Department of Chemistry and Applied Biosciences, ETH Zürich, 8093 Zürich, Switzerland.
J Chem Phys. 2023 Jul 7;159(1). doi: 10.1063/5.0155579.
We introduce an approach for calculating perturbative corrections to the ring-polymer instanton approximation to tunneling splittings (RPI+PC) by computing higher-order terms in the asymptotic expansion in ℏ. The resulting method goes beyond standard instanton theory by using information on the third and fourth derivatives of the potential along the tunneling path to include additional anharmonic effects. This leads to significant improvements both in systems with low barriers and in systems with anharmonic modes. We demonstrate the applicability of RPI+PC to molecular systems by computing the tunneling splitting in full-dimensional malonaldehyde and a deuterated derivative. Comparing to both experiment and recent quantum mechanical benchmark results, we find that our perturbative correction reduces the error from -11% to 2% for hydrogen transfer and performs even better for the deuterated case. This makes our approach more accurate than previous calculations using diffusion Monte Carlo and path-integral molecular dynamics while being more computationally efficient.
我们介绍了一种通过计算 ℏ 中的渐近展开式的高阶项来计算对环聚合物瞬时近似隧穿分裂（RPI+PC）的微扰修正的方法。该方法通过使用沿隧穿路径的势能的三阶和四阶导数来包含额外的非谐效应，超越了标准的瞬时理论。这在低势垒系统和非谐模式系统中都带来了显著的改进。我们通过计算全维丙二醛和氘代衍生物的隧穿分裂来证明 RPI+PC 在分子系统中的适用性。与实验和最近的量子力学基准结果进行比较，我们发现我们的微扰修正将氢转移的误差从-11%降低到 2%，对于氘代情况的效果甚至更好。这使得我们的方法比使用扩散蒙特卡罗和路径积分分子动力学的先前计算更准确，同时计算效率更高。
