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.     

Two more approaches for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics

We show two more approaches for generating trajectory-based dynamics in the phase space formulation of quantum mechanics: "equilibrium continuity dynamics" (ECD) in the spirit of the phase space continuity equation in classical mechanics, and "equilibrium Hamiltonian dynamics" (EHD) in the spirit of the Hamilton equations of motion in classical mechanics. Both ECD and EHD can recover 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. Both ECD and EHD conserve the quasi-probability within the infinitesimal volume dx(t)dp(t) around the phase point (x(t), p(t)) along the trajectory. Numerical tests of both approaches in the Wigner phase space have been made for two strongly anharmonic model problems and a double well system, for each potential auto-correlation functions of both linear and nonlinear operators have been calculated. The results suggest EHD and ECD are two additional potential useful approaches for describing quantum effects for complex systems in condense phase.     

Incorporation of quantum effects for selected degrees of freedom into the trajectory-based dynamics using spatial domains

The approach of defining quantum corrections on nuclear dynamics of molecular systems incorporated approximately into selected degrees of freedom, is described. The approach is based on the Madelung-de-Broglie-Bohm formulation of time-dependent quantum mechanics which represents a wavefunction in terms of an ensemble of trajectories. The trajectories follow classical laws of motion except that the quantum potential, dependent on the wavefunction amplitude and its derivatives, is added to the external, classical potential. In this framework the quantum potential, determined approximately for practical reasons, is included only into the "quantum" degrees of freedom describing light particles such as protons, while neglecting with the quantum force for the heavy, nearly classical nuclei. The entire system comprised of light and heavy particles is described by a single wavefunction of full dimensionality. The coordinate space of heavy particles is divided into spatial domains or subspaces. The quantum force acting on the light particles is determined for each domain of similar configurations of the heavy nuclei. This approach effectively introduces parametric dependence of the reduced dimensionality quantum force, on classical degrees of freedom. This strategy improves accuracy of the quantum force and does not restrict interaction between the domains. The concept is illustrated for two-dimensional scattering systems, where the quantum force is required to reproduce vibrational energy of the quantum degree of freedom.     

An efficient method for the calculation of quantum mechanics/molecular mechanics free energies

The combination of quantum mechanics (QM) with molecular mechanics (MM) offers a route to improved accuracy in the study of biological systems, and there is now significant research effort being spent to develop QM/MM methods that can be applied to the calculation of relative free energies. Currently, the computational expense of the QM part of the calculation means that there is no single method that achieves both efficiency and rigor; either the QM/MM free energy method is rigorous and computationally expensive, or the method introduces efficiency-led assumptions that can lead to errors in the result, or a lack of generality of application. In this paper we demonstrate a combined approach to form a single, efficient, and, in principle, exact QM/MM free energy method. We demonstrate the application of this method by using it to explore the difference in hydration of water and methane. We demonstrate that it is possible to calculate highly converged QM/MM relative free energies at the MP2/aug-cc-pVDZ/OPLS level within just two days of computation, using commodity processors, and show how the method allows consistent, high-quality sampling of complex solvent configurational change, both when perturbing hydrophilic water into hydrophobic methane, and also when moving from a MM Hamiltonian to a QM/MM Hamiltonian. The results demonstrate the validity and power of this methodology, and raise important questions regarding the compatibility of MM and QM/MM forcefields, and offer a potential route to improved compatibility.     

Femtosecond quantum control of molecular dynamics in the condensed phase

We review the progress in controlling quantum dynamical processes in the condensed phase with femtosecond laser pulses. Due to its high particle density the condensed phase has both high relevance and appeal for chemical synthesis. Thus, in recent years different methods have been developed to manipulate the dynamics of condensed-phase systems by changing one or multiple laser pulse parameters. Single-parameter control is often achieved by variation of the excitation pulse's wavelength, its linear chirp or its temporal subpulse separation in case of pulse sequences. Multiparameter control schemes are more flexible and provide a much larger parameter space for an optimal solution. This is realized in adaptive femtosecond quantum control, in which the optimal solution is iteratively obtained through the combination of an experimental feedback signal and an automated learning algorithm. Several experiments are presented that illustrate the different control concepts and highlight their broad applicability. These fascinating achievements show the continuous progress on the way towards the control of complex quantum reactions in the condensed phase.     

Development of a model for the rational design of molecular imprinted polymer: Computational approach for combined molecular dynamics/quantum mechanics calculations

A new rational approach for the preparation of molecularly imprinted polymer (MIP) based on the combination of molecular dynamics (MD) simulations and quantum mechanics (QM) calculations is described in this work. Before performing molecular modeling, a virtual library of functional monomers was created containing forty frequently used monomers. The MD simulations were first conducted to screen the top three monomers from virtual library in each porogen-acetonitrile, chloroform and carbon tetrachloride. QM simulations were then performed with an aim to select the optimum monomer and progen solvent in which the QM simulations were carried out; the monomers giving the highest binding energies were chosen as the candidate to prepare MIP in its corresponding solvent. The acetochlor, a widely used herbicide, was chosen as the target analyte. According to the theoretical calculation results, the MIP with acetochlor as template was prepared by emulsion polymerization method using N,N-methylene bisacrylamide (MBAAM) as functional monomer and divinylbenzene (DVB) as cross-linker in chloroform. The synthesized MIP was then tested by equilibrium-adsorption method, and the MIP demonstrated high removal efficiency to the acetochlor. Mulliken charge distribution and ¹H NMR spectroscopy of the synthesized MIP provided insight on the nature of recognition during the imprinting process probing the governing interactions for selective binding site formation at a molecular level. We think the computer simulation method first proposed in this paper is a novel and reliable method for the design and synthesis of MIP.     

自由高斯波包在量子相空间中的动力学研究

在Tortes—Vega和Frederick（简称T-F）量子相空间的理论框架下,将波函数表示成相应的极化形式,给．出了量子相空间中的含时Schrodinger方程的另一种等价表示形式,并且利用这种方法数值求解了自由高斯波包在相空间中的演化行为,对得到的结果进行了讨论,以期用这种方法探索更为实际和复杂的体系在量子相空间中的演化行为。     

Large amplitude quantum mechanics in polyatomic hydrides. I. A particles-on-a-sphere model for XH(n)

A framework is presented for converged quantum mechanical calculations on large amplitude dynamics in polyatomic hydrides (XH(n)) based on a relatively simple, but computationally tractable, "particles-on-a-sphere" (POS) model for the intramolecular motion of the light atoms. The model assumes independent two-dimensional (2D) angular motion of H atoms imbedded on the surface of a sphere with an arbitrary interatomic angular potential. This assumption permits systematic evolution from "free rotor" to "tunneling" to "quasi-rigid" polyatomic molecule behavior for small, but finite, values of total angular momentum J. This work focuses on simple triatom (n=2) and tetratom (n=3) systems as a function of interatomic potential stiffness, with explicit consideration of H2O, NH3, and H3O+ as limiting test cases. The POS model also establishes the necessary mathematical groundwork for calculations on dynamically much more challenging XH(n) species with n>3 (e.g., models of CH5+) where such a reduced dimensionality approach offers prospects for being quantum mechanically tractable at low J values (i.e., J=0, 1, 2) characteristic of supersonic jet expansion conditions.     

A study of entangled systems in the many‐body signed particle formulation of quantum mechanics

Recently a new formulation of quantum mechanics has been introduced, based on signed classical field‐less particles interacting with an external field by means of only creation and annihilation events. In this article, we extend this novel theory to the case of many‐body problems. We show that, when restricted to spatial finite domains and discrete momentum space, the proposed extended theory is equivalent to the time‐dependent many‐body Wigner Monte Carlo method. In this new picture, the treatment of entangled systems comes naturally and, therefore, we apply it to the study of quantum entangled systems. The latter is represented in terms of two Gaussian wave packets moving in opposite directions. We introduce the presence of a dissipative background and show how the entanglement is affected by different (controlled) configurations.     

Trajectory-based solution of the nonadiabatic quantum dynamics equations: an on-the-fly approach for molecular dynamics simulations

The non-relativistic quantum dynamics of nuclei and electrons is solved within the framework of quantum hydrodynamics using the adiabatic representation of the electronic states. An on-the-fly trajectory-based nonadiabatic molecular dynamics algorithm is derived, which is also able to capture nuclear quantum effects that are missing in the traditional trajectory surface hopping approach based on the independent trajectory approximation. The use of correlated trajectories produces quantum dynamics, which is in principle exact and computationally very efficient. The method is first tested on a series of model potentials and then applied to study the molecular collision of H with H(2) using on-the-fly TDDFT potential energy surfaces and nonadiabatic coupling vectors.     

On the solvation of the Zn2+ ion in methanol: a combined quantum mechanics, molecular dynamics, and EXAFS approach

The solvation properties of the Zn(2+) ion in methanol solution have been investigated using a combined approach based on molecular dynamics (MD) simulations and extended X-ray absorption fine structure (EXAFS) experimental results. The quantum mechanical potential energy surface for the interaction of the Zn(2+) ion with a methanol molecule has been calculated taking into account the effect of bulk solvent by the polarizable continuum model (PCM). The effective Zn-methanol interactions have been fitted by suitable analytical potentials, and have been utilized in the MD simulation to obtain the structural properties of the solution. The reliability of the whole procedure has been assessed by comparing the theoretical structural results with the EXAFS experimental data. The structural parameters of the first solvation shells issuing from the MD simulations provide an effective complement to the EXAFS experiments.     

A new formulation of the phase change approach in the theory of conical intersections

We have reformulated the phase change approach to the theory of conical intersections suggested by Zilberg and Haas [S. Zilberg, Y. Haas, Adv. Chem. Phys. 124 (2002) 433]. We use the fact that the phase change loop variable in polar co-ordinates in the space of nuclear co-ordinates is related to the transformation of the diabatic VB states defined at the apex of the cone in a conical intersection. Thus one can use the basis transformation generated by θ to yield a sequence of orthogonal pairs of VB structures (anchors) at any value of in the loop in nuclear configuration space. In this way the branching plane concept becomes related to VB wavefunctions based on the correspondence between the two angles. The theory is developed in detail using a simple three orbital three electron example. Examples are presented for four and six orbitals. In the later case, our results differ from those of Zilberg and Haas.     

Kinetics of thermally induced phase separation in ternary polymer solutions. I. Modeling of phase separation dynamics

Simulations based on Cahn–Hilliard spinodal decomposition theory for phase separation in thermally quenched polymer/solvent/nonsolvent systems are presented. Two common membrane‐forming systems are studied, cellulose acetate [CA]/acetone/water, and poly(ethersulfone) [PES]/dimethylsulfoxide [DMSO]/water. The effects of initial polymer and nonsolvent composition on the structure‐formation dynamics are elucidated, and growth rates at specific points within the ternary phase diagram are quantified. Predicted pore growth rate curves exhibit a relative maximum with nonsolvent composition. For shallow quenches (lower nonsolvent content) near a phase boundary, the pore growth rate increases with increasing quench depth, whereas for deep quenches, where the composition of the polymer‐rich phase approaches that of a glass, the pore growth rate decreases with increasing quench depth. With increasing initial polymer concentration, the overall rate of structure growth is lowered and the growth rate maximum shifts to higher nonsolvent compositions. This behavior appears to be a universal phenomenon in quenched polymer solutions which can undergo a glass transition, and is a result of an interplay between thermodynamic and kinetic driving forces. These results suggest a mechanism for the locking‐in of the two‐phase structure that occurs during nonsolvent‐induced phase inversion. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1449–1460, 1999     

Coordination number of zinc ions in the phosphotriesterase active site by molecular dynamics and quantum mechanics

We have run several molecular dynamics (MD) simulations on zinc-containing phosphotriesterase (PTE) with two bound substrates, sarin and paraoxon, and with the substrate analog diethyl 4-methylbenzylphosphonate. A standard nonbonded model was employed to treat the zinc ions with the commonly used charge of +2. In all the trajectories, we observed a tightly bound water (TBW) molecule in the active site that was coordinated to the less buried zinc ion. The phosphoryl oxygen of the substrate/inhibitor was found to be coordinated to the same zinc ion so that, considering all ligands, the less buried zinc was hexa-coordinated. The hexa-coordination of this zinc ion was not seen in the deposited X-ray pdb files for PTE. Several additional MD simulations were then performed using different charges (+1, +1.5) on the zinc ions, along with ab initio and density functional theory (DFT) calculations, to evaluate the following possibilities: the crystal diffraction data were not correctly interpreted; the hexa-coordinated zinc ion in PTE is only present in solution and not in the crystal; and the hexa-coordinated zinc ion in PTE is an artifact of the force field used. A charge of +1.5 leads to a coordination number (CN) of 5 on both zinc ions, which is consistent with the results from ab initio and DFT calculations and with the latest high resolution X-ray crystal structure. The commonly used charge of +2 produces a CN of 6 on the less buried zinc. The CN on the more buried zinc ion is 5 when the substrate/inhibitor is present in the simulation, and increases to 6 when the substrate/inhibitor is removed prior to the simulation. The results of both of the MD and quantum mechanical calculations lead to the conclusion that the zinc ions in the PTE active site are both penta-coordinated, and that the MD simulations performed with the charge of +2 overestimate the CN of the zinc ions in the PTE active site. The overall protein structures in the simulations remain unaffected by the change in zinc charge from +2 to +1.5. The results also suggest that the charge +1.5 is the most appropriate for the molecular dynamics simulations on zinc-containing PTE when a nonbonded model is used and no global thermodynamic conclusion is sought. We also show that the standard nonbonded model is not able to properly treat the CN and energy at the same time. A preliminary, promising charge-transfer model is discussed with the use of the zinc charge of +1.5.     

Structure of the enzyme-substrate complex for guanosine triphosphate hydrolysis by elongation factor EF-Tu: Comparison of quantum mechanics/molecular mechanics and molecular dynamics results

The equilibrium geometric configurations of the enzyme-substrate complex for guanosine triphosphate hydrolysis by elongation factor EF-Tu calculated using two theoretical approaches, a combined quantum mechanics/molecular mechanics (QM/MM) method and a molecular dynamics method, are compared. The reaction complex geometry determined by the QM/MM method is consistent with the accepted reaction mechanism, whereas, in the enzyme-substrate structure predicted by the molecular dynamics method with the CHARMM force field, the relative positions of the nucleophilic reagent (water molecules) and the base (a histidine side chain) do not correspond to the optimal reagent arrangement.     

Application of the finite element method to time-dependent quantum mechanics: I. H and He in a laser field

A finite element approach is described to solve the time- dependent Hartree-Fock equation of atoms in the presence of time-dependent electromagnetic fields. Time-dependent energy changes, ionization rates and high order nonlinear optical polarizabilities, 2n+1 (n >, 0) for the atoms H and He have been calculated. The finite element method is shown to be easily adaptable to treat intense short pulses and includes automatically both bound and continuum electronic states.     

The dynamics of gallamine: A potent neuromuscular blocker. A determination by quantum mechanics and molecular dynamics (i) in vacuo studies

The potent neuromuscular blocker, gallamine, possesses three chemically equivalent, flexible side chains, the motion of which has been proposed as important in its mode of action on the acetylcholine receptor in vivo. The flexibility of the side chains has been investigated in the present initial study by a combination of quantum mechanics and molecular dynamics on the isolated, unsolvated molecule. Net atomic charges for the gallamine molecule have been calculated using the semiempirical program MOPAC for use in the molecular dynamics simulation. The flexibility of the side chains has been shown to correlate with the range of fluctuations in torsion angles observed in the crystal structure of gallamine.