We investigate a simple and robust scheme for choosing the phases of adiabatic electronic states smoothly (as a function of geometry) so as to maximize the performance of ab initio non-adiabatic dynamics methods. Our approach is based upon consideration of the overlap matrix (U) between basis functions at successive points in time and selecting the phases so as to minimize the matrix norm of log(U). In so doing, one can extend the concept of parallel transport to cases with sharp curve crossings. We demonstrate that this algorithm performs well under extreme situations where dozens of states cross each other either through trivial crossings (where there is zero effective diabatic coupling), or through nontrivial crossings (when there is a nonzero diabatic coupling), or through a combination of both. In all cases, we compute the time-derivative coupling matrix elements (or equivalently non-adiabatic derivative coupling matrix elements) that are as smooth as possible.Our results should be of interest to all who are interested in either non-adiabatic dynamics, or more generally, parallel transport in large systems.
A new
scheme is proposed for modeling molecular nonadiabatic dynamics
near metal surfaces. The charge-transfer character of such dynamics
is exploited to construct an efficient reduced representation for
the electronic structure. In this representation, the fewest switches surface hopping (FSSH) approach can
be naturally modified to include electronic relaxation (ER). The resulting
FSSH-ER method is valid across a wide range of coupling strengths
as supported by tests applied to the Anderson–Holstein model
for electron transfer. Future work will combine this scheme with ab initio electronic structure calculations.
It is well-known that under conditions of fast electronic equilibration and weak nonadiabaticity, nonadiabatic effects induced by electron-hole pair excitations can be partly incorporated through a frictional force. However, ab initio computation of the electronic friction tensor suffers from numerical instability and usually demands a convergence check. In this study, we present an efficient and accurate interpolation method for computing the electronic friction tensor in a nearly black-box manner as appropriate for molecular dynamics. In almost all cases, our method agrees quite well with the exact friction tensor which is available for several quadratic Hamiltonians. As such, we outperform more conventional approaches that are based on the introduction of a broadening parameter. Future work will implement this interpolation approach within ab initio software packages.
Traditional ab initio electronic structure calculations of periodic systems yield delocalized eigenstates that should be understood as adiabatic states. For example, excitons are bands of extended states which superimpose localized excitations on every lattice site. However, in general, in order to study the effects of nuclear motion on exciton transport, it is standard to work with a localized description of excitons, especially in a hopping regime; even in a band regime, a localized description can be helpful. To extract localized excitons from a band requires essentially a diabatization procedure. In this paper, three distinct methods are proposed for such localized diabatization: (i) a simple projection method, (ii) a more general Pipek-Mezey localization scheme, and (iii) a variant of Boys diabatization. Approaches (i) and (ii) require localized, single-particle Wannier orbitals, while approach (iii) has no such dependence. These methods should be very useful for studying energy transfer through solids with ab initio calculations.
We analyze a model problem representing a multielectronic molecule sitting on a metal surface. Working with a reduced configuration interaction Hamiltonian, we show that one can extract very accurate ground state wave functions as compared with numerical renormalization group theory (NRG) even in the limit of weak metal-molecule coupling strength but strong intramolecular electron−electron repulsion. Moreover, we extract what appear to be meaningful excitation energies as well. Our findings should lay the groundwork for future ab initio studies of charge transfer processes and bond making/breaking processes on metal surfaces.
We develop several configuration interaction approaches for characterizing the electronic structure of an adsorbate on a metal surface (at least in model form). When one can separate adsorbate from substrate, these methods can achieve a reasonable description of adsorbate on-site electronelectron correlation in the presence of a continuum of states. While the present paper is restricted to the Anderson impurity model, there is hope that these methods can be extended to ab initio Hamiltonians, and provide insight into the structure and dynamics of molecule-metal surface interactions.
We present an efficient set of methods for propagating excited-state dynamics involving a large number of electronic states based on a configuration interaction singles (CIS) electronic state overlap scheme. Specifically, (i) following Head-Gordon et al we implement an exact evaluation of the overlap of singly-excited electronic states at different nuclear geometries using a biorthogonal basis and (ii) we employ a unified protocol 1 for choosing the correct phase for each adiabat at each geometry. For many-electron systems, the combination of these techniques significantly reduces the computational cost of integrating the electronic Schrodinger equation and imposes minimal overhead on top of the underlying electronic structure calculation. As a demonstration, we calculate the electronic excited-state dynamics for a hydrogen molecule scattering off a silver metal cluster, focusing on high-lying excited states where many electrons can be excited collectively and crossings are plentiful. Interestingly, we find that the high-lying, plasmon-like collective excitation spectrum changes with nuclear dynamics, highlighting the need to simulate non-adiabatic nuclear dynamics and plasmonic excitations simultaneously. In the future, the combination of methods presented here should help theorists build a mechanistic understanding of plasmon-assisted charge transfer and excitation energy relaxation processes near a nanoparticle or metal surface.
We present an efficient set of methods for propagating excited-state dynamics involving a large number of electronic states based on a CIS electronic state overlap scheme. Specifically, (i) following Head-Gordon et al, we implement an exact evaluation of the overlap of singly-excited electronic states at different nuclear geometries using a biorthogonal basis, and (ii) we employ a unified protocol for choosing the correct phase for each adiabat at each geometry. For many-electron systems, the combination of these techniques significantly reduces the computational cost of integrating the electronic Schrodinger equation and imposes minimal overhead on top of the underlying electronic structure calculation. As a demonstration, we calculate the electronic excited-state dynamics for a hydrogen molecule scattering off a silver metal cluster, focusing on high-lying excited states where many electrons can be excited collectively and crossings are plentiful. Interestingly, we find that the high-lying, plasmon-like collective excitation spectrum changes with nuclear dynamics, highlighting the need to simulate non-adiabatic nuclear dynamics and plasmonic excitations simultaneously. In the future, the combination of methods presented here should help theorists build a mechanistic understanding of plasmon-assisted charge transfer and excitation energy relaxation processes near a nanoparticle or metal surface.
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