Non-adiabatic effects in thermochemistry, spectroscopy and kinetics: The general importance of all three Born-Oppenheimer breakdown corrections

Reimers, Jeffrey R., McKemmish, Laura K., McKenzie, Ross H. and Hush, Noel S. (2015) Non-adiabatic effects in thermochemistry, spectroscopy and kinetics: The general importance of all three Born-Oppenheimer breakdown corrections. Physical Chemistry Chemical Physics, 17 38: 24641-24665. doi:10.1039/c5cp02238j


Author Reimers, Jeffrey R.
McKemmish, Laura K.
McKenzie, Ross H.
Hush, Noel S.
Title Non-adiabatic effects in thermochemistry, spectroscopy and kinetics: The general importance of all three Born-Oppenheimer breakdown corrections
Journal name Physical Chemistry Chemical Physics   Check publisher's open access policy
ISSN 1463-9076
1463-9084
Publication date 2015-10-14
Year available 2015
Sub-type Article (original research)
DOI 10.1039/c5cp02238j
Open Access Status Not Open Access
Volume 17
Issue 38
Start page 24641
End page 24665
Total pages 25
Place of publication Cambridge, United Kingdom
Publisher Royal Society of Chemistry
Language eng
Abstract Using a simple model Hamiltonian, the three correction terms for Born-Oppenheimer (BO) breakdown, the adiabatic diagonal correction (DC), the first-derivative momentum non-adiabatic correction (FD), and the second-derivative kinetic-energy non-adiabatic correction (SD), are shown to all contribute to thermodynamic and spectroscopic properties as well as to thermal non-diabatic chemical reaction rates. While DC often accounts for 480% of thermodynamic and spectroscopic property changes, the commonly used practice of including only the FD correction in kinetics calculations is rarely found to be adequate. For electron-transfer reactions not in the inverted region, the common physical picture that diabatic processes occur because of surface hopping at the transition state is proven inadequate as the DC acts first to block access, increasing the transition state energy by ((h) over bar omega)(2)lambda/16J(2) (where lambda is the reorganization energy, J the electronic coupling and omega the vibration frequency). However, the rate constant in the weakly-coupled Golden-Rule limit is identified as being only inversely proportional to this change rather than exponentially damped, owing to the effects of tunneling and surface hopping. Such weakly-coupled long-range electron-transfer processes should therefore not be described as "non-adiabatic'' processes as they are easily described by Born-Huang ground-state adiabatic surfaces made by adding the DC to the BO surfaces; instead, they should be called just "non-Born-Oppenheimer'' processes. The model system studied consists of two diabatic harmonic potential-energy surfaces coupled linearly through a single vibration, the "two-site Holstein model''. Analytical expressions are derived for the BO breakdown terms, and the model is solved over a large parameter space focusing on both the lowestenergy spectroscopic transitions and the quantum dynamics of coherent-state wavepackets. BO breakdown is investigated pertinent to: ammonia inversion, aromaticity in benzene, the Creutz-Taube ion, the bacterial photosynthetic reaction centre, BNB, the molecular conductor Alq3, and invertedregion charge recombination in a ferrocene-porphyrin-fullerene triad photosynthetic model compound. Throughout, the fundamental nature of BO breakdown is linked to the properties of the cusp catastrophe: the cusp diameter is shown to determine the magnitudes of all couplings, numerical basis-set and trajectory-integration requirements, and to determine the transmission coefficient k used to understand deviations from transition-state theory.
Formatted abstract
Using a simple model Hamiltonian, the three correction terms for Born–Oppenheimer (BO) breakdown, the adiabatic diagonal correction (DC), the first-derivative momentum non-adiabatic correction (FD), and the second-derivative kinetic-energy non-adiabatic correction (SD), are shown to all contribute to thermodynamic and spectroscopic properties as well as to thermal non-diabatic chemical reaction rates. While DC often accounts for >80% of thermodynamic and spectroscopic property changes, the commonly used practice of including only the FD correction in kinetics calculations is rarely found to be adequate. For electron-transfer reactions not in the inverted region, the common physical picture that diabatic processes occur because of surface hopping at the transition state is proven inadequate as the DC acts first to block access, increasing the transition state energy by (ℏω)2λ/16J2 (where λ is the reorganization energy, J the electronic coupling and ω the vibration frequency). However, the rate constant in the weakly-coupled Golden-Rule limit is identified as being only inversely proportional to this change rather than exponentially damped, owing to the effects of tunneling and surface hopping. Such weakly-coupled long-range electron-transfer processes should therefore not be described as “non-adiabatic” processes as they are easily described by Born–Huang ground-state adiabatic surfaces made by adding the DC to the BO surfaces; instead, they should be called just “non-Born–Oppenheimer” processes. The model system studied consists of two diabatic harmonic potential-energy surfaces coupled linearly through a single vibration, the “two-site Holstein model”. Analytical expressions are derived for the BO breakdown terms, and the model is solved over a large parameter space focusing on both the lowest-energy spectroscopic transitions and the quantum dynamics of coherent-state wavepackets. BO breakdown is investigated pertinent to: ammonia inversion, aromaticity in benzene, the Creutz–Taube ion, the bacterial photosynthetic reaction centre, BNB, the molecular conductor Alq3, and inverted-region charge recombination in a ferrocene–porphyrin–fullerene triad photosynthetic model compound. Throughout, the fundamental nature of BO breakdown is linked to the properties of the cusp catastrophe: the cusp diameter is shown to determine the magnitudes of all couplings, numerical basis-set and trajectory-integration requirements, and to determine the transmission coefficient κ used to understand deviations from transition-state theory.
Keyword Chemistry, Physical
Physics, Atomic, Molecular & Chemical
Chemistry
Physics
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2016 Collection
 
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