Article pubs.acs.org/JPCA
Theoretical Investigation of the He4Br2 Conformers Á lvaro Valdés,* Rita Prosmiti, Pablo Villarreal, and Gerardo Delgado-Barrio Instituto de Física Fundamental (IFF-CSIC), CSIC, Serrano 123, 28006 Madrid, Spain ABSTRACT: Full dimensional quantum dynamics calculations of the three lowest isomers of the He4Br2 van der Waals molecule in its ground electronic state are reported. The calculations are performed using the multiconfiguration timedependent Hartree (MCTDH) method and a realistic potential form that includes the sum of three body ab initio coupled-cluster single double triple [CCSD(T)] He−Br2 interactions plus the He−He and Br−Br interactions. This potential exhibits several multiple minima, with the three lowest ones lying very close in energy, just within 2 cm−1. Such small differences are also found in the calculated binding energies of the three most stable conformers, indicating the floppiness of the system and, thus, the need of accurate potential forms and quantum full dynamics methods to treat this kind of complexes. The 12 dimensional results reported in this work present benchmark data and, thus, can serve to evaluate approximate methods aiming to describe higher order rare gas−dihalogen (N > 4) complexes. A comparison with previous studies using different potential forms and approaches to the energetics for the He4Br2 cluster is also presented.
I. INTRODUCTION The weakly bound RgN−XY clusters, with Rg being a rare gas atom and XY a dihalogen molecule, have been the subject of a large number of studies over the last 30 years,1−10 since the first works of Levy et al. on HeI2.11,12 Many of these van der Waals (vdW) systems have been studied in their triatomic form. The rich dynamics of the processes involved and their relative simplicity for the theoretical investigations offer ideal conditions for the interaction between theory and experiment, which benefit reciprocally with the improvement of the experimental techniques and theoretical methods. For the triatomic systems, the development of the ab initio theory and the increase of the computational force lead to an almost quantitative description of the Rg−XY systems in their ground electronic states13−17 and even in some electronically excited ones.18,19 For tetra-atomic systems, the ab initio electronic structure calculations are computationally more expensive, and the representation of the potential energy surface (PES) is getting much more complicated. Thus, some model of the potential forms needs to be adopted. A potential form consisting of the sum of three-body (3B) Rg−XY terms based on high quality ab initio calculations at the CCSD(T) level, plus the He−He interaction, has been found to provide an accurate representation of the PES for larger RgNXY clusters.20−25 Moreover, using such a form, exact five-dimensional (5D) variational calculations have been performed for N = 2,20−23 and a very good quantitative agreement with the available experimental data has been achieved.26 When moving to larger clusters, the difficulty for the theoretical studies increases dramatically, and the limitations are present for both electronic structure and full dimensional nuclear quantum dynamics calculations. In particular, to calculate the energetics and structures of these complexes, different © 2012 American Chemical Society
approximated methods have emerged to deal with the nuclear part.27−29 Among the RgNXY species, the HeNBr2 clusters have been the most widely studied due to the implication of He nanodroplets in the experiments of “quantum environment”.30−32 Diffusion Monte Carlo (DMC) calculations of the ground state energies and wave functions have been performed up to N = 24, using two different model potentials based on the sum of pairwise additive two-body (2B) and 3B terms.33 Also, several studies have been carried out using quantum-chemistrylike methods and potential forms based on a sum of atom−atom pairwise interactions. On the basis of a Hartree-like approach, HeNBr2 clusters up to N = 60 have been characterized,27 while configuration-interaction and full-configuration-interaction methods have been applied up to only N = 5 and 4, respectively.28,29 Recent studies on He2Br2 and He2ICl24,25 showed that very accurate calculations are possible for these clusters using the multiconfiguration time-dependent Hartree (MCTDH) method34−36 as compared to the previous exact 5D variational calculations.20,22 Also, the combination of the MCTDH method with a reliable analytical potential form allows a direct comparison with the experimental measurements as have been recently shown for HeNBr2 and HeNICl, with N = 1, 2, 324−26 at their ground electronic states. Such potential form is based on the sum of three-body He−XY interactions plus the He−He interaction, with the He−XY potential being the ab initio CCSD(T) parametrized potential of He−Br2 and He−ICl, respectively.25,37−39 The MCTDH method allows the treatment of more degrees of freedom (applications of up to 24 have been Received: March 20, 2012 Revised: June 5, 2012 Published: June 5, 2012 7169
dx.doi.org/10.1021/jp3026682 | J. Phys. Chem. A 2012, 116, 7169−7176
The Journal of Physical Chemistry A
Article
reported in the literature)40,41 and reaches its best performance for systems with 4−12 degrees of freedom. Therefore, it becomes an excellent bridge between the exact variational quantum calculations and other approximated methods designed to deal with higher order clusters. In this work, we take advantage of the MCTDH method capabilities to perform a full dimensional (12D) computation for studying the He4Br2 system. Unfortunately, there is not yet any experimental evidence of this molecule, although other similar systems have been observed.26 The present study can serve as a useful guide for future spectroscopic investigations on small HeNBr2 clusters and provides benchmark results of the binding energies and isomeric structures of the He4Br2 complex. The paper is organized as follows. In the section II, we describe some computational and methodological details of the MCTDH computations of the lowest He4Br2 conformers. The results of these calculations are presented in section III. Three different conformers are characterized, and the present result of the lowest structures is discussed in comparison with the theoretical calculations available in the literature. The last section contains some concluding remarks.
Figure 1. Schematic representation of coordinate system for the He4Br2 complex.
V (r, R1, R 2, R3, R 4) 4
=
4
∑ VHeBr (r, R k) + ∑ VHe − He(R k , R l) + UBr (r) 2
k
II. METHODOLOGY AND COMPUTATIONAL DETAILS: MCTDH CALCULATIONS The Heidelberg MCTHD code is used to perform the calculation of the different conformers using the improved relaxation method.34−36 The molecular Hamiltonian of the He4−Br2 in satellite coordinates (r,Rk), with r being the vector between the two Br atoms and Rk (k = 1, 2, 3, 4) being the vectors from the center of mass of the Br2 molecule to the He atoms, can be written as: 2
j ℏ2 ∂ 2 + + Ĥ = − 2 2m ∂r 2mr 2 −
ℏ2 m Br2
⎛
(2)
where the corresponding VHeBr2(r,Rk) terms are the CCSD(T) parametrized potential of the HeBr 2 complex, 37 the VHe−He(Rk,Rl) terms are the potential function for He2 given in ref 44, and UBr2(r) is the diatomic interaction Br−Br potential from refs 37 and 45. The PESs of rare gas-homonuclear dihalogen complexes in the electronic ground state X support a double-minima topology, corresponding to linear and T-shaped configurations.16,37,45 Here, for the He4Br2 system, the three nonequivalent lowest minima of the potential form of eq 2 are calculated and presented in Table 1. These minima are formed by combinations of the
l2k ⎞ ∂2 ⎟ + 2 2μR k2 ⎠ k = 1 ⎝ 2μ ∂R k 4
2
k
