Conditions for favorable unimolecular reaction paths

On the applicability of a wavefunction-free, energy-based procedure for generating first-order non-adiabatic couplings around conical intersections

The primal definition of first-order non-adiabatic couplings among electronic states relies on the knowledge of how electronic wavefunctions vary with nuclear coordinates. However, the non-adiabatic coupling between two electronic states can be obtained in the vicinity of a conical intersection from energies only, as this vector spans the branching plane along which degeneracy is lifted to first order. The gradient difference and derivative coupling are responsible of the two-dimensional cusp of a conical intersection between both potential-energy surfaces and can be identified to the non-trivial eigenvectors of the second derivative of the square energy difference, as first pointed out in Köppel and Schubert [Mol. Phys. 104(5-7), 1069 (2006)]. Such quantities can always be computed in principle for the cost of two numerical Hessians in the worst-case scenario. Analytic-derivative techniques may help in terms of accuracy and efficiency but also raise potential traps due to singularities and ill-defined derivatives at degeneracies. We compare here two approaches, one fully numerical, the other semianalytic, where analytic gradients are available but Hessians are not, and investigate their respective conditions of applicability. Benzene and 3-hydroxychromone are used as illustrative application cases. It is shown that non-adiabatic couplings can thus be estimated with decent accuracy in regions of significant size around conical intersections. This procedure is robust and could be useful in the context of on-the-fly non-adiabatic dynamics or be used for producing model representations of intersecting potential energy surfaces with complete obviation of the electronic wavefunctions.

Fast and slow excited-state intramolecular proton transfer in 3-hydroxychromone: a two-state story?

The photodynamics of 3-hydroxychromone in its first-excited singlet electronic state (bright state of ππ* character) is investigated with special emphasis given to two types of reaction pathways: the excited-state intramolecular-proton-transfer coordinate and the hydrogen-torsion coordinate linking the excited cis and trans isomers. A newly-found conical intersection with the second-excited singlet electronic state (dark state of nπ* character) is suspected to be, to some extent, the reason for the slower rate constant. This hypothesis based on quantum-chemistry calculations is supported by quantum-dynamics simulations in full dimensionality. They show significant transfer of electronic population and provide consistently a vibronic interpretation for the forbidden band in the UV absorption spectrum.

Multiconfiguration Self-Consistent Field Study on Formonitrile Imine and N-Substituted Nitrile Imines HCN2-R: Energy Component Analysis of the Pseudo-Jahn-Teller Effect

Stable geometrical structures for formonitrile imine (1) and N-substituted nitrile imines HCN₂-R (R = Li, BeH, BH₂, CH₃, CN, CCH, C₆H₅, NH₂, OH, and F) (2-11) were examined by using the multiconfiguration self-consistent-field (MCSCF) method followed by second-order configuration interaction (SOCI) calculations and second-order multiconfiguration quasi-degenerate perturbation theory (MCQDPT2) calculations, together with the aug-cc-pVTZ basis sets. The results show that 1 suffers a pseudo-Jahn-Teller (JT) distortion from a linear C_∞v structure to a C₁ structure via a planar bent C_s structure. Each of the others is found to undergo pseudo-JT distortion from a symmetrical structure to a planar bent C_s structure for 2, 3, and 7 and to a C₁ structure for 4, 5, 6, 8, 9, 10, and 11. At the stationary structures of 1-11, the structural characteristics were briefly discussed in terms of allenic and propargylic. To elucidate the nature of pseudo-JT distortions, energy component analyses were carried out at the MCSCF+SOCI level of theory at all of the stationary structures for the relevant molecules. In most of the molecules examined, pseudo-JT stabilizations were classified into two groups, one in which the stability arises from a lowering of the energy of the attractive term V_en and the other in which the stability results from a lowering of the energy of the repulsive terms V_nn and V_ee. In addition to the above two groups, it was also found that the following three groups are responsible for the pseudo-JT stabilizations in a certain stage of the structural changes. Namely, one is a lowering of the energy of the term V_ee observed in 6, another is a lowering of the energy of the terms V_ee and V_en observed in 9-11, and the other is a lowering of the energy of the terms V_en and V_nn observed in 10. These energetic behaviors were accounted in terms of an elongation or a contraction of the molecular skeleton, a migration of electrons from one part of the molecule to other parts, and the combined effects arising from these two factors.

Spectroscopic and computational studies on the rearrangement of ionized [1.1.1]propellane and some of its valence isomers: the key role of vibronic coupling

The [1.1.1]propellane radical cation 1(•+), generated by radiolytic oxidation of the parent compound in argon and Freon matrices at low temperatures, undergoes a spontaneous rearrangement to form the distonic 1,1-dimethyleneallene (or 2-vinylideneallyl) radical cation 3(•+) consisting of an allyl radical substituted at the 2-position by a vinyl cation. In similar matrix studies, it is found that the isomeric dimethylenecyclopropane radical cation 2(•+) also rearranges to 3(•+). The unusual molecular and electronic structure of 3(•+) has been established by the results of ESR, UV-vis, and IR spectroscopic measurements in conjunction with detailed theoretical calculations. Also of particular interest is an NIR photoinduced reaction by which 3(•+) is cleanly converted to the vinylidenecyclopropane radical cation 4(•+), a process that can be represented in terms of a single electron transfer from the allyl radical to the vinyl cation followed by allyl cation cyclization. The specificity of this photochemical reaction provides additional strong chemical evidence for the structure of 3(•+). Theoretical calculations reveal the decisive role of vibronic coupling in shaping the potential energy surfaces on which the observed ring-opening reactions take place. Thus vibronic interaction in 1(•+) mixes the (2)A(1)' ground state, characterized by its "non-bonding" 3a(1)' SOMO, with the (2)E'' first excited state resulting in the destabilization of a lateral C-C bond and the initial formation of the methylenebicyclobutyl radical cation 5(•+). The further rearrangement of 5(•+) to 3(•+) occurs via 2(•+) and proceeds through two additional lateral C-C bond cleavages characterized by transition states of extremely low energy, thereby explaining the absence of identifiable intermediates along the reaction pathway. In these consecutive ring-opening rearrangements, the "non-bonding" bridgehead C-C bond in 1(•+) is conserved and ultimately transformed into a normal bond characterized by a shorter C-C bond length. This work provides strong support for the Heilbronner-Wiberg interpretation of the vibrational structure in the photoelectron spectrum of 1 in terms of vibronic coupling.

Insights into the Structure of Cyclohexane from Femtosecond Degenerate Four-Wave Mixing Spectroscopy and Ab Initio Calculations

In this paper, we report the use of femtosecond time-resolved degenerate four-wave mixing rotationally resolved spectroscopy to obtain very accurate structural information on the symmetric top cyclohexane. Apart from highlighting the versatility of this method in determining accurate structures of large and complex molecules without dipole moment, the present study also details the comparison of the experimentally determined rotational constant B(0) with that obtained from high-level ab initio calculations. The theoretical calculations, which were carried out at both the second-order Møller-Plesset (MP2) and coupled-cluster with single, double, and perturbative triple substitutions [CCSD(T)] levels of theory, also take into account vibrational averaging effects. A detailed investigation of the vibrational averaging effects reveals that the corrections emerge from only the six highly symmetric A(1g) modes, a justification of which is provided by an analysis of these modes.