The quantum divided basins: A new class of quantum subsystems

The rigorous theory of the quantum divided basins (QDB), the quantum subsystems emerging from the net zero‐flux equation, is considered in this article. This framework, the quantum theory of proper open subsystems, is derived from the extension of the quantum theory of atoms in molecules to encompass the new class of quantum subsystems. It is demonstrated that the regional hypervirial theorem and the associated regional observables as well as the subsystem variational procedure are all expressible for the QDB. The history of QDB is briefly reviewed and the bundles, which were introduced by other researchers, are offered as typical examples whereas new examples of QDB (not yet mentioned in literature) are also presented. Based on some model systems as well as the nitrogen molecule, the regional properties and the morphologies of typical QDB are scrutinized. It is also demonstrated that the QDB may be used to study the fine structure of the electron localization and delocalization. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Machine learning and signed particles,an alternative and efficient way to simulate quantum systems

Recently neural networks have been applied in the context of the signed particle formulation of quantum mechanics to rapidly and reliably compute the Wigner kernel of any provided potential. Important advantages were introduced, such as the reduction of the amount of memory required for the simulation of a quantum system by avoiding the storage of the kernel in a multi-dimensional array, as well as attainment of consistent speedup by the ability to realize the computation only on the cells occupied by signed particles. An inherent limitation was the number of hidden neurons to be equal to the number of cells of the discretized real space. In this work, anew network architecture is presented, decreasing the number of neurons in its hidden layer, thereby reducing the complexity of the network and achieving an additional speedup. The approach is validated on a onedimensional quantum system consisting of a Gaussian wave packet interacting with a potential barrier.     

Multiconfigurational expansions of density operators: equations of motion and their properties

 Multiconfigurational expansions of density operators which may be used in numerical treatments of the dynamics of closed and open quantum systems are introduced. The expansions of the density operators may be viewed as analogues of those used in the multiconfiguration time-dependent Hartree (MCTDH) method, which is a well-established and highly efficient method for propagating wavepackets in several dimensions. There is no unique multiconfigurational representation of a density operator and two sensible types of MCTDH-like expansions are studied. Equations of motion for these multiconfigurational expansions are presented by adopting the Dirac–Frenkel/McLachlan variational principle (or variants of thereof). Various properties of these sets of equations of motion are derived for closed and open system dynamics. The numerical and technical aspects of this approach have been recently discussed by us [(1999) J Chem Phys 111: 8759]. Here we discuss the formal aspects of the approach in a more general context. Received: 26 January 2000 / Accepted: 8 February 2000 / Published online: 12 May 2000     

Revisiting the foundations of the quantum theory of atoms in molecules: Some open problems

In a series of papers in the last 10 years, various aspects of the mathematical foundations of the quantum theory of atoms in molecules have been considered by this author and his coworkers in some details. Although these considerations answered part of the questions raised by some critics on the mathematical foundations of the quantum theory of atoms in molecules, however, new mathematical problems also emerged during these studies that were reviewed elsewhere [Sh. Shahbazian Int. J. Quantum Chem. 2011 , 111, 4497.]. Beyond mathematical subtleties of the formalism that were the original motivation for initial exchanges and disputes, the questions raised by critics had a constructive effect and prompted the author to propose a novel extension of the theory, now called the multi‐component quantum theory of atoms in molecules [M. Goli, Sh. Shahbazian Theor. Chem. Acc. 2013 , 132, 1365.]. Taking this background into account, in this paper a new set of open problems is put forward that the author believes proper answers to these questions, may open new doors for future theoretical developments of the quantum theory of atoms in molecules. Accordingly, rather than emphasizing on the rigorous mathematical formulation, the practical motivations behind proposing these questions are discussed in detail and the relevant literature are reviewed while when possible, evidence and routes to answers are also provided. The author hopes that proposing these open questions as a compact package may motivate more mathematically oriented people to participate in future developments of the quantum theory of atoms in molecules and its multi‐component version.     

Interaction of a finite quantum system with an infinite quantum system that contains a single one-parameter eigenvalue band

Interaction of a finite quantum system that contains ρ eigenvalues and eigenstates with an infinite quantum system that contains a single one-parameter eigenvalue band is considered. A new approach for the treatment of the combined system is developed. This system contains embedded eigenstates with continuous eigenvalues , and, in addition, it may contain isolated eigenstates with discrete eigenvalues . Two ρ × ρ eigenvalue equations, a generic eigenvalue equation and a fractional shift eigenvalue equation are derived. It is shown that all properties of the system that interacts with the system can be expressed in terms of the solutions to those two equations. The suggested method produces correct results, however strong the interaction between quantum systems and . In the case of the weak interaction this method reproduces results that are usually obtained within the formalism of the perturbation expansion approach. However, if the interaction is strong one may encounter new phenomena with much more complex behavior. This is also the region where standard perturbation expansion fails. The method is illustrated with an example of a two-dimensional system that interacts with the infinite system that contains a single one-parameter eigenvalue band. It is shown that all relevant completeness relations are satisfied, however strong the interaction between those two systems. This provides a strong verification of the suggested method.     

Is the Pauli exclusive principle an independent quantum mechanical postulate?

Foundation of the Pauli exclusive principle is discussed. It is demonstrated that the indistinguishability principle is insensitive to the permutation symmetry of the wave function and cannot be used as a criterion for the verification of the Pauli exclusive principle. The heuristic arguments are given in favor that the existence in nature of only the nondegenerate permutation representations (symmetrical and antisymmetrical) is not occasional. As follows from our analysis of possible scenarios, the permission of degenerate permutation representations leads to contradictions with the concept of particle identity and their independence. Thus, the prohibition of degenerate permutation states by the Pauli exclusive principle follows from the general physical assumptions inside quantum theory, but the problem of spin–statistics connection is still open. It is pointed out that the Pauli exclusive principle and the Jahn–Teller effect have some similar features. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Electrostatic effects in enzyme catalysis: a quantum mechanics/molecular mechanics study of the nucleophilic substitution reaction in haloalkane dehalogenase

Combined quantum mechanics/molecular mechanics molecular dynamics simulations have been carried out to study the cleavage of the carbon–chlorine bond in 1,2-dichloroethane catalysed by haloalkane dehalogenase from Xanthobacter Autotrophicus GJ10. The process has been compared with an adequate counterpart in aqueous solution, the nucleophilic attack of acetate anion on 1,2-dichloroethane. Within the limitations of the model, mainly due to the use of a semiempirical Hamiltonian, our results reproduce the magnitude and characteristics of the catalytic effect. Comparisons of the enzymatic and in solution potentials of mean force reveal that, irrespective of the reference state, the enzyme shows a larger affinity for the transition state. The origin of this increased affinity is found in the differences in the electrostatic pattern created by the environment in aqueous solution and in the enzyme.Proceedings of the 11th International Congress of Quantum Chemistry satellite meeting in honor of Jean-Louis Rivail     

Microwave enhanced non-alkaline bleaching of mechanical pulps: A new solution to an old problem

Since the granting of our first US patent on microwave induced catalytic decomposition of PCBs some 18 years ago, microwave technology has slowly begun to attract some industrial attention in the last few years. There was no doubt that microwaves had been applied to facilitate the conventional bleaching process of wood pulps in the past but with little or no success. The myth that microwaves can be regarded and manipulated as a rapid heat source probably caused most of the failures of unsuccessful microwave applications. It is therefore necessary to understand the real potential of microwaves as an energy source and to identify the many critical electromagnetic properties of the load (chemical systems), before a final choice of a proper microwave system be designed and installed. In this preliminary report, we demonstrate the real potential of pulsed microwave radiation for non-alkaline bleaching of mechanical pulps. Typically, very high consistency TMP up to 93% can be treated by pulsed microwave in the order of 90 seconds with an average increase of 20 to 25 points in brightness.     

The quantum theory of atoms in positronic molecules: A case study on diatomic species

This article presents the first systematic study of a series of diatomic positronic species using the recently proposed regional approach: the quantum theory of atoms in positronic molecules (QTAIPM). This survey includes the LiH,e⁺, NaH,e⁺, LiF,e⁺, NaF,e⁺, BeO,e⁺, MgO,e⁺, CN^?,e⁺, and OH^?,e⁺ species as typical examples. The computational algorithm of the whole analysis is communicated and reviewed in detail. The topological analysis of the joint density distribution reveals topological structures similar to those observed for the purely electronic systems; that is, each system decomposes into two quantum atoms. By considering some of the regional properties of these quantum atoms, it is demonstrated that the positron affects them seriously through two different mechanisms: direct and indirect contributions, the latter refers to electronic and geometric relaxations. The computational results clearly reveal the fact that the regional properties of the quantum atoms of positronic molecules are not deducible from their purely electronic counterparts; thus, an independent analysis is required for each positronic molecule. The positronic population is considered as a typical regional property showing that the attachment of a positron to a purely electronic system enhances the polarization of the electronic distribution. The concept of regional positron affinities is also introduced and discussed as a nonroutine application of the QTAIPM. The results of this article set the stage for further study on the quantum atoms of polyatomic positronic species. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

The quantum theory of atoms in positronic molecules: The subsystem variational procedure

This contribution deals with the subsystem variational procedure within the context of the quantum theory of atoms in positronic molecules (QTAIPM). Before introducing the subsystem energy functional termed as joint subsystem energy functional, a novel notation and the combination strategy are disclosed in detail by restating the positronic subsystem hypervirial theorem. They are employed in proposing the proper subsystem energy functional, the validity of which is checked by various criteria. The zero flux surfaces of the joint density distribution are used to define the topological atoms in the positronic molecules, and they are incorporated into the subsystem variational procedure as proper real space boundary conditions. The variational procedure finally yields the flux of the joint current property density that also appears in the positronic subsystem hypervirial theorem. At every stage, the corresponding equations for the purely electronic systems within the context of the quantum theory of atoms in molecules (QTAIM) are presented to clearly reveal the analogy between these two formalisms and to emphasize the importance of combining the property density distributions in the QTAIPM. The presented material demonstrates the internal consistency of the whole framework and discloses the fact that the QTAIM must be regarded as a variant of the QTAIPM. Furthermore, this formalism promises an extended QTAIM, which is hoped to resolve the issue of molecular structure beyond the clamp nuclei approximation. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Interaction of an isolated state with an infinite quantum system containing several one-parameter eigenvalue bands: I. Time-independent case

A new method for the exact solution of the interaction of an isolated state with an infinite dimensional quantum system §_∞ ^b containing several one-parameter eigenvalue bands is developed. Unlike standard perturbation expansion approach, this method produces correct results however strong the interaction between the state and the system . It is shown that in the case of the weak interaction this method correctly reproduces standard results obtained within the formalism of the perturbation expansion method. In particular, due to the interaction with the system , eigenvalue E of the state shifts to a new position. In addition, if this eigenvalue is embedded inside the range of the unperturbed eigenvalues, this shifted eigenvalue broadens and spectral distribution of the state has the shape of the universal resonance curve. However, if the interaction is strong, one finds much more complex and much more complicated behavior     

Interaction of an isolated state with an infinite quantum system containing several one-parameter eigenvalue bands: II. time-dependent case

Time-dependent properties of a state that interacts with an infinite dimensional quantum system containing several one-parameter eigenvalue bands are considered. This is done by a new mathematical method that produces correct results, however strong the interaction between the state and the system . It is shown that in the case of the weak interaction one obtains standard results that are usually obtained within the formalism of the perturbation expansion method. In particular, if the eigenvalue E of the state is embedded inside the range of the unperturbed eigenvalues, time evolution of the state that is initially prepared in the state has typical exponential decay behavior. One also reproduces standard results concerning probabilities of the transition of the state at infinite time (t=∞) into various eigenvalue bands. However, if the interaction is strong, one finds much more complex and much more complicated behavior.     

The mechanism for the conversion of uric acid into allantoin and dehydro-allantoin : A new look at an old problem

The reaction of uric acids 1 with iodine in alkaline solution yields, on acidification, new dehydro-allantoins 11, or normal oxidation products, allantoins 13, depending on whether an excess or a stoichiometric amount of oxidant was used. The structure and regiochemistry of dehydro-allantoins 11 was established by chemical, spectroscopic, and ¹⁴C-labelling methods. These experimental results, in combination with other data, generate a new mechanistic scheme for the uricolytic pathway to allantoin, ruling out the intervention of a symmetrical transition state prior to the decarboxylation step.     

The first branching point in porphyrin biosynthesis: a systematic docking, molecular dynamics and quantum mechanical/molecular mechanical study of substrate binding and mechanism of uroporphyrinogen-III decarboxylase

In humans, uroporphyrinogen decarboxylase is intimately involved in the synthesis of heme, where the decarboxylation of the uroporphyrinogen-III occurs in a single catalytic site. Several variants of the mechanistic proposal exist; however, the exact mechanism is still debated. Thus, using an ONIOM quantum mechanical/molecular mechanical approach, the mechanism by which uroporphyrinogen decarboxylase decarboxylates ring D of uroporphyrinogen-III has been investigated. From the study performed, it was found that both Arg37 and Arg50 are essential in the decarboxylation of ring D, where experimentally both have been shown to be critical to the catalytic behavior of the enzyme. Overall, the reaction was found to have a barrier of 10.3 kcal mol(-1) at 298.15 K. The rate-limiting step was found to be the initial proton transfer from Arg37 to the substrate before the decarboxylation. In addition, it has been found that several key interactions exist between the substrate carboxylate groups and backbone amides of various active site residues as well as several other functional groups.