General polarizability and hyperpolarizability estimators for the path-integral Monte Carlo method applied to small atoms, ions, and molecules at finite temperatures

Tiihonen, Juha; Kylänpää, Ilkka; Rantala, Tapio T.

doi:10.1103/physreva.94.032515

Cited by 7 publications

(17 citation statements)

References 64 publications

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“…in Refs. [5,10,11]. With only up to two electrons (or positrons), we can assume opposite spins and avoid the Fermion sign problem.…”

Section: Resultsmentioning

confidence: 99%

“…The derivation of field-free estimators is done in the spirit of the Hellman-Feynman theorem: we can solve for the polarizabilities by differentiating with respect to the perturbation in the zero-field limit. The differentiation of a diagonal observable is straightforward, and it is explained in more detail in our previous work [5]. Nevertheless, for field-gradient polarizabilities this results in…”

Section: Theorymentioning

confidence: 98%

“…Here, µ α and Θ αβ are the permanent dipole and quadrupole moments, respectively. Coefficients α, β and γ are static dipole polarizabilities of different order, and arXiv:1707.02829v2 [physics.chem-ph] 11 Aug 2017 they have been treated earlier [5]. A, B and C are called dipole-quadrupole, dipole-dipole-quadrupole, and quadrupole-quadrupole polarizabilities, respectively, and they are the main focus of this article.…”

Section: Theorymentioning

confidence: 99%

“…they have been treated earlier [5]. A, B and C are called dipole-quadrupole, dipole-dipole-quadrupole, and quadrupole-quadrupole polarizabilities, respectively, and they are the main focus of this article.…”

Section: Theorymentioning

confidence: 99%

“…In our recent article [5], we proposed a scheme for estimating static dipole polarizabilities in a field-free PIMC simulation. This was an imminent improvement to our earlier finite-field approach [6].…”

Section: Introductionmentioning

confidence: 99%

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Static field-gradient polarizabilities of small atoms and molecules at finite temperature

Tiihonen

Kylänpää

Rantala

2017

The Journal of Chemical Physics

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In this work, we propose new field-free estimators for static field-gradient polarizabilities in finite temperature PIMC simulation. Namely, dipole-quadrupole polarizability A, dipole-dipolequadrupole polarizability B and quadrupole-quadrupole polarizability C are computed for several up to two-electron systems: H, H − , He, Li + , Be 2+ , Ps2, PsH, H + 2 , H2, H + 3 and HeH + . We provide complementary data for ground state electronic properties within the adiabatic approximation, and demonstrate good agreement with available values in the literature. More importantly, we present fully non-adiabatic results from 50 K to 1600 K, which allow us to analyze and discuss strong thermal coupling and rovibrational effects in total field-gradient polarizabilities. These phenomena are most relevant but clearly overlooked, e.g., in the construction of modern polarizable force field models. However, our main purpose is demonstrating the accuracy and simplicity of our approach in a problem that is generally challenging.

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“…in Refs. [5,10,11]. With only up to two electrons (or positrons), we can assume opposite spins and avoid the Fermion sign problem.…”

Section: Resultsmentioning

confidence: 99%

Section: Theorymentioning

confidence: 98%

Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Static field-gradient polarizabilities of small atoms and molecules at finite temperature

Tiihonen

Kylänpää

Rantala

2017

The Journal of Chemical Physics

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Computation of Dynamic Polarizabilities and van der Waals Coefficients from Path-Integral Monte Carlo

Tiihonen

Kylänpää

Rantala

2018

J. Chem. Theory Comput.

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We demonstrate computation of total dynamic multipole polarizabilities using path-integral Monte Carlo method (PIMC). The PIMC approach enables accurate thermal and nonadiabatic mixing of electronic, rotational, and vibrational degrees of freedom. Therefore, we can study the thermal effects, or lack thereof, in the full multipole spectra of the chosen one- and two-electron systems: H, Ps, He, Ps2, H2, and HD+. We first compute multipole–multipole correlation functions up to octupole order in imaginary time. The real-domain spectral function is then obtained by analytical continuation with the maximum entropy method. In general, sharpness of the active spectra is limited, but the obtained off-resonant polarizabilities are in good agreement with the existing literature. Several weak and strong thermal effects are observed. Furthermore, the polarizabilities of Ps2 and some higher multipole and higher frequency data have not been published before. In addition, we compute isotropic dispersion coefficients C 6, C 8, and C 10 between pairs of species using the simplified Casimir–Polder formulas.

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Path integrals: From quantum mechanics to photonics

et al. 2021

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The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its dynamical evolution, is perhaps the most elegant and universal framework developed in theoretical physics, second only to the standard model of particle physics. In this Tutorial, we retrace the steps that led to the creation of such a remarkable framework, discuss its foundations, and present some of the classical examples of problems that can be solved using the path integral formalism, as a way to introduce the readers to the topic and help them get familiar with the formalism. Then, we focus our attention on the use of path integrals in optics and photonics and discuss in detail how they have been used in the past to approach several problems, ranging from the propagation of light in inhomogeneous media to parametric amplification and quantum nonlinear optics in arbitrary media. To complement this, we also briefly present the path integral Monte Carlo method, as a valuable computational resource for condensed matter physics, and discuss its potential applications and advantages if used in photonics.

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General polarizability and hyperpolarizability estimators for the path-integral Monte Carlo method applied to small atoms, ions, and molecules at finite temperatures

Cited by 7 publications

References 64 publications

Static field-gradient polarizabilities of small atoms and molecules at finite temperature

Static field-gradient polarizabilities of small atoms and molecules at finite temperature

Computation of Dynamic Polarizabilities and van der Waals Coefficients from Path-Integral Monte Carlo

Path integrals: From quantum mechanics to photonics

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