Phase-space dynamics and quantum mechanics

Ann-dimensional system with a classical HamiltonianH(p, q, t) may be described by a phase-space distribution function D(q, p, t). The dynamical equation for D(q, p, t) is postulated to be

Phase-space dynamics and quantum mechanics

Summary In a recent paper Deal has postulated a new dynamical equation for quantum mechanical phase-space distribution functions. We analyze the new equation and show that it may be related to the traditional standard and antistandard phase-space representations of quantum mechanics. A brief review of these and other representations is also given.     

Non-adiabatic molecular dynamics with quantum solvent effects

Three novel approaches extending quantum-classical non-adiabatic (NA) molecular dynamics (MD) to include quantum effects of solvent environments are described. In a standard NA-MD the solute subsystem is treated quantum mechanically, while the larger solvent part of a system is treated classically. The three novel approaches presented here are based on the Bohmian formulation of quantum mechanics, the stochastic Schrödinger equation for the evolution of open quantum systems and the quantized Hamilton dynamics generalization of classical mechanics. The approaches extend the standard NA-MD to incorporate the following quantum effects of the solvent. (1) Branching, i.e. the ability of solvent quantum wave packets to split and follow asymptotically diverging trajectories correlated with different quantum states of the solute. (2) Decoherence, i.e. loss of quantum interference within the solute subsystem induced by the diverging solvent trajectories. (3) Zero point energy that contributes to NA coupling and must be preserved during the energy exchange between solvent and solute degrees of freedom. The Bohmian quantum-classical mechanics, stochastic mean-field and quantized mean-field approximations incorporate the quantum solvent effects into the standard quantum-classical NA-MD in a straightforward and efficient way that can be easily applied to quantum dynamics of condensed phase chemical systems.     

Dimensional scaling and the quantum mechanical many-body problem

Summary A growing repertoire of electronic structure methods employ the spatial dimensionD as an interpolation or scaling parameter. It is advantageous to transform the Schrödinger equation to remove all dependence onD from the Jacobian volume element and the Laplacian operator; this introduces a centrifugal term, quadratic inD, that augments the effective potential. Here we explicitly formulate this procedure forS states of an arbitrary many-particle system, in two variants. One version reduces the Laplacian to a quasicartesian form, and is particularly suited to evaluating the exactly solvableD limit and perturbation expansions about this limit. The other version casts the Jacobian and Laplacian into the familiar forms forD=3, and is particularly suited to calculations employing conventional Rayleigh-Ritz variational methods.     

On the Inversion of Quantum Mechanical Systems: Determining the Amount and Type of Data for a Unique Solution

The inverse problem of extracting a quantum mechanical potential from laboratory data is studied from the perspective of determining the amount and type of data capable of giving a unique answer. Bound state spectral information and expectation values of time-independent operators are used as data. The Schrödinger equation is treated as finite dimensional and for these types of data there are algebraic equations relating the unknowns in the system to the experimental data (e.g., the spectrum of a matrix is related algebraically to the elements of the matrix). As these equations are polynomials in the unknown parameters of the system, it is possible to determine the multiplicity of the solution set. With a fixed number of unknowns the effect of increasing the number of equations on the multiplicity of solutions is assessed. In general, if the number of the equations matches the number of the unknowns, the solution set is denumerable. A result on the solvability of polynomial equations is extended to the case where the number of equations exceeds the number of unknowns. We show that if one has more equations than the number of unknowns, generically a unique solution exists. Several examples illustrating these results are provided.     

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.     

Relaxation and dephasing in open quantum systems time-dependent density functional theory: Properties of exact functionals from an exactly-solvable model system

The dissipative dynamics of many-electron systems interacting with a thermal environment has remained a long-standing challenge within time-dependent density functional theory (TDDFT). Recently, the formal foundations of open quantum systems time-dependent density functional theory (OQS-TDDFT) within the master equation approach were established. It was proven that the exact time-dependent density of a many-electron open quantum system evolving under a master equation can be reproduced with a closed (unitarily evolving) and non-interacting Kohn-Sham system. This potentially offers a great advantage over previous approaches to OQS-TDDFT, since with suitable functionals one could obtain the dissipative open-systems dynamics by simply propagating a set of Kohn-Sham orbitals as in usual TDDFT. However, the properties and exact conditions of such open-systems functionals are largely unknown. In the present article, we examine a simple and exactly-solvable model open quantum system: one electron in a harmonic well evolving under the Lindblad master equation. We examine two different representitive limits of the Lindblad equation (relaxation and pure dephasing) and are able to deduce a number of properties of the exact OQS-TDDFT functional. Challenges associated with developing approximate functionals for many-electron open quantum systems are also discussed.     

A theoretical study on the cyclopropane adsorption onto the copper surfaces by density functional theory and quantum chemical molecular dynamics methods

We report a theoretical study on the cyclopropane adsorption onto Cu(1 1 1) surfaces by density functional theory (DFT) and quantum chemical molecular dynamics methods. The equilibrium geometry of the physisorbed species was obtained using both periodic and cluster models by DFT methods that employ Cambridge serial total energy package (CASTEP), DMol ab initio quantum chemistry software of Accelrys’ materials studio (DMol), and Amsterdam density functional (ADF) program. It was found that the adsorbate molecule was tilted towards the metal surface with one C---C bond (upwards) parallel to the surface and that the physisorption occurred via a third carbon atom pointing (downwards) towards the surface. The electronic distribution and geometrical structure of physisorbed cyclopropane were slightly deviated from its gas phase molecule. The calculated vibrational frequencies and adsorption energies are close to experimental data, confirming the reliability of our DFT results. The adsorption process was simulated using our novel tight-binding quantum chemical molecular dynamics program, ‘Colors’. The calculation results indicated that both the adsorption and desorption processes of cyclopropane took place molecularly. The electron transfer and structural properties of equilibrium position obtained by ‘Colors’ are consistent with those by the first principles DFT methods.     

Superconvergent Perturbation Theory for an Anharmonic Oscillator

A computationally facile superconvergent perturbation theory for the energies and wavefunctions of the bound states of one-dimensional anharmonic oscillators is suggested. The proposed approach uses a Kolmogorov repartitioning of the Hamiltonian with perturbative order. The unperturbed and perturbed parts of the Hamiltonian are defined in terms of projections in Hilbert space, which allows for zero-order wavefunctions that are linear combinations of basis functions. The method is demonstrated on quartic anharmonic oscillators using a basis of generalized coherent states and, in contrast to usual perturbation theories, converges absolutely. Moreover, the method is shown to converge for excited states, and it is shown that the rate of convergence does not deteriorate appreciably with excitation.     

Solving restricted open-shell equations in excited state molecular dynamics simulations

Different approaches to the solution of restricted open-shell equations are summarized and a general implementation for the first excited singlet state in the Car–Parrinello molecular dynamics code (CPMD) is presented. For molecular dynamics simulations where energy conservation is an important criterion, different choices of parameters are necessary depending on the particular chemical situation.     

Semi-classical generalized Langevin equation for equilibrium and nonequilibrium molecular dynamics simulation

Molecular dynamics (MD) simulation based on Langevin equation has been widely used in the study of structural, thermal properties of matter in different phases. Normally, the atomic dynamics are described by classical equations of motion and the effect of the environment is taken into account through the fluctuating and frictional forces. Generally, the nuclear quantum effects and their coupling to other degrees of freedom are difficult to include in an efficient way. This could be a serious limitation on its application to the study of dynamical properties of materials made from light elements, in the presence of external driving electrical or thermal fields. One example of such system is single molecule dynamics on metal surface, an important system that has received intense study in surface science. In this review, we summarize recent effort in extending the Langevin MD to include nuclear quantum effect and their coupling to flowing electrical current. We discuss its applications in the study of adsorbate dynamics on metal surface, current-induced dynamics in molecular junctions, and quantum thermal transport between different reservoirs.     

Implementation of the IMOMM methodology for performing combined QM/MM molecular dynamics simulations and frequency calculations

A technique for implementing the integrated molecular orbital and molecular mechanics (IMOMM) methodology developed by Maseras and Morokuma that is used to perform combined quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations, frequency calculations and simulations of macromolecules including explicit solvent is presented. Although the IMOMM methodology is generalized to any coordinate system, the implementation first described by Maseras and Morokuma requires that the QM and MM gradients be transformed into internal coordinates before they are added together. This coordinate transformation can be cumbersome for macromolecular systems and can become ill-defined during the course of a molecular dynamics simulation. We describe an implementation of the IMOMM method in which the QM and MM gradients are combined in the cartesian coordinate system, thereby avoiding potential problems associated with using the internal coordinate system. The implementation can be used to perform combined QM/MM molecular dynamics simulations and frequency calculations within the IMOMM framework. Finally, we have examined the applicability of thermochemical data derived from IMOMM framework. Finally, we have examined the applicability of thermochemical data derived from IMOMM frequency calculations. Received: 11 May 1998 / Accepted: 14 August 1998 / Published online: 16 November 1998     

The Gaussian and augmented-plane-wave density functional method for ab initio molecular dynamics simulations

A new algorithm for density-functional-theory-based ab initio molecular dynamics simulations is presented. The Kohn–Sham orbitals are expanded in Gaussian-type functions and an augmented-plane-wave-type approach is used to represent the electronic density. This extends previous work of ours where the density was expanded only in plane waves. We describe the total density in a smooth extended part which we represent in plane waves as in our previous work and parts localised close to the nuclei which are expanded in Gaussians. Using this representation of the charge we show how the localised and extended part can be treated separately, achieving a computational cost for the calculation of the Kohn–Sham matrix that scales with the system size N as O(NlogN). Furthermore, we are able to reduce drastically the size of the plane-wave basis. In addition, we introduce a multiple-cutoff method that improves considerably the performance of this approach. Finally, we demonstrate with a series of numerical examples the accuracy and efficiency of the new algorithm, both for electronic structure calculations and for ab initio molecular dynamics simulations. Received: 15 December 1998 /Accepted: 18 February 1999 /Published online: 14 July 1999     

Aggregation mechanism of polyglutamine diseases revealed using quantum chemical calculations, fragment molecular orbital calculations, molecular dynamics simulations, and binding free energy calculations

Polyglutamine (polyQ) diseases, including Huntington’s disease (HD), are caused by expansion of polyQ-encoding repeats within otherwise unrelated gene products. The aggregation mechanism of polyQ diseases, the inhibition mechanism of Congo red, and the alleviation mechanism of trehalose were proposed here based on quantum chemical calculations and molecular dynamics simulations. The calculations and simulations revealed the following. The effective molecular bonding is between glutamine (Gln) and Gln (Gln + Gln), between Gln and Congo red (Gln + Congo red), and between Gln and trehalose (Gln + trehalose). The bonding strength is −13.1 kcal/mol for Gln + Gln, −24.4 kcal/mol for Gln + Congo red, and −12.0 kcal/mol for Gln + trehalose. In the polyQ region, both the number of intermolecular Gln + Gln formations and the total calories generated by the Gln + Gln formation are proportional to the number of repetitions of Gln. We propose an aggregation mechanism whose heat generated by the intermolecular Gln + Gln formation causes the pathogeny of polyQ disease. In our aggregation mechanism, this generated heat collapses the host protein and promotes fibrillogenesis. Without contradiction, our mechanism can explain all the experimental results reported to date. Our mechanism can also explain the inhibition mechanism by Congo red as an inhibitor of polyglutamine-induced protein aggregation and the alleviation mechanism by trehalose as an alleviator of that aggregation. The inhibition mechanism by Congo red is explained by the strong interaction with Gln and by the characteristic structure of Congo red.     

Post-adiabatic approach to atomic and molecular processes: The van der Waals interactions of some open shell systems

Summary Various properties of post-adiabatic representations of multichannel Schrödinger equations are described in the general context of adiabatic and classical path approximations as used in atomic and molecular physics. The van der Waals interactions of fluorine, chlorine, and oxygen atoms with rare gases, hydrogen, methane, and hydrogen halides are considered: it is found that in some of these systems, the first-order post-adiabatic scheme exhibits a smaller coupling than the adiabatic representation, thus providing an appropriate choice of the basis functions for a decoupling approximation.     

Response dynamics of 2-D quantum dots in the presence of time-varying fields: Anharmonicity and pulse shape effects

We explore the pattern of time evolution of different observables in a harmonically confined single carrier 2-D quantum dot when an external time-varying electric field is switched on. A static transverse magnetic field is also present. For given strengths of the confining field, cyclotron frequency, intensity and oscillation frequency of the external field, and pulse shape parameters, the system reveals a long time dynamics that leads to a kind of localization in the unperturbed state space. The presence of cubic anharmonicity in the confining field brings in new features in the dynamics. Frequency dependent linear and non-linear response properties of the dot are analyzed.     

Local physical quantities for spin based on the relativistic quantum field theory in molecular systems

Local physical quantities for spin are investigated on the basis of the four‐ and two‐component relativistic quantum theory. In the quantum field theory, local physical quantities for spin such as the spin angular momentum density, spin torque density, zeta force density, and zeta potential play important roles in spin dynamics. We discuss how to calculate these local physical quantities based on the two‐component relativistic quantum theory. Some different types of relativistic numerical calculations of local physical quantities in Li atom and C₆H₆ are demonstrated and compared. Local physical quantities for each orbital are also discussed, and it is seen that a total local zeta potential is given as a result of some cancellation of large contributions from each orbital. © 2016 Wiley Periodicals, Inc.     

Investigation on the isoform selectivity of novel kinesin-like protein 1 (KIF11) inhibitor using chemical feature based pharmacophore,molecular docking,and quantum mechanical studies

Kinesin-like protein (KIF11) is a molecular motor protein that is essential in mitosis. Removal of KIF11 prevents centrosome migration and causes cell arrest in mitosis. KIF11 defects are linked to the disease of microcephaly, lymph edema or mental retardation. The human KIF11 protein has been actively studied for its role in mitosis and its potential as a therapeutic target for cancer treatment. Pharmacophore modeling, molecular docking and density functional theory approaches was employed to reveal the structural, chemical and electronic features essential for the development of small molecule inhibitor for KIF11. Hence we have developed chemical feature based pharmacophore models using Discovery Studio v 2.5 (DS). The best hypothesis (Hypo1) consisting of four chemical features (two hydrogen bond acceptor, one hydrophobic and one ring aromatic) has exhibited high correlation co-efficient of 0.9521, cost difference of 70.63 and low RMS value of 0.9475. This Hypo1 is cross validated by Cat Scramble method; test set and decoy set to prove its robustness, statistical significance and predictability respectively. The well validated Hypo1 was used as 3Dquery to perform virtual screening. The hits obtained from the virtual screening were subjected to various scrupulous drug-like filters such as Lipinski’s rule of five and ADMET properties. Finally, six hit compounds were identified based on the molecular interaction and its electronic properties. Our final lead compound could serve as a powerful tool for the discovery of potent inhibitor as KIF11 agonists.