Absorption and fluorescence of PRODAN in phospholipid bilayers: a combined quantum mechanics and classical molecular dynamics study

Absorption and fluorescence spectra of PRODAN (6-propionyl-2-dimethylaminonaphthalene) were studied by means of the time-dependent density functional theory and the algebraic diagrammatic construction method. The influence of environment, a phosphatidylcholine lipid bilayer and water, was taken into account employing a combination of quantum chemical calculations with empirical force-field molecular dynamics simulations. Additionally, experimental absorption and emission spectra of PRODAN were measured in cyclohexane, water, and lipid vesicles. Both planar and twisted configurations of the first excited state of PRODAN were taken into account. The twisted structure is stabilized in both water and a lipid bilayer, and should be considered as an emitting state in polar environments. Orientation of the excited dye in the lipid bilayer significantly depends on configuration. In the bilayer, the fluorescence spectrum can be regarded as a combination of emission from both planar and twisted structures.     

Structure and ultrafast dynamics of liquid water: a quantum mechanics/molecular mechanics molecular dynamics simulations study

A quantum mechanics/molecular mechanics molecular dynamics simulation was performed for liquid water to investigate structural and dynamical properties of this peculiar liquid. The most important region containing a central reference molecule and all nearest surrounding molecules (first coordination shell) was treated by Hartree-Fock (HF), post-Hartree-Fock [second-order Moller-Plesset perturbation theory (MP2)], and hybrid density functional B3LYP [Becke's three parameter functional (B3) with the correlation functional of Lee, Yang, and Parr (LYP)] methods. In addition, another HF-level simulation (2HF) included the full second coordination shell. Site to site interactions between oxygen-oxygen, oxygen-hydrogen, and hydrogen-hydrogen atoms of all ab initio methods were compared to experimental data. The absence of a second peak and the appearance of a shoulder instead in the gO-O graph obtained from the 2HF simulation is notable, as this feature has been observed so far only for pressurized or heated water. Dynamical data show that the 2HF procedure compensates some of the deficiency of the HF one-shell simulation, reducing the difference between correlated (MP2) and HF results. B3LYP apparently leads to too rigid structures and thus to an artificial slow down of the dynamics.     

Quantum statistics and classical mechanics: real time correlation functions from ring polymer molecular dynamics

We propose an approximate method for calculating Kubo-transformed real-time correlation functions involving position-dependent operators, based on path integral (Parrinello-Rahman) molecular dynamics. The method gives the exact quantum mechanical correlation function at time zero, exactly satisfies the quantum mechanical detailed balance condition, and for correlation functions of the form C(Ax)(t) and C(xB)(t) it gives the exact result for a harmonic potential. It also works reasonably well at short times for more general potentials and correlation functions, as we illustrate with some example calculations. The method provides a consistent improvement over purely classical molecular dynamics that is most apparent in the low-temperature regime.     

Optimal control of classical molecular dynamics: A perturbation formulation and the existence of multiple solutions

This paper considers the prospect for there being multiple solutions to the control of classically modelled molecular dynamical systems. The research presented here follows up on a parallel study based on quantum mechanics. For polyatomic molecules it is generally expected that a classical mechanical model will be adequate and necessary as a means for designing optical fields for molecular control. The prospect for multiple control field solutions existing in this domain is important to establish in terms of ultimate laboratory realization of molecular control. A general formulation of the multiplicity problem is considered and the existence of a denumerably infinite number of solutions for the control field amplitude is shown to be the case under certain mild limitations on the physical variables.     

Inelastic collisions of molecular hydrogen: a comparison of results from quantum and classical mechanics

Full-dimensional quantum and classical calculations have been carried out for inelastic (nonreactive) energy transfer in H2+H2 on the ab initio potential energy surface of Boothroyd et al. [J. Chem. Phys. 116, 666 (2002)]. State-to-state cross sections are determined and compared for transitions from H2(0,j(ab))+H2(1,j(cd)). While there is excellent agreement for transitions involving small Deltaj, for larger Deltaj and for vibrational relaxation, significant differences are observed which exhibit no systematic trends. Reasons for this disagreement are discussed.     

Explicit proton transfer in classical molecular dynamics simulations

We present Hydrogen Dynamics (HYDYN), a method that allows explicit proton transfer in classical force field molecular dynamics simulations at thermodynamic equilibrium. HYDYN reproduces the characteristic properties of the excess proton in water, from the special pair dance, to the continuous fluctuation between the limiting Eigen and Zundel complexes, and the water reorientation beyond the first solvation layer. Advantages of HYDYN with respect to existing methods are computational efficiency, microscopic reversibility, and easy parameterization for any force field. © 2014 Wiley Periodicals, Inc.     

Multiple grid methods for classical molecular dynamics

Presented in the context of classical molecular mechanics and dynamics are multilevel summation methods for the fast calculation of energies/forces for pairwise interactions, which are based on the hierarchical interpolation of interaction potentials on multiple grids. The concepts and details underlying multigrid interpolation are described. For integration of molecular dynamics the use of different time steps for different interactions allows longer time steps for many of the interactions, and this can be combined with multiple grids in space. Comparison is made to the fast multipole method, and evidence is presented suggesting that for molecular simulations multigrid methods may be superior to the fast multipole method and other tree methods.     

Energy conservation in molecular dynamics simulations of classical systems

Classical Newtonian dynamics is analytic and the energy of an isolated system is conserved. The energy of such a system, obtained by the discrete "Verlet" algorithm commonly used in molecular dynamics simulations, fluctuates but is conserved in the mean. This is explained by the existence of a "shadow Hamiltonian" H [S. Toxvaerd, Phys. Rev. E 50, 2271 (1994)], i.e., a Hamiltonian close to the original H with the property that the discrete positions of the Verlet algorithm for H lie on the analytic trajectories of H. The shadow Hamiltonian can be obtained from H by an asymptotic expansion in the time step length. Here we use the first non-trivial term in this expansion to obtain an improved estimate of the discrete values of the energy. The investigation is performed for a representative system with Lennard-Jones pair interactions. The simulations show that inclusion of this term reduces the standard deviation of the energy fluctuations by a factor of 100 for typical values of the time step length. Simulations further show that the energy is conserved for at least one hundred million time steps provided the potential and its first four derivatives are continuous at the cutoff. Finally, we show analytically as well as numerically that energy conservation is not sensitive to round-off errors.     

Quaternion formulation of lattice dynamics of molecular crystals

The use of quaternions to specify rigid-molecule orientation is reviewed. Application of this formalism to lattice dynamics of molecular crystals is developed. Basic formulae for harmonic and anharmonic approximations are summarised.     

Interpretation of nuclear resonant vibrational spectra of rubredoxin using a combined quantum mechanics and molecular mechanics approach

Nuclear resonant vibrational spectra of the reduced and oxidized form of a mutant of rubredoxin from Pyrococcus abyssii were measured and are compared with simulated spectra that were calculated by a combined quantum mechanics (QM) and molecular mechanics (MM) method. Density functional theory was used for the QM level. Calculations were performed for different models of rubredoxin. Realistic spectra were simulated with reduced models that include at least the iron center, the four cysteins coordinating it, and the residues connected to the cysteins together with a QM layer that comprises the first two coordination shells of the iron center. Larger QM layers did not lead to significant changes of the simulated spectra.     

Electronic properties of liquid ammonia: a sequential molecular dynamics/quantum mechanics approach

The electronic properties of liquid ammonia are investigated by a sequential molecular dynamics/quantum mechanics approach. Quantum mechanics calculations for the liquid phase are based on a reparametrized hybrid exchange-correlation functional that reproduces the electronic properties of ammonia clusters [(NH3)n; n=1-5]. For these small clusters, electron binding energies based on Green's function or electron propagator theory, coupled cluster with single, double, and perturbative triple excitations, and density functional theory (DFT) are compared. Reparametrized DFT results for the dipole moment, electron binding energies, and electronic density of states of liquid ammonia are reported. The calculated average dipole moment of liquid ammonia (2.05+/-0.09 D) corresponds to an increase of 27% compared to the gas phase value and it is 0.23 D above a prediction based on a polarizable model of liquid ammonia [Deng et al., J. Chem. Phys. 100, 7590 (1994)]. Our estimate for the ionization potential of liquid ammonia is 9.74+/-0.73 eV, which is approximately 1.0 eV below the gas phase value for the isolated molecule. The theoretical vertical electron affinity of liquid ammonia is predicted as 0.16+/-0.22 eV, in good agreement with the experimental result for the location of the bottom of the conduction band (-V 0=0.2 eV). Vertical ionization potentials and electron affinities correlate with the total dipole moment of ammonia aggregates.     

Bohmian mechanics with complex action: a new trajectory-based formulation of quantum mechanics

In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared-it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification-a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynamics to give exact quantum mechanics. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10(-7) calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity.     

Conical intersections in solution: formulation, algorithm, and implementation with combined quantum mechanics/molecular mechanics method

The significance of conical intersections in photophysics, photochemistry, and photodissociation of polyatomic molecules in gas phase has been demonstrated by numerous experimental and theoretical studies. Optimization of conical intersections of small- and medium-size molecules in gas phase has currently become a routine optimization process, as it has been implemented in many electronic structure packages. However, optimization of conical intersections of small- and medium-size molecules in solution or macromolecules remains inefficient, even poorly defined, due to large number of degrees of freedom and costly evaluations of gradient difference and nonadiabatic coupling vectors. In this work, based on the sequential quantum mechanics and molecular mechanics (QM/MM) and QM/MM-minimum free energy path methods, we have designed two conical intersection optimization methods for small- and medium-size molecules in solution or macromolecules. The first one is sequential QM conical intersection optimization and MM minimization for potential energy surfaces; the second one is sequential QM conical intersection optimization and MM sampling for potential of mean force surfaces, i.e., free energy surfaces. In such methods, the region where electronic structures change remarkably is placed into the QM subsystem, while the rest of the system is placed into the MM subsystem; thus, dimensionalities of gradient difference and nonadiabatic coupling vectors are decreased due to the relatively small QM subsystem. Furthermore, in comparison with the concurrent optimization scheme, sequential QM conical intersection optimization and MM minimization or sampling reduce the number of evaluations of gradient difference and nonadiabatic coupling vectors because these vectors need to be calculated only when the QM subsystem moves, independent of the MM minimization or sampling. Taken together, costly evaluations of gradient difference and nonadiabatic coupling vectors in solution or macromolecules can be reduced significantly. Test optimizations of conical intersections of cyclopropanone and acetaldehyde in aqueous solution have been carried out successfully.     

Controlling the shape and flexibility of arylamides: a combined ab initio, ab initio molecular dynamics, and classical molecular dynamics study

Using quantum chemistry plus ab initio molecular dynamics and classical molecular dynamics methods, we address the relationship between molecular conformation and the biomedical function of arylamide polymers. Specifically, we have developed new torsional parameters for a class of these polymers and applied them in a study of the interaction between a representative arylamide and one of its biomedical targets, the anticoagulant drug heparin. Our main finding is that the torsional barrier of a C(aromatic)-C(carbonyl) bond increases significantly upon addition of an o-OCH2CH2NH3+ substituent on the benzene ring. Our molecular dynamics studies that are based on the original general AMBER force field (GAFF) and GAFF modified to include our newly developed torsional parameters show that the binding mechanism between the arylamide and heparin is very sensitive to the choice of torsional potentials. Ab initio molecular dynamics simulation of the arylamide independently confirms the degree of flexibility we obtain by classical molecular dynamics when newly developed torsional potentials are used.     

A new extension of classical molecular dynamics: An electron transfer algorithm

The molecular dynamics is one of the most widely used methods for the simulation of the properties corresponding to ionic motion. Unfortunately, classical molecular dynamics cannot be applied for electron transfer simulation. Suggested modification of the molecular dynamics allows performing the electron transfer from one particle to another during simulation runtime. All additional data structure and the corresponding algorithms are presented in this article. The method can be applied to the systems with pair Van der Waals and Coulomb interactions. Moreover, it may be extended for many‐bodied interatomic interactions. In addition, an algorithm of transference numbers calculation has been designed. This extension is not an independent method but it can be useful for simulating the systems with high concentration of electron donors and acceptors. © 2017 Wiley Periodicals, Inc.     

Minimum sequence requirements for selective RNA-ligand binding: a molecular mechanics algorithm using molecular dynamics and free-energy techniques

In vitro evolution techniques allow RNA molecules with unique functions to be developed. However, these techniques do not necessarily identify the simplest RNA structures for performing their functions. Determining the simplest RNA that binds to a particular ligand is currently limited to experimental protocols. Here, we introduce a molecular-mechanics based algorithm employing molecular dynamics simulations and free-energy methods to predict the minimum sequence requirements for selective ligand binding to RNA. The algorithm involves iteratively deleting nucleotides from an experimentally determined structure of an RNA-ligand complex, performing energy minimizations and molecular dynamics on each truncated structure, and assessing which truncations do not prohibit RNA binding to the ligand. The algorithm allows prediction of the effects of sequence modifications on RNA structural stability and ligand-binding energy. We have implemented the algorithm in the AMBER suite of programs, but it could be implemented in any molecular mechanics force field parameterized for nucleic acids. Test cases are presented to show the utility and accuracy of the methodology.     

Optimal non-linear dimension reduction scheme for classical molecular dynamics

The optimal creation of a reduced space that effectively captures the long timescale dynamics of a non-linear molecular system over a range of frequencies is described. The technique builds on a previously developed subspace method based on linear constant projective transformation of the original full space. The present work attempts to propose transformation that are spatially dependent thereby leading to an effective subspace for better representing the dynamics of interests. The algorithm seeks out an optimal transformation consistent with desired low frequency motion in a rather general way. The method is demonstrated for a six-dimensional nonlinear system reduced to two-dimensions. Superior performance is found in evaluating ensemble-averaged classical dynamical properties.