Stereographic projection path integral simulations of (HCl)n clusters (n=2–5): Evidence of quantum induced melting in small hydrogen bonded networks

Avilés, Michael W.; McCandless, Michelle L.; Curotto, E.

doi:10.1063/1.2837802

Cited by 18 publications

(25 citation statements)

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“…In a series of works [63][64][65][66][67][68][69][70] we have extended the reweighted random series approach [104][105][106][107][108][109][110] to the imaginary time path integral in manifolds that are mappable by stereographic projections. The random series expansion of the path consists of k m core terms and an additional 3k m tail terms,…”

Section: A Stereographic Projection Path Integralmentioning

confidence: 99%

“…64,67,69 We extend the reweighted random series method [104][105][106][107][108][109][110] and the finite difference estimators 108 for cubically convergent path integral simulations to manifolds. 68 DMC simulations are nearly as straightforward to implement in curved spaces mapped with stereographic projection coordinates as they are with Cartesian coordinates. 72 As the only difference, the distribution of the diffusion step in curved spaces is generally not a simple Gaussian, and several straight-forward rejection techniques have been tested successfully.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, diffusion in manifolds remains a topic of research in pure mathematics as well as mathematical physics. 103 In both PIMC [63][64][65][66][67][68][69][70] and DMC 71,72 simulations in curved spaces, we find it highly advantageous to make use of stereographic projections. Our methods based on stereographic projection coordinates have been tested on a number of simple systems solvable by basis set methods, and several molecular clusters.…”

Section: Introductionmentioning

confidence: 99%

“…43 One of our groups has been involved in the development of quantum methods for the efficient simulation of molecular aggregates. [63][64][65][66][67][68][69][70][71] Constraining intramolecular degrees of freedom proves crucial in overcoming convergence difficulties with path integral Monte Carlo ͑PIMC͒ and DMC simulations of molecular clusters. The time scale difference between the intramolecular and the intermolecular degrees of freedom in typical molecular aggregates is sufficiently large to cause inefficiencies in DMC simulations, and to make the convergence of PIMC simulations a formidable task.…”

Section: Introductionmentioning

confidence: 99%

“…71 Water clusters in the dimer through the octamer range have already served to gauge the feasibility of the stereographic projection path integral ͑SPPI͒ methods. 68 Recently, we have explored the possibility to control the adiabatic approximation for water by allowing for couplings with high frequency modes. 70 In a recent article we develop and test several importance sampling strategies for stereographic projection DMC in curved manifolds.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: A Stereographic Projection Path Integralmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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Quantum monte carlo methods for constrained systems

Wolf

Curotto

Mella

2014

Int. J. Quantum Chem.

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The torsional ground state for ethane, the torsional, rotational, and mixed torsional and rotational ground state of propane are computed with a version of diffusion Monte Carlo adapted to handle the geometric complexity of curved spaces such as the Ramachandra space. The quantum NVT ensemble average for the mixed torsional and rotational degrees of freedom of propane is computed, using a version of Monte Carlo path integral, also adapted to handle curved spaces. These three problems are selected to demonstrate the generality and the applicability of the approaches described. The spaces of coordinates can be best constructed from the parameters of continuous Lie groups, and alternative methods based on vector spaces, where extended Lagrangian terms would be too cumbersome to implement. We note that the geometric coupling between the torsions and the rotations of propane produces a substantial effect on the ground state energy of propane, and that the quantum effects on the energy of propane are quite large even well above room temperature.

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Re‐weighted random series path integral simulations of molecular clusters: Applications to lithium solvated by a mixed Stockmayer cluster

Hyers

Fodor

Bierwisch

et al. 2019

Int J of Quantum Chemistry

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Nuclear quantum effects in finite temperature simulations of molecular clusters are determined by taking advantage of a recently developed method based on the Feynman Path Integral. The structural and thermodynamic properties, including the nuclear quantum effects are determined for three Stockmayer clusters. The ionic system contain a lithium ion solvated by six strong dipoles and 12 weaker ones. The presence of the ion in the mixed Stockmayer cluster drastically enhances the fluxional nature of the less polar components which occupy the second solvation layer, whereas the neutral counterpart has the effect of reducing it. The nuclear quantum effects are significant at room temperature and above for the solvated ionic system. These are attributable to two factors: (a) the lightness of the lithium ion and (b) the stiffness of the ion-dipole interactions. At 300 K, the difference between the fully converged quantum and the classical heat capacities is about 1.3 K B for the ionic cluster. This difference is about 10 SDs obtained from 95% confidence estimates of the statistical fluctuations. Cubic convergence is confirmed for temperatures as low as 50 K by regression analysis. The nuclear quantum effects do not change the peak melting temperature of the cluster. K E Y W O R D S nuclear quantum effects, lithium ion, re-weighted random series path integral, generalized coordinates, stereographic projections 1 | INTRODUCTIONClusters are gas phase nano-sized aggregates of matter, they are vitally important for technological advances, and can serve as model systems to untangle and simplify the investigation of otherwise intractable problems at the fundamental level using a combination of theoretical and experimental methods. The contributions along these two lines are so numerous that it would be impossible to provide a meaningful comprehensive review of the literature [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] within the confines of a research article. One fundamental issue that can be addressed theoretically and experimentally using clusters is the determination of the nuclear quantum effects on the dynamics [20] and thermodynamics of microsolvation. Learning about the timescales of solvent rearrangement dynamics as a solute particle suddenly changes its charged state, and how these are impacted by the interaction parameters, the nuclear quantum effects, and the size of the cluster, are the long term objectives of our efforts. In this work we focus on the equilibrium properties since these will provide the needed insight as well as the starting points for later quantum dynamic studies.The determination of nuclear quantum effects in finite temperature simulations of molecular clusters, such as those concerning us here, remains challenging. In these complex systems, the intramolecular degrees of freedom are associated with frequencies that are many times larger than

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Stereographic projection path integral simulations of (HCl)n clusters (n=2–5): Evidence of quantum induced melting in small hydrogen bonded networks

Cited by 18 publications

References 81 publications

The thermodynamic and ground state properties of the TIP4P water octamer

The thermodynamic and ground state properties of the TIP4P water octamer

Quantum monte carlo methods for constrained systems

Re‐weighted random series path integral simulations of molecular clusters: Applications to lithium solvated by a mixed Stockmayer cluster

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