Time scales and other problems in linking simulations of simple chemical systems to more complex ones

We shall start with very small systems like H₂ and H₃, computed with very accurate methods (Hylleraas–CI ) or atomic systems up to Zn with accurate methods (CI ), then move to more complex ones, like C₆₀, but now with somewhat less accurate methods, specifically Hartree–Fock with density functionals, the latter for the correlation energy but not for the exchange energy. For even more complex tasks like geometry optimization of C₆₀, we have resorted to even simpler and parametrized methods, like local density functionals. Then, we could use quantum mechanics either to provide interaction potentials for classical molecular dynamics or to directly solve dynamical systems, in a quantum molecular dynamics approximation. Having demonstrated that we can use the computational output from small systems as input to larger ones, we discuss in detail a new model for liquid water, which is borne out entirely from ab initio methods and nicely links spectroscopic, thermodynamics, and other physicochemical data. Concerning time scales, we use classical molecular dynamics to determine friction coefficients, and with these we perform stochastic dynamic simulations. The use of simulation results from smaller systems to provide inputs for larger system simulations is the “global simulation” approach, which, today, with the easily available computers, is becoming more and more feasible. Projections on simulations in the 1996–1998 period are discussed, new computational areas are outlined, and a N⁴ complexity algorithm is compared to density functional approaches. © 1993 John Wiley & Sons, Inc.     

An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics. I. Theories

We have reformulated and generalized our recent work [J. Liu and W. H. Miller, J. Chem. Phys. 126, 234110 (2007)] into an approach for generating a family of trajectory-based dynamics methods in the phase space formulation of quantum mechanics. The approach (equilibrium Liouville dynamics) is in the spirit of Liouville's theorem in classical mechanics. The trajectory-based dynamics is able to conserve the quantum canonical distribution for the thermal equilibrium system and approaches classical dynamics in the classical (? → 0), high temperature (β → 0), and harmonic limits. Equilibrium Liouville dynamics provides the framework for the development of novel theoretical∕computational tools for studying quantum dynamical effects in large∕complex molecular systems.     

Concept of the “stability” of the quantum mechanical state

A new concept of the “stability” of the quantum mechanical state is presented. This concept is closely related to the hydrodynamical theory of quantum mechanics. For charged particles, the “stability” against the application of the external electromagnetic field is examined. Under a nonlinear interaction, a new type of the solitonlike phenomenon is shown as a novel, illustrative example of the “stable” state. An extension for the relativistic treatment is also examined.     

Different approaches to conformational analysis: A comparison of completeness,efficiency, and reliability based on the study of a nine-membered lactam

Different methods such as molecular dynamics, systematic, or stochastic search and a special “generic shape” algorithm have been employed in the conformational analysis of a nine-membered lactam. Furthermore, crystal data were used to generate conformations of the compound under consideration. The various methods are compared in terms of their efficiency and completeness in the search for conformations with an energy content of up to 60 kJ/mol above the global minimum. Additionally, the generated conformations have been optimized by different techniques, molecular mechanics and quantum chemical calculations, to compare the number of existing local minima and their relative energies and geometries.     

TITAN: A Code for Modeling and Generating Electric Fields—Features and Applications to Enzymatic Reactivity

We present here a versatile computational code named “elecTric fIeld generaTion And maNipulation (TITAN),” capable of generating various types of external electric fields, as well as quantifying the local (or intrinsic) electric fields present in proteins and other biological systems according to Coulomb's Law. The generated electric fields can be coupled with quantum mechanics (QM), molecular mechanics (MM), QM/MM, and molecular dynamics calculations in most available software packages. The capabilities of the TITAN code are illustrated throughout the text with the help of examples. We end by presenting an application, in which the effects of the local electric field on the hydrogen transfer reaction in cytochrome P450 OleT_JE enzyme and the modifications induced by the application of an oriented external electric field are examined. We find that the protein matrix in P450 OleT_JE acts as a moderate catalyst and that orienting an external electric field along the Fe─O bond of compound I has the biggest impact on the reaction barrier. The induced catalysis/inhibition correlates with the calculated spin density on the O-atom. © 2019 Wiley Periodicals, Inc.     

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.     

Characterization and quantification of the role of coherence in ultrafast quantum biological experiments using quantum master equations,atomistic simulations,and quantum process tomography

Long-lived electronic coherences in various photosynthetic complexes at cryogenic and room temperature have generated vigorous efforts both in theory and experiment to understand their origins and explore their potential role to biological function. The ultrafast signals resulting from the experiments that show evidence for these coherences result from many contributions to the molecular polarization. Quantum process tomography (QPT) is a technique whose goal is that of obtaining the time-evolution of all the density matrix elements based on a designed set of experiments with different preparation and measurements. The QPT procedure was conceived in the context of quantum information processing to characterize and understand general quantum evolution of controllable quantum systems, for example while carrying out quantum computational tasks. We introduce our QPT method for ultrafast experiments, and as an illustrative example, apply it to a simulation of a two-chromophore subsystem of the Fenna-Matthews-Olson photosynthetic complex, which was recently shown to have long-lived quantum coherences. Our Fenna-Matthews-Olson model is constructed using an atomistic approach to extract relevant parameters for the simulation of photosynthetic complexes that consists of a quantum mechanics/molecular mechanics approach combined with molecular dynamics and the use of state-of-the-art quantum master equations. We provide a set of methods that allow for quantifying the role of quantum coherence, dephasing, relaxation and other elementary processes in energy transfer efficiency in photosynthetic complexes, based on the information obtained from the atomistic simulations, or, using QPT, directly from the experiment. The ultimate goal of the combination of this diverse set of methodologies is to provide a reliable way of quantifying the role of long-lived quantum coherences and obtain atomistic insight of their causes.     

Molecular Dynamics Simulation and Density Functional Theory Study of Chemisorption of Propranolol Optical Isomers on a Uracil‐modified Carbon Paste Electrode

To reveal the nature of the interaction of the optical isomers of propranolol with the surface of carbon paste electrodes modified by uracil, we performed a combined computational and experimental study. Our study comprised the different modes of complexation between propranolol and uracil molecules covering the carbon paste electrode within two approaches: molecular dynamics simulation (MD ) and quantum mechanics (QM) modeling. A graphene layer was used as a model of the carbon paste electrode. The computations showed that uracil modification of the carbon paste electrode surface enhanced the selectivity toward the D‐isomer of propranolol as compared to the unmodified case. These theoretical results agree with our voltammetric measurements.     

DNA Nucleobase under Ionizing Radiation: Unexpected Proton Transfer by Thymine Cation in Water Nanodroplets

The effect of ionizing radiation on DNA constituents is a widely studied fundamental process using experimental and computational techniques. In particular, radiation effects on nucleobases are usually tackled by mass spectrometry in which the nucleobase is embedded in a water nanodroplet. Here, we present a multiscale theoretical study revealing the effects and the dynamics of water droplets towards neutral and ionized thymine. In particular, by using both hybrid quantum mechanics/molecular mechanics and full ab initio molecular dynamics, we reveal an unexpected proton transfer from thymine cation to a nearby water molecule. This leads to the formation of a neutral radical thymine and a Zundel structure, while the hydrated proton localizes at the interface between the deprotonated thymine and the water droplet. This observation opens entirely novel perspectives concerning the reactivity and further fragmentation of ionized nucleobases.     

Computational chemistry applied to the design of chiral stationary phases for enantiomeric separation

A general computational scheme for the rational design of chiral stationary phases for the chromatographic separation of enantiomers has been established. The developed scheme was based on applying different interaction models (force field methods versus semi empirical quantum chemical methods), different docking algorithms (systematic grid search methods versus interactive methods guided by rules based on binding modes) and different levels of approximations (rigid versus flexible docking) to a representative test problem containing the 3,5-dinitrobenzoyl group. The computational methods in use covered the most sophisticated methods which could presently be applied to problems of such a size (about 80 atoms). It has been shown that the current computational approaches using rigid body approximations for the docked molecules and simple molecular mechanics (not taking pi-“effects” into account) are invalid in view of the required predictive precision of about 1–2 Kcal/mole for the differential binding energy. Another surprising result was the failure of the commonly used systematic search methods in determining the most favorable binding modes. Based on our calculations on the representative test problem we propose a new arrangement for the most stable complexes without parallel stacking of the aromatic pi-donor and the 3,5-dinitrobenzoyl pi-acceptor systems.     

P.‐O. Löwdin and the International Journal of Quantum Chemistry: A kaleidoscopic agenda for quantum chemistry

This is a article about P.‐O. Löwdin's life, his work in shaping quantum chemistry into a mature discipline at the intersection of mathematics, physics, chemistry, and biology, and his founding of the International Journal of Quantum Chemistry in 1967. Unavoidably, it is, also, a article reflecting our views about the history of quantum chemistry. We attempt to convey the complexities in the becoming of a subdiscipline, like quantum chemistry, where a variety of factors will have to be taken into consideration for a comprehensive understanding of its historical developments: the relations of chemists to the Heisenberg‐Schrödinger formulation of quantum mechanics after 1926, the institutional dynamics centered around the establishment of new courses and chairs, the research agendas and the vying for dominance within the community of quantum chemists, the methodological, and philosophical issues that have never left the quantum chemists indifferent, and, of course, the dramatic role of the computer in transforming the culture for actually practicing quantum chemistry. Furthermore, attracted by American history, culture, and ways of life, Löwdin suggested in the late 1970s that the post‐WWII character of quantum chemistry was dependent on its ability to hub a “scientific melting pot,” much like the United States of America which he viewed as a fusion of people from diverse provenances and cultures. In this article, we attempt to investigate another metaphor, that of the “kaleidoscope.” Löwdin believed that quantum chemistry's strength arose from its ability to nurture a multiplicity of heterogeneous cultural elements/subcultures and practices, interacting with each other, exchanging perspectives and modes of action, which circulated in an increasingly extended network of actors and institutional frameworks. © 2013 Wiley Periodicals, Inc.     

Promenading in the enchanted realm of Kronecker powers: single monomial probabilistic evolution theory (PREVTH) in evolver dynamics

This paper takes a CMMSE 2107 proceedings paper about “Highest Monomiality Based Probabilistic Evolution Theory (PREVTH)” as starting point. The focus is again set of ODEs but, this time, not on function unknowns. Instead, we deal with the temporally evolving operators, quantum mechanics’ Heisenberg picture entities we call evolvers. Our work here uses the degree changing possibilities in Kronecker powers of vectors by using so-called constancy adding space extension. Beyond the degree escalation, vanishing expression addition is also used to introduce certain arbitrary parameters and therefore to increase the flexibility in the single monomial coefficient matrix. These two issues have been deeply investigated to learn how to get single monomiality in highest degree additive term. So, the PREVTH previous-to-this paper, somehow arrested by the conicality, has now been emancipated to single monomiality which is certainly much more relaxed than before.     

Algebrants in many-electron quantum mechanics: Applications of generalized determinants or matrix functions

We define the algebrant, a mathematical generalization of the determinant, the immanant, the permanent, and the Schur functions. Algebrants are classified as multilinear matrix functions or multicomponent symmetrized tensors. In applications, such as N-electron quantum mechanics, where extensive computation is required, it is vital to reduce computational effort, e.g., the well-known N-factorial problem. We derive certain mathematical properties that can be incorporated in efficient computing algorithms for algebrants. Foremost is our “elimination theorem,” which allows (in important special cases) zeros to be introduced into an algebrant in close analogy with Gaussian elimination for determinants. Savings accruing from such elimination can be substantial. We show examples from Matsen's spin-free quantum chemistry where elimination effectively removes the N-factorial problem that has hitherto stifled possible applications.     

Quantum Mechanics/Molecular Mechanics Studies on the Mechanism of Action of Cofactor Pyridoxal 5′‐Phosphate in Ornithine 4,5‐Aminomutase

A computational study was performed on the experimentally elusive cyclisation step in the cofactor pyridoxal 5′‐phosphate (PLP)‐dependent D ‐ornithine 4,5‐aminomutase (OAM)‐catalysed reaction. Calculations using both model systems and a combined quantum mechanics/molecular mechanics approach suggest that regulation of the cyclic radical intermediate is achieved through the synergy of the intrinsic catalytic power of cofactor PLP and the active site of the enzyme. The captodative effect of PLP is balanced by an enzyme active site that controls the deprotonation of both the pyridine nitrogen atom (N1) and the Schiff‐base nitrogen atom (N2). Furthermore, electrostatic interactions between the terminal carboxylate and amino groups of the substrate and Arg297 and Glu81 impose substantial “strain” energy on the orientation of the cyclic intermediate to control its trajectory. In addition the “strain” energy, which appears to be sensitive to both the number of carbon atoms in the substrate/analogue and the position of the radical intermediates, may play a key role in controlling the transition of the enzyme from the closed to the open state. Our results provide new insights into several aspects of the radical mechanism in aminomutase catalysis and broaden our understanding of cofactor PLP‐dependent reactions.