Paolo Celani

Multireference perturbation theory for large restricted and selected active space reference wave functions

A multireference second-order perturbation theory (MRPT2) has been developed which allows the use of reference wave functions with large active spaces and arbitrary configuration selection. Internally contracted configurations are used as a basis for all configuration subspaces of the first-order wave function for which the overlap matrix depends only on the second-order density matrix of the reference function. Some other subspaces which would require the third- or fourth-order density matrices are left uncontracted. This removes bottlenecks of the complete active space second order pertubation theory (CASPT2) caused by the need to construct and diagonalize large overlap matrices. Preliminary applications of the new method for 1,2-dihydronaphthalene (DHN) and free base porphin are presented in which the effect of applying occupancy restrictions in the reference wave function (restricted active space second-order perturbation theory, RASPT2) and reference configuration selection (general MRPT2) on electro...

Analytical energy gradients for internally contracted second-order multireference perturbation theory

The theory for computing analytical energy gradients for second-order multireference perturbation theory (MRPT2) with arbitrary multiconfiguration self-consistent field (MCSCF) reference functions is derived and implemented. MRPT2 with complete active space reference functions (CASPT2) is a special case. In our method the configurations with two electrons in the external orbital space are internally contracted. This ansatz strongly reduces the length of the configuration expansion as compared to uncontracted wave functions, but avoids bottlenecks occurring when fully contracted first-order wave functions are used. The method, which also allows the use of state-averaged MCSCF reference functions, is applied to optimize the structures of low-lying valence and Rydberg states of Pyrrole. Nonplanar equilibrium structures and large geometry relaxation effects on the excitation energies are found for the valence states. From the results it can be concluded that CASPT2 underestimates the excitation energies of the valence states, but leads to accurate results for the Rydberg states.

Potential-energy surfaces for ultrafast photochemistry Static and dynamic aspects

The first singlet excited states (S1) which control the ultrafast (i.e. sub-picosecond) photochemistry of 2-cis-penta-2,4-dieniminium cation (2-cis-C5H6NH2+), all-trans-hexa-1,3,5-triene (all-trans-HT) and cyclohexa-1,3-diene (CHD) have been investigated using abinitio MCSCF and multireference MP2 theories. The structure of the corresponding potential energy surfaces (PESs) has been characterized by computing novel unconstrained and symmetry-constrained minimum-energy paths (MEP) starting from Franck–Condon and S2/S1 conical intersection points on S1. Furthermore, analytical frequency computations have been used to produce quantitative information on the surface curvature. We show that the S1 energy surface is characterized by two domains, region I and region II. Region I controls the initial acceleration of the excited state molecule. In contrast, region II is a low-lying region of S1 and controls the evolution towards fully efficient decay to the ground state. The energy surface structure indicates that the double-bond isomerization of 2-cis-C5H6NH2+ and all-trans-HT and the ring-opening of CHD are prototypes of three classes of barrierless reactions characterized by a different excited state dynamics. In 2-cis-C5H6NH2+ and, more loosely, in all-trans-HT the initial relaxation results in the production of a totally symmetric S1 transient. The following triggering of the S1→S0 decay requires energy redistribution along a symmetry-breaking (torsional) mode leading to an S1/S0 conical intersection (CI). In contrast, the shape of region I of CHD indicates that an almost direct (i.e. impulsive) motion towards an asymmetric S1/S0 CI occurs upon initial relaxation. Previously reported and novel semi-classical trajectory computations and the available experimental evidence seem to support these conclusions.

Geometry optimisation on a hypersphere. Application to finding reaction paths from a conical intersection

A new method for performing constrained optimisation of critical points on the surface of an hypersphere using Newton-Raphson or rational function optimisation (RFO) steps is described. Through the parametrisation of a unitary matrix, it is possible to incorporate the constraint of the fixed distance from the centre of the hypersphere without using Lagrange multipliers. The method is applied to the problem of locating the initial relaxation directions from the vertex of a conical intersection and to the problem of following an intrinsic reaction coordinate along a ridge. An application to the [2π s + 2π s ] ethylene-ethylene photochemical cycloaddition reaction path, which occurs via a rhomboid conical intersection, shows that this reaction occurs in a single step only the reaction channel towards cyclobutane exists and any path to tetramethylene is avoided.

Minimum energy paths in the excited and ground states of short protonated Schiff bases and of the analogous polyenes

Abstract A theoretical study of the minimum energy paths (MEP) for the first excited state S 1 and for the ground state S 0 of two short-chain protonated Schiff bases (the protonated s-cis 1-iminium-2-propene H 2 C=CH-CH=NH 2 + and the protonated tZt 1-iminium-2,4-pentadiene H 2 C=CH-CH=CH-CH=NH 2 +) and of the two analogous polyenes ( s-cis butadiene H 2 C=CH-CH=CH 2 and tZt hexatriene H 2 C=CH- CH=CH-CH=CH 2 ) is reported. The geometries have been optimized at the CAS-SCF level and the energetics have been refined via single- point computations at the multi-reference MP2 level. It is demonstrated that the photochemistry of the protonated Schiff bases and of the analogous polyenes is driven by two different S 1 excited states, the spectroscopic 1B ionic state for the protonated Schiff bases and the covalent 2A 1 excited state for the analogous polyenes. This difference induces different electronic and geometric features in the computed MEP and conical intersections which depend on the nature of the involved excited states. The conical intersections between S 1 /S 0 in polyenes have a covalent tetraradicaloid nature and are characterized by the development of a typical (-CH-) 3 ‘kink’ in the carbon moiety, while the conical intersection points in the protonated Schiff bases have a twisted double bond. Thus in the protonated Schiff bases, the photoproducts arise only from isomerization processes, while in the analogous polyenes, the photoproducts arise from various types of recoupling schemes of the electrons of the quasi-tetraradical conical intersection point, leading to a more complex photoreactivity pattern.

Parallel implementation of the CI-vector evaluation in full CI/CAS-SCF

We present an implicitly parallel, direct reduced list method for integral-driven full CI (FCI) algorithms to be used in CAS-SCF. Our algorithm makes efficient use of modern supercomputer hardware supporting both shared memory and distributed memory architectures. The applicability and efficiency is demonstrated with a CAS-SCF(14,14) calculation on stilbene and a CAS-SCF(8,16) calculation on pentalene.

Characterization of the indacene S0/S1 conical intersection: An MMVB and CASSCF study

A conical intersection between the S0 and S1 states of s-indacene has been located with the molecular mechanics with valence bond (MMVB) and complete active space SCF (CASSCF) methods. In both cases the intersection minimum is close in energy and geometry to the overall minimum on the S1 surface, and can be reached directly along the coordinate which leads from the Franck—Condon geometry to the minimum on S1. The existence of such an accessible S1/S0 surface crossing leading to efficient non-radiative decay can explain the short S1 excited state lifetime and lack of fluorescence for s-indacene. Based on a comparison with X-ray structures for a derivative of s-indacene, we argue that the CASSCF ordering of S0 and S1 states is the correct one, whereas MMVB inverts the two states. However, because the energy differences involved are a few kcal mol-1, a definitive prediction will probably require a multi-reference correlated level of theory with gradient optimization.

Theoretical Modelling as a Possible Tool in the Design of Photochromic Systems

Abstract In photochemical processes, the reactant resides on an excited state potential energy surface and the products accumulate on the ground state. Thus the reaction path must have at least two branches: one located on the excited state and the other located on the ground state energy surface. The novel feature of photochemistry is the “funnel” region where the excited state reactant or intermediate is delivered to the ground state. A modelling strategy for the complete description of what happens at the molecular level from energy absorption to product formation, will be described. The nature of the ground/excited state surface topology that is a requirement for photochromism will be out-linedas well as the current theoretical tools that can be used in modelling. Applications will be briefly reviewed.