A new class of ensemble conserving algorithms for approximate quantum dynamics: Theoretical formulation and model problems

Matsubara dynamics is the quantum-Boltzmann-conserving classical dynamics which remains when real-time coherences are taken out of the exact quantum Liouvillian [T. J. H. Hele et al., J. Chem. Phys. 142, 134103 (2015)]; because of a phase-term, it cannot be used as a practical method without further approximation. Recently, Smith et al. [J. Chem. Phys. 142, 244112 (2015)] developed a "planetary" model dynamics which conserves the Feynman-Kleinert (FK) approximation to the quantum-Boltzmann distribution. Here, we show that for moderately anharmonic potentials, the planetary dynamics gives a good approximation to Matsubara trajectories on the FK potential surface by decoupling the centroid trajectory from the locally harmonic Matsubara fluctuations, which reduce to a single phase-less fluctuation particle (the "planet"). We also show that the FK effective frequency can be approximated by a direct integral over these fluctuations, obviating the need to solve iterative equations. This modification, together with use of thermostatted ring-polymer molecular dynamics, allows us to test the planetary model on water (gas-phase, liquid, and ice) using the q-TIP4P/F potential surface. The "planetary" fluctuations give a poor approximation to the rotational/librational bands in the infrared spectrum, but a good approximation to the bend and stretch bands, where the fluctuation lineshape is found to be motionally narrowed by the vibrations of the centroid.

Section: The Planetary Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Approximating Matsubara dynamics using the planetary model: Tests on liquid water and ice

Willatt

Ceriotti

Althorpe

2018

“…30 Furthermore, the linearized SC-IVR (LSC-IVR) approach, 31 obtained as the linearized approximation of the SC-IVR, 32 has been used for simulations of infrared spectroscopy, 33,34 although the method neglects interference effects and does not in general preserve quantum statistics. Methods based on the path-integral formalism that preserve the quantum Boltzmann distribution, such as Centroid Molecular Dynamics (CMD), 35,36 Ring Polymer Molecular Dynamics (RPMD), 37 or the planetary model, 38 provide a balance between accuracy and computational overhead. 23,27,28,[39][40][41] Very recently, it has been shown that these methods are approximations of the general Boltzmann conserving Matsubara dynamics.…”

Section: Introductionmentioning

confidence: 99%

Inclusion of nuclear quantum effects for simulations of nonlinear spectroscopy

Jung

Videla

Batista

2018

The computation and interpretation of nonlinear vibrational spectroscopy is of vital importance for understanding a wide range of dynamical processes in molecular systems. Here, we introduce an approach to evaluate multi-time response functions in terms of multi-time double symmetrized Kubo transformed thermal correlation functions. Furthermore, we introduce a multi-time extension of ring polymer molecular dynamics to evaluate these Kubo transforms. Benchmark calculations show that the approximations are useful for short times even for nonlinear operators, providing a consistent improvement over classical simulations of multi-time correlation functions. The introduced methodology thus provides a practical way of including nuclear quantum effects in multi-time response functions of non-linear optical spectroscopy.

“…These range from the simple replacement of the quantum Boltzmann operator with its classical counterpart, an approximation that is only appropriate at sufficiently high temperatures where the zero-point energy is negligible, to sophisticated path integral-based techniques. [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57] These approaches have proven useful in the investigation of, for instance, vibrational spectra and relaxation rates, 43,[58][59][60] proton transfer problems, 56 and quantum diffusion in parahydrogen 61 and liquid neon. 49 The benefits of these approximations notwithstanding, the general accuracy of approximate Wigner transformed density operators in complex systems has been difficult to assess, especially when used in conjunction with dynamical calculations.…”

Section: Introductionmentioning

confidence: 99%

Path integral approach to the Wigner representation of canonical density operators for discrete systems coupled to harmonic baths

Montoya−Castillo

Reichman

2017

We derive a semi-analytical form for the Wigner transform for the canonical density operator of a discrete system coupled to a harmonic bath based on the path integral expansion of the Boltzmann factor. The introduction of this simple and controllable approach allows for the exact rendering of the canonical distribution and permits systematic convergence of static properties with respect to the number of path integral steps. In additions, the expressions derived here provide an exact and facile interface with quasi-and semi-classical dynamical methods, which enables the direct calculation of equilibrium time correlation functions within a wide array of approaches. We demonstrate that the present method represents a practical path for the calculation of thermodynamic data for the spin-boson and related systems. We illustrate the power of the present approach by detailing the improvement of the quality of Ehrenfest theory for the correlation function C zz (t) = Re σ z (0)σ z (t) for the spin-boson model with systematic convergence to the exact sampling function. Importantly, the numerically exact nature of the scheme presented here and its compatibility with semiclassical methods allows for the systematic testing of commonly used approximations for the Wigner-transformed canonical density.