Unified quantum molecular dynamics method based on centroid molecular dynamics and semiempirical molecular orbital theory

Structural and electronic properties of guanine and guanosine

The isotopic fractionation factor in the monohydrated gas-phase cluster Cl−(H2O), i.e., the equilibrium constant for Cl−(H2O)(g)+D2O(g)⇄Cl−(D2O)(g) +H2O(g), is used to test models used for solution-phase simulations and to test semiempirical and ab initio molecular orbital theory for their detailed structural and vibrational predictions for both the solute–solvent bond properties and the interaction-induced intramolecular changes in water itself. The isotope effect is studied at a consistent level of vibration–rotation theory, i.e., the harmonic-oscillator-rigid-rotator approximation, using four different kinds of approach, namely extended-basis-set ab initio electronic structure calculations, both (i) with and (ii) without electron correlation, (iii) semiempirical molecular orbital theory at the level of neglect of diatomic differential overlap, and (iv) analytic force fields based on site–site interactions. The calculations of type (i) show good convergence and are compared both to experiment, which presumably tests the harmonic approximation, and to the results of efforts (ii), (iii), and (iv), which presumably tests the structural and vibrational properties predicted by these more approximate approaches. We find significant effects of anharmonicity and electron correlation; semiempirical molecular orbital theory does remarkably well; and there is a wide variation in predictions among the 25 analytic force fields tested. Finally we combine the well converged ab initio results for the properties of the well, the vibrational red and blue shifts, and the isotope effect on the equilibrium constant with the previous ab initio calculations of Dacre for the repulsive interactions to obtain a new interaction potential for chloride ion with nonrigid water that also predicts a more accurate enthalpy of complexation and binding energy than do the chloride–water potentials available in the literature.

A path integral centroid molecular dynamics method for Bose and Fermi statistics

We present the aspects of the path integral molecular dynamics (PIMD) method relative to (a) its theoretical fundamental principles, (b) its applicability to model quantum systems and (c) its implementation as a simulation tool. The PIMD method is based on the discretized path integral representation of quantum mechanics. In this representation, a quantum particle is isomorphic to a closed polymer chain. The problem of the indistinguishability of quantum particles is tackled with a non-local exchange potential. When the exact density matrix of the quantum particles is used, the exchange potential is exact. We use a high temperature approximation to the density matrix leading to an approximate form of the exchange potential. This quantum molecular dynamics method allows the simulation of collections of quantum particles at finite temperature. Our algorithm can be made to scale linearly with the number of quantum states on which the density matrix is projected. Therefore, it can be optimized to run efficiently on parallel computers. We apply the PIMD method to the electron plasma in 3-dimension. The kinetic and potential energies are calculated and compared with results for similar systems simulated with a variational Monte Carlo method. Both results show good agreements with each other at all the densities studied. The method is then use to model the thermodynamic behavior of a simple alkali metal. In these simulations, ions and valence electrons are treated as classical and quantum particles, respectively. The simple metal undergoes a phase transformation upon heating. Furthermore, to demonstrate the richness of behaviors that can be studied with the PIMD method, we also report on the metal to insulator transition in a hydrogenoid lattice. Finally, in previous studies of alkali metals, electrons interacted with ions via local pseudo-potentials, an extension of the method to modeling electrons in non-local pseudo-potentials is also presented with applications.

We present putative global minimum energy structures for nanoscopic transition metal clusters, with sizes ranging from N = 3 to 100 atoms, described by the original embedded atom potential of Finnis and Sinclair (FS), using their parameter sets for molybdenum and iron, and compare selected results with predictions from semi-empirical molecular orbital (SE-MO) theory via further optimization using the AM1* and PM6 Hamiltonians. We find that, for Fe clusters, the global minima found for the FS potential consist mainly of polyicosahedral structures with magic numbers N = 13, 19, 23, 26, 29, 39, 60 and 78, whereas, for Mo clusters with sizes N > 30, they are more likely to be bcc terminated by {110} and {100}-type surface facets. We find that the global minimum energy structures obtained for the FS potential are, in general, very good starting points for further SE-MO optimization, although the relative ordering of the resulting structures by energy compared to those obtained from global minima of other potentials used to model metal clusters does not, in general, agree.

The dynamics of the K atom attached to the 300-atom helium cluster upon photoexcitation has been studied theoretically based on the quantum molecular dynamics method. With the use of a hybrid method between time-dependent quantum dynamics and semiclassical path integral centroid molecular dynamics, the calculation includes the electronic state mixing for the K(2P) states as well as the quantum motions of helium atoms. It was found from the calculated trajectories that the K atom mostly desorbs by itself from the surface of the helium cluster without depending on the types of initial electronic excited states. It was also found that the K*He exciplex can be formed only as a minor product, following the initial excitation to the Π-type electronic state alone. Helium solvation structures of the K*Hen exciplexes were also investigated by path integral molecular dynamics simulations. The result implies that stable exciplexes can be formed up to n = 6 on the lowest excited state until the first solvation shell around the 4p orbital of K* is completed. Meanwhile, it was found that only two helium atoms can be bound to the K(2P) atom on the second lowest excited state.

We examine the short-time accuracy of a class of approximate quantum dynamical techniques that includes the centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD) methods. Both of these methods are based on the path integral molecular dynamics (PIMD) technique for calculating the exact static equilibrium properties of quantum mechanical systems. For Kubo-transformed real-time correlation functions involving operators that are linear functions of positions or momenta, the RPMD and (adiabatic) CMD approximations differ only in the choice of the artificial mass matrix of the system of ring polymer beads that is employed in PIMD. The obvious ansatz for a general method of this type is therefore to regard the elements of the PIMD (or Parrinello-Rahman) mass matrix as an adjustable set of parameters that can be chosen to improve the accuracy of the resulting approximation. We show here that this ansatz leads uniquely to the RPMD approximation when the criterion that is used to select the mass matrix is the short-time accuracy of the Kubo-transformed correlation function. In particular, we show that the leading error in the RPMD position autocorrelation function is O(t(8)) and the error in the velocity autocorrelation function is O(t(6)), for a general anharmonic potential. The corresponding errors in the CMD approximation are O(t(6)) and O(t(4)), respectively.

The impact of quantum nuclear effects on hydrogen (H-) bond strength has been inferred in earlier work from bond lengths obtained from path integral molecular dynamics (PIMD) simulations. To obtain a direct quantitative assessment of such effects, we use constrained-centroid PIMD simulations to calculate the free energy changes upon breaking the H-bonds in dimers of HF and water. Comparing ab initio simulations performed using PIMD and classical nucleus molecular dynamics (MD), we find smaller dissociation free energies with the PIMD method. Specifically, at 50 K, the H-bond in (HF)(2) is about 30% weaker when quantum nuclear effects are included, while that in (H(2)O)(2) is about 15% weaker. In a complementary set of simulations, we compare unconstrained PIMD and classical nucleus MD simulations to assess the influence of quantum nuclei on the structures of these systems. We find increased heavy atom distances, indicating weakening of the H-bond consistent with that observed by direct calculation of the free energies of dissociation.

Equilibrium magnesium isotope fractionation between aqueous Mg2+ and carbonate minerals: Insights from path integral molecular dynamics

Effects of temperature and isotopic substitution on electron attachment dynamics of guanine–cytosine base pair: Ring-polymer and classical molecular dynamics simulations

DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics

i-PI: A Python interface for ab initio path integral molecular dynamics simulations

In this chapter, we present current studies on molecular dynamics (MD) simulations of hydrogen-bonded systems with emphasis on vibrational spectra analysis. One of the most informative experimental data are spectroscopic data (infrared and Raman spectroscopy), which give information important in diverse fields, e.g. protein folding, drug design, sensors, nanotechnology, separations, etc. Spectroscopic data are very sensitive on inter- and intramolecular interactions. The processes of melting, boiling, unfolding and strand separation involve disruption of molecular interactions, that engage attractive or repulsive forces between molecules. In this chapter, we focus on calculations of IR spectra of hydrogen-bonded complexes based on linear response theory, in which the spectral density is the Fourier transform of the autocorrelation function of the dipole moment operator involved in the IR transitions. Recently, Born–Oppenheimer molecular dynamics (BOMD), Car–Parrinello molecular dynamics (CPMD), path integral molecular dynamics (PIMD), hybrid molecular dynamics (QM/MM) and other methods which use trajectories from molecular dynamics have been employed to simulate IR spectra of hydrogen-bonded systems. Each of these methods has some advantages and disadvantages which will be discussed in this chapter presenting also recent applications of these methods.

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.

Theoretical investigations of the equol molecule: semi-empirical and density functional theory calculations