A comparative study of imaginary time path integral based methods for quantum dynamics

Hone, Tyler D.; Rossky, Peter J.; Voth, Gregory A.

doi:10.1063/1.2186636

Cited by 147 publications

(177 citation statements)

References 42 publications

Supporting

Mentioning

167

Contrasting

Unclassified

Order By: Relevance

“…(73) withÂ =q,B =q) for some one-dimensional model systems. For consistency with previous work, 32,33 we considered the quartic potential…”

Section: Numerical Tests Of the Efficacy Of Matsubara Dynamicsmentioning

confidence: 99%

“…An intriguing property of CMD and RPMD is that, for some model systems (e.g. the one-dimensional quartic oscillator 32,33 ), these methods give better agreement than LSC-IVR with the exact quantum result, even though, like LSC-IVR, they completely neglect real-time quantum coherence.…”

Section: Introductionmentioning

confidence: 99%

“…Some of these methods are obtained by replacing the plain Newtonian dynamics in the LSC-IVR by an effective (classical) dynamics which preserves the Boltzmann distribution. [28][29][30] Others, such as the popular centroid molecular dynamics (CMD) 31,32 and ring-polymer molecular dynamics (RPMD), 5,7-9,33-53 are more heuristic (and still not fully understood) but have the advantage that they can be implemented directly in classical molecular dynamics codes. An intriguing property of CMD and RPMD is that, for some model systems (e.g.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Boltzmann-conserving classical dynamics in quantum time-correlation functions: “Matsubara dynamics”

Hele

Willatt

Muolo

et al. 2015

The Journal of Chemical Physics

113

225

View full text Add to dashboard Cite

We show that a single change in the derivation of the linearized semiclassical-initial value representation (LSC-IVR or 'classical Wigner approximation') results in a classical dynamics which conserves the quantum Boltzmann distribution. We rederive the (standard) LSC-IVR approach by writing the (exact) quantum time-correlation function in terms of the normal modes of a free ring-polymer (i.e. a discrete imaginary-time Feynman path), taking the limit that the number of polymer beads N → ∞, such that the lowest normal-mode frequencies take their 'Matsubara' values. The change we propose is to truncate the quantum Liouvillian, not explicitly in powers of 2 at 0 (which gives back the standard LSC-IVR approximation), but in the normalmode derivatives corresponding to the lowest Matsubara frequencies. The resulting 'Matsubara' dynamics is inherently classical (since all terms O( 2 ) disappear from the Matsubara Liouvillian in the limit N → ∞), and conserves the quantum Boltzmann distribution because the Matsubara Hamiltonian is symmetric with respect to imaginary-time translation. Numerical tests show that the Matsubara approximation to the quantum timecorrelation function converges with respect to the number of modes, and gives better agreement than LSC-IVR with the exact quantum result. Matsubara dynamics is too computationally expensive to be applied to complex systems, but its further approximation may lead to practical methods.

show abstract

“…(73) withÂ =q,B =q) for some one-dimensional model systems. For consistency with previous work, 32,33 we considered the quartic potential…”

Section: Numerical Tests Of the Efficacy Of Matsubara Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Boltzmann-conserving classical dynamics in quantum time-correlation functions: “Matsubara dynamics”

Hele

Willatt

Muolo

et al. 2015

The Journal of Chemical Physics

113

225

View full text Add to dashboard Cite

show abstract

“…The canonical partition function is approximated as (24) where dΓ = N j=1 L i=1 dR ij , and the particle indistinguishability has been considered by the N ! term.…”

Section: Many-body Extensionmentioning

confidence: 99%

“…The PI simulation of time dependent correlation functions is another aspect that is not discussed in this review (see Refs. [23][24][25][26] ). We summarize the computational requirements to simulate solids in the isothermal-isobaric (N P T ) ensemble, either using PIMC or PIMD sampling (N stands for the number of particles, while P and T denote pressure and temperature, respectively).…”

Section: Introductionmentioning

confidence: 99%

Path-integral simulation of solids

Herrero

Ramı́rez

2014

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

The path-integral formulation of the statistical mechanics of quantum many-body systems is described, with the purpose of introducing practical techniques for the simulation of solids. Monte Carlo and molecular dynamics methods for distinguishable quantum particles are presented, with particular attention to the isothermal-isobaric ensemble. Applications of these computational techniques to different types of solids are reviewed, including noble-gas solids (helium and heavier elements), group-IV materials (diamond and elemental semiconductors), and molecular solids (with emphasis on hydrogen and ice). Structural, vibrational, and thermodynamic properties of these materials are discussed. Applications also include point defects in solids (structure and diffusion), as well as nuclear quantum effects in solid surfaces and adsorbates. Different phenomena are discussed, as solid-to-solid and orientational phase transitions, rates of quantum processes, classical-to-quantum crossover, and various finite-temperature anharmonic effects (thermal expansion, isotopic effects, electron-phonon interactions). Nuclear quantum effects are most remarkable in the presence of light atoms, so that especial emphasis is laid on solids containing hydrogen as a constituent element or as an impurity.

show abstract

Path integral Brownian chain molecular dynamics: A simple approximation of quantum vibrational dynamics

Shiga

2022

J Comput Chem

View full text Add to dashboard Cite

An approximate approach to quantum vibrational dynamics, "Brownian chain molecular dynamics (BCMD)," is proposed to alleviate the chain resonance and curvature problems in the imaginary time-based path integral (PI) simulation. Here the noncentroid velocity is randomized at each step when solving the equation of motion of path integral molecular dynamics. This leads to a combination of the Newton equation and the overdamped Langevin equation for the centroid and non-centroid variables, respectively. BCMD shares the basic properties of other PI approaches such as centroid and ring polymer molecular dynamics: It gives the correct Kubo-transformed correlation function at short times, conserves the time symmetry, has the correct high-temperature/classical limits, gives exactly the position and velocity autocorrelations of harmonic oscillator systems, and does not have the zero-point leakage problem. Numerical tests were done on simple molecular models and liquid water.On-the-fly ab initio BCMD simulations were performed for the protonated water cluster, H 5 O þ 2 , and its isotopologue, D 5 O þ 2 .

show abstract

A comparative study of imaginary time path integral based methods for quantum dynamics

Cited by 147 publications

References 42 publications

Boltzmann-conserving classical dynamics in quantum time-correlation functions: “Matsubara dynamics”

Boltzmann-conserving classical dynamics in quantum time-correlation functions: “Matsubara dynamics”

Path-integral simulation of solids

Path integral Brownian chain molecular dynamics: A simple approximation of quantum vibrational dynamics

Contact Info

Product

Resources

About