Zhang Dong H, Shao Jiushu, Pollak Eli
Center of Theory and Computational Chemistry and State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China.
J Chem Phys. 2009 Jul 28;131(4):044116. doi: 10.1063/1.3190328.
Thawed Gaussian wavepackets have been used in recent years to compute approximations to the thermal density matrix. From a numerical point of view, it is cheaper to employ frozen Gaussian wavepackets. In this paper, we provide the formalism for the computation of thermal densities using frozen Gaussian wavepackets. We show that the exact density may be given in terms of a series, in which the zeroth order term is the frozen Gaussian. A numerical test of the methodology is presented for deep tunneling in the quartic double well potential. In all cases, the series is observed to converge. The convergence of the diagonal density matrix element is much faster than that of the antidiagonal one, suggesting that the methodology should be especially useful for the computation of partition functions. As a by product of this study, we find that the density matrix in configuration space can have more than two saddle points at low temperatures. This has implications for the use of the quantum instanton theory.
近年来，解冻的高斯波包已被用于计算热密度矩阵的近似值。从数值计算的角度来看，使用冻结的高斯波包成本更低。在本文中，我们提供了使用冻结高斯波包计算热密度的形式体系。我们表明，精确密度可以用一个级数表示，其中零阶项是冻结高斯。针对四次双阱势中的深隧穿问题，给出了该方法的数值测试。在所有情况下，该级数都收敛。对角密度矩阵元的收敛速度比非对角元快得多，这表明该方法对于配分函数的计算应该特别有用。作为这项研究的一个副产品，我们发现构型空间中的密度矩阵在低温下可以有不止两个鞍点。这对量子瞬子理论的应用有影响。
