Molecular Theory Including Quantum Effects and Thermal Fluctuations

Abstract

Recent progress in our theoretical developments and applications where thermal fluctuations and quantum effects are important are reviewed. We first show that motions of a confined atom coupled with a fullerene cage cause large thermal fluctuation of the effective charge on the confined atom and that the fluctuation is sensitive to applied temperature and the number of confined species. Second, two different approaches to treat nuclear quantum effects are discussed. One is nonBornOppenheimer (NBO) molecular theory, which is one of an extension of molecular orbital theory for electrons to nuclear motions. This method is suitable to describe static and stationary nuclear (vibrational) states so we apply this method to obtain vibrationally coupled electron density of a protonatable amino acid. We compare the obtained electron density through NBO treatment with conventional calculations. The other approach is referred as to quantum cumulant dynamics (QCD), which is a generalization of quantized Hamiltonian dynamics initially proposed by Prezhdo. This method is applied to vibrational analyses. The ordinary normal mode analysis (NMA) is extended to include quantum degrees of freedom based on QCD formalism, which gives a better description of the vibrational state, where ordinary NMA gives incorrect results. Vibrational frequencies of small molecules by the QCD simulation are compared with those by classical molecular dynamics (MD). It is found that QCD is superior to classical MD in that the results obtained by QCD are in good agreement with those by full quantum treatment. Finally the theoretical background of a real-space gridbased time-dependent density functional theory (RSTDDFT) is explained. This method is applied to solve a NBO problem by using an imaginary time propagator and electron dynamics driven by an off-resonant circularly polarized laser plus in addition to using a real time propagator. For the latter case, we investigate atom-centered dipole moment and induced current and detect the electronic fluctuation in a SiH 4 molecule after irradiation.

Quantal Cumulant Mechanics as Extended Ehrenfest Theorem

“…Recently Shigeta and co-workers derived a general expression for the expectation value of an arbitrary operator by means of cumulants rather than moments [9][10][11][12][13][14][15][16][17][18][19]. For one-dimensional case, the expectation value of a differential arbitrary operator, A s ( q, p ) , that consists of the symmetric sum of power series of q and p is derived as…”

Quantal cumulant mechanics and dynamics for multidimensional quantum many‐body clusters

“…According to the previous papers,26–31 we suggested that the expectation value of the operator composed of both position and momentum operators could be expressed as a function of positions, momentums, and cumulants 32, 33. Here, we also apply the same methodology to the evaluation of the total energy within a second‐order approximation.…”

“…One of the quite distinguished works to treat real‐time quantum effects with lower cost is the quantized Hamilton dynamics (QHD) approach,20–25 which Prezhdo and coworkers developed based on the Heisenberg's equations of motion (EOM). Recently, we have developed a quantal cumulant mechanics (QCM), where coordinates, momenta, and cumulants are essential variables in this extended formalism of the classical mechanics toward the quantum mechanics 26–30. The key ideas are that a coordinate shift operator acting on a potential operator is introduced and that a cumulant expansion is applied to the evaluation of the expectation value of the shift operator.…”

Quantal cumulant dynamics for real‐time simulations of quantum many‐body systems

“…Kanno et al have extended the nonadiabatic dynamics of chiral aromatic molecules, including vibronic couplings modulated by an atto‐sec linearly polarized pulse laser field. Since a full‐quantum description for many electron systems is limited to a few electron systems, such as H 2 and at most LiH, a time‐dependent density functional theory is alternatively used for the real‐time electron dynamics at fixed nuclei using real‐space density functional theory . However, it is difficult for this method to describe complex electronic structures, which requires the multiconfigurational nature of the electronic wave function.…”

“…Since a full-quantum description for many electron systems is limited to a few electron systems, such as H 2 and at most LiH, a time-dependent density functional theory is alternatively used for the real-time electron dynamics at fixed nuclei using real-space density functional theory. [10,11] However, it is difficult for this method to describe complex electronic structures, which requires the multiconfigurational nature of the electronic wave function. To address these issues, multiconfigurational electron dynamics and the time-dependent completeactive-space self-consistent field using the real-space grid basis are recently developed to investigate the ionization dynamics of small molecules in an intense laser field.…”