General exponential basis set parametrization: Application to time-dependent bivariational wave functions

The computation of the nuclear quantum dynamics of molecules is challenging, requiring both accuracy and efficiency to be applicable to systems of interest. Recently, theories have been developed for employing time-dependent basis functions (denoted modals) with vibrational coupled cluster theory (TDMVCC). The TDMVCC method was introduced along with a pilot implementation, which illustrated good accuracy in benchmark computations. In this paper, we report an efficient implementation of TDMVCC, covering the case where the wave function and Hamiltonian contain up to two-mode couplings. After a careful regrouping of terms, the wave function can be propagated with a cubic computational scaling with respect to the number of degrees of freedom. We discuss the use of a restricted set of active one-mode basis functions for each mode, as well as two interesting limits: (i) the use of a full active basis where the variational modal determination amounts essentially to the variational determination of a time-dependent reference state for the cluster expansion; and (ii) the use of a single function as an active basis for some degrees of freedom. The latter case defines a hybrid TDMVCC/TDH (time-dependent Hartree) approach that can obtain even lower computational scaling. The resulting computational scaling for hybrid and full TDMVCC[2] is illustrated for polyaromatic hydrocarbons with up to 264 modes. Finally, computations on the internal vibrational redistribution of benzoic acid (39 modes) are used to show the faster convergence of TDMVCC/TDH hybrid computations towards TDMVCC compared to simple neglect of some degrees of freedom.

Efficient time-dependent vibrational coupled cluster computations with time-dependent basis sets at the two-mode coupling level: Full and hybrid TDMVCC[2]

Jensen,

Højlund,

Zoccante

et al. 2023

Time-dependent coupled cluster with orthogonal adaptive basis functions: General formalism and application to the vibrational problem

Højlund,

Zoccante,

Christiansen

2024

We derive equations of motion for bivariational wave functions with orthogonal adaptive basis sets and specialize the formalism to the coupled cluster Ansatz. The equations are related to the biorthogonal case in a transparent way, and similarities and differences are analyzed. We show that the amplitude equations are identical in the orthogonal and biorthogonal formalisms, while the linear equations that determine the basis set time evolution differ by symmetrization. Applying the orthogonal framework to the nuclear dynamics problem, we introduce and implement the orthogonal time-dependent modal vibrational coupled cluster (oTDMVCC) method and benchmark it against exact reference results for four triatomic molecules as well as a reduced-dimensional (5D) trans-bithiophene model. We confirm numerically that the biorthogonal TDMVCC hierarchy converges to the exact solution, while oTDMVCC does not. The differences between TDMVCC and oTDMVCC are found to be small for three of the five cases, but we also identify one case where the formal deficiency of the oTDMVCC approach results in clear and visible errors relative to the exact result. For the remaining example, oTDMVCC exhibits rather modest but visible errors.

A bivariational, stable, and convergent hierarchy for time-dependent coupled cluster with adaptive basis sets

Højlund,

Christiansen

2024

We propose a new formulation of time-dependent coupled cluster with adaptive basis functions and division of the one-particle space into active and secondary subspaces. The formalism is fully bivariational in the sense of a real-valued time-dependent bivariational principle and converges to the complete-active-space solution, a property that is obtained by the use of biorthogonal basis functions. A key and distinguishing feature of the theory is that the active bra and ket functions span the same space by construction. This ensures numerical stability and is achieved by employing a split unitary/non-unitary basis set transformation: the unitary part changes the active space itself, while the non-unitary part transforms the active basis. The formulation covers vibrational as well as electron dynamics. Detailed equations of motion are derived and implemented in the context of vibrational dynamics, and the numerical behavior is studied and compared to related methods.