The global potential energy surfaces of the lowest two 1A\u27 states of the ozone molecule: theoretical determination and analysis

The two lowest 1A[superscript]\u27 potential energy surfaces (PES) of the ozone molecule are determined and analyzed using accurate ab-initio MCSCF calculations;As appropriate internal coordinates, the shape-scale perimetric coordinates for triatomic molecules are discussed and further developed;Because the previously determined intersection between these two surfaces of like symmetry is unusual, much of the present work involves this intersection. The relevant theory of intersections is reviewed, and a method for characterizing intersections according to the topology of the surfaces in their vicinity is developed;Furthermore, the reasons for this particular crossing in ozone are investigated. The analysis is based on a novel method for transforming the adiabatic states produced by quantum chemical calculations into diabatic states. The method is founded on the idea that a diabatic state should be dominated throughout coordinate space by a single set of configurations. Accordingly, the transformation to diabatic states is derived by maximizing the contribution of these configurations to their respective states. It is shown that the crossing in ozone is due to an additional exchange in dominance of configurations within each diabatic state;The intersection point in C[subscript] 2v symmetry is part of a larger, 1-dimensional intersection seam in C[subscript] s symmetry. This seam is shown to consist of four branches, one of which is a closed loop. The three other branches lie entirely in C[subscript] 2v restricted subspaces and connect to the first branch at nodes. Additional intersections must exist. A new method for determining an intersection point in a two-dimensional coordinate space, based on the wavefunction phase-change theorem of Herzberg-Longuet-Higgins, is also developed;Finally, global mappings of the two potential energy surfaces in the scale-shape perimetric coordinates are determined. The minima of the two surfaces, their dissociation and rearrangement paths, and the map of the energy difference between them are all discussed. It is shown that direct formation of the ring structure of ozone from O[subscript]2 and O is improbable and that there is no rearrangement pathway on the ground state representing the interchange of two atoms

A global picture of the S-1/S-0 conical intersection seam of benzene

A global picture of the S1/S0intersection seam of benzene is presented. Eleven new conical intersection critical points were located at the CASSCF level, the connectivity was mapped and the energies refined with CASPT 2. There are two seam branches related with pairs of degenerate A1g/B2uand Egstates at D6hsymmetry, respectively, and the two branches are connected by a seam segment of Cssymmetry. The global energy minimum of the seam is the half-boat shaped intersection that leads to a pre-fulvenic intermediate [I.J. Palmer, I.N. Ragazos, F. Bernardi, M. Olivucci, M.A. Robb, J. Am. Chem. Soc. 115 (1993) 673]. Several other intersections that can lead to the same intermediate or vibrationally hot benzene lie in a range of 3.7 eV above the global seam minimum. There is a recurrent connectivity pattern where permutationally isomeric seam segments are connected by intersections of a higher symmetry point groupThis work has been supported by Grant CTQ2008-06696 from the Spanish Ministerio de Ciencia e Innovación (MICINN

Optimal control theory - closing the gap between theory and experiment

Optimal control theory and optimal control experiments are state-of-the-art tools to control quantum systems. Both methods have been demonstrated successfully for numerous applications in molecular physics, chemistry and biology. Modulated light pulses could be realized, driving these various control processes. Next to the control efficiency, a key issue is the understanding of the control mechanism. An obvious way is to seek support from theory. However, the underlying search strategies in theory and experiment towards the optimal laser field differ. While the optimal control theory operates in the time domain, optimal control experiments optimize the laser fields in the frequency domain. This also implies that both search procedures experience a different bias and follow different pathways on the search landscape. In this perspective we review our recent developments in optimal control theory and their applications. Especially, we focus on approaches, which close the gap between theory and experiment. To this extent we followed two ways. One uses sophisticated optimization algorithms, which enhance the capabilities of optimal control experiments. The other is to extend and modify the optimal control theory formalism in order to mimic the experimental conditions

The global potential energy surfaces of the lowest two 1A' states of the ozone molecule: theoretical determination and analysis

The two lowest 1A[superscript]' potential energy surfaces (PES) of the ozone molecule are determined and analyzed using accurate ab-initio MCSCF calculations;As appropriate internal coordinates, the shape-scale perimetric coordinates for triatomic molecules are discussed and further developed;Because the previously determined intersection between these two surfaces of like symmetry is unusual, much of the present work involves this intersection. The relevant theory of intersections is reviewed, and a method for characterizing intersections according to the topology of the surfaces in their vicinity is developed;Furthermore, the reasons for this particular crossing in ozone are investigated. The analysis is based on a novel method for transforming the adiabatic states produced by quantum chemical calculations into diabatic states. The method is founded on the idea that a diabatic state should be dominated throughout coordinate space by a single set of configurations. Accordingly, the transformation to diabatic states is derived by maximizing the contribution of these configurations to their respective states. It is shown that the crossing in ozone is due to an additional exchange in dominance of configurations within each diabatic state;The intersection point in C[subscript] 2v symmetry is part of a larger, 1-dimensional intersection seam in C[subscript] s symmetry. This seam is shown to consist of four branches, one of which is a closed loop. The three other branches lie entirely in C[subscript] 2v restricted subspaces and connect to the first branch at nodes. Additional intersections must exist. A new method for determining an intersection point in a two-dimensional coordinate space, based on the wavefunction phase-change theorem of Herzberg-Longuet-Higgins, is also developed;Finally, global mappings of the two potential energy surfaces in the scale-shape perimetric coordinates are determined. The minima of the two surfaces, their dissociation and rearrangement paths, and the map of the energy difference between them are all discussed. It is shown that direct formation of the ring structure of ozone from O[subscript]2 and O is improbable and that there is no rearrangement pathway on the ground state representing the interchange of two atoms.</p

Existence of strictly diabatic basis sets for the two-state problem

Some new properties of the nonadiabatic coupling elements are derived, in particular the orthogonality and gauge invariance of their longitudinal and transverse components. A method for constructing a strictly diabatic basis set that makes both the transverse and longitudinal components of the nonadiabatic coupling elements of the two-state problem vanish identically and is based on introducing overlap between the electronic states in the vicinity of the crossing seam is proposed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 200