Path-Integral Calculation of the Two-Particle Slater Sum for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>

Fosdick, Lloyd D.; Jordan, Harry F.

doi:10.1103/physrev.143.58

Cited by 107 publications

(37 citation statements)

References 7 publications

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“…(27) and recalling the definition in Eq. (20), a temperature-dependent rigid-body Hamiltonian for the monomer can be defined as…”

Section: B the Improved Rigid-rotor Approximationmentioning

confidence: 99%

“…3,6,26,27 When applying this approach, it is convenient to use the position representation. Denoting by |X the eigenstate of the position operator having all the atoms in the position X (with an analogous definition of |XY in the twomolecule Hilbert space), the partition functions Q 1 and Q 2 -defined in Eqs.…”

Section: Second Virial Coefficient Including Intramolecular Flexmentioning

confidence: 99%

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Path-integral calculation of the second virial coefficient including intramolecular flexibility effects

Garberoglio

Jankowski

Szalewicz

et al. 2014

The Journal of Chemical Physics

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We present a path-integral Monte Carlo procedure for the fully quantum calculation of the second molecular virial coefficient accounting for intramolecular flexibility. This method is applied to molecular hydrogen (H2) and deuterium (D2) in the temperature range 15-2000 K, showing that the effect of molecular flexibility is not negligible. Our results are in good agreement with experimental data, as well as with virials given by recent empirical equations of state, although some discrepancies are observed for H2 between 100 and 200 K.

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“…(27) and recalling the definition in Eq. (20), a temperature-dependent rigid-body Hamiltonian for the monomer can be defined as…”

Section: B the Improved Rigid-rotor Approximationmentioning

confidence: 99%

Section: Second Virial Coefficient Including Intramolecular Flexmentioning

confidence: 99%

Path-integral calculation of the second virial coefficient including intramolecular flexibility effects

Garberoglio

Jankowski

Szalewicz

et al. 2014

The Journal of Chemical Physics

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“…We mention in passing that several alternative routes such as various semiclassical approaches [5][6][7][8] or quantum mode-coupling theory 9 have been successfully used to study quantum dynamics of large systems. Numerical PI simulation techniques [10][11][12] are based on the isomorphism 13 between the quantum partition function, represented as an imaginary time PI ͑Refs. 3, 4, 14, and 15͒ and the classical configurational integral of a system of interacting "ring polymers" subject to specific harmonic nearest neighbor interactions.…”

Section: Introductionmentioning

confidence: 99%

On the applicability of centroid and ring polymer path integral molecular dynamics for vibrational spectroscopy

Witt¹,

Ivanov²,

Shiga³

et al. 2009

The Journal of Chemical Physics

222

260

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Centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD) are two conceptually distinct extensions of path integral molecular dynamics that are able to generate approximate quantum dynamics of complex molecular systems. Both methods can be used to compute quasiclassical time correlation functions which have direct application in molecular spectroscopy; in particular, to infrared spectroscopy via dipole autocorrelation functions. The performance of both methods for computing vibrational spectra of several simple but representative molecular model systems is investigated systematically as a function of temperature and isotopic substitution. In this context both CMD and RPMD feature intrinsic problems which are quantified and investigated in detail. Based on the obtained results guidelines for using CMD and RPMD to compute infrared spectra of molecular systems are provided.

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“…by Monte Carlo methods [6], [7]. It turns out that these procedures work quite well in the high temperature regime (ß 0) but that errors are increasing for T 0.…”

Section: B) Functioned Integral Approachmentioning

confidence: 97%

All-Temperature Partition Function from Variationally Optimized Canonical Density Matrix

Baltin

1983

Zeitschrift Für Naturforschung A

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For the canonical density matrix C(r, r 0 ,ß) a variational ansatz C f = (1 -/) C cl + /C gr is made where C cl and C gr are the classical and the ground state expressions which are exact in the hightemperature (ß -> 0) and in the low-temperature limits (ß -* + x)^ respectively, and / is a trial function subject to the restriction that f0for ß -» 0 and f-*• 1 for ß -» oo. With the approximation that / be dependent only upon ß, not upon spatial variables, the mean square error arising when C f is inserted into the Bloch equation is made a minimum. The Euler equation for this variational problem is an ordinary second order differential equation for f=f(ß) to be solved numerically. The method is tested for the exactly solvable case of the onedimensional harmonic oscillator.

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Path-Integral Calculation of the Two-Particle Slater Sum forHe4

Cited by 107 publications

References 7 publications

Path-integral calculation of the second virial coefficient including intramolecular flexibility effects

Path-integral calculation of the second virial coefficient including intramolecular flexibility effects

On the applicability of centroid and ring polymer path integral molecular dynamics for vibrational spectroscopy

All-Temperature Partition Function from Variationally Optimized Canonical Density Matrix

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