Highly multidimensional quantum dynamics methods are required to simulate many complex chemical systems; however, development of these techniques requires a way to tackle the “curse of dimensionality,” in which the cost of standard grid-based methods grows exponentially with the number of degrees of freedom. We present a method that circumvents the curse of dimensionality for exact nuclear Chebyshev quantum dynamics, the functional tensor-train Chebyshev (FTTC) method. In the method, the initial state is represented as a functional tensor train, a continuous analogue of tensor train/matrix product states with cores comprised as univariate functions. The propagated wavefunction is then approximated as a sum of Chebyshev polynomials applied to the time-evolved wavepacket. Since all quantities are computed directly in functional tensor-train format either analytically or via the cross approximation, FTTC avoids the need to compute properties such as the potential energy surface at all points on a grid. This cost-efficiency enables the Chebyshev method, which is well-known for its capacity to reach machine precision given a sufficient number of Chebyshev polynomials for systems with up to four atoms, to be applied to chemical systems in up to fifty dimensions.

Multidimensional quantum dynamics via the functional tensor-train Chebyshev method

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