Electronic quantum trajectories in a quantum dot

This article gives a quantum‐trajectory demonstration of the observed electric, magnetic, and thermal effects on a quantum dot with circular or elliptic shape. By applying quantum trajectory method to a quantum dot, we reveal the quantum‐mechanical meanings of the classical concepts of backscattering and commensurability, which were used in the literature to explain the peak locations of the magnetoresistance curve. Under the quantum commensurability condition, electronic quantum trajectories in a circular quantum dot are shown to be stationary like a standing wave, whose presence increases the electrical resistance. A hidden quantum effect called magnetic stagnation is discovered and shown to be the main cause of the observed jumps of the magnetoresistance curve. Quantum trajectories in an elliptic quantum dot are found to be chaotic and an index of chaos called Lyapunov exponent is proposed to measure the irregularity of the various quantum trajectories. It is shown that the response of the Lyapunov exponent to the applied magnetic field captures the main features of the experimental magnetoresistance curve. © 2014 Wiley Periodicals, Inc.     

Synthesizing quantum probability by a single chaotic complex‐valued trajectory

The current trajectory interpretation of quantum mechanics is based on an ensemble viewpoint that the evolution of an ensemble of Bohmian trajectories guided by the same wavefunction Ψ converges asymptotically to the quantum probability . Instead of the Bohm's ensemble‐trajectory interpretation, the present paper gives a single‐trajectory interpretation of quantum mechanics by showing that the distribution of a single chaotic complex‐valued trajectory is enough to synthesize the quantum probability. A chaotic complex‐valued trajectory manifests both space‐filling (ergodic) and ensemble features. The space‐filling feature endows a chaotic trajectory with an invariant statistical distribution, while the ensemble feature enables a complex‐valued trajectory to envelop the motion of an ensemble of real trajectories. The comparison between complex‐valued and real‐valued Bohmian trajectories shows that without the participation of its imaginary part, a single real‐valued trajectory loses the ensemble information contained in the wavefunction Ψ, and this explains the reason why we have to employ an ensemble of real‐valued Bohmian trajectories to recover the quantum probability . © 2015 Wiley Periodicals, Inc.     

Two‐dimensional reactive scattering with transmitted quantum trajectories

A simple and easy‐to‐implement method is presented for the study of time‐dependent reaction dynamics by propagating an ensemble of transmitted quantum trajectories. During the trajectory evolution, reflected trajectories are gradually removed and all the remaining trajectories represent the transmitted subensemble. The removal process of reflected trajectories avoids numerical instabilities arising from node formation in the reactant region, and allows stable long‐time propagation of transmitted trajectories. This method is applied to a two‐dimensional model chemical reaction. Excellent computational results are obtained for the time‐dependent reaction probabilities evaluated by the time integration of the probability flux. © 2014 Wiley Periodicals, Inc.     

Quantum bifurcation in a coulombic‐like potential

Because of the lack of nonlinear dynamics, up to now no bifurcation phenomenon in its original sense has been discovered directly in quantum mechanical systems. Based on the formalism of complex‐valued quantum mechanics, this article derives the nonlinear Hamilton equations from the Schrödinger equation to provide the necessary mathematic framework for the analysis of quantum bifurcation. This new approach makes it possible to identify quantum bifurcation by the direct evidence of the sudden change of fixed points and their surrounding trajectories. As a practical application of the proposed approach, we consider the quantum motion in a Coulombic‐like potential modeled by V(r) = A/r² ? B/r, where the first term describes the centrifugal trend and the second deals with the Coulombic attraction. As the bifurcation parameter evolves, we demonstrate how local and global bifurcations in quantum dynamics can be identified by inspecting the changes of fixed points and their surrounding trajectories. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Improved excitation uniformity in multiple‐quantum NMR experiments of mixtures

Multiple‐quantum ¹H NMR spectroscopy has been finding a renewed interest for its possible applications in the analysis of mixtures of small molecules, due to its simplification properties. A crucial aspect of this application of multiple‐quantum NMR is the sensitivity of the spectrum intensity to the molecular structure and to the parameterization of the experiment, which could result in the missing of some components. We demonstrate that a general scheme to overcome this drawback consists in varying the experiment parameterizations over a small number of values, selected according the values of the couplings and the relaxation rates. Copyright © 2013 John Wiley & Sons, Ltd.     

Fragment‐based quantum mechanical calculation of protein–protein binding affinities

The electrostatically embedded generalized molecular fractionation with conjugate caps (EE‐GMFCC) method has been successfully utilized for efficient linear‐scaling quantum mechanical (QM) calculation of protein energies. In this work, we applied the EE‐GMFCC method for calculation of binding affinity of Endonuclease colicin–immunity protein complex. The binding free energy changes between the wild‐type and mutants of the complex calculated by EE‐GMFCC are in good agreement with experimental results. The correlation coefficient (R) between the predicted binding energy changes and experimental values is 0.906 at the B3LYP/6‐31G*‐D level, based on the snapshot whose binding affinity is closest to the average result from the molecular mechanics/Poisson–Boltzmann surface area (MM/PBSA) calculation. The inclusion of the QM effects is important for accurate prediction of protein–protein binding affinities. Moreover, the self‐consistent calculation of PB solvation energy is required for accurate calculations of protein–protein binding free energies. This study demonstrates that the EE‐GMFCC method is capable of providing reliable prediction of relative binding affinities for protein–protein complexes. © 2018 Wiley Periodicals, Inc.     

Superlinear scaling in master-slave quantum chemical calculations using in-core storage of two-electron integrals

We describe the implementation of a parallel, in-core, integral-direct Hartree-Fock and density functional theory code for the efficient calculation of Hartree-Fock wave functions and density functional theory. The algorithm is based on a parallel master-slave algorithm, and the two-electron integrals calculated by a slave are stored in available local memory. To ensure the greatest computational savings, the master node keeps track of all integral batches stored on the different slaves. The code can reuse undifferentiated two-electron integrals both in the wave function optimization and in the evaluation of second-, third-, and fourth-order molecular properties. Superlinear scaling is achieved in a series of test examples, with speedups of up to 55 achieved for calculations run on medium-sized molecules on 16 processors with respect to the time used on a single processor.     

石杉碱甲-AChE复合物中石杉碱甲的结构特征: 量子化学研究

在运用量子化学从头计算方法(HF/4-31G)结合点电荷模型方法对AChE-HupA复合物活性位点的410个原子和1929个点电荷进行理论计算的基础上, 比较了石杉碱甲分子在形成复合物前后的结构变化特征。发现复合物中石杉碱甲分子构象并非能量最低构象, 它的能量比HF/4-31G全优化得到的构象的能量高91.8kj/mol。和单分子状态相比, 形成复合物后季铵基和内酰胺基的N-H, C=O键的键长变长、键强减弱, 其总原子净电荷也发生了明显的变化。且这些基团的空间取向都有不同程度的改变, C(8)-N(21)键的旋转达20ⅲ。这些信息将有益于设计新的AChE抑制剂。     

碳量子点/壳聚糖复合物的制备及用于槲皮素检测

以柠檬酸三钠、11-氨基十一烷、聚乙二醇400为碳源,利用微波法制备了碳量子点,将其与壳聚糖反应,制备出碳量子点/壳聚糖复合物。采用荧光、紫外、红外光谱等对碳量子点和碳量子点/壳聚糖复合物进行表征,探究了温度、时间、缓冲溶液及pH对体系荧光强度的影响。在pH 7.6的硼酸—硼砂缓冲介质中,槲皮素可使碳量子点/壳聚糖复合物发生荧光猝灭,其猝灭程度与槲皮素浓度呈良好的线性关系,据此建立了碳量子点/壳聚糖荧光猝灭法测定槲皮素的新方法,方法线性范围为4~40μmol/L,相关系数为0.9940,检出限为0.5μmol/L。方法已应用于测定本地甜瓜中槲皮素的含量。     

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.     

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.     

Complexes of thiomandelate and captopril mercaptocarboxylate inhibitors to metallo-beta-lactamase by polarizable molecular mechanics. Validation on model binding sites by quantum chemistry

Using the polarizable molecular mechanics method SIBFA, we have performed a search for the most stable binding modes of D- and L-thiomandelate to a 104-residue model of the metallo-beta-lactamase from B. fragilis, an enzyme involved in the acquired resistance of bacteria to antibiotics. Energy balances taking into account solvation effects computed with a continuum reaction field procedure indicated the D-isomer to be more stably bound than the L-one, conform to the experimental result. The most stably bound complex has the S(-) ligand bridging monodentately the two Zn(II) cations and one carboxylate O(-) H-bonded to the Asn193 side chain. We have validated the SIBFA energy results by performing additional SIBFA as well as quantum chemical (QC) calculations on small (88 atoms) model complexes extracted from the 104-residue complexes, which include the residues involved in inhibitor binding. Computations were done in parallel using uncorrelated (HF) as well as correlated (DFT, LMP2, MP2) computations, and the comparisons extended to corresponding captopril complexes (Antony et al., J Comput Chem 2002, 23, 1281). The magnitudes of the SIBFA intermolecular interaction energies were found to correctly reproduce their QC counterparts and their trends for a total of twenty complexes.     

Trial introduction of a complex potential function for perturbation that causes quantum mechanical transition in a one‐dimensional harmonic oscillator

Some results of computer simulation of the behavior of a one‐dimensional quantum mechanical oscillator are reported in this article. This harmonic oscillator comprises a particle trapped within a hyperbolic potential V(x) = x². Further, a perturbation potential function V′(x, t) was superposed upon the hyperbolic potential in order to induce a quantum mechanical transition. This perturbation function V′(x, t) is a function of both of space and time variables, and is set to represent a wave packet that is enveloped by a Gaussian bell‐shaped curve. A wave that probably has an appropriate wave number and angular frequency was inputted into the expression for the wave packet. In the initial phase, while the harmonic oscillator was allowed to oscillate almost freely, the wave packet was allowed to approach the harmonic oscillator. In the middle phase, the wave packet passes through the harmonic oscillator, affecting the shape of the quantum mechanical wave that represents the physical state of the system. In the last phase, when the wave packet left the system of the harmonic oscillator, the system settled onto an energetically stable state. The main objective of the simulation was to simulate the instance of a quantum mechanical transition from one eigenstate to another. After several trials, it was found that the perturbation function consisting of a complex function was, at least superficially, able to cause one desired transition, that is, a transition from one eigenstate to another eigenstate. By using such a complex perturbation function, a transition from the first excited state to the ground state was observed to occur. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

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.