^{1}, A-R. Musah

^{1}, E. Curotto

^{1,a)}, David L. Freeman

^{2}and J. D. Doll

^{3}

### Abstract

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 (1983)] 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 . 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, 1981). p. 331] octamer have a ground statewave functions predominantly contained within the basin of attraction. This result contrasts with the structure of the global minimum for the TIP4P potential, which is an cube. Comparisons of the thermodynamic and ground-stateproperties are made with the SPC octamer as well.

We thank Professor K. D. Jordan for suggesting that we examine the quantum melting behavior of the water octamer using the TIP4P potential. This work has been supported by the National Science Foundation (Grant No. CHE0554922). Additionally, E.C. acknowledges the donors of the Petroleum Research Fund, administered by the ACS (Grant No. 48146-B6), The Stacy Ann Vitetta ‘82 Professorship Fund, and The Ellington Beavers Fund for Intellectual Inquiry from Arcadia University for partial support of this research.

I. INTRODUCTION

II. SIMULATION METHODS

A. Stereographic projection path integral

B. Green’s function stereographic projection diffusion Monte Carlo

C. Structural characterization methods

D. Quenching in curved manifolds

III. RESULTS

A. Thermodynamic and ground stateproperties

B. Structural analysis of the TIP4P octamer surface

C. Structural analysis of the VMC walk

D. Structural analysis of the DMC ground state

IV. CONCLUSIONS

### Key Topics

- Wave functions
- 29.0
- Ground states
- 28.0
- Heat capacity
- 20.0
- Thermodynamic properties
- 17.0
- Manifolds
- 16.0

## Figures

(a) Energy of the TIP4P water octamer as a function of temperature. The white squares are the classical simulation data, the gray squares are the quantum results [ and , respectively, in Eq. (7)]. (b) Variational ground state energy of the water TIP4P octamer in hartree graphed as a function of the parameter [cf. Eq. (20)]. (c) Ground state energy estimate from a single GF-SPDMC with a target population size of configurations and [cf. Eq. (20)]. (d) Heat capacity of the TIP4P water octamer in units of the Boltzmann constant, as a function of temperature in kelvin. The white squares are the classical simulation data and the black squares are the quantum results [ and respectively, in Eq. (8)].

(a) Energy of the TIP4P water octamer as a function of temperature. The white squares are the classical simulation data, the gray squares are the quantum results [ and , respectively, in Eq. (7)]. (b) Variational ground state energy of the water TIP4P octamer in hartree graphed as a function of the parameter [cf. Eq. (20)]. (c) Ground state energy estimate from a single GF-SPDMC with a target population size of configurations and [cf. Eq. (20)]. (d) Heat capacity of the TIP4P water octamer in units of the Boltzmann constant, as a function of temperature in kelvin. The white squares are the classical simulation data and the black squares are the quantum results [ and respectively, in Eq. (8)].

Left graph: A plot of the all-atoms SCA distance [cf. Eq. (22)] from the isomer as a function of energy measured for 933 distinct minima of the TIP4P water octamer. Right graph: A plot of the O-atoms SCA distance from the isomer as a function of energy measured for 933 distinct minima of the TIP4P water octamer.

Left graph: A plot of the all-atoms SCA distance [cf. Eq. (22)] from the isomer as a function of energy measured for 933 distinct minima of the TIP4P water octamer. Right graph: A plot of the O-atoms SCA distance from the isomer as a function of energy measured for 933 distinct minima of the TIP4P water octamer.

A graph of the ground state density projected along the all-atoms SCA distance [cf. Eq. (22)] from the cube obtained from the VMC simulations (dots) and the GF-SPDMC simulation (lines).

A graph of the ground state density projected along the all-atoms SCA distance [cf. Eq. (22)] from the cube obtained from the VMC simulations (dots) and the GF-SPDMC simulation (lines).

A graph of the ground state density projected along the all-atoms SCA distance [cf. Eq. (22)] from the cube obtained from the VMC simulations (dots) and the GF-SPDMC simulation (lines).

A graph of the ground state density projected along the O-atoms SCA distance from the cube [cf. Eq. (24)] obtained from the VMC simulations (dots) and the GF-SPDMC simulation (lines).

A graph of the ground state density projected along the O-atoms SCA distance from the cube [cf. Eq. (24)] obtained from the VMC simulations (dots) and the GF-SPDMC simulation (lines).

A plot of the all-atoms SCA distance [cf. Eq. (22)] from the global minimum ( cube) as a function of energy measured for all distinct minima of the TIP4P water octamer (black squares), compared to the same measure from the global minimum ( cube) for the SCP octamer.

A plot of the all-atoms SCA distance [cf. Eq. (22)] from the global minimum ( cube) as a function of energy measured for all distinct minima of the TIP4P water octamer (black squares), compared to the same measure from the global minimum ( cube) for the SCP octamer.

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