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Register a new userAn extension of the fewest switches surface hopping algorithm to complex Hamiltonians and photophysics in magnetic fields: Berrys phase and magnetic forces
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We present a preliminary extension of the fewest switches surface hopping (FSSH) algorithm to the case of complex Hamiltonians as appropriate for modeling the dynamics of photoexcited molecules in magnetic fields. We make ansatze for the direction of momentum rescaling and we account for Berrys phase effects through magnetic forces as applicable in the adiabatic limit. Because Berrys phase is a nonlocal, topological characteristic of a set of entangled potential energy surfaces, we find that Tullys local FSSH algorithm can only partially capture the correct physics.
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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 strength 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.
Strong magnetic fields have a large impact on the dynamics of molecules. In addition to the changes of the electronic structure, the nuclei are exposed to the Lorentz force with the magnetic field being screened by the electrons. In this work, we explore these effects using ab-initio molecular dynamics simulations based on an effective Hamiltonian calculated at the Hartree-Fock level of theory. To correctly include these non-conservative forces in the dynamics, we have designed a series of novel propagators that show both good efficiency and stability in test cases. As a first application, we analyze simulations of He and H$_2$ at two field strengths characteristic of magnetic white dwarfs (0.1 $B_0 = 2.35 times 10^4$ T and $B_0 = 2.35 times 10^5$ T). While the He simulations clearly demonstrate the importance of electron screening of the Lorentz force in the dynamics, the extracted rovibrational spectra of H$_2$ reveal a number of fascinating features not observed in the field-free case: couplings of rotations/vibrations with the cyclotron rotation, overtones with unusual selection rules, and hindered rotations that transmute into librations with increasing field strength. We conclude that our presented framework is a powerful tool to investigate molecules in these extreme environments.
Although the quantum classical Liouville equation (QCLE) arises by cutting off the exact equation of motion for a coupled nuclear-electronic system at order 1 (1 = $hbar^0$ ), we show that the QCLE does include Berrys phase effects and Berrys forces (which are proportional to a higher order, $hbar$ = $hbar^1$ ). Thus, the fundamental equation underlying mixed quantum-classical dynamics does not need a correction for Berrys phase effects and is valid for the case of complex Hamiltonians. Furthermore, we also show that, even though Tullys surface hopping model ignores Berrys phase, Berrys phase effects are included automatically within Ehrenfest dynamics. These findings should be of great importance if we seek to model coupled nuclear-electronic dynamics for systems with spin-orbit coupling, where the complex nature of the Hamiltonian is paramount.
Elastic and spin-changing inelastic collision cross sections are presented for cold and ultracold magnetically trapped NH. The cross sections are obtained from coupled-channel scattering calculations as a function of energy and magnetic field. We specifically investigate the influence of the intramolecular spin-spin, spin-rotation, and intermolecular magnetic dipole coupling on the collision dynamics. It is shown that $^{15}$NH is a very suitable candidate for evaporative cooling experiments. The dominant trap-loss mechanism in the ultracold regime originates from the intermolecular dipolar coupling term. At higher energies and fields, intramolecular spin-spin coupling becomes increasingly important. Our qualitative results and conclusions are fairly independent of the exact form of the potential and of the size of the channel basis set.
A new static and azimuthally symmetric magnetic monopolelike object, which looks like a Dirac monopole when seen from far away but smoothly changes to a dipole near the monopole position and vanishes at the origin, is discussed. This monopolelike object is inspired by an analysis of an exactly solvable model of Berrys phase in the parameter space. A salient feature of the monopolelike potential ${cal A}_{k}(r,theta)$ with a magnetic charge $e_{M}$ is that the Dirac string is naturally described by the potential ${cal A}_{k}(r,theta)$, and the origin of the Dirac string and the geometrical center of the monopole are displaced in the coordinate space. The smooth topology change from a monopole to a dipole takes place if the Dirac string, when coupled to the electron, becomes unobservable by satisfying the Dirac quantization condition. The electric charge is then quantized even if the monopole changes to a dipole near the origin. In the transitional region from a monopole to a dipole, a half-monopole with a magnetic charge $e_{M}/2$ appears.
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