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首页> 外文期刊>The journal of physical chemistry, A. Molecules, spectroscopy, kinetics, environment, & general theory >Using Nested Contractions and a Hierarchical Tensor Format To Compute Vibrational Spectra of Molecules with Seven Atoms
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Using Nested Contractions and a Hierarchical Tensor Format To Compute Vibrational Spectra of Molecules with Seven Atoms

机译：使用嵌套收缩和分层张量格式计算具有七个原子的分子的振动光谱

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We propose a method for solving the vibrational Schrodinger equation with which one can compute hundreds of energy levels of seven-atom molecules using at most a few gigabytes of memory. It uses nested contractions in conjunction with the reduced-rank block power method (RRBPM) described in J. Chem. Phys. 2014, 140, 174111. Successive basis contractions are organized into a tree, the nodes of which are associated with eigenfunctions of reduced-dimension Hamiltonians. The RRBPM is used recursively to compute eigenfunctions of nodes in bases of products of reduced-dimension eigenfunctions of nodes with fewer coordinates. The corresponding vectors are tensors in what is called CP-format. The final wave functions are therefore represented in a hierarchical CP-format. Computational efficiency and accuracy are significantly improved by representing the Hamiltonian in the same hierarchical format as the wave function. We demonstrate that with this hierarchical RRBPM it is possible to compute energy levels of a 64-D coupled-oscillator model Hamiltonian and also of acetonitrile (CH3CN) and ethylene oxide (C2H4O), for which we use quartic potentials. The most accurate acetonitrile calculation uses 139 MB of memory and takes 3.2 h on a single processor. The most accurate ethylene oxide calculation uses 6.1 GB of memory and takes 14 d on 63 processors. The hierarchical RRBPM shatters the memory barrier that impedes the calculation of vibrational spectra.
机译：我们提出了一种解决振动薛定inger方程的方法，利用该方法，最多可以使用几GB的内存来计算七原子分子的数百种能级。它结合了J. Chem。物理2014，140，174111.连续基础收缩被组织成一棵树，其节点与降维哈密顿量的本征函数相关。 RRBPM用于递归地以具有较少坐标的节点的降维本征函数的乘积为基础来计算节点的本征函数。相应的矢量是张量，称为CP格式。因此，最终波函数以分层CP格式表示。通过用与波动函数相同的层次结构表示哈密顿量，可以显着提高计算效率和准确性。我们证明，使用这种分层RRBPM，可以计算64维耦合振荡器模型哈密顿量以及乙腈（CH3CN）和环氧乙烷（C2H4O）的能级，对此我们使用四次电势。最准确的乙腈计算使用139 MB的内存，在单个处理器上需要3.2 h。最准确的环氧乙烷计算使用6.1 GB内存，在63个处理器上需要14 d。分层RRBPM打破了阻碍振动光谱计算的存储障碍。

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