Mixed quantum-classical equilibrium

Most of today's molecular-dynamics simulations of materials are based on the Born-Oppenheimer approximation. There are many cases, however, in which the coupling of the electrons and nuclei is important and it is necessary to go beyond the Born-Oppenheimer approximation. In these methods, the non-adiabatic coupling vectors are fundamental since they represent the link between the classical atomic motion of the nuclei and the time evolution of the quantum electronic state. In this paper we analyze the calculation of non-adiabatic coupling vectors in a basis set of local orbitals and derive an expression to calculate them in a practical and computationally efficient way. Some examples of the application of this expression using a local-orbital density functional theory approach are presented for a few simple molecules: H 3 , formaldimine, and azobenzene. These results show that the approach presented here, using the Slater transition-state density, is a very promising way for the practical calculation of non-adiabatic coupling vectors for large systems. © 2013 AIP Publishing LLC. [http://dx

Section: Theoretical Backgroundmentioning

confidence: 99%

Calculation of non-adiabatic coupling vectors in a local-orbital basis set

Abad

Lewis

Zobač

et al. 2013

“…15 On the other hand, surface-hopping provides a much better (but still incorrect) description of the expected equilibration behavior compared to the Ehrenfest method that often leads to an unphysical heating of the quantum mechanical subsystem. [16][17][18] A major difficulty of the mixed quantum-classical trajectory methods is that there is no simple way to improve their description of quantum coherence. Neither the Ehrenfest nor surface-hopping schemes contain any limit where they are guaranteed to converge to the correct quantum mechanical wavepacket evolution.…”

Section: Introductionmentioning

confidence: 99%

“…By cloning, we sidestep the prolonged mixed state propagation which is known to lead to erroneous retention of coherence 41,42 and violations of detailed balance. [15][16][17] The cloning procedure is analogous to spawning in AIMS, and the AIMS and AIMC methods can be viewed as complementary approaches.…”

Section: Introductionmentioning

confidence: 99%

Ab initio multiple cloning algorithm for quantum nonadiabatic molecular dynamics

Makhov

Glover

Martı́nez

et al. 2014

188

245

An atomic orbital-based formulation of analytical gradients and nonadiabatic coupling vector elements for the state-averaged complete active space self-consistent field method on graphical processing units We present a new algorithm for ab initio quantum nonadiabatic molecular dynamics that combines the best features of ab initio Multiple Spawning (AIMS) and Multiconfigurational Ehrenfest (MCE) methods. In this new method, ab initio multiple cloning (AIMC), the individual trajectory basis functions (TBFs) follow Ehrenfest equations of motion (as in MCE). However, the basis set is expanded (as in AIMS) when these TBFs become sufficiently mixed, preventing prolonged evolution on an averaged potential energy surface. We refer to the expansion of the basis set as "cloning," in analogy to the "spawning" procedure in AIMS. This synthesis of AIMS and MCE allows us to leverage the benefits of mean-field evolution during periods of strong nonadiabatic coupling while simultaneously avoiding mean-field artifacts in Ehrenfest dynamics. We explore the use of time-displaced basis sets, "trains," as a means of expanding the basis set for little cost. We also introduce a new bra-ket averaged Taylor expansion (BAT) to approximate the necessary potential energy and nonadiabatic coupling matrix elements. The BAT approximation avoids the necessity of computing electronic structure information at intermediate points between TBFs, as is usually done in saddle-point approximations used in AIMS. The efficiency of AIMC is demonstrated on the nonradiative decay of the first excited state of ethylene. The AIMC method has been implemented within the AIMS-MOLPRO package, which was extended to include Ehrenfest basis functions.

“…17 Perhaps the most significant of these questions concerns if such approximate treatments can reliably capture the energy transfer processes between the two subsystems so as to reproduce detailed balance and yield the correct long time thermal equilibrium energy distribution between the systems. 18 To overcome this difficulty, the mapping Hamiltonian idea that exactly maps discrete quantum states onto continuous coordinates, was proposed by Miller and co-workers 19 here and elsewhere and enables consistent treatment for all DOF, at the classical, semi-classical, and full quantum dynamical levels. This idea replaces the evolution of the electronic subsystem by the dynamics of a system of fictitious mapping harmonic oscillators.…”

Section: Introductionmentioning

confidence: 99%

Consistent schemes for non-adiabatic dynamics derived from partial linearized density matrix propagation

Huo¹,

Coker²

2012

100

115

Powerful approximate methods for propagating the density matrix of complex systems that are conveniently described in terms of electronic subsystem states and nuclear degrees of freedom have recently been developed that involve linearizing the density matrix propagator in the difference between the forward and backward paths of the nuclear degrees of freedom while keeping the interference effects between the different forward and backward paths of the electronic subsystem described in terms of the mapping Hamiltonian formalism and semi-classical mechanics. Here we demonstrate that different approaches to developing the linearized approximation to the density matrix propagator can yield a mean-field like approximate propagator in which the nuclear variables evolve classically subject to Ehrenfest-like forces that involve an average over quantum subsystem states, and by adopting an alternative approach to linearizing we obtain an algorithm that involves classical like nuclear dynamics influenced by a quantum subsystem state dependent force reminiscent of trajectory surface hopping methods. We show how these different short time approximations can be implemented iteratively to achieve accurate, stable long time propagation and explore their implementation in different representations. The merits of the different approximate quantum dynamics methods that are thus consistently derived from the density matrix propagator starting point and different partial linearization approximations are explored in various model system studies of multi-state scattering problems and dissipative non-adiabatic relaxation in condensed phase environments that demonstrate the capabilities of these different types of approximations for treating non-adiabatic electronic relaxation, bifurcation of nuclear distributions, and the passage from nonequilibrium coherent dynamics at short times to long time thermal equilibration in the presence of a model dissipative environment.