Tensor-decomposed vibrational coupled-cluster theory: Enabling large-scale, highly accurate vibrational-structure calculations

Abstract

A new implementation of vibrational coupled-cluster (VCC) theory is presented, where all amplitude tensors are represented in the canonical polyadic (CP) format. The CP-VCC algorithm solves the non-linear VCC equations without ever constructing the amplitudes or error vectors in full dimension but still formally includes the full parameter space of the VCC[n] model in question resulting in the same vibrational energies as the conventional method. In a previous publication, we have described the non-linear-equation solver for CP-VCC calculations. In this work, we discuss the general algorithm for evaluating VCC error vectors in CP format including the rank-reduction methods used during the summation of the many terms in the VCC amplitude equations. Benchmark calculations for studying the computational scaling and memory usage of the CP-VCC algorithm are performed on a set of molecules including thiadiazole and an array of polycyclic aromatic hydrocarbons. The results show that the reduced scaling and memory requirements of the CP-VCC algorithm allows for performing high-order VCC calculations on systems with up to 66 vibrational modes (anthracene), which indeed are not possible using the conventional VCC method. This paves the way for obtaining highly accurate vibrational spectra and properties of larger molecules.

Systematic and variational truncation of the configuration space in the multiconfiguration time-dependent Hartree method: The MCTDH[n] hierarchy

“…We propose a systematic way by formulating a hierarchy of MCTDH[n] methods, which include up to n-mode excitations with respect to a selected reference configuration. This choice of configurations is in line with our vibrational configuration interaction (VCI) 21,22 and vibrational coupled cluster (VCC) [23][24][25] methods for solving the time-independent Schrödinger equation. Thus, MCTDH[n] converges toward full MCTDH in the limit where n equals the number of degrees of freedom in the system, M. The equations of motion (EOMs) for MCTDH and MCTDH[n] are derived using a SQ formalism 21 to keep the formulation in line with our previous work on time-independent theory, TDH, 4 and time-dependent vibrational coupled cluster (TDVCC).…”

Vibrational Coupled Cluster Computations in Polyspherical Coordinates with the Exact Analytical Kinetic Energy Operator

“…Recent progress indicates that in the future similar high-accuracy computations can be made feasible from developments in integration of machine learning 105 and incremental expansion methods 101,145 for PES construction and tensor decomposition methods for anharmonic wave function calculations. 112 These prospects also apply to the use of PsCs and potentially extends the impact of these.…”

Hardware efficient quantum algorithms for vibrational structure calculations

“…Molecules with up to seven atoms and described by a maximum of four-mode excitations can be studied with VCC by adopting a tensor-factorized representation of the amplitudes. 84 , 85 The inclusion of three- and four-body coupling terms in the potential and in the VCC wavefunction leaves the number of qubits required unchanged. However, it also induces a raise in both the circuit depth and the number of measurements i.e.…”