_{2,3}Br

_{2}clusters

^{1,a)}, Rita Prosmiti

^{1}, Pablo Villarreal

^{1}and Gerardo Delgado-Barrio

^{1}

### Abstract

Quantum dynamics calculations are reported for the tetra-, and penta-atomic van der Waals He_{N}Br_{2} complexes using the multiconfiguration time-dependent Hartree (MCTDH) method. The computations are carried out in satellite coordinates, and the kinetic energy operator in this set of coordinates is given. A scheme for the representation of the potential energy surface based on the sum of the three-body HeBr_{2} interactions at CSSD(T) level plus the He-He interaction is employed. The potential surfaces show multiple close lying minima, and a quantum description of such highly floppy multiminima systems is presented. Benchmark, full-dimensional converged results on ground vibrational/zero-point energies are reported and compared with recent experimental data available for all these complexes, as well as with previous variational quantum calculations for the smaller HeBr_{2} and He_{2}Br_{2} complexes on the same surface. Some low-lying vibrationally excited eigenstates are also computed by block improved relaxation calculations. The binding energies and the corresponding vibrationally averaged structures are determined for different conformers of these complexes. Their relative stability is discussed, and contributes to evaluate the importance of the multiple-minima topology of the underlying potential surface.

The authors thank to Centro de Calculo (IFF), CTI (CSIC), and CESGA for allocation of computer time. This work has been supported by DGICYT, Spain, Grant No. FIS2010-18132. We also would like to thank O. Roncero for helpful discussions.

I. INTRODUCTION

II. METHODOLOGY AND COMPUTATIONAL DETAILS: BOUND STATE CALCULATIONS

A. Potential form

B. MCTDH: improved relaxation calculations

III. RESULTS AND DISCUSSION

IV. CONCLUSIONS

### Key Topics

- Potential energy surfaces
- 12.0
- Cluster dynamics
- 7.0
- Bound states
- 5.0
- Excited states
- 5.0
- Ab initio calculations
- 4.0

## Figures

Schematic representation of coordinate system for He_{3}Br_{2} complex.

Schematic representation of coordinate system for He_{3}Br_{2} complex.

Contour plots of the He_{3}Br_{2} potential energy surface, V(*r*, *R* _{1}, *R* _{2}, *R* _{3}, θ_{1}, θ_{2}, θ_{3}, φ_{1}, φ_{2}) in the ZX (a and b) and XY (c and d) Cartesian planes. The Br_{2} distance is fixed at 2.281 Å along the Z-axis, while the geometry of the tetra-atomic molecule is fixed to a linear (0,2) configuration (a), police-nightstick (1,1) configuration (b and c), and tetrahedral (2,0) configuration (d) with the He atoms in the equilibrium positions of Table I. Contour intervals are of 5 cm^{−1} for energies from 135 to 80 cm^{−1}.

Contour plots of the He_{3}Br_{2} potential energy surface, V(*r*, *R* _{1}, *R* _{2}, *R* _{3}, θ_{1}, θ_{2}, θ_{3}, φ_{1}, φ_{2}) in the ZX (a and b) and XY (c and d) Cartesian planes. The Br_{2} distance is fixed at 2.281 Å along the Z-axis, while the geometry of the tetra-atomic molecule is fixed to a linear (0,2) configuration (a), police-nightstick (1,1) configuration (b and c), and tetrahedral (2,0) configuration (d) with the He atoms in the equilibrium positions of Table I. Contour intervals are of 5 cm^{−1} for energies from 135 to 80 cm^{−1}.

Angular and radial probability density distributions of the indicated He_{2}Br_{2} (0,2), (1,1), and (2,0) conformers, respectively. The set of coordinates used to describe the He_{2}Br_{2} complex is (*r*, *R* _{1}, *R* _{3}, θ_{1}, θ_{3}, φ_{1}) (see Fig. 1). In the top and bottom panels we add a subindex to the legends indicating if we are considering the He_{1} (solid lines) or the He_{3} (dashed lines). In the top panel, we plot the distributions in θ_{1, 3}, in the central panel in φ_{1}, and in the bottom panel in R_{1, 3}.

Angular and radial probability density distributions of the indicated He_{2}Br_{2} (0,2), (1,1), and (2,0) conformers, respectively. The set of coordinates used to describe the He_{2}Br_{2} complex is (*r*, *R* _{1}, *R* _{3}, θ_{1}, θ_{3}, φ_{1}) (see Fig. 1). In the top and bottom panels we add a subindex to the legends indicating if we are considering the He_{1} (solid lines) or the He_{3} (dashed lines). In the top panel, we plot the distributions in θ_{1, 3}, in the central panel in φ_{1}, and in the bottom panel in R_{1, 3}.

Probability density distributions in θ_{1} (black/solid), θ_{2} (red/gray), and θ_{3} (blue/dashed) in degrees of the He_{3}Br_{2} (1,2), (2,1), and (3,0) conformers in the top, central, and bottom panels, respectively.

Probability density distributions in θ_{1} (black/solid), θ_{2} (red/gray), and θ_{3} (blue/dashed) in degrees of the He_{3}Br_{2} (1,2), (2,1), and (3,0) conformers in the top, central, and bottom panels, respectively.

Probability density distributions in R_{1} (black/solid), R_{2} (red/gray), and R_{3} (blue/dashed) in angstroms of the He_{3}Br_{2} (1,2), (2,1), and (3,0) conformers in the top, central, and bottom panels, respectively.

Probability density distributions in R_{1} (black/solid), R_{2} (red/gray), and R_{3} (blue/dashed) in angstroms of the He_{3}Br_{2} (1,2), (2,1), and (3,0) conformers in the top, central, and bottom panels, respectively.

Two dimensional angular density distributions in φ_{1} and φ_{2} in degrees of the He_{3}Br_{2} (1,2), (2,1), and (3,0) conformers in the top, central, and bottom panels, respectively.

Two dimensional angular density distributions in φ_{1} and φ_{2} in degrees of the He_{3}Br_{2} (1,2), (2,1), and (3,0) conformers in the top, central, and bottom panels, respectively.

## Tables

Potential well-depths (D_{ e } in cm^{−1}) and equilibrium distances (R_{ e } in angstroms and in degrees) for the different (#T,#L) minima of the He_{N}Br_{2} systems, with *N*=1,2,3 and r_{ e }= 2.281 Å.

Potential well-depths (D_{ e } in cm^{−1}) and equilibrium distances (R_{ e } in angstroms and in degrees) for the different (#T,#L) minima of the He_{N}Br_{2} systems, with *N*=1,2,3 and r_{ e }= 2.281 Å.

CCSD(T) interaction energies and their complete basis set limit values using small-core ECP10MDF pseudopotentials in conjunction with the indicated AVXZ-PP and AVXZ (with X=T, Q, and 5) basis sets for Br atoms and He atoms, respectively. B stands for a bending configuration of one of the He-atoms (see Fig. 2(a)).

CCSD(T) interaction energies and their complete basis set limit values using small-core ECP10MDF pseudopotentials in conjunction with the indicated AVXZ-PP and AVXZ (with X=T, Q, and 5) basis sets for Br atoms and He atoms, respectively. B stands for a bending configuration of one of the He-atoms (see Fig. 2(a)).

Parameters used in the POTFIT program. We include for each coordinate its range, the number of the primitive basis sets and the type of them. The number of natural potentials (see text) the relevant regions of the potential considered and the rms error for the fits are also listed. Contr indicates the mode over which a contraction is performed.

Parameters used in the POTFIT program. We include for each coordinate its range, the number of the primitive basis sets and the type of them. The number of natural potentials (see text) the relevant regions of the potential considered and the rms error for the fits are also listed. Contr indicates the mode over which a contraction is performed.

Number of SPF and least populated orbital population of the MCTDH *improved relaxation* calculations.

Number of SPF and least populated orbital population of the MCTDH *improved relaxation* calculations.

Vibrationally averaged structures (), ZPE, and binding energies (D_{0}) for the different He_{N}Br_{2} isomers, with *N*=1,2,3. The comparison with experimental observations (Ref. 9) and previous theoretical results (Refs. 29 and 34) is also included. Distances are in angstroms and energies are in cm^{−1}.

Vibrationally averaged structures (), ZPE, and binding energies (D_{0}) for the different He_{N}Br_{2} isomers, with *N*=1,2,3. The comparison with experimental observations (Ref. 9) and previous theoretical results (Refs. 29 and 34) is also included. Distances are in angstroms and energies are in cm^{−1}.

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