Density dynamics in some quantum systems

The quantum domain behavior of classical nonintegrable systems is well‐understood by the implementation of quantum fluid dynamics and quantum theory of motion. These approaches properly explain the quantum analogs of the classical Kolmogorov–Arnold–Moser type transitions from regular to chaotic domain in different anharmonic oscillators. Field‐induced tunneling and chaotic ionization in Rydberg atoms are also analyzed with the help of these theories. Quantum fluid density functional theory may be used to understand different time‐dependent processes like ion‐atom/molecule collisions, atom‐field interactions, and so forth. Regioselectivity as well as confined atomic/molecular systems and their reactivity dynamics have also been explained. © 2013 Wiley Periodicals, Inc.     

A combined molecular dynamics+quantum mechanics method for investigation of dynamic effects on local surface structures

A combined molecular dynamics (MD)+quantum mechanics (QM) method for studying processes on ionic surfaces is presented. Through the combination of classical MD and ab initio embedded-cluster calculations, this method allows the modeling of surface processes involving both the structural and dynamic features of the substrate, even for large-scale systems. The embedding approach used to link the information from the MD simulation to the cluster calculation is presented, and rigorous tests have been carried out to ensure the feasibility of the method. The electrostatic potential and electron density resulting from our embedded-cluster model have been compared with periodic slab results, and confirm the satisfying quality of our embedding scheme as well as the importance of applying embedding in our combined MD+QM approach. We show that a highly accurate representation of the Madelung potential becomes a prerequisite when the embedded-cluster approach is applied to temperature-distorted surface snapshots from the MD simulation.     

Second-order quantized Hamilton dynamics coupled to classical heat bath

Starting with a quantum Langevin equation describing in the Heisenberg representation a quantum system coupled to a quantum bath, the Markov approximation and, further, the closure approximation are applied to derive a semiclassical Langevin equation for the second-order quantized Hamilton dynamics (QHD) coupled to a classical bath. The expectation values of the system operators are decomposed into products of the first and second moments of the position and momentum operators that incorporate zero-point energy and moderate tunneling effects. The random force and friction as well as the system-bath coupling are decomposed to the lowest classical level. The resulting Langevin equation describing QHD-2 coupled to classical bath is analyzed and applied to free particle, harmonic oscillator, and the Morse potential representing the OH stretch of the SPC-flexible water model.     

A Bohmian total potential view to quantum effects. II: decay of temporarily trapped states

Formation, persistence and decay of temporarily trapped states, the time-dependent generalization of resonances, are analysed within the framework of Bohmian Mechanics. More specifically, the so-called Bohm’s total potential, the sum of classical plus Bohm’s quantum potential, is used. It is found that both formation and decay are triggered by the frequency in the oscillations of the total potential. These oscillations have been studied at the specific locations where the classical potential displays maxima, i.e. the ‘walls’ temporarily capturing the system’s density. Our main result is that the total potential oscillation frequency is solely dependent on the steepness of the classical potential ramp and, surprisingly, independent of the classical barrier height and width, well depth and width, collision energy or wavepacket width.     

Few-body quantum and many-body classical hyperspherical approaches to reactions and to cluster dynamics

The hyperspherical method is a widely used and successful approach for the quantum treatment of elementary chemical processes. It has been mostly applied to three-atomic systems, and current progress is here outlined concerning the basic theoretical framework for the extension to four-body bound state and reactive scattering problems. Although most applications only exploit the advantages of the hyperspherical coordinate systems for the formulation of the few-body problem, the full power of the technique implies representations explicitly involving quantum hyperangular momentum operators as dynamical quantities and hyperspherical harmonics as basis functions. In terms of discrete analogues of these harmonics one has a universal representation for the kinetic energy and a diagonal representation for the potential (hyperquantization algorithm). Very recently, advances have been made on the use of the approach in classical dynamics, provided that a hyperspherical formulation is given based on “classical” definitions of the hyperangular momenta and related quantities. The aim of the present paper is to offer a retrospective and prospective view of the hyperspherical methods both in quantum and classical dynamics. Specifically, regarding the general quantum hyperspherical approaches for three- and four-body systems, we first focus on the basis set issue, and then we present developments on the classical formulation that has led to applications involving the implementations of hyperspherical techniques for classical molecular dynamics simulations of simple nanoaggregates.     

Effective potential energy curves of H2 molecule evolving in a strong time‐dependent magnetic field

Evolution of hydrogen molecule, starting initially from its field‐free ground state, in a time‐dependent (TD) magnetic field of order 10¹¹ G is presented in a parallel internuclear axis and magnetic field‐axis configuration. Effective potential energy curves (EPECs), in terms of exchange and correlation energy, of the hydrogen molecule as a function of TD magnetic‐field strength, are analyzed through TD density functional computations based on a quantum fluid dynamics approach. The numerical computations are performed for internuclear separation R ranging from 0.1 to 14.0 a.u. The EPECs exhibit field‐dependent significant potential‐well minima both at large internuclear separations and at short internuclear separations with a considerable increase in the exchange and correlation energy of the hydrogen molecule. The results, when compared with the time‐independent (TI) studies involving static TI magnetic fields, reveal TD behavior of field‐dependent crossovers between different spin‐states of hydrogen molecule as indicated by the TI investigations in static magnetic fields. Besides this, present work reveals interesting dynamics in the TD total‐electronic charge‐density distribution of the hydrogen molecule. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Effective potential, Bohm’s potential plus classical potential, analysis of quantum transmission

The influence of spreading, in wavepacket transmission across a potential barrier has been analyzed, by considering several collisions between a wavepacket and a potential barrier, in which the initial distance between the packet and the barrier—the launching distance, is changed. An effective total potential (Bohm’s quantum potential plus classical potential), has been used, to show that, for suitable classical barrier widths and heights, light masses, as well as mean collision energies, one should expect an increase of the quantum transmission factor as the initial wavepacket—barrier distance is decreased. Numerically converged time-dependent wavepacket propagation calculations confirm that trend, leading to an increase as high as 20% per ?, in thin square and Eckart barrier problems. Possibilities of experimentally measuring this effect are also analyzed.     

Nuclear quantum effects on an enzyme-catalyzed reaction with reaction path potential: proton transfer in triosephosphate isomerase

Nuclear quantum mechanical effects have been examined for the proton transfer reaction catalyzed by triosephosphate isomerase, with the normal mode centroid path integral molecular dynamics based on the potential energy surface from the recently developed reaction path potential method. In the simulation, the primary and secondary hydrogens and the C and O atoms involving bond forming and bond breaking were treated quantum mechanically, while all other atoms were dealt classical mechanically. The quantum mechanical activation free energy and the primary kinetic isotope effects were examined. Because of the quantum mechanical effects in the proton transfer, the activation free energy was reduced by 2.3 kcal/mol in comparison with the classical one, which accelerates the rate of proton transfer by a factor of 47.5. The primary kinetic isotope effects of kH/kD and kH/kT were estimated to be 4.65 and 9.97, respectively, which are in agreement with the experimental value of 4+/-0.3 and 9. The corresponding Swain-Schadd exponent was predicted to be 3.01, less than the semiclassical limit value of 3.34, indicating that the quantum mechanical effects mainly arise from quantum vibrational motion rather than tunneling. The reaction path potential, in conjunction with the normal mode centroid molecular dynamics, is shown to be an efficient computational tool for investigating the quantum effects on enzymatic reactions involving proton transfer.     

Path integral calculation of free energies: quantum effects on the melting temperature of neon

The path integral formulation has been combined with several methods to determine free energies of quantum many-body systems, such as adiabatic switching and reversible scaling. These techniques are alternatives to the standard thermodynamic integration method. A quantum Einstein crystal is used as a model to demonstrate the accuracy and reliability of these free energy methods in quantum simulations. Our main interest focuses on the calculation of the melting temperature of Ne at ambient pressure, taking into account quantum effects in the atomic dynamics. The free energy of the solid was calculated by considering a quantum Einstein crystal as reference state, while for the liquid, the reference state was defined by the classical limit of the fluid. Our findings indicate that, while quantum effects in the melting temperature of this system are small, they still amount to about 6% of the melting temperature, and are therefore not negligible. The particle density as well as the melting enthalpy and entropy of the solid and liquid phases at coexistence is compared to results obtained in the classical limit and also to available experimental data.     

Effect of molecular vibrations on the MD/QC‐simulated absorption spectra

Effect of molecular vibrations on the absorption spectra simulated via a sequential approach combining molecular dynamics (MD) with quantum‐chemical calculations has been investigated. Simulated spectra have been obtained from the time‐dependent density functional theory results averaged over series of molecular geometries retrieved from Born–Oppenheimer MD trajectories. Distributions of bond lengths have been analyzed and related to the features of calculated spectra. For NVE simulations of small systems, absorption spectra exhibit bimodal bandshape as a result of classical treatment of vibrations. For NVE trajectories of larger systems or simulations in the NVT ensemble calculated absorption bands are symmetric, however, they may not agree with the results of Franck–Condon analysis. These results are practical manifestations of effects predicted theoretically from general principles. Consequences for the modeling of absorption spectra have been discussed. © 2013 Wiley Periodicals, Inc.     

An accurate and simple quantum model for liquid water

The path-integral molecular dynamics and centroid molecular dynamics methods have been applied to investigate the behavior of liquid water at ambient conditions starting from a recently developed simple point charge/flexible (SPC/Fw) model. Several quantum structural, thermodynamic, and dynamical properties have been computed and compared to the corresponding classical values, as well as to the available experimental data. The path-integral molecular dynamics simulations show that the inclusion of quantum effects results in a less structured liquid with a reduced amount of hydrogen bonding in comparison to its classical analog. The nuclear quantization also leads to a smaller dielectric constant and a larger diffusion coefficient relative to the corresponding classical values. Collective and single molecule time correlation functions show a faster decay than their classical counterparts. Good agreement with the experimental measurements in the low-frequency region is obtained for the quantum infrared spectrum, which also shows a higher intensity and a redshift relative to its classical analog. A modification of the original parametrization of the SPC/Fw model is suggested and tested in order to construct an accurate quantum model, called q-SPC/Fw, for liquid water. The quantum results for several thermodynamic and dynamical properties computed with the new model are shown to be in a significantly better agreement with the experimental data. Finally, a force-matching approach was applied to the q-SPC/Fw model to derive an effective quantum force field for liquid water in which the effects due to the nuclear quantization are explicitly distinguished from those due to the underlying molecular interactions. Thermodynamic and dynamical properties computed using standard classical simulations with this effective quantum potential are found in excellent agreement with those obtained from significantly more computationally demanding full centroid molecular dynamics simulations. The present results suggest that the inclusion of nuclear quantum effects into an empirical model for water enhances the ability of such model to faithfully represent experimental data, presumably through an increased ability of the model itself to capture realistic physical effects.     

An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics. II. Thermal correlation functions

We show the exact expression of the quantum mechanical time correlation function in the phase space formulation of quantum mechanics. The trajectory-based dynamics that conserves the quantum canonical distribution-equilibrium Liouville dynamics (ELD) proposed in Paper I is then used to approximately evaluate the exact expression. It gives exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Various methods have been presented for the implementation of ELD. Numerical tests of the ELD approach in the Wigner or Husimi phase space have been made for a harmonic oscillator and two strongly anharmonic model problems, for each potential autocorrelation functions of both linear and nonlinear operators have been calculated. It suggests ELD can be a potentially useful approach for describing quantum effects for complex systems in condense phase.     

Quantum dynamics of inelastic scattering with a moving grid

The time‐dependent discrete variable representation (TDDVR) of a wave function with grid points defined by the Hermite part of the Gauss–Hermite (G‐H) basis set introduces quantum corrections to classical mechanics. The grid points in this method follow classical trajectory and the approach converges to the exact quantum formulation with sufficient trajectories (TDDVR points) but just with a single grid point; only classical mechanics performs the dynamics. This newly formulated approach (developed for handling time‐dependent molecular quantum dynamics) has been explored to calculate vibrational transitions in the inelastic scattering processes. Traditional quantum mechanical results exhibit an excellent agreement with TDDVR profiles during the entire propagation when enough grid points are included in the quantum‐classical dynamics. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Approach to nonadiabatic transitions by density matrix evolution and molecular dynamics simulations

Many biological processes are characterized by an essentially quantum dynamical event, such as electron or proton transfer, in a complex classical environment. To treat such processes properly by computer simulation, allowing nonadiabatic transitions involving excited states, we recently developed a density matrix evolution (DME ) method [H. J. C. Berendsen and J. Mavri, J. Phys. Chem, 97 , 13464 (1993)] which simulates the dynamics of quantum systems embedded in a classical environment. The formalism of the method is presented and an overview of the applications ranging from collisions of a quantum harmonic oscillator with noble gas atoms to proton tunneling in a double-well hydrogen bond is given. The methodology for treatment of proton-transfer processes with inclusion of excited states is presented. Future application of the method on biologically interesting processes, such as proton transfer in enzymatic reactions, is discussed. © 1996 John Wiley & Sons, Inc.     

Time dependent density functional study of the photoionization dynamics of SF6

The B-spline linear combination of atomic orbitals method has been employed to study the valence and core photoionization dynamics of SF6. The cross section and asymmetry parameter profiles calculated at the time dependent density functional theory level have been found to be in fairly nice agreement with the experimental data, with the quality of the exchange-correlation statistical average of orbital potential results superior to the Van Leeuwen-Baerends 94 (LB94) ones [Phys. Rev. A 49, 2421 (1994)]. The role of response effects has been identified by a comparison of the time dependent density functional theory results with the Kohn-Sham ones interchannel coupling effects and autoionization resonances play an important role at low kinetic energies. Prominent shape resonances features have been analyzed in terms of "dipole prepared" continuum orbitals and interpreted as due to a large angular momentum centrifugal barrier as well as anisotropic (nonspherical) molecular effective potential. Finally, the method has been proven numerically stable, robust, and efficient, thanks to a noniterative implementation of the time dependent density functional theory equations and suitability of the multicentric B-spline basis set to describe continuum states from outer valence to deep core states.     

Quantum wavepacket ab initio molecular dynamics: an approach for computing dynamically averaged vibrational spectra including critical nuclear quantum effects

We have introduced a computational methodology to study vibrational spectroscopy in clusters inclusive of critical nuclear quantum effects. This approach is based on the recently developed quantum wavepacket ab initio molecular dynamics method that combines quantum wavepacket dynamics with ab initio molecular dynamics. The computational efficiency of the dynamical procedure is drastically improved (by several orders of magnitude) through the utilization of wavelet-based techniques combined with the previously introduced time-dependent deterministic sampling procedure measure to achieve stable, picosecond length, quantum-classical dynamics of electrons and nuclei in clusters. The dynamical information is employed to construct a novel cumulative flux/velocity correlation function, where the wavepacket flux from the quantized particle is combined with classical nuclear velocities to obtain the vibrational density of states. The approach is demonstrated by computing the vibrational density of states of [Cl-H-Cl]-, inclusive of critical quantum nuclear effects, and our results are in good agreement with experiment. A general hierarchical procedure is also provided, based on electronic structure harmonic frequencies, classical ab initio molecular dynamics, computation of nuclear quantum-mechanical eigenstates, and employing quantum wavepacket ab initio dynamics to understand vibrational spectroscopy in hydrogen-bonded clusters that display large degrees of anharmonicities.     

Ab initio centroid path integral molecular dynamics: application to vibrational dynamics of diatomic molecular systems

An ab initio centroid molecular dynamics (CMD) method is developed by combining the CMD method with the ab initio molecular orbital method. The ab initio CMD method is applied to vibrational dynamics of diatomic molecules, H2 and HF. For the H2 molecule, the temperature dependence of the peak frequency of the vibrational spectral density is investigated. The results are compared with those obtained by the ab initio classical molecular dynamics method and exact quantum mechanical treatment. It is shown that the vibrational frequency obtained from the ab initio CMD approaches the exact first excitation frequency as the temperature lowers. For the HF molecule, the position autocorrelation function is also analyzed in detail. The present CMD method is shown to well reproduce the exact quantum result for the information on the vibrational properties of the system.     

Applications of quantum-classical and quantum-stochastic molecular dynamics simulations for proton transfer processes

Quantum-classical and quantum-stochastic molecular dynamics models (QCMD/QSMD) are formulated and applied to describe proton transfer processes in three model systems - the proton bound ammonia-ammonia dimer in an external electrostatic field; malonaldehyde, which undergoes a quantum tautomeric rearrangement; and phospholipase A₂, an enzyme which induces a water dissociation process in its active site followed by proton hopping to a histidine imidazole ring. The proton dynamics are described by the time-dependent Schrödinger equation. The dynamics of the classical atoms are described using classical molecular dynamics. Coupling between the quantum proton (s) and the classical atoms is accomplished via conventional or extended Hellmann-Feynman forces, as well as the time-dependence of the potential energy function in the Schrödinger equation. The interaction of the system with its environment is described by stochastic forces. Possible extensions of the models as well as future applications in molecular structure and dynamics analysis will be briefly discussed.     

Multiscale modeling of materials based on force and charge density fidelity

The approximate representation of a quantum solid as an equivalent composite semiclassical solid is considered for insulating materials. The composite is comprised of point ions moving on a potential energy surface. In the classical bulk domain this potential energy is represented by potentials constructed to give the same structure and elastic properties as the underlying quantum solid. In a small local quantum domain the potential is determined from a detailed quantum calculation of the electronic structure. The new features of this well-studied problem are (1) a clearly stated theoretical context in which approximations leading to the model are introduced, (2) the representation of the classical domain by potentials focused on reproducing the specific quantum response being studied, (3) development of "pseudoatoms" for a realistic treatment of charge densities where bonds have been broken to define the environment of the quantum domain, and (4) inclusion of polarization effects on the quantum domain due to its distant bulk environment. This formal structure is illustrated in detail for a SiO(2) nanorod. More importantly, each component of the proposed modeling is tested quantitatively for this case, verifying its accuracy as a faithful multiscale model of the original quantum solid. To do so, the charge density of the entire nanorod is calculated quantum mechanically to provide the reference by which to judge the accuracy of the modeling. The construction of the classical potentials, the rod, the pseudoatoms, and the multipoles is discussed and tested in detail. It is then shown that the quantum rod, the rod constructed from the classical potentials, and the composite classical/quantum rod all have the same equilibrium structure and response to elastic strain. In more detail, the charge density and forces in the quantum subdomain are accurately reproduced by the proposed modeling of the environmental effects even for strains beyond the linear domain. The accuracy of the modeling is shown to apply for two quite different choices for the underlying quantum chemical method: transfer Hamiltonian and density functional methods.