A collocation-based multi-configuration time-dependent Hartree method using mode combination and improved relaxation

被引:13
作者
Wodraszka, Robert [1 ]
Carrington, Tucker, Jr. [1 ]
机构
[1] Queens Univ, Dept Chem, Kingston, ON K7L 3N6, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
VIBRATIONAL-ENERGY LEVELS; DISCRETE VARIABLE REPRESENTATION; WAVE-PACKET DYNAMICS; STOCHASTIC COLLOCATION; MOLECULAR-DYNAMICS; QUANTUM DYNAMICS; AB-INITIO; ALGORITHM; STATES; INTEGRATION;
D O I
10.1063/5.0006081
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
Although very useful, the original multi-configuration time-dependent Hartree (MCTDH) method has two weaknesses: (1) its cost scales exponentially with the number of atoms in the system; (2) the standard MCTDH implementation requires that the potential energy surface (PES) be in the sum-of-product (SOP) form in order to reduce the cost of computing integrals in the MCTDH basis. One way to deal with (1) is to lump coordinates into groups. This is mode combination (MC). One way to deal with (2) is to reformulate MCTDH using collocation so that there are no integrals. In this paper, we combine MC and collocation to formulate a MC collocation multi-configuration time-dependent Hartree (MC-C-MCTDH) method. In practice, its cost does not scale exponentially with the number of atoms, and it can be used with any general PES; the PES need not be an SOP and need not have a special form. No integrals and, hence, no quadratures are necessary. We demonstrate the accuracy and efficiency of the new method by computing vibrational energy eigenstates of methyl radical, methane, and acetonitrile. To do this, we use MC-C-MCTDH with a variant of improved relaxation, derived by evaluating a residual at points. Because the MC basis functions are multivariate, collocation points in multi-dimensional spaces are required. We use two types of collocation points: (1) discrete variable representation-like points obtained from (approximate) simultaneous diagonalization of matrices and (2) Leja points, which are known to be good interpolation points, determined from a generalized recipe suitable for any basis.
引用
收藏
页数:10
相关论文
共 89 条
[1]  
[Anonymous], 2012, Matrix computations
[2]  
[Anonymous], 2016, IEEE-ASME T MECH, DOI DOI 10.1017/S0007123415000642
[3]  
[Anonymous], 2017, EUR UROL SUPPL, V16, pe1, DOI DOI 10.1142/S0219633617300014
[4]   Computing vibrational energy levels of CH4 with a Smolyak collocation method [J].
Avila, Gustavo ;
Carrington, Tucker, Jr. .
JOURNAL OF CHEMICAL PHYSICS, 2017, 147 (14)
[5]   Solving the Schroedinger equation using Smolyak interpolants [J].
Avila, Gustavo ;
Carrington, Tucker, Jr. .
JOURNAL OF CHEMICAL PHYSICS, 2013, 139 (13)
[6]   Using nonproduct quadrature grids to solve the vibrational Schrodinger equation in 12D [J].
Avila, Gustavo ;
Carrington, Tucker, Jr. .
JOURNAL OF CHEMICAL PHYSICS, 2011, 134 (05)
[7]   THEORETICAL METHODS FOR ROVIBRATIONAL STATES OF FLOPPY MOLECULES [J].
BACIC, Z ;
LIGHT, JC .
ANNUAL REVIEW OF PHYSICAL CHEMISTRY, 1989, 40 :469-498
[8]  
Balgama J., 1998, ELECTRON T NUMER ANA, V7, P124
[9]   The multiconfiguration time-dependent Hartree (MCTDH) method:: a highly efficient algorithm for propagating wavepackets [J].
Beck, MH ;
Jäckle, A ;
Worth, GA ;
Meyer, HD .
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 2000, 324 (01) :1-105
[10]   An efficient and robust integration scheme for the equations of motion of the multiconfiguration time-dependent Hartree (MCTDH) method [J].
Beck, MH ;
Meyer, HD .
ZEITSCHRIFT FUR PHYSIK D-ATOMS MOLECULES AND CLUSTERS, 1997, 42 (02) :113-129