Ab initio study of water hexamer anions

17 May 1996

CHEMICAL PHYSICS LETTERS

ELSEVIER

Chemical Physics Letters 254 (1996) 128-134

Ab initio study of water hexamer anions Sik Lee

a,

Sang Joo Lee a, Jin Yong Lee a, Jongseob Kim a, Kwang S. Kim Ickjin Park b, K. Cho b, J.D. Joannopoulos b,,

a,*,

a Department of Chemistry and Center for Btofunctional Molecules, Pohang University of Science and Technology, San 31, Hyojadong, Namgu, Pohang 790-784, South Korea b Department of Physws, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Received 5 February 1996

Abstract

The wet electron - an electron interacting with a small cluster of water molecules - is a simple yet fundamental system for understanding the behavior of electrons in complex molecular systems. A comprehensive post Hartree-Fock ab initio study is performed on the wet electron in various water hexamer clusters including the low-lying energy conformers of the neutral species. The predicted geometries, total energies, photoemission ionization energies, electronic structure and orbital character of the excess electron in ground and excited states are discussed. To understand the behavior of the excess electron in the clusters, the s-orbital-like character of the HOMOs and the p-orbital-like character of the LUMOs are investigated.

1. Introduction

Hydrated electrons have been the subject of intensive investigation since their optical spectra were identified [ 1,2]. The solvation structure of an electron is of importance for understanding the behavior of localization/delocalization of the electron and its physical/chemical characteristics [3]. In the case of solvated electrons (i.e. electrons immersed in liquid water), Kevan [4] inferred that an electron is trapped in a cavity space bounded by six water molecules in an octahedral configuration, in which one O - H bond of each water molecule is oriented toward the center and the distance from the center to the nearest six hydrogens is 2.1 A. The existence of such a configuration suggests that it is also possible for an excess electron to be bound to an isolated water cluster. " Corresponding author.

However, despite theoretical predictions of the existence of a bound electron in the presence of strong dipole fields of molecules [5], the localization of an electron in molecular clusters has not yet been established. Although ab initio theoretical work in dealing with the liquid phase solvated electron is difficult, the gas phase solvated electron can be treated both accurately and tractably. To clarify the hydrated electron structure, a number of theoretical calculations have been performed. One of the most reliable calculational methods is ab initio calculations [6-10]. However, most of the calculations use Hartree-Fock (HF) theory with the excess electron orbitals assumed to lie only near the cavity center. Another type of calculation is based on molecular dynamics simulations along with quantum path integral calculations using e l e c t r o n - w a t e r pseudopotentials [11-171.

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S. Lee et a l . / Chemical Physics Letters 254 (1996) 128-134

In recent mass spectrometer experiments various gas phase water cluster anions, e + (HEO)n, were observed [18-24], but for the case of n < 10, clusters with only n = 2, 6 and 7 were identified with certainty. In general, the individual molecules of solvated electron systems do not bind excess electrons. However, the corresponding condensed phase systems readily solvate them, implying that the association of electrons with these solvents is a multibodied interaction. Of particular interest is the case of n = 6 (water hexamer anion), since the solvated electron is also coordinated to six water molecules. However, little is known experimentally about the water hexamer anion except for the photoemission ionization energies (IEs) [18-20], and most previous ab initio theoretical investigations of this system have also been limited because of the complexities of dealing with a fully quantum mechanical problem [6-10]. We have reported preliminary results of the water hexamer anion system which were investigated using both quantum theoretical chemistry and condensed matter theory [25]. In that preliminary report, we focused on the role of the dangling hydrogen atoms in the water cluster as generic elecirophilic sites. In this Letter, we discuss the geometries, energies, photoemission ionization energies and elecIronic structures in detail, based on post HartreeFock results. In particular, in order to understand the

129

physical/chemical behavior of the excess electron in the water hexamer clusters, the characteristics of the HOMOs and LUMOs are investigated.

2. Calculation methods As a quantum chemical approach, the post Hartree-Fock method based on M¢ller-Plesset second-order perturbation theory (MP2) is used with a Gaussian-type basis set including diffuse basis functions (6-31 + + G* and 6-311 + + G* * basis sets) [26]. The local energy minima of the predicted geometries were verified with second-order derivative calculations using 6-31 + + G* basis sets. In addition, we have performed single-point 6-311 + + G(2d, 2p) + (2slpld) calculations at the MP2/6-311 + + G * * optimized geometries. Here, the (2slpld) basis set was added to better describe the electron basis functions. The exponents were optimized to obtain the lowest energy for the water hexamer anion at Kevan's octahedral configuration [4]. The exponents of the two s functions are 0.0841 and 0.0062, and those for the p and d functions are 0.0613 and 0.0697, respectively. This extra basis set was centered at the center of the six oxygen atoms of the water cluster. All the calculations were performed using the Gaussian 92 suite of programs [26].

Table 1 Structural parameters of the water hexamer anions a MP2/6-31 + + G* A

MP2/6-311 + + G**

pb

r ( Ct-O) r ( C t - H b)

2.586 2.273

r(Ct-H, ) r ( O - H b)

2.673 0.993

r ( O - H n) /_(H-O-H)

0.977 104.6

r(O • • • H)

1.813

T

2.206 1.990 1.992 d 3.138 0.990 0.980 a 0.980 104.6 1.932 1.995 a

A

E,C

1.974

3.471 3.342

2.583 2.270

0.984

2.882 0.986

2.709 0.980

0.977 105.4

0.964 103.1

1.953

1.811

103.9 1.999

0.973 0.966 104.2 101.1 1.850 2.048

pb 2.215 2.003 2.007 d 3.134 0.975 0.968 a 0.968 103.0 1.968 2.012 o

T

1.979

3.463 3.345

0.970

2.856 0.972

102.3 2.028

0.965 102.4 1.998

a Distances are in ,~; angles in degrees. Ct denotes the center of six O atoms in each cluster; H b denotes the H atoms which are participating in hydrogen bonding while H n denotes the other case. b There are two types of water molecules of top and bottom tings due to C 3 symmetry. c There are two types of water molecules with and without dangling H atoms. d Distance between the nearest water molecules in different tings (See Fig. 1).

S. Lee et a l . / Chemical Physics Letters 254 (1996) 128-134

130

3. R e s u l t s a n d d i s c u s s i o n s

center of six oxygen atoms in the cluster (Ct) to atoms H, H' and O are 2.71, 2.27 and 2.58 A, respectively, where H and H' are the dangling hydrogen and non-dangling hydrogen, respectively. Angles / _ ( O - C t - O ) are 65 °, 115 ° and 180 °. Angles /_(CtO - H ) are 87*. For structure E', the shortest interoxygen distances are 2.81-2.89 ,~ (upper triangle!, 2.92-2.99 ,~ (lower triangle) and 2.70-2.87 A (between two triangles). Since a molecule with a high dipole moment is known to have a bound state for an excess electron [5], we devised the prism structure (P) which is expected to have a positive IE. For this structure, the shortest inter-oxygen distances are 2.86 ,~ (upper triangle), 2.92 ,~ (lower triangle) and 2.92 ,~ (between two triangles). We also devised a structure of an internal electron state so as to have a highly positive IE. This structure is the triangular-rings structure (T) which is related partially to Kevan's octahedral geometry. The relaxation of six water molecules in Kevan's octahedral geometry allows hydrogen bonding between adjacent molecules by forming two triangular rings: one trimer-like hydrogen-bonded cyclic structure o

We have studied various conformers of the water hexamer anions including the low-lying energy conformers of the neutral species [27-33]. Among them, we select four important conformers: (1) cyclic structure (A) with only six hydrogen bonds, (2) prism-derivative structure (E') with as many as nine hydrogen bonds, (3) prism structure (P) with a high dipole moment and (4) triangular-rings structure (T) of highly clustered H atoms with an extra electron trapped inside the cluster. Here, the notations A and E' follow those in previous works [27-30]. Table 1 lists structural parameters of the four water hexamer anions. The structures are shown in Fig. 1. Among the MP2/6-31 + + G * and M P 2 / 6 - 3 1 1 + + G * * structural parameters, our following discussion will be based on the latter results, unless otherwise specified. Both cyclic (A) and prism-derivative (E') structures, which were obtained from the nearly isoenergetic ground state structures of the neutral hexamer, do not change much from the corresponding neutral species. For structure A, the distances from the

A

T

E'

P

Fig. 1. Water hexamer anion geometries: cyclic structure (A), prism-derivativestructure (E'), prism structure (P) and triangular-rings structure (T).

S. Lee et al. / Chemical Physics Letters 254 (1996) 128-13~I

among the upper three water molecules and another same cyclic structure among the lower three water molecules. The distances from the cluster center (Ct) to atoms H, H' and O are 2.86, 3.34 and 3.46 ~,, respectively. Angles /_.(H-Ct-H) are 72 °, 108 ° and 180 °, while / _ ( O - C t - O ) are 49 °, 131 ° and 180 °. Angles /__(Ct-H-O) are 122 °. The relaxed structure is significantly different from Kevan's octahedral structure. The O - H bonds do not point directly toward the center of the cluster. This is due to a competition between two interaction forces: (1) the e . . . H interactions that the O - H bonds tend to orient toward the cluster center and (2) the hydrogen bonding interactions between neighboring water molecules. Compared with the prism structure, the triangular-rings structure has a higher energy (by = 6 kcal/mol), indicating that the e . . . H interactions are somewhat weaker than the hydrogen bonding interactions. Table 2 lists the total energies (E), relative binding energies with respect to structure A (AEre I) and photoemission ionization energy (IE). The IEs were calculated by subtracting the total energy of the anion species from those of the neutral species at the optimized geometry of the anion species. To obtain reliable energetics, anionic systems require much larger basis sets than neutral systems. The 6-311 + + G ~ * basis set used in this study comprises 222

131

basis functions which include diffuse functions. Recently, Pudzianovski [34] carried out an exhaustive study of structures, normal modes, thermodynamics and counterpoise energies of the ionic hydrogenbonded molecules using HF, MP2 and MP4, and found that the 6-311 + + G * * basis set is a reasonable one for the study of anions. Of all the geometries we have studied, we find that structures T and P bind an excess electron because these have positive IE values (see Table 2). The significant difference in electron distribution between structures T and P is reflected in a significant difference in the predicted IEs, which are respectively 0.45 and 0.06 eV for MP2/6-311 + + G* *, and respectively 0.51 and 0.15 eV for MP2/6-31 + + G*. The zero-point energy correction increases the IE of structure P up to 0.09 eV for M P 2 / 6 - 3 1 1 + + G * " and up to 0.18 eV for MP2/6-31 + + G *. The agreement with the two positive experimental IEs, which are 0.5 and 0.2 eV [6-8], is notable. This indicates that the observed IEs arise from two different classes of cluster geometries (which are at internal and surface electron states, respectively) rather than two different energy states of the same cluster. The 6-31 + + G * results are closer to the experimental values, but the results of the larger basis set 6-311 + + G * " can be more reliable. Although structure P has a lower energy than structure T, the experimental photoemission

Table 2 E n e r g i e s o f the w a t e r h e x a m e r a n i o n s a A MP2/6-31

E'

P

T

+ + G *

anion

- 457.32727

- 457.33413

- 457.32076

AE~e I neutral

0.0 - 457.33204

-4.31 - 457.32880

4.1 - 457.30189

VDE (eV)

(-0.13)

(0,15)

(0.51)

- 457.86088

- 457.85130

MP2/6-311

+ +G**

anion

- 457.85609

AEre 1

0.0

- 457.85745 -0.85

- 3.00

3.01

neutral

- 457.86503

- 457.87191

- 457.85874

- 457.83473

VDE (eV)

( - 0.24)

( - 0.39)

(0.06)

(0.45)

+ + G(2d,2p) + (2slpld)//MP2/6-311

+ + G **

MP2/6-311 anion

- 457.93820

AE~I

0.0

-

4 5 7 . 9 4 1 5 1

- 2.07

-

457.93088 4.60

a E n e r g i e s o f a n i o n i c a n d n e u t r a l w a t e r h e x a m e r s are in h a r t r e e s ; A E ~ I are r e l a t i v e b i n d i n g e n e r g i e s w i t h r e s p e c t to the c y c l i c w a t e r h e x a m e r a n i o n (in k c a l / m o l ) .

S. Lee et a l . / Chemical Physics Letters 254 (1996) 128-134

132

signal is found to be much stronger at 0.5 eV than at 0.2 eV. Our previous density functional theory (DFT) results [25] showed that the photoemission cross section of the HOMO of structure T is much larger than that of structure P (by ~ 103), which leads to consistency with the photoemission spectrum. In the case of single-point MP2/6-311 + + G(2d, 2 p ) + (2slpld) calculations at the MP2/6-311 + + G * " optimized geometries, all the energetics are similar to the MP2/6-311 + + G" " results, as shown in Table II. In this case, structure E' was beyond our computing capacity due to the lack of molecular symmetry. In Fig. 2, we show the schematics of HOMOs and LUMOs for the four structures. The density of the excess electron in the ground state can be seen from the HOMO electron density. In structure T, the electron is well localized inside the cluster as an internal state, and acts to bridge the two rings. This clearly shows the localization of the excess electron inside the cluster. The electron distributes spatially over the whole space of the cavity. This electron has somewhat of an s-orbital-like distribution which is similar in spirit to the predictions made in calculations of the condensed phase [ 17] and of the hexamer

H

II

I/

HOMO

at Kevan's geometry [10]. The electron density is distributed around the dangling H atoms which are not involved in hydrogen bonding. A similar effect is manifested in the electron density distribution for the HOMOs of structures A, E' and P, in which each excess electron is spread out around the dangling H atoms as a surface state. The dangling H atoms act as electrophilic sites attracting the excess electron, as noted in our preliminary report [25]. The LUMOs of structures A, P and T show that the excited states have somewhat of a p-orbital-like electron distribution, as shown in Fig. 2. There are two other p-orbital-like LUMOs for each structure which are not shown in the figure. The three p-orbital-like LUMOs for each structure do not have the same energies. These results are consistent with the work of Schnitker et al. [17] for an excess electron in the condensed phase, in which the electronic transition from an s-orbital-like ground state to three bound localized p-orbital-like excited states dominates the broad asymmetric spectrum with excited electrons. However, in the water hexamer anions, the p-orbital-like excited states are not bound, but are at resonance states, because the LUMO energies are positive ( ~ 0.1 hartree). In the case of

H

ll

LUMO

HOMO

A

ql

LUMO E'

11

LUMO T

Zr

HOMO

H

0

g-0

¢

r$i c~

. ,i

ql

HOMO

0

#-O

LUMO P

Fig. 2. Schematics of the HOMOs and LUMOs of the four structures; A, E', P and T.

S. Lee et al. / Chemical Physics Letters 254 (1996) 128-134

structure E', the p-orbital-like electron density distribution is not shown in the figure, but the other two (second and third) LUMOs show some of the porbital-like excited states. In the excited states of the four structures, the dangling H atoms also act as electrophilic sites attracting the excess electron, while the hydrogen-bonded H atoms are already saturated so that the excess electron cannot be near such H atoms, just as in the case of the ground states.

4. Conclusion We studied four important water hexamer anions with MP2 calculations using the 6-31 + + G * and 6-311 + + G" * basis sets. We analyzed the geometrical and electronic structures. From this analysis, the s-orbital-like characters of the HOMOs and three nearly-degenerate p-orbital-like characters of the LUMOs are noted even in small water clusters. However, the ground state is at least locally bound, while the excited states are unbound resonance states because the LUMO energies are slightly positive. In the triangular-rings structure (T), the excess electron is localized in the cavity surrounded by six water molecules as an internal state. This structure is slightly less stable in the gas phase than the prism, prism-derivative and cyclic structures (P, E' and A), in which each excess electron is spread out over the surface of the cluster as a surface state. The photo emission ionization energies of the water hexamer anions, T (internal electron state) and P (surface electron state), are in good agreement with the two experimentally detected values (0.5 and 0.2 eV). In both the ground and excited states of the four structures, the excess electron is distributed around the dangling hydrogen atoms, but not near the hydrogen-bonded H atoms.

Acknowledgement This work was supported in part by Korea Research Foundation and the Ministry of Education/ BSRI-95-3436, and also in part by ONR Contract No. N00014-94-I-0591 and US JSEP Contract No. DAAH-04-95-I-0038.

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