Diagonal Born-Oppenheimer Corrections in Condensed-Phase Ring Polymer Surface Hopping

Abstract

Ring polymer surface hopping (RPSH) is a mixed quantum-classical dynamics method for incorporating nuclear quantum effects (NQEs) into nonadiabatic dynamics simulations via the extended phase-space of a classical ring polymer. Here, we systematically investigate several variants of RPSH in the frameworks of centroid and bead approximations (RPSH-CA and RPSH-BA) in modeling the dynamics of the spin-boson system across different reaction regimes, reorganization energies, and temperatures. Moreover, the effects of including the diagonal Born-Oppenheimer correction (DBOC) on the performance of the RPSH-CA and RPSH-BA methods are investigated. Our simulations of symmetric potentials, i.e., without energy bias, show that the RPSH-CA method, where nonadiabatic transitions are handled at the centroid level, is satisfactorily accurate and robust across different reaction regimes. Adding DBOC improves the method's accuracy in specific intermediate and nonadiabatic reaction regimes at low temperature. Overall, the effect of DBOC in RPSH-CA is in moderation compared to conventional fewest-switches surface hopping method where DBOC over-damps the dynamics significantly and reduces accuracy considerably, especially at low temperatures. However, the RPSH-CA and its DBOC variant struggle in simulations of asymmetric potentials specially at low temperatures. On the other hand, RPSH-BA results, where nonadiabatic transitions are handled at the level of individual beads of the ring polymers, are generally unreliable unless in the high temperature adiabatic reaction regimes with symmetric potentials. The inclusion of DBOC is not particularly helpful in remedying this erratic behavior. Our findings clarify when geometric corrections are beneficial or detrimental to nonadiabatic simulations using RPSH, providing practical guidance for atomistic condensed-phase applications.

Figures (4)

• Figure 1: Population dynamics for the spin-boson model at the high temperature of 300 K and three reorganization energies, $E_r$ = 0.02 (top row), $E_r$ = 1 (middle row), and $E_r$ = 5 (bottom row), across different reaction regimes (columns). Model parameters include $\epsilon$ = 0, $\Delta$ = 1.0, and $\omega_c$ = {0.25$\Delta$, $\Delta$, 5$\Delta$}. All energies are in the unit of 104.25 cm$^{-1}$.
• Figure 2: Population dynamics of spin-boson model at the low temperature of 30 K for three reorganization energies and different reaction regimes. All the model parameters are the same as in Fig. \ref{['fig:pop-dboc-highT']}.
• Figure 3: Population dynamics of the asymmetric spin–boson model at 300 K (a-d, left panel) and 30 K (e-h, right panel) for low and high reorganization energies: $E_r = 0.02$, top panel, and $E_r = 5$, bottom panel, spanning both adiabatic and nonadiabatic reaction regimes. Results from RPSH-CA and RPSH-BA and their DBOC variants (RPSH-CA$^{\text{D}}$ and RPSH-BA$^{\text{D}}$) are compared against exact quantum dynamics results. Here, $\epsilon$ = 1.0 and all other model parameters are the same as in Fig. \ref{['fig:pop-dboc-highT']}.
• Figure 4: Population dynamics of the symmetric (a-b) and asymmetric (c-d) spin-boson models at a low temperature of 30 K, shown for different reorganization energies in the nonadiabatic reaction regime. The plots compare results from FSSH, RPSH, and their DBOC-corrected variants (FSSH$^{\text{D}}$ and RPSH-CA$^{\text{D}}$) against exact results.