parallel tempering monte carlo simulations of the water heptamer anion

Chemical Physics Letters 455 (2008) 135–138

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Chemical Physics Letters

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Parallel tempering Monte Carlo simulations of the water heptamer anion

Albert DeFusco a, Thomas Sommerfeld b, Kenneth D. Jordan a,*

a Department of Chemistry and the Center for Molecular and Materials Simulations, University of Pittsburgh, Pittsburgh, PA 15260, USAb Department of Chemistry and Physics, Southeastern Louisiana University, Hammond, LA 70402, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 8 February 2008In final form 25 February 2008Available online 29 February 2008

0009-2614/$ - see front matter � 2008 Elsevier B.V. Adoi:10.1016/j.cplett.2008.02.081

* Corresponding author. Fax: +1 412 624 8611.E-mail address: [email protected] (K.D. Jordan).

Parallel tempering Monte Carlo simulations of the water heptamer anion have been performed for tem-peratures ranging from 42 to 200 K. At low temperatures, a single peak near 250 meV in the electronbinding energy distribution is obtained, while at high temperatures a second, weak peak near 450 meVis obtained, in good agreement with those observed experimentally. It is further confirmed that the highelectron binding energies are due to hydrogen bonding networks with large net dipole moments and, inmost cases, also containing a single double-acceptor monomer, while weak electron binding arises fromconfigurations with smaller dipoles.

� 2008 Elsevier B.V. All rights reserved.

1. Introduction

Negatively charged water clusters have been known since theirobservation, mass spectroscopically, by Haberland et al. in 1984[1,2]. However, only recently, with the application of vibrationalpredissociation spectroscopy, has a clear picture of the geometricalstructures of small ðH2OÞ�n clusters emerged [3–14]. ðH2OÞ�7 is par-ticularly intriguing in that the recent predissociation studies ofRoscioli and co-workers have revealed the existence of at least fourisomers, three with high electron binding energies (EBE) and con-taining a double-acceptor (AA) monomer and one with low EBEand lacking an AA monomer [14]. In the present study paralleltempering Monte Carlo (PTMC) [15] simulations are used togetherwith the quantum Drude model [16–19] to characterize the ðH2OÞ�7cluster at finite temperatures. Configurations sampled at T = 200,142, and 100 K are quenched to local minima to provide insightinto the types of structures that are present under equilibriumconditions.

2. Computational details

In carrying out simulations of negatively charged water clus-ters, it is crucial to employ a theoretical method that accurately de-scribes both the water–water and the electron–water interactions[20–22]. In principle, this could be accomplished using ab initioelectronic structure methods; but to achieve the accuracy requirednecessitates the use of a large-basis set and inclusion of high-orderelectron correlation effects, e.g., using the CCSD(T) method [23,24].

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The high computational cost of such calculations precludes theiruse in Monte Carlo or molecular dynamics simulations where mil-lions of configurations need to be sampled. In this work, we cir-cumvent this problem by using the distributed point polarizable(DPP) [25] water model to describe the water–water interactionsand the quantum Drude model [16–19] to describe the excess elec-tron–water interactions. The total energy of the anion is given bythe energy of the neutral water cluster minus the electron bindingenergy. (Here we are employing the convention that a bound anionhas a positive EBE.) This model potential approach has been foundto give electron binding energies and relative energies of differentisomers in excellent agreement with the results of high-level abinitio electronic structure calculations, but because it is orders ofmagnitude computationally faster than ab initio calculations [26],it can be used in finite temperature simulations.

The DPP and quantum Drude models have been described indetail in Refs. [25,16–19]. Here we note that the DPP model, likethe TTM2-R model [27], employs rigid monomers, with the exper-imental gas-phase values of the OH bond distance and HOH angle,three point charges (0.574 jej on the H atoms and �1.148 jej on anM site, displaced 0.25 Å from O atom toward the H atoms along theHOH bisector). With these charges and their locations, the DPPmodel gives dipole and quadrupole moments close to the experi-mental values for the monomer. Each monomer has three, atomcentered, polarizable sites, and mutual interaction between polar-izable sites on a monomer are permitted. A Thole-type dampingprocedure [28] is used for charge–induced-dipole and induced-dipole–induced-dipole interactions. Damped C6/R6 dispersioninteractions are employed between O atoms, and exponentialrepulsion interactions are employed between all atoms of differentmonomers. The Hamiltonian for the excess electron includesinteractions with the point charges, the induced-dipoles, and a

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Fig. 2. Structural motifs sampled in the PTMC simulations of ðH2OÞ�7 . The non-AAspecies are labeled as prism, open-prism, and cage, drawing on their resemblance tolow-energy isomers of (H2O)6. Isosurfaces containing 80% of the excess electrondensity are plotted. The color codes match those in later figures.

136 A. DeFusco et al. / Chemical Physics Letters 455 (2008) 135–138

short-range repulsive core associated with each monomer. The ex-cess electron also interacts with a quantum Drude oscillator, cen-tered on the M site on each monomer, to account for theelectron–water induction and dispersion interactions. The electronbinding energy is calculated through a configuration interactionmethod with a Gaussian basis set [19] for the excess electronand harmonic oscillator functions for each Drude oscillator.

The simulations were carried out using the PTMC algorithm[15,29], which helps avoid trapping in local regions of configura-tion space. In the application of the PTMC method to ðH2OÞ�7 ,twelve replicas, with temperatures ranging from 42 to 200 K, wereemployed. Most moves within each replica are carried out withstandard Metropolis sampling [30], with every 250th move involv-ing attempted exchanges between replicas at adjacent tempera-tures. The Metropolis moves (translations and rotations) involveddisplacements of single water molecules only. The maximum stepsizes and the temperature values used were chosen so that about50% of the Metropolis and exchange moves are accepted. The sim-ulations employed an equilibration period of three million moves,followed by a production period of four million moves (for eachreplica). For the T = 100, 142, and 200 K replicas, every thousandthconfiguration was saved and used for subsequent quenching to alocal minimum through numerical geometry optimization usingthe Broyden–Fletcher–Goldfarb–Shanno (BFGS) method [31].

3. Results

Fig. 1 reports the temperature dependence of the EBE distribu-tions of ðH2OÞ�7 obtained from the PTMC simulations. At T = 50 K,there is a single relatively narrow peak centered near an EBE of240 meV. As the temperature increases, this feature broadensand moves to lower energies. At high (i.e., T = 200 K) temperatures,a weak, broad peak centered near an EBE of 450 meV, also appears.It is clear from these results that there are two classes of structures,one with low ([300 meV) EBEs and the other with high( J 400 meV) EBEs, with the latter acquiring sizable populationonly at high temperatures. The energies of the peaks in the EBE dis-tributions are in excellent agreement with those in the experimen-tal photoelectron spectra [14,32], although the experimentalstudies show a strong preference for the high EBE isomers, evenin the case of the Ar-tagged clusters, for which the temperatureis estimated to be �50 K.

Selected low-energy forms of ðH2OÞ�7 obtained from thequenching calculations are illustrated in Fig. 2. For each speciesthe isosurface encompassing 80% of the excess electron density

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Fig. 1. Electron binding energy distributions associated with the T = 100, 142, and200 K replicas in the PTMC simulations of ðH2OÞ�7 .

as calculated with the Drude/DPP model is plotted. All of these spe-cies can be viewed as originating from insertion of a water mono-mer into one of the edges of cage and prism isomers of (H2O)6 [33].It is also useful to differentiate the isomers according to whether ornot they contain an AA binding site.

Fig. 3 reports for ðH2OÞ�7 the total energies relative to that of theglobal minimum isomer as well as the electron binding energies ofthe quenched isomers. The global minimum is a prism-type non-AA species with an EBE of 246 meV. This isomer was identified inthe theoretical work of Kim et al. [34] who denoted it ‘PRB.’ (Theenergy of the PRB isomer appears to have been incorrectly reportedin Ref. [34], and as a result it was not recognized as the global min-imum in that work.) The quenching calculations locate a total of 35isomers energetically below the most stable AA isomer, PNFA,which was also identified in Ref. [34] and which is predicted inthe present study to be 61 meV above the global minimum. Mostof these low-energy structures, are prism-like and were not re-ported in earlier theoretical studies of ðH2OÞ�7 [34,35]. With oneexception, all isomers below the most stable AA species have low([250 meV) EBE’s. The exception is isomer H-b, which is calcu-lated to lie 56 meV above the global minimum, with an EBE of445 meV. This isomer is shown in Fig. 4 together with other se-lected low-energy isomers, including the global minimum. Fig. 5reports the EBEs vs. the dipole moments of the neutral clustersassociated with the anionic isomers obtained by quenching theconfigurations sampled in the T = 200 K replica. Overall there is astrong correlation between the EBE and dipole moment indepen-dent of whether or not the cluster contains an AA site.

As is apparent from Figs. 3c and 6, the T = 200 K replica includesa large number of AA isomers with high (up to 790 meV) EBE’s.Many of these have ‘branched structures’, some of which are de-picted in Fig. 6. Presumably, the barriers for rearranging these‘open’ isomers to the more stable, more ‘compact’ isomers, arerelatively low. In that case, the branched isomers, if formed exper-imentally, would be expected to be ‘annealed out’ in the supersonic

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Fig. 3. Relative total energies and electron binding energies of quenched structures from the T = (a) 100, (b) 142, and (c) 200 K replicas in the PTMC simulations of ðH2OÞ�7 . AAisomers are labeled with pluses (blue), cages as triangles (red), open structures as squares (green), and prisms as circles (black). Open circles (black) in (c) correspond toisomers which have structures that differ from the motifs shown in Fig. 2. The isomers have been ordered according to total energy, relative to that of the global minimumanion, PRB. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).

PRB

Rel. Energy 0EBE 246Dipole 7.54


H-b


PNFA


PF23A



Fig. 4. Selected low-energy isomers of ðH2OÞ�7 . Also reported are the relative ene-rgies and EBEs both in meV, and the dipole moments in Debye of the associatedneutral clusters. The PRB, PNFA, and PF23A isomers were reported previously in Ref.[34].

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Fig. 5. Electron binding energy (EBE) vs. dipole moment for quenched isomers fromthe T = 200 K replica in the PTMC simulation of ðH2OÞ�7 . AA isomers are labeled asfilled squares and non-AA isomers are labeled with open circles.

A. DeFusco et al. / Chemical Physics Letters 455 (2008) 135–138 137

jet expansion. We note also, that the AA isomers from the quench-ing calculations can be divided into two groups, one with EBEs near440 meV and the other with EBEs near 560 meV. This is mostapparent from the quenching of the structures sampled atT = 142 K (Fig. 3b). This is consistent with the recent experimentalresults of Ref. [14] where it was found that in addition to the AA

species with an EBE near 450 meV, under certain conditions a sec-ond AA species with an EBE near 600 meV is observed.

4. Conclusions

PTMC simulations using the quantum Drude model have beenperformed to calculate the electron binding energies and to enu-merate low-energy isomers of ðH2OÞ�7 . The PTMC simulations indi-cate that even at temperatures as high as 200 K, the equilibriumdistribution of ðH2OÞ�7 is dominated by non-AA structures withlow ([300 meV) electron binding energies, with the fraction ofhigh ( J 400 meV) EBE species, growing with increasing tempera-ture. A total of 35 isomers are found below the most stable AA iso-mer, which was previously reported by Kim and co-workers [34] tobe the global minimum. The high EBE species are dominated by AAclusters, although there is a small contribution from a non-AA iso-mer, with an EBE of 450 meV (H-b in Fig. 4).







Fig. 6. Representative high energy structures from quenching configurations sa-mpled in the T = 200 K replica from the PTMC simulations. Total energies (meV)relative to PRB, EBEs (meV), and dipole moments (D) of the associated neutralclusters are reported.

138 A. DeFusco et al. / Chemical Physics Letters 455 (2008) 135–138

The energies of the peaks in the calculated EBE distributions arein close agreement with those in the measured photoelectron spec-trum. However, although the low EBE species dominate the simu-lations, AA isomers with high EBEs dominate the experiments evenin the case of Ar-tagged clusters, which have temperatures around50 K. A similar disparity between theory and experiment has beennoted for ðH2OÞ�6 [20]. Comparison of the DPP/Drude model resultswith those from the large-basis set MP2 calculations reveals thatthe model potential approach displays a small (20–40 meV) biastoward the low EBE isomers [20,36]. However, this bias is relativelysmall, and this does not alter our main conclusion that an equilib-rium distribution of ðH2OÞ�7 should possess a significant populationof non-AA structures. We conclude, therefore, that the experimen-tal formation process, for some reason, selects out the high EBE iso-mers. It may be that the low EBE isomers are actually formed inhigh yield but that most of these species are destroyed, possiblythrough collisions with Ar atoms before they can be detected. Itis believed that in the experiments of Johnson and co-workers,most of the observed ðH2OÞ�7 Arm ions result from electron attach-ment to (H2O)7Arn clusters, where n > m. Even with the attached

Ar atoms, the internal energies of the neutral clusters should beon the order of 50–100 meV, which means that a large numberof different forms of ðH2OÞ�7 would be accessible upon attachmentof low-energy electrons.

Acknowledgement

This research was supported by a grant from DOE. We acknowl-edge many helpful discussions with Prof. M. Johnson.

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parallel tempering monte carlo simulations of the water heptamer anion

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