Abstract
In this work, we develop an approach to treat correlated many-electron dynamics, dressed by the presence of a finite-temperature harmonic bath. Our theory combines a small polaron transformation with the second-order time-convolutionless master equation and includes both electronic and system-bath correlations on equal footing. Our theory is based on the ab initio Hamiltonian, and is thus well-defined apart from any phenomenological choice of basis states or electronic system-bath coupling model. The equation-of-motion for the density matrix we derive includes non-markovian and non-perturbative bath effects and can be used to simulate environmentally broadened electronic spectra and dissipative dynamics, which are subjects of recent interest. The theory also goes beyond the adiabatic Born-Oppenheimer approximation, but with computational cost scaling such as the Born-Oppenheimer approach. Example propagations with a developmental code are performed, demonstrating the treatment of electron-correlation in absorption spectra, vibronic structure, and decay in an open system. An untransformed version of the theory is also presented to treat more general baths and larger systems.
Highlights
The small-polaron transformation of the electronic Hamiltonian was originally developed in the 1960s,1 and more recently revived2,3 in the many-electron context
To incorporate both bath and electron correlation effects, it was necessary to write down a second-order, timelocal equation of motion (EOM) for electronic dynamics based on the timeconvolutionless perturbation theory, which we will call “2TCL.”
The zeroth order poles of the correlation terms in this theory differ from those which occur in other secondorder theories of electronic response (SOPPA,73 ADC(2),55 configuration interaction singles (CIS)(D),59 and CC258), which arise from perturbative partitioning of what is essentially an energy-domain propagator matrix
Summary
The small-polaron transformation of the electronic Hamiltonian was originally developed in the 1960s,1 and more recently revived in the many-electron context. It is a classic example of the utility of canonical transformations in quantum physics. Its usefulness is well-established yet it is experiencing renewed interest.. Secondorder master equations in the polaron frame afford good results in all bath strength regimes employing the variational technique of Harris and Silbey.. In the many-electron case, there has been some recent pioneering work toward developing random-phase approximation equations.. The electronic structure community has produced some related work, including phenomenologically damped response theory Its usefulness is well-established yet it is experiencing renewed interest. In particular, secondorder master equations in the polaron frame afford good results in all bath strength regimes employing the variational technique of Harris and Silbey. In the many-electron case, there has been some recent pioneering work toward developing random-phase approximation equations. The electronic structure community has produced some related work, including phenomenologically damped response theory
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