The AIMD simulation can treat chemical bond formation and dissociation by performing electronic structure calculation every time step, which is not accessible with classical MD employing empirical force fields. Taking this great superiority, collision reaction in ground state involving ammonia cluster ion was investigated to understand the initial step of ionic nucleation process ^{[1]}.

AIMD is also suitable for elucidating chemical reaction process via excitation state since the time evolution of electronic state is yielded. As shown in Figure 2, application of excitation dynamics to psoralen compounds ^{[2]} found that 8-methoxypsoralen (8-MOP) exhibits the opening of pyrone ring in the lowest triplet state. Such unique structure leads to a different spin distribution from the non-substituted species and 5-methoxypsoralen (5-MOP), which seems to relate with the high performance of 8-MOP toward the phototherapy for skins. This is a representative example that AIMD is useful for drug design.

**Fig. 2.**(a) Molecular structures of psoralen compounds and (b) time evolution of their oxygen-carbon distances in the T1 state.

It is indispensable to establish the appropriate methodologies analyzing trajectories and other simulation results adjusted for AIMD in order to extend our knowledge on chemical reaction dynamics. According to Wiener-Khinchin theorem ^{[3, 4]}, the Foruier transform (FT) of velocity autocorrelation function (VACF) is connected with vibrational density of states. Hence, the peak pattern of resultant power spectra can be widely used for getting all vibrational frequencies of the system ^{[5]}. However, the dynamical information is not accessible from the conventional FT, as it is averaged and/or diminished. Here, we demonstrated that spectrogram generated with the use of short-time Fourier transform (ST-FT) allows to interpret the change of vibrational states with respect to time ^{[6]}. For example, the ST-FT analysis confirms the specific distribution of vibrational modes for three different reactions (nonreactive collision, incorporation, and substitution of radical species) between astrochemical molecules ^{[7]}. We could also effectively visualize the electron dynamics such as propagation of polarization ^{[8]}. On the other hand, it is difficult to apply the ST-FT analysis to ultrafast dynamics such as core-excitation of molecules due to the limited resolution of frequency domain. To overcome this issue, an alternative approach employing the wavelet transform technique was proposed ^{[9]}

Moreover, the ST-FT was combined with energy decomposition analysis (EDA) ^{[10]}. The so-called energy transfer spectrogram (ETS) ^{[11]} is easily able to capture the dynamics of energy transfer and its relationship with molecular vibrations. Figure 3 shows the typical pictures of ETS analysis for energy relaxation process of protonated water dimer by colliding with nitrogen ^{[12]}.

**Fig. 3.**Analysis of AIMD trajectories for H

^{+}(H

_{2}O)

_{2}+ N

_{2}collision reaction.

The heavy computational cost of AIMD simulation restricts the system size, time scale, and the number of trajectories compared with classical MD. We introduced the method improving the SCF convergence by using the several previous steps of molecular orbitals for estimation of better initial guess of next step (LIMO, Figure 4). This accelerates the SCF calculation, which is bottleneck of AIMD simulation, by 2~3 times ^{[13, 14]}. Although the original LIMO requires the physical time propagation, we successfully developed another way of prediction from geometrical information (LSMO) ^{[15]}. The strong point of LSMO is it reduces the computational cost of Monte Carlo simulation and geometry optimization as well as AIMD.

**Fig. 4.**Schematic of Lagrange interpolation of molecular orbital (LIMO) method.

There is a growing interest in simulating chemical reaction dynamics of nano-scale systems as accurate as possible. We recently formulated the DC-DFTB theory, where the density-functional tight-binding (DFTB) method ^{[16, 17]} known as reliable semi-empirical method is in conjunction with linear-scaling divide-and-conquer (DC) ^{[18, 19]} technique. Using massively parallel computer such as K computer, the system containing tens of thousands of atoms is readily manageable with close to chemical accuracy. At present, the elucidation of reaction mechanism between amine solvent system and carbon dioxides is ongoing, which is expected to contribute to achieve more efficient carbon dioxide capture and storage (CCS) process.

- “
*Ab initio*MD simulation of collision reaction between ammonia cluster ion and ammonia monomer”

H. Nakai, Y. Yamauchi, A. Matsuda, Y. Okada, and K. Takeuchi,*J. Mol. Struct. (THEOCHEM)*,**592**, 61 (2002). - “
*Ab initio*molecular dynamics study on the excitation dynamics of psoralen compounds”

H. Nakai, Y. Yamauchi, A. Nakata, T. Baba, and H. Takahashi,*J. Chem. Phys.*,**119**, 4223 (2003). - “Generalized harmonic analysis”

N. Winner,*Acta Math.*,**55**, 117 (1930). - “Korrelationstheorie der stationären stochastischen Prozesse”

A. Khintchine,*Math. Ann.*,**109**, 604 (1934). - “Computing vibrational spectra from
*ab initio*molecular dynamics”

M. Thomas, M. Brehm, R. Fligg, P. Vohringer and B. Kirchner,*Phys. Chem. Chem. Phys.*,**15**, 6608 (2013). - “Short-time Fourier transform analysis of
*ab initio*molecular dynamics simulation: Collision reaction between NH_{4}^{+}(NH_{3})_{2}and NH_{3}”

Y. Yamauchi, H. Nakai, and Y. Okada,*J. Chem. Phys.*,**121**, 11098 (2004). - “Short-time Fourier Transform Analysis of
*Ab Initio*Molecular Dynamics Simulation: Collision Reaction between CN and C_{4}H_{6}”

M. Tamaoki, Y. Yamauchi, and H. Nakai,*J. Comput. Chem.*,**26**, 436 (2005). - “Short-time Fourier transform analysis of real-time time-dependent Hartree-Fock and time-dependent density functional theory calculations with Gaussian basis functions”

T. Akama and H. Nakai,*J. Chem. Phys.*,**132**, 054104 (2010). - “Wavelet Transform Analysis of
*Ab Initio*Molecular Dynamics Simulation: Application to Core-Excitation Dynamics of BF_{3}”

T. Otsuka and H. Nakai,*J. Comput. Chem.*,**28**, 1137 (2007). - “Energy density analysis with Kohn-Sham orbitals”

H. Nakai,*Chem. Phys. Lett.*,**363**, 73 (2002). - “Hybrid approach for
*ab initio*molecular dynamics simulation combining energy density analysis and short-time Fourier transform: Energy transfer spectrogram”

Y. Yamauchi and H. Nakai,*J. Chem. Phys.*,**123**, 034101 (2005). - “
*Ab Initio*Molecular Dynamics Simulation of the Energy-Relaxation Process of the Protonated Water Dimer”

Y. Yamauchi, S. Ozawa, and H. Nakai,*J. Phys. Chem. A*,**111**, 2062 (2007). - “Molecular orbital propagation to accelerate self-consistent-field convergence in an
*ab initio*molecular dynamics simulation”

T. Atsumi and H. Nakai,*J. Chem. Phys.*,**128**, 094101 (2008). - “Acceleration of Self-Consistent Field Convergence in
*Ab Initio*Molecular Dynamics Simulation with Multiconfigurational Wave Function”

M. Okoshi and H. Nakai,*J. Comput. Chem.*,**35**, 1473 (2014). - “Acceleration of self-consistent-field convergence in
*ab initio*molecular dynamics and Monte Carlo simulations and geometry optimization”

T. Atsumi and H. Nakai,*Chem. Phys. Lett.*,**490**, 102 (2010). - “Direct calculation of electron density in density-functional theory”

W. Yang,*Phys. Rev. Lett.*,**66**, 1438 (1991). - “Divide-and-Conquer Approaches to Quantum Chemistry: Theory and Implementation”

M. Kobayashi and H. Nakai, in*Linear-Scaling Techniques in Computational Chemistry and Physics,*edited by R. Zaleśny*et al.*(Springer, 2011). - “Construction of tight-binding-like potentials on the basis of density-functional theory: Application to carbon”

D. Porezag, T. Frauenheim, T. Köhler, G. Seifert, and R. Kaschner,*Phys. Rev. B*,**51**, 12947 (1995). - “Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties”

M. Elstner, D. Porezag, G. Jungnickel, J. Elsner, M. Haugk, T. Frauenheim, S. Suhai, and G. Seifert,*Phys. Rev. B*,**58**, 7260 (1998).