Up to a Sign. The Insidious Effects of Energetically Inaccessible Conical Intersections on Unimolecular Reactions

Abstract

It is now well established that conical intersections play an essential role in nonadiabatic radiationless decay where their double-cone topography causes them to act as efficient funnels channeling wave packets from the upper to the lower adiabatic state. Until recently, little attention was paid to the effect of conical intersections on dynamics on the lower state, particularly when the total energy involved is significantly below that of the conical intersection seam. This energetic deficiency is routinely used as a sufficient condition to exclude consideration of excited states in ground state dynamics. In this account, we show that, this energy criterion notwithstanding, energy inaccessible conical intersections can and do exert significant influence on lower state dynamics. The origin of this influence is the geometric phase, a signature property of conical intersections, which is the fact that the real-valued electronic wave function changes sign when transported along a loop containing a conical intersection, making the wave function double-valued. This geometric phase is permitted by an often neglected property of the real-valued adiabatic electronic wave function; namely, it is determined only up to an overall sign. Noting that in order to change sign a normalized, continuous function must go through zero, for loops of ever decreasing radii, demonstrating the need for an electronic degeneracy (intersection) to accompany the geometric phase. Since the total wave function must be single-valued a compensating geometry dependent phase needs to be included in the total electronic-nuclear wave function. This Account focuses on how this consequence of the geometric phase can modify nuclear dynamics energetically restricted to the lower state, including tunneling dynamics, in directly measurable ways, including significantly altering tunneling lifetimes, thus confounding the relation between measured lifetimes and barrier heights and widths, and/or completely changing product rotational distributions. Some progress has been made in understanding the origin of this effect. It has emerged that for a system where the lower adiabatic potential energy surface exhibits a topography comprised of two saddle points separated by a high energy conical intersection, the effect of the geometric phase can be quite significant. In this case topologically distinct paths through the two adiabatic saddle points may lead to interference. This was pointed out by Mead and Truhlar almost 50 years ago and denoted the Molecular Aharonov-Bohm effect. Still, the difficulty in anticipating a significant geometric phase effect in tunneling dynamics due to energetically inaccessible conical intersections leads to the attribute insidious that appears in the title of this Account. Since any theory is only as relevant as the prevalence of the systems it describes, we include in this Account examples of real systems where these effects can be observed. The accuracy of the reviewed calculations is high since we use fully quantum mechanical dyna...

Observation of the geometric phase effect in the H+HD→H2+D reaction below the conical intersection

“…This is the physical origin of the difference between the GP and NGP DCS. This additional node in the GP wavefunction in the chemical reaction is very similar to the GP wavefunction in a photodissociation process 7,12 .…”

“…In a molecule, the presence of a conical intersection (CI) leads to the appearance of the GP and enables rapid conversion of the excess electronic energy into nuclear motion. The GP induces a sign change of the adiabatic electronic wave functions along a closed path of the nuclear configuration space encircling the CI 4 – 7 . For a molecular system with a CI, the theoretical treatment in the adiabatic picture requires the inclusion of the GP to make sure that at each nuclear geometry, the total wave function can be single-valued, although the nuclear wave function is localized away from the region of the CI.…”

“…The GP effect in the spectra of molecular vibrational bound states has been well studied with Jahn–Teller molecules 8 – 10 . Recently, the significant role of the GP in photodissociation process of phenol has been reported 7 , 11 , 12 . In larger molecules, the increased number of degrees of freedom and electronic states leads to the general presence of CIs in various molecular photoinduced chemical dynamics processes involving electronically excited states, where CIs play a very important role 13 .…”

Born–Oppenheimer approximation in optical cavities: from success to breakdown

“…[2][3][4][5][6][7] Nonadiabatic phenomena are ubiquitous in photochemistry, photophysics, particularly in molecular fragmentation, proton transfer, isomerization or radiationless deactivation processes of excited states as the CI can provide a very efficient channel for ultrafast interstate crossing on the femtosecond timescale. [8][9][10][11][12][13][14][15][16][17][18][19][20][21] Conical intersections and avoided crossings (ACs) can be created both by classical and quantum light, as well. To form a CI, the molecule must have at least two independent nuclear dofs.…”

Polariton Induced Conical Intersection and Berry Phase

“…[13][14][15][16][17][18][19][20][21] In addition, CIs introduce a nontrivial geoemtric phase, commonly referred to as the Berry phase, 22 for electronic wavefunctions that causes a sign change of the electron wavefunctions when the nuclei complete a closed path around the CI. [22][23][24][25][26][27] Both enhanced non-adiabatic transitions and the geometric phase are attributed to as characteristic features of the In addition to the intrinsic CIs in polyatomic molecules, CIs can also be created by either standing 29,30 or running [31][32][33] laser waves in a diatomic molecule. This type of CIs are artificially created through light-matter interactions, and are commonly referred to as the light-induced conical intersection (LICI).…”