Non-Adiabatic Energy Surfaces of the B+H\u3csub\u3e2\u3c/sub\u3e Systems

In order to solve the dynamics of a system, the kinetic energy operator of the Hamiltonian must be diagonalized. Diagonalization requires rotation of the system into a non-adiabatic representation. This rotation is a coupling angle determined by the derivative coupling terms. Derivative coupling terms are calculated using Columbus and Brooklyn, software packages. Separation of internal dynamics characterized by Jacobi coordinates, and external dynamics characterized by a set of Euler angles and the center of mass position, requires a transformation from Cartesian coordinates to Jacobi coordinates required for subsequent dynamical calculations. Previous attempts to solve for non-adiabatic energy surfaces in this manner have failed because of an ambiguity in selecting the correct variable for describing the overall rotation of the B+H2 system, giving answers that do not agree with theory. This error, which lies within the method of converting from one coordinate system to another, is discovered and corrected. By way of this correction, correct coupling angles are calculated, and non-adiabatic energy surfaces are calculated

Controlling vibrational cooling with Zero-Width Resonances: An adiabatic Floquet approach

In molecular photodissociation, some specific combinations of laser parameters (wavelength and intensity) lead to unexpected Zero-Width Resonances (ZWR), with in principle infinite lifetimes. Their interest in inducing basic quenching mechanisms have recently been devised in the laser control of vibrational cooling through filtration strategies [O. Atabek et al., Phys. Rev. A87, 031403(R) (2013)]. A full quantum adiabatic control theory based on the adiabatic Floquet Hamiltonian is developed to show how a laser pulse could be envelop-shaped and frequency-chirped so as to protect a given initial vibrational state against dissociation, taking advantage from its continuous transport on the corresponding ZWR, all along the pulse duration. As compared with previous control scenarios actually suffering from non-adiabatic contamination, drastically different and much more efficient filtration goals are achieved. A semiclassical analysis helps in finding and interpreting a complete map of ZWRs in the laser parameter plane. In addition, the choice of a given ZWR path, among the complete series identified by the semiclassical approach, amounts to be crucial for the cooling scheme, targeting a single vibrational state population left at the end of the pulse, while all others have almost completely decayed. The illustrative example, offering the potentiality to be transposed to other diatomics, is Na2 prepared by photoassociation in vibrationally hot but translationally and rotationally cold states.Comment: 15 pages, 14 figure

Effective non-adiabatic Hamiltonians for the quantum nuclear motion over coupled electronic states

The quantum mechanical motion of the atomic nuclei is considered over a single- or a multi-dimensional subspace of electronic states which is separated by a gap from the rest of the electronic spectrum over the relevant range of nuclear configurations. The electron-nucleus Hamiltonian is block-diagonalized up to $\mathcal{O}(\varepsilon^{n+1})$ through a unitary transformation of the electronic subspace and the corresponding $n$th-order effective Hamiltonian is derived for the quantum nuclear motion. Explicit but general formulae are given for the second- and the third-order corrections. As a special case, the second-order Hamiltonian corresponding to an isolated electronic state is recovered which contains the coordinate-dependent mass-correction terms in the nuclear kinetic energy operator. For a multi-dimensional, explicitly coupled electronic band, the second-order Hamiltonian contains the usual BO terms and non-adiabatic corrections but generalized mass-correction terms appear as well. These, earlier neglected terms, perturbatively account for the outlying (discrete and continuous) electronic states not included in the explicitly coupled electronic subspace

WavePacket: A Matlab package for numerical quantum dynamics. III: Quantum-classical simulations and surface hopping trajectories

WavePacket is an open-source program package for numerical simulations in quantum dynamics. Building on the previous Part I [Comp. Phys. Comm. 213, 223-234 (2017)] and Part II [Comp. Phys. Comm. 228, 229-244 (2018)] which dealt with quantum dynamics of closed and open systems, respectively, the present Part III adds fully classical and mixed quantum-classical propagations to WavePacket. In those simulations classical phase-space densities are sampled by trajectories which follow (diabatic or adiabatic) potential energy surfaces. In the vicinity of (genuine or avoided) intersections of those surfaces trajectories may switch between surfaces. To model these transitions, two classes of stochastic algorithms have been implemented: (1) J. C. Tully's fewest switches surface hopping and (2) Landau-Zener based single switch surface hopping. The latter one offers the advantage of being based on adiabatic energy gaps only, thus not requiring non-adiabatic coupling information any more. The present work describes the MATLAB version of WavePacket 6.0.2 which is essentially an object-oriented rewrite of previous versions, allowing to perform fully classical, quantum-classical and quantum-mechanical simulations on an equal footing, i.e., for the same physical system described by the same WavePacket input. The software package is hosted and further developed at the Sourceforge platform, where also extensive Wiki-documentation as well as numerous worked-out demonstration examples with animated graphics are available

Theory of Electronic Excitations in Slow Atomic Collisions

This review deals with quantitative descriptions of electronic transitions in atom-atom and ion-atom collisions. In one type of description, the nuclear motion is treated classically or semiclassically, and a wave function for the electrons satisfies a time-dependent Schrödinger equation. Expansion of this wave function in a suitable basis leads to time-dependent coupled equations. The role played by electron-translation factors in this expansion is noted, and their effects upon transition amplitudes are discussed. In a fully quantum-mechanical framework there is a wave function describing the motion of electrons and nuclei. Expansion of this wave function in a basis which spans the space of electron variables leads to quantum-mechanical close-coupled equations. In the conventional formulation, known as perturbed-stationary-states theory, certain difficulties arise because scattering boundary conditions cannot be exactly satisfied within a finite basis. These difficulties are examined, and a theory is developed which surmounts them. This theory is based upon an intersecting-curved-wave picture. The use of rotating or space-fixed electronic basis sets is discussed. Various bases are classified by Hund\u27s cases (a)-(e). For rotating basis sets, the angular motion of the nuclei is best described using symmetric-top eigenfunctions, and an example of partial-wave analysis in such functions is developed. Definitions of adiabatic and diabatic representations are given, and rules for choosing a good representation are presented. Finally, representations and excitation mechanisms for specific systems are reviewed. Processes discussed include spin-flip transitions, rotational coupling transitions, inner-shell excitations, covalent-ionic transitions, resonant and near-resonant charge exchange, fine-structure transitions, and collisional autoionization and electron detachment

Interpolation of multidimensional diabatic potential energy matrices

A method for constructing diabatic potential energy matrices by interpolation of ab initio quantum chemistry data is described and tested. This approach is applicable to any number of interacting electronic states, and relies on a formalism and a computational procedure that are more general than those presented previously for the case of two electronic states. The method is tested against an analytic model for three interacting electronic states of NH₃⁺

Simulation and control of electron and nuclear dynamics with strong and ultrashort laser pulses

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Químicas, Departamento de Química Física I, leída el 28/10/2016. Tesis formato europeo (compendio de artículos)Comprender la estructura y la dinámica de los procesos químicos a nivel molecular es un paso clave para el diseño de materiales con propiedades deseadas o para el control de las reacciones químicas. Desde los inicios de la mecánica cuática, el control de los fénomenos cuánticos ha sido uno de los principales objetivos en el campo de la física y la química. El desanollo de los láseres ultrarrápidos y ultraintensos ha permitido el uso de pulsos externos, no sólo para seguir el movimiento nuclear y electrónico [ 1-3], sino también para controlarlo de forma activa, es decir, manipular la dinámica molecular en la escala de tiempos en la que ocurren los procesos físicos y químicos, así como resolver las ecuaciones dinámicas que los gobiernan, de forma que pueda favorecerse un tipo de proceso en particular [4]. De esta forma, el campo de Control Cuántico (o coherente) se ha desarrollado conjuntamente con la Femtoquímica y la Attofísica. Las primeras propuestas de control surgieron independientemente con dos escenarios. Por un lado, Tannor y Rice propusieron un mecanismo de control en la variable temporal: el esquema pump-dump [5, 6], que es un precursor de lo que se llamaría control óptimo. Por otro lado, Brumer y Shapiro [7,8] propusieron un esquema de control coherente o resuelto en frecuencias. Sin embargo, estos esquemas sólo permiten el control de forma eficiente cuando se conocen el Hamiltoniano molecular y las superficies de energía potencial. Por ejemplo, en el esquema de Brumer y Shapiro, el mismo estado intermedio puede dar lugar a diferentes productos de reacción. En el esquema pump-dump, sólo es posible el control de transiciones verticales (ventana Frank-Condon) entre estados electrónicos...Understanding the structure and dynamics of chemical processes at the molecular level is a key step toward the design of materials with the desired properties, or the efficient control of chemical reactions. Many subtleties involving basic quantum properties, such as superposition of states and interfering pathways allow to highly increase the yield of a specific process, far beyond what the probability distribution would suggest, should it follow the classical rules of motion. The spectra of molecules is one of the strongest evidence of this phenomena. Rather than distributing its energy in a continuous way along the molecule, one can find resonances that relate to particular structures. The playground of quantum dynamics offers more spectacular predictions. Using the quantum correlations at our advantage, one can externally drive a molecule toward selecting specific states or chemical processes from the huge pool of competing processes that are energetically available. Much of the history of the probe and control of chemical processes has come side-byside with the development of lasers. As we will see, one can arguably relate this history as a process. The laser was first used as a tool to ignite and selectively probe specific states and processes given its fine-tunability and intensity. ·with ultrashort laser pulses came the first probe and control of the dynamics. Pulse shaping then allowed to promote the laser to the role of a chemical agent, using Rabitz's terminology [16]. Finally, the use of very strong non-resonant pulses is promoting the laser to the role of a catalyst. Obviously, all the different roles are still being enacted by the laser depending on the particular use we need. We will now review in more detail what particular features of lasers are mainly used and how they were developed in order to fullfil the different roles of igniting, probing, "reacting" with molecules, and "catalyzing" chemical processes...Depto. de Química FísicaFac. de Ciencias QuímicasTRUEunpu

Ab-initio non-relativistic quantum electrodynamics: Bridging quantum chemistry and quantum optics from weak to strong coupling

By applying the Born-Huang expansion, originally developed for coupled nucleus-electron systems, to the full nucleus-electron-photon Hamiltonian of non-relativistic quantum electrodynamics (QED) in the long-wavelength approximation, we deduce an exact set of coupled equations for electrons on photonic energy surfaces and the nuclei on the resulting polaritonic energy surfaces. This theory describes seamlessly many-body interactions between nuclei, electrons and photons including the quantum fluctuation of the electromagnetic field and provides a proper first-principle framework to describe QED-chemistry phenomena. Since the photonic surfaces and the corresponding non-adiabatic coupling elements can be solved analytically, the resulting expansion can be brought into a compact form which allows us to analyze aspects of coupled nucleus-electron-photon systems in a simple and intuitive manner. Furthermore, we discuss structural differences between the exact quantum treatment and Floquet theory and show how existing implementations of Floquet theory can be adjusted to adhere to QED. From this generalized Born-Huang expansion an adapted Born-Oppenheimer approximation for nuclei on polaritonic surfaces can be deduced. This form allows a direct application of first-principle methods of quantum chemistry such as coupled-cluster or configuration interaction approaches to QED chemistry. By restricting the basis set of this generalized Born-Oppenheimer approximation we furthermore bridge quantum chemistry and quantum optics by recovering simple models of coupled matter-photon systems employed in quantum optics and polaritonic chemistry. We finally highlight numerically that simple few-level models can lead to physically wrong predictions, even in weak-coupling regimes, and show how the presented derivations from first principles help to check and derive physically reliable simplified models

From low dimensions to full configuration space: Generalising models for nonadiabatic molecular dynamics

This thesis aims to bridge the development of nonadiabatic dynamics methods and their application for studies of real molecular systems. First, this work explores fundamental concepts of photochemistry by investigating two different pictures, arising from the Born-Oppenheimer and the exact factorisation representation. Based on a simplistic model, a photochemical experiment from the excitation up to the formation of photoproducts is simulated. This study then compares the Born-Oppenheimer and exact factorisation representations of the processes. Subsequently, the influence of the Born-Oppenheimer picture for approximate nonadiabatic dynamics is investigated on two-dimensional model systems around conical intersections. The effects of neglected couplings and geometric phase are evaluated for ab initio multiple spawning (AIMS), a method for nonadiabatic molecular dynamics based on classically moving Gaussians. Afterwards, this work introduces a standardised test set of molecules to connect between tests of newly developed nonadiabatic dynamics methods on one-dimensional model systems and their intended application to full-dimensional molecules. Inspired by the widely used one-dimensional Tully models, three molecules are selected to form the molecular Tully models, which undergo similar photophysical processes, but in a high-dimensional space. In addition, the recently proposed stochastic-selection AIMS framework is also tested on two molecules undergoing ring-opening reactions to explore the strengths and limitations of the method. Finally, a direct comparison between experimental and computational results is presented. The photochemistry of 2(5H)-thiophenone is probed during and after the initial ring opening using time-resolved photoelectron spectroscopy. Static and dynamic calculations unravel the photoprocesses and identify a variety of photoproducts. Using the computational results, the experimental signal can be translated to insights into the ongoing photochemistry. Overall, this thesis aims to bring models in nonadiabatic dynamics in a real-world context. This work contributes to facilitating the transfer of new nonadiabatic dynamics methods towards the study of molecules in their full dimensionality