arXiv subjects

Marcel Nooijen

Publications and source records attributed to Marcel Nooijen.

4 recordsLinked to original sources

arXiv2023

Time dependent Vibrational Electronic Coupled Cluster (VECC) theory for non-adiabatic nuclear dynamics

A time-dependent vibrational electronic coupled-cluster (VECC) approach is proposed to simulate photoelectron/ UV-VIS absorption spectra, as well as time-dependent properties for non-adiabatic vibronic models, going beyond the Born-Oppenheimer approximation. A detailed derivation of the equations of motion and a motivation of the ansatz are presented. The VECC method employs second-quantized bosonic construction operators and a mixed linear and exponential ansatz to form a compact representation of the time-dependent wave-function. Importantly, the method does not require a basis set, has only few user-defined inputs, and has a classical (polynomial) scaling with respect to the number of degrees of freedom (of the vibronic model), resulting in a favourable computational cost. In benchmark applications to small models and molecules the VECC method provides accurate results, compared to Multi-Configurational Time-dependent Hartree (MCTDH) calculations when predicting short-time dynamical properties (i.e. photo-elecron / UV-VIS absorption spectra) for non-adiabatic vibronic models. To illustrate the capabilities the VECC method is also applied successfully to a large vibronic model for hexahelicene with 14 electronic states and 63 normal modes, developed in the group by Santoro.

physics.chem-ph↗

arXiv2021

Normal ordered exponential approach to thermal properties and time-correlation functions: General theory and simple examples

A normal ordered exponential parametrization is used to obtain equations for thermal one-and two-particle reduced density matrices, as well as free energies, partition functions and entropy for both Fermionic (electronic) and Bosonic (vibrational) Hamiltonians. A first principles derivation of the equations, relying only on a simple Wick's theorem and starting from the differential equation $\frac{d \hat{D}}{d β}= - (\hat{H}-μ\hat{N})\hat{D}$, is presented that yields a differential equation for the amplitudes representing density cumulants, as well as the grand potential. In contrast to other approaches reported in the literature the theory does not use perturbation theory in the interaction picture and an integral formulation as a starting point, but rather requires a propagation of the resulting differential equation for the amplitudes. While the theory is applicable to general classes of many-body problems in principle, here, the theory is illustrated using simple model systems. For one-body Fermionic Hamiltonians, Fermi-Dirac one-body reduced density matrices are recovered for the grand-canonical formulation. For multidimensional harmonic oscillators numerically exact results are obtained using the thermal normal ordered exponential (TNOE) approach. As an application of the related time-dependent formulation numerically exact time-autocorrelation functions and absorption spectra are obtained for harmonic Franck Condon problems. These examples illustrate the basic soundness of the scheme and are used for pedagogical purposes. Other approaches in the literature are only discussed briefly and no detailed comparative discussion is attempted.

quant-ph↗

arXiv2019

Deterministic and quasi-random sampling of optimized Gaussian mixture distributions for vibronic Monte Carlo

It was recently shown that path integral Monte Carlo can be used to directly compute partition functions of Hamiltonians with vibronic coupling [J. Chem. Phys. 148, 194110 (2018)]. While the importance sampling Monte Carlo integration scheme was successful, it required many samples to reduce the stochastic error and suffered from the need to manually construct a sampling distribution for each system. We tackle these issues by using deterministic component selection for Gaussian mixture distributions (GMDs), introducing quasi-random numbers into the Monte Carlo sampling, and automatically optimizing the GMD parameters to obtain an improved sampling distribution. We demonstrate the effectiveness of our methods using vibronic model systems, but these methods are in principle widely applicable to general Monte Carlo sampling of GMDs.

physics.chem-ph↗

arXiv2019

A path integral methodology for obtaining thermodynamic properties of nonadiabatic systems using Gaussian mixture distributions

We introduce a new path integral Monte Carlo method for investigating nonadiabatic systems in thermal equilibrium and demonstrate an approach to reducing stochastic error. We derive a general path integral expression for the partition function in a product basis of continuous nuclear and discrete electronic degrees of freedom without the use of any mapping schemes. We separate our Hamiltonian into a harmonic portion and a coupling portion; the partition function can then be calculated as the product of a Monte Carlo estimator (of the coupling contribution to the partition function) and a normalization factor (that is evaluated analytically). A Gaussian mixture model is used to evaluate the Monte Carlo estimator in a computationally efficient manner. Using two model systems, we demonstrate our approach to reduce the stochastic error associated with the Monte Carlo estimator. We show that the selection of the harmonic oscillators comprising the sampling distribution directly affects the efficiency of the method. Our results demonstrate that our path integral Monte Carlo method's deviation from exact Trotter calculations is dominated by the choice of the sampling distribution. By improving the sampling distribution, we can drastically reduce the stochastic error leading to lower computational cost.

physics.chem-ph↗