Equations are derived for the time evolution of time-dependent vibrational coupled cluster (TDVCC) wave functions covering both the TDVCC ket state and the associated so-called Λ bra state. The equations are implemented in the special case of both the Hamiltonian and the cluster operator containing at most two-mode coupling terms. The nontrivial behavior of the evolution of norm, energy, and expectation values due to the nonunitary time-evolution of the nonvariational TDVCC theory is analyzed theoretically and confirmed in numerical experiments that also include time-dependent Hamiltonians. In the spirit of time-independent size-consistency analysis, the separability of both the coupled cluster and Λ states for noninteracting systems is studied. While the coupled cluster state clearly has the correct behavior, the behavior of the Λ state is more intricate, and the consequence for different properties is shown theoretically and numerically. Overall, the numerical experiments show that TDVCC in incomplete expansions gives higher accuracy than a standard linear variational wave function parameterization with the same number of independent parameters, while equivalent results are obtained for complete expansions. The efficiency of the methodology is illustrated in computations on polycyclic aromatic hydrocarbons with up to 156 modes.

The multi-configurational time-dependent Hartree approach in optimized second quantization: Imaginary time propagation and particle number conservation

We present a flexible scheme for calculating vibrational rectilinear coordinates with well-defined strict locality on a certain set of atoms. Introducing a method for Flexible Adaption of Local COordinates of Nuclei (FALCON) we show how vibrational subspaces can be "grown" in an adaptive manner. Subspace Hessian matrices are set up and used to calculate and analyze vibrational modes and frequencies. FALCON coordinates can more generally be used to construct vibrational coordinates for describing local and (semi-local) interacting modes with desired features. For instance, spatially local vibrations can be approximately described as internal motion within only a group of atoms and delocalized modes can be approximately expressed as relative motions of rigid groups of atoms. The FALCON method can support efficiency in the calculation and analysis of vibrational coordinates and energies in the context of harmonic and anharmonic calculations. The features of this method are demonstrated on a few small molecules, i.e., formylglycine, coumarin, and dimethylether as well as for the amide-I band and low-frequency modes of alanine oligomers and alpha conotoxin.

Semiclassical transition state theory based on fourth order vibrational perturbation theory: Model system studies beyond symmetric Eckart barrier Perspective: Computational chemistry software and its advancement as illustrated through three grand challenge cases for molecular science Communication: The pole structure of the dynamical polarizability tensor in equation-of-motion coupledcluster theoryWe derive equations for describing the time evolution of variational wave functions in linear and exponential parameterization with a second-quantization (SQ) formulation. The SQ formalism covers time-dependent Hartree (TDH), while exact states and approximate vibrational configuration interaction wave functions are described using state-transfer operators. We present detailed expressions for efficient evaluation of TDH in linear (L-TDH) and exponential (X-TDH) parametrization and an efficient implementation supporting linear scaling with respect to the number of degrees of freedom M when the Hamiltonian operator contains a constant number of terms per mode independently of the size of the system. The computational cost of the X-TDH method is reduced significantly compared to the L-TDH method for systems with many operator terms per mode such as is typical for accurate molecular potential-energy surfaces. Numerical results for L-TDH and X-TDH are presented which confirm the theoretical reduction of the M scaling compared to standard first-quantization formulations. Calculations on Henon-Heiles potentials with more than 10 5 dimensions and polycyclic aromatic hydrocarbons with up to 264 modes have been performed. Thus, the SQ formulation and the X-TDH method pave the way for studying the time-resolved quantum dynamics of large molecules. Published by AIP Publishing. https://doi.

We show how the eigenvalue equations of vibrational coupled cluster response theory can be solved using a subspace projection method with Davidson update, where basis vectors are stacked tensors decomposed into canonical (CP, Candecomp/Parafac) form. In each update step, new vectors are first orthogonalized to old vectors, followed by a tensor decomposition to a prescribed threshold TCP. The algorithm can provide excitation energies and eigenvectors of similar accuracy as a full vector approach and with only a very modest increase in the number of vectors required for convergence. The algorithm is illustrated with sample calculations for formaldehyde, 1,2,5-thiadiazole, and water. Analysis of the formaldehyde and thiadiazole calculations illustrate a number of interesting features of the algorithm. For example, the tensor decomposition threshold is optimally put to rather loose values, such as TCP = 10(-2). With such thresholds for the tensor decompositions, the original eigenvalue equations can still be solved accurately. It is thus possible to directly calculate vibrational wave functions in tensor decomposed format.