发表机构
Universit\'e Paris-Saclay, CNRS, Institut des Sciences Mol\'eculaires d'Orsay, 91405, Orsay, France.; Universit\'e Paris-Saclay, CNRS, Institut de Chimie Physique, 91405, Orsay, France.（; ）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出有界四次力场（bQFF）修正，使其适用于变分计算，并与MCTDH和ElVibRot软件结合，实现非谐振动本征态的高效自动计算。
AI 中文摘要
在本工作中，我们介绍了在变分计算背景下使用四次力场（QFF）势展开的方法。此类势能通常用于分子振动二阶微扰理论（VPT2）研究中，且存在显式依赖于QFF参数的方程。然而，QFF在偏离参考点较大位移时是无界势，这大多数情况下阻碍了其与基于变分波包计算的结合使用。在本工作中，我们提出了一种对QFF的通用修正，并引入了一种全自动数值方法来避免其无界特性。我们的修正势，即有界四次力场（bQFF），在红外光谱感兴趣区域附近不会表现出明显的局部地形改变。因此，我们可以断言振动本征结构（本征值、本征态）基本不受我们修正的影响。为了展示其数值稳定性，我们将bQFF程序与两个成熟的量子模拟软件包MCTDH和ElVibRot（均采用变分方法）进行了接口对接。更具体地说，我们的bQFF是可分离的，因此可直接表示为MCTDH算子。此外，关于bQFF展开的规模，我们展示了可以将其张量分解为典型多项式形式（CP-bQFF）。我们使用蒙特卡洛典型多项式分解算法来实现这一点。CP-bQFF的结果与未压缩的bQFF几乎相同，但计算效率大大提高。我们的方法为在基于QFF势的分子系统中自动进行非谐本征态的变分研究铺平了道路，可使用时间依赖或时间无关的方案。
英文摘要
In this work we introduce the use of Quartic Force fields (QFF) potential expansions in the context of variational calculations. Such potentials are commonly employed in molecular Vibrational Second-Order Perturbation Theory (VPT2) studies, for which equations explicitly dependent on the QFF parameters exist. However, QFF are unbound potentials for more or less large displacements from the reference point and, most of the time, this prevents their use in conjunction with variational wavepacket-based calculations. In this work, we propose a general correction to QFFs and introduce a fully automated numerical approach to avoid their unbound character. Our corrected potentials, bound QFF (bQFF), do not exhibit appreciable modification of the local topography around the region of interest for infrared spectroscopy. As a consequence of this, we can affirm that the vibrational eigenstructure (eigenvalues, eigenstates) remains essentially unaltered by our correction. To illustrate their numerical stability, we have interfaced our bQFF routines in combination with to two well-established quantum simulation software packages MCTDH and \textsc{ElVibRot} which feature variational approaches. More specifically, our bQFFs are separable and hence directly expressible as MCTDH operators. Furthermore, concerning the size of our bQFF expansion, we show that it is possible to tensor-decompose our bQFF in Canonical Polyadic form (CP-bQFF). We use the Monte Carlo Canonical Polyadic decomposition algorithm for this. CP-bQFF results are virtually identical to uncompressed bQFF, but the computational efficiency is largely improved. Our approach paves the way for the automated variational study of anharmonic eigenstates in molecular systems within the reach of QFF-based potentials, using either time-dependent or time-independent schemes.
