Molecular vibrational trapping revisited: A case study with D2+

The present theoretical study is concerned with the vibrational trapping or bond hardening, which is a well-known phenomenon predicted by a dressed state representation of small molecules like and in an intense laser field. This phenomenon is associated with a condition where the energy of the light induced, vibrational level coincides with one of the vibrational levels on the field-free potential curve, which at the same time maximizes the wave function overlap between these two levels. One-dimensional numerical simulations were performed to investigate this phenomenon in a more quantitative way than has been done previously by calculating the photodissociation probability of for a wide range of photon energy. The obtained results undoubtedly show that the nodal structure of the field-free vibrational wave functions plays a decisive role in the vibrational trapping, in addition to the current understanding of this phenomenon

The Effective Potential Energy Surfaces of the Nonadiabatic Collision B(\u3csup\u3e2\u3c/sup\u3eP\u3csub\u3ej\u3c/sub\u3e\u3csub\u3ea\u3c/sub\u3e) + H\u3csub\u3e2\u3c/sub\u3e(\u3csup\u3e1\u3c/sup\u3eΣ\u3csup\u3e+\u3c/sup\u3e\u3csub\u3eg\u3c/sub\u3e,ν,j) ↔ B(\u3csup\u3e2\u3c/sup\u3eP\u3csub\u3ej\u27\u3c/sub\u3e\u3csub\u3ea\u3c/sub\u3e) + H\u3csub\u3e2\u3c/sub\u3e(\u3csup\u3e1\u3c/sup\u3eΣ\u3csup\u3e+\u3c/sup\u3e\u3csub\u3eg\u3c/sub\u3e,ν\u27,j\u27)

Effective potential energy surfaces (PESs) are calculated for a nonadiabatic collision . This calculation employed 1 2A\u27, 2 2A\u27 and 1 2A adiabatic PESs numerically calculated at the state-averaged multiconfigurational self-consistent field (SA-MCSCF)/configuration interaction (CI) level for several values of the H2 bond length, H2 orientation angle, and boron distance. The associated nonadiabatic coupling terms (NACTs) were calculated from the SA-MCSCF/CI wave functions using analytic gradient techniques. A line integral through the NACTs was then used to determine the adiabatic-to-diabatic mixing angle required to transform from the 1 2A\u27 and 2 2A\u27 adiabatic basis to a corresponding diabatic basis. When all nonadiabatic coupling terms between all electronic states are considered, the line integral is path independent. However, only NACTs between the 1 2A\u27 and 2 2A\u27 states were considered in these calculations, and the line integral was therefore path dependent. The path dependence of the line integral was used to characterize the error introduced by employing a truncated set of adiabatic states. A method for reducing the effect of this error through the use of symmetry derived boundary conditions was developed. The resulting diabatic PESs were combined with the total B + H2 rotational kinetic energy and boron spin-orbit coupling to yield diabatic effective PESs. The diabatic effective PESs were diagonalized to yield adiabatic effective PESs. Diabatic effective PESs data was extracted for the equilibrium H2 bond length and used to calculate inelastic scattering matrix elements using the time dependent channel packet method

Controllability of spin-boson systems

In this paper we study the so-called spin-boson system, namely {a two-level system} in interaction with a distinguished mode of a quantized bosonic field. We give a brief description of the controlled Rabi and Jaynes--Cummings models and we discuss their appearance in the mathematics and physics literature. We then study the controllability of the Rabi model when the control is an external field acting on the bosonic part. Applying geometric control techniques to the Galerkin approximation and using perturbation theory to guarantee non-resonance of the spectrum of the drift operator, we prove approximate controllability of the system, for almost every value of the interaction parameter

Optimization of adiabatic control strategies along non-mixing curves with singularities

In this paper, we consider a system driven by a controlled Schrödinger equation with two external control inputs. Motivated by applications to the control of quantum systems having conical or semi-conical eigenvalue intersections, we propose to study the singularities and the parametric bifurcations of the associated non-mixing field, along whose integral curves in the space of controls the adiabatic approximation holds with higher precision. Our results can be applied to optimize the adiabatic control strategies of well known quantum systems such as Qubit systems, Stirap Processes and Eberly-Law models

Kato's theorem and ultralong-range Rydberg molecules

We consider non-adiabatic coupling in the "trilobite"-like long-range Rydberg molecules created by perturbing degenerate high-$\ell$ Rydberg states with a ground-state atom. Due to the flexibility granted by the high Rydberg level density, the avoided crossings between relevant potential energy curves can become extremely narrow, leading to highly singular non-adiabatic coupling. We find that the gap between the trilobite potential curve and neighboring "butterfly" or "dragonfly" potential curves can even vanish, as in a conical intersection, if the gap closes at an internuclear distance which matches a node of the $s$-wave radial wave function. This is an unanticipated outcome of Kato's theorem

Photochemistry and photophysics of chemical and biologically relevant systems: mechanisms, dynamics and methodologies

El proyecto presentado en esta Tesis se basa en la aplicación y desarrollo de métodos teóricos y computacionales con el fin de describir la fotoquímica y la fotofísica de compuestos moleculares químicos y de relevancia biológica. Más detalladamente, se lograron los siguientes objetivos: i.Aplicación de la metodología CASPT2//CASSCF al estudio de un modelo de la conformación giro-beta, formado por dos glicinas enlazadas a través de un enlace de hidrógeno. Se consiguieron calcular los caminos de mínima energía encontrados a partir de la irradiación UV que permiten finalmente, la disipación de la energía de excitación como energía vibracional. ii.Aplicación de la metodología CASPT2//CASSCF/AMBER al estudio de mecanismos de fotoestabilidad en la proteína gamma-B-cristalina, que forma (junto con otras proteínas cristalinas) el cristalino del ojo humano. Especialmente, se destaca el papel que puede jugar el elemento denominado "Tyrosine corner", una parte seleccionada de la cadena proteica que permite un giro de aproximadamente 180? a través de un enlace de hidrógeno entre la cadena principal y el grupo lateral de una tirosina. iii.Desarrollo de un método de determinación cuantitativa de la energía de excitación de un cromóforo con diferente sustitución, en el caso de que la sustitución química afecte al cromóforo solo a nivel estructural y no a la naturaleza electrónica del estado excitado considerado. iv.Tratamiento de los efectos del entorno sobre un interruptor molecular inducido por luz, como fuerzas externas que actúan en los dos extremos del cromóforo. En el caso del azobenceno (uno de los interruptores moleculares inducidos por luz más empleado), los isómeros cis y trans muestran una fotosensibilidad considerable respecto a las fuerzas aplicadas, permitiendo la modulación de la longitud de onda del máximo de absorción

Photochemistry and photophysics of chemical and biologically relevant systems: mechanisms, dynamics and methodologies

El proyecto presentado en esta Tesis se basa en la aplicación y desarrollo de métodos teóricos y computacionales con el fin de describir la fotoquímica y la fotofísica de compuestos moleculares químicos y de relevancia biológica. Más detalladamente, se lograron los siguientes objetivos: i.Aplicación de la metodología CASPT2//CASSCF al estudio de un modelo de la conformación giro-beta, formado por dos glicinas enlazadas a través de un enlace de hidrógeno. Se consiguieron calcular los caminos de mínima energía encontrados a partir de la irradiación UV que permiten finalmente, la disipación de la energía de excitación como energía vibracional. ii.Aplicación de la metodología CASPT2//CASSCF/AMBER al estudio de mecanismos de fotoestabilidad en la proteína gamma-B-cristalina, que forma (junto con otras proteínas cristalinas) el cristalino del ojo humano. Especialmente, se destaca el papel que puede jugar el elemento denominado "Tyrosine corner", una parte seleccionada de la cadena proteica que permite un giro de aproximadamente 180? a través de un enlace de hidrógeno entre la cadena principal y el grupo lateral de una tirosina. iii.Desarrollo de un método de determinación cuantitativa de la energía de excitación de un cromóforo con diferente sustitución, en el caso de que la sustitución química afecte al cromóforo solo a nivel estructural y no a la naturaleza electrónica del estado excitado considerado. iv.Tratamiento de los efectos del entorno sobre un interruptor molecular inducido por luz, como fuerzas externas que actúan en los dos extremos del cromóforo. En el caso del azobenceno (uno de los interruptores moleculares inducidos por luz más empleado), los isómeros cis y trans muestran una fotosensibilidad considerable respecto a las fuerzas aplicadas, permitiendo la modulación de la longitud de onda del máximo de absorción

Relation between molecular structure and ultrafast photoreactivity with application to molecular switches

Photoinduced ultrafast isomerizations are fundamental reactions in photochemistry and photobiology. This thesis aims for an understanding of the generic forces driving these reactions and a theoretical approach is set up, able to handle realistic systems, whose fast relaxation is mediated by conical intersections. The main focus is on the development of strategies for the prediction and accelerated optimization of conical intersections and their application to artificial compounds with promising physicochemical properties for technical applications as molecular switches. All calculations are based on advanced quantum chemical methods and mixed quantum-classical dynamics. In the first part of this thesis the two-electron two-orbital theory by Michl and Bonacic-Koutecky used in its original formulation to rationalize the structure of conical intersections in charged polyene systems is extended by including the interactions of the active pair of electrons with the remaining closed-shell electrons that are present in any realistic system. A set of conditions, called resonance and heterosymmetry conditions, for the formation of conical intersections in multielectronic systems are derived and verified by calculations on the basic units ethylene, cis-butadiene and 1,3-cyclohexadiene at various geometries and functionalizational patterns. The quantitative results help to understand the role of geometrical deformations and substituent effects for the formation of conical intersections and to derive rules of thumb for their qualitative prediction in arbitrary polyenes. An extension of the rules of thumb to conical intersection seams is formulated. The strategy pursued is to divide the molecular system into basic units and into functional groups. Each unit and its intersection space are treated independently, thereby reducing the dimensionality of the search space compared to the complete molecule. Subsequently, the interconnectivity of the intersection spaces of the different units is determined and an initial guess for the complete seam is constructed. This guess is then fed into a quantum chemistry package to finalize the optimization. The strategy is demonstrated for two multi-functionalized systems, hemithioindigo-hemistilbene and trifluoromethyl-pyrrolylfulgide. In the second part of this thesis state-of-the-art quantum chemical calculations and time-resolved transient and infrared spectroscopy are used to reconstruct the complex multi-channel isomerization mechanisms of hemithioindigo-hemistilbene and trifluoromethyl-indolylfulgide. Both the cis-trans isomerization in hemithioindigo-hemistilbene and the electrocyclic ring closure/opening in indolylfulgide are characterized by a charge transfer in the excited state. The ability of each system to stabilize this charge transfer is essential for the returning to the ground state. The relaxation to the ground state through extended regions of the seam is found to be the decisive step determining the reaction speed and the quantum yield. In the last part of this thesis mixed quantum-classical dynamics simulations at multi-configurational perturbation theory (MS-CASPT2) level, using Tully's fewest switches surface hopping approach, are performed to study the ultrafast photoreactivity of 1,3-cyclohexadiene in the gas-phase. For this purpose a numerical routine for the efficient calculation of non-adiabatic couplings at MS-CASPT2 level is presented. The major part of the excited molecules are found to circumvent the 1B2/2A1 conical intersection and reach the conical intersection seam between the excited state and the ground state instantaneuosly. Time constants for the evolution of the wavepacket on the bright 1B2-state, the relaxation into the 2A1-state and the return to the ground state are extracted. It is demonstrated that the accessibility of the conical intersection seam depends on its energetic and spatial relation to the minimum energy path, as well as on the momentum which is accumulated during relaxation on the excited state potential energy surface

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⁺