Compact Bases for Vibronic Coupling in Spectral Simulations: The Photoelectron Spectrum of Cyclopentoxide in the Full 39 Internal Modes

Abstract

We report an algorithm to automatically generate compact multimode vibrational bases for the Köppel–Domcke–Cederbaum (KDC) vibronic coupling wave function used in spectral simulations of moderate-sized molecules. As a full quantum method, the size of the vibronic expansion grows exponentially with respect to the number of vibrational modes, necessitating compact bases for moderate-sized systems. The problem of generating such a basis consists of two parts: one is the choice of vibrational normal modes, and the other is the number of phonons allowed in each mode. A previously developed final-state-biased technique addresses the former part, and this work focuses on the latter part: proposing an algorithm for generating an optimal phonon distribution. By virtue of this phonon distribution, compact and affordable bases can be automatically generated for systems with on the order of 15 atoms. Our algorithm is applied to determine the nonadiabatic photoelectron spectrum of cyclopentoxide in the full 39 internal modes.

Unified Description of the Jahn–Teller Effect in Molecules with Only CsSymmetry: Cyclohexoxy in Its Full 48-Dimensional Internal Coordinates

“…57 Solving the nonrelativistic VSE is the bottleneck because the curse of dimensionality gives rise to the exponential growth of the requisite computational effort over the number of vibrational modes. The size of the systems that can be treated is increased using a continuum model 37 to help reduce the size of the space needed to solve the VSE. The convergence of the continuummodel-based approach is established by a detailed comparison to the standard energy-based approach, where both approaches converge the lowest four vibronic states as required by the E ⊗ e Jahn−Teller problem, and the continuum-model-based approach outperforms the standard approach in faster convergence of the low-energy portion and the ability to give the spectral envelope.…”

“…To further test this idea, it is important to get examples with larger spaces of Jahn–Teller active modes and determine, accurately for low energies, the APE spectra. C 6 H 11 O is an excellent candidate for this analysis with its 48 internal modes, but it has not been possible to carry out requisite computations to validate this model until recent theoretical advancements. , …”

“…30−34 Dillon and Yarkony's (DY's) computational study 35 modes, but it has not been possible to carry out requisite computations to validate this model until recent theoretical advancements. 36,37 Thus, in this work, we will investigate C 6 H 11 O to understand the similarity of CH 3 O, C 3 H 7 O, and C 6 H 11 O X ̃−A ̃splittings. The work is made challenging by the need to determine the APE spectrum for a molecule with 48 internal coordinates.…”

A combined experimental and computational study on the transition of the calcium isopropoxide radical as a candidate for direct laser cooling

“…Both the anomalous anharmonicity and the unusually small SO splitting are not unexpected. The n 30 mode is a pJT-active mode, and the PES along this mode is highly anharmonic (see, for example, previous experimental and computational investigation of PESs of the nearly degenerate X ˜and A ˜states of alkoxy radicals belonging to the C s point group 46,58,[80][81][82][83][84][85] ). Rotationally resolved LIF spectra and a detailed spin-vibronic analysis similar to previous work on the CaOH A ˜2P(020)-X ˜2S + (000) band 86 and our work on the calcium ethoxide radical 42 are required to determine and model the energy level structure in the low-energy region.…”