Molecular Spectra Calculations Using an Optimized Quasi-Regular Gaussian Basis and the Collocation Method
Molecular Spectra Calculations Using an Optimized Quasi-Regular Gaussian Basis and the Collocation Method
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使用优化的拟正则高斯基和搭配方法进行分子光谱计算
DOI：
10.1021/acs.jctc.1c00805
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发表时间：
2021
影响因子：
5.5
通讯作者：
Mandelshtam, Vladimir A.
中科院分区：
文献类型：
--
作者：
Flynn, Shane W.;Mandelshtam, Vladimir A.
我们回顾了Manzhos和Carrington的搭配方法[J.Chem.其中，使用分布的局域(例如，高斯)基来建立广义本征值问题，以计算分子振动哈密顿量的本征能量和本征函数。虽然得到的线性代数问题涉及全矩阵，但该方法提供了许多重要的优点，即(I)它在概念和数值上都非常简单，(Ii)它可以使用任何一组内部分子坐标来表示，(Iii)它对于基的选择是灵活的，(Iv)不需要计算积分，以及(V)它有可能通过优化基函数的位置和形状来显著减小基的大小。在本文中，我们使用最近引入的并在此进一步改进的准规则网格(QRGs)来探索该方法的后一方面。通过计算甲醛四原子分子的本征能，我们证明了基于QRG的分布高斯基优于以往的选择。
We revisit the collocation method of Manzhos and Carrington [J. Chem. Phys., 2016, 145, 224110] in which a distributed localized (e.g., Gaussian) basis is used to set up a generalized eigenvalue problem to compute the eigenenergies and eigenfunctions of a molecular vibrational Hamiltonian. Although the resulting linear algebra problem involves full matrices, the method provides a number of important advantages, namely, (i) it is very simple both conceptually and numerically, (ii) it can be formulated using any set of internal molecular coordinates, (iii) it is flexible with respect to the choice of the basis, (iv) no integrals need to be computed, and (v) it has the potential to significantly reduce the basis size through optimizing the placement and the shapes of the basis functions. In the present paper, we explore the latter aspect of the method using the recently introduced, and here further improved, quasi-regular grids (QRGs). By computing the eigenenergies of the four-atom molecule of formaldehyde, we demonstrate that a QRG-based distributed Gaussian basis is superior to the previously used choices.