Excited States of Weakly Bound Bosonic Clusters:  Discrete Variable Representation and Quantum Monte Carlo

Nightingale, M. P.; Roy, Pierre‐Nicholas

doi:10.1021/jp056577q

Cited by 15 publications

(7 citation statements)

References 23 publications

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“…There have been extensive theoretical studies of the bound state energy levels and structures of weakly bound bosonic van der Waals trimers for J = 0 in the literature during the past two decades. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] Rovibrational calculations have been carried out only recently for Ne 3 by Salci et al, 18 and for Ar 3 by Márquez-Mijares et al 19 and Karlický et al, 20 while He 3 has been found to support no J > 0 bound state. 21 In the present work, we study theoretically the bosonic rare gas van der Waals trimer Ne 3 .…”

Section: Introductionmentioning

confidence: 99%

A theoretical study of Ne3 using hyperspherical coordinates and a slow variable discretization approach

Suno

2011

The Journal of Chemical Physics

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We study theoretically the ground and excited bound states of the bosonic rare gas van der Waals trimer Ne(3). A slow variable discretization approach is adopted to solve the nuclear Schrödinger equation, in which the Schrödinger equation in hyperangular coordinates is solved using basis splines at a series of fixed finite-element methods discrete variable representation hyper-radii. We consider not only zero total nuclear orbital angular momentum, J = 0, states but also J > 0 states. By using the best empirical neon dimer interaction potentials, all the bound state energy levels of Ne(3) will be calculated for total angular momenta up to J = 6, as well as their average root-mean-square radii. We also analyze the wave functions in hyperspherical coordinates for several selected bound states.

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Section: Introductionmentioning

confidence: 99%

A theoretical study of Ne3 using hyperspherical coordinates and a slow variable discretization approach

Suno

2011

The Journal of Chemical Physics

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“…Clearly, variational ͑VMC͒ and DMC are much simpler in flat manifolds. [87][88][89][90][91][92][93][94][95][96][97][98][99][100][101][102] The works we have cited are applications of VMC and DMC to clusters in Cartesian coordinates, and constitute only a small sample of the most recent investigations. On the other hand, diffusion in manifolds remains a topic of research in pure mathematics as well as mathematical physics.…”

Section: Introductionmentioning

confidence: 99%

The thermodynamic and ground state properties of the TIP4P water octamer

Asare

Musah

Curotto

et al. 2009

The Journal of Chemical Physics

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Several stochastic simulations of the TIP4P ͓W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, J. Chem. Phys. 79, 926 ͑1983͔͒ water octamer are performed. Use is made of the stereographic projection path integral and the Green's function stereographic projection diffusion Monte Carlo techniques, recently developed in one of our groups. The importance sampling for the diffusion Monte Carlo algorithm is obtained by optimizing a simple wave function using variational Monte Carlo enhanced with parallel tempering to overcome quasiergodicity problems. The quantum heat capacity of the TIP4P octamer contains a pronounced melting peak at 160 K, about 50 K lower than the classical melting peak. The zero point energy of the TIP4P water octamer is 0.0348Ϯ 0.0002 hartree. By characterizing several large samples of configurations visited by both guided and unguided diffusion walks, we determine that both the TIP4P and the SPC ͓H. J. C. Berendsen, J. P. Postma, W. F. von Gunsteren, and J. Hermans, ͑Intermolecular Forces, Reidel, 1981͒. p. 331͔ octamer have a ground state wave functions predominantly contained within the D 2d basin of attraction. This result contrasts with the structure of the global minimum for the TIP4P potential, which is an S 4 cube. Comparisons of the thermodynamic and ground-state properties are made with the SPC octamer as well.

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“…The vibrational shift for the trimers can also be calculated exactly and perturbatively using the Lanczos diagonalization in Pekeris coordinates. − These shifts are shown in Table , along with the simulation and experimental results. For each of the isotopologues, 90 dimensionless Jacobi DVR basis functions were used over 15000 iterations with a V max of 1000 cm –1 for all cases except for the Lanczos–Exact calculation with (pH 2 ) 3 ( V max = 1100 cm –1 ).…”

Section: Resultsmentioning

confidence: 99%

“…The results of the trimer bound state energy calculations, , performed using the Lanczos diagonalization scheme, are shown in Table using both the full pointwise H1-P and our fitted H1-MLR. We find two bound states for (pH 2 ) 3 , three for (oD 2 ) 3 , and four for (pT 2 ) 3 .…”

Section: Resultsmentioning

confidence: 99%

Raman Vibrational Shifts of Small Clusters of Hydrogen Isotopologues

et al. 2015

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Raman vibrational shifts of small parahydrogen (pH2), orthodeuterium (oD2), and paratritium (pT2) clusters with respect to the free molecules are calculated by combining a first order perturbation theory approach with Langevin equation Path Integral Ground State (LePIGS) simulations [ J. Phys. Chem. A 2013 , 117 , 7461 ]. Our theoretical predictions are compared to existing cryogenic free jet expansion results for pure (pH2)N clusters [ Phys. Rev. Lett. 2004 , 92 , 223401 ] and to new measurements for (oD2)N clusters reported here. This method has been successfully used before to predict the Raman vibrational shifts of (pH2)N clusters [ J. Chem. Phys. 2014 , 141 , 014310 ]. The 6-D interaction potential of Hinde [ J. Chem. Phys. 2008 , 128 , 154308 ] is reduced to 1-D using the Adiabatic Hindered Rotor approximation to yield effective pair potentials for both molecules being in the ground vibrational state, and for one of them carrying one quantum of vibrational excitation. These reduced 1-D potentials are fitted to a Morse Long Range analytic form for later convenience. Good agreement between experiment and theory is found for the smaller clusters, but significant deviations remain for the larger ones.

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Excited States of Weakly Bound Bosonic Clusters: Discrete Variable Representation and Quantum Monte Carlo

Cited by 15 publications

References 23 publications

A theoretical study of Ne3 using hyperspherical coordinates and a slow variable discretization approach

A theoretical study of Ne3 using hyperspherical coordinates and a slow variable discretization approach

The thermodynamic and ground state properties of the TIP4P water octamer

Raman Vibrational Shifts of Small Clusters of Hydrogen Isotopologues

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